Finite Group Databasebeta

← #7661869

Subgroups — #7661869

Order 512.

4388 conjugacy classes of subgroups.

The subgroup lattice has 1229 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52290C213yesmaximal
2#42972C213yesmaximal
3#42955C213yesmaximal
4#42826C213yesmaximal, complemented
5#42824C213yesmaximal, complemented
6#42822C213yesmaximal, complemented
7#42820C213yesmaximal, complemented
8#39987C213yesmaximal
9#39983C213yesmaximal
10#39978C213yesmaximal, complemented
11#39974C213yesmaximal, complemented
12#39754C213yesmaximal, complemented
13#39182C213yesmaximal, complemented
14#37429C213yesmaximal
15#37314C213yesmaximal
16#37311C213yesmaximal
17#36577C211yesmaximal, characteristic
18#36475C211yesmaximal, characteristic, complemented
19#36474C211yesmaximal, characteristic, complemented
20#36466C211yesmaximal, characteristic, complemented
21#36447C211yesmaximal, characteristic, complemented
22#36435C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35971C211yesmaximal, characteristic, complemented
25#35957C211yesmaximal, characteristic, complemented
26#35937C211yesmaximal, characteristic, complemented
27#35786C211yesmaximal, characteristic
28#35711C211yesmaximal, characteristic
29#34262C211yesmaximal, characteristic
30#34262C211yesmaximal, characteristic
31#34249C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2864C2213yes—
40#2862C2213yes—
41#2859C2213yes—
42#2859C2213yes—
43#2857C2213yes—
44#2851C2213yes—
45#2845C2216yes—
46#2843C2216yes—
47#2806C2213yes—
48#2806C2216yes—
49#2805C2213yes—
50#2805C2216yes—
51#2802C2216yes—
52#2802C2216yes—
53#2792C2216yes—
54#2791C2213yes—
55#2791C2216yes—
56#2791C2213yes—
57#2790C2216yes—
58#2788C2213yes—
59#2788C2216yes—
60#2788C2211yescharacteristic
61#2774C2216yes—
62#2774C2213yes—
63#2774C2213yes—
64#2768C2213yes—
65#2768C2213yes—
66#2768C2216yes—
67#2763C2216yes—
68#2755C2216yes—
69#2755C2216yes—
70#2755C2216yes—
71#2742C2216yes—
72#2734C2213yes—
73#2729C2216yes—
74#2729C2213yes—
75#2729C2213yes—
76#2726C2213yes—
77#2720C2213yes—
78#2720C2213yes—
79#2713C2216yes—
80#2713C2216yes—
81#2704C2216yes—
82#2666C2216yes—
83#2666C2216yes—
84#2666C2216yes—
85#2666C2216yes—
86#2660C2213yes—
87#2660C2216yes—
88#2660C2213yes—
89#2647C2216yes—
90#2647C2213yes—
91#2647C2213yes—
92#2629C2213yes—
93#2628C2213yes—
94#2612C2216yes—
95#2605C2216yes—
96#2605C2216yes—
97#2584C2213yes—
98#2584C2213yes—
99#2584C2213yes—
100#2584C2213yes—
101#2582C2213yes—
102#2582C2213yes—
103#2581C2213yes—
104#2581C2213yes—
105#2571C2216yes—
106#2571C2213yes—
107#2571C2213yes—
108#2571C2213yes—
109#2570C2213yes—
110#2570C2213yes—
111#2570C2216yes—
112#2570C2213yes—
113#2570C2213yes—
114#2568C2213yes—
115#2568C2213yes—
116#2567C2213yes—
117#2567C2213yes—
118#2565C2213yes—
119#2565C2213yes—
120#2552C2213yes—
121#2552C2213yes—
122#2552C2213yes—
123#2552C2213yes—
124#2551C2213yes—
125#2551C2213yes—
126#2551C2213yes—
127#2550C2216yes—
128#2550C2213yes—
129#2550C2213yes—
130#2550C2213yes—
131#2550C2213yes—
132#2550C2213yes—
133#2550C2213yes—
134#2550C2213yes—
135#2550C2213yes—
136#2550C2213yes—
137#2550C2213yes—
138#2546C2213yes—
139#2546C2213yes—
140#2509C2213yes—
141#2509C2213yes—
142#2509C2213yes—
143#2508C2213yes—
144#2508C2213yes—
145#2508C2213yes—
146#2508C2213yes—
147#2508C2213yes—
148#2508C2213yes—
149#2508C2213yes—
150#2507C2213yes—
151#2507C2213yes—
152#2507C2213yes—
153#2506C2213yes—
154#2506C2213yes—
155#2506C2213yes—
156#2453C2213yes—
157#2453C2213yes—
158#2453C2213yes—
159#2453C2213yes—
160#2451C2213yes—
161#2451C2213yes—
162#2451C2213yes—
163#2451C2213yes—
164#2442C2213yes—
165#2442C2213yes—
166#2442C2213yes—
167#2441C2213yes—
168#2440C2213yes—
169#2439C2213yes—
170#2439C2213yes—
171#2439C2213yes—
172#2402C2213yes—
173#2402C2213yes—
174#2399C2213yes—
175#2399C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2356C2213yes—
179#2356C2213yes—
180#2355C2213yes—
181#2355C2213yes—
182#2351C2213yes—
183#2351C2213yes—
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196Q8×C4⋊C4C2213yes—
197Q8×C4⋊C4C2213yes—
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206#2347C2213yes—
207#2347C2213yes—
208#2346C2213yes—
209#2346C2213yes—
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214#2331C2216yes—
215#2330C2216yes—
216#2320C2213yes—
217#2320C2213yes—
218#2317C2213yes—
219#2317C2213yes—
220#2314C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×C4⋊Q8C2213yes—
224C4×#125C2213yes—
225C4×#125C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228#2298C2213yes—
229#2298C2213yes—
230#2296C2213yes—
231#2296C2213yes—
232#2295C2213yes—
233#2295C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239Q82—44no—
240#557—44no—
241#557—44no—
242#557—44no—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2316yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2316yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263#519—44no—
264#519Q8116yescomplemented
265C2×C4×Q8—44no—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2313yes—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×#117C2313yes—
291C2×#117C2313yes—
292C2×#117C2313yes—
293C2×#117C2313yes—
294C22×C4⋊C4C2313yes—
295C22×C42C2313yes—
296#400C2313yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2313yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2313yes—
313#400C2313yes—
314#400C2316yes—
315#400C2311yescharacteristic
316#400C2311yescharacteristic
317#400C2313yes—
318#399C2313yes—
319#399C2313yes—
320#398C2313yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2313yes—
325#398C2313yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2313yes—
331#398C2316yes—
332#398C2316yes—
333#398C2313yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2316yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2316yes—
342#398C2316yes—
343#398C2316yes—
344#398C2313yes—
345#398C2316yes—
346#398C2313yes—
347#398C2313yes—
348#398C2316yes—
349#398C2316yes—
350#398C2311yescharacteristic
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2316yes—
358#398C2316yes—
359#396C2313yes—
360#396C2316yes—
361#396C2311yescharacteristic
362#396C2313yes—
363#396C2313yes—
364#395C2313yes—
365#395C2316yes—
366#395C2316yes—
367#395C2316yes—
368#395C2313yes—
369#395C2316yes—
370#395C2313yes—
371#395C2316yes—
372#395C2316yes—
373#395C2313yes—
374#395C2313yes—
375#395C2316yes—
376#395C2311yescharacteristic
377#395C2313yes—
378#395C2313yes—
379#395C2313yes—
380#395C2313yes—
381#395C2316yes—
382#395C2316yes—
383#393C2316yes—
384#393C2311yescharacteristic
385#393C2313yes—
386#391C2311yescharacteristic
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2316yes—
394#391C2316yes—
395#391C2313yes—
396#391C2313yes—
397#391C2316yes—
398#391C2316yes—
399#391C2316yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2316yes—
405#391C2316yes—
406#391C2313yes—
407#391C2316yes—
408#391C2316yes—
409#389C2311yescharacteristic
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2311yescharacteristic
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2316yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2316yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2313yes—
442#389C2316yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2316yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2316yes—
451#389C2316yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2316yes—
469#389C2316yes—
470#389C2316yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2316yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2316yes—
484#388C2316yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2311yescharacteristic
490#388C2311yescharacteristic
491#387C2311yescharacteristic
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2313yes—
521#387C2316yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2313yes—
528#385C2316yes—
529#385C2313yes—
530#385C2313yes—
531#385C2313yes—
532#385C2316yes—
533#385C2313yes—
534#385C2313yes—
535#385C2311yescharacteristic
536#385C2311yescharacteristic
537#385C2313yes—
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2316yes—
543#384C2313yes—
544#384C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2316yes—
548#384C2313yes—
549#384C2313yes—
550#383C2316yes—
551#383C2316yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2316yes—
565#382C2313yes—
566#382C2313yes—
567#382C2316yes—
568#382C2316yes—
569#382C2316yes—
570#382C2316yes—
571#382C2316yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2316yes—
577#380C2313yes—
578#380C2311yescharacteristic
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2316yes—
604C4×C4⋊C4C2316yes—
605C4×C4⋊C4C2316yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2316yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619#376C2313yes—
620#376C2313yes—
621#376C2316yes—
622#376C2316yes—
623C43C2313yes—
624C43C2313yes—
625C22×Q8—24no—
626C22×Q8—24no—
627C22×Q8C2×Q818yes—
628C22×Q8C2413yes—
629C22×Q8C2411yescharacteristic
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2416yes—
634C22×Q8C2411yescharacteristic
635C23×C4C2413yes—
636C23×C4C2411yescharacteristic
637C23×C4C2413yes—
638C4⋊Q8—46no—
639C4⋊Q8—46no—
640C4⋊Q8—46no—
641C4⋊Q8—46no—
642C4⋊Q8—46no—
643C4⋊Q8—46no—
644C4⋊Q8—46no—
645C4⋊Q8—46no—
646C4⋊Q8—412no—
647#125—412no—
648#125—46no—
649#125—46no—
650#125—46no—
651#125—46no—
652#125—46no—
653#125—46no—
654#125—46no—
655#125—46no—
656C22⋊Q8—46no—
657C22⋊Q8—46no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—46no—
671C4×Q8—46no—
672C4×Q8—46no—
673C4×Q8—46no—
674C4×Q8—46no—
675C4×Q8—46no—
676C4×Q8—46no—
677C4×Q8—46no—
678C4×Q8C2×Q8124yes—
679C4×Q8C2×Q8124yes—
680C4×Q8C2×Q818yes—
681C4×Q8C2×Q818yes—
682#117—46no—
683#117—46no—
684#117C2×Q8124yes—
685#117C2×Q8124yes—
686C2×C4⋊C4—46no—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2411yescharacteristic
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C42—46no—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2416yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2416yes—
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2416yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2416yes—
810#95C2411yescharacteristic
811#95C2411yescharacteristic
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2416yes—
823#95C2416yes—
824#95C2416yes—
825#95C2416yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2411yescharacteristic
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2416yes—
836#95C2416yes—
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2413yes—
841#95C2413yes—
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2416yes—
851#95C2416yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2416yes—
861#95C2413yes—
862#95C2416yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2416yes—
877#95C2416yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2416yes—
884C24C2511yescharacteristic
885C2×Q8—232no—
886C2×Q8—26no—
887C2×Q8—26no—
888C2×Q8—22no—
889C2×Q8—26no—
890C2×Q8—26no—
891C2×Q8—41no—
892C2×Q8—41no—
893C2×Q8—43no—
894C2×Q8—43no—
895C2×Q8—43no—
896C2×Q8—43no—
897C2×Q8—43no—
898C2×Q8—43no—
899C2×Q8—43no—
900C2×Q8—46no—
901C2×Q8—46no—
902C2×Q8—46no—
903C2×Q8C22×Q8112yes—
904C2×Q8C22×Q814yes—
905C2×Q8H(5,𝔽2)14yes—
906C2×Q82−1+414yes—
907C22×C4—26no—
908C22×C4—26no—
909C22×C4—22no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—43no—
913C22×C4—43no—
914C22×C4—43no—
915C22×C4C22×Q8112yes—
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2513yes—
920C22×C4C2511yescharacteristic
921C22×C4C2513yes—
922C22×C4C2513yes—
923C22×C4C2513yes—
924C22×C4C2511yescharacteristic
925C22×C4C2513yes—
926C22×C4C2513yes—
927C22×C4C2513yes—
928C22×C4C2513yes—
929C22×C4C2513yes—
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2513yes—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—22no—
966C4⋊C4—46no—
967C4⋊C4—43no—
968C4⋊C4—43no—
969C4⋊C4—41no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—41no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—46no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—46no—
982C4⋊C4—43no—
983C4⋊C4—41no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—46no—
1004C4⋊C4—46no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—46no—
1008C4⋊C4—46no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—46no—
1014C4⋊C4—46no—
1015C4⋊C4—46no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—46no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—46no—
1023C4⋊C4—43no—
1024C4⋊C4C22×Q8112yes—
1025C4⋊C4C22×Q8112yes—
1026C4⋊C4C22×Q8112yes—
1027C4⋊C4C22×Q8112yes—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—43no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—43no—
1035C22⋊C4—43no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4C22×Q814yes—
1039C22⋊C4C22×Q8112yes—
1040C42—26no—
1041C42—26no—
1042C42—26no—
1043C42—26no—
1044C42—26no—
1045C42—26no—
1046C42—26no—
1047C42—26no—
1048C42—26no—
1049C42—26no—
1050C42—26no—
1051C42—26no—
1052C42—26no—
1053C42—43no—
1054C42—43no—
1055C42—43no—
1056C42—46no—
1057C42—41no—
1058C42—43no—
1059C42—41no—
1060C42—46no—
1061C42—43no—
1062C42—43no—
1063C42—46no—
1064C42—43no—
1065C42C22×Q8124yes—
1066C42C22×Q8112yes—
1067C42C22×Q8112yes—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23C23×Q812yes—
1075C23C2611yescharacteristic
1076Q8—224no—
1077Q8—44no—
1078Q8—86no—
1079Q8—86no—
1080Q8—86no—
1081Q8—166no—
1082Q8#544116yes—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—224no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—44no—
1165C2×C4—86no—
1166C2×C4C23×Q816yes—
1167C2×C4C23×Q816yes—
1168C2×C4C23×Q812yes—
1169C2×C4C23×Q812yes—
1170C2×C4C23×Q816yes—
1171C2×C4C23×Q816yes—
1172C2×C4C2×H(5,𝔽2)16yes—
1173C2×C4C2×2−1+416yes—
1174C2×C4#58512yes—
1175C2×C4#58512yes—
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22C24×Q811yescharacteristic
1184C22C22×H(5,𝔽2)11yescharacteristic
1185C22C22×2−1+411yescharacteristic
1186C22C2×#58511yescharacteristic
1187C22C2×#58511yescharacteristic
1188C222−1+611yescharacteristic
1189C222−1+611yescharacteristic
1190C4—26no—
1191C4—22no—
1192C4—22no—
1193C4—26no—
1194C4—22no—
1195C4—22no—
1196C4—26no—
1197C4—41no—
1198C4—43no—
1199C4—43no—
1200C4—43no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—43no—
1205C4—43no—
1206C4—43no—
1207C4—41no—
1208C4—41no—
1209C4—43no—
1210C4—43no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—43no—
1216C4—43no—
1217C4—43no—
1218C4—43no—
1219C4C2×#544112yes—
1220C2—42no—
1221C2C22×#54411yescharacteristic
1222C2#6289711yescharacteristic
1223C2#6291911yescharacteristic
1224C2#6300411yescharacteristic
1225C2#6300411yescharacteristic
1226C2#6303411yescharacteristic
1227C2#6305711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #42826C2semidirect
5. #42824C2semidirect
6. #42822C2semidirect
7. #42820C2semidirect
10. #39978C2semidirect
11. #39974C2semidirect
12. #39754C2semidirect
13. #39182C2semidirect
18. #36475C2semidirect
19. #36474C2semidirect
20. #36466C2semidirect
21. #36447C2semidirect
23. #35971C2semidirect
24. #35971C2semidirect
25. #35957C2semidirect
26. #35937C2semidirect
264. #519Q8semidirect

Maximal subgroups

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

subgroupindex
#522902
#429722
#429552
#428262
#428242
#428222
#428202
#399872
#399832
#399782
#399742
#397542
#391822
#374292
#373142
#373112
#365772
#364752
#364742
#364662
#364472
#364352
#359712
#359572
#359372
#357862
#357112
#342622
#342492