Finite Group Databasebeta

← #8756211

Subgroups — #8756211

Order 512.

4412 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58863C214yesmaximal, complemented
2#57976C214yesmaximal, complemented
3#57672C214yesmaximal, complemented
4#56799C214yesmaximal, complemented
5#54084C214yesmaximal, complemented
6#53985C214yesmaximal, complemented
7#51993C212yesmaximal, complemented
8#51840C212yesmaximal, complemented
9#50559C214yesmaximal, complemented
10#48768C214yesmaximal, complemented
11#46879C214yesmaximal, complemented
12#46609C214yesmaximal, complemented
13#46455C212yesmaximal, complemented
14#46389C212yesmaximal, complemented
15#46239C212yesmaximal, complemented
16#46237C212yesmaximal, complemented
17#46227C212yesmaximal, complemented
18#46136C211yesmaximal, characteristic, complemented
19#46025C212yesmaximal, complemented
20#46024C212yesmaximal, complemented
21#45977C211yesmaximal, characteristic
22#35338C211yesmaximal, characteristic, complemented
23#35135C212yesmaximal, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×#563C2212yescomplemented
26C2×H(3,𝔽4)C2211yescharacteristic
27C2×#533C2211yescharacteristic, complemented
28C22×#124C2211yescharacteristic
29#2861C2212yes—
30#2861C2212yescomplemented
31#2861C2212yescomplemented
32#2859C2212yescomplemented
33#2851C2212yescomplemented
34#2850C2212yes—
35#2842C2212yescomplemented
36#2832C2214yescomplemented
37#2831C2214yescomplemented
38#2830C2214yescomplemented
39#2830C2214yescomplemented
40#2827C2214yescomplemented
41#2824C2214yescomplemented
42#2822C2212yescomplemented
43#2820C2212yes—
44#2820C2212yescomplemented
45#2819C2212yes—
46#2816C2212yes—
47#2809C2212yescomplemented
48#2808C2214yescomplemented
49#2807C2214yescomplemented
50#2804C2212yescomplemented
51#2804C2214yescomplemented
52#2803C2214yescomplemented
53#2799C2214yescomplemented
54#2798C2214yescomplemented
55#2797C2214yescomplemented
56#2796C2214yes—
57#2795C2214yescomplemented
58#2793C2214yescomplemented
59#2790C2214yescomplemented
60#2788C2214yescomplemented
61#2788C2214yescomplemented
62#2786C2214yescomplemented
63#2783C2214yescomplemented
64#2781C2214yescomplemented
65#2761C2214yescomplemented
66#2755C2214yescomplemented
67#2754C2214yescomplemented
68#2751C2214yescomplemented
69#2747C2214yescomplemented
70#2743C2214yescomplemented
71#2736C2214yescomplemented
72#2736C2214yescomplemented
73#2736C2214yescomplemented
74#2733C2212yes—
75#2731C2212yes—
76#2731C2214yescomplemented
77#2731C2214yescomplemented
78#2731C2212yescomplemented
79#2718C2214yescomplemented
80#2717C2212yescomplemented
81#2716C2214yescomplemented
82#2716C2214yescomplemented
83#2716C2214yescomplemented
84#2716C2214yescomplemented
85#2716C2214yescomplemented
86#2716C2214yescomplemented
87#2715C2214yescomplemented
88#2712C2214yes—
89#2710C2214yes—
90#2705C2214yes—
91#2705C2214yescomplemented
92#2702C2214yescomplemented
93#2702C2214yescomplemented
94#2702C2214yescomplemented
95#2701C2214yes—
96#2700C2214yescomplemented
97#2700C2214yescomplemented
98#2697C2214yescomplemented
99#2697C2212yescomplemented
100#2696C2214yescomplemented
101#2696C2214yescomplemented
102#2696C2214yescomplemented
103#2695C2214yescomplemented
104#2692C2214yescomplemented
105#2687C2214yescomplemented
106#2687C2214yescomplemented
107#2685C2214yes—
108#2685C2214yes—
109#2685C2214yes—
110#2685C2214yescomplemented
111#2685C2214yescomplemented
112#2684C2214yes—
113#2684C2212yes—
114#2681C2214yes—
115#2677C2214yescomplemented
116#2677C2214yescomplemented
117#2674C2214yescomplemented
118#2670C2214yes—
119#2654C2214yescomplemented
120#2650C2214yescomplemented
121#2650C2214yescomplemented
122#2650C2214yescomplemented
123#2649C2214yescomplemented
124#2648C2214yes—
125#2640C2212yes—
126#2640C2212yescomplemented
127#2630C2214yescomplemented
128#2626C2214yescomplemented
129#2607C2214yescomplemented
130#2607C2212yescomplemented
131#2602C2214yescomplemented
132#2601C2214yes—
133#2601C2214yescomplemented
134#2596C2214yescomplemented
135#2595C2214yescomplemented
136#2592C2214yescomplemented
137#2592C2214yescomplemented
138#2589C2214yescomplemented
139#2588C2214yescomplemented
140#2575C2214yescomplemented
141#2574C2214yescomplemented
142#2563C2214yescomplemented
143#2561C2214yescomplemented
144#2561C2214yescomplemented
145#2560C2214yescomplemented
146#2560C2214yescomplemented
147#2558C2214yescomplemented
148#2554C2214yes—
149#2554C2214yescomplemented
150#2554C2214yescomplemented
151#2545C2214yescomplemented
152#2534C2214yescomplemented
153#2530C2214yescomplemented
154#2529C2214yescomplemented
155#2521C2214yescomplemented
156#2521C2214yescomplemented
157#2521C2214yescomplemented
158#2519C2214yescomplemented
159#2516C2214yescomplemented
160#2512C2212yescomplemented
161#2511C2212yescomplemented
162#2492C2214yescomplemented
163#2492C2214yescomplemented
164#2490C2212yes—
165#2489C2212yescomplemented
166#2480C2214yescomplemented
167#2480C2214yescomplemented
168#2479C2214yescomplemented
169#2479C2214yescomplemented
170#2478C2214yescomplemented
171#2477C2214yescomplemented
172#2477C2214yescomplemented
173#2475C2214yescomplemented
174#2474C2214yescomplemented
175#2472C2214yes—
176#2472C2214yes—
177#2472C2214yescomplemented
178#2470C2214yescomplemented
179#2469C2214yescomplemented
180#2469C2214yescomplemented
181#2460C2214yescomplemented
182#2458C2214yescomplemented
183#2455C2214yescomplemented
184#2454C2212yescomplemented
185#2453C2212yescomplemented
186#2451C2214yescomplemented
187#2437C2214yescomplemented
188#2436C2212yes—
189#2434C2212yescomplemented
190#2429C2214yescomplemented
191#2423C2212yescomplemented
192#2422C2212yes—
193#2418C2214yes—
194#2410C2214yes—
195#2405C2212yes—
196#2405C2214yescomplemented
197#2405C2212yescomplemented
198#2403C2212yes—
199#2382C2212yescomplemented
200#2379C2211yescharacteristic
201#2379C2211yescharacteristic, complemented
202#2379C2212yescomplemented
203#2376C2212yescomplemented
204#2369C2212yescomplemented
205#2358C2212yescomplemented
206#2335C2214yescomplemented
207#2334C2214yescomplemented
208#2333C2212yes—
209#2332C2212yescomplemented
210#2312C2212yescomplemented
211#2310C2211yescharacteristic, complemented
212#2310C2211yescharacteristic, complemented
213#2309C2211yescharacteristic
214#2309C2211yescharacteristic
215#2309C2212yescomplemented
216C4×#125C2212yescomplemented
217C4×#124C2212yescomplemented
218C4×#117C2211yescharacteristic, complemented
219C23×Q8C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C23×D4C2312yes—
222#563—44no—
223#563—48no—
224H(3,𝔽4)—44no—
225#533—44no—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#125C2312yes—
238C2×#125C2312yes—
239C2×#125C2312yes—
240C2×#125C2312yes—
241C2×#124—44no—
242C2×#124C2311yescharacteristic
243C2×#124C2312yes—
244C2×#124C2311yescharacteristic
245C2×#124C2314yes—
246C2×#124C2312yes—
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2312yes—
250C2×#124C2314yes—
251C2×#124C2314yes—
252C2×#123C2314yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×#121C2312yes—
266C2×#121C2312yes—
267C2×#120C2312yes—
268C2×#120C2312yes—
269C2×#120C2314yes—
270C2×#120C2314yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2312yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2312yes—
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2314yes—
280C22×C22⋊C4C2314yes—
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2314yes—
283C22×C42C2311yescharacteristic
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#392C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2314yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2314yes—
444#390C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
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#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
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#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2312yes—
547#386C2312yes—
548#386C2312yes—
549#386C2312yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
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#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#384C2312yes—
571#384C2312yes—
572#382C2312yes—
573#382C2314yes—
574#382C2314yes—
575#382C2312yes—
576#381C2312yes—
577#381C2314yes—
578#381C2312yes—
579#381C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2312yes—
586#380C2312yes—
587#380C2314yes—
588#379C2312yes—
589#379C2312yes—
590#379C2314yes—
591#379C2312yes—
592#379C2314yes—
593#379C2312yes—
594#379C2314yes—
595#379C2314yes—
596#379C2314yes—
597#379C2314yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617#376C2312yes—
618C43C2312yes—
619C25C2412yes—
620C25C2412yes—
621C22×Q8—42no—
622C22×Q8—42no—
623C22×Q8—42no—
624C22×Q8C2412yes—
625C22×Q8C2411yescharacteristic
626C22×Q8C2412yes—
627C22×Q8C2411yescharacteristic
628C22×Q8C2414yes—
629C22×Q8C2412yes—
630C22×Q8C2414yes—
631C22×D4—42no—
632C22×D4—42no—
633C22×D4—42no—
634C22×D4—44no—
635C22×D4—84no—
636C22×D4C2412yes—
637C22×D4C2411yescharacteristic
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2411yescharacteristic
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2414yes—
649C23×C4C2412yes—
650C23×C4C2414yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C4⋊Q8—44no—
654C4⋊Q8—44no—
655C4⋊Q8—48no—
656C4⋊Q8—44no—
657C4⋊Q8—84no—
658#126—48no—
659#126—48no—
660#126—48no—
661#126—48no—
662#126—84no—
663#126—84no—
664#125—28no—
665#125—28no—
666#125—82no—
667#125—82no—
668#124—24no—
669#124—24no—
670#124—28no—
671#124—48no—
672#124—42no—
673#124—42no—
674#124—44no—
675#124—48no—
676#124—44no—
677#124—84no—
678#123—48no—
679#123—44no—
680#123—48no—
681#123—44no—
682#123—84no—
683#123—84no—
684C22⋊Q8—44no—
685C22⋊Q8—48no—
686C22⋊Q8—48no—
687C22⋊Q8—48no—
688C22⋊Q8—48no—
689C22⋊Q8—82no—
690C22⋊Q8—84no—
691#121—44no—
692#121—82no—
693#120—44no—
694#120—48no—
695#120—44no—
696#120—84no—
697C4×Q8—48no—
698C4×Q8—82no—
699C4×D4—82no—
700C4×D4—84no—
701#117—42no—
702#117—42no—
703#117—42no—
704#117—42no—
705#117—84no—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C22⋊C4—48no—
750C2×C22⋊C4—44no—
751C2×C22⋊C4—84no—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
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×C42—24no—
808C2×C42C2412yes—
809C2×C42C2411yescharacteristic
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829#95C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2412yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
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#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879C24—24no—
880C24—42no—
881C24—44no—
882C24—42no—
883C24—44no—
884C24—44no—
885C24—42no—
886C24—42no—
887C24—44no—
888C24—42no—
889C24C2512yes—
890C24C2512yes—
891C24C2514yes—
892C24C2511yescharacteristic
893C2×Q8—22no—
894C2×Q8—24no—
895C2×Q8—22no—
896C2×Q8—24no—
897C2×Q8—44no—
898C2×Q8—42no—
899C2×Q8—44no—
900C2×Q8—42no—
901C2×Q8—41no—
902C2×Q8—41no—
903C2×Q8—41no—
904C2×Q8—41no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—44no—
912C2×Q8—42no—
913C2×Q8—44no—
914C2×Q8—88no—
915C2×D4—28no—
916C2×D4—24no—
917C2×D4—22no—
918C2×D4—22no—
919C2×D4—24no—
920C2×D4—44no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—41no—
929C2×D4—41no—
930C2×D4—41no—
931C2×D4—41no—
932C2×D4—42no—
933C2×D4—44no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—42no—
938C2×D4—44no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4—88no—
943C2×D4—816no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—44no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—42no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2512yes—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2511yescharacteristic
983C22×C4C2512yes—
984C22×C4C2511yescharacteristic
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—42no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—42no—
1006C4⋊C4—44no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—42no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C22⋊C4—28no—
1029C22⋊C4—24no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—42no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—42no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C42—24no—
1084C42—22no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—42no—
1094C42—44no—
1095C42—44no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—44no—
1100C42—44no—
1101C42—42no—
1102C42—42no—
1103C42H(5,𝔽2)14yes—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—24no—
1110C23—22no—
1111C23—24no—
1112C23—22no—
1113C23—24no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23—24no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—84no—
1126C23—84no—
1127C23—84no—
1128C23—84no—
1129C23—88no—
1130C23—88no—
1131C23—164no—
1132C23—162no—
1133C23—162no—
1134C23—164no—
1135C23#58512yes—
1136C23C2611yescharacteristic
1137Q8—84no—
1138Q8—82no—
1139Q8—82no—
1140Q8—84no—
1141Q8—88no—
1142Q8—162no—
1143Q8—164no—
1144D4—84no—
1145D4—82no—
1146D4—82no—
1147D4—84no—
1148D4—88no—
1149D4—88no—
1150D4—88no—
1151D4—162no—
1152D4—164no—
1153C2×C4—28no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—48no—
1209C2×C4—84no—
1210C2×C4—84no—
1211C2×C4—162no—
1212C2×C4—164no—
1213C2×C4—162no—
1214C2×C4—164no—
1215C2×C4C2×H(5,𝔽2)14yes—
1216C2×C4C2×H(5,𝔽2)12yes—
1217C2×C4#58512yes—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—44no—
1225C22—42no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—44no—
1233C22—42no—
1234C22—42no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—168no—
1241C22—168no—
1242C22C22×H(5,𝔽2)11yescharacteristic
1243C22C2×#58511yescharacteristic
1244C22C2×#58511yescharacteristic
1245C22H(7,𝔽2)12yes—
1246C222−1+612yes—
1247C4—22no—
1248C4—22no—
1249C4—24no—
1250C4—44no—
1251C4—42no—
1252C4—44no—
1253C4—42no—
1254C4—44no—
1255C4—42no—
1256C4—44no—
1257C4—42no—
1258C4—42no—
1259C4—42no—
1260C4—44no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—44no—
1265C4—44no—
1266C2—42no—
1267C2—84no—
1268C2—82no—
1269C2—82no—
1270C2#6282411yescharacteristic
1271C2#6287812yes—
1272C2#6304611yescharacteristic
1273C2#6305612yes—
1274C2#6306411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#45977C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58863C2semidirect
2. #57976C2semidirect
3. #57672C2semidirect
4. #56799C2semidirect
5. #54084C2semidirect
6. #53985C2semidirect
7. #51993C2semidirect
8. #51840C2semidirect
9. #50559C2semidirect
10. #48768C2semidirect
11. #46879C2semidirect
12. #46609C2semidirect
13. #46455C2semidirect
14. #46389C2semidirect
15. #46239C2semidirect
16. #46237C2semidirect
17. #46227C2semidirect
18. #46136C2semidirect
19. #46025C2semidirect
20. #46024C2semidirect
22. #35338C2semidirect
23. #35135C2semidirect
24. C2×#563C22semidirect
25. C2×#563C22semidirect
27. C2×#533C22semidirect
30. #2861C22semidirect
31. #2861C22semidirect
32. #2859C22semidirect
33. #2851C22semidirect
35. #2842C22semidirect
36. #2832C22semidirect
37. #2831C22semidirect
38. #2830C22semidirect
39. #2830C22semidirect
40. #2827C22semidirect
41. #2824C22semidirect
42. #2822C22semidirect
44. #2820C22semidirect
47. #2809C22semidirect
48. #2808C22semidirect
49. #2807C22semidirect
50. #2804C22semidirect
51. #2804C22semidirect
52. #2803C22semidirect
53. #2799C22semidirect
54. #2798C22semidirect
55. #2797C22semidirect
57. #2795C22semidirect
58. #2793C22semidirect
59. #2790C22semidirect
60. #2788C22semidirect
61. #2788C22semidirect
62. #2786C22semidirect
63. #2783C22semidirect
64. #2781C22semidirect
65. #2761C22semidirect
66. #2755C22semidirect
67. #2754C22semidirect
68. #2751C22semidirect
69. #2747C22semidirect
70. #2743C22semidirect
71. #2736C22semidirect
72. #2736C22semidirect
73. #2736C22semidirect
76. #2731C22semidirect
77. #2731C22semidirect
78. #2731C22semidirect
79. #2718C22semidirect
80. #2717C22semidirect
81. #2716C22semidirect
82. #2716C22semidirect
83. #2716C22semidirect
84. #2716C22semidirect
85. #2716C22semidirect
86. #2716C22semidirect
87. #2715C22semidirect
91. #2705C22semidirect
92. #2702C22semidirect
93. #2702C22semidirect
94. #2702C22semidirect
96. #2700C22semidirect
97. #2700C22semidirect
98. #2697C22semidirect
99. #2697C22semidirect
100. #2696C22semidirect
101. #2696C22semidirect
102. #2696C22semidirect
103. #2695C22semidirect
104. #2692C22semidirect
105. #2687C22semidirect
106. #2687C22semidirect
110. #2685C22semidirect
111. #2685C22semidirect
115. #2677C22semidirect
116. #2677C22semidirect
117. #2674C22semidirect
119. #2654C22semidirect
120. #2650C22semidirect
121. #2650C22semidirect
122. #2650C22semidirect
123. #2649C22semidirect
126. #2640C22semidirect
127. #2630C22semidirect
128. #2626C22semidirect
129. #2607C22semidirect
130. #2607C22semidirect
131. #2602C22semidirect
133. #2601C22semidirect
134. #2596C22semidirect
135. #2595C22semidirect
136. #2592C22semidirect
137. #2592C22semidirect
138. #2589C22semidirect
139. #2588C22semidirect
140. #2575C22semidirect
141. #2574C22semidirect
142. #2563C22semidirect
143. #2561C22semidirect
144. #2561C22semidirect
145. #2560C22semidirect
146. #2560C22semidirect
147. #2558C22semidirect
149. #2554C22semidirect
150. #2554C22semidirect
151. #2545C22semidirect
152. #2534C22semidirect
153. #2530C22semidirect
154. #2529C22semidirect
155. #2521C22semidirect
156. #2521C22semidirect
157. #2521C22semidirect
158. #2519C22semidirect
159. #2516C22semidirect
160. #2512C22semidirect
161. #2511C22semidirect
162. #2492C22semidirect
163. #2492C22semidirect
165. #2489C22semidirect
166. #2480C22semidirect
167. #2480C22semidirect
168. #2479C22semidirect
169. #2479C22semidirect
170. #2478C22semidirect
171. #2477C22semidirect
172. #2477C22semidirect
173. #2475C22semidirect
174. #2474C22semidirect
177. #2472C22semidirect
178. #2470C22semidirect
179. #2469C22semidirect
180. #2469C22semidirect
181. #2460C22semidirect
182. #2458C22semidirect
183. #2455C22semidirect
184. #2454C22semidirect
185. #2453C22semidirect
186. #2451C22semidirect
187. #2437C22semidirect
189. #2434C22semidirect
190. #2429C22semidirect
191. #2423C22semidirect
196. #2405C22semidirect
197. #2405C22semidirect
199. #2382C22semidirect
201. #2379C22semidirect
202. #2379C22semidirect
203. #2376C22semidirect
204. #2369C22semidirect
205. #2358C22semidirect
206. #2335C22semidirect
207. #2334C22semidirect
209. #2332C22semidirect
210. #2312C22semidirect
211. #2310C22semidirect
212. #2310C22semidirect
215. #2309C22semidirect
216. C4×#125C22semidirect
217. C4×#124C22semidirect
218. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#588632
#579762
#576722
#567992
#540842
#539852
#519932
#518402
#505592
#487682
#468792
#466092
#464552
#463892
#462392
#462372
#462272
#461362
#460252
#460242
#459772
#353382
#351352