Finite Group Databasebeta

← #7624409

Subgroups — #7624409

Order 512.

1158 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62380C211yesmaximal, characteristic, complemented
2#61376C211yesmaximal, characteristic, complemented
3#33957C211yesmaximal, characteristic, complemented
4#33956C211yesmaximal, characteristic, complemented
5#33955C211yesmaximal, characteristic, complemented
6#33955C211yesmaximal, characteristic, complemented
7#33954C211yesmaximal, characteristic, complemented
8#33952C211yesmaximal, characteristic, complemented
9#33950C211yesmaximal, characteristic, complemented
10#33948C211yesmaximal, characteristic, complemented
11#33944C211yesmaximal, characteristic, complemented
12#33944C211yesmaximal, characteristic, complemented
13#33943C211yesmaximal, characteristic, complemented
14#33943C211yesmaximal, characteristic, complemented
15#33941C211yesmaximal, characteristic, complemented
16#33939C211yesmaximal, characteristic, complemented
17#33931C211yesmaximal, characteristic, complemented
18#33927C211yesmaximal, characteristic, complemented
19#33810C211yesmaximal, characteristic, complemented
20#33809C211yesmaximal, characteristic, complemented
21#33808C211yesmaximal, characteristic, complemented
22#33808C211yesmaximal, characteristic, complemented
23#33802C211yesmaximal, characteristic, complemented
24#33798C211yesmaximal, characteristic, complemented
25#33685C211yesmaximal, characteristic
26#33684C211yesmaximal, characteristic
27#33680C211yesmaximal, characteristic, complemented
28#33680C211yesmaximal, characteristic, complemented
29#33671C211yesmaximal, characteristic
30#33667C211yesmaximal, characteristic, complemented
31#33499C211yesmaximal, characteristic, complemented
32#3555—21no—
33#3504—21no—
34#3395C2211yescharacteristic
35#3393C2211yescharacteristic
36#3393C2211yescharacteristic
37#3393C2211yescharacteristic
38#3388—21no—
39#3388—21no—
40#3388—21no—
41#3388—21no—
42#3383C2211yescharacteristic
43#3383C2211yescharacteristic
44#3383C2211yescharacteristic
45#3383C2211yescharacteristic
46#3383C2211yescharacteristic
47#3383C2211yescharacteristic
48Q8×Q16C2211yescharacteristic
49#3380C2211yescharacteristic
50#3380C2211yescharacteristic
51#3380C2211yescharacteristic
52#3380C2211yescharacteristic
53#3380C2211yescharacteristic
54#3377—21no—
55#3377—21no—
56#3372—21no—
57#3369—21no—
58#3258—21no—
59#3258—21no—
60#3252—21no—
61#3177C2211yescharacteristic
62#3177C2211yescharacteristic
63#3175C2211yescharacteristic
64#3175C2211yescharacteristic
65#3170C2211yescharacteristic
66#3168C2211yescharacteristic
67#3164C2211yescharacteristic
68#3164C2211yescharacteristic
69C2×#499C2211yescharacteristic
70#3084—21no—
71#3084—21no—
72#3080—21no—
73#2960C2211yescharacteristic
74#2951C2211yescharacteristic
75#2951C2211yescharacteristic
76C4×#135C2211yescharacteristic
77#2255C2211yescharacteristic
78#2255C2211yescharacteristic
79#2255C2211yescharacteristic
80#2255C2211yescharacteristic
81#2255C2211yescharacteristic
82#2255C2211yescharacteristic
83#2254C2211yescharacteristic
84#2253C2211yescharacteristic
85#2253C2211yescharacteristic
86#2253C2211yescharacteristic
87#2253C2211yescharacteristic
88#2252C2211yescharacteristic
89#2245C2211yescharacteristic
90#2245C2211yescharacteristic
91#2245C2211yescharacteristic
92#2245C2211yescharacteristic
93#2243C2211yescharacteristic
94#2243C2211yescharacteristic
95#2242C2211yescharacteristic
96#2242C2211yescharacteristic
97#2242C2211yescharacteristic
98#2242C2211yescharacteristic
99#2241C2211yescharacteristic
100#2241C2211yescharacteristic
101#2237C2211yescharacteristic
102#2237C2211yescharacteristic
103#2237C2211yescharacteristic
104#2236C2211yescharacteristic
105#2236C2211yescharacteristic
106#2236C2211yescharacteristic
107#2235C2211yescharacteristic
108#2235C2211yescharacteristic
109#2235C2211yescharacteristic
110#2234C2211yescharacteristic
111#2233C2211yescharacteristic
112#2232C2211yescharacteristic
113#2229C2211yescharacteristic
114#2229C2211yescharacteristic
115#2229C2211yescharacteristic
116#2229C2211yescharacteristic
117#2229C2211yescharacteristic
118#2229C2211yescharacteristic
119#2229C2211yescharacteristic
120#2229C2211yescharacteristic
121#2229C2211yescharacteristic
122#2229C2211yescharacteristic
123#2229C2211yescharacteristic
124#2229C2211yescharacteristic
125#2229C2211yescharacteristic
126#2229C2211yescharacteristic
127#2229C2211yescharacteristic
128#2228C2211yescharacteristic
129#2228C2211yescharacteristic
130#2228C2211yescharacteristic
131#2228C2211yescharacteristic
132#2228C2211yescharacteristic
133#2228C2211yescharacteristic
134#2228C2211yescharacteristic
135#2227C2211yescharacteristic
136#2227C2211yescharacteristic
137#2227C2211yescharacteristic
138#2227C2211yescharacteristic
139#2226C2211yescharacteristic
140#2226C2211yescharacteristic
141#2225C2211yescharacteristic
142#2225C2211yescharacteristic
143#2225C2211yescharacteristic
144#2225C2211yescharacteristic
145#2225C2211yescharacteristic
146#2224C2211yescharacteristic
147#2224C2211yescharacteristic
148#2224C2211yescharacteristic
149#2211C2211yescharacteristic
150#2211C2211yescharacteristic
151#2211C2211yescharacteristic
152#2210C2211yescharacteristic
153#2210C2211yescharacteristic
154#2210C2211yescharacteristic
155#2209C2211yescharacteristic
156#2209C2211yescharacteristic
157#2209C2211yescharacteristic
158#2208C2211yescharacteristic
159#2208C2211yescharacteristic
160#2208C2211yescharacteristic
161#2189C2211yescharacteristic
162#2189C2211yescharacteristic
163#2189C2211yescharacteristic
164#2186C2211yescharacteristic
165#2183C2211yescharacteristic
166#2183C2211yescharacteristic
167#2183C2211yescharacteristic
168#2183C2211yescharacteristic
169#2183C2211yescharacteristic
170#2183C2211yescharacteristic
171Q8×C16C2211yescharacteristic
172Q8×C16C2211yescharacteristic
173#2177C2211yescharacteristic
174#2177C2211yescharacteristic
175#2176C2211yescharacteristic
176#2176C2211yescharacteristic
177#2176C2211yescharacteristic
178#2176C2211yescharacteristic
179#2175C2211yescharacteristic
180#2175C2211yescharacteristic
181#2175C2211yescharacteristic
182#2175C2211yescharacteristic
183#2175C2211yescharacteristic
184#2175C2211yescharacteristic
185C4×Q32C2211yescharacteristic
186C4×Q32C2211yescharacteristic
187C4×Q32C2211yescharacteristic
188C4×Q32C2211yescharacteristic
189C4×Q32C2211yescharacteristic
190C4×SD32C2211yescharacteristic
191C4×SD32C2211yescharacteristic
192C4×SD32C2211yescharacteristic
193C4×SD32C2211yescharacteristic
194C4×SD32C2211yescharacteristic
195C4×SD32C2211yescharacteristic
196C4×D16C2211yescharacteristic
197#2164C2211yescharacteristic
198#2164C2211yescharacteristic
199#2164C2211yescharacteristic
200#2164C2211yescharacteristic
201#2163C2211yescharacteristic
202#2162C2211yescharacteristic
203C2×#135C2311yescharacteristic
204#563—41no—
205#563—41no—
206Q82—21no—
207#557—21no—
208#557—21no—
209#557—21no—
210#557—21no—
211#557—21no—
212#557—21no—
213#557—21no—
214#556—21no—
215#556—21no—
216#556—21no—
217#556—41no—
218#554—21no—
219#554—21no—
220#554—21no—
221#554—21no—
222#554—21no—
223#554—41no—
224#554—41no—
225#554—41no—
226#554—41no—
227#552—41no—
228#544—21no—
229#544—21no—
230#544—41no—
231#544—41no—
232#544—41no—
233#542—21no—
234#542—21no—
235#541—21no—
236#541—21no—
237#541—41no—
238#541—41no—
239#541—41no—
240#533—21no—
241#533—41no—
242#533D411yescharacteristic
243#529—21no—
244C2×#125—21no—
245C2×#125—41no—
246#520—21no—
247#520—21no—
248C4×#41—21no—
249C2×Q32C2311yescharacteristic
250C2×Q32C2311yescharacteristic
251C2×Q32C2311yescharacteristic
252C2×SD32C2311yescharacteristic
253C2×SD32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×D16C2311yescharacteristic
257#501—21no—
258#501—21no—
259#501—21no—
260#501—21no—
261#500C2311yescharacteristic
262#500C2311yescharacteristic
263#500C2311yescharacteristic
264#500C2311yescharacteristic
265#500C2311yescharacteristic
266#500C2311yescharacteristic
267#500C2311yescharacteristic
268#499—21no—
269#499—21no—
270#499C2311yescharacteristic
271#499C2311yescharacteristic
272#499C2311yescharacteristic
273#499C2311yescharacteristic
274#499C2311yescharacteristic
275#499C2311yescharacteristic
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#499C2311yescharacteristic
281#495C2311yescharacteristic
282#495C2311yescharacteristic
283#495C2311yescharacteristic
284#494C2311yescharacteristic
285#494C2311yescharacteristic
286#494C2311yescharacteristic
287#491—21no—
288#491—21no—
289#489—21no—
290#489—21no—
291#488—21no—
292#487—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#479—21no—
302#479—21no—
303#479—21no—
304#479—21no—
305#478—21no—
306#478—21no—
307#478—21no—
308#478—21no—
309#478—21no—
310#478—21no—
311#478—21no—
312#478—21no—
313#478—21no—
314#478—21no—
315#477—21no—
316#477—21no—
317#477—21no—
318#476—21no—
319#476—21no—
320#476—21no—
321#476—21no—
322#476—21no—
323#475—21no—
324#475—21no—
325#475—21no—
326#475—21no—
327#475—21no—
328#475—21no—
329#470—21no—
330#470—21no—
331#468—21no—
332#468—21no—
333#467—21no—
334#467C2311yescharacteristic
335#467C2311yescharacteristic
336#467C2311yescharacteristic
337#466C2311yescharacteristic
338#465—21no—
339#464—21no—
340#464—21no—
341#464—21no—
342#464—21no—
343#464—21no—
344#464—21no—
345#462—21no—
346#462—21no—
347#462—21no—
348#461—21no—
349#461—21no—
350#461—21no—
351#446D411yescharacteristic
352#446D411yescharacteristic
353#446D411yescharacteristic
354#446D411yescharacteristic
355C8×Q8C2311yescharacteristic
356C8×Q8C2311yescharacteristic
357C8×Q8C2311yescharacteristic
358C8×Q8C2311yescharacteristic
359#441—21no—
360#441—21no—
361#440—21no—
362#440—21no—
363#440—21no—
364#440—21no—
365#440—21no—
366#440—21no—
367C4×Q16—21no—
368C4×Q16C2311yescharacteristic
369C4×Q16C2311yescharacteristic
370C4×Q16C2311yescharacteristic
371C4×Q16C2311yescharacteristic
372C4×Q16C2311yescharacteristic
373C4×Q16C2311yescharacteristic
374C4×Q16C2311yescharacteristic
375C4×Q16C2311yescharacteristic
376C4×Q16C2311yescharacteristic
377C4×Q16C2311yescharacteristic
378C4×Q16C2311yescharacteristic
379C4×Q16C2311yescharacteristic
380C4×Q16C2311yescharacteristic
381C4×Q16C2311yescharacteristic
382C4×Q16C2311yescharacteristic
383C4×SD16—21no—
384C4×SD16—21no—
385C4×SD16—21no—
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×#107C2311yescharacteristic
399C2×#107C2311yescharacteristic
400C2×#106—21no—
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#358C2311yescharacteristic
463#358C2311yescharacteristic
464#358C2311yescharacteristic
465#358C2311yescharacteristic
466#358C2311yescharacteristic
467#358C2311yescharacteristic
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
488C4×C16C2311yescharacteristic
489C4×C16C2311yescharacteristic
490C4×C16C2311yescharacteristic
491C4×C16C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495#135—22no—
496#135—22no—
497C2×Q16—21no—
498C2×Q16—21no—
499C2×Q16—21no—
500C2×Q16C2411yescharacteristic
501C2×Q16C2411yescharacteristic
502C2×Q16C2411yescharacteristic
503C2×Q16C2411yescharacteristic
504C2×SD16—21no—
505C2×SD16—21no—
506C2×SD16—21no—
507C2×SD16—21no—
508C2×D8C2411yescharacteristic
509C2×D8C2411yescharacteristic
510C2×M16C2×D411yescharacteristic
511C2×M16C2×D411yescharacteristic
512C22×C8C2×D411yescharacteristic
513C22×C8C2411yescharacteristic
514C4⋊Q8—21no—
515C4⋊Q8—21no—
516C4⋊Q8—21no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519C4⋊Q8—21no—
520C4⋊Q8—21no—
521C4⋊Q8—21no—
522C4⋊Q8—21no—
523C4⋊Q8—21no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8D811yescharacteristic
536C4⋊Q8D811yescharacteristic
537#126—41no—
538#126—41no—
539#126—41no—
540#126—41no—
541#126—41no—
542#126—41no—
543#126—41no—
544#126—41no—
545#126—41no—
546#126—41no—
547#126—41no—
548#126—41no—
549#126—41no—
550#125—21no—
551#125—21no—
552#125—21no—
553#125—21no—
554#125—21no—
555#125—21no—
556#125—21no—
557#125—21no—
558#125—21no—
559#125—21no—
560#125—21no—
561#125—41no—
562#125—41no—
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#125—41no—
576#125—41no—
577#125—41no—
578#125—41no—
579#125—41no—
580#125—41no—
581#125—41no—
582#125—41no—
583#125—41no—
584#125—41no—
585#125D811yescharacteristic
586#125D811yescharacteristic
587#124—21no—
588#124—21no—
589#124—21no—
590#124—41no—
591#124—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
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—
628C4×Q8—21no—
629C4×Q8—21no—
630C4×Q8—21no—
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×Q8—41no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8C2×D411yescharacteristic
653C4×Q8C2×D411yescharacteristic
654C4×Q8C2×D411yescharacteristic
655C4×Q8C2×D411yescharacteristic
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—
672#117—21no—
673#117—41no—
674#117—41no—
675#117—41no—
676#117—41no—
677#117—41no—
678#117—41no—
679#117—41no—
680#117—41no—
681#117C2×D411yescharacteristic
682#117C2×D411yescharacteristic
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
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—
698Q32—22no—
699SD32—22no—
700SD32—22no—
701SD32—22no—
702SD32—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#107C2411yescharacteristic
722#107C2411yescharacteristic
723#107C2411yescharacteristic
724#107C2411yescharacteristic
725#107C2411yescharacteristic
726#107C2411yescharacteristic
727#107C2411yescharacteristic
728#107C2411yescharacteristic
729#107C2411yescharacteristic
730#107C2411yescharacteristic
731#106—21no—
732#106—21no—
733#106—21no—
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#103—21no—
770#103—21no—
771#103—21no—
772#103—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—21no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—41no—
804C2×Q8—41no—
805C2×Q8—41no—
806C2×Q8—41no—
807C2×Q8—41no—
808C2×Q8C2×D811yescharacteristic
809C2×Q8C2×D811yescharacteristic
810C2×Q8C2×D811yescharacteristic
811C2×Q8C2×D811yescharacteristic
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—41no—
816C22×C4—41no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4C2×D811yescharacteristic
829C22×C4C2×D811yescharacteristic
830C22×C4C22×D411yescharacteristic
831Q16—21no—
832Q16—21no—
833Q16—21no—
834Q16—21no—
835Q16—21no—
836Q16—21no—
837Q16—21no—
838Q16—81no—
839Q16—81no—
840Q16—81no—
841Q162−1+412yes—
842SD16—24no—
843SD16—81no—
844SD16—81no—
845SD16—81no—
846D8—21no—
847D8—21no—
848D8—21no—
849D82−1+412yes—
850M16—41no—
851M16—41no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—41no—
855C2×C8C22×D411yescharacteristic
856C2×C8C22×D411yescharacteristic
857C2×C8C22×D411yescharacteristic
858C2×C8C22×D411yescharacteristic
859C2×C8C22×D411yescharacteristic
860C2×C8C22×D411yescharacteristic
861C2×C8C22×D411yescharacteristic
862C2×C8C2511yescharacteristic
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—41no—
874C4⋊C4—41no—
875C4⋊C4—41no—
876C4⋊C4—41no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—41no—
884C4⋊C4—41no—
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⋊C4C2×D811yescharacteristic
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
944C22⋊C4—41no—
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⋊C4C2×D811yescharacteristic
965C22⋊C4C2×D811yescharacteristic
966C22⋊C4C2×D811yescharacteristic
967C22⋊C4C2×D811yescharacteristic
968C42—41no—
969C42—41no—
970C42—41no—
971C42—41no—
972C42—41no—
973C42—41no—
974C42—41no—
975C42—41no—
976C42—41no—
977C42—41no—
978C42—41no—
979C42—41no—
980C42—41no—
981C42—41no—
982C42—41no—
983C42—41no—
984C42C2×D811yescharacteristic
985C42C2×D811yescharacteristic
986C42C22×D411yescharacteristic
987C42C22×D411yescharacteristic
988C42C22×D411yescharacteristic
989C42C22×D411yescharacteristic
990C42C22×D411yescharacteristic
991C42C22×D411yescharacteristic
992C16—21no—
993C16—21no—
994C16—21no—
995C16—21no—
996C16—21no—
997C16—21no—
998C16—21no—
999C16—21no—
1000C23—41no—
1001C23—41no—
1002C23C22×D811yescharacteristic
1003Q8—22no—
1004Q8—41no—
1005Q8—41no—
1006Q8—41no—
1007Q8—41no—
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—41no—
1015Q8—161no—
1016Q8—161no—
1017Q8—161no—
1018Q8—161no—
1019Q8—161no—
1020Q8—161no—
1021Q8—161no—
1022D4—22no—
1023D4—44no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—161no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—44no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—82no—
1048C2×C4—161no—
1049C2×C4—161no—
1050C2×C4—161no—
1051C2×C4—161no—
1052C2×C4—161no—
1053C2×C4—161no—
1054C2×C4—161no—
1055C2×C4—161no—
1056C2×C4—161no—
1057C2×C4—161no—
1058C2×C4C22×D811yescharacteristic
1059C2×C4C22×D811yescharacteristic
1060C2×C4C22×D811yescharacteristic
1061C2×C4C22×D811yescharacteristic
1062C2×C4C22×D811yescharacteristic
1063C2×C4C22×D811yescharacteristic
1064C2×C4C22×D811yescharacteristic
1065C2×C4C22×D811yescharacteristic
1066C2×C4C22×D811yescharacteristic
1067C2×C4C22×D811yescharacteristic
1068C2×C4C22×D811yescharacteristic
1069C2×C4C22×D811yescharacteristic
1070C2×C4C22×D811yescharacteristic
1071C2×C4C23×D411yescharacteristic
1072C8—21no—
1073C8—21no—
1074C8—21no—
1075C8—21no—
1076C8—21no—
1077C8—21no—
1078C8—21no—
1079C8C2×2−1+411yescharacteristic
1080C8C2×2−1+411yescharacteristic
1081C22—21no—
1082C22—21no—
1083C22—21no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22C23×D811yescharacteristic
1091C4—21no—
1092C4—21no—
1093C4—21no—
1094C4—21no—
1095C4—21no—
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—21no—
1102C4—21no—
1103C4—21no—
1104C4—42no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4#348611yescharacteristic
1119C4#358611yescharacteristic
1120C2—41no—
1121C2—82no—
1122C2—161no—
1123C2#6181711yescharacteristic
1124C2#6263511yescharacteristic
1125C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
prime radical#2186C22
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. #62380C2semidirect
2. #61376C2semidirect
3. #33957C2semidirect
4. #33956C2semidirect
5. #33955C2semidirect
6. #33955C2semidirect
7. #33954C2semidirect
8. #33952C2semidirect
9. #33950C2semidirect
10. #33948C2semidirect
11. #33944C2semidirect
12. #33944C2semidirect
13. #33943C2semidirect
14. #33943C2semidirect
15. #33941C2semidirect
16. #33939C2semidirect
17. #33931C2semidirect
18. #33927C2semidirect
19. #33810C2semidirect
20. #33809C2semidirect
21. #33808C2semidirect
22. #33808C2semidirect
23. #33802C2semidirect
24. #33798C2semidirect
27. #33680C2semidirect
28. #33680C2semidirect
30. #33667C2semidirect
31. #33499C2semidirect

Maximal subgroups

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

subgroupindex
#623802
#613762
#339572
#339562
#339552
#339542
#339522
#339502
#339482
#339442
#339432
#339412
#339392
#339312
#339272
#338102
#338092
#338082
#338022
#337982
#336852
#336842
#336802
#336712
#336672
#334992