Finite Group Databasebeta

← #7714909

Subgroups — #7714909

Order 512.

4066 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51795C214yesmaximal, complemented
2#51606C214yesmaximal, complemented
3#51603C214yesmaximal, complemented
4#51602C214yesmaximal, complemented
5#47774C214yesmaximal, complemented
6#47731C214yesmaximal, complemented
7#47730C214yesmaximal, complemented
8#47727C214yesmaximal, complemented
9#39751C212yesmaximal
10#39748C212yesmaximal
11#39623C212yesmaximal
12#39620C212yesmaximal
13#39178C214yesmaximal
14#39175C214yesmaximal
15#37623C212yesmaximal
16#37135C212yesmaximal
17#37135C212yesmaximal
18#35120C211yesmaximal, characteristic
19#35120C211yesmaximal, characteristic
20#35015C212yesmaximal
21#35013C212yesmaximal
22#34372C212yesmaximal
23C2×#2330C211yesmaximal, characteristic
24C22×#125C2211yescharacteristic
25#2857C2212yes—
26#2857C2212yes—
27#2855C2212yes—
28#2855C2212yes—
29#2855C2212yes—
30#2855C2212yes—
31#2851C2214yes—
32#2843C2214yes—
33#2843C2214yes—
34#2806C2212yes—
35#2806C2212yes—
36#2806C2214yes—
37#2806C2214yes—
38#2805C2214yes—
39#2805C2212yes—
40#2805C2212yes—
41#2805C2214yes—
42#2802C2214yes—
43#2802C2214yes—
44#2802C2214yes—
45#2802C2214yes—
46#2802C2214yes—
47#2802C2214yes—
48#2792C2214yes—
49#2792C2214yes—
50#2792C2214yes—
51#2792C2214yes—
52#2792C2214yes—
53#2792C2214yes—
54#2791C2214yes—
55#2791C2214yes—
56#2791C2214yes—
57#2791C2214yes—
58#2791C2214yes—
59#2791C2214yes—
60#2774C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2774C2214yes—
64#2774C2214yes—
65#2774C2214yes—
66#2755C2214yes—
67#2755C2214yes—
68#2755C2214yes—
69#2755C2214yes—
70#2755C2214yes—
71#2755C2214yes—
72#2734C2212yes—
73#2734C2212yes—
74#2734C2214yes—
75#2734C2214yes—
76#2726C2214yes—
77#2726C2212yes—
78#2726C2212yes—
79#2726C2214yes—
80#2713C2214yes—
81#2713C2214yes—
82#2713C2214yes—
83#2713C2214yes—
84#2713C2214yes—
85#2713C2214yes—
86#2660C2214yes—
87#2660C2214yes—
88#2659C2211yescharacteristic
89#2659C2211yescharacteristic
90#2659C2211yescharacteristic
91#2659C2211yescharacteristic
92#2659C2212yes—
93#2659C2212yes—
94#2647C2214yes—
95#2647C2214yes—
96#2646C2212yes—
97#2646C2214yes—
98#2646C2212yes—
99#2627C2214yes—
100#2627C2214yes—
101#2612C2214yes—
102#2612C2214yes—
103#2612C2214yes—
104#2612C2214yes—
105#2606C2214yes—
106#2606C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2590C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2588C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2586C2214yes—
121#2585C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2585C2214yes—
125#2584C2214yes—
126#2584C2214yes—
127#2571C2212yes—
128#2569C2214yes—
129#2569C2214yes—
130#2567C2214yes—
131#2552C2214yes—
132#2552C2212yes—
133#2552C2212yes—
134#2551C2212yes—
135#2551C2214yes—
136#2550C2214yes—
137#2550C2214yes—
138#2549C2214yes—
139#2549C2214yes—
140#2546C2214yes—
141#2520C2214yes—
142#2520C2214yes—
143#2520C2214yes—
144#2520C2214yes—
145#2511C2214yes—
146#2511C2212yes—
147#2511C2212yes—
148#2509C2214yes—
149#2509C2214yes—
150#2508C2214yes—
151#2508C2214yes—
152#2507C2214yes—
153#2507C2214yes—
154#2507C2212yes—
155#2507C2214yes—
156#2507C2212yes—
157#2506C2214yes—
158#2506C2214yes—
159#2462C2214yes—
160#2462C2214yes—
161#2462C2214yes—
162#2462C2214yes—
163#2451C2212yes—
164#2451C2214yes—
165#2451C2212yes—
166#2446C2214yes—
167#2446C2212yes—
168#2446C2212yes—
169#2442C2214yes—
170#2442C2214yes—
171#2442C2214yes—
172#2442C2214yes—
173#2440C2214yes—
174#2440C2214yes—
175#2440C2214yes—
176#2440C2214yes—
177#2382C2212yes—
178#2382C2212yes—
179#2382C2212yes—
180#2382C2212yes—
181#2371C2214yes—
182#2371C2214yes—
183#2345C2214yes—
184#2345C2214yes—
185#2345C2214yes—
186#2345C2214yes—
187#2336C2214yes—
188#2336C2214yes—
189#2336C2214yes—
190#2336C2214yes—
191#2330C2214yes—
192#2330C2214yes—
193#2330C2214yes—
194#2330C2214yes—
195#2329C2212yes—
196#2329C2214yes—
197#2329C2212yes—
198#2329C2212yes—
199#2329C2212yes—
200#2329C2212yes—
201#2329C2212yes—
202#2313C2214yes—
203#2313C2214yes—
204C4×C22⋊Q8C2214yes—
205C4×C22⋊Q8C2212yes—
206C4×C22⋊Q8C2212yes—
207C2×#389C2212yes—
208C2×#389C2211yescharacteristic
209C2×#389C2211yescharacteristic
210C2×#389C2212yes—
211C2×#387C2212yes—
212C2×#387C2212yes—
213C2×#384C2211yescharacteristic
214#2283C2212yes—
215#2283C2212yes—
216C2×C4×C4⋊C4C2211yescharacteristic
217C2×C4×C4⋊C4C2211yescharacteristic
218C2×#376C2211yescharacteristic
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2314yes—
225C2×#125Q8116yescomplemented
226C2×#125C2314yes—
227C2×#125C2314yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#125C2312yes—
233C2×#125C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#395C2314yes—
331#395C2314yes—
332#395C2314yes—
333#395C2314yes—
334#395C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2312yes—
363#391C2312yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2312yes—
371#391C2312yes—
372#391C2312yes—
373#391C2312yes—
374#391C2312yes—
375#391C2312yes—
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2312yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#384C2314yes—
537#384C2314yes—
538#384C2312yes—
539#384C2312yes—
540#384C2314yes—
541#384C2312yes—
542#384C2312yes—
543#384C2314yes—
544#384C2314yes—
545#383C2314yes—
546#383C2314yes—
547#382C2314yes—
548#382C2314yes—
549#382C2314yes—
550#382C2312yes—
551#382C2312yes—
552#382C2312yes—
553#382C2312yes—
554#382C2314yes—
555#382C2314yes—
556#381C2314yes—
557#381C2314yes—
558#380C2314yes—
559#380C2314yes—
560#380C2314yes—
561#380C2314yes—
562#380C2312yes—
563#380C2314yes—
564#380C2314yes—
565#380C2312yes—
566#380C2312yes—
567#380C2312yes—
568#380C2312yes—
569#380C2312yes—
570#380C2312yes—
571#380C2312yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2312yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603#376C2314yes—
604#376C2314yes—
605#376C2314yes—
606#376C2314yes—
607C2×#95C2312yes—
608C2×#95C2312yes—
609C2×#95C2311yescharacteristic
610C2×#95C2311yescharacteristic
611C2×#95C2312yes—
612C2×#95C2311yescharacteristic
613C2×#95C2311yescharacteristic
614C2×#95C2312yes—
615C22×Q8C2412yes—
616C22×Q8C2412yes—
617C22×Q8C2414yes—
618C22×Q8C2412yes—
619C22×Q8C2414yes—
620C22×Q8C2412yes—
621C23×C4C2411yescharacteristic
622C23×C4C2411yescharacteristic
623C23×C4C2412yes—
624C23×C4C2412yes—
625C23×C4C2411yescharacteristic
626C23×C4C2411yescharacteristic
627C23×C4C2412yes—
628C23×C4C2412yes—
629C23×C4C2411yescharacteristic
630C23×C4C2411yescharacteristic
631C23×C4C2411yescharacteristic
632C4⋊Q8—82no—
633C4⋊Q8—82no—
634C4⋊Q8—84no—
635C4⋊Q8—84no—
636C4⋊Q8—84no—
637C4⋊Q8—84no—
638#125—84no—
639#125—84no—
640#125—84no—
641#125—84no—
642#125—84no—
643#125C2×Q8132yes—
644#125C2×Q8116yes—
645#125C2×Q8116yes—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—44no—
649C22⋊Q8—44no—
650C22⋊Q8—48no—
651C22⋊Q8—48no—
652C4×Q8—82no—
653C4×Q8—84no—
654C4×Q8—82no—
655C2×C4⋊C4—42no—
656C2×C4⋊C4—42no—
657C2×C4⋊C4—82no—
658C2×C4⋊C4—82no—
659C2×C4⋊C4—82no—
660C2×C4⋊C4—82no—
661C2×C4⋊C4C2×Q818yes—
662C2×C4⋊C4C2×Q818yes—
663C2×C4⋊C4C2×Q8116yes—
664C2×C4⋊C4C2×Q8116yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C42—24no—
750C2×C42—42no—
751C2×C42—82no—
752C2×C42—82no—
753C2×C42C2×Q818yes—
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2412yes—
769C2×C42C2412yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2412yes—
783#95C2412yes—
784#95C2414yes—
785#95C2414yes—
786#95C2412yes—
787#95C2412yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848C24C2511yescharacteristic
849C2×Q8—24no—
850C2×Q8—24no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—44no—
854C2×Q8—44no—
855C2×Q8—44no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—42no—
859C2×Q8—42no—
860C2×Q8—44no—
861C2×Q8—44no—
862C2×Q8—44no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—42no—
881C22×C4—41no—
882C22×C4—42no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4C22×Q814yes—
895C22×C4C22×Q814yes—
896C22×C4C22×Q814yes—
897C22×C4C22×Q818yes—
898C22×C4C22×Q818yes—
899C22×C42−1+414yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2514yes—
911C22×C4C2512yes—
912C22×C4C2514yes—
913C22×C4C2512yes—
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2512yes—
917C22×C4C2512yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—41no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—41no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—44no—
962C4⋊C4—42no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—42no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—44no—
976C4⋊C4—42no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—42no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—44no—
993C4⋊C4C22×Q818yes—
994C4⋊C4C22×Q818yes—
995C4⋊C4C22×Q818yes—
996C4⋊C4C22×Q814yes—
997C4⋊C4C22×Q814yes—
998C4⋊C4C22×Q8116yes—
999C4⋊C4C22×Q8116yes—
1000C4⋊C4C22×Q8116yes—
1001C4⋊C4C22×Q8116yes—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C42—24no—
1007C42—24no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—44no—
1013C42—44no—
1014C42—42no—
1015C42—42no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C42—44no—
1020C42—44no—
1021C42—44no—
1022C42—44no—
1023C42—44no—
1024C42—44no—
1025C42—44no—
1026C42—44no—
1027C42—44no—
1028C42C22×Q818yes—
1029C42C22×Q818yes—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23C23×Q812yes—
1035C23C2×2−1+412yes—
1036C23#58512yes—
1037C23C2611yescharacteristic
1038Q8—84no—
1039Q8—84no—
1040Q8—88no—
1041Q8—162no—
1042Q8—164no—
1043Q8—162no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—28no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—48no—
1104C2×C4—48no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—84no—
1110C2×C4—84no—
1111C2×C4—82no—
1112C2×C4—82no—
1113C2×C4C23×Q812yes—
1114C2×C4C23×Q812yes—
1115C2×C4C23×Q814yes—
1116C2×C4C23×Q814yes—
1117C2×C4C23×Q814yes—
1118C2×C4C23×Q814yes—
1119C2×C4C23×Q818yes—
1120C2×C4C2×2−1+414yes—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22#350214yes—
1128C22C24×Q811yescharacteristic
1129C22C22×2−1+411yescharacteristic
1130C22C2×#58511yescharacteristic
1131C22H(7,𝔽2)11yescharacteristic
1132C22H(7,𝔽2)11yescharacteristic
1133C222−1+611yescharacteristic
1134C222−1+611yescharacteristic
1135C4—22no—
1136C4—22no—
1137C4—24no—
1138C4—24no—
1139C4—28no—
1140C4—24no—
1141C4—24no—
1142C4—24no—
1143C4—44no—
1144C4—44no—
1145C4—42no—
1146C4—44no—
1147C4—42no—
1148C4—42no—
1149C4—44no—
1150C4—44no—
1151C4—44no—
1152C4—42no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4—42no—
1157C2—24no—
1158C2C2×#350211yescharacteristic
1159C2#6285411yescharacteristic
1160C2#6285411yescharacteristic
1161C2#6286511yescharacteristic
1162C2#6287011yescharacteristic
1163C2#6287311yescharacteristic
1164C2#6287711yescharacteristic
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
1. #51795C2semidirect
2. #51606C2semidirect
3. #51603C2semidirect
4. #51602C2semidirect
5. #47774C2semidirect
6. #47731C2semidirect
7. #47730C2semidirect
8. #47727C2semidirect
225. C2×#125Q8semidirect

Maximal subgroups

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

subgroupindex
#517952
#516062
#516032
#516022
#477742
#477312
#477302
#477272
#397512
#397482
#396232
#396202
#391782
#391752
#376232
#371352
#351202
#350152
#350132
#343722
C2×#23302