Finite Group Databasebeta

← #8901617

Subgroups — #8901617

Order 512.

4190 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58821C214yesmaximal, complemented
2#58751C212yesmaximal, complemented
3#58708C214yesmaximal, complemented
4#58589C212yesmaximal, complemented
5#51648C214yesmaximal, complemented
6#51451C214yesmaximal, complemented
7#51369C214yesmaximal, complemented
8#47735C214yesmaximal, complemented
9#47211C212yesmaximal, complemented
10#47151C212yesmaximal
11#47151C212yesmaximal
12#46913C214yesmaximal, complemented
13#46815C212yesmaximal
14#46453C212yesmaximal, complemented
15#40202C214yesmaximal, complemented
16#39706C214yesmaximal, complemented
17#38389C214yesmaximal
18#37011C212yesmaximal, complemented
19#36708C211yesmaximal, characteristic
20#35672C211yesmaximal, characteristic
21#35670C212yesmaximal, complemented
22#35488C212yesmaximal
23#35391C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#543C2211yescharacteristic
26C2×#541C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C2×#519C2211yescharacteristic
29#2864C2214yescomplemented
30#2848C2212yes—
31#2845C2214yescomplemented
32#2843C2212yescomplemented
33#2839C2214yescomplemented
34#2834C2212yes—
35#2834C2212yes—
36#2833C2212yescomplemented
37#2817C2212yes—
38#2809C2212yescomplemented
39#2807C2212yes—
40#2807C2212yes—
41#2802C2214yescomplemented
42#2802C2214yescomplemented
43#2799C2212yescomplemented
44#2794C2212yescomplemented
45#2792C2214yescomplemented
46#2792C2212yescomplemented
47#2791C2214yescomplemented
48#2791C2214yescomplemented
49#2791C2214yescomplemented
50#2789C2214yescomplemented
51#2789C2214yescomplemented
52#2789C2214yescomplemented
53#2787C2214yes—
54#2787C2214yes—
55#2776C2214yescomplemented
56#2774C2214yescomplemented
57#2774C2214yescomplemented
58#2768C2214yes—
59#2768C2214yes—
60#2767C2214yescomplemented
61#2767C2214yescomplemented
62#2766C2214yescomplemented
63#2766C2214yescomplemented
64#2766C2214yescomplemented
65#2765C2214yes—
66#2765C2214yes—
67#2765C2214yes—
68#2765C2214yes—
69#2762C2214yescomplemented
70#2755C2214yescomplemented
71#2747C2214yes—
72#2747C2214yes—
73#2747C2214yes—
74#2744C2214yes—
75#2739C2214yes—
76#2734C2214yescomplemented
77#2729C2214yes—
78#2726C2214yescomplemented
79#2722C2212yes—
80#2722C2214yes—
81#2722C2212yes—
82#2720C2214yes—
83#2719C2214yescomplemented
84#2719C2214yescomplemented
85#2713C2214yescomplemented
86#2713C2214yescomplemented
87#2713C2214yescomplemented
88#2704C2214yes—
89#2698C2214yes—
90#2698C2214yes—
91#2690C2214yes—
92#2690C2214yes—
93#2690C2214yes—
94#2690C2214yes—
95#2690C2214yes—
96#2689C2214yes—
97#2689C2214yes—
98#2677C2214yes—
99#2677C2214yes—
100#2666C2214yescomplemented
101#2666C2214yescomplemented
102#2655C2214yescomplemented
103#2655C2214yescomplemented
104#2655C2214yescomplemented
105#2652C2214yes—
106#2652C2214yes—
107#2627C2212yes—
108#2608C2212yes—
109#2590C2214yescomplemented
110#2589C2214yes—
111#2588C2214yescomplemented
112#2588C2214yescomplemented
113#2586C2212yescomplemented
114#2583C2212yes—
115#2583C2212yes—
116#2583C2214yes—
117#2577C2214yes—
118#2573C2214yes—
119#2571C2212yescomplemented
120#2570C2214yescomplemented
121#2569C2214yes—
122#2569C2214yes—
123#2565C2212yescomplemented
124#2565C2212yescomplemented
125#2561C2212yes—
126#2556C2214yes—
127#2550C2214yescomplemented
128#2550C2214yescomplemented
129#2550C2214yescomplemented
130#2549C2214yes—
131#2549C2214yes—
132#2546C2212yescomplemented
133#2546C2212yescomplemented
134#2530C2214yes—
135#2528C2214yescomplemented
136#2523C2214yes—
137#2522C2214yes—
138#2522C2214yes—
139#2520C2214yescomplemented
140#2520C2214yescomplemented
141#2517C2212yes—
142#2517C2212yes—
143#2517C2214yes—
144#2515C2214yes—
145#2508C2214yescomplemented
146#2507C2214yescomplemented
147#2507C2214yescomplemented
148#2506C2214yescomplemented
149#2505C2214yes—
150#2502C2212yes—
151#2499C2212yes—
152#2499C2212yes—
153#2496C2214yes—
154#2494C2214yes—
155#2494C2214yes—
156#2489C2214yes—
157#2484C2212yes—
158#2484C2211yescharacteristic
159#2484C2211yescharacteristic
160#2484C2212yes—
161#2482C2211yescharacteristic
162#2482C2211yescharacteristic
163#2482C2212yes—
164#2482C2212yes—
165#2480C2214yes—
166#2480C2214yes—
167#2480C2214yes—
168#2480C2214yes—
169#2478C2214yes—
170#2478C2214yes—
171#2478C2214yes—
172#2478C2214yes—
173#2478C2214yes—
174#2478C2214yes—
175#2475C2214yes—
176#2475C2214yes—
177#2473C2214yes—
178#2465C2214yes—
179#2462C2214yescomplemented
180#2462C2214yescomplemented
181#2462C2214yescomplemented
182#2462C2214yescomplemented
183#2462C2214yescomplemented
184#2446C2214yescomplemented
185#2442C2214yes—
186#2440C2214yes—
187#2440C2214yes—
188#2434C2212yes—
189#2434C2212yes—
190#2423C2214yes—
191#2423C2214yes—
192#2421C2214yes—
193#2421C2214yes—
194#2421C2214yes—
195#2382C2214yescomplemented
196#2370C2214yescomplemented
197#2368C2214yes—
198#2345C2214yes—
199#2334C2214yes—
200#2334C2214yes—
201#2334C2214yes—
202#2334C2214yes—
203#2334C2214yes—
204#2332C2212yes—
205#2332C2212yes—
206#2327C2212yescomplemented
207#2327C2212yescomplemented
208#2317C2212yes—
209#2315C2212yes—
210#2313C2211yescharacteristic
211#2310C2211yescharacteristic
212C4×C4⋊Q8C2212yescomplemented
213C4×C4⋊Q8C2212yescomplemented
214C4×#126C2214yes—
215#2298C2212yes—
216C2×#385C2212yes—
217#2280C2212yes—
218#2273C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C24×C4C2311yescharacteristic
221#544—44no—
222#543—44no—
223#541—48no—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2312yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#125C2312yes—
235C2×#125C2314yes—
236C2×#125C2314yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#125C2314yes—
240C2×C22⋊Q8—44no—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250#519—44no—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C22⋊C4C2311yescharacteristic
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2312yes—
271#401C2314yes—
272#401C2314yes—
273#401C2314yes—
274#401C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2312yes—
284#400C2314yes—
285#400C2312yes—
286#400C2314yes—
287#400C2314yes—
288#400C2312yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2312yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#399C2312yes—
304#399C2312yes—
305#399C2314yes—
306#399C2312yes—
307#399C2312yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2312yes—
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#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2312yes—
357#397C2312yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2312yes—
364#397C2314yes—
365#397C2312yes—
366#397C2314yes—
367#397C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2312yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2312yes—
384#395C2314yes—
385#395C2314yes—
386#393C2314yes—
387#391C2312yes—
388#391C2312yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2312yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
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#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2312yes—
532#385C2312yes—
533#385C2314yes—
534#385C2312yes—
535#385C2312yes—
536#385C2314yes—
537#385C2312yes—
538#385C2312yes—
539#385C2312yes—
540#385C2312yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#384C2312yes—
554#384C2312yes—
555#384C2314yes—
556#384C2312yes—
557#384C2312yes—
558#383C2314yes—
559#383C2314yes—
560#382C2312yes—
561#382C2312yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#382C2314yes—
568#382C2314yes—
569#382C2314yes—
570#382C2314yes—
571#381C2314yes—
572#381C2312yes—
573#381C2311yescharacteristic
574#381C2311yescharacteristic
575#381C2312yes—
576#381C2312yes—
577#381C2312yes—
578#380C2312yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#379C2314yes—
589#379C2312yes—
590#379C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616#376C2312yes—
617C2×#95C2314yes—
618C43C2312yes—
619C25C2411yescharacteristic
620C22×Q8—24no—
621C22×Q8—44no—
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C23×C4—44no—
629C23×C4—42no—
630C23×C4C2411yescharacteristic
631C23×C4C2411yescharacteristic
632C23×C4C2411yescharacteristic
633C23×C4C2411yescharacteristic
634C23×C4C2414yes—
635C23×C4C2411yescharacteristic
636C23×C4C2414yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2411yescharacteristic
640C4⋊Q8—44no—
641C4⋊Q8—44no—
642C4⋊Q8—44no—
643C4⋊Q8—44no—
644C4⋊Q8—44no—
645C4⋊Q8—48no—
646#126—216no—
647#126—216no—
648#126—48no—
649#126—48no—
650#125—44no—
651#125—48no—
652#125—48no—
653#125—48no—
654#125—48no—
655#125—48no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—44no—
659C22⋊Q8—44no—
660C22⋊Q8—48no—
661C22⋊Q8—48no—
662C22⋊Q8—48no—
663C22⋊Q8—48no—
664C22⋊Q8—48no—
665C4×Q8—44no—
666C4×Q8—44no—
667C4×Q8—44no—
668C4×Q8—44no—
669C4×Q8—44no—
670C4×Q8—44no—
671#117—28no—
672#117—44no—
673#117—42no—
674#117—42no—
675#117—44no—
676#117—44no—
677C2×C4⋊C4—24no—
678C2×C4⋊C4—48no—
679C2×C4⋊C4—42no—
680C2×C4⋊C4—42no—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C22⋊C4—24no—
746C2×C22⋊C4—28no—
747C2×C22⋊C4—44no—
748C2×C22⋊C4—42no—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2414yes—
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2412yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
845#95C2414yes—
846#95C2412yes—
847#95C2412yes—
848#95C2414yes—
849#95C2412yes—
850#95C2412yes—
851#95C2412yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863C24—22no—
864C24—24no—
865C24—42no—
866C24—42no—
867C24C2511yescharacteristic
868C24C2512yes—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—24no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×Q8—44no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—416no—
887C22×C4—22no—
888C22×C4—24no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—28no—
894C22×C4—28no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—42no—
902C22×C4—44no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—88no—
909C22×C4H(5,𝔽2)14yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2514yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2512yes—
916C22×C4C2512yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2512yes—
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C4⋊C4—28no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—28no—
939C4⋊C4—28no—
940C4⋊C4—28no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C22⋊C4—28no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—28no—
999C22⋊C4—24no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C42−1+418yes—
1017C42—24no—
1018C42—24no—
1019C42—28no—
1020C42—28no—
1021C42—42no—
1022C42—44no—
1023C42—44no—
1024C42—42no—
1025C42—44no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—44no—
1031C42—44no—
1032C42—44no—
1033C42—44no—
1034C42—44no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C23—28no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—24no—
1045C23—22no—
1046C23—24no—
1047C23—82no—
1048C23—82no—
1049C23—88no—
1050C23C2×H(5,𝔽2)12yes—
1051C23C2×2−1+414yes—
1052C23C2611yescharacteristic
1053Q8—48no—
1054Q8—48no—
1055Q8—84no—
1056Q8—84no—
1057Q8—162no—
1058Q8—162no—
1059C2×C4—28no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—88no—
1116C2×C4—88no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—162no—
1120C2×C4—162no—
1121C2×C4C2×H(5,𝔽2)14yes—
1122C2×C4C2×2−1+418yes—
1123C2×C4#58514yes—
1124C22—22no—
1125C22—22no—
1126C22—24no—
1127C22—22no—
1128C22—28no—
1129C22—42no—
1130C22—42no—
1131C22—44no—
1132C22—44no—
1133C22—88no—
1134C22C22×H(5,𝔽2)11yescharacteristic
1135C22C22×2−1+412yes—
1136C22C2×#58512yes—
1137C222−1+612yes—
1138C4—24no—
1139C4—24no—
1140C4—28no—
1141C4—41no—
1142C4—41no—
1143C4—42no—
1144C4—44no—
1145C4—44no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C2—42no—
1160C2—44no—
1161C2#6282011yescharacteristic
1162C2#6283311yescharacteristic
1163C2#6288711yescharacteristic
1164C2#6295014yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58821C2semidirect
2. #58751C2semidirect
3. #58708C2semidirect
4. #58589C2semidirect
5. #51648C2semidirect
6. #51451C2semidirect
7. #51369C2semidirect
8. #47735C2semidirect
9. #47211C2semidirect
12. #46913C2semidirect
14. #46453C2semidirect
15. #40202C2semidirect
16. #39706C2semidirect
18. #37011C2semidirect
21. #35670C2semidirect
29. #2864C22semidirect
31. #2845C22semidirect
32. #2843C22semidirect
33. #2839C22semidirect
36. #2833C22semidirect
38. #2809C22semidirect
41. #2802C22semidirect
42. #2802C22semidirect
43. #2799C22semidirect
44. #2794C22semidirect
45. #2792C22semidirect
46. #2792C22semidirect
47. #2791C22semidirect
48. #2791C22semidirect
49. #2791C22semidirect
50. #2789C22semidirect
51. #2789C22semidirect
52. #2789C22semidirect
55. #2776C22semidirect
56. #2774C22semidirect
57. #2774C22semidirect
60. #2767C22semidirect
61. #2767C22semidirect
62. #2766C22semidirect
63. #2766C22semidirect
64. #2766C22semidirect
69. #2762C22semidirect
70. #2755C22semidirect
76. #2734C22semidirect
78. #2726C22semidirect
83. #2719C22semidirect
84. #2719C22semidirect
85. #2713C22semidirect
86. #2713C22semidirect
87. #2713C22semidirect
100. #2666C22semidirect
101. #2666C22semidirect
102. #2655C22semidirect
103. #2655C22semidirect
104. #2655C22semidirect
109. #2590C22semidirect
111. #2588C22semidirect
112. #2588C22semidirect
113. #2586C22semidirect
119. #2571C22semidirect
120. #2570C22semidirect
123. #2565C22semidirect
124. #2565C22semidirect
127. #2550C22semidirect
128. #2550C22semidirect
129. #2550C22semidirect
132. #2546C22semidirect
133. #2546C22semidirect
135. #2528C22semidirect
139. #2520C22semidirect
140. #2520C22semidirect
145. #2508C22semidirect
146. #2507C22semidirect
147. #2507C22semidirect
148. #2506C22semidirect
179. #2462C22semidirect
180. #2462C22semidirect
181. #2462C22semidirect
182. #2462C22semidirect
183. #2462C22semidirect
184. #2446C22semidirect
195. #2382C22semidirect
196. #2370C22semidirect
206. #2327C22semidirect
207. #2327C22semidirect
212. C4×C4⋊Q8C22semidirect
213. C4×C4⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#588212
#587512
#587082
#585892
#516482
#514512
#513692
#477352
#472112
#471512
#469132
#468152
#464532
#402022
#397062
#383892
#370112
#367082
#356722
#356702
#354882
#353912