Finite Group Databasebeta

← #31752541

Subgroups — #31752541

Order 17152.

1754 conjugacy classes of subgroups.

The subgroup lattice has 1682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574153C211yesmaximal, characteristic, complemented
2#22573148C211yesmaximal, characteristic, complemented
3#22573104C211yesmaximal, characteristic, complemented
4#22573001C211yesmaximal, characteristic, complemented
5#22572977C211yesmaximal, characteristic, complemented
6#22572754C211yesmaximal, characteristic, complemented
7#22572679C211yesmaximal, characteristic, complemented
8#22572673C211yesmaximal, characteristic, complemented
9#22572658C211yesmaximal, characteristic, complemented
10#22572582C211yesmaximal, characteristic, complemented
11#22572560C211yesmaximal, characteristic, complemented
12#22572344C211yesmaximal, characteristic, complemented
13#22572284C211yesmaximal, characteristic, complemented
14#22572239C211yesmaximal, characteristic, complemented
15#22572164C211yesmaximal, characteristic, complemented
16#22572053C211yesmaximal, characteristic, complemented
17#22572027C211yesmaximal, characteristic, complemented
18#22571674C211yesmaximal, characteristic, complemented
19#22571620C211yesmaximal, characteristic, complemented
20#22571556C211yesmaximal, characteristic, complemented
21#22571507C211yesmaximal, characteristic, complemented
22#22571462C211yesmaximal, characteristic, complemented
23#22571439C211yesmaximal, characteristic, complemented
24#22570480C211yesmaximal, characteristic, complemented
25#22570387C211yesmaximal, characteristic, complemented
26#22570343C211yesmaximal, characteristic, complemented
27#22570067C211yesmaximal, characteristic, complemented
28#22570034C211yesmaximal, characteristic, complemented
29C2×#16863683C211yesmaximal, characteristic, complemented
30#22569348C211yesmaximal, characteristic, complemented
31C67×#3552C211yesmaximal, characteristic, complemented
32#16864131C2211yescharacteristic
33#16864106C2211yescharacteristic
34#16864097—21no—
35#16864092C2211yescharacteristic
36#16864086C2211yescharacteristic
37#16864073—21no—
38#16864071—21no—
39#16864050C2211yescharacteristic
40#16864042C2211yescharacteristic
41#16864042C2211yescharacteristic
42#16864035—21no—
43D4×D268C2211yescharacteristic
44#16864017C2211yescharacteristic
45#16864001C2211yescharacteristic
46#16863994—21no—
47#16863980—21no—
48#16863930C2211yescharacteristic
49#16863904—21no—
50#123×D67—21no—
51#16863876C2211yescharacteristic
52#16863870C2211yescharacteristic
53C2×C4×D268C2211yescharacteristic
54#16863806C2211yescharacteristic, complemented
55#16863802C2211yescharacteristic, complemented
56#16863802C2211yescharacteristic, complemented
57#16863802C2211yescharacteristic, complemented
58#16863795C2211yescharacteristic, complemented
59#16863792C2211yescharacteristic, complemented
60#16863762C2211yescharacteristic
61#16863758C2211yescharacteristic, complemented
62#16863758C2211yescharacteristic, complemented
63#16863758C2211yescharacteristic, complemented
64#16863753C2211yescharacteristic, complemented
65#16863744C2211yescharacteristic
66#16863737C2211yescharacteristic, complemented
67#16863734C2211yescharacteristic, complemented
68#16863731C2211yescharacteristic, complemented
69#16863731C2211yescharacteristic, complemented
70#16863726C2211yescharacteristic, complemented
71#16863724C2211yescharacteristic, complemented
72#16863724C2211yescharacteristic, complemented
73#16863720C2211yescharacteristic
74#16863720C2211yescharacteristic, complemented
75#16863720C2211yescharacteristic, complemented
76#16863717C2211yescharacteristic, complemented
77#16863714C2211yescharacteristic
78#16863714C2211yescharacteristic
79#16863714C2211yescharacteristic
80#16863714C2211yescharacteristic, complemented
81#16863712C2211yescharacteristic, complemented
82#16863709C2211yescharacteristic, complemented
83#16863707C2211yescharacteristic, complemented
84#16863703C2211yescharacteristic, complemented
85#16863703C2211yescharacteristic, complemented
86#16863700C2211yescharacteristic, complemented
87#16863700C2211yescharacteristic, complemented
88#16863696C2211yescharacteristic, complemented
89#16863696C2211yescharacteristic, complemented
90#16863693C2211yescharacteristic
91#16863693C2211yescharacteristic
92#16863693C2211yescharacteristic
93#16863693C2211yescharacteristic, complemented
94#16863693C2211yescharacteristic, complemented
95#16863693C2211yescharacteristic, complemented
96#16863686C2211yescharacteristic, complemented
97#16863683C2211yescharacteristic
98#16863683C2211yescharacteristic
99#16863683C2211yescharacteristic
100#16863683C2211yescharacteristic
101#16863683C2211yescharacteristic
102#16863683C2211yescharacteristic, complemented
103#16863683C2211yescharacteristic, complemented
104#16863683C2211yescharacteristic, complemented
105#16863683C2211yescharacteristic, complemented
106#16863683C2211yescharacteristic, complemented
107#16863681C2211yescharacteristic, complemented
108#16863678C2211yescharacteristic, complemented
109#16863678C2211yescharacteristic, complemented
110#16863678C2211yescharacteristic, complemented
111#16863673C2211yescharacteristic
112#16863673C2211yescharacteristic, complemented
113#16863673C2211yescharacteristic, complemented
114#16863652C2211yescharacteristic, complemented
115#16863647C2211yescharacteristic
116#16863647C2211yescharacteristic, complemented
117#16863644C2211yescharacteristic, complemented
118#16863635C2211yescharacteristic, complemented
119#16863630C2211yescharacteristic
120#16863630C2211yescharacteristic, complemented
121#16863627C2211yescharacteristic
122#16863627C2211yescharacteristic
123#16863627C2211yescharacteristic, complemented
124#16863623C2211yescharacteristic, complemented
125#16863623C2211yescharacteristic, complemented
126#16863618C2211yescharacteristic, complemented
127#16863618C2211yescharacteristic, complemented
128#16863615C2211yescharacteristic, complemented
129#16863611C2211yescharacteristic, complemented
130#16863611C2211yescharacteristic, complemented
131#16863608C2211yescharacteristic
132#16863608C2211yescharacteristic, complemented
133#16863608C2211yescharacteristic, complemented
134#16863596C2211yescharacteristic
135#16863591C2211yescharacteristic
136#16863556C2211yescharacteristic
137#16863546C2211yescharacteristic
138#16863546C2211yescharacteristic
139#16863539C2211yescharacteristic
140#16863529C2211yescharacteristic
141#16863529C2211yescharacteristic
142#16863527C2211yescharacteristic, complemented
143#16863527C2211yescharacteristic, complemented
144#16863506C2211yescharacteristic
145#16863506C2211yescharacteristic
146#16863506C2211yescharacteristic, complemented
147#16863506C2211yescharacteristic, complemented
148#16863501C2211yescharacteristic, complemented
149#16863494C2211yescharacteristic
150#16863494C2211yescharacteristic
151#16863494C2211yescharacteristic, complemented
152C4×#11761615C2211yescharacteristic
153C4×#11761615C2211yescharacteristic, complemented
154C4×#11761616C2211yescharacteristic, complemented
155C4×#11761613C2211yescharacteristic
156#16863468C2211yescharacteristic
157#16863468C2211yescharacteristic, complemented
158#16863468C2211yescharacteristic, complemented
159#16863468C2211yescharacteristic, complemented
160D4×C67⋊C8C2211yescharacteristic
161D4×C67⋊C8C2211yescharacteristic, complemented
162#16863457C2211yescharacteristic, complemented
163#16863457C2211yescharacteristic, complemented
164#16863453C2211yescharacteristic, complemented
165#16863439C2211yescharacteristic, complemented
166#16863436C2211yescharacteristic, complemented
167#16863432C2211yescharacteristic, complemented
168C2×#14523974C2211yescharacteristic, complemented
169C2×#14523974C2211yescharacteristic, complemented
170C2×#14523974C2211yescharacteristic, complemented
171#16863423C2211yescharacteristic, complemented
172#16863423C2211yescharacteristic, complemented
173C2×C4⋊(C67⋊C8)C2211yescharacteristic, complemented
174#16863400C2211yescharacteristic
175#16863395C2211yescharacteristic
176#16863390C2211yescharacteristic
177C2×#14523963C2211yescharacteristic
178C2×#14523963C2211yescharacteristic
179C2×#14523963C2211yescharacteristic
180#563×C67—21no—
181#563×C67—21no—
182#557×C67C2211yescharacteristic, complemented
183#556×C67C2211yescharacteristic, complemented
184#554×C67C2211yescharacteristic
185#554×C67C2211yescharacteristic, complemented
186#553×C67C2211yescharacteristic
187#553×C67C2211yescharacteristic, complemented
188D4×Q8×C67—21no—
189D4×Q8×C67C2211yescharacteristic, complemented
190#548×C67—21no—
191#547×C67C2211yescharacteristic, complemented
192#544×C67C2211yescharacteristic, complemented
193#544×C67C2211yescharacteristic, complemented
194#542×C67C2211yescharacteristic, complemented
195#542×C67C2211yescharacteristic, complemented
196#541×C67—21no—
197#539×C67—21no—
198#539×C67—21no—
199#536×C67—21no—
200C2×C4⋊Q8×C67C2211yescharacteristic, complemented
201#529×C67C2211yescharacteristic
202#529×C67C2211yescharacteristic, complemented
203C2×#11761628C2311yescharacteristic
204C2×#11761627—21no—
205C22×D268C2311yescharacteristic
206C22×D268C2311yescharacteristic
207C2×D4×D67—21no—
208C22×C4×D67—21no—
209C2×#11761618C2311yescharacteristic
210C2×#11761616C2311yescharacteristic
211C2×#11761615C2311yescharacteristic
212C2×#11761615C2311yescharacteristic
213C2×#11761615C2311yescharacteristic
214C2×#11761613C2311yescharacteristic
215C2×#11761613C2311yescharacteristic
216C2×#11761613C2311yescharacteristic
217C2×#11761612C2311yescharacteristic
218C2×#11761612C2311yescharacteristic
219C22×C67⋊C8C2311yescharacteristic
220C22×C67⋊C8C2311yescharacteristic
221C22×C67⋊C8C2311yescharacteristic
222C22×C67⋊C8C2311yescharacteristic
223#14524043C2311yescharacteristic
224#14524040C2311yescharacteristic
225#14524038—21no—
226#14524038—21no—
227#14524037—21no—
228#14524036—21no—
229#14524035C2311yescharacteristic
230#14524035C2311yescharacteristic
231#14524033—21no—
232#14524032—21no—
233#14524031C2311yescharacteristic
234#14524031C2311yescharacteristic
235#14524029—21no—
236#14524028—21no—
237#14524028—21no—
238#14524028—21no—
239#14524028—21no—
240#14524028—21no—
241#14524028—21no—
242#14524027—21no—
243#14524027—21no—
244#14524026—21no—
245#14524025—21no—
246#14524025—21no—
247#14524024—21no—
248#14524023—21no—
249#14524022C2311yescharacteristic
250#14524022C2311yescharacteristic
251#14524021—21no—
252#14524021—21no—
253#14524021—21no—
254#14524019—21no—
255#14524018—21no—
256#14524017C2311yescharacteristic
257#14524017C2311yescharacteristic
258#14524017C2311yescharacteristic
259#14524017C2311yescharacteristic
260#14524016—21no—
261#14524016—21no—
262#14524016—21no—
263#14524016—21no—
264#14524015—21no—
265#14524013—21no—
266#14524013—21no—
267#14524011—21no—
268#14524011—21no—
269C4×Dic134C2311yescharacteristic
270C4×Dic134C2311yescharacteristic
271C4×D268—21no—
272C4×D268—21no—
273C4×D268C2311yescharacteristic
274C4×D268C2311yescharacteristic
275C4×D268C2311yescharacteristic
276C4×D268C2311yescharacteristic
277C4×D268C2311yescharacteristic
278C4×D268C2311yescharacteristic
279C4×D268C2311yescharacteristic
280C4×D268C2311yescharacteristic
281#14524005—21no—
282#14524005—21no—
283#14524005—21no—
284C4×C22⋊D67—21no—
285(C22⋊D67)⋊C4—21no—
286(C22⋊D67)⋊C4—21no—
287(C22⋊D67)⋊C4—21no—
288#14524002C2311yescharacteristic
289#14524001—21no—
290#14524000—21no—
291#14523999—21no—
292C2×C4⋊Dic67C2311yescharacteristic
293C2×C4⋊Dic67C2311yescharacteristic
294C4⋊C4×D67—21no—
295C4⋊C4×D67—21no—
296C2×(C2×D67)⋊C4—21no—
297C22⋊C4×D67—21no—
298C22⋊C4×D67—21no—
299C22⋊C4×D67—21no—
300C22⋊C4×D67—21no—
301#14523976C2311yescharacteristic
302#14523976C2311yescharacteristic
303#14523976C2311yescharacteristic
304#14523976C2311yescharacteristic
305#14523976C2311yescharacteristic
306#14523976C2311yescharacteristic
307#14523976C2311yescharacteristic
308#14523976C2311yescharacteristic
309#14523974C2311yescharacteristic
310#14523974C2311yescharacteristic
311#14523974C2311yescharacteristic
312#14523974C2311yescharacteristic
313#14523974C2311yescharacteristic
314#14523974C2311yescharacteristic
315#14523974C2311yescharacteristic
316#14523974C2311yescharacteristic
317#14523974C2311yescharacteristic
318#14523974C2311yescharacteristic
319#14523974C2311yescharacteristic
320#14523974C2311yescharacteristic
321#14523974C2311yescharacteristic
322#14523974C2311yescharacteristic
323#14523974C2311yescharacteristic
324#14523974C2311yescharacteristic
325C4⋊(C67⋊C8)C2311yescharacteristic
326C4⋊(C67⋊C8)C2311yescharacteristic
327C4⋊(C67⋊C8)C2311yescharacteristic
328C4⋊(C67⋊C8)C2311yescharacteristic
329C4⋊(C67⋊C8)C2311yescharacteristic
330C4⋊(C67⋊C8)C2311yescharacteristic
331C4⋊(C67⋊C8)C2311yescharacteristic
332C4⋊(C67⋊C8)C2311yescharacteristic
333C4⋊(C67⋊C8)C2311yescharacteristic
334C4⋊(C67⋊C8)C2311yescharacteristic
335#14523967C2311yescharacteristic
336#14523967C2311yescharacteristic
337#14523967C2311yescharacteristic
338#14523967C2311yescharacteristic
339#14523966C2311yescharacteristic
340#14523966C2311yescharacteristic
341#14523966C2311yescharacteristic
342#14523966C2311yescharacteristic
343#14523966C2311yescharacteristic
344#14523966C2311yescharacteristic
345#14523964C2311yescharacteristic
346#14523964C2311yescharacteristic
347#14523964C2311yescharacteristic
348#14523964C2311yescharacteristic
349#14523963C2311yescharacteristic
350#14523963C2311yescharacteristic
351#14523963C2311yescharacteristic
352#14523963C2311yescharacteristic
353#14523963C2311yescharacteristic
354#14523963C2311yescharacteristic
355#14523963C2311yescharacteristic
356#14523963C2311yescharacteristic
357#14523963C2311yescharacteristic
358#14523963C2311yescharacteristic
359#14523963C2311yescharacteristic
360#14523963C2311yescharacteristic
361#14523963C2311yescharacteristic
362#14523963C2311yescharacteristic
363#14523963C2311yescharacteristic
364#14523963C2311yescharacteristic
365#14523963C2311yescharacteristic
366#14523963C2311yescharacteristic
367C22⋊(C67⋊C8)C2311yescharacteristic
368C22⋊(C67⋊C8)C2311yescharacteristic
369C22⋊(C67⋊C8)C2311yescharacteristic
370C22⋊(C67⋊C8)C2311yescharacteristic
371C22⋊(C67⋊C8)C2311yescharacteristic
372C22⋊(C67⋊C8)C2311yescharacteristic
373#14523954C2311yescharacteristic
374#14523954C2311yescharacteristic
375#14523954C2311yescharacteristic
376#14523954C2311yescharacteristic
377C4×C67⋊C8C2311yescharacteristic
378C4×C67⋊C8C2311yescharacteristic
379C2×#41×C67—21no—
380C22×Q8×C67—21no—
381C22×Q8×C67—21no—
382C4⋊Q8×C67—21no—
383C4⋊Q8×C67—21no—
384C4⋊Q8×C67—21no—
385C4⋊Q8×C67—21no—
386C4⋊Q8×C67—21no—
387C4⋊Q8×C67C2311yescharacteristic
388C4⋊Q8×C67C2311yescharacteristic
389C4⋊Q8×C67C2311yescharacteristic
390C4⋊Q8×C67C2311yescharacteristic
391C4⋊Q8×C67C2311yescharacteristic
392C4⋊Q8×C67C2311yescharacteristic
393#126×C67—21no—
394#126×C67—21no—
395#126×C67—21no—
396#126×C67—21no—
397#126×C67—21no—
398#126×C67—21no—
399#126×C67—21no—
400#126×C67D411yescharacteristic
401#126×C67D411yescharacteristic
402#125×C67—21no—
403#125×C67—21no—
404#125×C67—21no—
405#125×C67—21no—
406#125×C67—21no—
407#125×C67—21no—
408#125×C67D411yescharacteristic
409#125×C67C2311yescharacteristic
410#125×C67C2311yescharacteristic
411#125×C67C2311yescharacteristic
412#124×C67—21no—
413#124×C67—21no—
414#124×C67—21no—
415#124×C67D411yescharacteristic
416#124×C67C2311yescharacteristic
417#123×C67—21no—
418#123×C67—21no—
419#123×C67—21no—
420#123×C67—21no—
421#123×C67—21no—
422#123×C67—21no—
423#123×C67—21no—
424#123×C67D411yescharacteristic
425#123×C67D411yescharacteristic
426C22⋊Q8×C67—21no—
427C22⋊Q8×C67—21no—
428C22⋊Q8×C67—21no—
429C22⋊Q8×C67—21no—
430C22⋊Q8×C67—21no—
431C22⋊Q8×C67—21no—
432C22⋊Q8×C67—21no—
433C22⋊Q8×C67—21no—
434C22⋊Q8×C67—21no—
435C22⋊Q8×C67—21no—
436C22⋊Q8×C67—21no—
437C22⋊Q8×C67—21no—
438C22⋊Q8×C67—21no—
439C22⋊Q8×C67—21no—
440C22⋊Q8×C67D411yescharacteristic
441C22⋊Q8×C67C2311yescharacteristic
442C22⋊Q8×C67C2311yescharacteristic
443C22⋊Q8×C67C2311yescharacteristic
444#121×C67—21no—
445#121×C67—21no—
446#121×C67D411yescharacteristic
447#121×C67C2311yescharacteristic
448#121×C67C2311yescharacteristic
449#121×C67C2311yescharacteristic
450C4×Q8×C67—21no—
451C4×Q8×C67—21no—
452C4×Q8×C67C2311yescharacteristic
453C4×Q8×C67C2311yescharacteristic
454C4×Q8×C67C2311yescharacteristic
455C4×Q8×C67C2311yescharacteristic
456C4×D4×C67—21no—
457C4×D4×C67—21no—
458C4×D4×C67—21no—
459C4×D4×C67—21no—
460C4×D4×C67—21no—
461C4×D4×C67C2311yescharacteristic
462C4×D4×C67C2311yescharacteristic
463C4×D4×C67C2311yescharacteristic
464C4×D4×C67C2311yescharacteristic
465C4×D4×C67C2311yescharacteristic
466C4×D4×C67C2311yescharacteristic
467#117×C67—21no—
468#117×C67C2311yescharacteristic
469#117×C67C2311yescharacteristic
470#117×C67C2311yescharacteristic
471#117×C67C2311yescharacteristic
472C2×C4⋊C4×C67—21no—
473C2×C4⋊C4×C67C2311yescharacteristic
474C2×C4⋊C4×C67C2311yescharacteristic
475C2×C4⋊C4×C67C2311yescharacteristic
476C2×C4⋊C4×C67C2311yescharacteristic
477C2×C42×C67C2311yescharacteristic
478C23×D67—21no—
479C23×D67—21no—
480#11761628—22no—
481#11761628—41no—
482#11761627—82no—
483C2×Dic134—21no—
484C2×Dic134C2411yescharacteristic
485C2×D268—22no—
486C2×D268—22no—
487C2×D268—21no—
488C2×D268—21no—
489C2×D268—21no—
490C2×D268—21no—
491C2×D268—41no—
492C2×D268—41no—
493C2×D268C2411yescharacteristic
494C2×D268C2411yescharacteristic
495C2×D268C2411yescharacteristic
496C2×C22⋊D67—21no—
497C2×C22⋊D67—21no—
498C2×C22⋊D67—21no—
499C2×C22⋊D67—21no—
500C2×C22⋊D67—21no—
501D4×D67—82no—
502C22×Dic67—21no—
503C22×Dic67—21no—
504C2×C4×D67—21no—
505C2×C4×D67—21no—
506C2×C4×D67—21no—
507C2×C4×D67—21no—
508C2×C4×D67—21no—
509C2×C4×D67—21no—
510C2×C4×D67—21no—
511C2×C4×D67—21no—
512C2×C4×D67—21no—
513C2×C4×D67—82no—
514#11761618—41no—
515#11761616—41no—
516#11761615—22no—
517#11761615—41no—
518#11761615—41no—
519#11761613—22no—
520#11761613—41no—
521#11761613—41no—
522#11761612—41no—
523#11761612—41no—
524C2×C67⋊C8—41no—
525C2×C67⋊C8—41no—
526C2×C67⋊C8—41no—
527C2×C67⋊C8—41no—
528C2×C67⋊C8C2411yescharacteristic
529C2×C67⋊C8C2411yescharacteristic
530C2×C67⋊C8C2411yescharacteristic
531C2×C67⋊C8C2411yescharacteristic
532C2×C67⋊C8C2411yescharacteristic
533C2×C67⋊C8C2411yescharacteristic
534C2×C67⋊C8C2411yescharacteristic
535C2×C67⋊C8C2411yescharacteristic
536C4⋊Dic67—21no—
537C4⋊Dic67—21no—
538C4⋊Dic67—21no—
539C4⋊Dic67C2411yescharacteristic
540C4⋊Dic67C2411yescharacteristic
541C4⋊Dic67C2411yescharacteristic
542C4⋊Dic67C2411yescharacteristic
543Dic67⋊C4—21no—
544Dic67⋊C4—21no—
545Dic67⋊C4—21no—
546Dic67⋊C4—21no—
547Dic67⋊C4—21no—
548Dic67⋊C4—21no—
549Dic67⋊C4—21no—
550Dic67⋊C4—21no—
551C22⋊Dic67—21no—
552C22⋊Dic67—21no—
553C22⋊Dic67—21no—
554(C2×D67)⋊C4—21no—
555(C2×D67)⋊C4—21no—
556(C2×D67)⋊C4—21no—
557(C2×D67)⋊C4—21no—
558(C2×D67)⋊C4—21no—
559(C2×D67)⋊C4—21no—
560(C2×D67)⋊C4—21no—
561(C2×D67)⋊C4—21no—
562(C2×D67)⋊C4—21no—
563(C2×D67)⋊C4—21no—
564(C2×D67)⋊C4—21no—
565(C2×D67)⋊C4—21no—
566(C2×D67)⋊C4—21no—
567(C2×D67)⋊C4—21no—
568(C2×D67)⋊C4—21no—
569(C2×D67)⋊C4—21no—
570C4×Dic67—21no—
571C4×Dic67—21no—
572C4×Dic67—21no—
573#41×C67—82no—
574C2×Q8×C67—21no—
575C2×Q8×C67—21no—
576C2×Q8×C67—21no—
577C2×Q8×C67—21no—
578C2×Q8×C67—21no—
579C2×Q8×C67—21no—
580C2×Q8×C67—82no—
581C2×Q8×C67—82no—
582C2×Q8×C67C2×D411yescharacteristic
583C2×Q8×C67C2411yescharacteristic
584C2×D4×C67—21no—
585C2×D4×C67—21no—
586C2×D4×C67—21no—
587C2×D4×C67C2×D411yescharacteristic
588C2×D4×C67C2×D411yescharacteristic
589C2×D4×C67C2×D411yescharacteristic
590C2×D4×C67C2411yescharacteristic
591C22×C4×C67—21no—
592C22×C4×C67—21no—
593C22×C4×C67—21no—
594C22×C4×C67—21no—
595C22×C4×C67—21no—
596C22×C4×C67—21no—
597C22×C4×C67—21no—
598C22×C4×C67C2×D411yescharacteristic
599C22×C4×C67C2×D411yescharacteristic
600C22×C4×C67C2411yescharacteristic
601C22×C4×C67C2411yescharacteristic
602C22×C4×C67C2411yescharacteristic
603C4⋊C4×C67—21no—
604C4⋊C4×C67—21no—
605C4⋊C4×C67—21no—
606C4⋊C4×C67—21no—
607C4⋊C4×C67—21no—
608C4⋊C4×C67—21no—
609C4⋊C4×C67—21no—
610C4⋊C4×C67—21no—
611C4⋊C4×C67—21no—
612C4⋊C4×C67—21no—
613C4⋊C4×C67—21no—
614C4⋊C4×C67—21no—
615C4⋊C4×C67—21no—
616C4⋊C4×C67—21no—
617C4⋊C4×C67—21no—
618C4⋊C4×C67—21no—
619C4⋊C4×C67—21no—
620C4⋊C4×C67—21no—
621C4⋊C4×C67—21no—
622C4⋊C4×C67—21no—
623C4⋊C4×C67—21no—
624C4⋊C4×C67—21no—
625C4⋊C4×C67C2×D411yescharacteristic
626C4⋊C4×C67C2×D411yescharacteristic
627C4⋊C4×C67C2×D411yescharacteristic
628C4⋊C4×C67C2×D411yescharacteristic
629C4⋊C4×C67C2×D411yescharacteristic
630C4⋊C4×C67C2×D411yescharacteristic
631C4⋊C4×C67C2×D411yescharacteristic
632C4⋊C4×C67C2×D411yescharacteristic
633C4⋊C4×C67C2×D411yescharacteristic
634C4⋊C4×C67C2×D411yescharacteristic
635C4⋊C4×C67C2411yescharacteristic
636C4⋊C4×C67C2411yescharacteristic
637C4⋊C4×C67C2411yescharacteristic
638C4⋊C4×C67C2411yescharacteristic
639C4⋊C4×C67C2411yescharacteristic
640C4⋊C4×C67C2411yescharacteristic
641C22⋊C4×C67—21no—
642C22⋊C4×C67—21no—
643C22⋊C4×C67—21no—
644C22⋊C4×C67—21no—
645C22⋊C4×C67—21no—
646C22⋊C4×C67—21no—
647C22⋊C4×C67—21no—
648C22⋊C4×C67—21no—
649C22⋊C4×C67—21no—
650C22⋊C4×C67—21no—
651C22⋊C4×C67—21no—
652C22⋊C4×C67—21no—
653C22⋊C4×C67—21no—
654C22⋊C4×C67C2×D411yescharacteristic
655C22⋊C4×C67C2×D411yescharacteristic
656C22⋊C4×C67C2×D411yescharacteristic
657C22⋊C4×C67C2×D411yescharacteristic
658C22⋊C4×C67C2×D411yescharacteristic
659C22⋊C4×C67C2×D411yescharacteristic
660C22⋊C4×C67C2×D411yescharacteristic
661C22⋊C4×C67C2×D411yescharacteristic
662C22⋊C4×C67C2×D411yescharacteristic
663C22⋊C4×C67C2×D411yescharacteristic
664C42×C67—21no—
665C42×C67—21no—
666C42×C67—21no—
667C42×C67—21no—
668C42×C67—21no—
669C42×C67C2×D411yescharacteristic
670C42×C67C2×D411yescharacteristic
671C42×C67C2411yescharacteristic
672C42×C67C2411yescharacteristic
673C42×C67C2411yescharacteristic
674C42×C67C2411yescharacteristic
675C23×C67—21no—
676C23×C67C22×D411yescharacteristic
677C23×C67C22×D411yescharacteristic
678C23×C67C22×D411yescharacteristic
679C22×D67—21no—
680C22×D67—21no—
681C22×D67—21no—
682C22×D67—42no—
683C22×D67—42no—
684C22×D67—42no—
685C22×D67—81no—
686C22×D67—81no—
687C22×D67—81no—
688Q8×C67—21no—
689Q8×C67—21no—
690Q8×C67—41no—
691Q8×C67—42no—
692Q8×C67—42no—
693Q8×C67—81no—
694Q8×C67—81no—
695Q8×C67—81no—
696Q8×C67—81no—
697D4×C67—22no—
698D4×C67—22no—
699D4×C67—21no—
700D4×C67—21no—
701D4×C67—41no—
702D4×C67—42no—
703D4×C67—81no—
704D4×C67—81no—
705C2×C4×C67—22no—
706C2×C4×C67—21no—
707C2×C4×C67—21no—
708C2×C4×C67—21no—
709C2×C4×C67—21no—
710C2×C4×C67—21no—
711C2×C4×C67—21no—
712C2×C4×C67—21no—
713C2×C4×C67—21no—
714C2×C4×C67—21no—
715C2×C4×C67—21no—
716C2×C4×C67—21no—
717C2×C4×C67—21no—
718C2×C4×C67—21no—
719C2×C4×C67—41no—
720C2×C4×C67—42no—
721C2×C4×C67—81no—
722C2×C4×C67—81no—
723C2×C4×C67—81no—
724C2×C4×C67—81no—
725C2×C4×C67—81no—
726C2×C4×C67—81no—
727C2×C4×C67C22×D411yescharacteristic
728C2×C4×C67C22×D411yescharacteristic
729C2×C4×C67C22×D411yescharacteristic
730C2×C4×C67C22×D411yescharacteristic
731C2×C4×C67C22×D411yescharacteristic
732C2×C4×C67C22×D411yescharacteristic
733C2×C4×C67C22×D411yescharacteristic
734C2×C4×C67C22×D411yescharacteristic
735C2×C4×C67C22×D411yescharacteristic
736C2×C4×C67C22×D411yescharacteristic
737C2×C4×C67C22×D411yescharacteristic
738C2×C4×C67C2511yescharacteristic
739C22⋊D67—42no—
740C22⋊D67—42no—
741C22⋊D67—81no—
742C22⋊D67—81no—
743C22⋊D67—81no—
744C2×Dic67—21no—
745C2×Dic67—21no—
746C2×Dic67—21no—
747C2×Dic67—21no—
748C2×Dic67—21no—
749C2×Dic67—42no—
750C2×Dic67—81no—
751D268—21no—
752D268—21no—
753D268—21no—
754D268—21no—
755D268—21no—
756D268—42no—
757D268—42no—
758D268—81no—
759D268—81no—
760D2682−1+412yes—
761C4×D67—42no—
762C4×D67—81no—
763C4×D67—81no—
764C4×D67—81no—
765C4×D67—81no—
766C4×D67—81no—
767C4×D67—81no—
768C4×D67—81no—
769C4×D67—81no—
770Dic134—21no—
771Dic134—21no—
772Dic134—81no—
773C67⋊C8—21no—
774C67⋊C8—21no—
775C67⋊C8—21no—
776C67⋊C8—21no—
777C67⋊C8—21no—
778C67⋊C8—21no—
779C67⋊C8—21no—
780C67⋊C8—21no—
781C22×C67—21no—
782C22×C67—21no—
783C22×C67—21no—
784C22×C67—21no—
785C22×C67—21no—
786C22×C67—21no—
787C22×C67—21no—
788C22×C67—21no—
789C22×C67—41no—
790C22×C67—41no—
791C22×C67—41no—
792C22×C67#57712yes—
793C22×C67C23×D411yescharacteristic
794C2×D67—22no—
795C2×D67—41no—
796C2×D67—41no—
797C2×D67—41no—
798C2×D67—41no—
799C2×D67—41no—
800C2×D67—41no—
801C2×D67—41no—
802C2×D67—41no—
803C2×D67—84no—
804C2×D67—162no—
805C4×C67—21no—
806C4×C67—21no—
807C4×C67—21no—
808C4×C67—21no—
809C4×C67—21no—
810C4×C67—21no—
811C4×C67—21no—
812C4×C67—21no—
813C4×C67—21no—
814C4×C67—21no—
815C4×C67—21no—
816C4×C67—41no—
817C4×C67—41no—
818C4×C67—41no—
819C4×C67—41no—
820C4×C67—41no—
821C4×C67—41no—
822C4×C67—41no—
823C4×C67C2×2−1+411yescharacteristic
824C4×C67#58511yescharacteristic
825Dic67—41no—
826Dic67—41no—
827Dic67—41no—
828Dic67—41no—
829Dic67—41no—
830#62156—671nomaximal, Sylow
831C2×C67—22no—
832C2×C67—41no—
833C2×C67—41no—
834C2×C67—81no—
835C2×C67#348911yescharacteristic
836C2×C67C2×#57711yescharacteristic
837C2×C67#358511yescharacteristic
838D67—42no—
839D67—81no—
840D67—81no—
841#3552D6711yescharacteristic, complemented
842#3513—671no—
843#3388—671no—
844#3384—671no—
845#3373—671no—
846#3371—671no—
847#3350—671no—
848#3345—671no—
849#3345—671no—
850#3344—671no—
851#3337—671no—
852#3335—671no—
853#3318—671no—
854#3314—671no—
855#3311—671no—
856#3306—671no—
857#3297—671no—
858#3295—671no—
859#3263—671no—
860#3257—671no—
861#3250—671no—
862#3244—671no—
863#3241—671no—
864#3239—671no—
865#3125—671no—
866#3118—671no—
867#3114—671no—
868#3084—671no—
869#3081—671no—
870C2×#476—671no—
871#2992—671no—
872C67#6215611yescharacteristic, complemented, Sylow
873#563—21no—
874#563—21no—
875#559—671no—
876#557C2×D6711yescharacteristic, complemented
877#556C2×D6711yescharacteristic, complemented
878#554—671no—
879#554C2×D6711yescharacteristic
880#554C2×D6711yescharacteristic, complemented
881#553—671no—
882#553—1341no—
883#553C2×D6711yescharacteristic
884#553C2×D6711yescharacteristic, complemented
885#552—671no—
886#551—1341no—
887#551—1341no—
888D4×Q8—21no—
889D4×Q8C2×D6711yescharacteristic, complemented
890#548—21no—
891#547—671no—
892#547C2×D6711yescharacteristic, complemented
893#546—671no—
894#546—671no—
895#546—1341no—
896D42—671no—
897#544C2×D6711yescharacteristic, complemented
898#544C2×D6711yescharacteristic, complemented
899#542—671no—
900#542C2×D6711yescharacteristic, complemented
901#542C2×D6711yescharacteristic, complemented
902#541—21no—
903#540—671no—
904#539—21no—
905#539—21no—
906#539—1341no—
907#538—1341no—
908#536—21no—
909C2×C4⋊Q8C2×D6711yescharacteristic, complemented
910#529—671no—
911#529C2×D6711yescharacteristic
912#529C2×D6711yescharacteristic, complemented
913#525—1341no—
914C2×#123—1341no—
915#520—671no—
916#518—671no—
917C2×C4×D4—671no—
918#501—671no—
919#501—671no—
920#501—671no—
921#501—671no—
922#499—671no—
923#498—671no—
924#490—671no—
925#489—671no—
926#489—671no—
927#489—671no—
928#488—671no—
929#486—671no—
930#485—671no—
931#485—671no—
932#484—671no—
933#484—671no—
934#483—671no—
935#483—671no—
936#483—671no—
937#482—671no—
938#482—671no—
939#482—671no—
940#482—671no—
941#481—671no—
942#481—671no—
943#481—671no—
944#481—671no—
945#481—671no—
946#480—671no—
947#480—671no—
948#479—671no—
949#479—671no—
950#479—671no—
951#479—671no—
952#478—671no—
953#478—671no—
954#478—671no—
955#478—671no—
956#478—671no—
957#478—671no—
958#478—671no—
959#478—671no—
960#476—671no—
961#476—671no—
962#476—671no—
963#476—671no—
964#476—671no—
965#476—671no—
966#476—671no—
967#476—671no—
968#476—671no—
969#476—671no—
970#476—671no—
971#475—671no—
972#475—671no—
973#475—671no—
974#475—671no—
975#474—671no—
976#474—671no—
977#474—671no—
978#470—671no—
979#469—671no—
980#469—671no—
981#468—671no—
982#467—671no—
983#466—671no—
984#466—671no—
985#465—671no—
986#465—671no—
987#465—671no—
988#465—671no—
989#465—671no—
990#464—671no—
991#464—671no—
992#464—671no—
993#463—671no—
994#463—671no—
995#463—671no—
996#463—671no—
997#463—671no—
998#460—671no—
999#459—671no—
1000#452—671no—
1001#450—671no—
1002#450—671no—
1003#449—671no—
1004#447—671no—
1005#447—671no—
1006#446—671no—
1007#446—671no—
1008#442—671no—
1009#442—671no—
1010#442—671no—
1011#442—671no—
1012#441—671no—
1013#440—671no—
1014#440—671no—
1015#440—671no—
1016C4×SD16—671no—
1017C4×SD16—671no—
1018C4×SD16—671no—
1019C4×D8—671no—
1020#435—671no—
1021#435—671no—
1022#435—671no—
1023#435—671no—
1024C8×D4—671no—
1025C8×D4—671no—
1026#433—671no—
1027#433—671no—
1028#432—671no—
1029#428—671no—
1030#428—671no—
1031#427—671no—
1032C2×#106—671no—
1033C2×#106—671no—
1034C2×#106—671no—
1035#424—671no—
1036#424—671no—
1037C2×C4⋊C8—671no—
1038#418—671no—
1039#417—671no—
1040#416—671no—
1041C2×#102—671no—
1042C2×#102—671no—
1043C2×#102—671no—
1044C2×#41—21no—
1045C2×#41—671no—
1046C2×#41—1341no—
1047C22×Q8—21no—
1048C22×Q8—21no—
1049C22×D4—671no—
1050C22×D4—671no—
1051C22×D4—1341no—
1052C23×C4—1341no—
1053C2×Q16—671no—
1054C2×SD16—671no—
1055C2×SD16—671no—
1056C2×SD16—671no—
1057C2×SD16—671no—
1058C2×D8—671no—
1059C2×D8—671no—
1060C2×D8—671no—
1061C2×M16—671no—
1062C2×M16—671no—
1063C22×C8—671no—
1064C22×C8—671no—
1065C22×C8—671no—
1066C22×C8—671no—
1067C4⋊Q8—21no—
1068C4⋊Q8—21no—
1069C4⋊Q8—21no—
1070C4⋊Q8—21no—
1071C4⋊Q8—21no—
1072C4⋊Q8—671no—
1073C4⋊Q8C22×D6711yescharacteristic
1074C4⋊Q8C22×D6711yescharacteristic
1075C4⋊Q8C22×D6711yescharacteristic
1076C4⋊Q8C22×D6711yescharacteristic
1077C4⋊Q8C22×D6711yescharacteristic
1078C4⋊Q8C22×D6711yescharacteristic
1079#127—671no—
1080#126—21no—
1081#126—21no—
1082#126—21no—
1083#126—21no—
1084#126—21no—
1085#126—21no—
1086#126—21no—
1087#126—1341no—
1088#126—1341no—
1089#126—1341no—
1090#126—1341no—
1091#126C22⋊D6711yescharacteristic
1092#126C22⋊D6711yescharacteristic
1093#125—21no—
1094#125—21no—
1095#125—21no—
1096#125—21no—
1097#125—21no—
1098#125—21no—
1099#125—671no—
1100#125—671no—
1101#125—1341no—
1102#125C22⋊D6711yescharacteristic
1103#125C22×D6711yescharacteristic
1104#125C22×D6711yescharacteristic
1105#125C22×D6711yescharacteristic
1106#124—21no—
1107#124—21no—
1108#124—21no—
1109#124—671no—
1110#124—671no—
1111#124—1341no—
1112#124—1341no—
1113#124C22⋊D6711yescharacteristic
1114#124C22×D6711yescharacteristic
1115#123—21no—
1116#123—21no—
1117#123—21no—
1118#123—21no—
1119#123—21no—
1120#123—21no—
1121#123—21no—
1122#123—1341no—
1123#123—1341no—
1124#123—1341no—
1125#123—1341no—
1126#123—1341no—
1127#123—1341no—
1128#123—1341no—
1129#123—1341no—
1130#123—1341no—
1131#123—1341no—
1132#123—1341no—
1133#123—1341no—
1134#123C22⋊D6711yescharacteristic
1135#123C22⋊D6711yescharacteristic
1136C22⋊Q8—21no—
1137C22⋊Q8—21no—
1138C22⋊Q8—21no—
1139C22⋊Q8—21no—
1140C22⋊Q8—21no—
1141C22⋊Q8—21no—
1142C22⋊Q8—21no—
1143C22⋊Q8—21no—
1144C22⋊Q8—21no—
1145C22⋊Q8—21no—
1146C22⋊Q8—21no—
1147C22⋊Q8—21no—
1148C22⋊Q8—21no—
1149C22⋊Q8—21no—
1150C22⋊Q8—671no—
1151C22⋊Q8—671no—
1152C22⋊Q8—1341no—
1153C22⋊Q8—1341no—
1154C22⋊Q8—1341no—
1155C22⋊Q8—1341no—
1156C22⋊Q8—1341no—
1157C22⋊Q8C22⋊D6711yescharacteristic
1158C22⋊Q8C22×D6711yescharacteristic
1159C22⋊Q8C22×D6711yescharacteristic
1160C22⋊Q8C22×D6711yescharacteristic
1161#121—21no—
1162#121—21no—
1163#121—671no—
1164#121—671no—
1165#121—671no—
1166#121—671no—
1167#121—1341no—
1168#121—1341no—
1169#121—1341no—
1170#121—1341no—
1171#121—1341no—
1172#121—1341no—
1173#121C22⋊D6711yescharacteristic
1174#121C22×D6711yescharacteristic
1175#121C22×D6711yescharacteristic
1176#121C22×D6711yescharacteristic
1177#120—1341no—
1178#120—1341no—
1179#120—1341no—
1180#120—1341no—
1181C4×Q8—21no—
1182C4×Q8—21no—
1183C4×Q8—671no—
1184C4×Q8—671no—
1185C4×Q8C22×D6711yescharacteristic
1186C4×Q8C22×D6711yescharacteristic
1187C4×Q8C22×D6711yescharacteristic
1188C4×Q8C22×D6711yescharacteristic
1189C4×D4—21no—
1190C4×D4—21no—
1191C4×D4—21no—
1192C4×D4—21no—
1193C4×D4—21no—
1194C4×D4—671no—
1195C4×D4—671no—
1196C4×D4—671no—
1197C4×D4—671no—
1198C4×D4—671no—
1199C4×D4—671no—
1200C4×D4—671no—
1201C4×D4—671no—
1202C4×D4—1341no—
1203C4×D4—1341no—
1204C4×D4—1341no—
1205C4×D4—1341no—
1206C4×D4—1341no—
1207C4×D4—1341no—
1208C4×D4—1341no—
1209C4×D4—1341no—
1210C4×D4—1341no—
1211C4×D4C22×D6711yescharacteristic
1212C4×D4C22×D6711yescharacteristic
1213C4×D4C22×D6711yescharacteristic
1214C4×D4C22×D6711yescharacteristic
1215C4×D4C22×D6711yescharacteristic
1216C4×D4C22×D6711yescharacteristic
1217#117—21no—
1218#117—671no—
1219#117—1341no—
1220#117—1341no—
1221#117—1341no—
1222#117C22×D6711yescharacteristic
1223#117C22×D6711yescharacteristic
1224#117C22×D6711yescharacteristic
1225#117C22×D6711yescharacteristic
1226C2×C4⋊C4—21no—
1227C2×C4⋊C4—671no—
1228C2×C4⋊C4—671no—
1229C2×C4⋊C4—1341no—
1230C2×C4⋊C4—1341no—
1231C2×C4⋊C4C22×D6711yescharacteristic
1232C2×C4⋊C4C22×D6711yescharacteristic
1233C2×C4⋊C4C22×D6711yescharacteristic
1234C2×C4⋊C4C22×D6711yescharacteristic
1235C2×C22⋊C4—1341no—
1236C2×C22⋊C4—1341no—
1237C2×C22⋊C4—1341no—
1238C2×C22⋊C4—1341no—
1239C2×C22⋊C4—1341no—
1240C2×C42C22×D6711yescharacteristic
1241#107—671no—
1242#107—671no—
1243#107—671no—
1244#107—671no—
1245#107—671no—
1246#107—671no—
1247#107—671no—
1248#107—671no—
1249#106—671no—
1250#106—671no—
1251#106—671no—
1252#106—671no—
1253#106—671no—
1254#106—671no—
1255#106—671no—
1256#106—671no—
1257#106—671no—
1258#106—671no—
1259#106—671no—
1260#106—671no—
1261#106—671no—
1262#106—671no—
1263#106—671no—
1264#106—671no—
1265C4⋊C8—671no—
1266C4⋊C8—671no—
1267C4⋊C8—671no—
1268C4⋊C8—671no—
1269C4⋊C8—671no—
1270C4⋊C8—671no—
1271C4⋊C8—671no—
1272C4⋊C8—671no—
1273C4⋊C8—671no—
1274C4⋊C8—671no—
1275#103—671no—
1276#103—671no—
1277#103—671no—
1278#103—671no—
1279#103—671no—
1280#103—671no—
1281#103—671no—
1282#103—671no—
1283#103—671no—
1284#103—671no—
1285#102—671no—
1286#102—671no—
1287#102—671no—
1288#102—671no—
1289#102—671no—
1290#102—671no—
1291#102—671no—
1292#102—671no—
1293#102—671no—
1294#102—671no—
1295#102—671no—
1296#102—671no—
1297#102—671no—
1298#102—671no—
1299#102—671no—
1300#102—671no—
1301#102—671no—
1302#102—671no—
1303#102—671no—
1304#102—671no—
1305#102—671no—
1306#102—671no—
1307C22⋊C8—671no—
1308C22⋊C8—671no—
1309C22⋊C8—671no—
1310C22⋊C8—671no—
1311C22⋊C8—671no—
1312C22⋊C8—671no—
1313#97—671no—
1314#97—671no—
1315#97—671no—
1316#97—671no—
1317C4×C8—671no—
1318C4×C8—671no—
1319C24—1341no—
1320C24—1341no—
1321#41—82no—
1322#41—2681no—
1323#41—5362no—
1324#41—1342no—
1325C2×Q8—21no—
1326C2×Q8—21no—
1327C2×Q8—21no—
1328C2×Q8—21no—
1329C2×Q8—21no—
1330C2×Q8—21no—
1331C2×Q8—82no—
1332C2×Q8—82no—
1333C2×Q8—671no—
1334C2×Q8—1341no—
1335C2×Q8C2×C22⋊D6711yescharacteristic
1336C2×Q8C23×D6711yescharacteristic
1337C2×D4—21no—
1338C2×D4—21no—
1339C2×D4—21no—
1340C2×D4—2681no—
1341C2×D4—2681no—
1342C2×D4—5362no—
1343C2×D4—671no—
1344C2×D4—671no—
1345C2×D4—671no—
1346C2×D4—1342no—
1347C2×D4—1342no—
1348C2×D4—1341no—
1349C2×D4—1341no—
1350C2×D4—1341no—
1351C2×D4—1341no—
1352C2×D4—1341no—
1353C2×D4—1341no—
1354C2×D4—1341no—
1355C2×D4—1341no—
1356C2×D4—1341no—
1357C2×D4C2×C22⋊D6711yescharacteristic
1358C2×D4C2×C22⋊D6711yescharacteristic
1359C2×D4C2×C22⋊D6711yescharacteristic
1360C2×D4C23×D6711yescharacteristic
1361C22×C4—21no—
1362C22×C4—21no—
1363C22×C4—21no—
1364C22×C4—21no—
1365C22×C4—21no—
1366C22×C4—21no—
1367C22×C4—21no—
1368C22×C4—5362no—
1369C22×C4—1341no—
1370C22×C4—1341no—
1371C22×C4—1341no—
1372C22×C4—1341no—
1373C22×C4—1341no—
1374C22×C4—1341no—
1375C22×C4—1341no—
1376C22×C4—1341no—
1377C22×C4—1341no—
1378C22×C4—1341no—
1379C22×C4—1341no—
1380C22×C4C2×C22⋊D6711yescharacteristic
1381C22×C4C2×C22⋊D6711yescharacteristic
1382C22×C4C23×D6711yescharacteristic
1383C22×C4C23×D6711yescharacteristic
1384C22×C4C23×D6711yescharacteristic
1385Q16—2681no—
1386SD16—2681no—
1387SD16—2681no—
1388SD16—2681no—
1389SD16—1342no—
1390D8—2681no—
1391D8—2681no—
1392D8—1342no—
1393M16—2681no—
1394M16—2681no—
1395C2×C8—2681no—
1396C2×C8—2681no—
1397C2×C8—2681no—
1398C2×C8—2681no—
1399C2×C8—671no—
1400C2×C8—671no—
1401C2×C8—671no—
1402C2×C8—671no—
1403C2×C8—671no—
1404C2×C8—671no—
1405C2×C8—671no—
1406C2×C8—671no—
1407C4⋊C4—21no—
1408C4⋊C4—21no—
1409C4⋊C4—21no—
1410C4⋊C4—21no—
1411C4⋊C4—21no—
1412C4⋊C4—21no—
1413C4⋊C4—21no—
1414C4⋊C4—21no—
1415C4⋊C4—21no—
1416C4⋊C4—21no—
1417C4⋊C4—21no—
1418C4⋊C4—21no—
1419C4⋊C4—21no—
1420C4⋊C4—21no—
1421C4⋊C4—21no—
1422C4⋊C4—21no—
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—21no—
1427C4⋊C4—21no—
1428C4⋊C4—21no—
1429C4⋊C4—671no—
1430C4⋊C4—671no—
1431C4⋊C4—671no—
1432C4⋊C4—671no—
1433C4⋊C4—1341no—
1434C4⋊C4—1341no—
1435C4⋊C4—1341no—
1436C4⋊C4—1341no—
1437C4⋊C4—1341no—
1438C4⋊C4—1341no—
1439C4⋊C4—1341no—
1440C4⋊C4—1341no—
1441C4⋊C4—1341no—
1442C4⋊C4—1341no—
1443C4⋊C4—1341no—
1444C4⋊C4C2×C22⋊D6711yescharacteristic
1445C4⋊C4C2×C22⋊D6711yescharacteristic
1446C4⋊C4C2×C22⋊D6711yescharacteristic
1447C4⋊C4C2×C22⋊D6711yescharacteristic
1448C4⋊C4C2×C22⋊D6711yescharacteristic
1449C4⋊C4C2×C22⋊D6711yescharacteristic
1450C4⋊C4C2×C22⋊D6711yescharacteristic
1451C4⋊C4C2×C22⋊D6711yescharacteristic
1452C4⋊C4C2×C22⋊D6711yescharacteristic
1453C4⋊C4C2×C22⋊D6711yescharacteristic
1454C4⋊C4C23×D6711yescharacteristic
1455C4⋊C4C23×D6711yescharacteristic
1456C4⋊C4C23×D6711yescharacteristic
1457C4⋊C4C23×D6711yescharacteristic
1458C4⋊C4C23×D6711yescharacteristic
1459C4⋊C4C23×D6711yescharacteristic
1460C22⋊C4—21no—
1461C22⋊C4—21no—
1462C22⋊C4—21no—
1463C22⋊C4—21no—
1464C22⋊C4—21no—
1465C22⋊C4—21no—
1466C22⋊C4—21no—
1467C22⋊C4—21no—
1468C22⋊C4—21no—
1469C22⋊C4—21no—
1470C22⋊C4—21no—
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—1341no—
1474C22⋊C4—1341no—
1475C22⋊C4—1341no—
1476C22⋊C4—1341no—
1477C22⋊C4—1341no—
1478C22⋊C4—1341no—
1479C22⋊C4—1341no—
1480C22⋊C4—1341no—
1481C22⋊C4—1341no—
1482C22⋊C4—1341no—
1483C22⋊C4—1341no—
1484C22⋊C4—1341no—
1485C22⋊C4—1341no—
1486C22⋊C4—1341no—
1487C22⋊C4—1341no—
1488C22⋊C4—1341no—
1489C22⋊C4—1341no—
1490C22⋊C4—1341no—
1491C22⋊C4—1341no—
1492C22⋊C4C2×C22⋊D6711yescharacteristic
1493C22⋊C4C2×C22⋊D6711yescharacteristic
1494C22⋊C4C2×C22⋊D6711yescharacteristic
1495C22⋊C4C2×C22⋊D6711yescharacteristic
1496C22⋊C4C2×C22⋊D6711yescharacteristic
1497C22⋊C4C2×C22⋊D6711yescharacteristic
1498C22⋊C4C2×C22⋊D6711yescharacteristic
1499C22⋊C4C2×C22⋊D6711yescharacteristic
1500C22⋊C4C2×C22⋊D6711yescharacteristic
1501C22⋊C4C2×C22⋊D6711yescharacteristic
1502C42—21no—
1503C42—21no—
1504C42—21no—
1505C42—21no—
1506C42—21no—
1507C42—1341no—
1508C42—1341no—
1509C42—1341no—
1510C42C2×C22⋊D6711yescharacteristic
1511C42C2×C22⋊D6711yescharacteristic
1512C42C23×D6711yescharacteristic
1513C42C23×D6711yescharacteristic
1514C42C23×D6711yescharacteristic
1515C42C23×D6711yescharacteristic
1516C23—21no—
1517C23—2682no—
1518C23—2682no—
1519C23—2682no—
1520C23—5361no—
1521C23—5361no—
1522C23—5361no—
1523C23—1341no—
1524C23—1341no—
1525C23—1341no—
1526C23C22×C22⋊D6711yescharacteristic
1527C23C22×C22⋊D6711yescharacteristic
1528C23C22×C22⋊D6711yescharacteristic
1529Q8—21no—
1530Q8—21no—
1531Q8—41no—
1532Q8—42no—
1533Q8—42no—
1534Q8—81no—
1535Q8—81no—
1536Q8—81no—
1537Q8—81no—
1538Q8—5361no—
1539Q8—1341no—
1540Q8—1341no—
1541D4—22no—
1542D4—22no—
1543D4—21no—
1544D4—21no—
1545D4—41no—
1546D4—42no—
1547D4—81no—
1548D4—81no—
1549D4—2682no—
1550D4—2682no—
1551D4—2682no—
1552D4—2682no—
1553D4—5361no—
1554D4—5361no—
1555D4—5361no—
1556D4—5361no—
1557D4—5361no—
1558D4—672no—
1559D4—1341no—
1560D4—1341no—
1561D4—1341no—
1562D4—1341no—
1563D4—1341no—
1564C2×C4—22no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—41no—
1579C2×C4—42no—
1580C2×C4—81no—
1581C2×C4—81no—
1582C2×C4—81no—
1583C2×C4—81no—
1584C2×C4—81no—
1585C2×C4—81no—
1586C2×C4—2682no—
1587C2×C4—2682no—
1588C2×C4—5361no—
1589C2×C4—5361no—
1590C2×C4—5361no—
1591C2×C4—5361no—
1592C2×C4—5361no—
1593C2×C4—5361no—
1594C2×C4—5361no—
1595C2×C4—5361no—
1596C2×C4—5361no—
1597C2×C4—1341no—
1598C2×C4—1341no—
1599C2×C4—1341no—
1600C2×C4—1341no—
1601C2×C4—1341no—
1602C2×C4C22×C22⋊D6711yescharacteristic
1603C2×C4C22×C22⋊D6711yescharacteristic
1604C2×C4C22×C22⋊D6711yescharacteristic
1605C2×C4C22×C22⋊D6711yescharacteristic
1606C2×C4C22×C22⋊D6711yescharacteristic
1607C2×C4C22×C22⋊D6711yescharacteristic
1608C2×C4C22×C22⋊D6711yescharacteristic
1609C2×C4C22×C22⋊D6711yescharacteristic
1610C2×C4C22×C22⋊D6711yescharacteristic
1611C2×C4C22×C22⋊D6711yescharacteristic
1612C2×C4C22×C22⋊D6711yescharacteristic
1613C2×C4C24×D6711yescharacteristic
1614C8—1341no—
1615C8—1341no—
1616C8—1341no—
1617C8—1341no—
1618C8—1341no—
1619C8—1341no—
1620C8—1341no—
1621C8—1341no—
1622C22—21no—
1623C22—21no—
1624C22—21no—
1625C22—21no—
1626C22—21no—
1627C22—21no—
1628C22—21no—
1629C22—21no—
1630C22—41no—
1631C22—41no—
1632C22—41no—
1633C22—2681no—
1634C22—2681no—
1635C22—2681no—
1636C22—2681no—
1637C22—2681no—
1638C22—2681no—
1639C22—2681no—
1640C22—2681no—
1641C22—5364no—
1642C22—10722no—
1643C22—1342no—
1644C22#1686420412yes—
1645C22C23×C22⋊D6711yescharacteristic
1646C4—21no—
1647C4—21no—
1648C4—21no—
1649C4—21no—
1650C4—21no—
1651C4—21no—
1652C4—21no—
1653C4—21no—
1654C4—21no—
1655C4—21no—
1656C4—21no—
1657C4—41no—
1658C4—41no—
1659C4—41no—
1660C4—41no—
1661C4—41no—
1662C4—41no—
1663C4—41no—
1664C4—2681no—
1665C4—2681no—
1666C4—2681no—
1667C4—2681no—
1668C4—2681no—
1669C42−1+4×D6711yescharacteristic
1670C4#1686423311yescharacteristic
1671C2—22no—
1672C2—41no—
1673C2—41no—
1674C2—81no—
1675C2—2682no—
1676C2—5361no—
1677C2—5361no—
1678C2#2257388211yescharacteristic
1679C2C2×#1686420411yescharacteristic
1680C2#2257498911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3552C2
socleC22×C67C23×D4
hypercenter#3552D67
hypocenterC67#62156
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #529 ◁ #3552

Complements

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

NH ≅ G/Ntype
1. #22574153C2semidirect
2. #22573148C2semidirect
3. #22573104C2semidirect
4. #22573001C2semidirect
5. #22572977C2semidirect
6. #22572754C2semidirect
7. #22572679C2semidirect
8. #22572673C2semidirect
9. #22572658C2semidirect
10. #22572582C2semidirect
11. #22572560C2semidirect
12. #22572344C2semidirect
13. #22572284C2semidirect
14. #22572239C2semidirect
15. #22572164C2semidirect
16. #22572053C2semidirect
17. #22572027C2semidirect
18. #22571674C2semidirect
19. #22571620C2semidirect
20. #22571556C2semidirect
21. #22571507C2semidirect
22. #22571462C2semidirect
23. #22571439C2semidirect
24. #22570480C2semidirect
25. #22570387C2semidirect
26. #22570343C2semidirect
27. #22570067C2semidirect
28. #22570034C2semidirect
29. C2×#16863683C2semidirect
30. #22569348C2semidirect
31. C67×#3552C2semidirect
54. #16863806C22semidirect
55. #16863802C22semidirect
56. #16863802C22semidirect
57. #16863802C22semidirect
58. #16863795C22semidirect
59. #16863792C22semidirect
61. #16863758C22semidirect
62. #16863758C22semidirect
63. #16863758C22semidirect
64. #16863753C22semidirect
66. #16863737C22semidirect
67. #16863734C22semidirect
68. #16863731C22semidirect
69. #16863731C22semidirect
70. #16863726C22semidirect
71. #16863724C22semidirect
72. #16863724C22semidirect
74. #16863720C22semidirect
75. #16863720C22semidirect
76. #16863717C22semidirect
80. #16863714C22semidirect
81. #16863712C22semidirect
82. #16863709C22semidirect
83. #16863707C22semidirect
84. #16863703C22semidirect
85. #16863703C22semidirect
86. #16863700C22semidirect
87. #16863700C22semidirect
88. #16863696C22semidirect
89. #16863696C22semidirect
93. #16863693C22semidirect
94. #16863693C22semidirect
95. #16863693C22semidirect
96. #16863686C22semidirect
102. #16863683C22semidirect
103. #16863683C22semidirect
104. #16863683C22semidirect
105. #16863683C22semidirect
106. #16863683C22semidirect
107. #16863681C22semidirect
108. #16863678C22semidirect
109. #16863678C22semidirect
110. #16863678C22semidirect
112. #16863673C22semidirect
113. #16863673C22semidirect
114. #16863652C22semidirect
116. #16863647C22semidirect
117. #16863644C22semidirect
118. #16863635C22semidirect
120. #16863630C22semidirect
123. #16863627C22semidirect
124. #16863623C22semidirect
125. #16863623C22semidirect
126. #16863618C22semidirect
127. #16863618C22semidirect
128. #16863615C22semidirect
129. #16863611C22semidirect
130. #16863611C22semidirect
132. #16863608C22semidirect
133. #16863608C22semidirect
142. #16863527C22semidirect
143. #16863527C22semidirect
146. #16863506C22semidirect
147. #16863506C22semidirect
148. #16863501C22semidirect
151. #16863494C22semidirect
153. C4×#11761615C22semidirect
154. C4×#11761616C22semidirect
157. #16863468C22semidirect
158. #16863468C22semidirect
159. #16863468C22semidirect
161. D4×C67⋊C8C22semidirect
162. #16863457C22semidirect
163. #16863457C22semidirect
164. #16863453C22semidirect
165. #16863439C22semidirect
166. #16863436C22semidirect
167. #16863432C22semidirect
168. C2×#14523974C22semidirect
169. C2×#14523974C22semidirect
170. C2×#14523974C22semidirect
171. #16863423C22semidirect
172. #16863423C22semidirect
173. C2×C4⋊(C67⋊C8)C22semidirect
182. #557×C67C22semidirect
183. #556×C67C22semidirect
185. #554×C67C22semidirect
187. #553×C67C22semidirect
189. D4×Q8×C67C22semidirect
191. #547×C67C22semidirect
192. #544×C67C22semidirect
193. #544×C67C22semidirect
194. #542×C67C22semidirect
195. #542×C67C22semidirect
200. C2×C4⋊Q8×C67C22semidirect
202. #529×C67C22semidirect
841. #3552D67semidirect
872. C67#62156semidirect
876. #557C2×D67semidirect
877. #556C2×D67semidirect
880. #554C2×D67semidirect
884. #553C2×D67semidirect
889. D4×Q8C2×D67semidirect
892. #547C2×D67semidirect
897. #544C2×D67semidirect
898. #544C2×D67semidirect
900. #542C2×D67semidirect
901. #542C2×D67semidirect
909. C2×C4⋊Q8C2×D67semidirect
912. #529C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225741532
#225731482
#225731042
#225730012
#225729772
#225727542
#225726792
#225726732
#225726582
#225725822
#225725602
#225723442
#225722842
#225722392
#225721642
#225720532
#225720272
#225716742
#225716202
#225715562
#225715072
#225714622
#225714392
#225704802
#225703872
#225703432
#225700672
#225700342
C2×#168636832
#225693482
C67×#35522
#6215667