Finite Group Databasebeta

← #31732822

Subgroups — #31732822

Order 17152.

2254 conjugacy classes of subgroups.

The subgroup lattice has 1880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22573770C211yesmaximal, characteristic, complemented
2#546×D67C211yesmaximal, characteristic, complemented
3#22572431C211yesmaximal, characteristic, complemented
4#22572429C211yesmaximal, characteristic, complemented
5#22572408C211yesmaximal, characteristic, complemented
6#22572406C211yesmaximal, characteristic, complemented
7#22572367C211yesmaximal, characteristic, complemented
8#22572365C211yesmaximal, characteristic, complemented
9#22572297C211yesmaximal, characteristic, complemented
10#22572295C211yesmaximal, characteristic, complemented
11#22572239C211yesmaximal, characteristic, complemented
12#22572169C211yesmaximal, characteristic, complemented
13#22572167C211yesmaximal, characteristic, complemented
14#22572062C211yesmaximal, characteristic, complemented
15#22572060C211yesmaximal, characteristic, complemented
16#22572039C211yesmaximal, characteristic, complemented
17#22572037C211yesmaximal, characteristic, complemented
18#22570594C211yesmaximal, characteristic, complemented
19#22570156C211yesmaximal, characteristic, complemented
20#22570148C211yesmaximal, characteristic, complemented
21#22570007C211yesmaximal, characteristic, complemented
22#22569838C211yesmaximal, characteristic, complemented
23#22569821C211yesmaximal, characteristic, complemented
24#22569700C211yesmaximal, characteristic, complemented
25#22569452C211yesmaximal, characteristic, complemented
26#22569437C211yesmaximal, characteristic, complemented
27#22569014C211yesmaximal, characteristic, complemented
28#22568942C211yesmaximal, characteristic, complemented
29#22568724C211yesmaximal, characteristic, complemented
30#418×D67C211yesmaximal, characteristic, complemented
31C67×#3311C211yesmaximal, characteristic, complemented
32C2×#41×D67C2211yescharacteristic
33C22×D4×D67C2211yescharacteristic
34C2×#14524075C2211yescharacteristic, complemented
35C2×#14524070C2211yescharacteristic
36C2×#14524070C2211yescharacteristic
37C22×#11761611C2211yescharacteristic, complemented
38C2×M16×D67C2211yescharacteristic
39#16864111C2211yescharacteristic, complemented
40#16864106C2211yescharacteristic, complemented
41#16864090C2211yescharacteristic, complemented
42#16864090C2211yescharacteristic, complemented
43#16864087—21no—
44#16864080C2211yescharacteristic, complemented
45#16864080C2211yescharacteristic, complemented
46#16864071—21no—
47#16864071—21no—
48#16864049C2211yescharacteristic, complemented
49#16864043C2211yescharacteristic
50#16864042C2211yescharacteristic
51#16864041C2211yescharacteristic
52#16864040C2211yescharacteristic
53#16864039—21no—
54#16864039C2211yescharacteristic
55#16864038—21no—
56#16864037C2211yescharacteristic
57#16864036—21no—
58#16864035—21no—
59#16864034C2211yescharacteristic
60#16864033—21no—
61#16863951C2211yescharacteristic, complemented
62#16863929—21no—
63#16863929—21no—
64#16863925—21no—
65#124×D67C2211yescharacteristic
66#16863909C2211yescharacteristic
67#16863909C2211yescharacteristic, complemented
68#123×D67—21no—
69C22⋊Q8×D67C2211yescharacteristic
70#121×D67—21no—
71#121×D67C2211yescharacteristic
72#120×D67—21no—
73C4×#11761629—21no—
74C4×#11761629C2211yescharacteristic, complemented
75C4×D4×D67C2211yescharacteristic
76C4×D4×D67C2211yescharacteristic
77#117×D67C2211yescharacteristic
78#117×D67C2211yescharacteristic, complemented
79C2×C22⋊C4×D67—21no—
80#16863758C2211yescharacteristic, complemented
81#16863756C2211yescharacteristic, complemented
82#16863755C2211yescharacteristic, complemented
83#16863752C2211yescharacteristic, complemented
84#16863752C2211yescharacteristic, complemented
85#16863749C2211yescharacteristic, complemented
86#16863749C2211yescharacteristic, complemented
87#16863738C2211yescharacteristic, complemented
88#16863737C2211yescharacteristic, complemented
89#16863734C2211yescharacteristic, complemented
90#16863733C2211yescharacteristic, complemented
91#16863730C2211yescharacteristic, complemented
92#16863728C2211yescharacteristic, complemented
93#16863725C2211yescharacteristic, complemented
94#16863721C2211yescharacteristic, complemented
95#16863720C2211yescharacteristic, complemented
96#16863717C2211yescharacteristic, complemented
97#16863716C2211yescharacteristic, complemented
98#16863713C2211yescharacteristic, complemented
99#16863711C2211yescharacteristic, complemented
100#16863708C2211yescharacteristic, complemented
101#16863695C2211yescharacteristic, complemented
102#16863695C2211yescharacteristic, complemented
103#16863694C2211yescharacteristic, complemented
104#16863694C2211yescharacteristic, complemented
105#16863683C2211yescharacteristic, complemented
106#16863677C2211yescharacteristic, complemented
107#16863676C2211yescharacteristic, complemented
108#16863652C2211yescharacteristic, complemented
109#16863650C2211yescharacteristic, complemented
110#16863648C2211yescharacteristic, complemented
111#16863645C2211yescharacteristic, complemented
112#16863644C2211yescharacteristic, complemented
113#16863642C2211yescharacteristic, complemented
114#16863639C2211yescharacteristic, complemented
115#16863636C2211yescharacteristic, complemented
116#16863634C2211yescharacteristic, complemented
117#16863632C2211yescharacteristic, complemented
118#16863630C2211yescharacteristic, complemented
119#16863628C2211yescharacteristic, complemented
120#16863627C2211yescharacteristic, complemented
121#16863626C2211yescharacteristic, complemented
122#16863620C2211yescharacteristic, complemented
123#16863618C2211yescharacteristic, complemented
124#16863616C2211yescharacteristic, complemented
125#16863614C2211yescharacteristic, complemented
126#16863612C2211yescharacteristic, complemented
127#16863610C2211yescharacteristic, complemented
128#16863608C2211yescharacteristic, complemented
129#16863557C2211yescharacteristic, complemented
130#16863556C2211yescharacteristic, complemented
131#16863555C2211yescharacteristic, complemented
132#16863546C2211yescharacteristic, complemented
133#16863545C2211yescharacteristic, complemented
134#16863545C2211yescharacteristic, complemented
135#16863544C2211yescharacteristic, complemented
136#16863543C2211yescharacteristic, complemented
137#16863542C2211yescharacteristic, complemented
138#16863541C2211yescharacteristic, complemented
139#16863532C2211yescharacteristic, complemented
140#16863531C2211yescharacteristic, complemented
141#16863531C2211yescharacteristic, complemented
142#16863530C2211yescharacteristic, complemented
143#16863509C2211yescharacteristic, complemented
144#16863506C2211yescharacteristic, complemented
145#16863494C2211yescharacteristic, complemented
146SD16×Dic67C2211yescharacteristic, complemented
147#16863481C2211yescharacteristic, complemented
148#16863478C2211yescharacteristic, complemented
149#16863476C2211yescharacteristic, complemented
150#16863472C2211yescharacteristic, complemented
151#16863471C2211yescharacteristic, complemented
152#16863469C2211yescharacteristic, complemented
153#16863468C2211yescharacteristic, complemented
154#16863466C2211yescharacteristic, complemented
155C8×C22⋊D67C2211yescharacteristic, complemented
156(C22⋊D67)⋊C8C2211yescharacteristic, complemented
157#16863437C2211yescharacteristic, complemented
158#16863435C2211yescharacteristic, complemented
159#16863435C2211yescharacteristic, complemented
160#16863418C2211yescharacteristic, complemented
161#16863403C2211yescharacteristic, complemented
162#16863403C2211yescharacteristic, complemented
163#16863403C2211yescharacteristic, complemented
164#16863402C2211yescharacteristic, complemented
165#16863401C2211yescharacteristic, complemented
166#16863400C2211yescharacteristic, complemented
167#16863399C2211yescharacteristic
168#16863399C2211yescharacteristic
169#16863399C2211yescharacteristic
170#16863399C2211yescharacteristic
171#16863399C2211yescharacteristic
172#16863399C2211yescharacteristic
173#16863396C2211yescharacteristic, complemented
174#16863396C2211yescharacteristic, complemented
175#16863396C2211yescharacteristic, complemented
176#16863394C2211yescharacteristic, complemented
177#16863394C2211yescharacteristic, complemented
178#16863393C2211yescharacteristic, complemented
179#16863392C2211yescharacteristic, complemented
180#16863390C2211yescharacteristic, complemented
181#102×D67C2211yescharacteristic, complemented
182#102×D67C2211yescharacteristic, complemented
183#102×D67C2211yescharacteristic, complemented
184#102×D67C2211yescharacteristic, complemented
185#16863358C2211yescharacteristic
186#16863358C2211yescharacteristic, complemented
187#16863348C2211yescharacteristic, 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—
204C2×#11761629—21no—
205C2×#11761629C2311yescharacteristic
206C2×#11761629C2311yescharacteristic
207C2×#11761628—21no—
208C2×#11761628C2311yescharacteristic
209C2×#11761627—21no—
210C2×#11761627C2311yescharacteristic
211#41×D67—24no—
212#41×D67—42no—
213C2×Q8×D67C2311yescharacteristic
214C22×D268C2311yescharacteristic
215C22×C22⋊D67—21no—
216C2×D4×D67—24no—
217C2×D4×D67—21no—
218C2×D4×D67—21no—
219C2×D4×D67—21no—
220C2×D4×D67—21no—
221C2×D4×D67—42no—
222C2×D4×D67D411yescharacteristic
223C2×D4×D67C2311yescharacteristic
224C2×D4×D67C2311yescharacteristic
225C2×D4×D67C2311yescharacteristic
226C2×D4×D67C2311yescharacteristic
227C22×C4×D67—21no—
228C22×C4×D67—21no—
229C22×C4×D67C2311yescharacteristic
230C22×C4×D67C2311yescharacteristic
231#14524075—42no—
232#14524070—24no—
233#14524070—42no—
234C2×#11761618C2311yescharacteristic, complemented
235C2×#11761617C2311yescharacteristic, complemented
236C2×#11761615C2311yescharacteristic
237C2×#11761615C2311yescharacteristic
238C2×#11761615C2311yescharacteristic, complemented
239C2×D536C2311yescharacteristic
240C2×D536C2311yescharacteristic
241C2×#11761613C2311yescharacteristic
242C2×#11761613C2311yescharacteristic
243C2×#11761612C2311yescharacteristic
244C2×#11761611—42no—
245C2×#11761611C2311yescharacteristic
246C2×#11761611C2311yescharacteristic
247C2×#11761611C2311yescharacteristic
248C2×#11761611C2311yescharacteristic
249C2×#11761611C2311yescharacteristic, complemented
250C2×#11761611C2311yescharacteristic, complemented
251M16×D67—42no—
252C22×C67⋊C8C2311yescharacteristic, complemented
253C2×C8×D67C2311yescharacteristic
254C2×C8×D67C2311yescharacteristic
255#14524043C2311yescharacteristic, complemented
256#14524037—21no—
257#14524037—21no—
258#14524036—21no—
259#14524036—21no—
260#14524035—21no—
261#14524034C2311yescharacteristic, complemented
262#14524034C2311yescharacteristic, complemented
263#14524033—21no—
264#14524033—21no—
265#14524032C2311yescharacteristic
266#14524031C2311yescharacteristic
267#14524030C2311yescharacteristic
268#14524029—21no—
269#14524029—21no—
270#14524029—21no—
271#14524029—21no—
272#14524028—21no—
273#14524028—21no—
274#14524028—21no—
275#14524028—21no—
276#14524028—21no—
277#14524028—21no—
278#14524027—21no—
279#14524026—21no—
280#14524025—21no—
281#14524025—21no—
282#14524025—21no—
283#14524025—21no—
284#14524025—21no—
285#14524025—21no—
286#14524024—21no—
287#14524023—21no—
288#14524023C2311yescharacteristic
289#14524022C2311yescharacteristic
290#14524021—21no—
291#14524021—21no—
292#14524021—21no—
293#14524020—21no—
294#14524019—21no—
295#14524019—21no—
296#14524019C2311yescharacteristic
297#14524019C2311yescharacteristic
298#14524019C2311yescharacteristic, complemented
299#14524018—21no—
300#14524018C2311yescharacteristic
301#14524018C2311yescharacteristic
302#14524018C2311yescharacteristic, complemented
303#14524017—21no—
304#14524017C2311yescharacteristic
305#14524017C2311yescharacteristic
306#14524017C2311yescharacteristic, complemented
307#14524016—21no—
308#14524016—21no—
309#14524016—21no—
310#14524016—21no—
311#14524016—21no—
312#14524015—21no—
313#14524015—21no—
314#14524015—21no—
315#14524014—21no—
316#14524014—21no—
317#14524014C2311yescharacteristic
318#14524013—21no—
319#14524013—21no—
320#14524013—21no—
321#14524013—21no—
322#14524013—21no—
323#14524012—21no—
324#14524011—21no—
325#14524011—21no—
326#14524011—21no—
327Q8×Dic67—21no—
328Q8×Dic67C2311yescharacteristic, complemented
329#14524008—21no—
330C4×D268—21no—
331C4×D268—21no—
332C4×D268—21no—
333C4×D268—21no—
334C4×D268C2311yescharacteristic
335C4×D268C2311yescharacteristic
336C4×D268C2311yescharacteristic, complemented
337D4×Dic67D411yescharacteristic
338D4×Dic67C2311yescharacteristic
339#14524005—21no—
340#14524005—21no—
341#14524005—21no—
342#14524005D411yescharacteristic
343#14524005C2311yescharacteristic
344#14524005C2311yescharacteristic, complemented
345C4×C22⋊D67—21no—
346C4×C22⋊D67C2311yescharacteristic
347C4×C22⋊D67C2311yescharacteristic
348(C22⋊D67)⋊C4—21no—
349(C22⋊D67)⋊C4—21no—
350(C22⋊D67)⋊C4—21no—
351(C22⋊D67)⋊C4D411yescharacteristic
352(C22⋊D67)⋊C4D411yescharacteristic
353#14524002C2311yescharacteristic
354#14524002C2311yescharacteristic, complemented
355#14524001—21no—
356#14524001—21no—
357#14524001—21no—
358#14524001—21no—
359#14524001C2311yescharacteristic
360#14524001C2311yescharacteristic
361#14524001C2311yescharacteristic
362#14524000—21no—
363#14524000—21no—
364#14523999—21no—
365#14523999—21no—
366C4⋊C4×D67—21no—
367C4⋊C4×D67D411yescharacteristic
368C4⋊C4×D67C2311yescharacteristic
369C4⋊C4×D67C2311yescharacteristic
370C4⋊C4×D67C2311yescharacteristic
371C4⋊C4×D67C2311yescharacteristic, complemented
372C4⋊C4×D67C2311yescharacteristic, complemented
373C2×C22⋊Dic67—21no—
374C2×(C2×D67)⋊C4—21no—
375C2×(C2×D67)⋊C4—21no—
376C22⋊C4×D67—21no—
377C22⋊C4×D67—21no—
378C22⋊C4×D67—21no—
379C22⋊C4×D67—21no—
380C22⋊C4×D67—21no—
381C22⋊C4×D67—21no—
382C22⋊C4×D67—21no—
383C22⋊C4×D67—21no—
384C22⋊C4×D67—21no—
385C22⋊C4×D67—21no—
386C22⋊C4×D67—21no—
387C22⋊C4×D67D411yescharacteristic
388C22⋊C4×D67D411yescharacteristic
389C42×D67—21no—
390C42×D67—21no—
391C42×D67—21no—
392C42×D67C2311yescharacteristic
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#14523968C2311yescharacteristic, complemented
407#14523968C2311yescharacteristic, complemented
408#14523967C2311yescharacteristic, complemented
409#14523967C2311yescharacteristic, complemented
410#14523967C2311yescharacteristic, complemented
411#14523967C2311yescharacteristic, complemented
412#14523966C2311yescharacteristic, complemented
413#14523966C2311yescharacteristic, complemented
414#14523966C2311yescharacteristic, complemented
415#14523965C2311yescharacteristic
416#14523965C2311yescharacteristic
417#14523965C2311yescharacteristic
418#14523965C2311yescharacteristic
419#14523965C2311yescharacteristic
420#14523965C2311yescharacteristic
421#14523965C2311yescharacteristic, complemented
422#14523964C2311yescharacteristic
423#14523964C2311yescharacteristic
424#14523964C2311yescharacteristic
425#14523964C2311yescharacteristic
426#14523964C2311yescharacteristic
427#14523964C2311yescharacteristic
428#14523963C2311yescharacteristic
429#14523963C2311yescharacteristic
430#14523963C2311yescharacteristic
431#14523963C2311yescharacteristic
432#14523963C2311yescharacteristic
433#14523963C2311yescharacteristic
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#14523954C2311yescharacteristic, complemented
442C8×Dic67C2311yescharacteristic, 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—44no—
493C23×D67—44no—
494C23×D67—82no—
495C23×D67C2×D411yescharacteristic
496C23×D67C2×D411yescharacteristic
497#11761629—22no—
498#11761629—22no—
499#11761629—22no—
500#11761629—41no—
501#11761629—44no—
502#11761628—22no—
503#11761628—41no—
504#11761628—44no—
505#11761627—22no—
506#11761627—41no—
507#11761627—44no—
508C2×Dic134—21no—
509C2×Dic134—21no—
510C2×Dic134C2411yescharacteristic
511Q8×D67—22no—
512Q8×D67—22no—
513C2×D268—22no—
514C2×D268—21no—
515C2×D268—21no—
516C2×D268—21no—
517C2×D268—21no—
518C2×D268—21no—
519C2×D268—21no—
520C2×D268—41no—
521C2×D268C2×D411yescharacteristic
522C2×D268C2411yescharacteristic
523C2×D268C2411yescharacteristic
524C2×D268C2411yescharacteristic
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⋊D67C2×D411yescharacteristic
537C2×C22⋊D67C2×D411yescharacteristic
538D4×D67—22no—
539D4×D67—22no—
540D4×D67—22no—
541D4×D67—22no—
542D4×D67—22no—
543D4×D67—41no—
544D4×D67—41no—
545D4×D67—44no—
546D4×D67—44no—
547D4×D67—42no—
548D4×D67—44no—
549D4×D67—82no—
550D4×D67#4114yescomplemented
551C22×Dic67—21no—
552C22×Dic67—21no—
553C22×Dic67C2×D411yescharacteristic
554C22×Dic67C2×D411yescharacteristic
555C2×C4×D67—22no—
556C2×C4×D67—22no—
557C2×C4×D67—22no—
558C2×C4×D67—22no—
559C2×C4×D67—21no—
560C2×C4×D67—21no—
561C2×C4×D67—21no—
562C2×C4×D67—21no—
563C2×C4×D67—21no—
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×D67—44no—
573C2×C4×D67—82no—
574C2×C4×D67C2×D411yescharacteristic
575C2×C4×D67C2×D411yescharacteristic
576C2×C4×D67C2×D411yescharacteristic
577C2×C4×D67C2×D411yescharacteristic
578C2×C4×D67C2×D411yescharacteristic
579C2×C4×D67C2×D411yescharacteristic
580C2×C4×D67C2411yescharacteristic
581C2×C4×D67C2411yescharacteristic
582C2×C4×D67C2411yescharacteristic
583#11761618—41no—
584#11761617—41no—
585#11761615—22no—
586#11761615—41no—
587#11761615—41no—
588D536—22no—
589D536—41no—
590#11761613—22no—
591#11761613—41no—
592#11761612—41no—
593#11761611—22no—
594#11761611—22no—
595#11761611—22no—
596#11761611—22no—
597#11761611—41no—
598#11761611—41no—
599C2×C67⋊C8—41no—
600C2×C67⋊C8C2411yescharacteristic
601C2×C67⋊C8C2411yescharacteristic
602C2×C67⋊C8C2411yescharacteristic
603C2×C67⋊C8C2411yescharacteristic
604C8×D67—41no—
605C8×D67—41no—
606C4⋊Dic67—21no—
607C4⋊Dic67—21no—
608C4⋊Dic67—21no—
609C4⋊Dic67—21no—
610C4⋊Dic67—21no—
611C4⋊Dic67C2×D411yescharacteristic
612C4⋊Dic67C2411yescharacteristic
613C4⋊Dic67C2411yescharacteristic
614C4⋊Dic67C2411yescharacteristic
615C4⋊Dic67C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
628Dic67⋊C4C2×D411yescharacteristic
629C22⋊Dic67—21no—
630C22⋊Dic67—21no—
631C22⋊Dic67—21no—
632C22⋊Dic67—21no—
633C22⋊Dic67—21no—
634C22⋊Dic67—21no—
635C22⋊Dic67—21no—
636C22⋊Dic67C2×D411yescharacteristic
637C22⋊Dic67C2×D411yescharacteristic
638(C2×D67)⋊C4—21no—
639(C2×D67)⋊C4—21no—
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)⋊C4—21no—
658(C2×D67)⋊C4—21no—
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×Dic67C2×D411yescharacteristic
670C4×Dic67C2×D411yescharacteristic
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—24no—
734C22×D67—22no—
735C22×D67—22no—
736C22×D67—21no—
737C22×D67—21no—
738C22×D67—41no—
739C22×D67—41no—
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—42no—
750C22×D67—42no—
751C22×D67—42no—
752C22×D67—81no—
753C22×D67—81no—
754C22×D67—81no—
755C22×D67—816no—
756C22×D67C22×D411yescharacteristic
757C22×D67C22×D411yescharacteristic
758C22×D67C22×D411yescharacteristic
759Q8×C67—21no—
760Q8×C67—21no—
761Q8×C67—21no—
762Q8×C67—21no—
763Q8×C67—42no—
764D4×C67—21no—
765D4×C67—21no—
766D4×C67—21no—
767D4×C67—41no—
768D4×C67—42no—
769D4×C67—42no—
770D4×C67—81no—
771D4×C67C2×#4112yes—
772C2×C4×C67—21no—
773C2×C4×C67—21no—
774C2×C4×C67—21no—
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—42no—
783C2×C4×C67—81no—
784C2×C4×C67C22×D411yescharacteristic
785C2×C4×C67C22×D411yescharacteristic
786C2×C4×C67C22×D411yescharacteristic
787C2×C4×C67C22×D411yescharacteristic
788C2×C4×C67C2511yescharacteristic
789C22⋊D67—22no—
790C22⋊D67—24no—
791C22⋊D67—41no—
792C22⋊D67—42no—
793C22⋊D67—42no—
794C22⋊D67—42no—
795C22⋊D67—42no—
796C22⋊D67—42no—
797C22⋊D67—81no—
798C22⋊D67—81no—
799C22⋊D67—81no—
800C22⋊D67—81no—
801C2×Dic67—22no—
802C2×Dic67—22no—
803C2×Dic67—21no—
804C2×Dic67—21no—
805C2×Dic67—21no—
806C2×Dic67—21no—
807C2×Dic67—21no—
808C2×Dic67—42no—
809C2×Dic67—81no—
810C2×Dic67C22×D411yescharacteristic
811C2×Dic67C22×D411yescharacteristic
812C2×Dic67C22×D411yescharacteristic
813C2×Dic67C22×D411yescharacteristic
814C2×Dic67C22×D411yescharacteristic
815D268—22no—
816D268—21no—
817D268—21no—
818D268—21no—
819D268—21no—
820D268—21no—
821D268—42no—
822D268—42no—
823D268—42no—
824D268—42no—
825D268—42no—
826D268—81no—
827D268C2×#4112yes—
828C4×D67—22no—
829C4×D67—22no—
830C4×D67—21no—
831C4×D67—21no—
832C4×D67—21no—
833C4×D67—21no—
834C4×D67—22no—
835C4×D67—22no—
836C4×D67—41no—
837C4×D67—41no—
838C4×D67—42no—
839C4×D67—42no—
840C4×D67—42no—
841C4×D67—42no—
842C4×D67—42no—
843C4×D67—42no—
844C4×D67—42no—
845C4×D67—42no—
846C4×D67—81no—
847C4×D67—81no—
848C4×D67—81no—
849C4×D67—81no—
850C4×D67—81no—
851C4×D67C2×#4112yes—
852C4×D67H(5,𝔽2)12yes—
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—48no—
889C2×D67—41no—
890C2×D67—41no—
891C2×D67—41no—
892C2×D67—41no—
893C2×D67—41no—
894C2×D67—41no—
895C2×D67—41no—
896C2×D67—41no—
897C2×D67—82no—
898C2×D67—84no—
899C2×D67—84no—
900C2×D67—84no—
901C2×D67—84no—
902C2×D67#54612yes—
903C2×D67#57512yes—
904C4×C67—21no—
905C4×C67—21no—
906C4×C67—21no—
907C4×C67—21no—
908C4×C67—41no—
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#54612yes—
926#61156—671nomaximal, Sylow
927C2×C67—41no—
928C2×C67—42no—
929C2×C67—41no—
930C2×C67—81no—
931C2×C67C2×#54611yescharacteristic
932C2×C67C2×#57511yescharacteristic
933C2×C67#358511yescharacteristic
934D67—22no—
935D67—22no—
936D67—41no—
937D67—42no—
938D67—81no—
939D67—81no—
940#3475—671no—
941C2×#546—671no—
942#3323—671no—
943#3323—671no—
944#3322—671no—
945#3322—671no—
946#3319—671no—
947#3319—671no—
948#3314—671no—
949#3314—671no—
950#3311—671no—
951#3311D6711yescharacteristic, complemented
952#3306—671no—
953#3306—671no—
954#3297—671no—
955#3297—671no—
956#3296—671no—
957#3296—671no—
958#3140—671no—
959#3095—671no—
960#3094—671no—
961#3077—671no—
962#3056—671no—
963#3055—671no—
964#3040—671no—
965#3005—671no—
966#3003—671no—
967C4×AGL(1,ℤ/8)—671no—
968D4×M16—671no—
969#2896—671no—
970C2×#418—671no—
971C67#6115611yescharacteristic, complemented, Sylow
972C22×#41—671no—
973C23×D4—671no—
974C2×#137—671no—
975C2×AGL(1,ℤ/8)—671no—
976C2×AGL(1,ℤ/8)—671no—
977C22×M16—671no—
978C22×M16—671no—
979#556C2×D6711yescharacteristic, complemented
980#555—671no—
981#554—671no—
982#553—671no—
983#553—671no—
984#552—671no—
985#552—671no—
986#552—1341no—
987#551—1341no—
988#551—1341no—
989#547—671no—
990#546—671no—
991#546—671no—
992#546—671no—
993#546—671no—
994#546—671no—
995#546—671no—
996#546—671no—
997#546—1341no—
998#546—1341no—
999#546—1341no—
1000#546—1341no—
1001#546—1341no—
1002#546C2×D6711yescharacteristic
1003#533—671no—
1004#529—1341no—
1005#529—1341no—
1006#529—1341no—
1007C2×#124—671no—
1008#525—671no—
1009#525—671no—
1010C2×#123—1341no—
1011C2×C22⋊Q8—671no—
1012C2×#121—671no—
1013C2×#121—1341no—
1014C2×#120—1341no—
1015C4×#41—671no—
1016C4×#41—1341no—
1017C2×C4×D4—671no—
1018C2×C4×D4—671no—
1019C2×#117—671no—
1020C2×#117—671no—
1021C22×C22⋊C4—1341no—
1022#489—671no—
1023#489—671no—
1024#489—671no—
1025#489C2×D6711yescharacteristic, complemented
1026#488—671no—
1027#488—671no—
1028#488—671no—
1029#488—671no—
1030#485—671no—
1031#485—671no—
1032#485—671no—
1033#485C2×D6711yescharacteristic, complemented
1034#484—671no—
1035#484—671no—
1036#483—671no—
1037#483—671no—
1038#482—671no—
1039#482—671no—
1040#482—671no—
1041#482C2×D6711yescharacteristic, complemented
1042#481—671no—
1043#481—671no—
1044#480—671no—
1045#480—671no—
1046#478—671no—
1047#478—671no—
1048#478—671no—
1049#478—671no—
1050#476—671no—
1051#476C2×D6711yescharacteristic, complemented
1052#474—671no—
1053#474—671no—
1054#470—671no—
1055#470C2×D6711yescharacteristic, complemented
1056#469—671no—
1057#469—671no—
1058#468—671no—
1059#468—671no—
1060#468—671no—
1061#468—671no—
1062#467—671no—
1063#467—671no—
1064#466—671no—
1065#466—671no—
1066#465—671no—
1067#465—671no—
1068#465—671no—
1069#465C2×D6711yescharacteristic, complemented
1070#464—671no—
1071#464—671no—
1072#464—671no—
1073#464C2×D6711yescharacteristic, complemented
1074#463—671no—
1075#463—671no—
1076#463—671no—
1077#463—671no—
1078#452—671no—
1079#452—671no—
1080#452—671no—
1081#452C2×D6711yescharacteristic, complemented
1082#450—671no—
1083#450—671no—
1084#450—671no—
1085#450C2×D6711yescharacteristic, complemented
1086#449—671no—
1087#449—671no—
1088#449—671no—
1089#449—671no—
1090#447—671no—
1091#447—671no—
1092#447—671no—
1093#447—671no—
1094#442—671no—
1095#442—671no—
1096#440—671no—
1097#440C2×D6711yescharacteristic, complemented
1098C4×SD16—671no—
1099C4×SD16—671no—
1100C4×D8—671no—
1101C4×D8—671no—
1102#436—671no—
1103#436—671no—
1104#435—671no—
1105#435—671no—
1106#435—671no—
1107#435C2×D6711yescharacteristic, complemented
1108C8×D4—671no—
1109C8×D4—671no—
1110#428—671no—
1111#428—671no—
1112#428—671no—
1113#423—671no—
1114#419—671no—
1115#419—671no—
1116#419—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#418—671no—
1126#418C2×D6711yescharacteristic, complemented
1127#417—671no—
1128#417—671no—
1129#417—671no—
1130#417—671no—
1131#417—671no—
1132#416—671no—
1133#416—671no—
1134#416—671no—
1135#416C2×D6711yescharacteristic, complemented
1136C2×#102—671no—
1137C2×#102—671no—
1138C2×#102—671no—
1139C2×#102—671no—
1140#407—671no—
1141#407—671no—
1142C4×M16—671no—
1143C25—1341no—
1144C2×#41—2682no—
1145C2×#41—671no—
1146C2×#41—671no—
1147C2×#41—671no—
1148C2×#41—671no—
1149C2×#41—1341no—
1150C2×#41—1344no—
1151C2×#41—1341no—
1152C2×#41—1341no—
1153C2×#41C22×D6711yescharacteristic
1154C22×Q8—671no—
1155C22×D4—2682no—
1156C22×D4—671no—
1157C22×D4—671no—
1158C22×D4—671no—
1159C22×D4—671no—
1160C22×D4—671no—
1161C22×D4—671no—
1162C22×D4—1341no—
1163C22×D4—1341no—
1164C22×D4—1341no—
1165C22×D4—1341no—
1166C22×D4—1344no—
1167C22×D4—1341no—
1168C22×D4C22×D6711yescharacteristic
1169C23×C4—671no—
1170C23×C4—671no—
1171C23×C4—1341no—
1172C23×C4—1341no—
1173#137—2682no—
1174AGL(1,ℤ/8)—2682no—
1175AGL(1,ℤ/8)—1344no—
1176C2×Q16—671no—
1177C2×Q16C22×D6711yescharacteristic, complemented
1178C2×SD16—671no—
1179C2×SD16—671no—
1180C2×SD16—671no—
1181C2×SD16—671no—
1182C2×SD16C22×D6711yescharacteristic
1183C2×SD16C22×D6711yescharacteristic
1184C2×D8—671no—
1185C2×D8—671no—
1186C2×D8—671no—
1187C2×D8—671no—
1188C2×M16—2682no—
1189C2×M16—2682no—
1190C2×M16—671no—
1191C2×M16—671no—
1192C2×M16—671no—
1193C2×M16—671no—
1194C2×M16—671no—
1195C2×M16—671no—
1196C2×M16—671no—
1197C2×M16C22×D6711yescharacteristic
1198C22×C8—671no—
1199C22×C8—671no—
1200C22×C8—671no—
1201C22×C8C22×D6711yescharacteristic, complemented
1202C4⋊Q8—671no—
1203C4⋊Q8C22×D6711yescharacteristic, complemented
1204#126—21no—
1205#126—21no—
1206#126—1341no—
1207#126—1341no—
1208#126—1341no—
1209#126—1341no—
1210#125—671no—
1211#125—671no—
1212#125—1341no—
1213#125—1341no—
1214#125—1341no—
1215#124—21no—
1216#124—671no—
1217#124—671no—
1218#124—671no—
1219#124—1341no—
1220#124—1341no—
1221#124—1341no—
1222#124—1341no—
1223#124C22×D6711yescharacteristic
1224#123—21no—
1225#123—1341no—
1226#123—1341no—
1227#123—1341no—
1228#123—1341no—
1229#123—1341no—
1230#123—1341no—
1231#123—1341no—
1232#123—1341no—
1233#123—1341no—
1234#123—1341no—
1235#123—1341no—
1236#123—1341no—
1237#123—1341no—
1238#123—1341no—
1239#123—1341no—
1240C22⋊Q8—671no—
1241C22⋊Q8—671no—
1242C22⋊Q8—671no—
1243C22⋊Q8—671no—
1244C22⋊Q8—671no—
1245C22⋊Q8—1341no—
1246C22⋊Q8—1341no—
1247C22⋊Q8—1341no—
1248C22⋊Q8—1341no—
1249C22⋊Q8—1341no—
1250C22⋊Q8—1341no—
1251C22⋊Q8—1341no—
1252C22⋊Q8C22×D6711yescharacteristic
1253C22⋊Q8C22×D6711yescharacteristic
1254C22⋊Q8C22×D6711yescharacteristic, complemented
1255#121—21no—
1256#121—671no—
1257#121—671no—
1258#121—671no—
1259#121—671no—
1260#121—671no—
1261#121—671no—
1262#121—671no—
1263#121—1341no—
1264#121—1341no—
1265#121—1341no—
1266#121—1341no—
1267#121—1341no—
1268#121—1341no—
1269#121—1341no—
1270#121—1341no—
1271#121—1341no—
1272#121—1341no—
1273#121—1341no—
1274#121—1341no—
1275#121C22×D6711yescharacteristic
1276#120—21no—
1277#120—1341no—
1278#120—1341no—
1279#120—1341no—
1280#120—1341no—
1281#120—1341no—
1282#120—1341no—
1283#120—1341no—
1284#120—1341no—
1285#120—1341no—
1286C4×Q8—21no—
1287C4×Q8—671no—
1288C4×Q8—1341no—
1289C4×Q8—1341no—
1290C4×Q8C22×D6711yescharacteristic, complemented
1291C4×D4—671no—
1292C4×D4—671no—
1293C4×D4—671no—
1294C4×D4—671no—
1295C4×D4—671no—
1296C4×D4—671no—
1297C4×D4—671no—
1298C4×D4—671no—
1299C4×D4—671no—
1300C4×D4—671no—
1301C4×D4—671no—
1302C4×D4—671no—
1303C4×D4—1341no—
1304C4×D4—1341no—
1305C4×D4—1341no—
1306C4×D4—1341no—
1307C4×D4—1341no—
1308C4×D4—1341no—
1309C4×D4—1341no—
1310C4×D4—1341no—
1311C4×D4—1341no—
1312C4×D4—1341no—
1313C4×D4—1341no—
1314C4×D4C22×D6711yescharacteristic
1315C4×D4C22×D6711yescharacteristic
1316#117—671no—
1317#117—671no—
1318#117—671no—
1319#117—671no—
1320#117—671no—
1321#117—1341no—
1322#117—1341no—
1323#117—1341no—
1324#117—1341no—
1325#117—1341no—
1326#117—1341no—
1327#117—1341no—
1328#117—1341no—
1329#117C22×D6711yescharacteristic
1330#117C22×D6711yescharacteristic, complemented
1331C2×C4⋊C4—671no—
1332C2×C4⋊C4—671no—
1333C2×C4⋊C4—671no—
1334C2×C4⋊C4—671no—
1335C2×C4⋊C4—671no—
1336C2×C4⋊C4—671no—
1337C2×C4⋊C4—1341no—
1338C2×C22⋊C4—21no—
1339C2×C22⋊C4—671no—
1340C2×C22⋊C4—671no—
1341C2×C22⋊C4—1341no—
1342C2×C22⋊C4—1341no—
1343C2×C22⋊C4—1341no—
1344C2×C22⋊C4—1341no—
1345C2×C22⋊C4—1341no—
1346C2×C22⋊C4—1341no—
1347C2×C22⋊C4—1341no—
1348C2×C22⋊C4—1341no—
1349C2×C22⋊C4—1341no—
1350C2×C22⋊C4—1341no—
1351C2×C22⋊C4—1341no—
1352C2×C22⋊C4—1341no—
1353C2×C22⋊C4—1341no—
1354C2×C22⋊C4—1341no—
1355C2×C42—671no—
1356C2×C42—1341no—
1357C2×C42—1341no—
1358C2×C42—1341no—
1359#107—671no—
1360#107—671no—
1361#107—671no—
1362#107—671no—
1363#107—671no—
1364#107C22×D6711yescharacteristic, complemented
1365#106—671no—
1366#106—671no—
1367#106—671no—
1368#106—671no—
1369#106C22×D6711yescharacteristic, complemented
1370#106C22×D6711yescharacteristic, complemented
1371C4⋊C8—671no—
1372C4⋊C8—671no—
1373C4⋊C8—671no—
1374C4⋊C8C22×D6711yescharacteristic, complemented
1375#103—671no—
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#103C22×D6711yescharacteristic, complemented
1387#103C22×D6711yescharacteristic, complemented
1388#103C22×D6711yescharacteristic, complemented
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#102C22×D6711yescharacteristic
1410#102C22×D6711yescharacteristic
1411#102C22×D6711yescharacteristic
1412#102C22×D6711yescharacteristic
1413#102C22×D6711yescharacteristic
1414#102C22×D6711yescharacteristic
1415C22⋊C8—671no—
1416C22⋊C8—671no—
1417C22⋊C8—671no—
1418C22⋊C8—671no—
1419C22⋊C8—671no—
1420C22⋊C8—671no—
1421C22⋊C8C22×D6711yescharacteristic
1422C22⋊C8C22×D6711yescharacteristic, complemented
1423#97—671no—
1424#97C22×D6711yescharacteristic, complemented
1425C4×C8—671no—
1426C4×C8—671no—
1427C24—21no—
1428C24—2684no—
1429C24—2684no—
1430C24—5362no—
1431C24—671no—
1432C24—671no—
1433C24—1341no—
1434C24—1341no—
1435C24—1341no—
1436C24—1341no—
1437C24—1341no—
1438#41—22no—
1439#41—41no—
1440#41—2681no—
1441#41—2684no—
1442#41—2684no—
1443#41—2681no—
1444#41—2684no—
1445#41—2681no—
1446#41—1342no—
1447#41—1342no—
1448#41—1342no—
1449#41—1342no—
1450#41—1342no—
1451C2×Q8—21no—
1452C2×Q8—671no—
1453C2×Q8—1341no—
1454C2×Q8—1342no—
1455C2×Q8—1342no—
1456C2×Q8—1341no—
1457C2×Q8C23×D6711yescharacteristic
1458C2×Q8C23×D6711yescharacteristic
1459C2×D4—22no—
1460C2×D4—21no—
1461C2×D4—21no—
1462C2×D4—21no—
1463C2×D4—41no—
1464C2×D4—2681no—
1465C2×D4—2684no—
1466C2×D4—2682no—
1467C2×D4—2681no—
1468C2×D4—2681no—
1469C2×D4—2684no—
1470C2×D4—2684no—
1471C2×D4—2684no—
1472C2×D4—5362no—
1473C2×D4—671no—
1474C2×D4—674no—
1475C2×D4—671no—
1476C2×D4—671no—
1477C2×D4—671no—
1478C2×D4—671no—
1479C2×D4—671no—
1480C2×D4—1341no—
1481C2×D4—1341no—
1482C2×D4—1341no—
1483C2×D4—1341no—
1484C2×D4—1342no—
1485C2×D4—1341no—
1486C2×D4—1342no—
1487C2×D4—1342no—
1488C2×D4—1342no—
1489C2×D4—1341no—
1490C2×D4—1341no—
1491C2×D4—1341no—
1492C2×D4—1341no—
1493C2×D4—1342no—
1494C2×D4—1341no—
1495C2×D4—1341no—
1496C2×D4—1342no—
1497C2×D4—1341no—
1498C2×D4—1341no—
1499C2×D4—1341no—
1500C2×D4—1341no—
1501C2×D4—1341no—
1502C2×D4D4×D6711yescharacteristic
1503C2×D4C23×D6711yescharacteristic
1504C2×D4C23×D6711yescharacteristic
1505C22×C4—21no—
1506C22×C4—21no—
1507C22×C4—2684no—
1508C22×C4—5362no—
1509C22×C4—671no—
1510C22×C4—671no—
1511C22×C4—671no—
1512C22×C4—671no—
1513C22×C4—671no—
1514C22×C4—671no—
1515C22×C4—671no—
1516C22×C4—671no—
1517C22×C4—671no—
1518C22×C4—671no—
1519C22×C4—671no—
1520C22×C4—1341no—
1521C22×C4—1341no—
1522C22×C4—1341no—
1523C22×C4—1341no—
1524C22×C4—1341no—
1525C22×C4—1341no—
1526C22×C4—1341no—
1527C22×C4—1341no—
1528C22×C4—1341no—
1529C22×C4—1341no—
1530C22×C4—1342no—
1531C22×C4—1342no—
1532C22×C4—1342no—
1533C22×C4—1342no—
1534C22×C4—1341no—
1535C22×C4—1341no—
1536C22×C4—1341no—
1537C22×C4—1341no—
1538C22×C4—1341no—
1539C22×C4C23×D6711yescharacteristic
1540C22×C4C23×D6711yescharacteristic
1541Q16—41no—
1542Q16—2681no—
1543SD16—22no—
1544SD16—41no—
1545SD16—2681no—
1546SD16—2681no—
1547SD16—2681no—
1548SD16—1342no—
1549D8—2681no—
1550D8—2681no—
1551D8—1342no—
1552D8—1342no—
1553M16—41no—
1554M16—2681no—
1555M16—2681no—
1556M16—2681no—
1557M16—1342no—
1558M16—1342no—
1559M16—1342no—
1560M16—1342no—
1561C2×C8—41no—
1562C2×C8—2681no—
1563C2×C8—2681no—
1564C2×C8—2681no—
1565C2×C8—671no—
1566C2×C8—671no—
1567C2×C8—671no—
1568C2×C8—671no—
1569C2×C8C23×D6711yescharacteristic
1570C2×C8C23×D6711yescharacteristic
1571C2×C8C23×D6711yescharacteristic
1572C2×C8C23×D6711yescharacteristic
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—1341no—
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⋊C4D4×D6711yescharacteristic
1602C4⋊C4C23×D6711yescharacteristic
1603C4⋊C4C23×D6711yescharacteristic
1604C4⋊C4C23×D6711yescharacteristic
1605C4⋊C4C23×D6711yescharacteristic
1606C22⋊C4—21no—
1607C22⋊C4—21no—
1608C22⋊C4—21no—
1609C22⋊C4—21no—
1610C22⋊C4—21no—
1611C22⋊C4—21no—
1612C22⋊C4—21no—
1613C22⋊C4—21no—
1614C22⋊C4—21no—
1615C22⋊C4—671no—
1616C22⋊C4—671no—
1617C22⋊C4—671no—
1618C22⋊C4—671no—
1619C22⋊C4—671no—
1620C22⋊C4—671no—
1621C22⋊C4—1341no—
1622C22⋊C4—1341no—
1623C22⋊C4—1341no—
1624C22⋊C4—1341no—
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⋊C4D4×D6711yescharacteristic
1650C22⋊C4D4×D6711yescharacteristic
1651C42—21no—
1652C42—21no—
1653C42—21no—
1654C42—671no—
1655C42—671no—
1656C42—671no—
1657C42—1341no—
1658C42—1341no—
1659C42—1341no—
1660C42—1341no—
1661C42—1341no—
1662C42—1341no—
1663C42C23×D6711yescharacteristic
1664C23—21no—
1665C23—21no—
1666C23—42no—
1667C23—42no—
1668C23—81no—
1669C23—2681no—
1670C23—2682no—
1671C23—2682no—
1672C23—2682no—
1673C23—2681no—
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—53616no—
1687C23—671no—
1688C23—671no—
1689C23—671no—
1690C23—1344no—
1691C23—1342no—
1692C23—1342no—
1693C23—1342no—
1694C23—1341no—
1695C23—1341no—
1696C23—1341no—
1697C23C2×D4×D6711yescharacteristic
1698C23C2×D4×D6711yescharacteristic
1699Q8—21no—
1700Q8—21no—
1701Q8—21no—
1702Q8—21no—
1703Q8—42no—
1704Q8—2682no—
1705Q8—5361no—
1706Q8—1341no—
1707Q8—1341no—
1708D4—21no—
1709D4—21no—
1710D4—21no—
1711D4—41no—
1712D4—42no—
1713D4—42no—
1714D4—81no—
1715D4—2682no—
1716D4—2682no—
1717D4—2682no—
1718D4—2682no—
1719D4—2682no—
1720D4—2682no—
1721D4—2682no—
1722D4—2682no—
1723D4—2682no—
1724D4—2681no—
1725D4—2682no—
1726D4—5361no—
1727D4—5361no—
1728D4—5361no—
1729D4—5361no—
1730D4—5361no—
1731D4—672no—
1732D4—1342no—
1733D4—1344no—
1734D4—1342no—
1735D4—1341no—
1736D4—1341no—
1737D4—1341no—
1738D4—1341no—
1739D4—1341no—
1740D4#41×D6712yes—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—21no—
1750C2×C4—21no—
1751C2×C4—42no—
1752C2×C4—81no—
1753C2×C4—2682no—
1754C2×C4—2682no—
1755C2×C4—2681no—
1756C2×C4—2681no—
1757C2×C4—2682no—
1758C2×C4—2682no—
1759C2×C4—2682no—
1760C2×C4—2682no—
1761C2×C4—2682no—
1762C2×C4—2682no—
1763C2×C4—2682no—
1764C2×C4—5361no—
1765C2×C4—5361no—
1766C2×C4—5361no—
1767C2×C4—5361no—
1768C2×C4—5361no—
1769C2×C4—5361no—
1770C2×C4—671no—
1771C2×C4—672no—
1772C2×C4—672no—
1773C2×C4—671no—
1774C2×C4—671no—
1775C2×C4—671no—
1776C2×C4—671no—
1777C2×C4—1342no—
1778C2×C4—1342no—
1779C2×C4—1342no—
1780C2×C4—1342no—
1781C2×C4—1341no—
1782C2×C4—1341no—
1783C2×C4—1341no—
1784C2×C4—1341no—
1785C2×C4—1341no—
1786C2×C4—1342no—
1787C2×C4—1342no—
1788C2×C4—1341no—
1789C2×C4—1341no—
1790C2×C4—1341no—
1791C2×C4—1341no—
1792C2×C4C2×D4×D6711yescharacteristic
1793C2×C4C2×D4×D6711yescharacteristic
1794C2×C4C2×D4×D6711yescharacteristic
1795C2×C4C2×D4×D6711yescharacteristic
1796C2×C4C24×D6711yescharacteristic
1797C8—21no—
1798C8—21no—
1799C8—21no—
1800C8—21no—
1801C8—1341no—
1802C8—1341no—
1803C8—1341no—
1804C8—1341no—
1805C22—21no—
1806C22—21no—
1807C22—22no—
1808C22—21no—
1809C22—21no—
1810C22—21no—
1811C22—21no—
1812C22—41no—
1813C22—41no—
1814C22—41no—
1815C22—41no—
1816C22—41no—
1817C22—84no—
1818C22—2688no—
1819C22—2684no—
1820C22—2681no—
1821C22—2681no—
1822C22—2681no—
1823C22—2681no—
1824C22—2681no—
1825C22—2681no—
1826C22—2681no—
1827C22—2681no—
1828C22—5364no—
1829C22—5362no—
1830C22—5364no—
1831C22—5364no—
1832C22—5364no—
1833C22—672no—
1834C22—672no—
1835C22—1342no—
1836C22—1341no—
1837C22—1341no—
1838C22—1341no—
1839C22—1341no—
1840C22—1341no—
1841C22—1341no—
1842C22—1341no—
1843C22C22×D4×D6711yescharacteristic
1844C4—21no—
1845C4—21no—
1846C4—21no—
1847C4—21no—
1848C4—41no—
1849C4—41no—
1850C4—41no—
1851C4—41no—
1852C4—41no—
1853C4—41no—
1854C4—2681no—
1855C4—2681no—
1856C4—2681no—
1857C4—2681no—
1858C4—2681no—
1859C4—672no—
1860C4—1341no—
1861C4—1341no—
1862C4—1341no—
1863C4—1341no—
1864C4C2×#41×D6711yescharacteristic
1865C4H(5,𝔽2)×D6711yescharacteristic
1866C2—41no—
1867C2—41no—
1868C2—42no—
1869C2—81no—
1870C2—2682no—
1871C2—2681no—
1872C2—5361no—
1873C2—5361no—
1874C2—1342no—
1875C2—1342no—
1876C2#546×D6711yescharacteristic
1877C2#575×D6711yescharacteristic
1878C2#2257498711yescharacteristic
subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3311C2
socleC22×C67C23×D4
hypercenter#3311D67
hypocenterC67#61156
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. #22573770C2semidirect
2. #546×D67C2semidirect
3. #22572431C2semidirect
4. #22572429C2semidirect
5. #22572408C2semidirect
6. #22572406C2semidirect
7. #22572367C2semidirect
8. #22572365C2semidirect
9. #22572297C2semidirect
10. #22572295C2semidirect
11. #22572239C2semidirect
12. #22572169C2semidirect
13. #22572167C2semidirect
14. #22572062C2semidirect
15. #22572060C2semidirect
16. #22572039C2semidirect
17. #22572037C2semidirect
18. #22570594C2semidirect
19. #22570156C2semidirect
20. #22570148C2semidirect
21. #22570007C2semidirect
22. #22569838C2semidirect
23. #22569821C2semidirect
24. #22569700C2semidirect
25. #22569452C2semidirect
26. #22569437C2semidirect
27. #22569014C2semidirect
28. #22568942C2semidirect
29. #22568724C2semidirect
30. #418×D67C2semidirect
31. C67×#3311C2semidirect
34. C2×#14524075C22semidirect
37. C22×#11761611C22semidirect
39. #16864111C22semidirect
40. #16864106C22semidirect
41. #16864090C22semidirect
42. #16864090C22semidirect
44. #16864080C22semidirect
45. #16864080C22semidirect
48. #16864049C22semidirect
61. #16863951C22semidirect
67. #16863909C22semidirect
74. C4×#11761629C22semidirect
78. #117×D67C22semidirect
80. #16863758C22semidirect
81. #16863756C22semidirect
82. #16863755C22semidirect
83. #16863752C22semidirect
84. #16863752C22semidirect
85. #16863749C22semidirect
86. #16863749C22semidirect
87. #16863738C22semidirect
88. #16863737C22semidirect
89. #16863734C22semidirect
90. #16863733C22semidirect
91. #16863730C22semidirect
92. #16863728C22semidirect
93. #16863725C22semidirect
94. #16863721C22semidirect
95. #16863720C22semidirect
96. #16863717C22semidirect
97. #16863716C22semidirect
98. #16863713C22semidirect
99. #16863711C22semidirect
100. #16863708C22semidirect
101. #16863695C22semidirect
102. #16863695C22semidirect
103. #16863694C22semidirect
104. #16863694C22semidirect
105. #16863683C22semidirect
106. #16863677C22semidirect
107. #16863676C22semidirect
108. #16863652C22semidirect
109. #16863650C22semidirect
110. #16863648C22semidirect
111. #16863645C22semidirect
112. #16863644C22semidirect
113. #16863642C22semidirect
114. #16863639C22semidirect
115. #16863636C22semidirect
116. #16863634C22semidirect
117. #16863632C22semidirect
118. #16863630C22semidirect
119. #16863628C22semidirect
120. #16863627C22semidirect
121. #16863626C22semidirect
122. #16863620C22semidirect
123. #16863618C22semidirect
124. #16863616C22semidirect
125. #16863614C22semidirect
126. #16863612C22semidirect
127. #16863610C22semidirect
128. #16863608C22semidirect
129. #16863557C22semidirect
130. #16863556C22semidirect
131. #16863555C22semidirect
132. #16863546C22semidirect
133. #16863545C22semidirect
134. #16863545C22semidirect
135. #16863544C22semidirect
136. #16863543C22semidirect
137. #16863542C22semidirect
138. #16863541C22semidirect
139. #16863532C22semidirect
140. #16863531C22semidirect
141. #16863531C22semidirect
142. #16863530C22semidirect
143. #16863509C22semidirect
144. #16863506C22semidirect
145. #16863494C22semidirect
146. SD16×Dic67C22semidirect
147. #16863481C22semidirect
148. #16863478C22semidirect
149. #16863476C22semidirect
150. #16863472C22semidirect
151. #16863471C22semidirect
152. #16863469C22semidirect
153. #16863468C22semidirect
154. #16863466C22semidirect
155. C8×C22⋊D67C22semidirect
156. (C22⋊D67)⋊C8C22semidirect
157. #16863437C22semidirect
158. #16863435C22semidirect
159. #16863435C22semidirect
160. #16863418C22semidirect
161. #16863403C22semidirect
162. #16863403C22semidirect
163. #16863403C22semidirect
164. #16863402C22semidirect
165. #16863401C22semidirect
166. #16863400C22semidirect
173. #16863396C22semidirect
174. #16863396C22semidirect
175. #16863396C22semidirect
176. #16863394C22semidirect
177. #16863394C22semidirect
178. #16863393C22semidirect
179. #16863392C22semidirect
180. #16863390C22semidirect
181. #102×D67C22semidirect
182. #102×D67C22semidirect
183. #102×D67C22semidirect
184. #102×D67C22semidirect
186. #16863358C22semidirect
187. #16863348C22semidirect
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
234. C2×#11761618C23semidirect
235. C2×#11761617C23semidirect
238. C2×#11761615C23semidirect
249. C2×#11761611C23semidirect
250. C2×#11761611C23semidirect
252. C22×C67⋊C8C23semidirect
255. #14524043C23semidirect
261. #14524034C23semidirect
262. #14524034C23semidirect
298. #14524019C23semidirect
302. #14524018C23semidirect
306. #14524017C23semidirect
328. Q8×Dic67C23semidirect
336. C4×D268C23semidirect
344. #14524005C23semidirect
354. #14524002C23semidirect
371. C4⋊C4×D67C23semidirect
372. 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. #14523968C23semidirect
407. #14523968C23semidirect
408. #14523967C23semidirect
409. #14523967C23semidirect
410. #14523967C23semidirect
411. #14523967C23semidirect
412. #14523966C23semidirect
413. #14523966C23semidirect
414. #14523966C23semidirect
421. #14523965C23semidirect
434. #14523963C23semidirect
436. C22⋊(C67⋊C8)C23semidirect
439. (C2×D67)⋊C8C23semidirect
440. (C2×D67)⋊C8C23semidirect
441. #14523954C23semidirect
442. C8×Dic67C23semidirect
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
550. D4×D67#41semidirect
951. #3311D67semidirect
971. C67#61156semidirect
979. #556C2×D67semidirect
1025. #489C2×D67semidirect
1033. #485C2×D67semidirect
1041. #482C2×D67semidirect
1051. #476C2×D67semidirect
1055. #470C2×D67semidirect
1069. #465C2×D67semidirect
1073. #464C2×D67semidirect
1081. #452C2×D67semidirect
1085. #450C2×D67semidirect
1097. #440C2×D67semidirect
1107. #435C2×D67semidirect
1126. #418C2×D67semidirect
1135. #416C2×D67semidirect
1177. C2×Q16C22×D67semidirect
1201. C22×C8C22×D67semidirect
1203. C4⋊Q8C22×D67semidirect
1254. C22⋊Q8C22×D67semidirect
1290. C4×Q8C22×D67semidirect
1330. #117C22×D67semidirect
1364. #107C22×D67semidirect
1369. #106C22×D67semidirect
1370. #106C22×D67semidirect
1374. C4⋊C8C22×D67semidirect
1385. #103C22×D67semidirect
1386. #103C22×D67semidirect
1387. #103C22×D67semidirect
1388. #103C22×D67semidirect
1422. C22⋊C8C22×D67semidirect
1424. #97C22×D67semidirect

Maximal subgroups

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

subgroupindex
#225737702
#546×D672
#225724312
#225724292
#225724082
#225724062
#225723672
#225723652
#225722972
#225722952
#225722392
#225721692
#225721672
#225720622
#225720602
#225720392
#225720372
#225705942
#225701562
#225701482
#225700072
#225698382
#225698212
#225697002
#225694522
#225694372
#225690142
#225689422
#225687242
#418×D672
C67×#33112
#6115667