Finite Group Databasebeta

← #31733436

Subgroups — #31733436

Order 17152.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22573960C211yesmaximal, characteristic, complemented
2#22573837C211yesmaximal, characteristic
3#22572440C211yesmaximal, characteristic, complemented
4#22572435C211yesmaximal, characteristic, complemented
5#22572421C211yesmaximal, characteristic, complemented
6#22572419C211yesmaximal, characteristic, complemented
7#22572295C211yesmaximal, characteristic, complemented
8#22572293C211yesmaximal, characteristic, complemented
9#22572247C211yesmaximal, characteristic, complemented
10#22572238C211yesmaximal, characteristic, complemented
11#22572233C211yesmaximal, characteristic, complemented
12#22572229C211yesmaximal, characteristic, complemented
13#22572223C211yesmaximal, characteristic, complemented
14#22572041C211yesmaximal, characteristic, complemented
15#22572039C211yesmaximal, characteristic, complemented
16#22572036C211yesmaximal, characteristic, complemented
17#22572029C211yesmaximal, characteristic, complemented
18#22570564C211yesmaximal, characteristic, complemented
19#22570160C211yesmaximal, characteristic, complemented
20#22570121C211yesmaximal, characteristic, complemented
21#22570039C211yesmaximal, characteristic, complemented
22#22569843C211yesmaximal, characteristic, complemented
23#22569834C211yesmaximal, characteristic, complemented
24#22569725C211yesmaximal, characteristic, complemented
25#22569481C211yesmaximal, characteristic, complemented
26#450×D67C211yesmaximal, characteristic, complemented
27#22569065C211yesmaximal, characteristic, complemented
28#22568932C211yesmaximal, characteristic, complemented
29#22568730C211yesmaximal, characteristic, complemented
30#418×D67C211yesmaximal, characteristic, complemented
31C67×#3310C211yesmaximal, characteristic, complemented
32C2×#14524088C2211yescharacteristic
33C22×D4×D67C2211yescharacteristic
34C2×#14524072C2211yescharacteristic, complemented
35C2×SD16×D67C2211yescharacteristic
36C2×SD16×D67C2211yescharacteristic, complemented
37C2×#14524049C2211yescharacteristic, complemented
38C2×M16×D67C2211yescharacteristic, complemented
39#16864117C2211yescharacteristic, complemented
40#16864116C2211yescharacteristic, complemented
41#16864106C2211yescharacteristic, complemented
42#16864101C2211yescharacteristic, complemented
43#16864085—21no—
44#16864085C2211yescharacteristic, complemented
45#16864084C2211yescharacteristic, complemented
46#16864080C2211yescharacteristic, complemented
47#16864078—21no—
48#16864074—21no—
49#16864071—21no—
50#16864043C2211yescharacteristic
51#16864042C2211yescharacteristic
52#16864041C2211yescharacteristic
53#16864040C2211yescharacteristic
54#16864035—21no—
55#16864033—21no—
56#16864031C2211yescharacteristic
57#16864030C2211yescharacteristic
58D4×C22⋊D67—21no—
59D4×C22⋊D67C2211yescharacteristic
60#16864028—21no—
61#16864026C2211yescharacteristic, complemented
62#16864014—21no—
63#16864003—21no—
64#16863969C2211yescharacteristic, complemented
65#16863962C2211yescharacteristic
66#16863959C2211yescharacteristic
67#16863956—21no—
68#16863954—21no—
69#16863952—21no—
70#16863924—21no—
71#16863906C2211yescharacteristic
72#16863905C2211yescharacteristic
73C22⋊Q8×D67C2211yescharacteristic, complemented
74C2×#14524011—21no—
75#120×D67—21no—
76#16863877C2211yescharacteristic, complemented
77#16863872C2211yescharacteristic, complemented
78#16863868C2211yescharacteristic
79#117×D67C2211yescharacteristic, complemented
80#16863759C2211yescharacteristic, complemented
81#16863756C2211yescharacteristic, complemented
82#16863754C2211yescharacteristic, complemented
83#16863753C2211yescharacteristic, complemented
84#16863749C2211yescharacteristic, complemented
85#16863742C2211yescharacteristic, complemented
86#16863741C2211yescharacteristic, complemented
87#16863738C2211yescharacteristic, complemented
88#16863737C2211yescharacteristic, complemented
89#16863733C2211yescharacteristic, complemented
90#16863728C2211yescharacteristic, complemented
91#16863723C2211yescharacteristic, complemented
92#16863721C2211yescharacteristic, complemented
93#16863718C2211yescharacteristic, complemented
94#16863717C2211yescharacteristic, complemented
95#16863717C2211yescharacteristic, complemented
96#16863714C2211yescharacteristic, complemented
97#16863713C2211yescharacteristic, complemented
98#16863713C2211yescharacteristic, complemented
99#16863711C2211yescharacteristic, complemented
100#16863708C2211yescharacteristic, complemented
101#16863698C2211yescharacteristic, complemented
102#16863695C2211yescharacteristic, complemented
103#16863693C2211yescharacteristic, complemented
104#16863687C2211yescharacteristic, complemented
105#16863684C2211yescharacteristic, complemented
106#16863676C2211yescharacteristic, complemented
107#16863675C2211yescharacteristic, complemented
108#16863654C2211yescharacteristic, complemented
109#16863652C2211yescharacteristic, complemented
110#16863645C2211yescharacteristic, complemented
111#16863644C2211yescharacteristic, complemented
112#16863641C2211yescharacteristic, complemented
113#16863640C2211yescharacteristic, complemented
114#16863640C2211yescharacteristic, complemented
115#16863638C2211yescharacteristic, complemented
116#16863636C2211yescharacteristic, complemented
117#16863626C2211yescharacteristic, complemented
118#16863625C2211yescharacteristic, complemented
119#16863624C2211yescharacteristic, complemented
120#16863622C2211yescharacteristic, complemented
121#16863622C2211yescharacteristic, complemented
122#16863619C2211yescharacteristic, complemented
123#16863618C2211yescharacteristic, complemented
124#16863617C2211yescharacteristic, complemented
125#16863616C2211yescharacteristic, complemented
126#16863595C2211yescharacteristic, complemented
127#16863594C2211yescharacteristic, complemented
128#16863593C2211yescharacteristic, complemented
129#16863560C2211yescharacteristic, complemented
130#16863559C2211yescharacteristic, complemented
131#16863556C2211yescharacteristic, complemented
132#16863555C2211yescharacteristic, complemented
133#16863549C2211yescharacteristic, complemented
134#16863548C2211yescharacteristic, complemented
135#16863548C2211yescharacteristic, complemented
136#16863548C2211yescharacteristic, complemented
137#16863547C2211yescharacteristic, complemented
138#16863547C2211yescharacteristic, complemented
139#16863546C2211yescharacteristic, complemented
140#16863545C2211yescharacteristic, complemented
141#16863545C2211yescharacteristic, complemented
142#16863545C2211yescharacteristic, complemented
143#16863498C2211yescharacteristic, complemented
144#16863497C2211yescharacteristic, complemented
145#16863495C2211yescharacteristic, complemented
146#16863487C2211yescharacteristic, complemented
147C4×#11761615C2211yescharacteristic, complemented
148C4×#11761616C2211yescharacteristic, complemented
149#16863481C2211yescharacteristic, complemented
150#16863474C2211yescharacteristic, complemented
151#16863472C2211yescharacteristic, complemented
152#16863470C2211yescharacteristic, complemented
153#16863470C2211yescharacteristic, complemented
154#16863469C2211yescharacteristic, complemented
155#16863461C2211yescharacteristic, complemented
156C8×C22⋊D67C2211yescharacteristic, complemented
157#16863437C2211yescharacteristic, complemented
158#16863433C2211yescharacteristic, complemented
159#16863431C2211yescharacteristic, complemented
160#16863421C2211yescharacteristic, complemented
161#16863403C2211yescharacteristic, complemented
162#16863402C2211yescharacteristic, complemented
163#16863401C2211yescharacteristic, complemented
164#16863401C2211yescharacteristic, complemented
165#16863400C2211yescharacteristic, complemented
166#16863399C2211yescharacteristic
167#16863399C2211yescharacteristic
168#16863399C2211yescharacteristic, complemented
169#16863399C2211yescharacteristic, complemented
170#16863399C2211yescharacteristic, complemented
171#16863395C2211yescharacteristic, complemented
172#16863394C2211yescharacteristic, complemented
173#16863394C2211yescharacteristic, complemented
174#16863393C2211yescharacteristic, complemented
175#16863389C2211yescharacteristic, complemented
176#16863389C2211yescharacteristic, complemented
177#16863389C2211yescharacteristic, complemented
178#102×D67C2211yescharacteristic
179#102×D67C2211yescharacteristic, complemented
180#102×D67C2211yescharacteristic, complemented
181#102×D67C2211yescharacteristic, complemented
182#102×D67C2211yescharacteristic, complemented
183#102×D67C2211yescharacteristic, complemented
184#102×D67C2211yescharacteristic, complemented
185#16863361C2211yescharacteristic, complemented
186C22⋊C8×D67C2211yescharacteristic, complemented
187#16863353C2211yescharacteristic, complemented
188#552×C67C2211yescharacteristic, complemented
189D42×C67C2211yescharacteristic
190#490×C67C2211yescharacteristic, complemented
191#482×C67C2211yescharacteristic, complemented
192#480×C67C2211yescharacteristic, complemented
193#478×C67C2211yescharacteristic, complemented
194#468×C67C2211yescharacteristic, complemented
195#465×C67C2211yescharacteristic, complemented
196#460×C67C2211yescharacteristic, complemented
197#450×C67C2211yescharacteristic, complemented
198#450×C67C2211yescharacteristic, complemented
199#440×C67C2211yescharacteristic, complemented
200#435×C67C2211yescharacteristic, complemented
201#418×C67C2211yescharacteristic, complemented
202C2×#102×C67C2211yescharacteristic, complemented
203C24×D67—21no—
204#14524088—24no—
205#14524088—42no—
206C2×#11761628C2311yescharacteristic
207C2×#11761628C2311yescharacteristic
208C2×#11761627—21no—
209C2×#11761627C2311yescharacteristic
210C2×#11761627C2311yescharacteristic
211C2×Q8×D67C2311yescharacteristic
212C22×D268C2311yescharacteristic
213C22×C22⋊D67—21no—
214C22×C22⋊D67—21no—
215C22×C22⋊D67—21no—
216C22×C22⋊D67—21no—
217C2×D4×D67—24no—
218C2×D4×D67—21no—
219C2×D4×D67—21no—
220C2×D4×D67—21no—
221C2×D4×D67—21no—
222C2×D4×D67—21no—
223C2×D4×D67—42no—
224C2×D4×D67C2311yescharacteristic
225C2×D4×D67C2311yescharacteristic
226C2×D4×D67C2311yescharacteristic
227C2×D4×D67C2311yescharacteristic
228C2×D4×D67C2311yescharacteristic
229C22×C4×D67C2311yescharacteristic
230#14524072—42no—
231C2×Dic268C2311yescharacteristic, complemented
232C2×#11761618C2311yescharacteristic, complemented
233C2×#11761617C2311yescharacteristic
234C2×#11761617C2311yescharacteristic
235C2×#11761616C2311yescharacteristic
236C2×#11761616C2311yescharacteristic
237C2×#11761616C2311yescharacteristic, complemented
238C2×#11761615C2311yescharacteristic
239C2×#11761615C2311yescharacteristic
240SD16×D67—24no—
241SD16×D67—42no—
242#14524049—42no—
243C2×#11761612C2311yescharacteristic
244C2×#11761612C2311yescharacteristic, complemented
245C2×#11761611C2311yescharacteristic
246C2×#11761611C2311yescharacteristic
247C2×#11761611C2311yescharacteristic, complemented
248M16×D67—42no—
249C2×C8×D67C2311yescharacteristic
250C2×C8×D67C2311yescharacteristic
251C2×C8×D67C2311yescharacteristic
252C2×C8×D67C2311yescharacteristic
253C2×C8×D67C2311yescharacteristic, complemented
254#14524043C2311yescharacteristic, complemented
255#14524042—21no—
256#14524042—21no—
257#14524042C2311yescharacteristic, complemented
258#14524039—21no—
259#14524039C2311yescharacteristic
260#14524038—21no—
261#14524038—21no—
262#14524036—21no—
263#14524036—21no—
264#14524036—21no—
265#14524036—21no—
266#14524036—21no—
267#14524035—21no—
268#14524035—21no—
269#14524034—21no—
270#14524034C2311yescharacteristic, complemented
271#14524033—21no—
272#14524033—21no—
273#14524033—21no—
274#14524031C2311yescharacteristic
275#14524030—21no—
276#14524030C2311yescharacteristic
277#14524029—21no—
278#14524029—21no—
279#14524029—21no—
280#14524028—21no—
281#14524028—21no—
282#14524028—21no—
283#14524028D411yescharacteristic
284#14524027—21no—
285#14524025—21no—
286#14524025—21no—
287#14524025—21no—
288#14524025—21no—
289#14524025—21no—
290#14524025D411yescharacteristic
291#14524024—21no—
292#14524023—21no—
293#14524023C2311yescharacteristic
294#14524023C2311yescharacteristic
295#14524023C2311yescharacteristic, complemented
296#14524022—21no—
297#14524022C2311yescharacteristic
298#14524022C2311yescharacteristic
299#14524022C2311yescharacteristic, complemented
300#14524021—21no—
301#14524021—21no—
302#14524021—21no—
303#14524021—21no—
304#14524021—21no—
305#14524021D411yescharacteristic
306#14524020—21no—
307#14524020D411yescharacteristic
308#14524019C2311yescharacteristic
309#14524019C2311yescharacteristic, complemented
310#14524018C2311yescharacteristic
311#14524017—21no—
312#14524017C2311yescharacteristic
313#14524016—21no—
314#14524016—21no—
315#14524016D411yescharacteristic
316#14524015—21no—
317#14524015—21no—
318#14524015—21no—
319#14524015—21no—
320#14524015D411yescharacteristic
321#14524014—21no—
322#14524014—21no—
323#14524014C2311yescharacteristic
324#14524014C2311yescharacteristic
325#14524013—21no—
326#14524013—21no—
327#14524013—21no—
328#14524013D411yescharacteristic
329#14524012—21no—
330#14524012—21no—
331#14524011—21no—
332#14524011—21no—
333#14524011—21no—
334#14524011—21no—
335#14524011—21no—
336#14524011—21no—
337#14524011—21no—
338#14524011—21no—
339#14524011—21no—
340#14524011—21no—
341#14524011D411yescharacteristic
342Q8×Dic67C2311yescharacteristic, complemented
343C4×Dic134—21no—
344C4×Dic134C2311yescharacteristic, complemented
345#14524008—21no—
346#14524008—21no—
347#14524008—21no—
348#14524008—21no—
349#14524008C2311yescharacteristic, complemented
350C4×D268—21no—
351C4×D268C2311yescharacteristic
352C4×D268C2311yescharacteristic
353D4×Dic67—21no—
354D4×Dic67C2311yescharacteristic
355#14524005—21no—
356#14524005C2311yescharacteristic
357C4×C22⋊D67—21no—
358C4×C22⋊D67—21no—
359C4×C22⋊D67—21no—
360C4×C22⋊D67—21no—
361C4×C22⋊D67C2311yescharacteristic
362C4×C22⋊D67C2311yescharacteristic
363(C22⋊D67)⋊C4—21no—
364(C22⋊D67)⋊C4—21no—
365#14524002C2311yescharacteristic
366#14524002C2311yescharacteristic, complemented
367#14524001—21no—
368#14524001—21no—
369#14524001—21no—
370#14524001C2311yescharacteristic
371#14524001C2311yescharacteristic
372#14524001C2311yescharacteristic
373#14524001C2311yescharacteristic, complemented
374#14524000—21no—
375#14524000—21no—
376#14524000—21no—
377#14524000C2311yescharacteristic
378#14523999—21no—
379C4⋊C4×D67—21no—
380C4⋊C4×D67C2311yescharacteristic
381C4⋊C4×D67C2311yescharacteristic
382C4⋊C4×D67C2311yescharacteristic
383C4⋊C4×D67C2311yescharacteristic, complemented
384C2×C22⋊Dic67—21no—
385C2×(C2×D67)⋊C4—21no—
386C2×(C2×D67)⋊C4—21no—
387C22⋊C4×D67—21no—
388C22⋊C4×D67—21no—
389C22⋊C4×D67—21no—
390C22⋊C4×D67—21no—
391C22⋊C4×D67—21no—
392C42×D67—21no—
393#14523977C2311yescharacteristic, complemented
394#14523976C2311yescharacteristic, complemented
395#14523976C2311yescharacteristic, complemented
396#14523976C2311yescharacteristic, complemented
397#14523975C2311yescharacteristic, complemented
398#14523975C2311yescharacteristic, complemented
399#14523974C2311yescharacteristic, complemented
400#14523974C2311yescharacteristic, complemented
401#14523974C2311yescharacteristic, complemented
402C4⋊(C67⋊C8)C2311yescharacteristic, complemented
403Dic67⋊C8C2311yescharacteristic, complemented
404Dic67⋊C8C2311yescharacteristic, complemented
405#14523968C2311yescharacteristic, complemented
406#14523968C2311yescharacteristic, complemented
407#14523968C2311yescharacteristic, complemented
408#14523968C2311yescharacteristic, complemented
409#14523967C2311yescharacteristic, complemented
410#14523966C2311yescharacteristic, complemented
411#14523966C2311yescharacteristic, complemented
412#14523966C2311yescharacteristic, complemented
413#14523966C2311yescharacteristic, complemented
414#14523965C2311yescharacteristic
415#14523965C2311yescharacteristic
416#14523965C2311yescharacteristic
417#14523965C2311yescharacteristic
418#14523965C2311yescharacteristic
419#14523965C2311yescharacteristic
420#14523964C2311yescharacteristic
421#14523964C2311yescharacteristic
422#14523964C2311yescharacteristic
423#14523964C2311yescharacteristic
424#14523964C2311yescharacteristic
425#14523964C2311yescharacteristic
426#14523964C2311yescharacteristic, complemented
427#14523964C2311yescharacteristic, complemented
428#14523964C2311yescharacteristic, complemented
429#14523963C2311yescharacteristic
430#14523963C2311yescharacteristic
431#14523963C2311yescharacteristic
432#14523963C2311yescharacteristic
433#14523963C2311yescharacteristic
434#14523963C2311yescharacteristic
435C22⋊(C67⋊C8)C2311yescharacteristic
436C22⋊(C67⋊C8)C2311yescharacteristic, complemented
437(C2×D67)⋊C8C2311yescharacteristic
438(C2×D67)⋊C8C2311yescharacteristic
439(C2×D67)⋊C8C2311yescharacteristic, complemented
440(C2×D67)⋊C8C2311yescharacteristic, complemented
441#14523953C2311yescharacteristic, complemented
442C4×C67⋊C8C2311yescharacteristic, complemented
443C8×Dic67C2311yescharacteristic, complemented
444C22×D4×C67—21no—
445C22×D4×C67C2311yescharacteristic
446C22×D4×C67C2311yescharacteristic
447C2×SD16×C67C2311yescharacteristic
448C2×SD16×C67C2311yescharacteristic
449C2×SD16×C67C2311yescharacteristic, complemented
450C2×M16×C67C2311yescharacteristic
451C22×C8×C67C2311yescharacteristic, complemented
452#127×C67C2311yescharacteristic
453#126×C67—21no—
454#125×C67—21no—
455#125×C67C2311yescharacteristic, complemented
456#123×C67—21no—
457C22⋊Q8×C67C2311yescharacteristic
458C22⋊Q8×C67C2311yescharacteristic, complemented
459#121×C67—21no—
460#121×C67C2311yescharacteristic
461#121×C67C2311yescharacteristic
462#120×C67—21no—
463#120×C67—21no—
464C4×Q8×C67C2311yescharacteristic, complemented
465C4×D4×C67C2311yescharacteristic
466C4×D4×C67C2311yescharacteristic
467#117×C67—21no—
468#117×C67C2311yescharacteristic
469C2×C4⋊C4×C67C2311yescharacteristic, complemented
470#107×C67C2311yescharacteristic, complemented
471#107×C67C2311yescharacteristic, complemented
472#106×C67C2311yescharacteristic, complemented
473C4⋊C8×C67C2311yescharacteristic, complemented
474#103×C67C2311yescharacteristic, complemented
475#102×C67C2311yescharacteristic
476#102×C67C2311yescharacteristic
477#102×C67C2311yescharacteristic
478#102×C67C2311yescharacteristic
479#102×C67C2311yescharacteristic
480#102×C67C2311yescharacteristic
481#102×C67C2311yescharacteristic, complemented
482#102×C67C2311yescharacteristic, complemented
483#102×C67C2311yescharacteristic, complemented
484C22⋊C8×C67C2311yescharacteristic
485C22⋊C8×C67C2311yescharacteristic, complemented
486#97×C67C2311yescharacteristic, complemented
487C23×D67—21no—
488C23×D67—21no—
489C23×D67—21no—
490C23×D67—21no—
491C23×D67—21no—
492C23×D67—21no—
493C23×D67—44no—
494C23×D67—82no—
495C23×D67—82no—
496C23×D67C2×D411yescharacteristic
497#11761628—22no—
498#11761628—22no—
499#11761628—22no—
500#11761628—41no—
501#11761627—22no—
502#11761627—22no—
503#11761627—22no—
504#11761627—41no—
505#11761627—44no—
506C2×Dic134—21no—
507C2×Dic134—21no—
508C2×Dic134—21no—
509C2×Dic134C2×D411yescharacteristic
510C2×Dic134C2411yescharacteristic
511C2×Dic134C2411yescharacteristic
512Q8×D67—22no—
513Q8×D67—22no—
514C2×D268—22no—
515C2×D268—21no—
516C2×D268—21no—
517C2×D268—41no—
518C2×D268C2×D411yescharacteristic
519C2×D268C2×D411yescharacteristic
520C2×D268C2411yescharacteristic
521C2×D268C2411yescharacteristic
522C2×C22⋊D67—21no—
523C2×C22⋊D67—21no—
524C2×C22⋊D67—21no—
525C2×C22⋊D67—21no—
526C2×C22⋊D67—21no—
527C2×C22⋊D67—21no—
528C2×C22⋊D67—21no—
529C2×C22⋊D67—21no—
530C2×C22⋊D67—21no—
531C2×C22⋊D67—21no—
532C2×C22⋊D67—21no—
533C2×C22⋊D67—21no—
534C2×C22⋊D67—21no—
535C2×C22⋊D67—44no—
536C2×C22⋊D67—44no—
537C2×C22⋊D67—44no—
538C2×C22⋊D67—82no—
539C2×C22⋊D67C2×D411yescharacteristic
540C2×C22⋊D67C2×D411yescharacteristic
541C2×C22⋊D67C2×D411yescharacteristic
542C2×C22⋊D67C2×D411yescharacteristic
543D4×D67—22no—
544D4×D67—22no—
545D4×D67—22no—
546D4×D67—22no—
547D4×D67—22no—
548D4×D67—22no—
549D4×D67—41no—
550D4×D67—41no—
551D4×D67—41no—
552D4×D67—44no—
553D4×D67—44no—
554D4×D67—44no—
555D4×D67—82no—
556D4×D67—82no—
557D4×D67#4114yes—
558C22×Dic67—21no—
559C22×Dic67—21no—
560C22×Dic67—21no—
561C22×Dic67C2×D411yescharacteristic
562C2×C4×D67—22no—
563C2×C4×D67—22no—
564C2×C4×D67—21no—
565C2×C4×D67—21no—
566C2×C4×D67—21no—
567C2×C4×D67—21no—
568C2×C4×D67—21no—
569C2×C4×D67—21no—
570C2×C4×D67—21no—
571C2×C4×D67—21no—
572C2×C4×D67C2×D411yescharacteristic
573C2×C4×D67C2×D411yescharacteristic
574C2×C4×D67C2411yescharacteristic
575C2×C4×D67C2411yescharacteristic
576C2×C4×D67C2411yescharacteristic
577Dic268—41no—
578#11761618—41no—
579#11761617—22no—
580#11761617—41no—
581#11761616—22no—
582#11761616—41no—
583#11761616—41no—
584#11761615—22no—
585#11761615—41no—
586#11761612—41no—
587#11761612—41no—
588#11761611—22no—
589#11761611—22no—
590#11761611—41no—
591C2×C67⋊C8C2411yescharacteristic
592C2×C67⋊C8C2411yescharacteristic
593C2×C67⋊C8C2411yescharacteristic
594C2×C67⋊C8C2411yescharacteristic
595C8×D67—22no—
596C8×D67—22no—
597C8×D67—41no—
598C8×D67—41no—
599C8×D67—41no—
600C4⋊Dic67—21no—
601C4⋊Dic67—21no—
602C4⋊Dic67—21no—
603C4⋊Dic67—21no—
604C4⋊Dic67—21no—
605C4⋊Dic67—21no—
606C4⋊Dic67C2×D411yescharacteristic
607C4⋊Dic67C2411yescharacteristic
608C4⋊Dic67C2411yescharacteristic
609C4⋊Dic67C2411yescharacteristic
610C4⋊Dic67C2411yescharacteristic
611Dic67⋊C4—21no—
612Dic67⋊C4—21no—
613Dic67⋊C4—21no—
614Dic67⋊C4—21no—
615Dic67⋊C4—21no—
616Dic67⋊C4—21no—
617Dic67⋊C4—21no—
618Dic67⋊C4—21no—
619Dic67⋊C4—21no—
620Dic67⋊C4—21no—
621Dic67⋊C4—21no—
622Dic67⋊C4—21no—
623Dic67⋊C4—21no—
624Dic67⋊C4C2×D411yescharacteristic
625Dic67⋊C4C2×D411yescharacteristic
626Dic67⋊C4C2×D411yescharacteristic
627Dic67⋊C4C2×D411yescharacteristic
628C22⋊Dic67—21no—
629C22⋊Dic67—21no—
630C22⋊Dic67—21no—
631C22⋊Dic67—21no—
632C22⋊Dic67—21no—
633C22⋊Dic67—21no—
634C22⋊Dic67—21no—
635C22⋊Dic67—21no—
636C22⋊Dic67—21no—
637C22⋊Dic67—21no—
638C22⋊Dic67C2×D411yescharacteristic
639C22⋊Dic67C2×D411yescharacteristic
640(C2×D67)⋊C4—21no—
641(C2×D67)⋊C4—21no—
642(C2×D67)⋊C4—21no—
643(C2×D67)⋊C4—21no—
644(C2×D67)⋊C4—21no—
645(C2×D67)⋊C4—21no—
646(C2×D67)⋊C4—21no—
647(C2×D67)⋊C4—21no—
648(C2×D67)⋊C4—21no—
649(C2×D67)⋊C4—21no—
650(C2×D67)⋊C4—21no—
651(C2×D67)⋊C4—21no—
652(C2×D67)⋊C4—21no—
653(C2×D67)⋊C4—21no—
654(C2×D67)⋊C4—21no—
655(C2×D67)⋊C4C2×D411yescharacteristic
656(C2×D67)⋊C4C2×D411yescharacteristic
657(C2×D67)⋊C4C2×D411yescharacteristic
658(C2×D67)⋊C4C2×D411yescharacteristic
659(C2×D67)⋊C4C2×D411yescharacteristic
660(C2×D67)⋊C4C2×D411yescharacteristic
661C4×Dic67—21no—
662C4×Dic67—21no—
663C4×Dic67—21no—
664C4×Dic67—21no—
665C4×Dic67—21no—
666C4×Dic67—21no—
667C4×Dic67—21no—
668C4×Dic67—21no—
669C4×Dic67—21no—
670C4×Dic67C2411yescharacteristic
671C24×C67—21no—
672C24×C67—21no—
673C2×Q8×C67C2411yescharacteristic
674C2×D4×C67—22no—
675C2×D4×C67—22no—
676C2×D4×C67—21no—
677C2×D4×C67—21no—
678C2×D4×C67—21no—
679C2×D4×C67—21no—
680C2×D4×C67—21no—
681C2×D4×C67—21no—
682C2×D4×C67—41no—
683C2×D4×C67—41no—
684C2×D4×C67—82no—
685C2×D4×C67C2×D411yescharacteristic
686C2×D4×C67C2411yescharacteristic
687C2×D4×C67C2411yescharacteristic
688C2×D4×C67C2411yescharacteristic
689C22×C4×C67—21no—
690C22×C4×C67—21no—
691C22×C4×C67C2411yescharacteristic
692C22×C4×C67C2411yescharacteristic
693SD16×C67—22no—
694SD16×C67—41no—
695SD16×C67—41no—
696M16×C67—41no—
697C2×C8×C67—41no—
698C2×C8×C67C2411yescharacteristic
699C2×C8×C67C2411yescharacteristic
700C2×C8×C67C2411yescharacteristic
701C2×C8×C67C2411yescharacteristic
702C4⋊C4×C67—21no—
703C4⋊C4×C67—21no—
704C4⋊C4×C67—21no—
705C4⋊C4×C67—21no—
706C4⋊C4×C67—21no—
707C4⋊C4×C67—21no—
708C4⋊C4×C67C2×D411yescharacteristic
709C4⋊C4×C67C2411yescharacteristic
710C4⋊C4×C67C2411yescharacteristic
711C4⋊C4×C67C2411yescharacteristic
712C4⋊C4×C67C2411yescharacteristic
713C22⋊C4×C67—21no—
714C22⋊C4×C67—21no—
715C22⋊C4×C67—21no—
716C22⋊C4×C67—21no—
717C22⋊C4×C67—21no—
718C22⋊C4×C67—21no—
719C22⋊C4×C67C2×D411yescharacteristic
720C22⋊C4×C67C2×D411yescharacteristic
721C42×C67—21no—
722C42×C67—21no—
723C42×C67C2411yescharacteristic
724C23×C67—21no—
725C23×C67—21no—
726C23×C67—21no—
727C23×C67—42no—
728C23×C67—42no—
729C23×C67—42no—
730C23×C67—81no—
731C23×C67—81no—
732C23×C67—81no—
733C23×C67C22×D411yescharacteristic
734C23×C67C22×D411yescharacteristic
735C22×D67—21no—
736C22×D67—22no—
737C22×D67—22no—
738C22×D67—24no—
739C22×D67—21no—
740C22×D67—41no—
741C22×D67—42no—
742C22×D67—42no—
743C22×D67—42no—
744C22×D67—42no—
745C22×D67—42no—
746C22×D67—42no—
747C22×D67—42no—
748C22×D67—42no—
749C22×D67—81no—
750C22×D67—81no—
751C22×D67—81no—
752C22×D67—81no—
753C22×D67—81no—
754C22×D67—81no—
755C22×D67—81no—
756C22×D67—81no—
757C22×D67—81no—
758C22×D67—816no—
759C22×D67C22×D411yescharacteristic
760C22×D67C22×D411yescharacteristic
761C22×D67C22×D411yescharacteristic
762Q8×C67—21no—
763Q8×C67—21no—
764D4×C67—21no—
765D4×C67—21no—
766D4×C67—21no—
767D4×C67—21no—
768D4×C67—21no—
769D4×C67—41no—
770D4×C67—42no—
771D4×C67—42no—
772D4×C67—42no—
773D4×C67—81no—
774D4×C67—81no—
775D4×C67—81no—
776D4×C67C2×#4112yes—
777C2×C4×C67—21no—
778C2×C4×C67—21no—
779C2×C4×C67—21no—
780C2×C4×C67—21no—
781C2×C4×C67—21no—
782C2×C4×C67—21no—
783C2×C4×C67—21no—
784C2×C4×C67—21no—
785C2×C4×C67—21no—
786C2×C4×C67—81no—
787C2×C4×C67—81no—
788C2×C4×C67C22×D411yescharacteristic
789C2×C4×C67C22×D411yescharacteristic
790C2×C4×C67C22×D411yescharacteristic
791C2×C4×C67C22×D411yescharacteristic
792C2×C4×C67C2511yescharacteristic
793C22⋊D67—22no—
794C22⋊D67—22no—
795C22⋊D67—24no—
796C22⋊D67—22no—
797C22⋊D67—41no—
798C22⋊D67—42no—
799C22⋊D67—42no—
800C22⋊D67—42no—
801C22⋊D67—42no—
802C22⋊D67—42no—
803C22⋊D67—42no—
804C22⋊D67—42no—
805C22⋊D67—42no—
806C22⋊D67—81no—
807C22⋊D67—81no—
808C22⋊D67—81no—
809C22⋊D67—81no—
810C2×Dic67—22no—
811C2×Dic67—21no—
812C2×Dic67—21no—
813C2×Dic67—21no—
814C2×Dic67—21no—
815C2×Dic67—21no—
816C2×Dic67—21no—
817C2×Dic67—42no—
818C2×Dic67—42no—
819C2×Dic67—81no—
820C2×Dic67C22×D411yescharacteristic
821C2×Dic67C22×D411yescharacteristic
822C2×Dic67C22×D411yescharacteristic
823C2×Dic67C22×D411yescharacteristic
824C2×Dic67C22×D411yescharacteristic
825D268—22no—
826D268—22no—
827D268—21no—
828D268—21no—
829D268—21no—
830D268—42no—
831D268—81no—
832D268C2×#4112yes—
833C4×D67—22no—
834C4×D67—21no—
835C4×D67—21no—
836C4×D67—21no—
837C4×D67—21no—
838C4×D67—22no—
839C4×D67—42no—
840C4×D67—42no—
841C4×D67—42no—
842C4×D67—81no—
843C4×D67—81no—
844C4×D67—81no—
845C4×D67—81no—
846C4×D67—81no—
847C4×D67C2×#4112yes—
848C4×D67H(5,𝔽2)12yes—
849Dic134—22no—
850Dic134—21no—
851Dic134—21no—
852Dic134—21no—
853Dic134—21no—
854Dic134—42no—
855Dic134—81no—
856Dic134—81no—
857C8×C67—21no—
858C8×C67—21no—
859C8×C67—21no—
860C8×C67—21no—
861C67⋊C8—21no—
862C67⋊C8—21no—
863C67⋊C8—21no—
864C67⋊C8—21no—
865C22×C67—21no—
866C22×C67—21no—
867C22×C67—21no—
868C22×C67—22no—
869C22×C67—21no—
870C22×C67—21no—
871C22×C67—21no—
872C22×C67—41no—
873C22×C67—41no—
874C22×C67—41no—
875C22×C67—41no—
876C22×C67—41no—
877C22×C67—41no—
878C22×C67—41no—
879C22×C67—41no—
880C22×C67—84no—
881C22×C67—162no—
882C22×C67C23×D411yescharacteristic
883C2×D67—21no—
884C2×D67—21no—
885C2×D67—21no—
886C2×D67—21no—
887C2×D67—21no—
888C2×D67—21no—
889C2×D67—22no—
890C2×D67—21no—
891C2×D67—44no—
892C2×D67—41no—
893C2×D67—41no—
894C2×D67—41no—
895C2×D67—41no—
896C2×D67—41no—
897C2×D67—84no—
898C2×D67—84no—
899C2×D67—84no—
900C2×D67—84no—
901C2×D67—84no—
902C2×D67—162no—
903C2×D67#54612yes—
904C2×D67#57712yes—
905C4×C67—21no—
906C4×C67—21no—
907C4×C67—21no—
908C4×C67—21no—
909C4×C67—41no—
910C4×C67—41no—
911C4×C67—41no—
912C4×C67—41no—
913C4×C67—41no—
914C4×C67C22×#4111yescharacteristic
915C4×C67C2×H(5,𝔽2)11yescharacteristic
916Dic67—21no—
917Dic67—21no—
918Dic67—21no—
919Dic67—21no—
920Dic67—41no—
921Dic67—41no—
922Dic67—41no—
923Dic67—41no—
924Dic67—41no—
925Dic67—41no—
926Dic67#54612yes—
927#61184—671nomaximal, Sylow
928C2×C67—41no—
929C2×C67—42no—
930C2×C67—41no—
931C2×C67—81no—
932C2×C67—81no—
933C2×C67C2×#54611yescharacteristic
934C2×C67C2×#57711yescharacteristic
935C2×C67#358511yescharacteristic
936D67—22no—
937D67—22no—
938D67—41no—
939D67—42no—
940D67—81no—
941#3495—671no—
942#3484—671no—
943#3324—671no—
944#3324—671no—
945#3323—671no—
946#3323—671no—
947#3314—671no—
948#3314—671no—
949#3311—671no—
950#3311—671no—
951#3310—671no—
952#3310—671no—
953#3310—671no—
954#3310D6711yescharacteristic, complemented
955#3296—671no—
956#3296—671no—
957#3295—671no—
958#3295—671no—
959#3136—671no—
960#3096—671no—
961#3091—671no—
962#3081—671no—
963#3057—671no—
964#3056—671no—
965#3043—671no—
966#3009—671no—
967C2×#450—671no—
968#2949—671no—
969#2933—671no—
970#2897—671no—
971C2×#418—671no—
972C67#6118411yescharacteristic, complemented, Sylow
973C2×H(5,𝔽2)—671no—
974C23×D4—671no—
975C2×#137—671no—
976C22×SD16—671no—
977C22×SD16—671no—
978C2×#131—671no—
979C22×M16—671no—
980#556—671no—
981#556—671no—
982#554—671no—
983#554—671no—
984#552—671no—
985#552—671no—
986#552—671no—
987#552—1341no—
988#552—1341no—
989#552C2×D6711yescharacteristic, complemented
990#551—1341no—
991#551—1341no—
992#546—671no—
993#546—671no—
994#546—671no—
995#546—671no—
996#546—1341no—
997#546—1341no—
998D42—671no—
999D42—671no—
1000D42—671no—
1001D42—1341no—
1002D42—1341no—
1003D42C2×D6711yescharacteristic
1004#544—671no—
1005#542—1341no—
1006#541—1341no—
1007#536—671no—
1008#535—671no—
1009#535—671no—
1010#534—1341no—
1011#534—1341no—
1012#533—1341no—
1013#529—1341no—
1014#525—671no—
1015#525—671no—
1016C2×C22⋊Q8—671no—
1017C2×#120—1341no—
1018C2×#120—1341no—
1019#520—671no—
1020#519—671no—
1021#518—671no—
1022C2×#117—671no—
1023#490—671no—
1024#490C2×D6711yescharacteristic, complemented
1025#489—671no—
1026#489—671no—
1027#488—671no—
1028#488—671no—
1029#486—671no—
1030#486—671no—
1031#485—671no—
1032#485—671no—
1033#484—671no—
1034#483—671no—
1035#482—671no—
1036#482—671no—
1037#482—671no—
1038#482—671no—
1039#482—671no—
1040#482C2×D6711yescharacteristic, complemented
1041#481—671no—
1042#481—671no—
1043#481—671no—
1044#480—671no—
1045#480—671no—
1046#480C2×D6711yescharacteristic, complemented
1047#478—671no—
1048#478—671no—
1049#478—671no—
1050#478C2×D6711yescharacteristic, complemented
1051#476—671no—
1052#476—671no—
1053#474—671no—
1054#474—671no—
1055#470—671no—
1056#470—671no—
1057#468—671no—
1058#468—671no—
1059#468—671no—
1060#468—671no—
1061#468—671no—
1062#468C2×D6711yescharacteristic, complemented
1063#467—671no—
1064#467—671no—
1065#465—671no—
1066#465—671no—
1067#465—671no—
1068#465—671no—
1069#465—671no—
1070#465C2×D6711yescharacteristic, complemented
1071#464—671no—
1072#464—671no—
1073#464—671no—
1074#464—671no—
1075#460—671no—
1076#460—671no—
1077#460—671no—
1078#460C2×D6711yescharacteristic, complemented
1079#452—671no—
1080#452—671no—
1081#452—671no—
1082#452—671no—
1083#450—671no—
1084#450—671no—
1085#450—671no—
1086#450—671no—
1087#450—671no—
1088#450—671no—
1089#450—671no—
1090#450—671no—
1091#450—671no—
1092#450—671no—
1093#450C2×D6711yescharacteristic, complemented
1094#450C2×D6711yescharacteristic, complemented
1095#440—671no—
1096#440—671no—
1097#440—671no—
1098#440C2×D6711yescharacteristic, complemented
1099C4×SD16—671no—
1100C4×SD16—671no—
1101C4×SD16—671no—
1102C4×SD16—671no—
1103#436—671no—
1104#436—671no—
1105#435—671no—
1106#435—671no—
1107#435—671no—
1108#435C2×D6711yescharacteristic, complemented
1109C8×D4—671no—
1110C8×D4—671no—
1111#428—671no—
1112#427—671no—
1113#427—671no—
1114#424—671no—
1115#419—671no—
1116#418—671no—
1117#418—671no—
1118#418—671no—
1119#418—671no—
1120#418—671no—
1121#418—671no—
1122#418—671no—
1123#418—671no—
1124#418—671no—
1125#418C2×D6711yescharacteristic, complemented
1126#417—671no—
1127#417—671no—
1128#417—671no—
1129#416—671no—
1130#416—671no—
1131#416—671no—
1132#416—671no—
1133C2×#102—671no—
1134C2×#102—671no—
1135C2×#102—671no—
1136C2×#102—671no—
1137C2×#102—671no—
1138C2×#102—671no—
1139C2×#102—671no—
1140C2×#102C2×D6711yescharacteristic, complemented
1141#408—671no—
1142C2×C22⋊C8—671no—
1143#405—671no—
1144C25—1341no—
1145H(5,𝔽2)—2682no—
1146H(5,𝔽2)—1344no—
1147C2×#41—671no—
1148C2×#41—671no—
1149C2×#41—671no—
1150C2×#41—671no—
1151C2×#41—1341no—
1152C22×Q8—671no—
1153C22×D4—21no—
1154C22×D4—2682no—
1155C22×D4—671no—
1156C22×D4—671no—
1157C22×D4—671no—
1158C22×D4—671no—
1159C22×D4—671no—
1160C22×D4—671no—
1161C22×D4—1341no—
1162C22×D4—1341no—
1163C22×D4—1341no—
1164C22×D4—1341no—
1165C22×D4—1344no—
1166C22×D4—1341no—
1167C22×D4—1341no—
1168C22×D4—1341no—
1169C22×D4—1341no—
1170C22×D4—1341no—
1171C22×D4C22×D6711yescharacteristic
1172C22×D4C22×D6711yescharacteristic
1173C23×C4—671no—
1174#137—2682no—
1175C2×Q16—671no—
1176C2×Q16—671no—
1177C2×SD16—2682no—
1178C2×SD16—671no—
1179C2×SD16—671no—
1180C2×SD16—671no—
1181C2×SD16—671no—
1182C2×SD16—671no—
1183C2×SD16—671no—
1184C2×SD16—671no—
1185C2×SD16—1344no—
1186C2×SD16C22×D6711yescharacteristic
1187C2×SD16C22×D6711yescharacteristic
1188C2×SD16C22×D6711yescharacteristic, complemented
1189#131—2682no—
1190C2×M16—2682no—
1191C2×M16—671no—
1192C2×M16—671no—
1193C2×M16—671no—
1194C2×M16—671no—
1195C2×M16—671no—
1196C2×M16C22×D6711yescharacteristic
1197C22×C8—671no—
1198C22×C8—671no—
1199C22×C8—671no—
1200C22×C8—671no—
1201C22×C8—671no—
1202C22×C8C22×D6711yescharacteristic, complemented
1203C4⋊Q8—671no—
1204C4⋊Q8—671no—
1205C4⋊Q8—1341no—
1206C4⋊Q8—1341no—
1207#127—671no—
1208#127—1341no—
1209#127C22×D6711yescharacteristic
1210#126—21no—
1211#126—1341no—
1212#126—1341no—
1213#126—1341no—
1214#126—1341no—
1215#126—1341no—
1216#126—1341no—
1217#126—1341no—
1218#125—21no—
1219#125—671no—
1220#125—1341no—
1221#125—1341no—
1222#125—1341no—
1223#125—1341no—
1224#125—1341no—
1225#125—1341no—
1226#125C22×D6711yescharacteristic, complemented
1227#124—671no—
1228#124—671no—
1229#124—1341no—
1230#124—1341no—
1231#124—1341no—
1232#124—1341no—
1233#123—21no—
1234#123—671no—
1235#123—671no—
1236#123—1341no—
1237#123—1341no—
1238#123—1341no—
1239#123—1341no—
1240#123—1341no—
1241#123—1341no—
1242#123—1341no—
1243#123—1341no—
1244#123—1341no—
1245#123—1341no—
1246C22⋊Q8—671no—
1247C22⋊Q8—671no—
1248C22⋊Q8—671no—
1249C22⋊Q8—671no—
1250C22⋊Q8—671no—
1251C22⋊Q8—671no—
1252C22⋊Q8—671no—
1253C22⋊Q8—671no—
1254C22⋊Q8—671no—
1255C22⋊Q8—671no—
1256C22⋊Q8—1341no—
1257C22⋊Q8—1341no—
1258C22⋊Q8—1341no—
1259C22⋊Q8—1341no—
1260C22⋊Q8—1341no—
1261C22⋊Q8—1341no—
1262C22⋊Q8—1341no—
1263C22⋊Q8—1341no—
1264C22⋊Q8C22×D6711yescharacteristic
1265C22⋊Q8C22×D6711yescharacteristic, complemented
1266#121—21no—
1267#121—671no—
1268#121—671no—
1269#121—671no—
1270#121—671no—
1271#121—671no—
1272#121—671no—
1273#121—1341no—
1274#121—1341no—
1275#121—1341no—
1276#121—1341no—
1277#121—1341no—
1278#121—1341no—
1279#121—1341no—
1280#121—1341no—
1281#121—1341no—
1282#121C22×D6711yescharacteristic
1283#121C22×D6711yescharacteristic
1284#120—21no—
1285#120—21no—
1286#120—671no—
1287#120—671no—
1288#120—1341no—
1289#120—1341no—
1290#120—1341no—
1291#120—1341no—
1292#120—1341no—
1293#120—1341no—
1294#120—1341no—
1295#120—1341no—
1296#120—1341no—
1297#120—1341no—
1298#120—1341no—
1299#120—1341no—
1300#120—1341no—
1301#120—1341no—
1302#120—1341no—
1303C4×Q8—671no—
1304C4×Q8—671no—
1305C4×Q8—671no—
1306C4×Q8—1341no—
1307C4×Q8—1341no—
1308C4×Q8—1341no—
1309C4×Q8—1341no—
1310C4×Q8—1341no—
1311C4×Q8C22×D6711yescharacteristic, complemented
1312C4×D4—671no—
1313C4×D4—671no—
1314C4×D4—671no—
1315C4×D4—671no—
1316C4×D4—671no—
1317C4×D4—671no—
1318C4×D4—1341no—
1319C4×D4—1341no—
1320C4×D4—1341no—
1321C4×D4—1341no—
1322C4×D4—1341no—
1323C4×D4—1341no—
1324C4×D4—1341no—
1325C4×D4—1341no—
1326C4×D4—1341no—
1327C4×D4C22×D6711yescharacteristic
1328C4×D4C22×D6711yescharacteristic
1329#117—21no—
1330#117—671no—
1331#117—671no—
1332#117—671no—
1333#117—671no—
1334#117—671no—
1335#117—671no—
1336#117—671no—
1337#117—1341no—
1338#117—1341no—
1339#117—1341no—
1340#117—1341no—
1341#117—1341no—
1342#117—1341no—
1343#117—1341no—
1344#117C22×D6711yescharacteristic
1345C2×C4⋊C4—671no—
1346C2×C4⋊C4—671no—
1347C2×C4⋊C4—671no—
1348C2×C4⋊C4—671no—
1349C2×C4⋊C4—1341no—
1350C2×C4⋊C4C22×D6711yescharacteristic, complemented
1351C2×C22⋊C4—1341no—
1352C2×C22⋊C4—1341no—
1353C2×C22⋊C4—1341no—
1354C2×C22⋊C4—1341no—
1355C2×C22⋊C4—1341no—
1356C2×C22⋊C4—1341no—
1357C2×C22⋊C4—1341no—
1358C2×C22⋊C4—1341no—
1359C2×C42—1341no—
1360#107—671no—
1361#107—671no—
1362#107—671no—
1363#107—671no—
1364#107C22×D6711yescharacteristic, complemented
1365#107C22×D6711yescharacteristic, complemented
1366#106—671no—
1367#106—671no—
1368#106—671no—
1369#106—671no—
1370#106—671no—
1371#106C22×D6711yescharacteristic, complemented
1372C4⋊C8—671no—
1373C4⋊C8—671no—
1374C4⋊C8—671no—
1375C4⋊C8C22×D6711yescharacteristic, complemented
1376#103—671no—
1377#103—671no—
1378#103—671no—
1379#103—671no—
1380#103—671no—
1381#103—671no—
1382#103—671no—
1383#103—671no—
1384#103—671no—
1385#103C22×D6711yescharacteristic, complemented
1386#102—671no—
1387#102—671no—
1388#102—671no—
1389#102—671no—
1390#102—671no—
1391#102—671no—
1392#102—671no—
1393#102—671no—
1394#102—671no—
1395#102—671no—
1396#102—671no—
1397#102—671no—
1398#102—671no—
1399#102—671no—
1400#102—671no—
1401#102—671no—
1402#102—671no—
1403#102—671no—
1404#102—671no—
1405#102—671no—
1406#102—671no—
1407#102C22×D6711yescharacteristic
1408#102C22×D6711yescharacteristic
1409#102C22×D6711yescharacteristic
1410#102C22×D6711yescharacteristic
1411#102C22×D6711yescharacteristic
1412#102C22×D6711yescharacteristic
1413#102C22×D6711yescharacteristic, complemented
1414#102C22×D6711yescharacteristic, complemented
1415#102C22×D6711yescharacteristic, complemented
1416C22⋊C8—671no—
1417C22⋊C8—671no—
1418C22⋊C8—671no—
1419C22⋊C8—671no—
1420C22⋊C8—671no—
1421C22⋊C8—671no—
1422C22⋊C8C22×D6711yescharacteristic
1423C22⋊C8C22×D6711yescharacteristic, complemented
1424#97—671no—
1425#97C22×D6711yescharacteristic, complemented
1426C4×C8—671no—
1427C4×C8—671no—
1428C24—21no—
1429C24—21no—
1430C24—2684no—
1431C24—5362no—
1432C24—5362no—
1433C24—671no—
1434C24—1341no—
1435C24—1341no—
1436C24—1341no—
1437C24—1341no—
1438C24—1341no—
1439C24—1341no—
1440#41—2681no—
1441#41—2684no—
1442#41—2681no—
1443#41—1342no—
1444#41—1342no—
1445#41—1342no—
1446#41—1342no—
1447#41—1342no—
1448#41—1342no—
1449C2×Q8—671no—
1450C2×Q8—671no—
1451C2×Q8—671no—
1452C2×Q8—1341no—
1453C2×Q8—1341no—
1454C2×Q8—1342no—
1455C2×Q8—1342no—
1456C2×Q8—1341no—
1457C2×Q8C23×D6711yescharacteristic
1458C2×D4—22no—
1459C2×D4—22no—
1460C2×D4—21no—
1461C2×D4—21no—
1462C2×D4—21no—
1463C2×D4—21no—
1464C2×D4—21no—
1465C2×D4—21no—
1466C2×D4—41no—
1467C2×D4—41no—
1468C2×D4—82no—
1469C2×D4—2681no—
1470C2×D4—2684no—
1471C2×D4—2684no—
1472C2×D4—2684no—
1473C2×D4—2681no—
1474C2×D4—2681no—
1475C2×D4—2681no—
1476C2×D4—2684no—
1477C2×D4—2684no—
1478C2×D4—2684no—
1479C2×D4—5362no—
1480C2×D4—5362no—
1481C2×D4—5362no—
1482C2×D4—671no—
1483C2×D4—674no—
1484C2×D4—671no—
1485C2×D4—671no—
1486C2×D4—671no—
1487C2×D4—671no—
1488C2×D4—671no—
1489C2×D4—671no—
1490C2×D4—671no—
1491C2×D4—1342no—
1492C2×D4—1341no—
1493C2×D4—1342no—
1494C2×D4—1342no—
1495C2×D4—1342no—
1496C2×D4—1341no—
1497C2×D4—1341no—
1498C2×D4—1341no—
1499C2×D4—1341no—
1500C2×D4—1341no—
1501C2×D4—1341no—
1502C2×D4—1341no—
1503C2×D4—1342no—
1504C2×D4—1342no—
1505C2×D4—1341no—
1506C2×D4—1341no—
1507C2×D4—1341no—
1508C2×D4—1341no—
1509C2×D4—1342no—
1510C2×D4—1341no—
1511C2×D4—1341no—
1512C2×D4—1341no—
1513C2×D4D4×D6711yescharacteristic
1514C2×D4C23×D6711yescharacteristic
1515C2×D4C23×D6711yescharacteristic
1516C2×D4C23×D6711yescharacteristic
1517C22×C4—21no—
1518C22×C4—21no—
1519C22×C4—671no—
1520C22×C4—671no—
1521C22×C4—671no—
1522C22×C4—671no—
1523C22×C4—671no—
1524C22×C4—671no—
1525C22×C4—1341no—
1526C22×C4—1341no—
1527C22×C4—1341no—
1528C22×C4—1341no—
1529C22×C4—1341no—
1530C22×C4—1341no—
1531C22×C4—1342no—
1532C22×C4—1342no—
1533C22×C4—1341no—
1534C22×C4—1341no—
1535C22×C4—1341no—
1536C22×C4—1341no—
1537C22×C4—1341no—
1538C22×C4C23×D6711yescharacteristic
1539C22×C4C23×D6711yescharacteristic
1540Q16—2681no—
1541Q16—2681no—
1542SD16—22no—
1543SD16—41no—
1544SD16—41no—
1545SD16—2681no—
1546SD16—2681no—
1547SD16—2681no—
1548SD16—2681no—
1549SD16—1342no—
1550SD16—1342no—
1551SD16—1342no—
1552M16—41no—
1553M16—2681no—
1554M16—2681no—
1555M16—2681no—
1556M16—1342no—
1557M16—1342no—
1558C2×C8—41no—
1559C2×C8—2681no—
1560C2×C8—2681no—
1561C2×C8—2681no—
1562C2×C8—671no—
1563C2×C8—671no—
1564C2×C8—671no—
1565C2×C8—671no—
1566C2×C8—1342no—
1567C2×C8—1342no—
1568C2×C8C23×D6711yescharacteristic
1569C2×C8C23×D6711yescharacteristic
1570C2×C8C23×D6711yescharacteristic
1571C2×C8C23×D6711yescharacteristic
1572C4⋊C4—21no—
1573C4⋊C4—21no—
1574C4⋊C4—21no—
1575C4⋊C4—21no—
1576C4⋊C4—21no—
1577C4⋊C4—21no—
1578C4⋊C4—671no—
1579C4⋊C4—671no—
1580C4⋊C4—671no—
1581C4⋊C4—671no—
1582C4⋊C4—671no—
1583C4⋊C4—671no—
1584C4⋊C4—671no—
1585C4⋊C4—671no—
1586C4⋊C4—671no—
1587C4⋊C4—1341no—
1588C4⋊C4—1341no—
1589C4⋊C4—1341no—
1590C4⋊C4—1341no—
1591C4⋊C4—1341no—
1592C4⋊C4—1341no—
1593C4⋊C4—1341no—
1594C4⋊C4—1341no—
1595C4⋊C4—1341no—
1596C4⋊C4—1341no—
1597C4⋊C4—1341no—
1598C4⋊C4—1341no—
1599C4⋊C4—1341no—
1600C4⋊C4—1341no—
1601C4⋊C4—1341no—
1602C4⋊C4—1341no—
1603C4⋊C4—1341no—
1604C4⋊C4—1341no—
1605C4⋊C4—1341no—
1606C4⋊C4D4×D6711yescharacteristic
1607C4⋊C4C23×D6711yescharacteristic
1608C4⋊C4C23×D6711yescharacteristic
1609C4⋊C4C23×D6711yescharacteristic
1610C4⋊C4C23×D6711yescharacteristic
1611C22⋊C4—21no—
1612C22⋊C4—21no—
1613C22⋊C4—21no—
1614C22⋊C4—21no—
1615C22⋊C4—21no—
1616C22⋊C4—21no—
1617C22⋊C4—671no—
1618C22⋊C4—671no—
1619C22⋊C4—671no—
1620C22⋊C4—671no—
1621C22⋊C4—671no—
1622C22⋊C4—671no—
1623C22⋊C4—671no—
1624C22⋊C4—671no—
1625C22⋊C4—1341no—
1626C22⋊C4—1341no—
1627C22⋊C4—1341no—
1628C22⋊C4—1341no—
1629C22⋊C4—1341no—
1630C22⋊C4—1341no—
1631C22⋊C4—1341no—
1632C22⋊C4—1341no—
1633C22⋊C4—1341no—
1634C22⋊C4—1341no—
1635C22⋊C4—1341no—
1636C22⋊C4—1341no—
1637C22⋊C4—1341no—
1638C22⋊C4—1341no—
1639C22⋊C4—1341no—
1640C22⋊C4—1341no—
1641C22⋊C4—1341no—
1642C22⋊C4—1341no—
1643C22⋊C4—1341no—
1644C22⋊C4—1341no—
1645C22⋊C4—1341no—
1646C22⋊C4—1341no—
1647C22⋊C4—1341no—
1648C22⋊C4—1341no—
1649C22⋊C4—1341no—
1650C22⋊C4D4×D6711yescharacteristic
1651C22⋊C4D4×D6711yescharacteristic
1652C42—21no—
1653C42—21no—
1654C42—671no—
1655C42—1341no—
1656C42—1341no—
1657C42—1341no—
1658C42—1341no—
1659C42—1341no—
1660C42—1341no—
1661C42—1341no—
1662C42—1341no—
1663C42—1341no—
1664C42C23×D6711yescharacteristic
1665C23—21no—
1666C23—21no—
1667C23—21no—
1668C23—42no—
1669C23—42no—
1670C23—42no—
1671C23—81no—
1672C23—81no—
1673C23—81no—
1674C23—2681no—
1675C23—2682no—
1676C23—2682no—
1677C23—2682no—
1678C23—2682no—
1679C23—2682no—
1680C23—2682no—
1681C23—2682no—
1682C23—2682no—
1683C23—5361no—
1684C23—5361no—
1685C23—5361no—
1686C23—5361no—
1687C23—5361no—
1688C23—5361no—
1689C23—5361no—
1690C23—5361no—
1691C23—5361no—
1692C23—53616no—
1693C23—671no—
1694C23—671no—
1695C23—671no—
1696C23—1342no—
1697C23—1342no—
1698C23—1344no—
1699C23—1341no—
1700C23—1341no—
1701C23C2×D4×D6711yescharacteristic
1702C23C2×D4×D6711yescharacteristic
1703Q8—21no—
1704Q8—21no—
1705Q8—2682no—
1706Q8—5361no—
1707Q8—5361no—
1708Q8—1342no—
1709Q8—1341no—
1710Q8—1341no—
1711Q8—1341no—
1712Q8—1341no—
1713D4—21no—
1714D4—21no—
1715D4—21no—
1716D4—21no—
1717D4—21no—
1718D4—41no—
1719D4—42no—
1720D4—42no—
1721D4—42no—
1722D4—81no—
1723D4—81no—
1724D4—81no—
1725D4—2682no—
1726D4—2682no—
1727D4—2682no—
1728D4—2682no—
1729D4—2682no—
1730D4—2682no—
1731D4—2682no—
1732D4—2681no—
1733D4—2682no—
1734D4—2682no—
1735D4—5361no—
1736D4—5361no—
1737D4—5361no—
1738D4—5361no—
1739D4—5361no—
1740D4—672no—
1741D4—1342no—
1742D4—1342no—
1743D4—1344no—
1744D4—1342no—
1745D4—1342no—
1746D4—1342no—
1747D4—1341no—
1748D4—1341no—
1749D4—1341no—
1750D4#41×D6712yes—
1751C2×C4—21no—
1752C2×C4—21no—
1753C2×C4—21no—
1754C2×C4—21no—
1755C2×C4—21no—
1756C2×C4—21no—
1757C2×C4—21no—
1758C2×C4—21no—
1759C2×C4—21no—
1760C2×C4—81no—
1761C2×C4—81no—
1762C2×C4—2682no—
1763C2×C4—2682no—
1764C2×C4—2682no—
1765C2×C4—2682no—
1766C2×C4—2682no—
1767C2×C4—5361no—
1768C2×C4—5361no—
1769C2×C4—5361no—
1770C2×C4—5361no—
1771C2×C4—5361no—
1772C2×C4—5361no—
1773C2×C4—671no—
1774C2×C4—672no—
1775C2×C4—672no—
1776C2×C4—671no—
1777C2×C4—671no—
1778C2×C4—671no—
1779C2×C4—671no—
1780C2×C4—1342no—
1781C2×C4—1342no—
1782C2×C4—1341no—
1783C2×C4—1341no—
1784C2×C4—1341no—
1785C2×C4—1341no—
1786C2×C4—1341no—
1787C2×C4—1341no—
1788C2×C4—1342no—
1789C2×C4—1341no—
1790C2×C4—1341no—
1791C2×C4—1341no—
1792C2×C4—1341no—
1793C2×C4C2×D4×D6711yescharacteristic
1794C2×C4C2×D4×D6711yescharacteristic
1795C2×C4C2×D4×D6711yescharacteristic
1796C2×C4C2×D4×D6711yescharacteristic
1797C2×C4C24×D6711yescharacteristic
1798C8—21no—
1799C8—21no—
1800C8—21no—
1801C8—21no—
1802C8—1341no—
1803C8—1341no—
1804C8—1341no—
1805C8—1341no—
1806C22—21no—
1807C22—21no—
1808C22—22no—
1809C22—21no—
1810C22—21no—
1811C22—21no—
1812C22—21no—
1813C22—41no—
1814C22—41no—
1815C22—41no—
1816C22—41no—
1817C22—41no—
1818C22—41no—
1819C22—41no—
1820C22—41no—
1821C22—84no—
1822C22—2684no—
1823C22—2681no—
1824C22—2681no—
1825C22—2681no—
1826C22—2681no—
1827C22—2681no—
1828C22—162no—
1829C22—5364no—
1830C22—5364no—
1831C22—5364no—
1832C22—5364no—
1833C22—5364no—
1834C22—10722no—
1835C22—672no—
1836C22—672no—
1837C22—1342no—
1838C22—1341no—
1839C22—1341no—
1840C22—1341no—
1841C22—1341no—
1842C22—1341no—
1843C22—1341no—
1844C22—1341no—
1845C22C22×D4×D6711yescharacteristic
1846C4—21no—
1847C4—21no—
1848C4—21no—
1849C4—21no—
1850C4—41no—
1851C4—41no—
1852C4—41no—
1853C4—41no—
1854C4—41no—
1855C4—2681no—
1856C4—2681no—
1857C4—2681no—
1858C4—2681no—
1859C4—2681no—
1860C4—2681no—
1861C4—672no—
1862C4—1341no—
1863C4—1341no—
1864C4—1341no—
1865C4—1341no—
1866C4C2×#41×D6711yescharacteristic
1867C4H(5,𝔽2)×D6711yescharacteristic
1868C2—41no—
1869C2—41no—
1870C2—42no—
1871C2—81no—
1872C2—81no—
1873C2—2682no—
1874C2—2681no—
1875C2—5361no—
1876C2—1342no—
1877C2—1342no—
1878C2#546×D6711yescharacteristic
1879C2#577×D6711yescharacteristic
1880C2#2257498511yescharacteristic
subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3310C2
socleC22×C67C23×D4
prime radical#22573837C2
hypercenter#3310D67
hypocenterC67#61184
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3310

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22573960C2semidirect
3. #22572440C2semidirect
4. #22572435C2semidirect
5. #22572421C2semidirect
6. #22572419C2semidirect
7. #22572295C2semidirect
8. #22572293C2semidirect
9. #22572247C2semidirect
10. #22572238C2semidirect
11. #22572233C2semidirect
12. #22572229C2semidirect
13. #22572223C2semidirect
14. #22572041C2semidirect
15. #22572039C2semidirect
16. #22572036C2semidirect
17. #22572029C2semidirect
18. #22570564C2semidirect
19. #22570160C2semidirect
20. #22570121C2semidirect
21. #22570039C2semidirect
22. #22569843C2semidirect
23. #22569834C2semidirect
24. #22569725C2semidirect
25. #22569481C2semidirect
26. #450×D67C2semidirect
27. #22569065C2semidirect
28. #22568932C2semidirect
29. #22568730C2semidirect
30. #418×D67C2semidirect
31. C67×#3310C2semidirect
34. C2×#14524072C22semidirect
36. C2×SD16×D67C22semidirect
37. C2×#14524049C22semidirect
38. C2×M16×D67C22semidirect
39. #16864117C22semidirect
40. #16864116C22semidirect
41. #16864106C22semidirect
42. #16864101C22semidirect
44. #16864085C22semidirect
45. #16864084C22semidirect
46. #16864080C22semidirect
61. #16864026C22semidirect
64. #16863969C22semidirect
73. C22⋊Q8×D67C22semidirect
76. #16863877C22semidirect
77. #16863872C22semidirect
79. #117×D67C22semidirect
80. #16863759C22semidirect
81. #16863756C22semidirect
82. #16863754C22semidirect
83. #16863753C22semidirect
84. #16863749C22semidirect
85. #16863742C22semidirect
86. #16863741C22semidirect
87. #16863738C22semidirect
88. #16863737C22semidirect
89. #16863733C22semidirect
90. #16863728C22semidirect
91. #16863723C22semidirect
92. #16863721C22semidirect
93. #16863718C22semidirect
94. #16863717C22semidirect
95. #16863717C22semidirect
96. #16863714C22semidirect
97. #16863713C22semidirect
98. #16863713C22semidirect
99. #16863711C22semidirect
100. #16863708C22semidirect
101. #16863698C22semidirect
102. #16863695C22semidirect
103. #16863693C22semidirect
104. #16863687C22semidirect
105. #16863684C22semidirect
106. #16863676C22semidirect
107. #16863675C22semidirect
108. #16863654C22semidirect
109. #16863652C22semidirect
110. #16863645C22semidirect
111. #16863644C22semidirect
112. #16863641C22semidirect
113. #16863640C22semidirect
114. #16863640C22semidirect
115. #16863638C22semidirect
116. #16863636C22semidirect
117. #16863626C22semidirect
118. #16863625C22semidirect
119. #16863624C22semidirect
120. #16863622C22semidirect
121. #16863622C22semidirect
122. #16863619C22semidirect
123. #16863618C22semidirect
124. #16863617C22semidirect
125. #16863616C22semidirect
126. #16863595C22semidirect
127. #16863594C22semidirect
128. #16863593C22semidirect
129. #16863560C22semidirect
130. #16863559C22semidirect
131. #16863556C22semidirect
132. #16863555C22semidirect
133. #16863549C22semidirect
134. #16863548C22semidirect
135. #16863548C22semidirect
136. #16863548C22semidirect
137. #16863547C22semidirect
138. #16863547C22semidirect
139. #16863546C22semidirect
140. #16863545C22semidirect
141. #16863545C22semidirect
142. #16863545C22semidirect
143. #16863498C22semidirect
144. #16863497C22semidirect
145. #16863495C22semidirect
146. #16863487C22semidirect
147. C4×#11761615C22semidirect
148. C4×#11761616C22semidirect
149. #16863481C22semidirect
150. #16863474C22semidirect
151. #16863472C22semidirect
152. #16863470C22semidirect
153. #16863470C22semidirect
154. #16863469C22semidirect
155. #16863461C22semidirect
156. C8×C22⋊D67C22semidirect
157. #16863437C22semidirect
158. #16863433C22semidirect
159. #16863431C22semidirect
160. #16863421C22semidirect
161. #16863403C22semidirect
162. #16863402C22semidirect
163. #16863401C22semidirect
164. #16863401C22semidirect
165. #16863400C22semidirect
168. #16863399C22semidirect
169. #16863399C22semidirect
170. #16863399C22semidirect
171. #16863395C22semidirect
172. #16863394C22semidirect
173. #16863394C22semidirect
174. #16863393C22semidirect
175. #16863389C22semidirect
176. #16863389C22semidirect
177. #16863389C22semidirect
179. #102×D67C22semidirect
180. #102×D67C22semidirect
181. #102×D67C22semidirect
182. #102×D67C22semidirect
183. #102×D67C22semidirect
184. #102×D67C22semidirect
185. #16863361C22semidirect
186. C22⋊C8×D67C22semidirect
187. #16863353C22semidirect
188. #552×C67C22semidirect
190. #490×C67C22semidirect
191. #482×C67C22semidirect
192. #480×C67C22semidirect
193. #478×C67C22semidirect
194. #468×C67C22semidirect
195. #465×C67C22semidirect
196. #460×C67C22semidirect
197. #450×C67C22semidirect
198. #450×C67C22semidirect
199. #440×C67C22semidirect
200. #435×C67C22semidirect
201. #418×C67C22semidirect
202. C2×#102×C67C22semidirect
231. C2×Dic268C23semidirect
232. C2×#11761618C23semidirect
237. C2×#11761616C23semidirect
244. C2×#11761612C23semidirect
247. C2×#11761611C23semidirect
253. C2×C8×D67C23semidirect
254. #14524043C23semidirect
257. #14524042C23semidirect
270. #14524034C23semidirect
295. #14524023C23semidirect
299. #14524022C23semidirect
309. #14524019C23semidirect
342. Q8×Dic67C23semidirect
344. C4×Dic134C23semidirect
349. #14524008C23semidirect
366. #14524002C23semidirect
373. #14524001C23semidirect
383. C4⋊C4×D67C23semidirect
393. #14523977C23semidirect
394. #14523976C23semidirect
395. #14523976C23semidirect
396. #14523976C23semidirect
397. #14523975C23semidirect
398. #14523975C23semidirect
399. #14523974C23semidirect
400. #14523974C23semidirect
401. #14523974C23semidirect
402. C4⋊(C67⋊C8)C23semidirect
403. Dic67⋊C8C23semidirect
404. Dic67⋊C8C23semidirect
405. #14523968C23semidirect
406. #14523968C23semidirect
407. #14523968C23semidirect
408. #14523968C23semidirect
409. #14523967C23semidirect
410. #14523966C23semidirect
411. #14523966C23semidirect
412. #14523966C23semidirect
413. #14523966C23semidirect
426. #14523964C23semidirect
427. #14523964C23semidirect
428. #14523964C23semidirect
436. C22⋊(C67⋊C8)C23semidirect
439. (C2×D67)⋊C8C23semidirect
440. (C2×D67)⋊C8C23semidirect
441. #14523953C23semidirect
442. C4×C67⋊C8C23semidirect
443. C8×Dic67C23semidirect
449. C2×SD16×C67C23semidirect
451. C22×C8×C67C23semidirect
455. #125×C67C23semidirect
458. C22⋊Q8×C67C23semidirect
464. C4×Q8×C67C23semidirect
469. C2×C4⋊C4×C67C23semidirect
470. #107×C67C23semidirect
471. #107×C67C23semidirect
472. #106×C67C23semidirect
473. C4⋊C8×C67C23semidirect
474. #103×C67C23semidirect
481. #102×C67C23semidirect
482. #102×C67C23semidirect
483. #102×C67C23semidirect
485. C22⋊C8×C67C23semidirect
486. #97×C67C23semidirect
954. #3310D67semidirect
972. C67#61184semidirect
989. #552C2×D67semidirect
1024. #490C2×D67semidirect
1040. #482C2×D67semidirect
1046. #480C2×D67semidirect
1050. #478C2×D67semidirect
1062. #468C2×D67semidirect
1070. #465C2×D67semidirect
1078. #460C2×D67semidirect
1093. #450C2×D67semidirect
1094. #450C2×D67semidirect
1098. #440C2×D67semidirect
1108. #435C2×D67semidirect
1125. #418C2×D67semidirect
1140. C2×#102C2×D67semidirect
1188. C2×SD16C22×D67semidirect
1202. C22×C8C22×D67semidirect
1226. #125C22×D67semidirect
1265. C22⋊Q8C22×D67semidirect
1311. C4×Q8C22×D67semidirect
1350. C2×C4⋊C4C22×D67semidirect
1364. #107C22×D67semidirect
1365. #107C22×D67semidirect
1371. #106C22×D67semidirect
1375. C4⋊C8C22×D67semidirect
1385. #103C22×D67semidirect
1413. #102C22×D67semidirect
1414. #102C22×D67semidirect
1415. #102C22×D67semidirect
1423. C22⋊C8C22×D67semidirect
1425. #97C22×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225739602
#225738372
#225724402
#225724352
#225724212
#225724192
#225722952
#225722932
#225722472
#225722382
#225722332
#225722292
#225722232
#225720412
#225720392
#225720362
#225720292
#225705642
#225701602
#225701212
#225700392
#225698432
#225698342
#225697252
#225694812
#450×D672
#225690652
#225689322
#225687302
#418×D672
C67×#33102
#6118467