Finite Group Databasebeta

← #8418138

Subgroups — #8418138

Order 512.

4421 conjugacy classes of subgroups.

The subgroup lattice has 1504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58168C214yesmaximal, complemented
2#56552C214yesmaximal, complemented
3#56351C214yesmaximal, complemented
4#55379C214yesmaximal, complemented
5#54310C214yesmaximal, complemented
6#54278C214yesmaximal, complemented
7#53074C212yesmaximal, complemented
8#53066C212yesmaximal, complemented
9#52646C214yesmaximal, complemented
10#52424C214yesmaximal, complemented
11#45428C211yesmaximal, characteristic, complemented
12#45335C211yesmaximal, characteristic, complemented
13#45271C211yesmaximal, characteristic, complemented
14#44985C212yesmaximal, complemented
15#44979C211yesmaximal, characteristic, complemented
16#44918C212yesmaximal, complemented
17#42895C212yesmaximal, complemented
18#42772C212yesmaximal, complemented
19#42652C211yesmaximal, characteristic, complemented
20#42651C211yesmaximal, characteristic, complemented
21#42519C212yesmaximal, complemented
22#42459C212yesmaximal, complemented
23#39756C211yesmaximal, characteristic, complemented
24#39502C211yesmaximal, characteristic, complemented
25#39173C211yesmaximal, characteristic, complemented
26#38951C211yesmaximal, characteristic, complemented
27#37397C211yesmaximal, characteristic, complemented
28#36693C211yesmaximal, characteristic, complemented
29#35712C211yesmaximal, characteristic, complemented
30#35693C211yesmaximal, characteristic, complemented
31#35534C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#547C2211yescharacteristic
36C2×#540C2211yescharacteristic
37C2×#520C2211yescharacteristic
38#2862C2211yescharacteristic
39#2859C2211yescharacteristic
40#2839C2212yes—
41#2839C2214yes—
42#2838C2212yes—
43#2838C2212yes—
44#2837C2214yes—
45#2837C2212yes—
46#2832C2212yes—
47#2831C2212yes—
48#2830C2212yes—
49#2829C2214yes—
50#2829C2212yes—
51#2828C2214yes—
52#2828C2214yes—
53#2828C2214yes—
54#2828C2214yes—
55#2827C2214yes—
56#2824C2214yes—
57#2824C2214yes—
58#2824C2214yes—
59#2816C2212yes—
60#2815C2212yes—
61#2813C2214yes—
62#2808C2214yes—
63#2807C2214yes—
64#2803C2214yes—
65#2800C2214yes—
66#2798C2214yes—
67#2797C2214yes—
68#2796C2214yes—
69#2790C2214yes—
70#2790C2214yes—
71#2786C2214yes—
72#2786C2214yes—
73#2784C2214yes—
74#2783C2214yes—
75#2782C2214yes—
76#2782C2214yes—
77#2780C2214yes—
78#2779C2214yes—
79#2778C2214yes—
80#2777C2214yes—
81#2773C2214yes—
82#2773C2214yes—
83#2772C2214yes—
84#2770C2214yes—
85#2767C2214yes—
86#2767C2214yes—
87#2766C2214yes—
88#2757C2214yes—
89#2755C2214yes—
90#2753C2214yes—
91#2753C2214yes—
92#2748C2214yes—
93#2737C2214yes—
94#2737C2214yes—
95#2728C2214yes—
96#2727C2214yes—
97#2724C2214yes—
98#2722C2214yes—
99#2718C2214yes—
100#2714C2214yes—
101#2711C2214yes—
102#2708C2214yes—
103#2706C2214yes—
104#2706C2214yes—
105#2706C2214yes—
106#2705C2214yes—
107#2703C2214yes—
108#2696C2214yes—
109#2695C2214yes—
110#2694C2214yes—
111#2691C2214yes—
112#2690C2214yes—
113#2690C2214yes—
114#2689C2214yes—
115#2682C2214yes—
116#2681C2214yes—
117#2680C2214yes—
118#2663C2212yes—
119#2661C2212yes—
120#2661C2214yes—
121#2652C2214yes—
122#2652C2214yes—
123#2648C2214yes—
124#2648C2214yes—
125#2647C2214yes—
126#2642C2212yes—
127#2641C2212yes—
128#2638C2212yes—
129#2637C2214yes—
130#2633C2212yes—
131#2630C2214yes—
132#2628C2211yescharacteristic
133#2623C2212yes—
134#2623C2212yes—
135#2621C2211yescharacteristic
136#2620C2212yes—
137#2620C2212yes—
138#2611C2212yes—
139#2604C2214yes—
140#2603C2214yes—
141#2602C2214yes—
142#2599C2212yes—
143#2592C2212yes—
144#2592C2212yes—
145#2592C2212yes—
146#2583C2212yes—
147#2580C2211yescharacteristic
148#2580C2214yes—
149#2580C2211yescharacteristic
150#2578C2214yes—
151#2567C2211yescharacteristic
152#2566C2211yescharacteristic
153#2565C2212yes—
154#2565C2211yescharacteristic
155#2559C2214yes—
156#2552C2212yes—
157#2548C2211yescharacteristic
158#2548C2212yes—
159#2547C2212yes—
160#2547C2211yescharacteristic
161#2547C2211yescharacteristic
162#2542C2211yescharacteristic
163#2541C2211yescharacteristic
164#2540C2212yes—
165#2536C2211yescharacteristic
166#2535C2211yescharacteristic
167#2531C2214yes—
168#2531C2214yes—
169#2530C2214yes—
170#2530C2214yes—
171#2526C2214yes—
172#2518C2214yes—
173#2512C2212yes—
174#2512C2212yes—
175#2512C2212yes—
176#2511C2212yes—
177#2511C2212yes—
178#2504C2212yes—
179#2504C2211yescharacteristic
180#2502C2212yes—
181#2501C2212yes—
182#2501C2211yescharacteristic
183#2490C2212yes—
184#2490C2212yes—
185#2490C2212yes—
186#2489C2212yes—
187#2489C2212yes—
188#2489C2212yes—
189#2473C2214yes—
190#2473C2214yes—
191#2471C2214yes—
192#2470C2214yes—
193#2467C2214yes—
194#2467C2214yes—
195#2466C2214yes—
196#2466C2214yes—
197#2465C2214yes—
198#2464C2214yes—
199#2460C2214yes—
200#2458C2214yes—
201#2458C2214yes—
202#2458C2214yes—
203#2456C2214yes—
204#2455C2214yes—
205#2455C2214yes—
206#2453C2212yes—
207#2446C2212yes—
208#2445C2212yes—
209#2443C2214yes—
210#2443C2214yes—
211#2442C2214yes—
212#2442C2212yes—
213#2432C2212yes—
214#2432C2212yes—
215#2431C2212yes—
216#2431C2212yes—
217#2431C2211yescharacteristic
218#2431C2211yescharacteristic
219#2429C2212yes—
220#2428C2212yes—
221#2423C2212yes—
222#2423C2212yes—
223#2422C2212yes—
224#2422C2212yes—
225#2421C2214yes—
226#2417C2214yes—
227#2407C2214yes—
228#2407C2214yes—
229#2407C2212yes—
230#2407C2212yes—
231#2406C2212yes—
232#2401C2212yes—
233#2399C2211yescharacteristic
234#2398C2211yescharacteristic
235#2398C2212yes—
236#2398C2212yes—
237#2396C2212yes—
238#2396C2211yescharacteristic
239#2395C2212yes—
240#2392C2211yescharacteristic
241#2388C2212yes—
242#2367C2212yes—
243#2361C2212yes—
244#2360C2212yes—
245#2360C2212yes—
246#2357C2211yescharacteristic
247#2357C2211yescharacteristic
248#2357C2211yescharacteristic
249#2356C2212yes—
250#2356C2211yescharacteristic
251Q8×C4⋊C4C2212yes—
252D4×C4⋊C4C2212yes—
253#2341C2212yes—
254#2331C2211yescharacteristic
255#2330C2212yes—
256#2328C2211yescharacteristic
257#2327C2211yescharacteristic
258#2326C2212yes—
259#2326C2211yescharacteristic
260#2314C2212yes—
261#2311C2212yes—
262C4×#127C2211yescharacteristic
263C4×#124C2211yescharacteristic
264#2298C2211yescharacteristic
265#2295C2211yescharacteristic
266#2293C2211yescharacteristic
267C22×#41C2312yes—
268C22×#41C2311yescharacteristic
269C22×#41C2312yes—
270#557—44no—
271#554—44no—
272#547—44no—
273#547—44no—
274#540—44no—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×#127C2311yescharacteristic
279C2×#127C2311yescharacteristic
280C2×#127C2311yescharacteristic
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#125C2311yescharacteristic
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2311yescharacteristic
293C2×#123C2312yes—
294C2×#123C2312yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2311yescharacteristic
313C2×#121C2311yescharacteristic
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317#520—44no—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2314yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×#117C2311yescharacteristic
339C2×#117C2312yes—
340C2×#117C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2312yes—
346#401C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2312yes—
360#400C2312yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2311yescharacteristic
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#400C2312yes—
371#399C2312yes—
372#399C2312yes—
373#399C2314yes—
374#399C2312yes—
375#399C2314yes—
376#399C2314yes—
377#399C2312yes—
378#399C2312yes—
379#399C2314yes—
380#399C2311yescharacteristic
381#399C2312yes—
382#399C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2312yes—
396#398C2311yescharacteristic
397#398C2312yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2312yes—
420#397C2312yes—
421#397C2312yes—
422#397C2312yes—
423#397C2312yes—
424#397C2312yes—
425#397C2312yes—
426#397C2312yes—
427#397C2314yes—
428#397C2311yescharacteristic
429#397C2314yes—
430#397C2312yes—
431#397C2312yes—
432#397C2312yes—
433#397C2312yes—
434#397C2312yes—
435#397C2312yes—
436#397C2314yes—
437#397C2314yes—
438#397C2312yes—
439#397C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2312yes—
444#396C2312yes—
445#396C2314yes—
446#396C2314yes—
447#396C2312yes—
448#396C2312yes—
449#396C2312yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#395C2312yes—
455#395C2312yes—
456#395C2312yes—
457#395C2311yescharacteristic
458#395C2312yes—
459#395C2312yes—
460#395C2312yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2312yes—
477#394C2312yes—
478#394C2312yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2312yes—
487#394C2312yes—
488#394C2314yes—
489#394C2311yescharacteristic
490#394C2312yes—
491#394C2314yes—
492#394C2314yes—
493#394C2312yes—
494#393C2311yescharacteristic
495#393C2312yes—
496#393C2314yes—
497#393C2312yes—
498#393C2312yes—
499#393C2312yes—
500#393C2314yes—
501#393C2314yes—
502#393C2312yes—
503#393C2312yes—
504#393C2312yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2311yescharacteristic
517#392C2312yes—
518#391C2312yes—
519#391C2311yescharacteristic
520#391C2312yes—
521#391C2311yescharacteristic
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2314yes—
528#391C2312yes—
529#391C2314yes—
530#391C2312yes—
531#390C2311yescharacteristic
532#390C2311yescharacteristic
533#390C2314yes—
534#390C2311yescharacteristic
535#390C2312yes—
536#390C2314yes—
537#390C2314yes—
538#390C2314yes—
539#390C2314yes—
540#390C2312yes—
541#390C2314yes—
542#390C2312yes—
543#390C2314yes—
544#390C2312yes—
545#390C2314yes—
546#390C2311yescharacteristic
547#390C2311yescharacteristic
548#390C2311yescharacteristic
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2314yes—
553#390C2314yes—
554#390C2314yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2314yes—
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2312yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2312yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2312yes—
586#388C2314yes—
587#388C2312yes—
588#388C2312yes—
589#388C2312yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2314yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2314yes—
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#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#384C2311yescharacteristic
679#384C2312yes—
680#384C2311yescharacteristic
681#384C2312yes—
682#384C2312yes—
683#384C2314yes—
684#383C2314yes—
685#383C2312yes—
686#382C2311yescharacteristic
687#382C2311yescharacteristic
688#382C2311yescharacteristic
689#382C2311yescharacteristic
690#382C2314yes—
691#382C2314yes—
692#382C2314yes—
693#382C2314yes—
694#381C2312yes—
695#381C2312yes—
696#381C2312yes—
697#380C2314yes—
698#380C2314yes—
699#380C2312yes—
700#380C2312yes—
701#380C2314yes—
702#380C2312yes—
703#380C2314yes—
704#380C2314yes—
705#380C2314yes—
706#380C2314yes—
707#380C2314yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2311yescharacteristic
711C4×C4⋊C4C2311yescharacteristic
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2311yescharacteristic
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2314yes—
731C4×C22⋊C4C2311yescharacteristic
732C4×C22⋊C4C2311yescharacteristic
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2314yes—
735#376C2311yescharacteristic
736#376C2312yes—
737#376C2314yes—
738#376C2312yes—
739C43C2311yescharacteristic
740C2×#41—42no—
741C2×#41—42no—
742C2×#41—42no—
743C2×#41—44no—
744C2×#41—44no—
745C2×#41—44no—
746C2×#41—44no—
747C2×#41—84no—
748C22×Q8C2411yescharacteristic
749C22×Q8C2412yes—
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×Q8C2412yes—
753C22×D4C2411yescharacteristic
754C22×D4C2411yescharacteristic
755C22×D4C2411yescharacteristic
756C22×D4C2411yescharacteristic
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2414yes—
760C22×D4C2414yes—
761C22×D4C2412yes—
762C22×D4C2412yes—
763C22×D4C2412yes—
764C22×D4C2414yes—
765C22×D4C2414yes—
766C22×D4C2412yes—
767C22×D4C2414yes—
768C23×C4C2411yescharacteristic
769C23×C4C2412yes—
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2412yes—
773C23×C4C2412yes—
774C23×C4C2412yes—
775C23×C4C2412yes—
776C23×C4C2414yes—
777C23×C4C2414yes—
778C23×C4C2414yes—
779C4⋊Q8—24no—
780C4⋊Q8—24no—
781C4⋊Q8—44no—
782#127—42no—
783#127—42no—
784#127—42no—
785#126—84no—
786#126—84no—
787#126—84no—
788#125—44no—
789#125—42no—
790#125—44no—
791#125—44no—
792#125—48no—
793#124—42no—
794#124—44no—
795#124—44no—
796#124—42no—
797#123—48no—
798#123—48no—
799#123—44no—
800#123—44no—
801#123—84no—
802#123—84no—
803#123—84no—
804#123—84no—
805C22⋊Q8—48no—
806C22⋊Q8—44no—
807C22⋊Q8—44no—
808C22⋊Q8—44no—
809C22⋊Q8—44no—
810C22⋊Q8—44no—
811C22⋊Q8—84no—
812#121—44no—
813#121—44no—
814#121—44no—
815#121—42no—
816#121—42no—
817#121—44no—
818#121—44no—
819#121—84no—
820#121—84no—
821C4×Q8—24no—
822C4×Q8—24no—
823C4×Q8—44no—
824C4×Q8—44no—
825C4×Q8—42no—
826C4×Q8—44no—
827C4×Q8—44no—
828C4×Q8—84no—
829C4×D4—24no—
830C4×D4—24no—
831C4×D4—24no—
832C4×D4—24no—
833C4×D4—44no—
834C4×D4—42no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—44no—
838C4×D4—84no—
839C4×D4—84no—
840C4×D4—84no—
841#117—24no—
842#117—44no—
843#117—44no—
844C2×C4⋊C4—42no—
845C2×C4⋊C4—44no—
846C2×C4⋊C4—44no—
847C2×C4⋊C4—44no—
848C2×C4⋊C4—44no—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C22⋊C4C2411yescharacteristic
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C42C2411yescharacteristic
968C2×C42C2412yes—
969C2×C42C2411yescharacteristic
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2414yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2414yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987#95C2411yescharacteristic
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2411yescharacteristic
1002#95C2411yescharacteristic
1003#95C2411yescharacteristic
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053C24C2511yescharacteristic
1054C24C2512yes—
1055C24C2512yes—
1056C24C2512yes—
1057C24C2512yes—
1058#41—416no—
1059#41—816no—
1060#41—816no—
1061C2×Q8—22no—
1062C2×Q8—22no—
1063C2×Q8—24no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—22no—
1067C2×Q8—22no—
1068C2×Q8—24no—
1069C2×Q8—42no—
1070C2×Q8—42no—
1071C2×Q8—42no—
1072C2×Q8—42no—
1073C2×Q8—44no—
1074C2×D4—22no—
1075C2×D4—22no—
1076C2×D4—22no—
1077C2×D4—22no—
1078C2×D4—22no—
1079C2×D4—22no—
1080C2×D4—22no—
1081C2×D4—22no—
1082C2×D4—22no—
1083C2×D4—22no—
1084C2×D4—42no—
1085C2×D4—42no—
1086C2×D4—42no—
1087C2×D4—42no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C22×C4—22no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—22no—
1118C22×C4—24no—
1119C22×C4—22no—
1120C22×C4—24no—
1121C22×C4—24no—
1122C22×C4—24no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—42no—
1136C22×C4—42no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4C2511yescharacteristic
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2514yes—
1152C22×C4C2512yes—
1153C22×C4C2514yes—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2514yes—
1159C22×C4C2512yes—
1160C22×C4C2514yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C22×C4C2511yescharacteristic
1168C4⋊C4—22no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—22no—
1178C4⋊C4—22no—
1179C4⋊C4—22no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C22⋊C4—22no—
1229C22⋊C4—22no—
1230C22⋊C4—24no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—42no—
1253C22⋊C4—44no—
1254C22⋊C4—42no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—42no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C42—22no—
1287C42—24no—
1288C42—24no—
1289C42—22no—
1290C42—24no—
1291C42—24no—
1292C42—22no—
1293C42—22no—
1294C42—22no—
1295C42—42no—
1296C42—44no—
1297C42—42no—
1298C42—42no—
1299C42—44no—
1300C42—44no—
1301C42—44no—
1302C42—44no—
1303C42—44no—
1304C42—44no—
1305C42H(5,𝔽2)14yes—
1306C23—21no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—21no—
1313C23—22no—
1314C23—22no—
1315C23—21no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—24no—
1322C23—22no—
1323C23—22no—
1324C23—24no—
1325C23—24no—
1326C23—22no—
1327C23—22no—
1328C23—24no—
1329C23—22no—
1330C23—22no—
1331C23—24no—
1332C23—24no—
1333C23C2611yescharacteristic
1334Q8—44no—
1335Q8—48no—
1336Q8—44no—
1337Q8—48no—
1338Q8—84no—
1339D4—44no—
1340D4—48no—
1341D4—48no—
1342D4—44no—
1343D4—44no—
1344D4—44no—
1345D4—88no—
1346D4—88no—
1347D4—88no—
1348D4—88no—
1349D4—164no—
1350D4—162no—
1351D4—162no—
1352D4—162no—
1353D4—162no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—21no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—48no—
1420C2×C4—44no—
1421C2×C4—48no—
1422C2×C4—84no—
1423C2×C4—84no—
1424C2×C4—84no—
1425C2×C4—88no—
1426C2×C4—88no—
1427C2×C4—162no—
1428C2×C4—164no—
1429C2×C4—162no—
1430C2×C4C2×H(5,𝔽2)12yes—
1431C2×C4C2×H(5,𝔽2)12yes—
1432C2×C4C2×H(5,𝔽2)12yes—
1433C2×C4#58512yes—
1434C2×C4#58512yes—
1435C22—42no—
1436C22—41no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—44no—
1443C22—44no—
1444C22—42no—
1445C22—44no—
1446C22—42no—
1447C22—44no—
1448C22—44no—
1449C22—44no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—42no—
1455C22—41no—
1456C22—42no—
1457C22—42no—
1458C22—41no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22C22×H(5,𝔽2)11yescharacteristic
1463C22C2×#58511yescharacteristic
1464C22C2×#58511yescharacteristic
1465C22H(7,𝔽2)12yes—
1466C222−1+612yes—
1467C4—22no—
1468C4—22no—
1469C4—41no—
1470C4—42no—
1471C4—42no—
1472C4—44no—
1473C4—42no—
1474C4—42no—
1475C4—42no—
1476C4—42no—
1477C4—42no—
1478C4—42no—
1479C4—44no—
1480C4—44no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4—44no—
1485C4—42no—
1486C4—42no—
1487C4—42no—
1488C4—41no—
1489C4—42no—
1490C4—41no—
1491C4—42no—
1492C4#354014yes—
1493C2—81no—
1494C2—82no—
1495C2—82no—
1496C2—82no—
1497C2—82no—
1498C2C2×#354011yescharacteristic
1499C2#6287611yescharacteristic
1500C2#6288711yescharacteristic
1501C2#6304712yes—
1502C2#6305612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58168C2semidirect
2. #56552C2semidirect
3. #56351C2semidirect
4. #55379C2semidirect
5. #54310C2semidirect
6. #54278C2semidirect
7. #53074C2semidirect
8. #53066C2semidirect
9. #52646C2semidirect
10. #52424C2semidirect
11. #45428C2semidirect
12. #45335C2semidirect
13. #45271C2semidirect
14. #44985C2semidirect
15. #44979C2semidirect
16. #44918C2semidirect
17. #42895C2semidirect
18. #42772C2semidirect
19. #42652C2semidirect
20. #42651C2semidirect
21. #42519C2semidirect
22. #42459C2semidirect
23. #39756C2semidirect
24. #39502C2semidirect
25. #39173C2semidirect
26. #38951C2semidirect
27. #37397C2semidirect
28. #36693C2semidirect
29. #35712C2semidirect
30. #35693C2semidirect
31. #35534C2semidirect

Maximal subgroups

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

subgroupindex
#581682
#565522
#563512
#553792
#543102
#542782
#530742
#530662
#526462
#524242
#454282
#453352
#452712
#449852
#449792
#449182
#428952
#427722
#426522
#426512
#425192
#424592
#397562
#395022
#391732
#389512
#373972
#366932
#357122
#356932
#355342