Finite Group Databasebeta

← #9912965

Subgroups — #9912965

Order 512.

4437 conjugacy classes of subgroups.

The subgroup lattice has 1255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58933C214yesmaximal, complemented
2#58355C212yesmaximal, complemented
3#57684C214yesmaximal, complemented
4#57615C214yesmaximal, complemented
5#57446C214yesmaximal, complemented
6#57048C214yesmaximal, complemented
7#55273C214yesmaximal, complemented
8#55260C214yesmaximal, complemented
9#53376C212yesmaximal, complemented
10#53175C214yesmaximal, complemented
11#51992C212yesmaximal, complemented
12#50892C212yesmaximal, complemented
13#50700C212yesmaximal, complemented
14#48949C212yesmaximal, complemented
15#48345C214yesmaximal, complemented
16#46240C211yesmaximal, characteristic, complemented
17#45946C212yesmaximal, complemented
18#45728C212yesmaximal, complemented
19#45456C214yesmaximal, complemented
20#38957C211yesmaximal, characteristic
21#38022C212yesmaximal
22#37162C211yesmaximal, characteristic, complemented
23#36747C212yesmaximal, complemented
24C2×#563C2212yes—
25C2×#556C2211yescharacteristic
26C2×D42C2211yescharacteristic
27C22×#123C2212yes—
28#2864C2212yescomplemented
29#2863C2212yescomplemented
30#2858C2211yescharacteristic
31#2849C2212yes—
32#2848C2214yescomplemented
33#2848C2214yescomplemented
34#2845C2212yescomplemented
35#2839C2214yescomplemented
36#2836C2214yescomplemented
37#2836C2214yescomplemented
38#2831C2214yescomplemented
39#2827C2214yescomplemented
40#2827C2214yescomplemented
41#2823C2212yescomplemented
42#2814C2214yescomplemented
43#2814C2214yescomplemented
44#2809C2212yescomplemented
45#2808C2212yescomplemented
46#2806C2212yescomplemented
47#2805C2212yescomplemented
48#2804C2211yescharacteristic
49#2800C2214yescomplemented
50#2795C2212yescomplemented
51#2793C2214yescomplemented
52#2792C2214yescomplemented
53#2790C2214yescomplemented
54#2790C2214yescomplemented
55#2790C2214yescomplemented
56#2788C2214yescomplemented
57#2786C2214yescomplemented
58#2784C2214yescomplemented
59#2782C2212yescomplemented
60#2780C2214yescomplemented
61#2780C2214yescomplemented
62#2779C2214yescomplemented
63#2770C2214yescomplemented
64#2770C2214yescomplemented
65#2769C2212yescomplemented
66#2768C2214yescomplemented
67#2764C2214yescomplemented
68#2761C2214yescomplemented
69#2757C2214yescomplemented
70#2757C2214yescomplemented
71#2757C2214yescomplemented
72#2750C2214yescomplemented
73#2748C2212yes—
74#2748C2212yes—
75#2741C2214yescomplemented
76#2739C2214yescomplemented
77#2738C2214yescomplemented
78#2738C2214yescomplemented
79#2737C2214yescomplemented
80#2735C2214yescomplemented
81#2735C2214yescomplemented
82#2735C2214yescomplemented
83#2734C2214yescomplemented
84#2732C2212yes—
85#2732C2214yescomplemented
86#2732C2212yescomplemented
87#2728C2214yescomplemented
88#2727C2212yescomplemented
89#2726C2212yescomplemented
90#2725C2214yescomplemented
91#2724C2211yescharacteristic
92#2724C2212yes—
93#2723C2214yescomplemented
94#2722C2214yescomplemented
95#2720C2214yescomplemented
96#2720C2214yescomplemented
97#2718C2214yescomplemented
98#2718C2214yescomplemented
99#2717C2212yes—
100#2717C2214yes—
101#2715C2214yescomplemented
102#2715C2214yescomplemented
103#2709C2214yes—
104#2708C2214yes—
105#2707C2214yescomplemented
106#2707C2214yescomplemented
107#2707C2214yescomplemented
108#2704C2214yescomplemented
109#2704C2214yescomplemented
110#2704C2214yescomplemented
111#2702C2214yescomplemented
112#2701C2214yes—
113#2700C2214yescomplemented
114#2698C2214yescomplemented
115#2697C2214yes—
116#2695C2214yescomplemented
117#2695C2214yescomplemented
118#2695C2214yescomplemented
119#2694C2214yescomplemented
120#2694C2214yescomplemented
121#2692C2214yescomplemented
122#2692C2214yescomplemented
123#2690C2214yescomplemented
124#2690C2214yescomplemented
125#2689C2214yescomplemented
126#2689C2214yescomplemented
127#2685C2214yes—
128#2685C2214yes—
129#2683C2212yes—
130#2683C2212yescomplemented
131#2680C2214yescomplemented
132#2680C2214yescomplemented
133#2674C2214yescomplemented
134#2674C2214yescomplemented
135#2667C2214yescomplemented
136#2664C2214yescomplemented
137#2651C2214yescomplemented
138#2650C2214yescomplemented
139#2649C2214yescomplemented
140#2634C2212yescomplemented
141#2634C2212yescomplemented
142#2633C2214yescomplemented
143#2629C2214yescomplemented
144#2626C2214yescomplemented
145#2622C2212yes—
146#2620C2212yes—
147#2618C2212yes—
148#2609C2212yescomplemented
149#2595C2214yescomplemented
150#2591C2212yes—
151#2585C2214yescomplemented
152#2584C2212yescomplemented
153#2579C2212yes—
154#2575C2214yescomplemented
155#2565C2212yescomplemented
156#2560C2214yescomplemented
157#2558C2214yescomplemented
158#2556C2214yescomplemented
159#2552C2214yescomplemented
160#2549C2214yescomplemented
161#2548C2211yescharacteristic
162#2542C2211yescharacteristic
163#2534C2214yes—
164#2525C2214yescomplemented
165#2523C2214yescomplemented
166#2522C2214yescomplemented
167#2522C2214yescomplemented
168#2505C2214yescomplemented
169#2500C2212yes—
170#2496C2214yescomplemented
171#2482C2214yescomplemented
172#2480C2214yescomplemented
173#2480C2214yescomplemented
174#2480C2214yescomplemented
175#2480C2214yescomplemented
176#2480C2214yescomplemented
177#2480C2214yescomplemented
178#2479C2214yescomplemented
179#2478C2214yescomplemented
180#2475C2214yescomplemented
181#2474C2214yescomplemented
182#2473C2214yescomplemented
183#2473C2214yescomplemented
184#2470C2214yescomplemented
185#2468C2214yescomplemented
186#2460C2214yescomplemented
187#2446C2214yescomplemented
188#2440C2214yescomplemented
189#2440C2214yescomplemented
190#2438C2214yescomplemented
191#2438C2214yescomplemented
192#2437C2214yescomplemented
193#2437C2214yescomplemented
194#2437C2214yescomplemented
195#2435C2212yes—
196#2435C2214yes—
197#2426C2214yes—
198#2425C2214yes—
199#2419C2214yes—
200#2415C2214yescomplemented
201#2412C2212yes—
202#2412C2212yes—
203#2405C2212yes—
204#2405C2212yes—
205#2405C2214yes—
206#2379C2211yescharacteristic
207#2379C2211yescharacteristic
208#2376C2212yes—
209#2376C2214yes—
210#2374C2212yes—
211D4×C22⋊C4C2212yes—
212#2337C2212yes—
213#2322C2212yes—
214#2309C2212yes—
215#2308C2212yes—
216C4×#124C2211yescharacteristic
217#2293C2211yescharacteristic
218C2×#386C2212yes—
219C23×D4C2312yes—
220C23×D4C2312yes—
221C24×C4C2312yes—
222#563—48no—
223#556—44no—
224D42—44no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2314yes—
227C2×#127C2311yescharacteristic
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#125C2312yes—
234C2×#125C2312yes—
235C2×#125C2314yes—
236C2×#125C2314yes—
237C2×#125C2314yes—
238C2×#124C2312yes—
239C2×#124C2311yescharacteristic
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#123—48no—
243C2×#123C2312yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#120C2312yes—
264C2×#120C2312yes—
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2312yes—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2314yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2312yes—
296#400C2312yes—
297#399C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2312yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2312yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2312yes—
391#394C2312yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2311yescharacteristic
418#391C2314yes—
419#391C2314yes—
420#390C2314yes—
421#390C2311yescharacteristic
422#390C2314yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2314yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#386C2314yes—
518#386C2312yes—
519#386C2312yes—
520#386C2312yes—
521#386C2312yes—
522#386C2314yes—
523#386C2314yes—
524#386C2312yes—
525#386C2314yes—
526#386C2312yes—
527#386C2312yes—
528#386C2312yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2312yes—
533#386C2314yes—
534#386C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2312yes—
541#385C2314yes—
542#385C2312yes—
543#385C2312yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#384C2312yes—
568#384C2312yes—
569#384C2314yes—
570#384C2314yes—
571#383C2312yes—
572#383C2314yes—
573#383C2314yes—
574#382C2312yes—
575#382C2312yes—
576#382C2311yescharacteristic
577#382C2312yes—
578#381C2314yes—
579#381C2312yes—
580#381C2314yes—
581#381C2314yes—
582#380C2312yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#379C2314yes—
597#379C2314yes—
598#379C2314yes—
599#379C2314yes—
600#379C2314yes—
601#379C2312yes—
602#379C2312yes—
603#379C2314yes—
604#379C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2311yescharacteristic
609C4×C4⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C2×#95C2314yes—
617C43C2311yescharacteristic
618C25C2412yes—
619C25C2412yes—
620C22×Q8C2412yes—
621C22×Q8C2411yescharacteristic
622C22×Q8C2414yes—
623C22×Q8C2412yes—
624C22×D4—28no—
625C22×D4—28no—
626C22×D4—44no—
627C22×D4—82no—
628C22×D4—84no—
629C22×D4C2412yes—
630C22×D4C2412yes—
631C22×D4C2412yes—
632C22×D4C2412yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2411yescharacteristic
636C22×D4C2411yescharacteristic
637C22×D4C2411yescharacteristic
638C22×D4C2411yescharacteristic
639C23×C4—44no—
640C23×C4—84no—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2414yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2414yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2414yes—
651C4⋊Q8—42no—
652C4⋊Q8—48no—
653#127—42no—
654#126—48no—
655#126—48no—
656#126—48no—
657#126—84no—
658#126—84no—
659#125—44no—
660#125—44no—
661#125—84no—
662#125—84no—
663#125—84no—
664#124—28no—
665#124—24no—
666#124—82no—
667#124—84no—
668#123—216no—
669#123—28no—
670#123—48no—
671#123—48no—
672#123—48no—
673#123—82no—
674#123—82no—
675#123—84no—
676C22⋊Q8—44no—
677C22⋊Q8—48no—
678C22⋊Q8—48no—
679C22⋊Q8—84no—
680C22⋊Q8—84no—
681C22⋊Q8—84no—
682C22⋊Q8—84no—
683C22⋊Q8—84no—
684C22⋊Q8—84no—
685C22⋊Q8—84no—
686#121—44no—
687#121—44no—
688#120—44no—
689#120—44no—
690C4×Q8—42no—
691C4×Q8—44no—
692C4×D4—24no—
693C4×D4—42no—
694C4×D4—84no—
695#117—44no—
696#117—82no—
697#117—84no—
698C2×C4⋊C4—44no—
699C2×C4⋊C4—44no—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C22⋊C4—44no—
757C2×C22⋊C4—44no—
758C2×C22⋊C4—44no—
759C2×C22⋊C4—82no—
760C2×C22⋊C4—82no—
761C2×C22⋊C4—84no—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C42C2411yescharacteristic
811C2×C42C2412yes—
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875C24—24no—
876C24—24no—
877C24—24no—
878C24—24no—
879C24—42no—
880C24—44no—
881C24—42no—
882C24—44no—
883C24—44no—
884C24—44no—
885C24C2512yes—
886C24C2512yes—
887C24C2512yes—
888C24C2512yes—
889C2×Q8—24no—
890C2×Q8—22no—
891C2×Q8—41no—
892C2×Q8—44no—
893C2×Q8—41no—
894C2×Q8—44no—
895C2×Q8—42no—
896C2×Q8—44no—
897C2×Q8—42no—
898C2×Q8—44no—
899C2×Q8—42no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—41no—
907C2×D4—44no—
908C2×D4—41no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—44no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—44no—
918C2×D4—41no—
919C2×D4—41no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—816no—
923C2×D4—816no—
924C2×D4H(5,𝔽2)14yes—
925C2×D42−1+414yes—
926C22×C4—24no—
927C22×C4—28no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—42no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—816no—
953C22×C4C2512yes—
954C22×C4C2514yes—
955C22×C4C2511yescharacteristic
956C22×C4C2512yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2514yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—22no—
975C4⋊C4—28no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—42no—
979C4⋊C4—44no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—41no—
986C4⋊C4—42no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—41no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—44no—
1003C4⋊C4—42no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—44no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—24no—
1033C22⋊C4—28no—
1034C22⋊C4—24no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—42no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—42no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C42—22no—
1077C42—24no—
1078C42—22no—
1079C42—44no—
1080C42—42no—
1081C42—44no—
1082C42—41no—
1083C42—42no—
1084C42—42no—
1085C42—44no—
1086C42—44no—
1087C42—42no—
1088C42—44no—
1089C42—44no—
1090C42—42no—
1091C23—22no—
1092C23—22no—
1093C23—24no—
1094C23—22no—
1095C23—22no—
1096C23—24no—
1097C23—24no—
1098C23—24no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—24no—
1105C23—24no—
1106C23—22no—
1107C23—24no—
1108C23—24no—
1109C23—48no—
1110C23—48no—
1111C23—48no—
1112C23—88no—
1113C23—84no—
1114C23—84no—
1115C23—88no—
1116C23—84no—
1117C23—88no—
1118C23—164no—
1119C23C2×H(5,𝔽2)14yes—
1120C23C2×2−1+414yes—
1121C23C2611yescharacteristic
1122Q8—84no—
1123Q8—82no—
1124Q8—164no—
1125Q8—162no—
1126D4—44no—
1127D4—44no—
1128D4—48no—
1129D4—84no—
1130D4—84no—
1131D4—84no—
1132D4—84no—
1133D4—84no—
1134D4—161no—
1135D4—161no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—48no—
1188C2×C4—84no—
1189C2×C4—84no—
1190C2×C4—88no—
1191C2×C4—84no—
1192C2×C4—88no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4—88no—
1196C2×C4—164no—
1197C2×C4C2×H(5,𝔽2)12yes—
1198C2×C4C2×2−1+412yes—
1199C22—28no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—44no—
1205C22—42no—
1206C22—42no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—44no—
1218C22—44no—
1219C22—816no—
1220C22—168no—
1221C22C22×H(5,𝔽2)11yescharacteristic
1222C22C22×2−1+411yescharacteristic
1223C22H(7,𝔽2)12yes—
1224C22H(7,𝔽2)11yescharacteristic
1225C222−1+612yes—
1226C4—22no—
1227C4—22no—
1228C4—42no—
1229C4—44no—
1230C4—42no—
1231C4—44no—
1232C4—41no—
1233C4—44no—
1234C4—44no—
1235C4—42no—
1236C4—44no—
1237C4—42no—
1238C4—44no—
1239C4—42no—
1240C4—44no—
1241C4—44no—
1242C4—44no—
1243C4—44no—
1244C4—42no—
1245C2—44no—
1246C2—44no—
1247C2—82no—
1248C2—82no—
1249C2#6286211yescharacteristic
1250C2#6289411yescharacteristic
1251C2#6297512yes—
1252C2#6305812yes—
1253C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×D42C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58933C2semidirect
2. #58355C2semidirect
3. #57684C2semidirect
4. #57615C2semidirect
5. #57446C2semidirect
6. #57048C2semidirect
7. #55273C2semidirect
8. #55260C2semidirect
9. #53376C2semidirect
10. #53175C2semidirect
11. #51992C2semidirect
12. #50892C2semidirect
13. #50700C2semidirect
14. #48949C2semidirect
15. #48345C2semidirect
16. #46240C2semidirect
17. #45946C2semidirect
18. #45728C2semidirect
19. #45456C2semidirect
22. #37162C2semidirect
23. #36747C2semidirect
28. #2864C22semidirect
29. #2863C22semidirect
32. #2848C22semidirect
33. #2848C22semidirect
34. #2845C22semidirect
35. #2839C22semidirect
36. #2836C22semidirect
37. #2836C22semidirect
38. #2831C22semidirect
39. #2827C22semidirect
40. #2827C22semidirect
41. #2823C22semidirect
42. #2814C22semidirect
43. #2814C22semidirect
44. #2809C22semidirect
45. #2808C22semidirect
46. #2806C22semidirect
47. #2805C22semidirect
49. #2800C22semidirect
50. #2795C22semidirect
51. #2793C22semidirect
52. #2792C22semidirect
53. #2790C22semidirect
54. #2790C22semidirect
55. #2790C22semidirect
56. #2788C22semidirect
57. #2786C22semidirect
58. #2784C22semidirect
59. #2782C22semidirect
60. #2780C22semidirect
61. #2780C22semidirect
62. #2779C22semidirect
63. #2770C22semidirect
64. #2770C22semidirect
65. #2769C22semidirect
66. #2768C22semidirect
67. #2764C22semidirect
68. #2761C22semidirect
69. #2757C22semidirect
70. #2757C22semidirect
71. #2757C22semidirect
72. #2750C22semidirect
75. #2741C22semidirect
76. #2739C22semidirect
77. #2738C22semidirect
78. #2738C22semidirect
79. #2737C22semidirect
80. #2735C22semidirect
81. #2735C22semidirect
82. #2735C22semidirect
83. #2734C22semidirect
85. #2732C22semidirect
86. #2732C22semidirect
87. #2728C22semidirect
88. #2727C22semidirect
89. #2726C22semidirect
90. #2725C22semidirect
93. #2723C22semidirect
94. #2722C22semidirect
95. #2720C22semidirect
96. #2720C22semidirect
97. #2718C22semidirect
98. #2718C22semidirect
101. #2715C22semidirect
102. #2715C22semidirect
105. #2707C22semidirect
106. #2707C22semidirect
107. #2707C22semidirect
108. #2704C22semidirect
109. #2704C22semidirect
110. #2704C22semidirect
111. #2702C22semidirect
113. #2700C22semidirect
114. #2698C22semidirect
116. #2695C22semidirect
117. #2695C22semidirect
118. #2695C22semidirect
119. #2694C22semidirect
120. #2694C22semidirect
121. #2692C22semidirect
122. #2692C22semidirect
123. #2690C22semidirect
124. #2690C22semidirect
125. #2689C22semidirect
126. #2689C22semidirect
130. #2683C22semidirect
131. #2680C22semidirect
132. #2680C22semidirect
133. #2674C22semidirect
134. #2674C22semidirect
135. #2667C22semidirect
136. #2664C22semidirect
137. #2651C22semidirect
138. #2650C22semidirect
139. #2649C22semidirect
140. #2634C22semidirect
141. #2634C22semidirect
142. #2633C22semidirect
143. #2629C22semidirect
144. #2626C22semidirect
148. #2609C22semidirect
149. #2595C22semidirect
151. #2585C22semidirect
152. #2584C22semidirect
154. #2575C22semidirect
155. #2565C22semidirect
156. #2560C22semidirect
157. #2558C22semidirect
158. #2556C22semidirect
159. #2552C22semidirect
160. #2549C22semidirect
164. #2525C22semidirect
165. #2523C22semidirect
166. #2522C22semidirect
167. #2522C22semidirect
168. #2505C22semidirect
170. #2496C22semidirect
171. #2482C22semidirect
172. #2480C22semidirect
173. #2480C22semidirect
174. #2480C22semidirect
175. #2480C22semidirect
176. #2480C22semidirect
177. #2480C22semidirect
178. #2479C22semidirect
179. #2478C22semidirect
180. #2475C22semidirect
181. #2474C22semidirect
182. #2473C22semidirect
183. #2473C22semidirect
184. #2470C22semidirect
185. #2468C22semidirect
186. #2460C22semidirect
187. #2446C22semidirect
188. #2440C22semidirect
189. #2440C22semidirect
190. #2438C22semidirect
191. #2438C22semidirect
192. #2437C22semidirect
193. #2437C22semidirect
194. #2437C22semidirect
200. #2415C22semidirect

Maximal subgroups

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

subgroupindex
#589332
#583552
#576842
#576152
#574462
#570482
#552732
#552602
#533762
#531752
#519922
#508922
#507002
#489492
#483452
#462402
#459462
#457282
#454562
#389572
#380222
#371622
#367472