Finite Group Databasebeta

← #8458912

Subgroups — #8458912

Order 512.

3879 conjugacy classes of subgroups.

The subgroup lattice has 1491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic
2#59870C211yesmaximal, characteristic
3#59870C211yesmaximal, characteristic
4#58606C214yesmaximal
5#58407C214yesmaximal
6#58404C214yesmaximal
7#53143C212yesmaximal
8#52996C212yesmaximal
9#51351C214yesmaximal
10#46344C212yesmaximal
11#46181C212yesmaximal
12#45073C212yesmaximal
13#44982C212yesmaximal
14#42782C212yesmaximal
15#42701C212yesmaximal
16#42527C212yesmaximal
17#42511C212yesmaximal
18#39762C211yesmaximal, characteristic
19#39754C211yesmaximal, characteristic
20#39683C212yesmaximal
21#39180C211yesmaximal, characteristic
22#39003C212yesmaximal
23#38976C212yesmaximal
24#38976C211yesmaximal, characteristic
25#38243C212yesmaximal
26#37638C211yesmaximal, characteristic
27#37413C212yesmaximal
28#37344C212yesmaximal
29#36574C211yesmaximal, characteristic
30#36535C211yesmaximal, characteristic
31#36285C211yesmaximal, characteristic
32#35208C211yesmaximal, characteristic
33#35208C211yesmaximal, characteristic
34#34951C211yesmaximal, characteristic
35#34950C211yesmaximal, characteristic
36#2864C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2863C2212yes—
40#2859C2212yes—
41#2859C2211yescharacteristic
42#2859C2212yes—
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2839C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2833C2214yes—
51#2833C2214yes—
52#2833C2214yes—
53#2810C2214yes—
54#2806C2214yes—
55#2805C2214yes—
56#2805C2214yes—
57#2805C2214yes—
58#2802C2214yes—
59#2802C2214yes—
60#2802C2214yes—
61#2802C2214yes—
62#2791C2214yes—
63#2776C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2776C2214yes—
67#2776C2214yes—
68#2776C2214yes—
69#2776C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2774C2214yes—
73#2769C2214yes—
74#2769C2214yes—
75#2767C2214yes—
76#2767C2214yes—
77#2766C2214yes—
78#2766C2214yes—
79#2766C2214yes—
80#2766C2214yes—
81#2766C2214yes—
82#2762C2214yes—
83#2762C2214yes—
84#2758C2214yes—
85#2758C2214yes—
86#2758C2214yes—
87#2758C2214yes—
88#2755C2214yes—
89#2755C2214yes—
90#2755C2214yes—
91#2726C2214yes—
92#2726C2214yes—
93#2726C2214yes—
94#2719C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2719C2214yes—
99#2719C2214yes—
100#2719C2214yes—
101#2713C2214yes—
102#2666C2214yes—
103#2666C2214yes—
104#2666C2214yes—
105#2660C2212yes—
106#2655C2214yes—
107#2655C2214yes—
108#2647C2212yes—
109#2647C2212yes—
110#2647C2212yes—
111#2645C2212yes—
112#2645C2212yes—
113#2645C2214yes—
114#2645C2212yes—
115#2642C2212yes—
116#2634C2214yes—
117#2634C2214yes—
118#2606C2214yes—
119#2590C2214yes—
120#2590C2214yes—
121#2588C2214yes—
122#2588C2214yes—
123#2586C2212yes—
124#2586C2212yes—
125#2585C2212yes—
126#2585C2212yes—
127#2584C2214yes—
128#2584C2212yes—
129#2584C2212yes—
130#2584C2214yes—
131#2584C2214yes—
132#2584C2212yes—
133#2584C2212yes—
134#2582C2211yescharacteristic
135#2582C2212yes—
136#2582C2212yes—
137#2582C2211yescharacteristic
138#2582C2211yescharacteristic
139#2582C2211yescharacteristic
140#2582C2212yes—
141#2582C2211yescharacteristic
142#2581C2212yes—
143#2581C2212yes—
144#2581C2214yes—
145#2581C2214yes—
146#2581C2212yes—
147#2571C2212yes—
148#2571C2211yescharacteristic
149#2571C2212yes—
150#2571C2212yes—
151#2570C2212yes—
152#2570C2212yes—
153#2570C2212yes—
154#2568C2212yes—
155#2568C2211yescharacteristic
156#2568C2212yes—
157#2567C2211yescharacteristic
158#2567C2211yescharacteristic
159#2567C2211yescharacteristic
160#2567C2211yescharacteristic
161#2567C2211yescharacteristic
162#2567C2211yescharacteristic
163#2565C2212yes—
164#2565C2212yes—
165#2552C2212yes—
166#2552C2212yes—
167#2552C2211yescharacteristic
168#2552C2211yescharacteristic
169#2552C2211yescharacteristic
170#2552C2212yes—
171#2551C2211yescharacteristic
172#2550C2212yes—
173#2550C2212yes—
174#2546C2211yescharacteristic
175#2533C2214yes—
176#2528C2214yes—
177#2520C2214yes—
178#2514C2212yes—
179#2514C2212yes—
180#2514C2212yes—
181#2514C2212yes—
182#2514C2212yes—
183#2514C2212yes—
184#2514C2212yes—
185#2511C2212yes—
186#2511C2211yescharacteristic
187#2511C2212yes—
188#2511C2212yes—
189#2511C2212yes—
190#2511C2212yes—
191#2511C2211yescharacteristic
192#2511C2212yes—
193#2511C2212yes—
194#2509C2212yes—
195#2509C2212yes—
196#2509C2212yes—
197#2509C2212yes—
198#2509C2212yes—
199#2509C2212yes—
200#2509C2212yes—
201#2509C2214yes—
202#2509C2212yes—
203#2509C2212yes—
204#2508C2212yes—
205#2508C2212yes—
206#2508C2212yes—
207#2508C2212yes—
208#2507C2212yes—
209#2507C2211yescharacteristic
210#2507C2212yes—
211#2507C2212yes—
212#2507C2212yes—
213#2507C2212yes—
214#2507C2211yescharacteristic
215#2507C2212yes—
216#2506C2212yes—
217#2506C2214yes—
218#2506C2212yes—
219#2506C2212yes—
220#2506C2212yes—
221#2506C2212yes—
222#2506C2212yes—
223#2506C2212yes—
224#2462C2214yes—
225#2462C2214yes—
226#2462C2214yes—
227#2462C2214yes—
228#2462C2214yes—
229#2453C2212yes—
230#2453C2212yes—
231#2453C2212yes—
232#2453C2212yes—
233#2453C2212yes—
234#2453C2212yes—
235#2453C2212yes—
236#2451C2211yescharacteristic
237#2451C2211yescharacteristic
238#2451C2212yes—
239#2446C2211yescharacteristic
240#2446C2212yes—
241#2446C2214yes—
242#2446C2211yescharacteristic
243#2446C2212yes—
244#2402C2212yes—
245#2402C2212yes—
246#2399C2212yes—
247#2399C2212yes—
248#2382C2214yes—
249#2370C2212yes—
250#2370C2212yes—
251#2370C2212yes—
252#2370C2212yes—
253#2369C2212yes—
254#2365C2212yes—
255#2365C2212yes—
256#2365C2212yes—
257#2356C2212yes—
258#2355C2211yescharacteristic
259#2355C2212yes—
260#2355C2211yescharacteristic
261#2355C2211yescharacteristic
262#2355C2211yescharacteristic
263#2351C2212yes—
264Q8×C4⋊C4C2211yescharacteristic
265Q8×C4⋊C4C2212yes—
266Q8×C4⋊C4C2211yescharacteristic
267Q8×C4⋊C4C2212yes—
268#2330C2212yes—
269#2330C2212yes—
270#2330C2212yes—
271#2330C2212yes—
272#2330C2212yes—
273#2320C2212yes—
274#2320C2212yes—
275#2320C2214yes—
276#2320C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2212yes—
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×C4⋊Q8C2211yescharacteristic
283C4×C4⋊Q8C2211yescharacteristic
284C4×C4⋊Q8C2211yescharacteristic
285C4×C4⋊Q8C2211yescharacteristic
286C4×C4⋊Q8C2211yescharacteristic
287C4×#125C2212yes—
288C4×#125C2212yes—
289#2295C2212yes—
290#2295C2211yescharacteristic
291#2295C2211yescharacteristic
292#2295C2212yes—
293#2295C2211yescharacteristic
294#2295C2211yescharacteristic
295#2295C2212yes—
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×Q8C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2311yescharacteristic
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2312yes—
307C2×#125C2312yes—
308C2×#125C2312yes—
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2314yes—
313C2×#125C2314yes—
314C2×#125C2314yes—
315C2×#125C2312yes—
316C2×#125C2314yes—
317C2×#125C2314yes—
318C2×#125C2314yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2314yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2314yes—
340#401C2314yes—
341#401C2314yes—
342#401C2314yes—
343#401C2314yes—
344#401C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2312yes—
375#400C2312yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2312yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2312yes—
394#400C2314yes—
395#400C2314yes—
396#400C2312yes—
397#400C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2312yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2312yes—
416#398C2312yes—
417#398C2312yes—
418#398C2312yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2312yes—
423#398C2312yes—
424#398C2312yes—
425#398C2312yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2312yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2312yes—
438#398C2312yes—
439#398C2314yes—
440#398C2314yes—
441#398C2312yes—
442#398C2312yes—
443#398C2312yes—
444#398C2314yes—
445#398C2312yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#395C2312yes—
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2312yes—
455#395C2312yes—
456#395C2312yes—
457#395C2312yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2312yes—
463#395C2314yes—
464#395C2312yes—
465#395C2312yes—
466#391C2311yescharacteristic
467#391C2311yescharacteristic
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2311yescharacteristic
475#391C2311yescharacteristic
476#391C2311yescharacteristic
477#391C2311yescharacteristic
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2311yescharacteristic
490#391C2311yescharacteristic
491#391C2314yes—
492#391C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2311yescharacteristic
497#391C2311yescharacteristic
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2312yes—
502#391C2314yes—
503#391C2311yescharacteristic
504#391C2311yescharacteristic
505#391C2311yescharacteristic
506#391C2314yes—
507#391C2312yes—
508#391C2311yescharacteristic
509#391C2312yes—
510#391C2312yes—
511#391C2314yes—
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2311yescharacteristic
517#389C2312yes—
518#389C2311yescharacteristic
519#389C2311yescharacteristic
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2311yescharacteristic
524#389C2311yescharacteristic
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2311yescharacteristic
548#389C2312yes—
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2312yes—
575#389C2312yes—
576#389C2314yes—
577#389C2312yes—
578#389C2311yescharacteristic
579#389C2311yescharacteristic
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2312yes—
592#389C2314yes—
593#389C2312yes—
594#389C2314yes—
595#389C2314yes—
596#389C2314yes—
597#389C2314yes—
598#389C2314yes—
599#389C2312yes—
600#389C2314yes—
601#389C2314yes—
602#389C2314yes—
603#389C2314yes—
604#389C2314yes—
605#389C2314yes—
606#389C2314yes—
607#389C2314yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2314yes—
612#389C2314yes—
613#389C2314yes—
614#389C2311yescharacteristic
615#389C2311yescharacteristic
616#389C2312yes—
617#389C2312yes—
618#387C2314yes—
619#387C2312yes—
620#387C2314yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
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#387C2312yes—
643#387C2312yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2312yes—
677#387C2312yes—
678#387C2312yes—
679#387C2312yes—
680#387C2312yes—
681#387C2312yes—
682#387C2312yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2314yes—
692#387C2314yes—
693#387C2314yes—
694#387C2314yes—
695#387C2314yes—
696#387C2314yes—
697#387C2314yes—
698#387C2314yes—
699#387C2314yes—
700#387C2314yes—
701#384C2311yescharacteristic
702#384C2311yescharacteristic
703#384C2312yes—
704#384C2311yescharacteristic
705#384C2311yescharacteristic
706#384C2311yescharacteristic
707#384C2311yescharacteristic
708#384C2311yescharacteristic
709#384C2311yescharacteristic
710#384C2311yescharacteristic
711#384C2312yes—
712#384C2312yes—
713#384C2312yes—
714#384C2312yes—
715#384C2312yes—
716#384C2312yes—
717#384C2312yes—
718#384C2312yes—
719#383C2314yes—
720#383C2314yes—
721#383C2314yes—
722#383C2314yes—
723#383C2314yes—
724#383C2314yes—
725#383C2314yes—
726#382C2312yes—
727#382C2312yes—
728#382C2312yes—
729#382C2312yes—
730#382C2314yes—
731#382C2314yes—
732#382C2312yes—
733#382C2312yes—
734#382C2314yes—
735#382C2312yes—
736#382C2312yes—
737#382C2314yes—
738#382C2314yes—
739#382C2314yes—
740#382C2314yes—
741#382C2312yes—
742#382C2312yes—
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2314yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2314yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800#376C2312yes—
801#376C2312yes—
802#376C2314yes—
803#376C2312yes—
804#376C2312yes—
805C43C2312yes—
806C43C2311yescharacteristic
807C43C2311yescharacteristic
808C43C2311yescharacteristic
809C43C2312yes—
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2412yes—
815C22×Q8C2411yescharacteristic
816C22×Q8C2412yes—
817C22×Q8C2412yes—
818C22×Q8C2412yes—
819C4⋊Q8—24no—
820C4⋊Q8—24no—
821C4⋊Q8—24no—
822C4⋊Q8—24no—
823C4⋊Q8—24no—
824C4⋊Q8—42no—
825C4⋊Q8—42no—
826C4⋊Q8—44no—
827#125—28no—
828#125—28no—
829#125—28no—
830#125—44no—
831#125—48no—
832#125—44no—
833#125—84no—
834#125—84no—
835#125—84no—
836#125—82no—
837#125—84no—
838#125—84no—
839C4×Q8—24no—
840C4×Q8—24no—
841C4×Q8—24no—
842C4×Q8—24no—
843C4×Q8—24no—
844C4×Q8—24no—
845C4×Q8—24no—
846C4×Q8—24no—
847C4×Q8—24no—
848C4×Q8—44no—
849C4×Q8—44no—
850C4×Q8—44no—
851C4×Q8—44no—
852C4×Q8—42no—
853C4×Q8—44no—
854C4×Q8—44no—
855C4×Q8—42no—
856C4×Q8—48no—
857C4×Q8—82no—
858C4×Q8—84no—
859C4×Q8—82no—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2414yes—
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2411yescharacteristic
977C2×C42C2412yes—
978C2×C42C2411yescharacteristic
979C2×C42C2412yes—
980C2×C42C2411yescharacteristic
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2414yes—
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2412yes—
998C2×C42C2414yes—
999C2×C42C2414yes—
1000C2×C42C2414yes—
1001C2×C42C2414yes—
1002C2×C42C2412yes—
1003C2×C42C2412yes—
1004C2×C42C2411yescharacteristic
1005C2×C42C2412yes—
1006C2×C42C2412yes—
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009C2×C42C2411yescharacteristic
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2411yescharacteristic
1031#95C2411yescharacteristic
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2411yescharacteristic
1037#95C2412yes—
1038#95C2411yescharacteristic
1039#95C2411yescharacteristic
1040#95C2412yes—
1041#95C2412yes—
1042#95C2411yescharacteristic
1043#95C2412yes—
1044#95C2414yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2414yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2412yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2412yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2414yes—
1078#95C2412yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2414yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114C2×Q8—22no—
1115C2×Q8—22no—
1116C2×Q8—22no—
1117C2×Q8—22no—
1118C2×Q8—22no—
1119C2×Q8—22no—
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—22no—
1123C2×Q8—24no—
1124C2×Q8—24no—
1125C2×Q8—24no—
1126C2×Q8—22no—
1127C2×Q8—22no—
1128C2×Q8—24no—
1129C2×Q8—24no—
1130C2×Q8—22no—
1131C2×Q8—22no—
1132C2×Q8—22no—
1133C2×Q8—42no—
1134C2×Q8—42no—
1135C2×Q8—42no—
1136C2×Q8—41no—
1137C2×Q8—42no—
1138C2×Q8—42no—
1139C2×Q8—42no—
1140C2×Q8—42no—
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2514yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2514yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2514yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2512yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2514yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2511yescharacteristic
1169C22×C4C2512yes—
1170C22×C4C2511yescharacteristic
1171C22×C4C2511yescharacteristic
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C4⋊C4—22no—
1177C4⋊C4—22no—
1178C4⋊C4—22no—
1179C4⋊C4—22no—
1180C4⋊C4—22no—
1181C4⋊C4—22no—
1182C4⋊C4—22no—
1183C4⋊C4—22no—
1184C4⋊C4—22no—
1185C4⋊C4—22no—
1186C4⋊C4—24no—
1187C4⋊C4—22no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—28no—
1198C4⋊C4—28no—
1199C4⋊C4—28no—
1200C4⋊C4—28no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—22no—
1214C4⋊C4—22no—
1215C4⋊C4—22no—
1216C4⋊C4—22no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—44no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—41no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—44no—
1267C4⋊C4—42no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—42no—
1271C4⋊C4—44no—
1272C4⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—42no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—42no—
1279C4⋊C4—42no—
1280C4⋊C4—42no—
1281C4⋊C42−1+414yes—
1282C42—22no—
1283C42—22no—
1284C42—22no—
1285C42—24no—
1286C42—24no—
1287C42—24no—
1288C42—24no—
1289C42—22no—
1290C42—24no—
1291C42—24no—
1292C42—24no—
1293C42—22no—
1294C42—24no—
1295C42—22no—
1296C42—22no—
1297C42—24no—
1298C42—22no—
1299C42—22no—
1300C42—24no—
1301C42—28no—
1302C42—24no—
1303C42—22no—
1304C42—22no—
1305C42—41no—
1306C42—41no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—42no—
1311C42—44no—
1312C42—41no—
1313C42—41no—
1314C42—44no—
1315C42—44no—
1316C42—44no—
1317C42—44no—
1318C42—42no—
1319C42—41no—
1320C42—42no—
1321C42—42no—
1322C42—42no—
1323C422−1+414yes—
1324C422−1+414yes—
1325C422−1+414yes—
1326C23C2611yescharacteristic
1327Q8—48no—
1328Q8—44no—
1329Q8—48no—
1330Q8—48no—
1331Q8—44no—
1332Q8—44no—
1333Q8—44no—
1334Q8—44no—
1335Q8—84no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—22no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—21no—
1389C2×C4—22no—
1390C2×C4—21no—
1391C2×C4—22no—
1392C2×C4—21no—
1393C2×C4—22no—
1394C2×C4—21no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—21no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—21no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—24no—
1422C2×C4—21no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4C2×2−1+412yes—
1429C2×C4C2×2−1+412yes—
1430C2×C4C2×2−1+414yes—
1431C2×C4C2×2−1+412yes—
1432C2×C4C2×2−1+412yes—
1433C2×C4C2×2−1+412yes—
1434C2×C4C2×2−1+412yes—
1435C2×C4C2×2−1+412yes—
1436C2×C4C2×2−1+412yes—
1437C2×C4C2×2−1+412yes—
1438C2×C4C2×2−1+412yes—
1439C2×C4#58512yes—
1440C2×C4#58512yes—
1441C22C22×2−1+411yescharacteristic
1442C22C22×2−1+411yescharacteristic
1443C22C22×2−1+411yescharacteristic
1444C22C22×2−1+411yescharacteristic
1445C22C2×#58511yescharacteristic
1446C22C2×#58511yescharacteristic
1447C22H(7,𝔽2)11yescharacteristic
1448C4—24no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—42no—
1456C4—42no—
1457C4—42no—
1458C4—42no—
1459C4—41no—
1460C4—42no—
1461C4—42no—
1462C4—42no—
1463C4—41no—
1464C4—44no—
1465C4—41no—
1466C4—41no—
1467C4—42no—
1468C4—41no—
1469C4—42no—
1470C4—42no—
1471C4—42no—
1472C4—42no—
1473C4—44no—
1474C4—44no—
1475C4—42no—
1476C4—42no—
1477C4—41no—
1478C4—42no—
1479C4—41no—
1480C4—44no—
1481C4#355514yes—
1482C4#355614yes—
1483C2C2×#355511yescharacteristic
1484C2C2×#355611yescharacteristic
1485C2#6283711yescharacteristic
1486C2#6292611yescharacteristic
1487C2#6292611yescharacteristic
1488C2#6294311yescharacteristic
1489C2#6302311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#598712
#598702
#586062
#584072
#584042
#531432
#529962
#513512
#463442
#461812
#450732
#449822
#427822
#427012
#425272
#425112
#397622
#397542
#396832
#391802
#390032
#389762
#382432
#376382
#374132
#373442
#365742
#365352
#362852
#352082
#349512
#349502