Finite Group Databasebeta

← #8757272

Subgroups — #8757272

Order 512.

4146 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58980C212yesmaximal, complemented
2#58962C212yesmaximal, complemented
3#58797C212yesmaximal, complemented
4#58458C214yesmaximal, complemented
5#58385C214yesmaximal, complemented
6#56568C212yesmaximal, complemented
7#55674C214yesmaximal, complemented
8#54228C214yesmaximal, complemented
9#50409C214yesmaximal, complemented
10#50389C214yesmaximal, complemented
11#48997C212yesmaximal
12#48797C212yesmaximal, complemented
13#47151C212yesmaximal, complemented
14#47101C214yesmaximal, complemented
15#47054C214yesmaximal, complemented
16#47035C211yesmaximal, characteristic
17#46999C211yesmaximal, characteristic
18#45778C214yesmaximal, complemented
19#45763C214yesmaximal, complemented
20#45474C212yesmaximal, complemented
21#45456C212yesmaximal
22#35325C212yesmaximal, complemented
23#35097C211yesmaximal, characteristic
24C2×#563C2212yes—
25C2×#533C2212yescomplemented
26C22×#123C2211yescharacteristic
27C22×#117C2211yescharacteristic
28#2855C2214yescomplemented
29#2853C2214yes—
30#2848C2214yes—
31#2842C2211yescharacteristic
32#2841C2212yescomplemented
33#2839C2214yescomplemented
34#2838C2214yescomplemented
35#2834C2212yes—
36#2834C2214yescomplemented
37#2833C2214yescomplemented
38#2833C2214yescomplemented
39#2831C2214yescomplemented
40#2817C2211yescharacteristic
41#2817C2212yescomplemented
42#2814C2214yes—
43#2807C2212yes—
44#2806C2214yescomplemented
45#2804C2212yes—
46#2802C2214yescomplemented
47#2798C2214yescomplemented
48#2792C2214yescomplemented
49#2791C2214yescomplemented
50#2789C2214yescomplemented
51#2787C2214yes—
52#2787C2214yes—
53#2783C2214yescomplemented
54#2781C2214yes—
55#2777C2214yescomplemented
56#2776C2214yescomplemented
57#2775C2214yescomplemented
58#2774C2214yescomplemented
59#2773C2214yescomplemented
60#2772C2214yescomplemented
61#2771C2212yes—
62#2771C2212yes—
63#2771C2212yescomplemented
64#2770C2214yescomplemented
65#2768C2214yescomplemented
66#2768C2214yescomplemented
67#2767C2214yescomplemented
68#2767C2214yescomplemented
69#2765C2214yescomplemented
70#2765C2214yescomplemented
71#2765C2214yescomplemented
72#2765C2214yescomplemented
73#2764C2212yescomplemented
74#2763C2214yes—
75#2762C2214yescomplemented
76#2762C2214yescomplemented
77#2759C2214yescomplemented
78#2755C2214yescomplemented
79#2751C2214yes—
80#2747C2214yescomplemented
81#2745C2214yes—
82#2745C2214yescomplemented
83#2744C2214yescomplemented
84#2744C2214yescomplemented
85#2743C2214yes—
86#2743C2214yes—
87#2742C2214yescomplemented
88#2738C2214yes—
89#2736C2214yes—
90#2736C2212yes—
91#2735C2212yes—
92#2734C2214yescomplemented
93#2729C2214yescomplemented
94#2725C2214yescomplemented
95#2724C2212yes—
96#2722C2212yes—
97#2719C2214yescomplemented
98#2718C2214yes—
99#2717C2212yes—
100#2717C2212yes—
101#2716C2214yescomplemented
102#2713C2214yescomplemented
103#2713C2214yescomplemented
104#2707C2214yes—
105#2704C2214yescomplemented
106#2700C2214yes—
107#2700C2214yes—
108#2698C2214yes—
109#2698C2214yes—
110#2698C2214yescomplemented
111#2695C2214yes—
112#2689C2214yes—
113#2689C2214yescomplemented
114#2687C2214yes—
115#2680C2214yes—
116#2674C2214yes—
117#2667C2214yescomplemented
118#2665C2212yescomplemented
119#2654C2214yescomplemented
120#2653C2214yes—
121#2647C2214yescomplemented
122#2645C2214yescomplemented
123#2628C2212yes—
124#2628C2212yescomplemented
125#2625C2212yescomplemented
126#2623C2214yes—
127#2621C2212yes—
128#2621C2212yescomplemented
129#2612C2214yescomplemented
130#2612C2214yescomplemented
131#2611C2212yes—
132#2611C2212yes—
133#2611C2212yescomplemented
134#2611C2212yescomplemented
135#2607C2211yescharacteristic
136#2606C2214yescomplemented
137#2599C2214yes—
138#2599C2214yescomplemented
139#2589C2214yes—
140#2589C2214yescomplemented
141#2588C2214yescomplemented
142#2585C2214yescomplemented
143#2583C2214yescomplemented
144#2576C2214yes—
145#2575C2214yescomplemented
146#2574C2214yescomplemented
147#2570C2214yescomplemented
148#2561C2214yes—
149#2561C2212yes—
150#2549C2214yescomplemented
151#2530C2214yes—
152#2530C2214yescomplemented
153#2529C2214yescomplemented
154#2529C2214yescomplemented
155#2528C2214yescomplemented
156#2527C2214yes—
157#2527C2214yescomplemented
158#2527C2214yescomplemented
159#2526C2214yes—
160#2522C2214yescomplemented
161#2517C2212yes—
162#2516C2214yes—
163#2505C2214yescomplemented
164#2498C2214yes—
165#2498C2214yes—
166#2494C2214yescomplemented
167#2494C2214yescomplemented
168#2493C2214yescomplemented
169#2484C2212yes—
170#2484C2212yes—
171#2484C2212yescomplemented
172#2484C2212yescomplemented
173#2483C2211yescharacteristic
174#2482C2212yes—
175#2482C2212yes—
176#2482C2212yes—
177#2482C2212yes—
178#2482C2212yes—
179#2480C2214yes—
180#2480C2214yes—
181#2480C2214yes—
182#2480C2214yes—
183#2478C2214yescomplemented
184#2478C2214yescomplemented
185#2474C2214yes—
186#2473C2214yes—
187#2470C2214yes—
188#2470C2214yes—
189#2469C2214yescomplemented
190#2469C2214yescomplemented
191#2465C2214yescomplemented
192#2462C2214yescomplemented
193#2453C2214yescomplemented
194#2451C2214yescomplemented
195#2446C2214yescomplemented
196#2440C2214yes—
197#2438C2214yescomplemented
198#2437C2214yes—
199#2435C2212yes—
200#2421C2214yescomplemented
201#2405C2212yes—
202#2378C2212yescomplemented
203#2378C2214yescomplemented
204#2376C2212yes—
205#2376C2212yes—
206#2372C2212yes—
207#2346C2212yescomplemented
208#2334C2214yes—
209#2332C2212yes—
210#2323C2214yes—
211#2323C2214yescomplemented
212#2315C2211yescharacteristic
213#2315C2211yescharacteristic
214#2312C2212yes—
215#2308C2211yescharacteristic
216#2308C2211yescharacteristic
217#2283C2212yescomplemented
218C2×#381C2211yescharacteristic
219C23×D4C2311yescharacteristic
220C24×C4C2311yescharacteristic
221#563—48no—
222#533—48no—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#125C2312yes—
230C2×#125C2312yes—
231C2×#125C2314yes—
232C2×#124C2312yes—
233C2×#124C2312yes—
234C2×#123—44no—
235C2×#123C2312yes—
236C2×#123C2312yes—
237C2×#123C2312yes—
238C2×#123C2312yes—
239C2×#123C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×#117—44no—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C22⋊C4C2311yescharacteristic
260C22×C22⋊C4C2311yescharacteristic
261C22×C22⋊C4C2311yescharacteristic
262C22×C22⋊C4C2311yescharacteristic
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2311yescharacteristic
265C22×C22⋊C4C2312yes—
266C22×C42C2312yes—
267#401C2314yes—
268#401C2314yes—
269#401C2314yes—
270#401C2314yes—
271#401C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2312yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2312yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2312yes—
296#400C2312yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#399C2312yes—
302#399C2312yes—
303#399C2314yes—
304#399C2314yes—
305#399C2312yes—
306#399C2312yes—
307#399C2312yes—
308#399C2312yes—
309#399C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2312yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2312yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2312yes—
339#398C2314yes—
340#398C2314yes—
341#397C2312yes—
342#397C2312yes—
343#397C2314yes—
344#397C2314yes—
345#397C2312yes—
346#397C2314yes—
347#397C2312yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2312yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2312yes—
359#397C2312yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2312yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#393C2312yes—
392#393C2314yes—
393#393C2314yes—
394#393C2312yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#390C2312yes—
414#390C2312yes—
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#389C2314yes—
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#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#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#386C2314yes—
527#386C2314yes—
528#386C2312yes—
529#386C2312yes—
530#386C2314yes—
531#386C2312yes—
532#386C2312yes—
533#385C2314yes—
534#385C2312yes—
535#385C2312yes—
536#385C2312yes—
537#385C2314yes—
538#385C2312yes—
539#385C2314yes—
540#385C2314yes—
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#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#384C2314yes—
559#383C2314yes—
560#383C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2312yes—
567#382C2312yes—
568#382C2314yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#381C2311yescharacteristic
573#381C2312yes—
574#381C2311yescharacteristic
575#381C2312yes—
576#381C2312yes—
577#381C2312yes—
578#381C2314yes—
579#381C2312yes—
580#381C2312yes—
581#381C2312yes—
582#381C2312yes—
583#380C2314yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#379C2314yes—
595#379C2314yes—
596#379C2311yescharacteristic
597#379C2311yescharacteristic
598#379C2312yes—
599#379C2312yes—
600#379C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613#376C2314yes—
614#376C2314yes—
615#376C2312yes—
616#376C2312yes—
617C2×#95C2314yes—
618C25C2411yescharacteristic
619C25C2411yescharacteristic
620C22×Q8C2414yes—
621C22×Q8C2414yes—
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×D4—42no—
625C22×D4—42no—
626C22×D4—42no—
627C22×D4C2412yes—
628C22×D4C2412yes—
629C23×C4—24no—
630C23×C4—42no—
631C23×C4—42no—
632C23×C4C2412yes—
633C23×C4C2412yes—
634C23×C4C2412yes—
635C23×C4C2412yes—
636C23×C4C2412yes—
637C23×C4C2411yescharacteristic
638C23×C4C2411yescharacteristic
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2411yescharacteristic
644C4⋊Q8—44no—
645C4⋊Q8—44no—
646C4⋊Q8—48no—
647#126—48no—
648#126—48no—
649#126—48no—
650#125—44no—
651#125—44no—
652#125—48no—
653#124—44no—
654#124—44no—
655#123—28no—
656#123—44no—
657#123—44no—
658#123—48no—
659#123—44no—
660C22⋊Q8—216no—
661C22⋊Q8—48no—
662C22⋊Q8—48no—
663C22⋊Q8—44no—
664C22⋊Q8—44no—
665C22⋊Q8—48no—
666C22⋊Q8—48no—
667C4×Q8—48no—
668C4×Q8—48no—
669#117—44no—
670#117—44no—
671#117—44no—
672#117—44no—
673#117—44no—
674#117—44no—
675#117—44no—
676C2×C4⋊C4—44no—
677C2×C4⋊C4—44no—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
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×C22⋊C4—44no—
731C2×C22⋊C4—44no—
732C2×C22⋊C4—42no—
733C2×C22⋊C4—42no—
734C2×C22⋊C4—42no—
735C2×C22⋊C4—42no—
736C2×C22⋊C4—42no—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2411yescharacteristic
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2411yescharacteristic
749C2×C22⋊C4C2411yescharacteristic
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2411yescharacteristic
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2411yescharacteristic
755C2×C22⋊C4C2411yescharacteristic
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C42—28no—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2412yes—
785C2×C42C2412yes—
786C2×C42C2414yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2412yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2412yes—
806#95C2414yes—
807#95C2412yes—
808#95C2412yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2412yes—
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#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2412yes—
843#95C2414yes—
844#95C2414yes—
845#95C2412yes—
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—
861C24—22no—
862C24—22no—
863C24—22no—
864C24—22no—
865C24—41no—
866C24—44no—
867C24—44no—
868C24—41no—
869C24C2512yes—
870C24C2511yescharacteristic
871C24C2511yescharacteristic
872C24C2511yescharacteristic
873C2×Q8—28no—
874C2×Q8—44no—
875C2×Q8—44no—
876C2×Q8—44no—
877C2×Q8—44no—
878C2×Q8—44no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×Q8—44no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—88no—
891C22×C4—24no—
892C22×C4—22no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—44no—
907C22×C4—42no—
908C22×C4—41no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—41no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—416no—
921C22×C4H(5,𝔽2)14yes—
922C22×C4C2512yes—
923C22×C4C2514yes—
924C22×C4C2514yes—
925C22×C4C2514yes—
926C22×C4C2512yes—
927C22×C4C2512yes—
928C22×C4C2514yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2512yes—
936C22×C4C2514yes—
937C22×C4C2512yes—
938C22×C4C2514yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
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—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—42no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—42no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C22⋊C4—24no—
994C22⋊C4—28no—
995C22⋊C4—28no—
996C22⋊C4—28no—
997C22⋊C4—24no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—41no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—44no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—42no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—42no—
1012C22⋊C4—41no—
1013C22⋊C4—42no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—44no—
1032C42—24no—
1033C42—24no—
1034C42—24no—
1035C42—24no—
1036C42—44no—
1037C42—44no—
1038C42—44no—
1039C42—44no—
1040C42—44no—
1041C42—44no—
1042C42—44no—
1043C42—44no—
1044C42—42no—
1045C42—42no—
1046C42—44no—
1047C42—44no—
1048C23—28no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—24no—
1062C23—24no—
1063C23—84no—
1064C23—84no—
1065C23—84no—
1066C23—82no—
1067C23—84no—
1068C23—84no—
1069C23—162no—
1070C23C2×H(5,𝔽2)12yes—
1071C23#58512yes—
1072C23#58512yes—
1073C23C2611yescharacteristic
1074Q8—88no—
1075Q8—88no—
1076Q8—162no—
1077Q8—162no—
1078D4—84no—
1079D4—84no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—44no—
1131C2×C4—48no—
1132C2×C4—48no—
1133C2×C4—48no—
1134C2×C4—44no—
1135C2×C4—84no—
1136C2×C4—84no—
1137C2×C4—82no—
1138C2×C4—84no—
1139C2×C4—162no—
1140C2×C4—162no—
1141C2×C4—162no—
1142C2×C4C2×H(5,𝔽2)14yes—
1143C22—24no—
1144C22—24no—
1145C22—22no—
1146C22—22no—
1147C22—22no—
1148C22—24no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—44no—
1158C22—42no—
1159C22—44no—
1160C22—88no—
1161C22—164no—
1162C22C22×H(5,𝔽2)11yescharacteristic
1163C22C2×#58511yescharacteristic
1164C22C2×#58511yescharacteristic
1165C222−1+614yes—
1166C4—24no—
1167C4—44no—
1168C4—44no—
1169C4—42no—
1170C4—42no—
1171C4—44no—
1172C4—44no—
1173C4—44no—
1174C4—42no—
1175C4—42no—
1176C4—44no—
1177C4—44no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—44no—
1182C4—42no—
1183C4—44no—
1184C4—44no—
1185C2—42no—
1186C2—42no—
1187C2—42no—
1188C2—82no—
1189C2#6282011yescharacteristic
1190C2#6288612yes—
1191C2#6306412yes—
1192C2#6306412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58980C2semidirect
2. #58962C2semidirect
3. #58797C2semidirect
4. #58458C2semidirect
5. #58385C2semidirect
6. #56568C2semidirect
7. #55674C2semidirect
8. #54228C2semidirect
9. #50409C2semidirect
10. #50389C2semidirect
12. #48797C2semidirect
13. #47151C2semidirect
14. #47101C2semidirect
15. #47054C2semidirect
18. #45778C2semidirect
19. #45763C2semidirect
20. #45474C2semidirect
22. #35325C2semidirect
25. C2×#533C22semidirect
28. #2855C22semidirect
32. #2841C22semidirect
33. #2839C22semidirect
34. #2838C22semidirect
36. #2834C22semidirect
37. #2833C22semidirect
38. #2833C22semidirect
39. #2831C22semidirect
41. #2817C22semidirect
44. #2806C22semidirect
46. #2802C22semidirect
47. #2798C22semidirect
48. #2792C22semidirect
49. #2791C22semidirect
50. #2789C22semidirect
53. #2783C22semidirect
55. #2777C22semidirect
56. #2776C22semidirect
57. #2775C22semidirect
58. #2774C22semidirect
59. #2773C22semidirect
60. #2772C22semidirect
63. #2771C22semidirect
64. #2770C22semidirect
65. #2768C22semidirect
66. #2768C22semidirect
67. #2767C22semidirect
68. #2767C22semidirect
69. #2765C22semidirect
70. #2765C22semidirect
71. #2765C22semidirect
72. #2765C22semidirect
73. #2764C22semidirect
75. #2762C22semidirect
76. #2762C22semidirect
77. #2759C22semidirect
78. #2755C22semidirect
80. #2747C22semidirect
82. #2745C22semidirect
83. #2744C22semidirect
84. #2744C22semidirect
87. #2742C22semidirect
92. #2734C22semidirect
93. #2729C22semidirect
94. #2725C22semidirect
97. #2719C22semidirect
101. #2716C22semidirect
102. #2713C22semidirect
103. #2713C22semidirect
105. #2704C22semidirect
110. #2698C22semidirect
113. #2689C22semidirect
117. #2667C22semidirect
118. #2665C22semidirect
119. #2654C22semidirect
121. #2647C22semidirect
122. #2645C22semidirect
124. #2628C22semidirect
125. #2625C22semidirect
128. #2621C22semidirect
129. #2612C22semidirect
130. #2612C22semidirect
133. #2611C22semidirect
134. #2611C22semidirect
136. #2606C22semidirect
138. #2599C22semidirect
140. #2589C22semidirect
141. #2588C22semidirect
142. #2585C22semidirect
143. #2583C22semidirect
145. #2575C22semidirect
146. #2574C22semidirect
147. #2570C22semidirect
150. #2549C22semidirect
152. #2530C22semidirect
153. #2529C22semidirect
154. #2529C22semidirect
155. #2528C22semidirect
157. #2527C22semidirect
158. #2527C22semidirect
160. #2522C22semidirect
163. #2505C22semidirect
166. #2494C22semidirect
167. #2494C22semidirect
168. #2493C22semidirect
171. #2484C22semidirect
172. #2484C22semidirect
183. #2478C22semidirect
184. #2478C22semidirect
189. #2469C22semidirect
190. #2469C22semidirect
191. #2465C22semidirect
192. #2462C22semidirect
193. #2453C22semidirect
194. #2451C22semidirect
195. #2446C22semidirect
197. #2438C22semidirect
200. #2421C22semidirect
202. #2378C22semidirect
203. #2378C22semidirect
207. #2346C22semidirect
211. #2323C22semidirect
217. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#589802
#589622
#587972
#584582
#583852
#565682
#556742
#542282
#504092
#503892
#489972
#487972
#471512
#471012
#470542
#470352
#469992
#457782
#457632
#454742
#454562
#353252
#350972