Finite Group Databasebeta

← #7624426

Subgroups — #7624426

Order 512.

1179 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62377C211yesmaximal, characteristic, complemented
2#61373C211yesmaximal, characteristic, complemented
3#33957C211yesmaximal, characteristic, complemented
4#33956C211yesmaximal, characteristic, complemented
5#33955C211yesmaximal, characteristic, complemented
6#33955C211yesmaximal, characteristic, complemented
7#33954C211yesmaximal, characteristic, complemented
8#33953C211yesmaximal, characteristic, complemented
9#33952C211yesmaximal, characteristic, complemented
10#33951C211yesmaximal, characteristic, complemented
11#33944C211yesmaximal, characteristic, complemented
12#33943C211yesmaximal, characteristic, complemented
13#33942C211yesmaximal, characteristic, complemented
14#33940C211yesmaximal, characteristic, complemented
15#33938C211yesmaximal, characteristic, complemented
16#33937C211yesmaximal, characteristic, complemented
17#33936C211yesmaximal, characteristic, complemented
18#33934C211yesmaximal, characteristic, complemented
19#33810C211yesmaximal, characteristic, complemented
20#33809C211yesmaximal, characteristic, complemented
21#33808C211yesmaximal, characteristic, complemented
22#33807C211yesmaximal, characteristic, complemented
23#33805C211yesmaximal, characteristic, complemented
24#33804C211yesmaximal, characteristic, complemented
25#33685C211yesmaximal, characteristic, complemented
26#33684C211yesmaximal, characteristic, complemented
27#33680C211yesmaximal, characteristic, complemented
28#33679C211yesmaximal, characteristic
29#33671C211yesmaximal, characteristic, complemented
30#33671C211yesmaximal, characteristic, complemented
31#33501C211yesmaximal, characteristic, complemented
32#3557—21no—
33#3503—21no—
34#3396C2211yescharacteristic
35#3396C2211yescharacteristic
36#3393C2211yescharacteristic
37#3393C2211yescharacteristic
38#3386—21no—
39#3386—21no—
40#3385—21no—
41#3385—21no—
42#3383C2211yescharacteristic
43#3383C2211yescharacteristic
44#3383C2211yescharacteristic
45#3383C2211yescharacteristic
46Q8×Q16C2211yescharacteristic
47Q8×Q16C2211yescharacteristic
48#3380C2211yescharacteristic
49#3380C2211yescharacteristic
50#3380C2211yescharacteristic
51#3380C2211yescharacteristic
52Q8×D8C2211yescharacteristic
53Q8×D8C2211yescharacteristic
54#3376—21no—
55#3376—21no—
56#3371—21no—
57#3371—21no—
58#3263—21no—
59#3260—21no—
60#3256—21no—
61#3177C2211yescharacteristic
62#3176C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic
65#3168C2211yescharacteristic
66#3168C2211yescharacteristic
67#3164C2211yescharacteristic
68#3164C2211yescharacteristic
69C2×#500C2211yescharacteristic
70#3083—21no—
71#3083—21no—
72#3079—21no—
73#2960C2211yescharacteristic
74#2951C2211yescharacteristic
75#2951C2211yescharacteristic
76C4×#135C2211yescharacteristic
77#2255C2211yescharacteristic
78#2255C2211yescharacteristic
79#2255C2211yescharacteristic
80#2255C2211yescharacteristic
81#2255C2211yescharacteristic
82#2255C2211yescharacteristic
83#2255C2211yescharacteristic
84#2255C2211yescharacteristic
85#2254C2211yescharacteristic
86#2253C2211yescharacteristic
87#2253C2211yescharacteristic
88#2252C2211yescharacteristic
89#2245C2211yescharacteristic
90#2244C2211yescharacteristic
91#2243C2211yescharacteristic
92#2243C2211yescharacteristic
93#2243C2211yescharacteristic
94#2243C2211yescharacteristic
95#2243C2211yescharacteristic
96#2243C2211yescharacteristic
97#2242C2211yescharacteristic
98#2242C2211yescharacteristic
99#2241C2211yescharacteristic
100#2240C2211yescharacteristic
101#2237C2211yescharacteristic
102#2237C2211yescharacteristic
103#2236C2211yescharacteristic
104#2236C2211yescharacteristic
105#2235C2211yescharacteristic
106#2235C2211yescharacteristic
107#2234C2211yescharacteristic
108#2234C2211yescharacteristic
109#2233C2211yescharacteristic
110#2233C2211yescharacteristic
111#2232C2211yescharacteristic
112#2232C2211yescharacteristic
113#2229C2211yescharacteristic
114#2229C2211yescharacteristic
115#2229C2211yescharacteristic
116#2229C2211yescharacteristic
117#2229C2211yescharacteristic
118#2229C2211yescharacteristic
119#2229C2211yescharacteristic
120#2229C2211yescharacteristic
121#2228C2211yescharacteristic
122#2228C2211yescharacteristic
123#2228C2211yescharacteristic
124#2228C2211yescharacteristic
125#2228C2211yescharacteristic
126#2228C2211yescharacteristic
127#2228C2211yescharacteristic
128#2228C2211yescharacteristic
129#2227C2211yescharacteristic
130#2227C2211yescharacteristic
131#2227C2211yescharacteristic
132#2227C2211yescharacteristic
133#2227C2211yescharacteristic
134#2226C2211yescharacteristic
135#2226C2211yescharacteristic
136#2226C2211yescharacteristic
137#2226C2211yescharacteristic
138#2226C2211yescharacteristic
139#2225C2211yescharacteristic
140#2225C2211yescharacteristic
141#2225C2211yescharacteristic
142#2225C2211yescharacteristic
143#2225C2211yescharacteristic
144#2224C2211yescharacteristic
145#2224C2211yescharacteristic
146#2224C2211yescharacteristic
147#2224C2211yescharacteristic
148#2224C2211yescharacteristic
149#2211C2211yescharacteristic
150#2211C2211yescharacteristic
151#2211C2211yescharacteristic
152#2211C2211yescharacteristic
153#2210C2211yescharacteristic
154#2210C2211yescharacteristic
155#2210C2211yescharacteristic
156#2210C2211yescharacteristic
157#2209C2211yescharacteristic
158#2208C2211yescharacteristic
159#2207C2211yescharacteristic
160#2206C2211yescharacteristic
161#2189C2211yescharacteristic
162#2189C2211yescharacteristic
163#2186C2211yescharacteristic
164#2186C2211yescharacteristic
165#2183C2211yescharacteristic
166#2183C2211yescharacteristic
167#2183C2211yescharacteristic
168#2183C2211yescharacteristic
169#2183C2211yescharacteristic
170#2183C2211yescharacteristic
171#2183C2211yescharacteristic
172#2183C2211yescharacteristic
173#2177C2211yescharacteristic
174#2177C2211yescharacteristic
175#2177C2211yescharacteristic
176#2177C2211yescharacteristic
177#2176C2211yescharacteristic
178#2176C2211yescharacteristic
179#2176C2211yescharacteristic
180#2176C2211yescharacteristic
181#2175C2211yescharacteristic
182#2175C2211yescharacteristic
183#2175C2211yescharacteristic
184#2175C2211yescharacteristic
185#2175C2211yescharacteristic
186#2175C2211yescharacteristic
187#2175C2211yescharacteristic
188#2175C2211yescharacteristic
189C4×Q32C2211yescharacteristic
190C4×Q32C2211yescharacteristic
191C4×SD32C2211yescharacteristic
192C4×SD32C2211yescharacteristic
193C4×SD32C2211yescharacteristic
194C4×SD32C2211yescharacteristic
195C4×D16C2211yescharacteristic
196C4×D16C2211yescharacteristic
197#2164C2211yescharacteristic
198#2164C2211yescharacteristic
199#2164C2211yescharacteristic
200#2164C2211yescharacteristic
201#2163C2211yescharacteristic
202#2163C2211yescharacteristic
203C2×#135C2311yescharacteristic
204#563—41no—
205#563—41no—
206#559—21no—
207#559—21no—
208Q82—21no—
209Q82—21no—
210#557—21no—
211#557—21no—
212#557—21no—
213#557—21no—
214#556—21no—
215#556—21no—
216#554—21no—
217#554—21no—
218#554—21no—
219#554—21no—
220#554—41no—
221#554—41no—
222#552—41no—
223#552—41no—
224D4×Q8—21no—
225D4×Q8—21no—
226D4×Q8—41no—
227D4×Q8—41no—
228#544—21no—
229#544—21no—
230#544—41no—
231#544—41no—
232#542—21no—
233#542—21no—
234#542—41no—
235#542—41no—
236#541—21no—
237#540—21no—
238#539—41no—
239#539—41no—
240#533—41no—
241#533D411yescharacteristic
242C2×C4⋊Q8—21no—
243C2×C4⋊Q8—41no—
244#529—21no—
245#529—21no—
246#520—21no—
247#520—21no—
248C4×#41—21no—
249C2×Q32C2311yescharacteristic
250C2×Q32C2311yescharacteristic
251C2×SD32C2311yescharacteristic
252C2×SD32C2311yescharacteristic
253C2×SD32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×D16C2311yescharacteristic
256C2×D16C2311yescharacteristic
257#501—21no—
258#501—21no—
259#501—21no—
260#501—21no—
261#500—21no—
262#500—21no—
263#500C2311yescharacteristic
264#500C2311yescharacteristic
265#500C2311yescharacteristic
266#500C2311yescharacteristic
267#500C2311yescharacteristic
268#500C2311yescharacteristic
269#500C2311yescharacteristic
270#500C2311yescharacteristic
271#500C2311yescharacteristic
272#500C2311yescharacteristic
273#499C2311yescharacteristic
274#499C2311yescharacteristic
275#499C2311yescharacteristic
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#499C2311yescharacteristic
281#495C2311yescharacteristic
282#495C2311yescharacteristic
283#495C2311yescharacteristic
284#495C2311yescharacteristic
285#494C2311yescharacteristic
286#493C2311yescharacteristic
287#491—21no—
288#490—21no—
289#489—21no—
290#489—21no—
291#488—21no—
292#488—21no—
293#479—21no—
294#479—21no—
295#479—21no—
296#479—21no—
297#479—21no—
298#479—21no—
299#479—21no—
300#479—21no—
301#478—21no—
302#478—21no—
303#478—21no—
304#478—21no—
305#478—21no—
306#478—21no—
307#478—21no—
308#478—21no—
309#477—21no—
310#477—21no—
311#477—21no—
312#477—21no—
313#477—21no—
314#477—21no—
315#476—21no—
316#476—21no—
317#476—21no—
318#476—21no—
319#475—21no—
320#475—21no—
321#475—21no—
322#475—21no—
323#474—21no—
324#474—21no—
325#474—21no—
326#474—21no—
327#474—21no—
328#474—21no—
329#470—21no—
330#469—21no—
331#468—21no—
332#468—21no—
333#467C2311yescharacteristic
334#467C2311yescharacteristic
335#466C2311yescharacteristic
336#466C2311yescharacteristic
337#465—21no—
338#465—21no—
339#464—21no—
340#464—21no—
341#464—21no—
342#464—21no—
343#463—21no—
344#463—21no—
345#463—21no—
346#463—21no—
347#461—21no—
348#461—21no—
349#460—21no—
350#460—21no—
351#446D411yescharacteristic
352#446D411yescharacteristic
353#446D411yescharacteristic
354#446D411yescharacteristic
355C8×Q8C2311yescharacteristic
356C8×Q8C2311yescharacteristic
357C8×Q8C2311yescharacteristic
358C8×Q8C2311yescharacteristic
359#442—21no—
360#441—21no—
361#440—21no—
362#440—21no—
363#440—21no—
364#440—21no—
365#440—21no—
366#440—21no—
367C4×Q16C2311yescharacteristic
368C4×Q16C2311yescharacteristic
369C4×Q16C2311yescharacteristic
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×Q16C2311yescharacteristic
377C4×Q16C2311yescharacteristic
378C4×Q16C2311yescharacteristic
379C4×SD16—21no—
380C4×SD16—21no—
381C4×SD16—21no—
382C4×SD16—21no—
383C4×D8C2311yescharacteristic
384C4×D8C2311yescharacteristic
385C4×D8C2311yescharacteristic
386C4×D8C2311yescharacteristic
387C4×D8C2311yescharacteristic
388C4×D8C2311yescharacteristic
389C4×D8C2311yescharacteristic
390C4×D8C2311yescharacteristic
391C4×D8C2311yescharacteristic
392C4×D8C2311yescharacteristic
393C4×D8C2311yescharacteristic
394C4×D8C2311yescharacteristic
395#428—21no—
396#428—21no—
397#427C2311yescharacteristic
398C2×#107—21no—
399C2×#107C2311yescharacteristic
400C2×#107C2311yescharacteristic
401#424D411yescharacteristic
402#424D411yescharacteristic
403#423D411yescharacteristic
404#417—21no—
405#417—21no—
406#416—21no—
407#405C2311yescharacteristic
408#405C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410#367C2311yescharacteristic
411#367C2311yescharacteristic
412#367C2311yescharacteristic
413#367C2311yescharacteristic
414#367C2311yescharacteristic
415#367C2311yescharacteristic
416#367C2311yescharacteristic
417#367C2311yescharacteristic
418#367C2311yescharacteristic
419#367C2311yescharacteristic
420#367C2311yescharacteristic
421#367C2311yescharacteristic
422#366C2311yescharacteristic
423#366C2311yescharacteristic
424#366C2311yescharacteristic
425#366C2311yescharacteristic
426#366C2311yescharacteristic
427#366C2311yescharacteristic
428#366C2311yescharacteristic
429#366C2311yescharacteristic
430#366C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434C4⋊C16C2311yescharacteristic
435C4⋊C16C2311yescharacteristic
436C4⋊C16C2311yescharacteristic
437C4⋊C16C2311yescharacteristic
438C4⋊C16C2311yescharacteristic
439C4⋊C16C2311yescharacteristic
440C4⋊C16C2311yescharacteristic
441C4⋊C16C2311yescharacteristic
442C4⋊C16C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446#358C2311yescharacteristic
447#358C2311yescharacteristic
448#358C2311yescharacteristic
449#358C2311yescharacteristic
450#358C2311yescharacteristic
451#358C2311yescharacteristic
452#358C2311yescharacteristic
453#358C2311yescharacteristic
454#358C2311yescharacteristic
455#358C2311yescharacteristic
456#358C2311yescharacteristic
457#358C2311yescharacteristic
458#358C2311yescharacteristic
459#358C2311yescharacteristic
460#358C2311yescharacteristic
461#358C2311yescharacteristic
462#357C2311yescharacteristic
463#357C2311yescharacteristic
464#357C2311yescharacteristic
465#357C2311yescharacteristic
466#357C2311yescharacteristic
467#357C2311yescharacteristic
468#357C2311yescharacteristic
469#357C2311yescharacteristic
470#357C2311yescharacteristic
471#357C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478C22⋊C16C2311yescharacteristic
479C22⋊C16C2311yescharacteristic
480C22⋊C16C2311yescharacteristic
481C22⋊C16C2311yescharacteristic
482#346C2311yescharacteristic
483#346C2311yescharacteristic
484#346C2311yescharacteristic
485#346C2311yescharacteristic
486#346C2311yescharacteristic
487#346C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490C4×C16C2311yescharacteristic
491C4×C16C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8—41no—
498#135—22no—
499#135—22no—
500C2×Q16—21no—
501C2×Q16C2411yescharacteristic
502C2×Q16C2411yescharacteristic
503C2×Q16C2411yescharacteristic
504C2×SD16—21no—
505C2×SD16—21no—
506C2×SD16—21no—
507C2×SD16—21no—
508C2×SD16—21no—
509C2×D8—21no—
510C2×D8C2411yescharacteristic
511C2×D8C2411yescharacteristic
512C2×D8C2411yescharacteristic
513C2×M16C2×D411yescharacteristic
514C2×M16C2×D411yescharacteristic
515C22×C8C2×D411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519C4⋊Q8—21no—
520C4⋊Q8—21no—
521C4⋊Q8—21no—
522C4⋊Q8—21no—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8—21no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8D811yescharacteristic
543C4⋊Q8D811yescharacteristic
544#127—21no—
545#126—41no—
546#126—41no—
547#126—41no—
548#126—41no—
549#126—41no—
550#126—41no—
551#126—41no—
552#126—41no—
553#126—41no—
554#126—41no—
555#125—21no—
556#125—21no—
557#125—21no—
558#125—21no—
559#125—21no—
560#125—21no—
561#125—21no—
562#125—21no—
563#125—41no—
564#125—41no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125D811yescharacteristic
576#125D811yescharacteristic
577#124—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#123—41no—
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—41no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8D811yescharacteristic
624C22⋊Q8D811yescharacteristic
625C22⋊Q8D811yescharacteristic
626C22⋊Q8D811yescharacteristic
627#121—21no—
628#121—21no—
629#121—41no—
630#121—41no—
631C4×Q8—21no—
632C4×Q8—21no—
633C4×Q8—21no—
634C4×Q8—21no—
635C4×Q8—21no—
636C4×Q8—21no—
637C4×Q8—21no—
638C4×Q8—21no—
639C4×Q8—21no—
640C4×Q8—21no—
641C4×Q8—21no—
642C4×Q8—21no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×Q8—41no—
649C4×Q8C2×D411yescharacteristic
650C4×Q8C2×D411yescharacteristic
651C4×Q8C2×D411yescharacteristic
652C4×Q8C2×D411yescharacteristic
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—41no—
666C4×D4—41no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4—41no—
672C4×D4—41no—
673C4×D4—41no—
674C4×D4—41no—
675#117—21no—
676#117—41no—
677#117—41no—
678#117—41no—
679#117—41no—
680#117—41no—
681#117—41no—
682#117—41no—
683#117C2×D411yescharacteristic
684#117C2×D411yescharacteristic
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C42—41no—
695C2×C42C2×D411yescharacteristic
696Q32—22no—
697Q32—22no—
698SD32—22no—
699SD32—22no—
700SD32—22no—
701SD32—22no—
702D16—22no—
703D16—22no—
704C2×C16C2411yescharacteristic
705C2×C16C2411yescharacteristic
706C2×C16C2411yescharacteristic
707C2×C16C2411yescharacteristic
708C2×C16C2411yescharacteristic
709C2×C16C2411yescharacteristic
710C2×C16C2411yescharacteristic
711C2×C16C2411yescharacteristic
712#107—21no—
713#107—21no—
714#107—21no—
715#107—21no—
716#107—21no—
717#107—21no—
718#107—21no—
719#107—21no—
720#107—21no—
721#107—21no—
722#107—21no—
723#107—21no—
724#107C2411yescharacteristic
725#107C2411yescharacteristic
726#107C2411yescharacteristic
727#107C2411yescharacteristic
728#107C2411yescharacteristic
729#107C2411yescharacteristic
730#107C2411yescharacteristic
731#107C2411yescharacteristic
732#107C2411yescharacteristic
733#107C2411yescharacteristic
734#106—21no—
735#106—21no—
736#106—21no—
737#106—21no—
738#106—21no—
739#106—21no—
740#106—21no—
741#106—21no—
742#106—21no—
743C4⋊C8C2×D411yescharacteristic
744C4⋊C8C2×D411yescharacteristic
745C4⋊C8C2×D411yescharacteristic
746C4⋊C8C2×D411yescharacteristic
747C4⋊C8C2×D411yescharacteristic
748C4⋊C8C2×D411yescharacteristic
749C4⋊C8C2×D411yescharacteristic
750C4⋊C8C2×D411yescharacteristic
751C4⋊C8C2×D411yescharacteristic
752C4⋊C8C2×D411yescharacteristic
753C4⋊C8C2×D411yescharacteristic
754C4⋊C8C2×D411yescharacteristic
755#103—21no—
756#103—21no—
757#103—21no—
758#103—21no—
759#103—21no—
760#103—21no—
761#103—21no—
762#103—21no—
763#103—21no—
764#103—21no—
765#103—21no—
766#103—21no—
767#103—21no—
768#103—21no—
769#102—21no—
770#102—21no—
771#102—21no—
772#102—21no—
773#102—21no—
774#102—21no—
775#102—21no—
776#102—21no—
777#102—21no—
778#102—21no—
779#102—21no—
780#102—21no—
781#102—21no—
782#102—21no—
783#97C2×D411yescharacteristic
784#97C2×D411yescharacteristic
785#97C2×D411yescharacteristic
786#97C2×D411yescharacteristic
787C4×C8C2×D411yescharacteristic
788C4×C8C2×D411yescharacteristic
789C4×C8C2411yescharacteristic
790C4×C8C2411yescharacteristic
791C4×C8C2411yescharacteristic
792C4×C8C2411yescharacteristic
793C4×C8C2411yescharacteristic
794C4×C8C2411yescharacteristic
795#41—24no—
796#41—42no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—41no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—41no—
804C2×Q8—41no—
805C2×Q8—41no—
806C2×Q8—41no—
807C2×Q8—41no—
808C2×Q8—41no—
809C2×Q8—41no—
810C2×Q8—162no—
811C2×Q8—162no—
812C2×Q8—162no—
813C2×Q8C2×D811yescharacteristic
814C2×Q8C2×D811yescharacteristic
815C2×Q8C2×D811yescharacteristic
816C2×Q8C2×D811yescharacteristic
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4C2×D811yescharacteristic
841C22×C4C2×D811yescharacteristic
842C22×C4C22×D411yescharacteristic
843Q16—21no—
844Q16—21no—
845Q16—21no—
846Q16—21no—
847Q16—21no—
848Q16—81no—
849Q162−1+412yes—
850SD16—24no—
851SD16—81no—
852SD16—81no—
853SD16—81no—
854SD16—81no—
855D8—21no—
856D8—21no—
857D8—21no—
858D8—21no—
859D8—21no—
860D8—81no—
861D82−1+412yes—
862M16—41no—
863M16—41no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—41no—
867C2×C8C22×D411yescharacteristic
868C2×C8C22×D411yescharacteristic
869C2×C8C22×D411yescharacteristic
870C2×C8C22×D411yescharacteristic
871C2×C8C22×D411yescharacteristic
872C2×C8C22×D411yescharacteristic
873C2×C8C22×D411yescharacteristic
874C2×C8C2511yescharacteristic
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4C2×D811yescharacteristic
930C4⋊C4C2×D811yescharacteristic
931C4⋊C4C2×D811yescharacteristic
932C4⋊C4C2×D811yescharacteristic
933C4⋊C4C2×D811yescharacteristic
934C4⋊C4C2×D811yescharacteristic
935C4⋊C4C2×D811yescharacteristic
936C4⋊C4C2×D811yescharacteristic
937C4⋊C4C2×D811yescharacteristic
938C4⋊C4C2×D811yescharacteristic
939C4⋊C4C2×D811yescharacteristic
940C4⋊C4C2×D811yescharacteristic
941C4⋊C4C2×D811yescharacteristic
942C4⋊C4C2×D811yescharacteristic
943C4⋊C4C2×D811yescharacteristic
944C4⋊C4C2×D811yescharacteristic
945C22⋊C4—41no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4C2×D811yescharacteristic
971C22⋊C4C2×D811yescharacteristic
972C22⋊C4C2×D811yescharacteristic
973C22⋊C4C2×D811yescharacteristic
974C42—41no—
975C42—41no—
976C42—41no—
977C42—41no—
978C42—41no—
979C42—41no—
980C42—41no—
981C42—41no—
982C42—41no—
983C42—41no—
984C42—41no—
985C42—41no—
986C42—41no—
987C42C2×D811yescharacteristic
988C42C2×D811yescharacteristic
989C42C22×D411yescharacteristic
990C42C22×D411yescharacteristic
991C42C22×D411yescharacteristic
992C42C22×D411yescharacteristic
993C42C22×D411yescharacteristic
994C42C22×D411yescharacteristic
995C16—21no—
996C16—21no—
997C16—21no—
998C16—21no—
999C16—21no—
1000C16—21no—
1001C16—21no—
1002C16—21no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23C22×D811yescharacteristic
1007Q8—22no—
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—82no—
1018Q8—82no—
1019Q8—161no—
1020Q8—161no—
1021Q8—161no—
1022Q8—161no—
1023Q8—161no—
1024Q8—161no—
1025Q8—161no—
1026Q8—161no—
1027D4—22no—
1028D4—44no—
1029D4—41no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—161no—
1035D4—161no—
1036D4—161no—
1037D4—161no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—44no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—82no—
1057C2×C4—82no—
1058C2×C4—161no—
1059C2×C4—161no—
1060C2×C4—161no—
1061C2×C4—161no—
1062C2×C4—161no—
1063C2×C4—161no—
1064C2×C4—161no—
1065C2×C4—161no—
1066C2×C4—161no—
1067C2×C4—161no—
1068C2×C4—161no—
1069C2×C4—161no—
1070C2×C4C22×D811yescharacteristic
1071C2×C4C22×D811yescharacteristic
1072C2×C4C22×D811yescharacteristic
1073C2×C4C22×D811yescharacteristic
1074C2×C4C22×D811yescharacteristic
1075C2×C4C22×D811yescharacteristic
1076C2×C4C22×D811yescharacteristic
1077C2×C4C22×D811yescharacteristic
1078C2×C4C22×D811yescharacteristic
1079C2×C4C22×D811yescharacteristic
1080C2×C4C22×D811yescharacteristic
1081C2×C4C22×D811yescharacteristic
1082C2×C4C22×D811yescharacteristic
1083C2×C4C23×D411yescharacteristic
1084C8—21no—
1085C8—21no—
1086C8—21no—
1087C8—21no—
1088C8—21no—
1089C8—21no—
1090C8—21no—
1091C8C2×2−1+411yescharacteristic
1092C8C2×2−1+411yescharacteristic
1093C22—21no—
1094C22—21no—
1095C22—21no—
1096C22—42no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22C23×D811yescharacteristic
1106C4—21no—
1107C4—21no—
1108C4—21no—
1109C4—21no—
1110C4—21no—
1111C4—21no—
1112C4—21no—
1113C4—21no—
1114C4—21no—
1115C4—21no—
1116C4—21no—
1117C4—21no—
1118C4—21no—
1119C4—42no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4—81no—
1131C4—81no—
1132C4#348611yescharacteristic
1133C4#358611yescharacteristic
1134C2—41no—
1135C2—82no—
1136C2—161no—
1137C2—161no—
1138C2#6181711yescharacteristic
1139C2#6263611yescharacteristic
1140C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
prime radical#33679C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #533 ◁ #2960 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62377C2semidirect
2. #61373C2semidirect
3. #33957C2semidirect
4. #33956C2semidirect
5. #33955C2semidirect
6. #33955C2semidirect
7. #33954C2semidirect
8. #33953C2semidirect
9. #33952C2semidirect
10. #33951C2semidirect
11. #33944C2semidirect
12. #33943C2semidirect
13. #33942C2semidirect
14. #33940C2semidirect
15. #33938C2semidirect
16. #33937C2semidirect
17. #33936C2semidirect
18. #33934C2semidirect
19. #33810C2semidirect
20. #33809C2semidirect
21. #33808C2semidirect
22. #33807C2semidirect
23. #33805C2semidirect
24. #33804C2semidirect
25. #33685C2semidirect
26. #33684C2semidirect
27. #33680C2semidirect
29. #33671C2semidirect
30. #33671C2semidirect
31. #33501C2semidirect

Maximal subgroups

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

subgroupindex
#623772
#613732
#339572
#339562
#339552
#339542
#339532
#339522
#339512
#339442
#339432
#339422
#339402
#339382
#339372
#339362
#339342
#338102
#338092
#338082
#338072
#338052
#338042
#336852
#336842
#336802
#336792
#336712
#335012