Finite Group Databasebeta

← #7661629

Subgroups — #7661629

Order 512.

4384 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52290C213yesmaximal
2#42981C213yesmaximal
3#42932C213yesmaximal
4#42825C213yesmaximal, complemented
5#42824C213yesmaximal, complemented
6#42821C213yesmaximal, complemented
7#42819C213yesmaximal, complemented
8#39986C213yesmaximal
9#39983C213yesmaximal
10#39979C213yesmaximal, complemented
11#39974C213yesmaximal, complemented
12#39183C213yesmaximal, complemented
13#39180C213yesmaximal, complemented
14#37429C213yesmaximal
15#37313C213yesmaximal
16#37311C213yesmaximal
17#36584C211yesmaximal, characteristic, complemented
18#36577C211yesmaximal, characteristic
19#36475C211yesmaximal, characteristic, complemented
20#36466C211yesmaximal, characteristic, complemented
21#36466C211yesmaximal, characteristic, complemented
22#36435C211yesmaximal, characteristic
23#35957C211yesmaximal, characteristic, complemented
24#35957C211yesmaximal, characteristic, complemented
25#35868C211yesmaximal, characteristic, complemented
26#35868C211yesmaximal, characteristic, complemented
27#35845C211yesmaximal, characteristic
28#35786C211yesmaximal, characteristic
29#34262C211yesmaximal, characteristic
30#34262C211yesmaximal, characteristic
31#34249C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2864C2213yes—
40#2859C2213yes—
41#2859C2213yes—
42#2859C2213yes—
43#2857C2213yes—
44#2851C2213yes—
45#2844C2216yes—
46#2843C2216yes—
47#2807C2216yes—
48#2806C2213yes—
49#2805C2213yes—
50#2805C2216yes—
51#2802C2216yes—
52#2802C2216yes—
53#2802C2216yes—
54#2792C2216yes—
55#2792C2216yes—
56#2791C2213yes—
57#2791C2216yes—
58#2791C2213yes—
59#2790C2216yes—
60#2788C2213yes—
61#2788C2213yes—
62#2788C2216yes—
63#2774C2213yes—
64#2774C2213yes—
65#2774C2216yes—
66#2768C2213yes—
67#2768C2216yes—
68#2768C2211yescharacteristic
69#2755C2216yes—
70#2755C2216yes—
71#2742C2216yes—
72#2734C2213yes—
73#2729C2213yes—
74#2729C2213yes—
75#2726C2213yes—
76#2726C2216yes—
77#2720C2216yes—
78#2720C2213yes—
79#2720C2213yes—
80#2713C2216yes—
81#2704C2216yes—
82#2666C2216yes—
83#2666C2216yes—
84#2666C2216yes—
85#2666C2216yes—
86#2660C2213yes—
87#2660C2213yes—
88#2647C2216yes—
89#2647C2216yes—
90#2647C2213yes—
91#2647C2213yes—
92#2629C2213yes—
93#2628C2213yes—
94#2612C2216yes—
95#2606C2216yes—
96#2605C2216yes—
97#2584C2213yes—
98#2584C2213yes—
99#2584C2213yes—
100#2584C2213yes—
101#2584C2213yes—
102#2584C2213yes—
103#2582C2213yes—
104#2582C2213yes—
105#2581C2213yes—
106#2581C2213yes—
107#2571C2213yes—
108#2571C2213yes—
109#2570C2216yes—
110#2570C2213yes—
111#2570C2213yes—
112#2570C2213yes—
113#2570C2213yes—
114#2568C2213yes—
115#2567C2213yes—
116#2567C2213yes—
117#2567C2213yes—
118#2565C2213yes—
119#2565C2213yes—
120#2552C2216yes—
121#2552C2213yes—
122#2552C2213yes—
123#2552C2213yes—
124#2552C2213yes—
125#2552C2213yes—
126#2552C2213yes—
127#2552C2213yes—
128#2552C2213yes—
129#2551C2213yes—
130#2551C2213yes—
131#2550C2216yes—
132#2550C2213yes—
133#2550C2213yes—
134#2550C2213yes—
135#2550C2213yes—
136#2550C2213yes—
137#2550C2213yes—
138#2550C2213yes—
139#2550C2213yes—
140#2509C2213yes—
141#2509C2213yes—
142#2509C2213yes—
143#2509C2213yes—
144#2509C2213yes—
145#2509C2213yes—
146#2509C2213yes—
147#2508C2213yes—
148#2507C2213yes—
149#2507C2213yes—
150#2507C2213yes—
151#2506C2213yes—
152#2506C2213yes—
153#2506C2213yes—
154#2506C2213yes—
155#2506C2213yes—
156#2453C2213yes—
157#2453C2213yes—
158#2453C2213yes—
159#2453C2213yes—
160#2453C2213yes—
161#2453C2213yes—
162#2451C2213yes—
163#2451C2213yes—
164#2442C2213yes—
165#2442C2213yes—
166#2442C2213yes—
167#2441C2213yes—
168#2441C2213yes—
169#2441C2213yes—
170#2440C2213yes—
171#2439C2213yes—
172#2402C2213yes—
173#2402C2213yes—
174#2399C2213yes—
175#2399C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2356C2213yes—
179#2356C2213yes—
180#2355C2213yes—
181#2355C2213yes—
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2213yes—
187#2351C2213yes—
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
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#2330C2216yes—
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
239#557—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×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2316yes—
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#400C2316yes—
297#400C2316yes—
298#400C2313yes—
299#400C2313yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2316yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2316yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2316yes—
317#400C2313yes—
318#399C2316yes—
319#399C2311yescharacteristic
320#399C2313yes—
321#398C2313yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2313yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2313yes—
332#398C2316yes—
333#398C2316yes—
334#398C2313yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2313yes—
341#398C2316yes—
342#398C2313yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2313yes—
347#398C2311yescharacteristic
348#398C2311yescharacteristic
349#398C2313yes—
350#398C2313yes—
351#398C2311yescharacteristic
352#398C2311yescharacteristic
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2316yes—
359#398C2316yes—
360#398C2316yes—
361#396C2313yes—
362#396C2316yes—
363#396C2311yescharacteristic
364#396C2313yes—
365#396C2313yes—
366#395C2313yes—
367#395C2313yes—
368#395C2313yes—
369#395C2316yes—
370#395C2316yes—
371#395C2316yes—
372#395C2316yes—
373#395C2316yes—
374#395C2316yes—
375#395C2316yes—
376#395C2316yes—
377#395C2313yes—
378#395C2313yes—
379#395C2313yes—
380#395C2313yes—
381#395C2313yes—
382#395C2313yes—
383#395C2313yes—
384#393C2313yes—
385#393C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2316yes—
395#391C2316yes—
396#391C2313yes—
397#391C2316yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2316yes—
403#391C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2316yes—
442#389C2316yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2313yes—
455#389C2316yes—
456#389C2316yes—
457#389C2316yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2316yes—
464#389C2316yes—
465#389C2316yes—
466#389C2316yes—
467#389C2316yes—
468#389C2316yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2316yes—
473#389C2316yes—
474#389C2316yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2316yes—
481#389C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2316yes—
485#388C2316yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2311yescharacteristic
491#388C2311yescharacteristic
492#387C2311yescharacteristic
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2313yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2313yes—
528#387C2313yes—
529#385C2316yes—
530#385C2313yes—
531#385C2313yes—
532#385C2313yes—
533#385C2316yes—
534#385C2313yes—
535#385C2313yes—
536#385C2313yes—
537#385C2311yescharacteristic
538#385C2311yescharacteristic
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2316yes—
544#384C2313yes—
545#384C2313yes—
546#384C2316yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2316yes—
553#384C2313yes—
554#383C2316yes—
555#383C2316yes—
556#382C2311yescharacteristic
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
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⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2316yes—
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×Q8C2413yes—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2411yescharacteristic
634C23×C4C2413yes—
635C23×C4C2411yescharacteristic
636C23×C4C2413yes—
637C4⋊Q8—46no—
638C4⋊Q8—46no—
639C4⋊Q8—46no—
640C4⋊Q8—46no—
641C4⋊Q8—46no—
642C4⋊Q8—46no—
643#125—46no—
644#125—46no—
645#125—46no—
646#125—46no—
647#125—46no—
648#125—46no—
649#125—46no—
650#125—46no—
651#125—46no—
652#125—46no—
653#125—412no—
654#125—412no—
655C22⋊Q8—46no—
656C22⋊Q8—46no—
657C4×Q8—24no—
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—46no—
670C4×Q8—46no—
671C4×Q8—46no—
672C4×Q8—46no—
673C4×Q8—46no—
674C4×Q8—46no—
675C4×Q8—46no—
676C4×Q8—46no—
677C4×Q8C2×Q8124yes—
678C4×Q8C2×Q8124yes—
679C4×Q8C2×Q818yes—
680C4×Q8C2×Q818yes—
681#117—46no—
682#117—46no—
683#117C2×Q8124yes—
684#117C2×Q8124yes—
685C2×C4⋊C4—46no—
686C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2413yes—
783C2×C42—46no—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2411yescharacteristic
797C2×C42C2416yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2416yes—
802C2×C42C2416yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2411yescharacteristic
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2416yes—
812#95C2411yescharacteristic
813#95C2411yescharacteristic
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2416yes—
825#95C2416yes—
826#95C2416yes—
827#95C2416yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2416yes—
837#95C2416yes—
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2411yescharacteristic
842#95C2413yes—
843#95C2413yes—
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2416yes—
850#95C2416yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2416yes—
855#95C2413yes—
856#95C2416yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
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#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2416yes—
884C24C2511yescharacteristic
885C2×Q8—232no—
886C2×Q8—26no—
887C2×Q8—26no—
888C2×Q8—26no—
889C2×Q8—43no—
890C2×Q8—43no—
891C2×Q8—43no—
892C2×Q8—43no—
893C2×Q8—43no—
894C2×Q8—43no—
895C2×Q8—43no—
896C2×Q8—43no—
897C2×Q8—43no—
898C2×Q8—43no—
899C2×Q8—43no—
900C2×Q8C22×Q8112yes—
901C2×Q8C22×Q814yes—
902C2×Q8H(5,𝔽2)14yes—
903C2×Q82−1+414yes—
904C22×C4—26no—
905C22×C4—26no—
906C22×C4—22no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—43no—
910C22×C4—43no—
911C22×C4—43no—
912C22×C4C22×Q8112yes—
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2513yes—
917C22×C4C2513yes—
918C22×C4C2513yes—
919C22×C4C2513yes—
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2513yes—
924C22×C4C2513yes—
925C22×C4C2513yes—
926C22×C4C2511yescharacteristic
927C22×C4C2513yes—
928C22×C4C2513yes—
929C22×C4C2513yes—
930C22×C4C2513yes—
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2513yes—
943C4⋊C4—26no—
944C4⋊C4—26no—
945C4⋊C4—26no—
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—22no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—46no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—46no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—46no—
975C4⋊C4—43no—
976C4⋊C4—41no—
977C4⋊C4—46no—
978C4⋊C4—43no—
979C4⋊C4—41no—
980C4⋊C4—43no—
981C4⋊C4—46no—
982C4⋊C4—43no—
983C4⋊C4—41no—
984C4⋊C4—43no—
985C4⋊C4—41no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
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—43no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—46no—
1013C4⋊C4—46no—
1014C4⋊C4—46no—
1015C4⋊C4—43no—
1016C4⋊C4—46no—
1017C4⋊C4—46no—
1018C4⋊C4—46no—
1019C4⋊C4—46no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4C22×Q8112yes—
1025C4⋊C4C22×Q8112yes—
1026C4⋊C4C22×Q8112yes—
1027C4⋊C4C22×Q8112yes—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—43no—
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—22no—
1053C42—43no—
1054C42—43no—
1055C42—43no—
1056C42—43no—
1057C42—43no—
1058C42—41no—
1059C42—46no—
1060C42—43no—
1061C42—46no—
1062C42—46no—
1063C42—43no—
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—86no—
1078Q8—86no—
1079Q8—86no—
1080Q8—86no—
1081Q8#544116yes—
1082C2×C4—21no—
1083C2×C4—23no—
1084C2×C4—21no—
1085C2×C4—23no—
1086C2×C4—21no—
1087C2×C4—23no—
1088C2×C4—21no—
1089C2×C4—23no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—224no—
1097C2×C4—21no—
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—23no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
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—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—21no—
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—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—44no—
1164C2×C4—86no—
1165C2×C4C23×Q812yes—
1166C2×C4C23×Q816yes—
1167C2×C4C23×Q816yes—
1168C2×C4C23×Q812yes—
1169C2×C4C23×Q816yes—
1170C2×C4C23×Q816yes—
1171C2×C4C2×H(5,𝔽2)16yes—
1172C2×C4C2×2−1+416yes—
1173C2×C4#58512yes—
1174C2×C4#58512yes—
1175C22—22no—
1176C22—22no—
1177C22—22no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22C24×Q811yescharacteristic
1183C22C22×H(5,𝔽2)11yescharacteristic
1184C22C22×2−1+411yescharacteristic
1185C22C2×#58511yescharacteristic
1186C22C2×#58511yescharacteristic
1187C222−1+611yescharacteristic
1188C222−1+611yescharacteristic
1189C4—22no—
1190C4—26no—
1191C4—22no—
1192C4—26no—
1193C4—22no—
1194C4—22no—
1195C4—26no—
1196C4—43no—
1197C4—43no—
1198C4—43no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—43no—
1203C4—41no—
1204C4—43no—
1205C4—43no—
1206C4—43no—
1207C4—43no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—43no—
1214C4—43no—
1215C4—43no—
1216C4—43no—
1217C4—41no—
1218C4C2×#544112yes—
1219C2—42no—
1220C2C22×#54411yescharacteristic
1221C2#6289711yescharacteristic
1222C2#6292211yescharacteristic
1223C2#6300411yescharacteristic
1224C2#6300411yescharacteristic
1225C2#6303311yescharacteristic
1226C2#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. #42825C2semidirect
5. #42824C2semidirect
6. #42821C2semidirect
7. #42819C2semidirect
10. #39979C2semidirect
11. #39974C2semidirect
12. #39183C2semidirect
13. #39180C2semidirect
17. #36584C2semidirect
19. #36475C2semidirect
20. #36466C2semidirect
21. #36466C2semidirect
23. #35957C2semidirect
24. #35957C2semidirect
25. #35868C2semidirect
26. #35868C2semidirect
264. #519Q8semidirect

Maximal subgroups

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

subgroupindex
#522902
#429812
#429322
#428252
#428242
#428212
#428192
#399862
#399832
#399792
#399742
#391832
#391802
#374292
#373132
#373112
#365842
#365772
#364752
#364662
#364352
#359572
#358682
#358452
#357862
#342622
#342492