Finite Group Databasebeta

← #8746496

Subgroups — #8746496

Order 512.

4725 conjugacy classes of subgroups.

The subgroup lattice has 1511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59827C211yesmaximal, characteristic, complemented
2#59496C212yesmaximal, complemented
3#56058C214yesmaximal, complemented
4#55464C214yesmaximal, complemented
5#54723C214yesmaximal, complemented
6#53815C212yesmaximal, complemented
7#53621C214yesmaximal, complemented
8#53061C212yesmaximal, complemented
9#52968C211yesmaximal, characteristic, complemented
10#52762C212yesmaximal, complemented
11#52681C214yesmaximal, complemented
12#47786C212yesmaximal, complemented
13#45333C212yesmaximal, complemented
14#45330C211yesmaximal, characteristic, complemented
15#45087C212yesmaximal, complemented
16#44922C212yesmaximal, complemented
17#44915C212yesmaximal, complemented
18#42985C211yesmaximal, characteristic, complemented
19#42894C212yesmaximal, complemented
20#42593C212yesmaximal, complemented
21#42463C212yesmaximal, complemented
22#42453C212yesmaximal, complemented
23#42211C212yesmaximal, complemented
24#41956C214yesmaximal, complemented
25#39747C211yesmaximal, characteristic, complemented
26#39406C212yesmaximal, complemented
27#36696C211yesmaximal, characteristic, complemented
28#36076C211yesmaximal, characteristic, complemented
29#35701C212yesmaximal, complemented
30C2×#559C2212yes—
31C2×#556C2211yescharacteristic
32C2×#554C2212yes—
33C2×#550C2211yescharacteristic
34C2×#542C2214yes—
35C2×#537C2211yescharacteristic
36C2×#520C2211yescharacteristic
37#2858C2211yescharacteristic
38#2843C2211yescharacteristic
39#2838C2214yes—
40#2833C2212yes—
41#2830C2211yescharacteristic
42#2830C2214yes—
43#2830C2212yes—
44#2829C2214yes—
45#2829C2212yes—
46#2829C2212yes—
47#2829C2212yes—
48#2829C2214yes—
49#2828C2211yescharacteristic
50#2828C2212yes—
51#2828C2214yes—
52#2827C2214yes—
53#2826C2214yes—
54#2825C2214yes—
55#2823C2211yescharacteristic
56#2819C2214yes—
57#2818C2212yes—
58#2817C2212yes—
59#2815C2212yes—
60#2800C2214yes—
61#2797C2214yes—
62#2796C2214yes—
63#2796C2214yes—
64#2786C2214yes—
65#2780C2214yes—
66#2777C2214yes—
67#2773C2214yes—
68#2771C2212yes—
69#2764C2212yes—
70#2759C2214yes—
71#2758C2214yes—
72#2757C2214yes—
73#2757C2214yes—
74#2754C2214yes—
75#2754C2214yes—
76#2751C2214yes—
77#2751C2214yes—
78#2749C2214yes—
79#2749C2214yes—
80#2740C2214yes—
81#2740C2214yes—
82#2734C2212yes—
83#2733C2214yes—
84#2733C2214yes—
85#2732C2214yes—
86#2730C2214yes—
87#2730C2214yes—
88#2728C2212yes—
89#2725C2214yes—
90#2724C2212yes—
91#2724C2212yes—
92#2723C2214yes—
93#2715C2214yes—
94#2714C2214yes—
95#2714C2214yes—
96#2711C2214yes—
97#2710C2214yes—
98#2708C2214yes—
99#2701C2214yes—
100#2700C2214yes—
101#2698C2214yes—
102#2692C2214yes—
103#2692C2214yes—
104#2689C2214yes—
105#2688C2214yes—
106#2681C2214yes—
107#2674C2214yes—
108#2674C2214yes—
109#2674C2214yes—
110#2673C2214yes—
111#2673C2214yes—
112#2672C2214yes—
113#2672C2214yes—
114#2662C2214yes—
115#2657C2212yes—
116#2651C2214yes—
117#2648C2214yes—
118#2648C2214yes—
119#2639C2212yes—
120#2638C2214yes—
121#2638C2212yes—
122#2636C2214yes—
123#2635C2214yes—
124#2633C2214yes—
125#2632C2214yes—
126#2631C2214yes—
127#2628C2212yes—
128#2624C2211yescharacteristic
129#2624C2212yes—
130#2624C2212yes—
131#2615C2211yescharacteristic
132#2611C2214yes—
133#2610C2214yes—
134#2604C2214yes—
135#2602C2214yes—
136#2600C2212yes—
137#2598C2214yes—
138#2598C2214yes—
139#2589C2214yes—
140#2586C2212yes—
141#2585C2214yes—
142#2582C2212yes—
143#2570C2212yes—
144#2556C2214yes—
145#2551C2212yes—
146#2548C2212yes—
147#2547C2211yescharacteristic
148#2547C2212yes—
149#2547C2212yes—
150#2544C2212yes—
151#2543C2212yes—
152#2542C2212yes—
153#2541C2211yescharacteristic
154#2540C2214yes—
155#2538C2212yes—
156#2535C2212yes—
157#2535C2212yes—
158#2529C2214yes—
159#2527C2214yes—
160#2525C2214yes—
161#2524C2214yes—
162#2512C2212yes—
163#2510C2214yes—
164#2509C2212yes—
165#2508C2212yes—
166#2504C2211yescharacteristic
167#2504C2212yes—
168#2504C2211yescharacteristic
169#2501C2212yes—
170#2497C2212yes—
171#2497C2212yes—
172#2495C2212yes—
173#2494C2212yes—
174#2491C2212yes—
175#2491C2212yes—
176#2486C2211yescharacteristic
177#2486C2212yes—
178#2486C2212yes—
179#2486C2211yescharacteristic
180#2485C2212yes—
181#2485C2212yes—
182#2479C2214yes—
183#2470C2214yes—
184#2466C2214yes—
185#2464C2214yes—
186#2463C2214yes—
187#2463C2214yes—
188#2463C2214yes—
189#2462C2214yes—
190#2461C2214yes—
191#2461C2214yes—
192#2461C2214yes—
193#2459C2214yes—
194#2456C2214yes—
195#2456C2214yes—
196#2452C2212yes—
197#2451C2212yes—
198#2449C2214yes—
199#2449C2214yes—
200#2447C2214yes—
201#2447C2214yes—
202#2445C2214yes—
203#2445C2212yes—
204#2445C2214yes—
205#2440C2212yes—
206#2440C2212yes—
207#2439C2212yes—
208#2439C2212yes—
209#2438C2214yes—
210#2429C2214yes—
211#2428C2212yes—
212#2423C2212yes—
213#2423C2212yes—
214#2421C2212yes—
215#2420C2212yes—
216#2420C2214yes—
217#2420C2212yes—
218#2416C2212yes—
219#2414C2212yes—
220#2414C2212yes—
221#2414C2212yes—
222#2414C2212yes—
223#2407C2212yes—
224#2407C2212yes—
225#2407C2212yes—
226#2397C2214yes—
227#2395C2212yes—
228#2395C2212yes—
229#2395C2211yescharacteristic
230#2392C2212yes—
231#2392C2212yes—
232#2392C2212yes—
233#2388C2211yescharacteristic
234#2388C2212yes—
235#2362C2212yes—
236#2361C2212yes—
237#2361C2212yes—
238#2356C2212yes—
239#2356C2214yes—
240#2354C2212yes—
241#2352C2212yes—
242#2351C2212yes—
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2212yes—
245D4×C4⋊C4C2212yes—
246#2347C2212yes—
247#2341C2212yes—
248#2341C2211yescharacteristic
249#2339C2211yescharacteristic
250#2326C2212yes—
251#2324C2212yes—
252#2323C2212yes—
253#2317C2212yes—
254#2311C2212yes—
255C4×C4⋊Q8C2212yes—
256C4×#127C2211yescharacteristic
257C4×#126C2212yes—
258#2295C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262#559—48no—
263#556—44no—
264#554—48no—
265#550—44no—
266#542—416no—
267#537—44no—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×#127C2311yescharacteristic
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#127C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2314yes—
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#124C2314yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#123C2314yes—
289C2×#123C2312yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2312yes—
293C2×#123C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2311yescharacteristic
307C2×#121C2312yes—
308C2×#121C2311yescharacteristic
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316#520—44no—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2311yescharacteristic
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2312yes—
350#401C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2311yescharacteristic
358#400C2314yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#399C2312yes—
363#399C2314yes—
364#399C2311yescharacteristic
365#399C2312yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#398C2312yes—
374#398C2311yescharacteristic
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#397C2311yescharacteristic
389#397C2314yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#397C2312yes—
400#397C2312yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2312yes—
406#397C2312yes—
407#397C2314yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2312yes—
412#397C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2312yes—
417#397C2312yes—
418#397C2314yes—
419#397C2312yes—
420#397C2314yes—
421#396C2312yes—
422#396C2312yes—
423#396C2312yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2312yes—
428#396C2312yes—
429#396C2312yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2311yescharacteristic
439#395C2312yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#394C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2312yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2312yes—
455#394C2311yescharacteristic
456#394C2314yes—
457#394C2314yes—
458#394C2312yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2312yes—
472#394C2312yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2311yescharacteristic
486#393C2312yes—
487#393C2314yes—
488#393C2314yes—
489#393C2312yes—
490#392C2312yes—
491#392C2312yes—
492#392C2312yes—
493#392C2312yes—
494#392C2312yes—
495#392C2312yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2312yes—
500#392C2312yes—
501#392C2314yes—
502#392C2314yes—
503#392C2311yescharacteristic
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2314yes—
510#392C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2312yes—
514#391C2312yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2312yes—
519#391C2314yes—
520#391C2314yes—
521#390C2312yes—
522#390C2311yescharacteristic
523#390C2312yes—
524#390C2311yescharacteristic
525#390C2314yes—
526#390C2314yes—
527#390C2314yes—
528#390C2314yes—
529#390C2314yes—
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2312yes—
534#390C2312yes—
535#390C2314yes—
536#390C2312yes—
537#390C2312yes—
538#390C2314yes—
539#390C2312yes—
540#390C2314yes—
541#390C2314yes—
542#390C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
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#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#384C2311yescharacteristic
659#384C2312yes—
660#384C2312yes—
661#384C2312yes—
662#383C2312yes—
663#383C2314yes—
664#383C2314yes—
665#383C2314yes—
666#382C2314yes—
667#382C2312yes—
668#382C2312yes—
669#382C2314yes—
670#382C2312yes—
671#381C2312yes—
672#381C2312yes—
673#381C2312yes—
674#381C2314yes—
675#381C2314yes—
676#381C2314yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2312yes—
681#380C2312yes—
682#380C2312yes—
683#380C2311yescharacteristic
684#380C2312yes—
685#380C2311yescharacteristic
686#380C2314yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2312yes—
691#380C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2311yescharacteristic
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715#376C2312yes—
716#376C2314yes—
717C2×#95C2312yes—
718C43C2311yescharacteristic
719C2×#41—24no—
720C2×#41—24no—
721C2×#41—42no—
722C2×#41—44no—
723C2×#41—44no—
724C2×#41—44no—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2414yes—
728C22×Q8C2414yes—
729C22×Q8C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2411yescharacteristic
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2412yes—
746C22×D4C2412yes—
747C22×D4C2412yes—
748C22×D4C2414yes—
749C22×D4C2411yescharacteristic
750C22×D4C2412yes—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2412yes—
754C23×C4C2411yescharacteristic
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2412yes—
758C23×C4C2414yes—
759C23×C4C2414yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C23×C4C2414yes—
763C4⋊Q8—44no—
764C4⋊Q8—44no—
765C4⋊Q8—42no—
766C4⋊Q8—48no—
767#127—24no—
768#127—42no—
769#127—44no—
770#127—82no—
771#126—28no—
772#126—48no—
773#126—48no—
774#125—48no—
775#124—28no—
776#124—48no—
777#124—44no—
778#124—48no—
779#124—48no—
780#124—48no—
781#124—82no—
782#124—82no—
783#123—48no—
784#123—48no—
785#123—44no—
786#123—48no—
787#123—44no—
788#123—84no—
789C22⋊Q8—28no—
790C22⋊Q8—28no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794C22⋊Q8—48no—
795C22⋊Q8—48no—
796C22⋊Q8—44no—
797C22⋊Q8—84no—
798C22⋊Q8—84no—
799#121—44no—
800#121—48no—
801#121—48no—
802#121—44no—
803#121—44no—
804#121—44no—
805#121—44no—
806#121—42no—
807#121—42no—
808#121—44no—
809#121—44no—
810#121—84no—
811C4×Q8—28no—
812C4×Q8—24no—
813C4×Q8—216no—
814C4×Q8—44no—
815C4×Q8—44no—
816C4×D4—48no—
817C4×D4—48no—
818C4×D4—44no—
819C4×D4—48no—
820C4×D4—44no—
821C4×D4—48no—
822C4×D4—48no—
823C4×D4—44no—
824C4×D4—44no—
825C4×D4—44no—
826C4×D4—44no—
827C4×D4—42no—
828C4×D4—44no—
829C4×D4—44no—
830C4×D4—42no—
831C4×D4—84no—
832C4×D4—84no—
833#117—44no—
834#117—44no—
835#117—42no—
836#117—48no—
837#117—44no—
838#117—44no—
839C2×C4⋊C4—42no—
840C2×C4⋊C4—44no—
841C2×C4⋊C4—42no—
842C2×C4⋊C4—44no—
843C2×C4⋊C4—44no—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2411yescharacteristic
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2411yescharacteristic
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2411yescharacteristic
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2411yescharacteristic
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2411yescharacteristic
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2411yescharacteristic
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2411yescharacteristic
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035C24C2512yes—
1036C24C2512yes—
1037C24C2512yes—
1038C24C2512yes—
1039C24C2511yescharacteristic
1040C24C2511yescharacteristic
1041#41—416no—
1042#41—88no—
1043#41—88no—
1044C2×Q8—28no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—42no—
1048C2×Q8—41no—
1049C2×Q8—42no—
1050C2×Q8—44no—
1051C2×Q8—44no—
1052C2×Q8—42no—
1053C2×Q8—44no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8H(5,𝔽2)14yes—
1057C2×D4—24no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—22no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—22no—
1065C2×D4—22no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—42no—
1077C2×D4—42no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—41no—
1081C2×D4—42no—
1082C2×D4—41no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—42no—
1086C2×D4—41no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—42no—
1090C2×D4—41no—
1091C2×D4—42no—
1092C2×D4—41no—
1093C2×D4—42no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—44no—
1101C2×D4—42no—
1102C2×D4—42no—
1103C2×D4—42no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—22no—
1115C22×C4—24no—
1116C22×C4—22no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—24no—
1121C22×C4—24no—
1122C22×C4—24no—
1123C22×C4—24no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—42no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—42no—
1134C22×C4—42no—
1135C22×C4—44no—
1136C22×C4—42no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—42no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—42no—
1144C22×C4C2511yescharacteristic
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2514yes—
1148C22×C4C2514yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2514yes—
1157C22×C4C2512yes—
1158C22×C4C2514yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2514yes—
1162C22×C4C2514yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—28no—
1171C4⋊C4—22no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—28no—
1176C4⋊C4—28no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—41no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—41no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—42no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C22⋊C4—28no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—42no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—42no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—44no—
1283C42—28no—
1284C42—28no—
1285C42—24no—
1286C42—22no—
1287C42—24no—
1288C42—28no—
1289C42—24no—
1290C42—24no—
1291C42—24no—
1292C42—42no—
1293C42—44no—
1294C42—44no—
1295C42—44no—
1296C42—44no—
1297C42—44no—
1298C42—41no—
1299C42—42no—
1300C42H(5,𝔽2)14yes—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—21no—
1308C23—21no—
1309C23—22no—
1310C23—21no—
1311C23—22no—
1312C23—21no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—24no—
1318C23—24no—
1319C23—22no—
1320C23—22no—
1321C23—21no—
1322C23—21no—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—24no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—24no—
1334C23—22no—
1335C23C2611yescharacteristic
1336Q8—28no—
1337Q8—84no—
1338Q8—88no—
1339Q8—82no—
1340Q8—164no—
1341D4—48no—
1342D4—48no—
1343D4—48no—
1344D4—48no—
1345D4—48no—
1346D4—44no—
1347D4—44no—
1348D4—82no—
1349D4—82no—
1350D4—84no—
1351D4—84no—
1352D4—84no—
1353D4—88no—
1354D4—88no—
1355D4—82no—
1356D4—84no—
1357D4—164no—
1358D4—162no—
1359D4—162no—
1360D4—162no—
1361D4—164no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—21no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—48no—
1421C2×C4—48no—
1422C2×C4—44no—
1423C2×C4—48no—
1424C2×C4—44no—
1425C2×C4—84no—
1426C2×C4—88no—
1427C2×C4—162no—
1428C2×C4—164no—
1429C2×C4—164no—
1430C2×C4—164no—
1431C2×C4—162no—
1432C2×C4C2×H(5,𝔽2)14yes—
1433C2×C4C2×H(5,𝔽2)14yes—
1434C2×C4C2×H(5,𝔽2)12yes—
1435C2×C4C2×H(5,𝔽2)12yes—
1436C2×C4#58514yes—
1437C22—42no—
1438C22—41no—
1439C22—41no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—44no—
1448C22—42no—
1449C22—44no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—41no—
1454C22—42no—
1455C22—42no—
1456C22—41no—
1457C22—42no—
1458C22—42no—
1459C22—41no—
1460C22—41no—
1461C22—42no—
1462C22—42no—
1463C22—44no—
1464C22—42no—
1465C22—42no—
1466C22—42no—
1467C22—42no—
1468C22—42no—
1469C22—44no—
1470C22—42no—
1471C22C22×H(5,𝔽2)11yescharacteristic
1472C22C22×H(5,𝔽2)11yescharacteristic
1473C22C2×#58512yes—
1474C22H(7,𝔽2)11yescharacteristic
1475C222−1+612yes—
1476C4—24no—
1477C4—22no—
1478C4—24no—
1479C4—42no—
1480C4—41no—
1481C4—41no—
1482C4—42no—
1483C4—42no—
1484C4—42no—
1485C4—42no—
1486C4—44no—
1487C4—42no—
1488C4—42no—
1489C4—41no—
1490C4—44no—
1491C4—44no—
1492C4—42no—
1493C4—44no—
1494C4—42no—
1495C4—42no—
1496C4—44no—
1497C4—44no—
1498C4#353314yes—
1499C2—81no—
1500C2—82no—
1501C2—81no—
1502C2—82no—
1503C2—82no—
1504C2—82no—
1505C2C2×#353311yescharacteristic
1506C2#6291611yescharacteristic
1507C2#6292512yes—
1508C2#6304312yes—
1509C2#6304811yescharacteristic
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. #59827C2semidirect
2. #59496C2semidirect
3. #56058C2semidirect
4. #55464C2semidirect
5. #54723C2semidirect
6. #53815C2semidirect
7. #53621C2semidirect
8. #53061C2semidirect
9. #52968C2semidirect
10. #52762C2semidirect
11. #52681C2semidirect
12. #47786C2semidirect
13. #45333C2semidirect
14. #45330C2semidirect
15. #45087C2semidirect
16. #44922C2semidirect
17. #44915C2semidirect
18. #42985C2semidirect
19. #42894C2semidirect
20. #42593C2semidirect
21. #42463C2semidirect
22. #42453C2semidirect
23. #42211C2semidirect
24. #41956C2semidirect
25. #39747C2semidirect
26. #39406C2semidirect
27. #36696C2semidirect
28. #36076C2semidirect
29. #35701C2semidirect

Maximal subgroups

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

subgroupindex
#598272
#594962
#560582
#554642
#547232
#538152
#536212
#530612
#529682
#527622
#526812
#477862
#453332
#453302
#450872
#449222
#449152
#429852
#428942
#425932
#424632
#424532
#422112
#419562
#397472
#394062
#366962
#360762
#357012