Finite Group Databasebeta

← #7989535

Subgroups — #7989535

Order 512.

4183 conjugacy classes of subgroups.

The subgroup lattice has 1509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59963C212yesmaximal
2#59673C211yesmaximal, characteristic
3#59667C211yesmaximal, characteristic
4#59665C211yesmaximal, characteristic
5#59456C212yesmaximal
6#51376C214yesmaximal
7#49714C214yesmaximal
8#46181C212yesmaximal
9#46181C212yesmaximal
10#45277C212yesmaximal
11#44994C212yesmaximal
12#43456C214yesmaximal
13#42553C212yesmaximal
14#42511C212yesmaximal
15#41194C214yesmaximal
16#40189C212yesmaximal
17#40143C212yesmaximal
18#39999C212yesmaximal
19#39642C211yesmaximal, characteristic
20#39003C212yesmaximal
21#38986C211yesmaximal, characteristic
22#38229C212yesmaximal
23#36598C211yesmaximal, characteristic
24#36563C211yesmaximal, characteristic
25#36556C211yesmaximal, characteristic
26#36556C211yesmaximal, characteristic
27#36497C212yesmaximal
28#36286C211yesmaximal, characteristic
29#35208C211yesmaximal, characteristic
30#35187C211yesmaximal, characteristic
31#35115C212yesmaximal
32#34950C211yesmaximal, characteristic
33#34920C211yesmaximal, characteristic
34#34488C212yesmaximal
35C4×#557C211yesmaximal, characteristic
36C2×#557C2212yes—
37C2×#557C2211yescharacteristic
38#2868C2211yescharacteristic
39#2864C2212yes—
40#2864C2212yes—
41#2864C2212yes—
42#2863C2212yes—
43#2863C2212yes—
44#2863C2212yes—
45#2862C2211yescharacteristic
46#2862C2211yescharacteristic
47#2859C2212yes—
48#2859C2212yes—
49#2839C2214yes—
50#2839C2214yes—
51#2799C2214yes—
52#2799C2214yes—
53#2794C2214yes—
54#2789C2214yes—
55#2789C2214yes—
56#2776C2214yes—
57#2769C2214yes—
58#2767C2214yes—
59#2767C2214yes—
60#2767C2214yes—
61#2767C2214yes—
62#2766C2214yes—
63#2762C2214yes—
64#2762C2214yes—
65#2758C2214yes—
66#2758C2214yes—
67#2758C2214yes—
68#2758C2214yes—
69#2755C2214yes—
70#2755C2214yes—
71#2726C2214yes—
72#2726C2214yes—
73#2719C2214yes—
74#2719C2214yes—
75#2719C2214yes—
76#2719C2214yes—
77#2719C2214yes—
78#2719C2214yes—
79#2713C2214yes—
80#2713C2214yes—
81#2713C2214yes—
82#2713C2214yes—
83#2713C2214yes—
84#2666C2214yes—
85#2655C2214yes—
86#2655C2214yes—
87#2655C2214yes—
88#2655C2214yes—
89#2647C2212yes—
90#2645C2212yes—
91#2634C2214yes—
92#2634C2214yes—
93#2605C2214yes—
94#2590C2212yes—
95#2588C2214yes—
96#2588C2212yes—
97#2588C2214yes—
98#2588C2214yes—
99#2586C2214yes—
100#2585C2214yes—
101#2585C2214yes—
102#2584C2212yes—
103#2584C2211yescharacteristic
104#2582C2212yes—
105#2582C2212yes—
106#2582C2211yescharacteristic
107#2581C2212yes—
108#2581C2214yes—
109#2581C2212yes—
110#2581C2211yescharacteristic
111#2571C2211yescharacteristic
112#2571C2212yes—
113#2571C2212yes—
114#2570C2212yes—
115#2570C2212yes—
116#2570C2212yes—
117#2570C2212yes—
118#2568C2212yes—
119#2568C2211yescharacteristic
120#2567C2211yescharacteristic
121#2567C2211yescharacteristic
122#2567C2211yescharacteristic
123#2567C2211yescharacteristic
124#2565C2211yescharacteristic
125#2565C2214yes—
126#2552C2211yescharacteristic
127#2552C2212yes—
128#2552C2212yes—
129#2552C2212yes—
130#2551C2211yescharacteristic
131#2551C2212yes—
132#2550C2212yes—
133#2550C2212yes—
134#2550C2212yes—
135#2550C2214yes—
136#2550C2211yescharacteristic
137#2546C2211yescharacteristic
138#2533C2214yes—
139#2533C2214yes—
140#2533C2214yes—
141#2528C2214yes—
142#2528C2214yes—
143#2528C2214yes—
144#2524C2214yes—
145#2524C2214yes—
146#2520C2214yes—
147#2520C2214yes—
148#2520C2214yes—
149#2520C2212yes—
150#2520C2214yes—
151#2514C2212yes—
152#2514C2212yes—
153#2514C2212yes—
154#2514C2212yes—
155#2514C2212yes—
156#2511C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2511C2212yes—
160#2511C2212yes—
161#2511C2212yes—
162#2511C2212yes—
163#2511C2212yes—
164#2509C2212yes—
165#2509C2212yes—
166#2509C2212yes—
167#2509C2212yes—
168#2509C2212yes—
169#2509C2212yes—
170#2508C2212yes—
171#2508C2212yes—
172#2508C2212yes—
173#2508C2212yes—
174#2508C2212yes—
175#2508C2211yescharacteristic
176#2507C2212yes—
177#2507C2212yes—
178#2507C2212yes—
179#2507C2212yes—
180#2507C2212yes—
181#2506C2212yes—
182#2506C2212yes—
183#2506C2212yes—
184#2506C2212yes—
185#2506C2212yes—
186#2506C2212yes—
187#2506C2211yescharacteristic
188#2506C2212yes—
189#2462C2214yes—
190#2462C2214yes—
191#2462C2214yes—
192#2462C2212yes—
193#2462C2214yes—
194#2462C2214yes—
195#2462C2214yes—
196#2462C2214yes—
197#2453C2214yes—
198#2453C2212yes—
199#2453C2214yes—
200#2453C2212yes—
201#2453C2214yes—
202#2453C2212yes—
203#2453C2211yescharacteristic
204#2451C2212yes—
205#2451C2214yes—
206#2451C2212yes—
207#2451C2212yes—
208#2451C2211yescharacteristic
209#2451C2212yes—
210#2451C2214yes—
211#2451C2214yes—
212#2446C2212yes—
213#2446C2212yes—
214#2446C2212yes—
215#2446C2212yes—
216#2446C2212yes—
217#2402C2212yes—
218#2399C2212yes—
219#2399C2214yes—
220#2382C2214yes—
221#2382C2214yes—
222#2370C2212yes—
223#2370C2214yes—
224#2370C2211yescharacteristic
225#2370C2212yes—
226#2370C2212yes—
227#2370C2211yescharacteristic
228#2369C2211yescharacteristic
229#2369C2211yescharacteristic
230#2369C2211yescharacteristic
231#2369C2211yescharacteristic
232#2365C2212yes—
233#2365C2211yescharacteristic
234#2365C2211yescharacteristic
235#2365C2212yes—
236#2365C2212yes—
237#2365C2212yes—
238#2365C2211yescharacteristic
239#2365C2212yes—
240#2365C2214yes—
241#2365C2212yes—
242#2365C2212yes—
243#2356C2212yes—
244#2355C2211yescharacteristic
245#2355C2212yes—
246#2355C2212yes—
247#2355C2212yes—
248#2355C2212yes—
249#2355C2212yes—
250#2355C2212yes—
251#2355C2212yes—
252#2355C2212yes—
253#2351C2211yescharacteristic
254#2351C2214yes—
255#2351C2211yescharacteristic
256Q8×C4⋊C4C2212yes—
257Q8×C4⋊C4C2211yescharacteristic
258#2336C2214yes—
259#2336C2214yes—
260#2336C2214yes—
261#2330C2212yes—
262#2330C2212yes—
263#2327C2212yes—
264#2327C2214yes—
265#2320C2212yes—
266#2320C2214yes—
267#2320C2212yes—
268#2320C2212yes—
269C4×C4⋊Q8C2211yescharacteristic
270C4×C4⋊Q8C2211yescharacteristic
271C4×C4⋊Q8C2211yescharacteristic
272C4×C4⋊Q8C2211yescharacteristic
273C4×C4⋊Q8C2211yescharacteristic
274C4×C4⋊Q8C2212yes—
275C4×C4⋊Q8C2212yes—
276C4×C4⋊Q8C2212yes—
277C4×C4⋊Q8C2212yes—
278C4×#125C2211yescharacteristic
279C4×#125C2211yescharacteristic
280C4×#125C2211yescharacteristic
281C4×#125C2211yescharacteristic
282C4×#125C2212yes—
283C4×#125C2212yes—
284C4×#125C2212yes—
285C4×#125C2212yes—
286C4×#125C2212yes—
287#2295C2212yes—
288#2295C2212yes—
289#2295C2212yes—
290#2295C2211yescharacteristic
291#2295C2212yes—
292#2295C2211yescharacteristic
293C42×Q8C2212yes—
294C42×Q8C2211yescharacteristic
295C42×Q8C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×Q8C2211yescharacteristic
299#557—216no—
300#557—28no—
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2311yescharacteristic
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2314yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×#125C2311yescharacteristic
314C2×#125C2311yescharacteristic
315C2×#125C2311yescharacteristic
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2314yes—
320C2×#125C2314yes—
321C2×#125C2312yes—
322C2×#125C2314yes—
323C2×#125C2314yes—
324C2×#125C2314yes—
325C2×#125C2314yes—
326C2×#125C2314yes—
327C2×#125C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2314yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2314yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2314yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2314yes—
354#401C2314yes—
355#401C2314yes—
356#401C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2312yes—
382#400C2312yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2312yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2312yes—
420#398C2312yes—
421#398C2312yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2312yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2312yes—
441#395C2314yes—
442#395C2314yes—
443#395C2312yes—
444#395C2312yes—
445#395C2314yes—
446#395C2312yes—
447#395C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2311yescharacteristic
459#391C2311yescharacteristic
460#391C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2311yescharacteristic
480#391C2311yescharacteristic
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2314yes—
489#391C2312yes—
490#391C2312yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2311yescharacteristic
497#389C2311yescharacteristic
498#389C2312yes—
499#389C2311yescharacteristic
500#389C2312yes—
501#389C2311yescharacteristic
502#389C2312yes—
503#389C2312yes—
504#389C2311yescharacteristic
505#389C2311yescharacteristic
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2311yescharacteristic
531#389C2311yescharacteristic
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2311yescharacteristic
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2311yescharacteristic
544#389C2312yes—
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2312yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2311yescharacteristic
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2311yescharacteristic
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2312yes—
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#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#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2312yes—
679#387C2312yes—
680#387C2314yes—
681#384C2311yescharacteristic
682#384C2312yes—
683#384C2311yescharacteristic
684#384C2312yes—
685#384C2312yes—
686#384C2312yes—
687#384C2311yescharacteristic
688#384C2312yes—
689#384C2312yes—
690#384C2312yes—
691#384C2312yes—
692#384C2312yes—
693#384C2312yes—
694#383C2314yes—
695#383C2314yes—
696#383C2314yes—
697#383C2314yes—
698#383C2314yes—
699#383C2314yes—
700#382C2311yescharacteristic
701#382C2312yes—
702#382C2312yes—
703#382C2311yescharacteristic
704#382C2311yescharacteristic
705#382C2312yes—
706#382C2311yescharacteristic
707#382C2312yes—
708#382C2312yes—
709#382C2314yes—
710#382C2312yes—
711#382C2314yes—
712#382C2312yes—
713#382C2312yes—
714#382C2312yes—
715#382C2312yes—
716#382C2314yes—
717#382C2314yes—
718#382C2314yes—
719#382C2314yes—
720#382C2314yes—
721#382C2314yes—
722C4×C4⋊C4C2312yes—
723C4×C4⋊C4C2312yes—
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2311yescharacteristic
726C4×C4⋊C4C2311yescharacteristic
727C4×C4⋊C4C2312yes—
728C4×C4⋊C4C2311yescharacteristic
729C4×C4⋊C4C2311yescharacteristic
730C4×C4⋊C4C2311yescharacteristic
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2311yescharacteristic
736C4×C4⋊C4C2311yescharacteristic
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2311yescharacteristic
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
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⋊C4C2314yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2312yes—
800C4×C4⋊C4C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2314yes—
804#376C2314yes—
805C43C2311yescharacteristic
806C43C2312yes—
807C43C2311yescharacteristic
808C43C2312yes—
809C43C2311yescharacteristic
810C43C2312yes—
811C43C2312yes—
812C22×Q8C2412yes—
813C22×Q8C2411yescharacteristic
814C22×Q8C2412yes—
815C22×Q8C2414yes—
816C22×Q8C2411yescharacteristic
817C22×Q8C2412yes—
818C22×Q8C2411yescharacteristic
819C22×Q8C2412yes—
820C22×Q8C2412yes—
821C4⋊Q8—28no—
822C4⋊Q8—28no—
823C4⋊Q8—216no—
824C4⋊Q8—24no—
825C4⋊Q8—28no—
826C4⋊Q8—24no—
827C4⋊Q8—28no—
828C4⋊Q8—24no—
829C4⋊Q8—24no—
830C4⋊Q8—24no—
831C4⋊Q8—44no—
832C4⋊Q8—82no—
833#125—28no—
834#125—216no—
835#125—28no—
836#125—24no—
837#125—216no—
838#125—28no—
839#125—24no—
840#125—24no—
841#125—48no—
842#125—44no—
843#125—48no—
844#125—84no—
845#125—84no—
846#125—84no—
847#125#4118yes—
848C4×Q8—24no—
849C4×Q8—24no—
850C4×Q8—24no—
851C4×Q8—24no—
852C4×Q8—28no—
853C4×Q8—216no—
854C4×Q8—28no—
855C4×Q8—28no—
856C4×Q8—24no—
857C4×Q8—24no—
858C4×Q8—24no—
859C4×Q8—28no—
860C4×Q8—28no—
861C4×Q8—24no—
862C4×Q8—28no—
863C4×Q8—24no—
864C4×Q8—24no—
865C4×Q8—24no—
866C4×Q8—24no—
867C4×Q8—44no—
868C4×Q8—42no—
869C4×Q8—84no—
870C4×Q8—82no—
871C4×Q8—82no—
872C4×Q8—84no—
873C4×Q8—84no—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2411yescharacteristic
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2411yescharacteristic
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2411yescharacteristic
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C42C2411yescharacteristic
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2412yes—
983C2×C42C2411yescharacteristic
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2412yes—
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2412yes—
1002C2×C42C2412yes—
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2412yes—
1006C2×C42C2412yes—
1007C2×C42C2412yes—
1008C2×C42C2412yes—
1009C2×C42C2411yescharacteristic
1010C2×C42C2412yes—
1011C2×C42C2411yescharacteristic
1012C2×C42C2414yes—
1013C2×C42C2414yes—
1014C2×C42C2414yes—
1015C2×C42C2414yes—
1016C2×C42C2414yes—
1017C2×C42C2412yes—
1018C2×C42C2411yescharacteristic
1019C2×C42C2412yes—
1020C2×C42C2411yescharacteristic
1021C2×C42C2412yes—
1022C2×C42C2412yes—
1023C2×C42C2414yes—
1024C2×C42C2411yescharacteristic
1025C2×C42C2411yescharacteristic
1026C2×C42C2411yescharacteristic
1027C2×C42C2411yescharacteristic
1028#95C2412yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2411yescharacteristic
1045#95C2411yescharacteristic
1046#95C2411yescharacteristic
1047#95C2412yes—
1048#95C2411yescharacteristic
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2414yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2411yescharacteristic
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2414yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2411yescharacteristic
1065#95C2412yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2412yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2414yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2412yes—
1097#95C2412yes—
1098#95C2414yes—
1099#95C2412yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2414yes—
1110#95C2412yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2412yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128C2×Q8—22no—
1129C2×Q8—24no—
1130C2×Q8—22no—
1131C2×Q8—24no—
1132C2×Q8—28no—
1133C2×Q8—24no—
1134C2×Q8—22no—
1135C2×Q8—22no—
1136C2×Q8—24no—
1137C2×Q8—22no—
1138C2×Q8—22no—
1139C2×Q8—22no—
1140C2×Q8—24no—
1141C2×Q8—28no—
1142C2×Q8—24no—
1143C2×Q8—24no—
1144C2×Q8—24no—
1145C2×Q8—24no—
1146C2×Q8—41no—
1147C2×Q8—42no—
1148C2×Q8—42no—
1149C2×Q8—44no—
1150C2×Q8—42no—
1151C2×Q8—42no—
1152C2×Q8—42no—
1153C2×Q8—42no—
1154C2×Q82−1+414yes—
1155C22×C4C2512yes—
1156C22×C4C2514yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2511yescharacteristic
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2514yes—
1172C22×C4C2514yes—
1173C22×C4C2514yes—
1174C22×C4C2511yescharacteristic
1175C22×C4C2512yes—
1176C22×C4C2511yescharacteristic
1177C22×C4C2512yes—
1178C22×C4C2511yescharacteristic
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2511yescharacteristic
1182C22×C4C2512yes—
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C22×C4C2512yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C4⋊C4—24no—
1191C4⋊C4—22no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—28no—
1198C4⋊C4—24no—
1199C4⋊C4—22no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—28no—
1203C4⋊C4—28no—
1204C4⋊C4—22no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—28no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—22no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—22no—
1217C4⋊C4—24no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—22no—
1225C4⋊C4—24no—
1226C4⋊C4—24no—
1227C4⋊C4—24no—
1228C4⋊C4—24no—
1229C4⋊C4—24no—
1230C4⋊C4—24no—
1231C4⋊C4—24no—
1232C4⋊C4—24no—
1233C4⋊C4—22no—
1234C4⋊C4—22no—
1235C4⋊C4—22no—
1236C4⋊C4—24no—
1237C4⋊C4—28no—
1238C4⋊C4—28no—
1239C4⋊C4—28no—
1240C4⋊C4—24no—
1241C4⋊C4—24no—
1242C4⋊C4—24no—
1243C4⋊C4—22no—
1244C4⋊C4—24no—
1245C4⋊C4—24no—
1246C4⋊C4—24no—
1247C4⋊C4—24no—
1248C4⋊C4—22no—
1249C4⋊C4—24no—
1250C4⋊C4—22no—
1251C4⋊C4—24no—
1252C4⋊C4—24no—
1253C4⋊C4—28no—
1254C4⋊C4—41no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
1259C4⋊C4—42no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—42no—
1273C4⋊C4—42no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—42no—
1279C4⋊C4—42no—
1280C4⋊C4—44no—
1281C4⋊C4—42no—
1282C4⋊C4—44no—
1283C4⋊C4—42no—
1284C4⋊C4—44no—
1285C4⋊C4—44no—
1286C4⋊C4—44no—
1287C4⋊C4C2×#4114yes—
1288C4⋊C4C2×#4114yes—
1289C4⋊C4C2×#4118yes—
1290C4⋊C4C2×#4118yes—
1291C4⋊C42−1+414yes—
1292C42—24no—
1293C42—24no—
1294C42—28no—
1295C42—22no—
1296C42—24no—
1297C42—28no—
1298C42—24no—
1299C42—28no—
1300C42—24no—
1301C42—22no—
1302C42—24no—
1303C42—24no—
1304C42—22no—
1305C42—22no—
1306C42—24no—
1307C42—22no—
1308C42—24no—
1309C42—24no—
1310C42—22no—
1311C42—22no—
1312C42—24no—
1313C42—24no—
1314C42—24no—
1315C42—22no—
1316C42—24no—
1317C42—22no—
1318C42—22no—
1319C42—24no—
1320C42—24no—
1321C42—24no—
1322C42—22no—
1323C42—41no—
1324C42—41no—
1325C42—42no—
1326C42—42no—
1327C42—42no—
1328C42—42no—
1329C42—41no—
1330C42—44no—
1331C42—42no—
1332C42—44no—
1333C42—41no—
1334C42—44no—
1335C42—44no—
1336C42—44no—
1337C42—44no—
1338C42—42no—
1339C42—42no—
1340C42—41no—
1341C42C2×#4114yes—
1342C422−1+414yes—
1343C422−1+414yes—
1344C23C2611yescharacteristic
1345Q8—28no—
1346Q8—416no—
1347Q8—48no—
1348Q8—44no—
1349Q8—48no—
1350Q8—48no—
1351Q8—44no—
1352Q8—84no—
1353Q8—84no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—21no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—21no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—24no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—21no—
1427C2×C4—24no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—21no—
1431C2×C4—22no—
1432C2×C4—21no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—24no—
1439C2×C4—21no—
1440C2×C4—22no—
1441C2×C4—21no—
1442C2×C4—22no—
1443C2×C4C22×#4112yes—
1444C2×C4C22×#4114yes—
1445C2×C4C22×#4114yes—
1446C2×C4C22×#4112yes—
1447C2×C4C22×#4112yes—
1448C2×C4C2×2−1+414yes—
1449C2×C4C2×2−1+412yes—
1450C2×C4C2×2−1+414yes—
1451C2×C4C2×2−1+412yes—
1452C2×C4C2×2−1+412yes—
1453C2×C4C2×2−1+412yes—
1454C2×C4C2×2−1+412yes—
1455C2×C4C2×2−1+412yes—
1456C2×C4C2×2−1+412yes—
1457C2×C4C2×2−1+412yes—
1458C2×C4#58512yes—
1459C22C23×#4111yescharacteristic
1460C22C22×2−1+411yescharacteristic
1461C22C22×2−1+411yescharacteristic
1462C22C22×2−1+411yescharacteristic
1463C22C22×2−1+411yescharacteristic
1464C22C2×#58511yescharacteristic
1465C22H(7,𝔽2)11yescharacteristic
1466C4—24no—
1467C4—22no—
1468C4—24no—
1469C4—22no—
1470C4—24no—
1471C4—22no—
1472C4—24no—
1473C4—22no—
1474C4—22no—
1475C4—22no—
1476C4—41no—
1477C4—41no—
1478C4—44no—
1479C4—42no—
1480C4—42no—
1481C4—41no—
1482C4—41no—
1483C4—42no—
1484C4—42no—
1485C4—44no—
1486C4—42no—
1487C4—42no—
1488C4—42no—
1489C4—41no—
1490C4—41no—
1491C4—42no—
1492C4—42no—
1493C4—41no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—44no—
1498C4—44no—
1499C4#352314yes—
1500C4#355614yes—
1501C2C2×#355611yescharacteristic
1502C2C2×#352311yescharacteristic
1503C2#6280511yescharacteristic
1504C2#6294311yescharacteristic
1505C2#6296211yescharacteristic
1506C2#6300011yescharacteristic
1507C2#6303811yescharacteristic
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
#599632
#596732
#596672
#596652
#594562
#513762
#497142
#461812
#452772
#449942
#434562
#425532
#425112
#411942
#401892
#401432
#399992
#396422
#390032
#389862
#382292
#365982
#365632
#365562
#364972
#362862
#352082
#351872
#351152
#349502
#349202
#344882
C4×#5572