Finite Group Databasebeta

← #31733428

Subgroups — #31733428

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#22573954C211yesmaximal, characteristic, complemented
2#22573839C211yesmaximal, characteristic
3#22572436C211yesmaximal, characteristic, complemented
4#22572434C211yesmaximal, characteristic, complemented
5#22572431C211yesmaximal, characteristic, complemented
6#22572425C211yesmaximal, characteristic, complemented
7#22572289C211yesmaximal, characteristic, complemented
8#22572283C211yesmaximal, characteristic, complemented
9#22572248C211yesmaximal, characteristic, complemented
10#22572235C211yesmaximal, characteristic, complemented
11#22572233C211yesmaximal, characteristic, complemented
12#22572232C211yesmaximal, characteristic, complemented
13#22572223C211yesmaximal, characteristic, complemented
14#22572051C211yesmaximal, characteristic, complemented
15#22572045C211yesmaximal, characteristic, complemented
16#22572030C211yesmaximal, characteristic, complemented
17#22572028C211yesmaximal, characteristic, complemented
18#22570560C211yesmaximal, characteristic, complemented
19#22570164C211yesmaximal, characteristic, complemented
20#22570127C211yesmaximal, characteristic, complemented
21#22570035C211yesmaximal, characteristic, complemented
22#22569843C211yesmaximal, characteristic, complemented
23#22569838C211yesmaximal, characteristic, complemented
24#22569728C211yesmaximal, characteristic, complemented
25#22569483C211yesmaximal, characteristic, complemented
26#450×D67C211yesmaximal, characteristic, complemented
27#22569065C211yesmaximal, characteristic, complemented
28#22568932C211yesmaximal, characteristic, complemented
29#22568731C211yesmaximal, characteristic, complemented
30#418×D67C211yesmaximal, characteristic, complemented
31C67×#3311C211yesmaximal, characteristic, complemented
32C2×#14524089C2211yescharacteristic
33C22×D4×D67C2211yescharacteristic
34C2×#14524075C2211yescharacteristic, complemented
35C2×SD16×D67C2211yescharacteristic
36C2×SD16×D67C2211yescharacteristic, complemented
37C2×#14524049C2211yescharacteristic, complemented
38C2×M16×D67C2211yescharacteristic, complemented
39#16864114C2211yescharacteristic, complemented
40#16864107C2211yescharacteristic, complemented
41#16864104C2211yescharacteristic, complemented
42#16864087—21no—
43#16864087C2211yescharacteristic, complemented
44#16864086C2211yescharacteristic, complemented
45#16864085C2211yescharacteristic, complemented
46#16864082—21no—
47#16864080C2211yescharacteristic, complemented
48#16864076—21no—
49#16864071—21no—
50#16864039C2211yescharacteristic
51#16864038—21no—
52#16864037C2211yescharacteristic
53#16864036—21no—
54#16864034C2211yescharacteristic
55D4×D268C2211yescharacteristic
56D4×D268C2211yescharacteristic
57#16864030—21no—
58#16864030C2211yescharacteristic
59D4×C22⋊D67C2211yescharacteristic
60#16864028—21no—
61#16864023C2211yescharacteristic, complemented
62#16864010—21no—
63#16864003—21no—
64#16863969C2211yescharacteristic, complemented
65#16863964C2211yescharacteristic
66#16863962C2211yescharacteristic
67#16863957—21no—
68#16863954—21no—
69#16863950—21no—
70#16863929—21no—
71#16863909C2211yescharacteristic
72#16863905C2211yescharacteristic
73C22⋊Q8×D67C2211yescharacteristic, complemented
74C2×#14524013—21no—
75#120×D67—21no—
76#16863876C2211yescharacteristic, complemented
77#16863872C2211yescharacteristic, complemented
78#16863868C2211yescharacteristic
79#117×D67C2211yescharacteristic, complemented
80#16863761C2211yescharacteristic, complemented
81#16863759C2211yescharacteristic, complemented
82#16863757C2211yescharacteristic, complemented
83#16863752C2211yescharacteristic, complemented
84#16863750C2211yescharacteristic, complemented
85#16863744C2211yescharacteristic, complemented
86#16863741C2211yescharacteristic, complemented
87#16863734C2211yescharacteristic, complemented
88#16863730C2211yescharacteristic, complemented
89#16863725C2211yescharacteristic, complemented
90#16863723C2211yescharacteristic, complemented
91#16863721C2211yescharacteristic, complemented
92#16863720C2211yescharacteristic, complemented
93#16863720C2211yescharacteristic, complemented
94#16863718C2211yescharacteristic, complemented
95#16863716C2211yescharacteristic, complemented
96#16863716C2211yescharacteristic, complemented
97#16863712C2211yescharacteristic, complemented
98#16863711C2211yescharacteristic, complemented
99#16863710C2211yescharacteristic, complemented
100#16863708C2211yescharacteristic, complemented
101#16863698C2211yescharacteristic, complemented
102#16863697C2211yescharacteristic, complemented
103#16863696C2211yescharacteristic, complemented
104#16863695C2211yescharacteristic, complemented
105#16863685C2211yescharacteristic, complemented
106#16863674C2211yescharacteristic, complemented
107#16863673C2211yescharacteristic, complemented
108#16863652C2211yescharacteristic, complemented
109#16863645C2211yescharacteristic, complemented
110#16863644C2211yescharacteristic, complemented
111#16863644C2211yescharacteristic, complemented
112#16863642C2211yescharacteristic, complemented
113#16863641C2211yescharacteristic, complemented
114#16863640C2211yescharacteristic, complemented
115#16863636C2211yescharacteristic, complemented
116#16863634C2211yescharacteristic, complemented
117#16863628C2211yescharacteristic, complemented
118#16863626C2211yescharacteristic, complemented
119#16863626C2211yescharacteristic, complemented
120#16863625C2211yescharacteristic, complemented
121#16863622C2211yescharacteristic, complemented
122#16863621C2211yescharacteristic, complemented
123#16863620C2211yescharacteristic, complemented
124#16863615C2211yescharacteristic, complemented
125#16863597C2211yescharacteristic, complemented
126#16863596C2211yescharacteristic, complemented
127#16863595C2211yescharacteristic, complemented
128#16863594C2211yescharacteristic, complemented
129#16863561C2211yescharacteristic, complemented
130#16863558C2211yescharacteristic, complemented
131#16863557C2211yescharacteristic, complemented
132#16863549C2211yescharacteristic, complemented
133#16863549C2211yescharacteristic, complemented
134#16863548C2211yescharacteristic, complemented
135#16863548C2211yescharacteristic, complemented
136#16863548C2211yescharacteristic, complemented
137#16863547C2211yescharacteristic, complemented
138#16863546C2211yescharacteristic, 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#16863435C2211yescharacteristic, complemented
158#16863433C2211yescharacteristic, complemented
159#16863431C2211yescharacteristic, complemented
160#16863421C2211yescharacteristic, complemented
161#16863403C2211yescharacteristic, complemented
162#16863402C2211yescharacteristic, complemented
163#16863401C2211yescharacteristic, complemented
164#16863400C2211yescharacteristic, complemented
165#16863400C2211yescharacteristic, complemented
166#16863399C2211yescharacteristic
167#16863399C2211yescharacteristic
168#16863399C2211yescharacteristic, complemented
169#16863399C2211yescharacteristic, complemented
170#16863399C2211yescharacteristic, complemented
171#16863397C2211yescharacteristic, complemented
172#16863396C2211yescharacteristic, complemented
173#16863396C2211yescharacteristic, complemented
174#16863391C2211yescharacteristic, complemented
175#16863391C2211yescharacteristic, complemented
176#16863391C2211yescharacteristic, complemented
177C2×#14523965C2211yescharacteristic, 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#556×C67C2211yescharacteristic, complemented
189#546×C67C2211yescharacteristic
190#489×C67C2211yescharacteristic, complemented
191#485×C67C2211yescharacteristic, complemented
192#482×C67C2211yescharacteristic, complemented
193#476×C67C2211yescharacteristic, complemented
194#470×C67C2211yescharacteristic, complemented
195#465×C67C2211yescharacteristic, complemented
196#464×C67C2211yescharacteristic, complemented
197#452×C67C2211yescharacteristic, complemented
198#450×C67C2211yescharacteristic, complemented
199#440×C67C2211yescharacteristic, complemented
200#435×C67C2211yescharacteristic, complemented
201#418×C67C2211yescharacteristic, complemented
202#416×C67C2211yescharacteristic, complemented
203C24×D67—21no—
204#14524089—24no—
205#14524089—42no—
206C2×#11761629C2311yescharacteristic
207C2×#11761629C2311yescharacteristic
208C2×#11761628—21no—
209C2×#11761628C2311yescharacteristic
210C2×Q8×D67C2311yescharacteristic
211C22×D268—21no—
212C22×D268—21no—
213C22×D268C2311yescharacteristic
214C22×D268C2311yescharacteristic
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—21no—
224C2×D4×D67—42no—
225C2×D4×D67C2311yescharacteristic
226C2×D4×D67C2311yescharacteristic
227C2×D4×D67C2311yescharacteristic
228C2×D4×D67C2311yescharacteristic
229C2×D4×D67C2311yescharacteristic
230C22×C4×D67C2311yescharacteristic
231#14524075—42no—
232C2×#11761618C2311yescharacteristic, complemented
233C2×#11761617C2311yescharacteristic
234C2×#11761617C2311yescharacteristic
235C2×#11761617C2311yescharacteristic, complemented
236C2×#11761616C2311yescharacteristic
237C2×#11761616C2311yescharacteristic
238C2×#11761615C2311yescharacteristic
239C2×#11761615C2311yescharacteristic
240C2×#11761615C2311yescharacteristic, complemented
241SD16×D67—24no—
242SD16×D67—42no—
243#14524049—42no—
244C2×#11761612C2311yescharacteristic
245C2×#11761612C2311yescharacteristic, complemented
246C2×#11761611C2311yescharacteristic
247C2×#11761611C2311yescharacteristic
248C2×#11761611C2311yescharacteristic, complemented
249M16×D67—42no—
250C2×C8×D67C2311yescharacteristic
251C2×C8×D67C2311yescharacteristic
252C2×C8×D67C2311yescharacteristic
253C2×C8×D67C2311yescharacteristic
254C2×C8×D67C2311yescharacteristic, complemented
255#14524042—21no—
256#14524042C2311yescharacteristic, complemented
257#14524041—21no—
258#14524040C2311yescharacteristic
259#14524039—21no—
260#14524039C2311yescharacteristic
261#14524037—21no—
262#14524037—21no—
263#14524036—21no—
264#14524036—21no—
265#14524036—21no—
266#14524036—21no—
267#14524035—21no—
268#14524035C2311yescharacteristic, complemented
269#14524034—21no—
270#14524034C2311yescharacteristic, complemented
271#14524033—21no—
272#14524033—21no—
273#14524033—21no—
274#14524033—21no—
275#14524033—21no—
276#14524032C2311yescharacteristic
277#14524029—21no—
278#14524029—21no—
279#14524029—21no—
280#14524028—21no—
281#14524028—21no—
282#14524028—21no—
283#14524028—21no—
284#14524028D411yescharacteristic
285#14524026—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, complemented
295#14524022C2311yescharacteristic
296#14524022C2311yescharacteristic, complemented
297#14524021—21no—
298#14524021—21no—
299#14524021D411yescharacteristic
300#14524020—21no—
301#14524020—21no—
302#14524020D411yescharacteristic
303#14524019—21no—
304#14524019—21no—
305#14524019—21no—
306#14524019C2311yescharacteristic
307#14524019C2311yescharacteristic
308#14524019C2311yescharacteristic, complemented
309#14524018—21no—
310#14524018—21no—
311#14524018C2311yescharacteristic
312#14524018C2311yescharacteristic
313#14524017—21no—
314#14524017C2311yescharacteristic
315#14524017C2311yescharacteristic
316#14524016—21no—
317#14524016—21no—
318#14524016—21no—
319#14524016—21no—
320#14524016D411yescharacteristic
321#14524015—21no—
322#14524015—21no—
323#14524015D411yescharacteristic
324#14524014C2311yescharacteristic
325#14524013—21no—
326#14524013—21no—
327#14524013—21no—
328#14524013—21no—
329#14524013—21no—
330#14524013—21no—
331#14524013—21no—
332#14524013—21no—
333#14524013—21no—
334#14524013—21no—
335#14524013—21no—
336#14524013D411yescharacteristic
337#14524012—21no—
338#14524011—21no—
339#14524011—21no—
340#14524011—21no—
341#14524011—21no—
342#14524011D411yescharacteristic
343Q8×Dic67C2311yescharacteristic, complemented
344C4×Dic134—21no—
345C4×Dic134—21no—
346C4×Dic134—21no—
347C4×Dic134C2311yescharacteristic, complemented
348#14524008—21no—
349#14524008C2311yescharacteristic, complemented
350C4×D268—21no—
351C4×D268C2311yescharacteristic
352C4×D268C2311yescharacteristic
353D4×Dic67C2311yescharacteristic
354#14524005—21no—
355#14524005—21no—
356#14524005C2311yescharacteristic
357C4×C22⋊D67—21no—
358C4×C22⋊D67C2311yescharacteristic
359C4×C22⋊D67C2311yescharacteristic
360(C22⋊D67)⋊C4—21no—
361(C22⋊D67)⋊C4—21no—
362(C22⋊D67)⋊C4—21no—
363(C22⋊D67)⋊C4—21no—
364(C22⋊D67)⋊C4—21no—
365#14524002C2311yescharacteristic
366#14524001—21no—
367#14524001—21no—
368#14524001C2311yescharacteristic
369#14524001C2311yescharacteristic
370#14524001C2311yescharacteristic
371#14524001C2311yescharacteristic, complemented
372#14524000—21no—
373#14524000—21no—
374#14524000—21no—
375#14524000—21no—
376#14524000C2311yescharacteristic
377#14523999—21no—
378#14523999—21no—
379C2×C4⋊Dic67C2311yescharacteristic, complemented
380C4⋊C4×D67—21no—
381C4⋊C4×D67C2311yescharacteristic
382C4⋊C4×D67C2311yescharacteristic
383C4⋊C4×D67C2311yescharacteristic
384C4⋊C4×D67C2311yescharacteristic, complemented
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#14523977C2311yescharacteristic, complemented
395#14523976C2311yescharacteristic, complemented
396#14523976C2311yescharacteristic, complemented
397#14523976C2311yescharacteristic, 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#14523967C2311yescharacteristic, complemented
407#14523967C2311yescharacteristic, complemented
408#14523967C2311yescharacteristic, complemented
409#14523967C2311yescharacteristic, complemented
410#14523966C2311yescharacteristic, complemented
411#14523965C2311yescharacteristic
412#14523965C2311yescharacteristic
413#14523965C2311yescharacteristic
414#14523965C2311yescharacteristic
415#14523965C2311yescharacteristic
416#14523965C2311yescharacteristic
417#14523965C2311yescharacteristic, complemented
418#14523965C2311yescharacteristic, complemented
419#14523965C2311yescharacteristic, complemented
420#14523964C2311yescharacteristic
421#14523964C2311yescharacteristic
422#14523964C2311yescharacteristic
423#14523964C2311yescharacteristic
424#14523964C2311yescharacteristic
425#14523964C2311yescharacteristic
426#14523963C2311yescharacteristic
427#14523963C2311yescharacteristic
428#14523963C2311yescharacteristic
429#14523963C2311yescharacteristic
430#14523963C2311yescharacteristic
431#14523963C2311yescharacteristic
432#14523963C2311yescharacteristic, complemented
433#14523963C2311yescharacteristic, complemented
434#14523963C2311yescharacteristic, complemented
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
444C2×#41×C67C2311yescharacteristic
445C22×D4×C67C2311yescharacteristic
446C2×Q16×C67C2311yescharacteristic, complemented
447C2×SD16×C67C2311yescharacteristic
448C2×SD16×C67C2311yescharacteristic
449C2×M16×C67C2311yescharacteristic
450C22×C8×C67C2311yescharacteristic, complemented
451C4⋊Q8×C67C2311yescharacteristic, complemented
452#126×C67—21no—
453#126×C67—21no—
454#124×C67—21no—
455#124×C67C2311yescharacteristic
456#123×C67—21no—
457C22⋊Q8×C67C2311yescharacteristic
458C22⋊Q8×C67C2311yescharacteristic
459C22⋊Q8×C67C2311yescharacteristic, complemented
460#121×C67—21no—
461#121×C67C2311yescharacteristic
462#120×C67—21no—
463C4×Q8×C67—21no—
464C4×Q8×C67C2311yescharacteristic, complemented
465C4×D4×C67C2311yescharacteristic
466C4×D4×C67C2311yescharacteristic
467#117×C67C2311yescharacteristic
468#117×C67C2311yescharacteristic, complemented
469C2×C22⋊C4×C67—21no—
470#107×C67C2311yescharacteristic, complemented
471#106×C67C2311yescharacteristic, complemented
472#106×C67C2311yescharacteristic, complemented
473C4⋊C8×C67C2311yescharacteristic, complemented
474#103×C67C2311yescharacteristic, complemented
475#103×C67C2311yescharacteristic, complemented
476#103×C67C2311yescharacteristic, complemented
477#103×C67C2311yescharacteristic, complemented
478#102×C67C2311yescharacteristic
479#102×C67C2311yescharacteristic
480#102×C67C2311yescharacteristic
481#102×C67C2311yescharacteristic
482#102×C67C2311yescharacteristic
483#102×C67C2311yescharacteristic
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—21no—
494C23×D67—44no—
495C23×D67—82no—
496C23×D67—82no—
497C23×D67C2×D411yescharacteristic
498#11761629—22no—
499#11761629—22no—
500#11761629—22no—
501#11761629—41no—
502#11761628—22no—
503#11761628—22no—
504#11761628—44no—
505C2×Dic134—21no—
506C2×Dic134—21no—
507C2×Dic134C2×D411yescharacteristic
508C2×Dic134C2411yescharacteristic
509Q8×D67—22no—
510Q8×D67—22no—
511C2×D268—22no—
512C2×D268—22no—
513C2×D268—21no—
514C2×D268—21no—
515C2×D268—21no—
516C2×D268—21no—
517C2×D268—21no—
518C2×D268—21no—
519C2×D268—21no—
520C2×D268—21no—
521C2×D268—41no—
522C2×D268—41no—
523C2×D268—44no—
524C2×D268—82no—
525C2×D268C2×D411yescharacteristic
526C2×D268C2×D411yescharacteristic
527C2×D268C2411yescharacteristic
528C2×D268C2411yescharacteristic
529C2×D268C2411yescharacteristic
530C2×C22⋊D67—21no—
531C2×C22⋊D67—21no—
532C2×C22⋊D67—21no—
533C2×C22⋊D67—21no—
534C2×C22⋊D67—21no—
535C2×C22⋊D67—21no—
536C2×C22⋊D67—21no—
537C2×C22⋊D67—21no—
538C2×C22⋊D67—21no—
539C2×C22⋊D67—21no—
540C2×C22⋊D67—44no—
541C2×C22⋊D67—82no—
542C2×C22⋊D67C2×D411yescharacteristic
543C2×C22⋊D67C2×D411yescharacteristic
544C2×C22⋊D67C2×D411yescharacteristic
545C2×C22⋊D67C2×D411yescharacteristic
546D4×D67—22no—
547D4×D67—22no—
548D4×D67—22no—
549D4×D67—22no—
550D4×D67—22no—
551D4×D67—22no—
552D4×D67—41no—
553D4×D67—41no—
554D4×D67—41no—
555D4×D67—44no—
556D4×D67—44no—
557D4×D67—44no—
558D4×D67—44no—
559D4×D67—82no—
560D4×D67—82no—
561D4×D67#4114yes—
562C22×Dic67—21no—
563C22×Dic67—21no—
564C22×Dic67C2×D411yescharacteristic
565C2×C4×D67—22no—
566C2×C4×D67—22no—
567C2×C4×D67—21no—
568C2×C4×D67—21no—
569C2×C4×D67—21no—
570C2×C4×D67—21no—
571C2×C4×D67—21no—
572C2×C4×D67—21no—
573C2×C4×D67—21no—
574C2×C4×D67—21no—
575C2×C4×D67—21no—
576C2×C4×D67C2×D411yescharacteristic
577C2×C4×D67C2×D411yescharacteristic
578C2×C4×D67C2411yescharacteristic
579C2×C4×D67C2411yescharacteristic
580C2×C4×D67C2411yescharacteristic
581#11761618—41no—
582#11761617—22no—
583#11761617—41no—
584#11761617—41no—
585#11761616—22no—
586#11761616—41no—
587#11761615—22no—
588#11761615—41no—
589#11761615—41no—
590#11761612—41no—
591#11761612—41no—
592#11761611—22no—
593#11761611—22no—
594#11761611—41no—
595C2×C67⋊C8C2411yescharacteristic
596C2×C67⋊C8C2411yescharacteristic
597C2×C67⋊C8C2411yescharacteristic
598C2×C67⋊C8C2411yescharacteristic
599C8×D67—22no—
600C8×D67—22no—
601C8×D67—41no—
602C8×D67—41no—
603C8×D67—41no—
604C4⋊Dic67—21no—
605C4⋊Dic67—21no—
606C4⋊Dic67—21no—
607C4⋊Dic67—21no—
608C4⋊Dic67—21no—
609C4⋊Dic67C2×D411yescharacteristic
610C4⋊Dic67C2411yescharacteristic
611C4⋊Dic67C2411yescharacteristic
612C4⋊Dic67C2411yescharacteristic
613C4⋊Dic67C2411yescharacteristic
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⋊C4—21no—
625Dic67⋊C4—21no—
626Dic67⋊C4—21no—
627Dic67⋊C4—21no—
628Dic67⋊C4—21no—
629Dic67⋊C4C2×D411yescharacteristic
630Dic67⋊C4C2×D411yescharacteristic
631Dic67⋊C4C2×D411yescharacteristic
632Dic67⋊C4C2×D411yescharacteristic
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)⋊C4—21no—
656(C2×D67)⋊C4—21no—
657(C2×D67)⋊C4C2×D411yescharacteristic
658(C2×D67)⋊C4C2×D411yescharacteristic
659(C2×D67)⋊C4C2×D411yescharacteristic
660(C2×D67)⋊C4C2×D411yescharacteristic
661(C2×D67)⋊C4C2×D411yescharacteristic
662(C2×D67)⋊C4C2×D411yescharacteristic
663C4×Dic67—21no—
664C4×Dic67—21no—
665C4×Dic67—21no—
666C4×Dic67—21no—
667C4×Dic67—21no—
668C4×Dic67—21no—
669C4×Dic67—21no—
670C4×Dic67—21no—
671C4×Dic67C2411yescharacteristic
672C24×C67—21no—
673#41×C67—22no—
674#41×C67—41no—
675C2×Q8×C67—21no—
676C2×Q8×C67C2411yescharacteristic
677C2×Q8×C67C2411yescharacteristic
678C2×D4×C67—22no—
679C2×D4×C67—21no—
680C2×D4×C67—21no—
681C2×D4×C67—21no—
682C2×D4×C67—41no—
683C2×D4×C67C2×D411yescharacteristic
684C2×D4×C67C2411yescharacteristic
685C2×D4×C67C2411yescharacteristic
686C22×C4×C67—21no—
687C22×C4×C67—21no—
688C22×C4×C67C2411yescharacteristic
689C22×C4×C67C2411yescharacteristic
690Q16×C67—41no—
691SD16×C67—22no—
692SD16×C67—41no—
693M16×C67—41no—
694C2×C8×C67—41no—
695C2×C8×C67C2411yescharacteristic
696C2×C8×C67C2411yescharacteristic
697C2×C8×C67C2411yescharacteristic
698C2×C8×C67C2411yescharacteristic
699C4⋊C4×C67—21no—
700C4⋊C4×C67—21no—
701C4⋊C4×C67—21no—
702C4⋊C4×C67—21no—
703C4⋊C4×C67—21no—
704C4⋊C4×C67C2×D411yescharacteristic
705C4⋊C4×C67C2411yescharacteristic
706C4⋊C4×C67C2411yescharacteristic
707C4⋊C4×C67C2411yescharacteristic
708C4⋊C4×C67C2411yescharacteristic
709C22⋊C4×C67—21no—
710C22⋊C4×C67—21no—
711C22⋊C4×C67—21no—
712C22⋊C4×C67—21no—
713C22⋊C4×C67—21no—
714C22⋊C4×C67—21no—
715C22⋊C4×C67—21no—
716C22⋊C4×C67—21no—
717C22⋊C4×C67—21no—
718C22⋊C4×C67C2×D411yescharacteristic
719C22⋊C4×C67C2×D411yescharacteristic
720C42×C67—21no—
721C42×C67—21no—
722C42×C67—21no—
723C42×C67C2411yescharacteristic
724C23×C67—21no—
725C23×C67—21no—
726C23×C67—42no—
727C23×C67—42no—
728C23×C67—81no—
729C23×C67C22×D411yescharacteristic
730C23×C67C22×D411yescharacteristic
731C22×D67—21no—
732C22×D67—22no—
733C22×D67—22no—
734C22×D67—24no—
735C22×D67—21no—
736C22×D67—21no—
737C22×D67—41no—
738C22×D67—42no—
739C22×D67—42no—
740C22×D67—42no—
741C22×D67—42no—
742C22×D67—42no—
743C22×D67—42no—
744C22×D67—42no—
745C22×D67—42no—
746C22×D67—42no—
747C22×D67—81no—
748C22×D67—81no—
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—
764Q8×C67—21no—
765Q8×C67—21no—
766Q8×C67—81no—
767D4×C67—21no—
768D4×C67—21no—
769D4×C67—21no—
770D4×C67—41no—
771D4×C67—42no—
772D4×C67—42no—
773D4×C67—81no—
774D4×C67C2×#4112yes—
775C2×C4×C67—21no—
776C2×C4×C67—21no—
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—42no—
786C2×C4×C67—81no—
787C2×C4×C67C22×D411yescharacteristic
788C2×C4×C67C22×D411yescharacteristic
789C2×C4×C67C22×D411yescharacteristic
790C2×C4×C67C22×D411yescharacteristic
791C2×C4×C67C2511yescharacteristic
792C22⋊D67—22no—
793C22⋊D67—22no—
794C22⋊D67—24no—
795C22⋊D67—22no—
796C22⋊D67—41no—
797C22⋊D67—42no—
798C22⋊D67—42no—
799C22⋊D67—42no—
800C22⋊D67—42no—
801C22⋊D67—42no—
802C22⋊D67—81no—
803C22⋊D67—81no—
804C22⋊D67—81no—
805C22⋊D67—81no—
806C2×Dic67—22no—
807C2×Dic67—21no—
808C2×Dic67—21no—
809C2×Dic67—21no—
810C2×Dic67—21no—
811C2×Dic67—21no—
812C2×Dic67—81no—
813C2×Dic67—81no—
814C2×Dic67C22×D411yescharacteristic
815C2×Dic67C22×D411yescharacteristic
816C2×Dic67C22×D411yescharacteristic
817C2×Dic67C22×D411yescharacteristic
818C2×Dic67C22×D411yescharacteristic
819D268—22no—
820D268—22no—
821D268—21no—
822D268—21no—
823D268—21no—
824D268—21no—
825D268—21no—
826D268—42no—
827D268—42no—
828D268—42no—
829D268—42no—
830D268—42no—
831D268—81no—
832D268—81no—
833D268—81no—
834D268C2×#4112yes—
835C4×D67—22no—
836C4×D67—21no—
837C4×D67—21no—
838C4×D67—21no—
839C4×D67—21no—
840C4×D67—22no—
841C4×D67—42no—
842C4×D67—42no—
843C4×D67—42no—
844C4×D67—42no—
845C4×D67—81no—
846C4×D67—81no—
847C4×D67—81no—
848C4×D67—81no—
849C4×D67—81no—
850C4×D67C2×#4112yes—
851C4×D67H(5,𝔽2)12yes—
852Dic134—22no—
853Dic134—21no—
854Dic134—21no—
855Dic134—42no—
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—21no—
869C22×C67—22no—
870C22×C67—21no—
871C22×C67—21no—
872C22×C67—41no—
873C22×C67—41no—
874C22×C67—41no—
875C22×C67—41no—
876C22×C67—41no—
877C22×C67—84no—
878C22×C67C23×D411yescharacteristic
879C2×D67—21no—
880C2×D67—21no—
881C2×D67—21no—
882C2×D67—21no—
883C2×D67—21no—
884C2×D67—21no—
885C2×D67—22no—
886C2×D67—21no—
887C2×D67—44no—
888C2×D67—41no—
889C2×D67—41no—
890C2×D67—41no—
891C2×D67—41no—
892C2×D67—41no—
893C2×D67—41no—
894C2×D67—41no—
895C2×D67—41no—
896C2×D67—84no—
897C2×D67—84no—
898C2×D67—84no—
899C2×D67—84no—
900C2×D67—84no—
901C2×D67—162no—
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×C67—41no—
915C4×C67C22×#4111yescharacteristic
916C4×C67C2×H(5,𝔽2)11yescharacteristic
917Dic67—21no—
918Dic67—21no—
919Dic67—21no—
920Dic67—21no—
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×C67C2×#54611yescharacteristic
933C2×C67C2×#57711yescharacteristic
934C2×C67#358511yescharacteristic
935D67—22no—
936D67—22no—
937D67—41no—
938D67—42no—
939D67—81no—
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#3311D6711yescharacteristic, complemented
951#3310—671no—
952#3310—671no—
953#3310—671no—
954#3310—671no—
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#556C2×D6711yescharacteristic, complemented
982#554—671no—
983#554—671no—
984#552—671no—
985#552—671no—
986#552—671no—
987#552—671no—
988#552—1341no—
989#552—1341no—
990#551—1341no—
991#551—1341no—
992#546—671no—
993#546—671no—
994#546—671no—
995#546—1341no—
996#546—1341no—
997#546C2×D6711yescharacteristic
998D42—671no—
999D42—671no—
1000D42—671no—
1001D42—671no—
1002D42—1341no—
1003D42—1341no—
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#490—671no—
1025#489—671no—
1026#489C2×D6711yescharacteristic, complemented
1027#488—671no—
1028#488—671no—
1029#486—671no—
1030#486—671no—
1031#485—671no—
1032#485C2×D6711yescharacteristic, complemented
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#480—671no—
1047#478—671no—
1048#478—671no—
1049#478—671no—
1050#478—671no—
1051#476—671no—
1052#476C2×D6711yescharacteristic, complemented
1053#474—671no—
1054#474—671no—
1055#470—671no—
1056#470C2×D6711yescharacteristic, complemented
1057#468—671no—
1058#468—671no—
1059#468—671no—
1060#468—671no—
1061#468—671no—
1062#468—671no—
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#464C2×D6711yescharacteristic, complemented
1075#460—671no—
1076#460—671no—
1077#460—671no—
1078#460—671no—
1079#452—671no—
1080#452—671no—
1081#452—671no—
1082#452C2×D6711yescharacteristic, complemented
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#450—671no—
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#416C2×D6711yescharacteristic, complemented
1133C2×#102—671no—
1134C2×#102—671no—
1135C2×#102—671no—
1136C2×#102—671no—
1137C2×#102—671no—
1138C2×#102—671no—
1139C2×#102—671no—
1140C2×#102—671no—
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—1341no—
1151C2×#41C22×D6711yescharacteristic
1152C22×Q8—671no—
1153C22×D4—2682no—
1154C22×D4—671no—
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—1341no—
1166C22×D4—1341no—
1167C22×D4—1341no—
1168C22×D4—1344no—
1169C22×D4—1341no—
1170C22×D4—1341no—
1171C22×D4—1341no—
1172C22×D4C22×D6711yescharacteristic
1173C23×C4—671no—
1174#137—2682no—
1175C2×Q16—671no—
1176C2×Q16C22×D6711yescharacteristic, complemented
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—671no—
1186C2×SD16—1344no—
1187C2×SD16C22×D6711yescharacteristic
1188C2×SD16C22×D6711yescharacteristic
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—1341no—
1205C4⋊Q8—1341no—
1206C4⋊Q8C22×D6711yescharacteristic, complemented
1207#127—671no—
1208#127—671no—
1209#127—1341no—
1210#126—21no—
1211#126—21no—
1212#126—1341no—
1213#126—1341no—
1214#126—1341no—
1215#126—1341no—
1216#126—1341no—
1217#126—1341no—
1218#125—671no—
1219#125—671no—
1220#125—1341no—
1221#125—1341no—
1222#125—1341no—
1223#125—1341no—
1224#125—1341no—
1225#125—1341no—
1226#125—1341no—
1227#124—21no—
1228#124—671no—
1229#124—1341no—
1230#124—1341no—
1231#124—1341no—
1232#124C22×D6711yescharacteristic
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—1341no—
1256C22⋊Q8—1341no—
1257C22⋊Q8—1341no—
1258C22⋊Q8—1341no—
1259C22⋊Q8—1341no—
1260C22⋊Q8—1341no—
1261C22⋊Q8—1341no—
1262C22⋊Q8—1341no—
1263C22⋊Q8C22×D6711yescharacteristic
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—671no—
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#121—1341no—
1283#121C22×D6711yescharacteristic
1284#120—21no—
1285#120—671no—
1286#120—671no—
1287#120—1341no—
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—21no—
1304C4×Q8—671no—
1305C4×Q8—671no—
1306C4×Q8—671no—
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—671no—
1330#117—671no—
1331#117—671no—
1332#117—671no—
1333#117—671no—
1334#117—671no—
1335#117—1341no—
1336#117—1341no—
1337#117—1341no—
1338#117—1341no—
1339#117—1341no—
1340#117—1341no—
1341#117—1341no—
1342#117—1341no—
1343#117C22×D6711yescharacteristic
1344#117C22×D6711yescharacteristic, complemented
1345C2×C4⋊C4—671no—
1346C2×C4⋊C4—671no—
1347C2×C4⋊C4—671no—
1348C2×C4⋊C4—671no—
1349C2×C4⋊C4—671no—
1350C2×C4⋊C4—1341no—
1351C2×C22⋊C4—21no—
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#107—671no—
1365#107C22×D6711yescharacteristic, complemented
1366#106—671no—
1367#106—671no—
1368#106—671no—
1369#106—671no—
1370#106C22×D6711yescharacteristic, complemented
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#103C22×D6711yescharacteristic, complemented
1383#103C22×D6711yescharacteristic, complemented
1384#103C22×D6711yescharacteristic, complemented
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#102—671no—
1408#102—671no—
1409#102—671no—
1410#102C22×D6711yescharacteristic
1411#102C22×D6711yescharacteristic
1412#102C22×D6711yescharacteristic
1413#102C22×D6711yescharacteristic
1414#102C22×D6711yescharacteristic
1415#102C22×D6711yescharacteristic
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—2684no—
1430C24—5362no—
1431C24—5362no—
1432C24—671no—
1433C24—1341no—
1434C24—1341no—
1435C24—1341no—
1436C24—1341no—
1437C24—1341no—
1438C24—1341no—
1439C24—1341no—
1440#41—22no—
1441#41—41no—
1442#41—2684no—
1443#41—2681no—
1444#41—1342no—
1445#41—1342no—
1446#41—1342no—
1447#41—1342no—
1448#41—1342no—
1449C2×Q8—21no—
1450C2×Q8—671no—
1451C2×Q8—671no—
1452C2×Q8—1341no—
1453C2×Q8—1341no—
1454C2×Q8—1342no—
1455C2×Q8—1342no—
1456C2×Q8C23×D6711yescharacteristic
1457C2×Q8C23×D6711yescharacteristic
1458C2×D4—22no—
1459C2×D4—21no—
1460C2×D4—21no—
1461C2×D4—21no—
1462C2×D4—41no—
1463C2×D4—2681no—
1464C2×D4—2681no—
1465C2×D4—2684no—
1466C2×D4—2684no—
1467C2×D4—2684no—
1468C2×D4—2681no—
1469C2×D4—2681no—
1470C2×D4—2681no—
1471C2×D4—2684no—
1472C2×D4—2684no—
1473C2×D4—2684no—
1474C2×D4—5362no—
1475C2×D4—5362no—
1476C2×D4—5362no—
1477C2×D4—5362no—
1478C2×D4—671no—
1479C2×D4—674no—
1480C2×D4—671no—
1481C2×D4—671no—
1482C2×D4—671no—
1483C2×D4—671no—
1484C2×D4—671no—
1485C2×D4—671no—
1486C2×D4—671no—
1487C2×D4—671no—
1488C2×D4—1341no—
1489C2×D4—1341no—
1490C2×D4—1341no—
1491C2×D4—1342no—
1492C2×D4—1342no—
1493C2×D4—1341no—
1494C2×D4—1342no—
1495C2×D4—1342no—
1496C2×D4—1342no—
1497C2×D4—1341no—
1498C2×D4—1341no—
1499C2×D4—1341no—
1500C2×D4—1341no—
1501C2×D4—1341no—
1502C2×D4—1341no—
1503C2×D4—1341no—
1504C2×D4—1342no—
1505C2×D4—1341no—
1506C2×D4—1342no—
1507C2×D4—1342no—
1508C2×D4—1341no—
1509C2×D4—1341no—
1510C2×D4—1341no—
1511C2×D4—1341no—
1512C2×D4—1341no—
1513C2×D4—1341no—
1514C2×D4D4×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—1341no—
1532C22×C4—1341no—
1533C22×C4—1342no—
1534C22×C4—1342no—
1535C22×C4—1341no—
1536C22×C4—1341no—
1537C22×C4—1341no—
1538C22×C4C23×D6711yescharacteristic
1539C22×C4C23×D6711yescharacteristic
1540Q16—41no—
1541Q16—2681no—
1542SD16—22no—
1543SD16—41no—
1544SD16—2681no—
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—671no—
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—1341no—
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—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—671no—
1621C22⋊C4—671no—
1622C22⋊C4—671no—
1623C22⋊C4—671no—
1624C22⋊C4—671no—
1625C22⋊C4—671no—
1626C22⋊C4—671no—
1627C22⋊C4—671no—
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—21no—
1655C42—671no—
1656C42—1341no—
1657C42—1341no—
1658C42—1341no—
1659C42—1341no—
1660C42—1341no—
1661C42—1341no—
1662C42—1341no—
1663C42—1341no—
1664C42C23×D6711yescharacteristic
1665C23—21no—
1666C23—21no—
1667C23—42no—
1668C23—42no—
1669C23—81no—
1670C23—2681no—
1671C23—2682no—
1672C23—2682no—
1673C23—2682no—
1674C23—2682no—
1675C23—2682no—
1676C23—2682no—
1677C23—2682no—
1678C23—2682no—
1679C23—2682no—
1680C23—5361no—
1681C23—5361no—
1682C23—5361no—
1683C23—5361no—
1684C23—5361no—
1685C23—5361no—
1686C23—5361no—
1687C23—5361no—
1688C23—5361no—
1689C23—5361no—
1690C23—5361no—
1691C23—53616no—
1692C23—671no—
1693C23—671no—
1694C23—671no—
1695C23—1342no—
1696C23—1342no—
1697C23—1344no—
1698C23—1341no—
1699C23—1341no—
1700C23—1341no—
1701C23C2×D4×D6711yescharacteristic
1702C23C2×D4×D6711yescharacteristic
1703Q8—21no—
1704Q8—21no—
1705Q8—21no—
1706Q8—21no—
1707Q8—81no—
1708Q8—2682no—
1709Q8—5361no—
1710Q8—1342no—
1711Q8—1341no—
1712Q8—1341no—
1713D4—21no—
1714D4—21no—
1715D4—21no—
1716D4—41no—
1717D4—42no—
1718D4—42no—
1719D4—81no—
1720D4—2682no—
1721D4—2682no—
1722D4—2682no—
1723D4—2682no—
1724D4—2682no—
1725D4—2682no—
1726D4—2682no—
1727D4—2682no—
1728D4—2682no—
1729D4—2681no—
1730D4—2682no—
1731D4—5361no—
1732D4—5361no—
1733D4—5361no—
1734D4—5361no—
1735D4—5361no—
1736D4—5361no—
1737D4—5361no—
1738D4—672no—
1739D4—1342no—
1740D4—1342no—
1741D4—1344no—
1742D4—1342no—
1743D4—1342no—
1744D4—1342no—
1745D4—1341no—
1746D4—1341no—
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—21no—
1761C2×C4—42no—
1762C2×C4—81no—
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—5361no—
1774C2×C4—671no—
1775C2×C4—672no—
1776C2×C4—672no—
1777C2×C4—671no—
1778C2×C4—671no—
1779C2×C4—671no—
1780C2×C4—671no—
1781C2×C4—1342no—
1782C2×C4—1342no—
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—84no—
1819C22—2684no—
1820C22—2681no—
1821C22—2681no—
1822C22—2681no—
1823C22—2681no—
1824C22—2681no—
1825C22—2681no—
1826C22—2681no—
1827C22—2681no—
1828C22—5364no—
1829C22—5364no—
1830C22—5364no—
1831C22—5364no—
1832C22—5364no—
1833C22—10722no—
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—41no—
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—2682no—
1873C2—2681no—
1874C2—5361no—
1875C2—5361no—
1876C2—1342no—
1877C2—1342no—
1878C2#546×D6711yescharacteristic
1879C2#577×D6711yescharacteristic
1880C2#2257498611yescharacteristic
subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3311C2
socleC22×C67C23×D4
prime radical#22573839C2
hypercenter#3311D67
hypocenterC67#61184
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3311

Complements

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

NH ≅ G/Ntype
1. #22573954C2semidirect
3. #22572436C2semidirect
4. #22572434C2semidirect
5. #22572431C2semidirect
6. #22572425C2semidirect
7. #22572289C2semidirect
8. #22572283C2semidirect
9. #22572248C2semidirect
10. #22572235C2semidirect
11. #22572233C2semidirect
12. #22572232C2semidirect
13. #22572223C2semidirect
14. #22572051C2semidirect
15. #22572045C2semidirect
16. #22572030C2semidirect
17. #22572028C2semidirect
18. #22570560C2semidirect
19. #22570164C2semidirect
20. #22570127C2semidirect
21. #22570035C2semidirect
22. #22569843C2semidirect
23. #22569838C2semidirect
24. #22569728C2semidirect
25. #22569483C2semidirect
26. #450×D67C2semidirect
27. #22569065C2semidirect
28. #22568932C2semidirect
29. #22568731C2semidirect
30. #418×D67C2semidirect
31. C67×#3311C2semidirect
34. C2×#14524075C22semidirect
36. C2×SD16×D67C22semidirect
37. C2×#14524049C22semidirect
38. C2×M16×D67C22semidirect
39. #16864114C22semidirect
40. #16864107C22semidirect
41. #16864104C22semidirect
43. #16864087C22semidirect
44. #16864086C22semidirect
45. #16864085C22semidirect
47. #16864080C22semidirect
61. #16864023C22semidirect
64. #16863969C22semidirect
73. C22⋊Q8×D67C22semidirect
76. #16863876C22semidirect
77. #16863872C22semidirect
79. #117×D67C22semidirect
80. #16863761C22semidirect
81. #16863759C22semidirect
82. #16863757C22semidirect
83. #16863752C22semidirect
84. #16863750C22semidirect
85. #16863744C22semidirect
86. #16863741C22semidirect
87. #16863734C22semidirect
88. #16863730C22semidirect
89. #16863725C22semidirect
90. #16863723C22semidirect
91. #16863721C22semidirect
92. #16863720C22semidirect
93. #16863720C22semidirect
94. #16863718C22semidirect
95. #16863716C22semidirect
96. #16863716C22semidirect
97. #16863712C22semidirect
98. #16863711C22semidirect
99. #16863710C22semidirect
100. #16863708C22semidirect
101. #16863698C22semidirect
102. #16863697C22semidirect
103. #16863696C22semidirect
104. #16863695C22semidirect
105. #16863685C22semidirect
106. #16863674C22semidirect
107. #16863673C22semidirect
108. #16863652C22semidirect
109. #16863645C22semidirect
110. #16863644C22semidirect
111. #16863644C22semidirect
112. #16863642C22semidirect
113. #16863641C22semidirect
114. #16863640C22semidirect
115. #16863636C22semidirect
116. #16863634C22semidirect
117. #16863628C22semidirect
118. #16863626C22semidirect
119. #16863626C22semidirect
120. #16863625C22semidirect
121. #16863622C22semidirect
122. #16863621C22semidirect
123. #16863620C22semidirect
124. #16863615C22semidirect
125. #16863597C22semidirect
126. #16863596C22semidirect
127. #16863595C22semidirect
128. #16863594C22semidirect
129. #16863561C22semidirect
130. #16863558C22semidirect
131. #16863557C22semidirect
132. #16863549C22semidirect
133. #16863549C22semidirect
134. #16863548C22semidirect
135. #16863548C22semidirect
136. #16863548C22semidirect
137. #16863547C22semidirect
138. #16863546C22semidirect
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. #16863435C22semidirect
158. #16863433C22semidirect
159. #16863431C22semidirect
160. #16863421C22semidirect
161. #16863403C22semidirect
162. #16863402C22semidirect
163. #16863401C22semidirect
164. #16863400C22semidirect
165. #16863400C22semidirect
168. #16863399C22semidirect
169. #16863399C22semidirect
170. #16863399C22semidirect
171. #16863397C22semidirect
172. #16863396C22semidirect
173. #16863396C22semidirect
174. #16863391C22semidirect
175. #16863391C22semidirect
176. #16863391C22semidirect
177. C2×#14523965C22semidirect
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. #556×C67C22semidirect
190. #489×C67C22semidirect
191. #485×C67C22semidirect
192. #482×C67C22semidirect
193. #476×C67C22semidirect
194. #470×C67C22semidirect
195. #465×C67C22semidirect
196. #464×C67C22semidirect
197. #452×C67C22semidirect
198. #450×C67C22semidirect
199. #440×C67C22semidirect
200. #435×C67C22semidirect
201. #418×C67C22semidirect
202. #416×C67C22semidirect
232. C2×#11761618C23semidirect
235. C2×#11761617C23semidirect
240. C2×#11761615C23semidirect
245. C2×#11761612C23semidirect
248. C2×#11761611C23semidirect
254. C2×C8×D67C23semidirect
256. #14524042C23semidirect
268. #14524035C23semidirect
270. #14524034C23semidirect
294. #14524023C23semidirect
296. #14524022C23semidirect
308. #14524019C23semidirect
343. Q8×Dic67C23semidirect
347. C4×Dic134C23semidirect
349. #14524008C23semidirect
371. #14524001C23semidirect
379. C2×C4⋊Dic67C23semidirect
384. C4⋊C4×D67C23semidirect
393. #14523977C23semidirect
394. #14523977C23semidirect
395. #14523976C23semidirect
396. #14523976C23semidirect
397. #14523976C23semidirect
398. #14523975C23semidirect
399. #14523974C23semidirect
400. #14523974C23semidirect
401. #14523974C23semidirect
402. C4⋊(C67⋊C8)C23semidirect
403. Dic67⋊C8C23semidirect
404. Dic67⋊C8C23semidirect
405. #14523968C23semidirect
406. #14523967C23semidirect
407. #14523967C23semidirect
408. #14523967C23semidirect
409. #14523967C23semidirect
410. #14523966C23semidirect
417. #14523965C23semidirect
418. #14523965C23semidirect
419. #14523965C23semidirect
432. #14523963C23semidirect
433. #14523963C23semidirect
434. #14523963C23semidirect
436. C22⋊(C67⋊C8)C23semidirect
439. (C2×D67)⋊C8C23semidirect
440. (C2×D67)⋊C8C23semidirect
441. #14523953C23semidirect
442. C4×C67⋊C8C23semidirect
443. C8×Dic67C23semidirect
446. C2×Q16×C67C23semidirect
450. C22×C8×C67C23semidirect
451. C4⋊Q8×C67C23semidirect
459. C22⋊Q8×C67C23semidirect
464. C4×Q8×C67C23semidirect
468. #117×C67C23semidirect
470. #107×C67C23semidirect
471. #106×C67C23semidirect
472. #106×C67C23semidirect
473. C4⋊C8×C67C23semidirect
474. #103×C67C23semidirect
475. #103×C67C23semidirect
476. #103×C67C23semidirect
477. #103×C67C23semidirect
485. C22⋊C8×C67C23semidirect
486. #97×C67C23semidirect
950. #3311D67semidirect
972. C67#61184semidirect
981. #556C2×D67semidirect
1026. #489C2×D67semidirect
1032. #485C2×D67semidirect
1040. #482C2×D67semidirect
1052. #476C2×D67semidirect
1056. #470C2×D67semidirect
1070. #465C2×D67semidirect
1074. #464C2×D67semidirect
1082. #452C2×D67semidirect
1094. #450C2×D67semidirect
1098. #440C2×D67semidirect
1108. #435C2×D67semidirect
1125. #418C2×D67semidirect
1132. #416C2×D67semidirect
1176. C2×Q16C22×D67semidirect
1202. C22×C8C22×D67semidirect
1206. C4⋊Q8C22×D67semidirect
1265. C22⋊Q8C22×D67semidirect
1311. C4×Q8C22×D67semidirect
1344. #117C22×D67semidirect
1365. #107C22×D67semidirect
1370. #106C22×D67semidirect
1371. #106C22×D67semidirect
1375. C4⋊C8C22×D67semidirect
1382. #103C22×D67semidirect
1383. #103C22×D67semidirect
1384. #103C22×D67semidirect
1385. #103C22×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
#225739542
#225738392
#225724362
#225724342
#225724312
#225724252
#225722892
#225722832
#225722482
#225722352
#225722332
#225722322
#225722232
#225720512
#225720452
#225720302
#225720282
#225705602
#225701642
#225701272
#225700352
#225698432
#225698382
#225697282
#225694832
#450×D672
#225690652
#225689322
#225687312
#418×D672
C67×#33112
#6118467