Finite Group Databasebeta

← #7989527

Subgroups — #7989527

Order 512.

4077 conjugacy classes of subgroups.

The subgroup lattice has 1502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59925C212yesmaximal
2#59870C211yesmaximal, characteristic
3#59464C212yesmaximal
4#59459C211yesmaximal, characteristic
5#59456C211yesmaximal, characteristic
6#51219C214yesmaximal
7#50910C214yesmaximal
8#46243C214yesmaximal
9#45426C212yesmaximal
10#45278C212yesmaximal
11#45276C212yesmaximal
12#45164C212yesmaximal
13#42825C212yesmaximal
14#42821C212yesmaximal
15#42821C212yesmaximal
16#42821C212yesmaximal
17#39754C211yesmaximal, characteristic
18#39715C214yesmaximal
19#39673C212yesmaximal
20#39638C212yesmaximal
21#39182C211yesmaximal, characteristic
22#39181C211yesmaximal, characteristic
23#39180C211yesmaximal, characteristic
24#36584C211yesmaximal, characteristic
25#36574C211yesmaximal, characteristic
26#36535C212yesmaximal
27#36535C211yesmaximal, characteristic
28#36475C212yesmaximal
29#35221C212yesmaximal
30#35221C212yesmaximal
31#34950C211yesmaximal, characteristic
32#34920C211yesmaximal, characteristic
33#34488C211yesmaximal, characteristic
34#34488C211yesmaximal, characteristic
35C4×#557C211yesmaximal, characteristic
36C2×#557C2211yescharacteristic
37#2864C2214yes—
38#2864C2212yes—
39#2864C2214yes—
40#2863C2214yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2212yes—
44#2859C2211yescharacteristic
45#2844C2214yes—
46#2844C2214yes—
47#2805C2214yes—
48#2805C2214yes—
49#2805C2214yes—
50#2805C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2792C2214yes—
55#2792C2214yes—
56#2792C2214yes—
57#2792C2214yes—
58#2791C2214yes—
59#2774C2214yes—
60#2774C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2774C2214yes—
64#2774C2214yes—
65#2774C2214yes—
66#2774C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2755C2214yes—
70#2755C2214yes—
71#2755C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2755C2214yes—
75#2755C2214yes—
76#2734C2214yes—
77#2726C2214yes—
78#2713C2214yes—
79#2713C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2666C2214yes—
86#2660C2212yes—
87#2647C2212yes—
88#2647C2212yes—
89#2647C2212yes—
90#2590C2214yes—
91#2590C2214yes—
92#2590C2214yes—
93#2590C2212yes—
94#2590C2214yes—
95#2590C2214yes—
96#2590C2214yes—
97#2588C2214yes—
98#2588C2214yes—
99#2588C2214yes—
100#2588C2212yes—
101#2588C2214yes—
102#2588C2214yes—
103#2586C2214yes—
104#2586C2214yes—
105#2586C2214yes—
106#2586C2214yes—
107#2586C2212yes—
108#2586C2214yes—
109#2586C2212yes—
110#2585C2214yes—
111#2585C2214yes—
112#2585C2214yes—
113#2585C2214yes—
114#2584C2212yes—
115#2584C2212yes—
116#2584C2212yes—
117#2584C2212yes—
118#2584C2212yes—
119#2584C2211yescharacteristic
120#2584C2212yes—
121#2582C2212yes—
122#2582C2211yescharacteristic
123#2581C2212yes—
124#2581C2212yes—
125#2581C2212yes—
126#2581C2212yes—
127#2581C2212yes—
128#2581C2211yescharacteristic
129#2581C2212yes—
130#2571C2211yescharacteristic
131#2571C2212yes—
132#2571C2211yescharacteristic
133#2571C2212yes—
134#2571C2212yes—
135#2571C2212yes—
136#2571C2211yescharacteristic
137#2570C2212yes—
138#2570C2214yes—
139#2570C2214yes—
140#2570C2214yes—
141#2570C2212yes—
142#2570C2212yes—
143#2568C2212yes—
144#2568C2212yes—
145#2567C2212yes—
146#2567C2212yes—
147#2567C2212yes—
148#2567C2211yescharacteristic
149#2567C2211yescharacteristic
150#2565C2212yes—
151#2565C2211yescharacteristic
152#2565C2212yes—
153#2552C2211yescharacteristic
154#2552C2211yescharacteristic
155#2552C2212yes—
156#2551C2211yescharacteristic
157#2551C2212yes—
158#2551C2211yescharacteristic
159#2550C2212yes—
160#2550C2212yes—
161#2550C2212yes—
162#2550C2214yes—
163#2550C2214yes—
164#2550C2211yescharacteristic
165#2550C2212yes—
166#2550C2212yes—
167#2546C2212yes—
168#2520C2214yes—
169#2520C2212yes—
170#2511C2214yes—
171#2509C2212yes—
172#2509C2214yes—
173#2509C2214yes—
174#2509C2212yes—
175#2509C2212yes—
176#2509C2212yes—
177#2509C2214yes—
178#2509C2212yes—
179#2509C2212yes—
180#2509C2214yes—
181#2509C2212yes—
182#2508C2212yes—
183#2508C2212yes—
184#2508C2212yes—
185#2508C2214yes—
186#2508C2212yes—
187#2508C2211yescharacteristic
188#2508C2214yes—
189#2508C2212yes—
190#2507C2214yes—
191#2507C2214yes—
192#2507C2212yes—
193#2507C2211yescharacteristic
194#2507C2211yescharacteristic
195#2507C2212yes—
196#2506C2212yes—
197#2506C2214yes—
198#2506C2211yescharacteristic
199#2462C2212yes—
200#2453C2212yes—
201#2453C2212yes—
202#2453C2212yes—
203#2453C2211yescharacteristic
204#2453C2212yes—
205#2453C2212yes—
206#2453C2212yes—
207#2451C2212yes—
208#2451C2212yes—
209#2451C2212yes—
210#2451C2212yes—
211#2451C2212yes—
212#2451C2211yescharacteristic
213#2451C2211yescharacteristic
214#2451C2211yescharacteristic
215#2402C2212yes—
216#2399C2212yes—
217#2399C2212yes—
218#2399C2212yes—
219#2382C2214yes—
220#2382C2214yes—
221#2370C2214yes—
222#2370C2212yes—
223#2370C2212yes—
224#2370C2212yes—
225#2370C2212yes—
226#2370C2212yes—
227#2370C2212yes—
228#2370C2212yes—
229#2369C2214yes—
230#2365C2211yescharacteristic
231#2365C2211yescharacteristic
232#2365C2211yescharacteristic
233#2365C2212yes—
234#2365C2212yes—
235#2365C2212yes—
236#2355C2211yescharacteristic
237#2355C2211yescharacteristic
238#2355C2212yes—
239#2355C2212yes—
240#2355C2212yes—
241#2355C2212yes—
242#2355C2211yescharacteristic
243#2355C2212yes—
244#2355C2212yes—
245#2351C2212yes—
246#2351C2212yes—
247#2351C2212yes—
248#2351C2212yes—
249#2351C2212yes—
250#2351C2212yes—
251#2351C2212yes—
252Q8×C4⋊C4C2211yescharacteristic
253Q8×C4⋊C4C2211yescharacteristic
254Q8×C4⋊C4C2211yescharacteristic
255Q8×C4⋊C4C2212yes—
256Q8×C4⋊C4C2212yes—
257#2336C2214yes—
258#2336C2214yes—
259#2331C2212yes—
260#2331C2212yes—
261#2330C2212yes—
262#2330C2212yes—
263#2330C2212yes—
264#2330C2212yes—
265#2327C2212yes—
266#2327C2212yes—
267#2320C2212yes—
268#2320C2212yes—
269#2320C2212yes—
270#2320C2212yes—
271C4×C4⋊Q8C2211yescharacteristic
272C4×C4⋊Q8C2211yescharacteristic
273C4×C4⋊Q8C2212yes—
274C4×C4⋊Q8C2211yescharacteristic
275C4×C4⋊Q8C2211yescharacteristic
276C4×C4⋊Q8C2211yescharacteristic
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2212yes—
279C4×C4⋊Q8C2211yescharacteristic
280C4×#125C2211yescharacteristic
281C4×#125C2212yes—
282C4×#125C2212yes—
283C4×#125C2214yes—
284C4×#125C2214yes—
285C4×#125C2211yescharacteristic
286C4×#125C2212yes—
287C4×#125C2212yes—
288#2295C2211yescharacteristic
289#2295C2211yescharacteristic
290#2295C2211yescharacteristic
291#2295C2211yescharacteristic
292#2295C2212yes—
293#2295C2212yes—
294C42×Q8C2211yescharacteristic
295C42×Q8C2211yescharacteristic
296C42×Q8C2212yes—
297C42×Q8C2211yescharacteristic
298C42×Q8C2212yes—
299#557Q8116yescomplemented
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2314yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×#125C2312yes—
311C2×#125C2311yescharacteristic
312C2×#125C2312yes—
313C2×#125C2311yescharacteristic
314C2×#125C2314yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×#125C2314yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2312yes—
376#400C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2312yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2312yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2314yes—
408#398C2312yes—
409#398C2314yes—
410#398C2312yes—
411#398C2312yes—
412#398C2314yes—
413#398C2312yes—
414#398C2312yes—
415#398C2314yes—
416#398C2312yes—
417#398C2312yes—
418#398C2312yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2312yes—
438#395C2312yes—
439#395C2312yes—
440#395C2314yes—
441#395C2312yes—
442#395C2314yes—
443#395C2312yes—
444#395C2314yes—
445#395C2312yes—
446#395C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2311yescharacteristic
462#391C2311yescharacteristic
463#391C2312yes—
464#391C2314yes—
465#391C2311yescharacteristic
466#391C2314yes—
467#391C2311yescharacteristic
468#391C2312yes—
469#391C2311yescharacteristic
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2311yescharacteristic
474#391C2311yescharacteristic
475#391C2311yescharacteristic
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2312yes—
486#389C2312yes—
487#389C2311yescharacteristic
488#389C2311yescharacteristic
489#389C2312yes—
490#389C2312yes—
491#389C2311yescharacteristic
492#389C2312yes—
493#389C2311yescharacteristic
494#389C2312yes—
495#389C2312yes—
496#389C2311yescharacteristic
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2311yescharacteristic
503#389C2311yescharacteristic
504#389C2312yes—
505#389C2312yes—
506#389C2311yescharacteristic
507#389C2312yes—
508#389C2312yes—
509#389C2311yescharacteristic
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2314yes—
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2314yes—
542#389C2312yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2314yes—
553#389C2311yescharacteristic
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2314yes—
560#389C2311yescharacteristic
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2311yescharacteristic
565#389C2311yescharacteristic
566#389C2314yes—
567#389C2314yes—
568#389C2312yes—
569#389C2312yes—
570#389C2314yes—
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2314yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2312yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2314yes—
590#389C2314yes—
591#389C2312yes—
592#389C2311yescharacteristic
593#389C2314yes—
594#389C2311yescharacteristic
595#389C2312yes—
596#389C2312yes—
597#389C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2314yes—
607#387C2312yes—
608#387C2314yes—
609#387C2312yes—
610#387C2314yes—
611#387C2314yes—
612#387C2312yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2312yes—
619#387C2314yes—
620#387C2312yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2312yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2312yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2314yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#387C2314yes—
672#387C2312yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2312yes—
678#387C2312yes—
679#387C2312yes—
680#387C2312yes—
681#387C2312yes—
682#387C2314yes—
683#387C2314yes—
684#384C2311yescharacteristic
685#384C2311yescharacteristic
686#384C2311yescharacteristic
687#384C2311yescharacteristic
688#384C2312yes—
689#384C2311yescharacteristic
690#384C2311yescharacteristic
691#384C2312yes—
692#384C2311yescharacteristic
693#384C2312yes—
694#384C2312yes—
695#384C2314yes—
696#384C2314yes—
697#384C2312yes—
698#384C2312yes—
699#383C2314yes—
700#383C2314yes—
701#382C2311yescharacteristic
702#382C2311yescharacteristic
703#382C2312yes—
704#382C2314yes—
705#382C2314yes—
706#382C2312yes—
707#382C2312yes—
708#382C2312yes—
709#382C2312yes—
710#382C2312yes—
711#382C2312yes—
712#382C2312yes—
713#382C2314yes—
714#382C2314yes—
715#382C2314yes—
716#382C2312yes—
717#382C2314yes—
718#382C2314yes—
719#382C2312yes—
720#382C2312yes—
721#382C2312yes—
722#382C2314yes—
723#382C2314yes—
724#382C2314yes—
725#382C2314yes—
726#382C2312yes—
727C4×C4⋊C4C2314yes—
728C4×C4⋊C4C2312yes—
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2311yescharacteristic
731C4×C4⋊C4C2311yescharacteristic
732C4×C4⋊C4C2314yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2311yescharacteristic
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2311yescharacteristic
739C4×C4⋊C4C2311yescharacteristic
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2314yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2314yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2314yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2314yes—
790C4×C4⋊C4C2314yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2314yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2311yescharacteristic
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2312yes—
805C43C2312yes—
806C43C2312yes—
807C43C2314yes—
808C43C2311yescharacteristic
809C43C2311yescharacteristic
810C43C2311yescharacteristic
811C22×Q8C2412yes—
812C22×Q8C2411yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2411yescharacteristic
815C22×Q8C2412yes—
816C22×Q8C2412yes—
817C22×Q8C2412yes—
818C22×Q8C2412yes—
819C22×Q8C2414yes—
820C4⋊Q8—42no—
821C4⋊Q8—42no—
822C4⋊Q8—44no—
823C4⋊Q8—44no—
824C4⋊Q8—42no—
825C4⋊Q8—42no—
826C4⋊Q8—44no—
827C4⋊Q8—48no—
828C4⋊Q8C2×Q818yes—
829C4⋊Q8C2×Q8116yes—
830#125—28no—
831#125—24no—
832#125—44no—
833#125—44no—
834#125—42no—
835#125—44no—
836#125—44no—
837#125—44no—
838#125—48no—
839#125C2×Q8116yes—
840#125C2×Q8132yes—
841C4×Q8—24no—
842C4×Q8—24no—
843C4×Q8—44no—
844C4×Q8—42no—
845C4×Q8—44no—
846C4×Q8—44no—
847C4×Q8—44no—
848C4×Q8—42no—
849C4×Q8—44no—
850C4×Q8—44no—
851C4×Q8—44no—
852C4×Q8—44no—
853C4×Q8—44no—
854C4×Q8—42no—
855C4×Q8—42no—
856C4×Q8—44no—
857C4×Q8—42no—
858C4×Q8—44no—
859C4×Q8—44no—
860C4×Q8—44no—
861C4×Q8C2×Q8116yes—
862C4×Q8C2×Q8116yes—
863C4×Q8C2×Q818yes—
864C4×Q8C2×Q818yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2411yescharacteristic
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2412yes—
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2412yes—
977C2×C42C2411yescharacteristic
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2411yescharacteristic
988C2×C42C2412yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2414yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2414yes—
999C2×C42C2411yescharacteristic
1000C2×C42C2414yes—
1001C2×C42C2414yes—
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2414yes—
1006C2×C42C2412yes—
1007C2×C42C2414yes—
1008C2×C42C2412yes—
1009C2×C42C2414yes—
1010C2×C42C2412yes—
1011C2×C42C2412yes—
1012C2×C42C2411yescharacteristic
1013C2×C42C2411yescharacteristic
1014C2×C42C2411yescharacteristic
1015C2×C42C2414yes—
1016C2×C42C2412yes—
1017C2×C42C2414yes—
1018C2×C42C2411yescharacteristic
1019C2×C42C2412yes—
1020C2×C42C2411yescharacteristic
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2411yescharacteristic
1038#95C2412yes—
1039#95C2411yescharacteristic
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2411yescharacteristic
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2411yescharacteristic
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2411yescharacteristic
1062#95C2411yescharacteristic
1063#95C2414yes—
1064#95C2414yes—
1065#95C2412yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2414yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2412yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2412yes—
1102#95C2412yes—
1103#95C2412yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119C2×Q8—22no—
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—24no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—22no—
1126C2×Q8—24no—
1127C2×Q8—41no—
1128C2×Q8—41no—
1129C2×Q8—42no—
1130C2×Q8—42no—
1131C2×Q8—42no—
1132C2×Q8—42no—
1133C2×Q8—42no—
1134C2×Q8—42no—
1135C2×Q8—42no—
1136C2×Q8—42no—
1137C2×Q8—42no—
1138C2×Q8—42no—
1139C2×Q8—42no—
1140C2×Q8—44no—
1141C2×Q8—44no—
1142C2×Q8—44no—
1143C2×Q8C22×Q814yes—
1144C2×Q8C22×Q818yes—
1145C2×Q8C22×Q814yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2512yes—
1149C22×C4C2514yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2514yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2514yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2512yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2514yes—
1176C22×C4C2511yescharacteristic
1177C22×C4C2511yescharacteristic
1178C22×C4C2511yescharacteristic
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C4⋊C4—24no—
1182C4⋊C4—22no—
1183C4⋊C4—22no—
1184C4⋊C4—22no—
1185C4⋊C4—22no—
1186C4⋊C4—24no—
1187C4⋊C4—28no—
1188C4⋊C4—24no—
1189C4⋊C4—28no—
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—22no—
1193C4⋊C4—24no—
1194C4⋊C4—22no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—22no—
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—22no—
1209C4⋊C4—22no—
1210C4⋊C4—24no—
1211C4⋊C4—22no—
1212C4⋊C4—22no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—44no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—41no—
1226C4⋊C4—42no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—42no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—42no—
1237C4⋊C4—42no—
1238C4⋊C4—44no—
1239C4⋊C4—41no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—42no—
1248C4⋊C4—42no—
1249C4⋊C4—41no—
1250C4⋊C4—42no—
1251C4⋊C4—42no—
1252C4⋊C4—41no—
1253C4⋊C4—42no—
1254C4⋊C4—42no—
1255C4⋊C4—44no—
1256C4⋊C4—42no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—42no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—42no—
1266C4⋊C4—44no—
1267C4⋊C4—42no—
1268C4⋊C4—42no—
1269C4⋊C4—44no—
1270C4⋊C4—42no—
1271C4⋊C4—42no—
1272C4⋊C4—42no—
1273C4⋊C4—44no—
1274C4⋊C4—42no—
1275C4⋊C4—44no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—44no—
1279C4⋊C4—44no—
1280C4⋊C4C22×Q814yes—
1281C4⋊C4C22×Q8116yes—
1282C4⋊C4C22×Q818yes—
1283C4⋊C4C22×Q818yes—
1284C4⋊C4C22×Q814yes—
1285C4⋊C4C22×Q8116yes—
1286C4⋊C4C22×Q818yes—
1287C4⋊C4C22×Q8116yes—
1288C4⋊C4C22×Q818yes—
1289C42—24no—
1290C42—22no—
1291C42—22no—
1292C42—22no—
1293C42—22no—
1294C42—24no—
1295C42—22no—
1296C42—24no—
1297C42—22no—
1298C42—24no—
1299C42—22no—
1300C42—24no—
1301C42—22no—
1302C42—22no—
1303C42—22no—
1304C42—24no—
1305C42—24no—
1306C42—22no—
1307C42—22no—
1308C42—42no—
1309C42—41no—
1310C42—42no—
1311C42—44no—
1312C42—41no—
1313C42—41no—
1314C42—44no—
1315C42—42no—
1316C42—44no—
1317C42—41no—
1318C42—41no—
1319C42—42no—
1320C42—44no—
1321C42—44no—
1322C42—44no—
1323C42—44no—
1324C42—42no—
1325C42—44no—
1326C42—44no—
1327C42—44no—
1328C42—42no—
1329C42—44no—
1330C42—42no—
1331C42—44no—
1332C42C22×Q8116yes—
1333C42C22×Q818yes—
1334C42C22×Q818yes—
1335C42C22×Q814yes—
1336C422−1+414yes—
1337C23C2611yescharacteristic
1338Q8—28no—
1339Q8—216no—
1340Q8—28no—
1341Q8—44no—
1342Q8—84no—
1343Q8—84no—
1344Q8—84no—
1345Q8—84no—
1346Q8—164no—
1347C2×C4—22no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—21no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—21no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—21no—
1411C2×C4—24no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—21no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—21no—
1427C2×C4—22no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—24no—
1431C2×C4—22no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4C23×Q814yes—
1438C2×C4C23×Q814yes—
1439C2×C4C23×Q812yes—
1440C2×C4C23×Q814yes—
1441C2×C4C23×Q818yes—
1442C2×C4C23×Q814yes—
1443C2×C4C23×Q812yes—
1444C2×C4C23×Q812yes—
1445C2×C4C2×2−1+412yes—
1446C2×C4C2×2−1+412yes—
1447C2×C4C2×2−1+412yes—
1448C2×C4#58512yes—
1449C2×C4#58512yes—
1450C2×C4#58512yes—
1451C2×C4#58512yes—
1452C22C24×Q811yescharacteristic
1453C22C22×2−1+411yescharacteristic
1454C22C2×#58511yescharacteristic
1455C22C2×#58511yescharacteristic
1456C22C2×#58511yescharacteristic
1457C22C2×#58511yescharacteristic
1458C222−1+611yescharacteristic
1459C4—22no—
1460C4—24no—
1461C4—24no—
1462C4—22no—
1463C4—22no—
1464C4—24no—
1465C4—24no—
1466C4—28no—
1467C4—22no—
1468C4—42no—
1469C4—42no—
1470C4—44no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C4—42no—
1475C4—41no—
1476C4—42no—
1477C4—42no—
1478C4—44no—
1479C4—42no—
1480C4—41no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4—41no—
1487C4—41no—
1488C4—41no—
1489C4—41no—
1490C4—42no—
1491C4—44no—
1492C4#350214yes—
1493C4#350414yes—
1494C2#6276111yescharacteristic
1495C2C2×#350211yescharacteristic
1496C2C2×#350411yescharacteristic
1497C2#6293611yescharacteristic
1498C2#6295611yescharacteristic
1499C2#6300411yescharacteristic
1500C2#6302911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
299. #557Q8semidirect

Maximal subgroups

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

subgroupindex
#599252
#598702
#594642
#594592
#594562
#512192
#509102
#462432
#454262
#452782
#452762
#451642
#428252
#428212
#397542
#397152
#396732
#396382
#391822
#391812
#391802
#365842
#365742
#365352
#364752
#352212
#349502
#349202
#344882
C4×#5572