Finite Group Databasebeta

← #8990781

Subgroups — #8990781

Order 512.

5160 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59248C211yesmaximal, characteristic, complemented
2#58801C212yesmaximal, complemented
3#57488C214yesmaximal, complemented
4#53534C214yesmaximal, complemented
5#53490C212yesmaximal, complemented
6#52414C212yesmaximal, complemented
7#52005C212yesmaximal, complemented
8#50446C214yesmaximal, complemented
9#50285C214yesmaximal, complemented
10#47658C212yesmaximal, complemented
11#46758C212yesmaximal, complemented
12#46357C214yesmaximal, complemented
13#46232C211yesmaximal, characteristic, complemented
14#45241C214yesmaximal, complemented
15#44758C212yesmaximal, complemented
16#44079C214yesmaximal, complemented
17#43011C214yesmaximal, complemented
18#41305C214yesmaximal, complemented
19#41168C214yesmaximal, complemented
20#39420C212yesmaximal, complemented
21#38762C212yesmaximal, complemented
22#35740C212yesmaximal, complemented
23#35531C211yesmaximal, characteristic, complemented
24C2×#550C2212yes—
25C2×#548C2212yescomplemented
26C2×#547C2214yescomplemented
27C2×#543C2212yes—
28C2×#538C2212yes—
29C2×#536C2214yescomplemented
30C2×#535C2211yescharacteristic
31C2×#520C2211yescharacteristic
32#2850C2212yes—
33#2844C2211yescharacteristic, complemented
34#2838C2214yescomplemented
35#2837C2214yescomplemented
36#2834C2212yes—
37#2831C2214yescomplemented
38#2830C2212yes—
39#2825C2214yescomplemented
40#2819C2211yescharacteristic, complemented
41#2817C2214yescomplemented
42#2806C2212yescomplemented
43#2804C2212yescomplemented
44#2804C2212yescomplemented
45#2803C2214yes—
46#2795C2212yescomplemented
47#2790C2214yescomplemented
48#2789C2212yescomplemented
49#2789C2212yescomplemented
50#2778C2214yescomplemented
51#2778C2214yescomplemented
52#2776C2214yescomplemented
53#2774C2214yescomplemented
54#2761C2214yescomplemented
55#2760C2214yescomplemented
56#2753C2214yescomplemented
57#2753C2214yescomplemented
58#2749C2214yes—
59#2746C2214yescomplemented
60#2738C2214yescomplemented
61#2730C2214yes—
62#2728C2214yes—
63#2728C2214yescomplemented
64#2723C2214yes—
65#2710C2214yescomplemented
66#2708C2214yes—
67#2703C2214yes—
68#2700C2214yescomplemented
69#2700C2214yescomplemented
70#2699C2212yes—
71#2697C2214yes—
72#2696C2214yes—
73#2696C2214yescomplemented
74#2693C2212yes—
75#2692C2214yes—
76#2692C2214yescomplemented
77#2689C2214yescomplemented
78#2688C2214yescomplemented
79#2687C2214yescomplemented
80#2687C2214yescomplemented
81#2686C2214yes—
82#2683C2212yes—
83#2682C2214yescomplemented
84#2682C2212yescomplemented
85#2681C2214yes—
86#2681C2214yescomplemented
87#2680C2212yescomplemented
88#2678C2214yes—
89#2677C2212yes—
90#2677C2214yescomplemented
91#2676C2214yes—
92#2676C2214yes—
93#2676C2214yescomplemented
94#2674C2214yescomplemented
95#2673C2214yes—
96#2673C2214yes—
97#2673C2214yescomplemented
98#2672C2214yescomplemented
99#2671C2214yes—
100#2669C2214yes—
101#2668C2214yes—
102#2667C2214yescomplemented
103#2653C2214yescomplemented
104#2653C2214yescomplemented
105#2651C2214yescomplemented
106#2650C2214yescomplemented
107#2643C2214yescomplemented
108#2638C2212yes—
109#2632C2212yes—
110#2632C2212yescomplemented
111#2631C2212yes—
112#2626C2212yes—
113#2618C2212yescomplemented
114#2617C2212yes—
115#2610C2212yes—
116#2599C2212yes—
117#2599C2212yes—
118#2598C2212yes—
119#2594C2214yescomplemented
120#2593C2214yescomplemented
121#2591C2214yescomplemented
122#2589C2214yescomplemented
123#2583C2212yescomplemented
124#2582C2211yescharacteristic, complemented
125#2576C2214yescomplemented
126#2576C2214yescomplemented
127#2561C2214yes—
128#2560C2214yes—
129#2560C2214yescomplemented
130#2559C2214yescomplemented
131#2557C2214yescomplemented
132#2557C2214yescomplemented
133#2555C2212yes—
134#2551C2211yescharacteristic, complemented
135#2544C2214yescomplemented
136#2543C2212yes—
137#2540C2214yes—
138#2532C2214yescomplemented
139#2526C2214yes—
140#2514C2214yescomplemented
141#2505C2214yescomplemented
142#2504C2212yes—
143#2501C2212yes—
144#2500C2212yes—
145#2500C2212yes—
146#2494C2214yes—
147#2492C2214yes—
148#2492C2214yescomplemented
149#2481C2214yescomplemented
150#2477C2214yes—
151#2477C2214yescomplemented
152#2474C2214yescomplemented
153#2472C2214yes—
154#2472C2214yes—
155#2470C2214yes—
156#2465C2214yescomplemented
157#2464C2214yes—
158#2463C2212yes—
159#2461C2214yes—
160#2461C2214yes—
161#2461C2214yescomplemented
162#2461C2214yescomplemented
163#2459C2214yescomplemented
164#2459C2214yescomplemented
165#2458C2214yescomplemented
166#2449C2214yes—
167#2449C2214yescomplemented
168#2449C2214yescomplemented
169#2449C2214yescomplemented
170#2448C2214yes—
171#2445C2214yes—
172#2445C2214yescomplemented
173#2444C2214yes—
174#2443C2214yescomplemented
175#2443C2214yescomplemented
176#2440C2214yescomplemented
177#2432C2214yescomplemented
178#2431C2214yescomplemented
179#2430C2214yes—
180#2430C2214yes—
181#2429C2214yescomplemented
182#2426C2214yes—
183#2426C2214yes—
184#2425C2214yescomplemented
185#2418C2214yes—
186#2418C2214yes—
187#2418C2214yes—
188#2413C2214yescomplemented
189#2410C2214yes—
190#2409C2212yes—
191#2409C2214yescomplemented
192#2407C2214yescomplemented
193#2406C2212yescomplemented
194#2404C2214yes—
195#2399C2212yescomplemented
196#2392C2214yescomplemented
197#2388C2212yes—
198C2×#395C2212yescomplemented
199#2380C2212yes—
200#2379C2212yescomplemented
201#2374C2214yescomplemented
202#2365C2214yescomplemented
203#2361C2214yes—
204#2359C2214yescomplemented
205#2359C2214yescomplemented
206#2358C2214yes—
207#2355C2212yescomplemented
208#2353C2212yescomplemented
209#2333C2214yes—
210#2332C2214yescomplemented
211#2324C2214yescomplemented
212#2322C2214yes—
213#2317C2211yescharacteristic
214#2309C2211yescharacteristic
215C4×C22⋊Q8C2212yes—
216#2297C2211yescharacteristic
217C2×#390C2211yescharacteristic
218#2285C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C22×#41C2312yes—
221C22×#41C2314yes—
222C23×Q8C2312yes—
223C23×D4C2311yescharacteristic
224#550—48no—
225#548—48no—
226#547—416no—
227#543—48no—
228#538—48no—
229#536—416no—
230#535—44no—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2314yes—
233C2×#127C2312yes—
234C2×#127C2314yes—
235C2×#126C2314yes—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2314yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242C2×#124C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2312yes—
270C2×#121C2314yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2312yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281#520—44no—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2312yes—
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C2×#117C2314yes—
299C2×#117C2312yes—
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2314yes—
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2312yes—
307C22×C42C2311yescharacteristic
308#401C2314yes—
309#401C2314yes—
310#401C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#399C2312yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2312yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
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#397C2312yes—
355#397C2314yes—
356#397C2314yes—
357#397C2312yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#395C2312yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2312yes—
373#395C2312yes—
374#395C2312yes—
375#395C2312yes—
376#395C2314yes—
377#395C2312yes—
378#395C2314yes—
379#395C2312yes—
380#394C2314yes—
381#394C2314yes—
382#394C2312yes—
383#394C2312yes—
384#394C2312yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2312yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2312yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2312yes—
414#393C2312yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2312yes—
424#392C2312yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#390C2314yes—
444#390C2314yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2312yes—
457#390C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
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#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#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#385C2312yes—
557#385C2312yes—
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#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#384C2312yes—
578#384C2311yescharacteristic
579#384C2311yescharacteristic
580#383C2312yes—
581#383C2312yes—
582#383C2312yes—
583#382C2311yescharacteristic
584#382C2312yes—
585#382C2314yes—
586#382C2312yes—
587#382C2311yescharacteristic
588#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2314yes—
592#381C2312yes—
593#380C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#379C2314yes—
600#379C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619#376C2312yes—
620C2×#95C2312yes—
621C2×#95C2314yes—
622C25C2412yes—
623C2×#41—24no—
624C2×#41—42no—
625C2×#41—42no—
626C2×#41—44no—
627C2×#41—48no—
628C2×#41—48no—
629C2×#41—48no—
630C2×#41—48no—
631C22×Q8—44no—
632C22×Q8—48no—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2411yescharacteristic
636C22×Q8C2412yes—
637C22×Q8C2414yes—
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×D4—42no—
641C22×D4—42no—
642C22×D4—42no—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2412yes—
651C22×D4C2412yes—
652C22×D4C2414yes—
653C22×D4C2412yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2412yes—
657C22×D4C2412yes—
658C22×D4C2411yescharacteristic
659C23×C4C2411yescharacteristic
660C23×C4C2414yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2414yes—
664C23×C4C2412yes—
665C23×C4C2414yes—
666C23×C4C2412yes—
667C23×C4C2411yescharacteristic
668C23×C4C2411yescharacteristic
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2414yes—
672C23×C4C2414yes—
673C4⋊Q8—216no—
674C4⋊Q8—48no—
675#127—28no—
676#127—48no—
677#126—48no—
678#124—44no—
679#124—48no—
680#124—44no—
681#124—44no—
682#124—48no—
683#124—48no—
684#124—48no—
685#123—216no—
686#123—216no—
687#123—48no—
688#123—48no—
689#123—48no—
690#123—48no—
691#123—48no—
692#123—48no—
693#123—48no—
694C22⋊Q8—216no—
695C22⋊Q8—28no—
696C22⋊Q8—44no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—48no—
702C22⋊Q8—48no—
703C22⋊Q8—48no—
704C22⋊Q8—48no—
705C22⋊Q8—48no—
706C22⋊Q8—44no—
707C22⋊Q8—48no—
708#121—216no—
709#121—44no—
710#121—48no—
711#121—48no—
712#121—48no—
713#121—48no—
714#121—48no—
715#121—48no—
716#121—48no—
717#121—44no—
718#121—44no—
719#121—44no—
720#120—48no—
721#120—48no—
722#120—48no—
723C4×Q8—44no—
724C4×Q8—44no—
725C4×Q8—44no—
726C4×Q8—44no—
727C4×D4—28no—
728C4×D4—48no—
729C4×D4—48no—
730C4×D4—44no—
731C4×D4—48no—
732C4×D4—44no—
733C4×D4—44no—
734C4×D4—48no—
735C4×D4—48no—
736#117—42no—
737#117—42no—
738#117—48no—
739#117—42no—
740#117—44no—
741C2×C4⋊C4—42no—
742C2×C4⋊C4—48no—
743C2×C4⋊C4—48no—
744C2×C4⋊C4—44no—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C22⋊C4—44no—
788C2×C22⋊C4—48no—
789C2×C22⋊C4—44no—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
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×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C42—42no—
843C2×C42C2414yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2411yescharacteristic
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858#95C2412yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2412yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2412yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906C24—24no—
907C24—42no—
908C24—42no—
909C24—42no—
910C24—42no—
911C24—42no—
912C24—42no—
913C24C2514yes—
914C24C2514yes—
915C24C2512yes—
916C24C2511yescharacteristic
917#41—416no—
918#41—832no—
919#41—816no—
920C2×Q8—22no—
921C2×Q8—28no—
922C2×Q8—28no—
923C2×Q8—28no—
924C2×Q8—24no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—41no—
928C2×Q8—41no—
929C2×Q8—42no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—42no—
933C2×Q8—44no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×Q8—42no—
937C2×Q8—42no—
938C2×Q8—816no—
939C2×D4—24no—
940C2×D4—28no—
941C2×D4—24no—
942C2×D4—28no—
943C2×D4—28no—
944C2×D4—28no—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—24no—
949C2×D4—24no—
950C2×D4—44no—
951C2×D4—41no—
952C2×D4—41no—
953C2×D4—42no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—42no—
957C2×D4—44no—
958C2×D4—42no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—42no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—42no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—42no—
982C2×D4—44no—
983C2×D4—42no—
984C2×D4—88no—
985C2×D4H(5,𝔽2)14yes—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—24no—
990C22×C4—28no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—28no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—28no—
997C22×C4—28no—
998C22×C4—44no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—42no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—42no—
1018C22×C4—44no—
1019C22×C4—42no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—41no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4H(5,𝔽2)18yes—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—24no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C42—24no—
1138C42—28no—
1139C42—24no—
1140C42—22no—
1141C42—22no—
1142C42—42no—
1143C42—44no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C23—22no—
1153C23—24no—
1154C23—21no—
1155C23—22no—
1156C23—21no—
1157C23—22no—
1158C23—24no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—48no—
1175C23—84no—
1176C23—84no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23—162no—
1181C23C2×H(5,𝔽2)14yes—
1182C23#58512yes—
1183C23C2611yescharacteristic
1184Q8—48no—
1185Q8—48no—
1186Q8—44no—
1187Q8—84no—
1188Q8—88no—
1189Q8—84no—
1190Q8—162no—
1191D4—44no—
1192D4—416no—
1193D4—48no—
1194D4—84no—
1195D4—84no—
1196D4—88no—
1197D4—88no—
1198D4—88no—
1199D4—88no—
1200D4—88no—
1201D4—84no—
1202D4—88no—
1203D4—84no—
1204D4—164no—
1205D4—162no—
1206D4—164no—
1207C2×C4—28no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—416no—
1256C2×C4—48no—
1257C2×C4—84no—
1258C2×C4—88no—
1259C2×C4—88no—
1260C2×C4—84no—
1261C2×C4—84no—
1262C2×C4—88no—
1263C2×C4—88no—
1264C2×C4—88no—
1265C2×C4—161no—
1266C2×C4—161no—
1267C2×C4—164no—
1268C2×C4C2×H(5,𝔽2)12yes—
1269C2×C4C2×H(5,𝔽2)14yes—
1270C2×C4C2×H(5,𝔽2)18yes—
1271C2×C4#58512yes—
1272C22—24no—
1273C22—24no—
1274C22—22no—
1275C22—24no—
1276C22—24no—
1277C22—41no—
1278C22—41no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22—44no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—168no—
1297C22C22×H(5,𝔽2)11yescharacteristic
1298C22C22×H(5,𝔽2)12yes—
1299C22C2×#58511yescharacteristic
1300C22C2×#58511yescharacteristic
1301C222−1+612yes—
1302C4—28no—
1303C4—22no—
1304C4—22no—
1305C4—24no—
1306C4—44no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—44no—
1318C4—42no—
1319C4—44no—
1320C4—44no—
1321C2—44no—
1322C2—42no—
1323C2—84no—
1324C2—84no—
1325C2#6282011yescharacteristic
1326C2#6289712yes—
1327C2#6293112yes—
1328C2#6301111yescharacteristic
1329C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59248C2semidirect
2. #58801C2semidirect
3. #57488C2semidirect
4. #53534C2semidirect
5. #53490C2semidirect
6. #52414C2semidirect
7. #52005C2semidirect
8. #50446C2semidirect
9. #50285C2semidirect
10. #47658C2semidirect
11. #46758C2semidirect
12. #46357C2semidirect
13. #46232C2semidirect
14. #45241C2semidirect
15. #44758C2semidirect
16. #44079C2semidirect
17. #43011C2semidirect
18. #41305C2semidirect
19. #41168C2semidirect
20. #39420C2semidirect
21. #38762C2semidirect
22. #35740C2semidirect
23. #35531C2semidirect
25. C2×#548C22semidirect
26. C2×#547C22semidirect
29. C2×#536C22semidirect
33. #2844C22semidirect
34. #2838C22semidirect
35. #2837C22semidirect
37. #2831C22semidirect
39. #2825C22semidirect
40. #2819C22semidirect
41. #2817C22semidirect
42. #2806C22semidirect
43. #2804C22semidirect
44. #2804C22semidirect
46. #2795C22semidirect
47. #2790C22semidirect
48. #2789C22semidirect
49. #2789C22semidirect
50. #2778C22semidirect
51. #2778C22semidirect
52. #2776C22semidirect
53. #2774C22semidirect
54. #2761C22semidirect
55. #2760C22semidirect
56. #2753C22semidirect
57. #2753C22semidirect
59. #2746C22semidirect
60. #2738C22semidirect
63. #2728C22semidirect
65. #2710C22semidirect
68. #2700C22semidirect
69. #2700C22semidirect
73. #2696C22semidirect
76. #2692C22semidirect
77. #2689C22semidirect
78. #2688C22semidirect
79. #2687C22semidirect
80. #2687C22semidirect
83. #2682C22semidirect
84. #2682C22semidirect
86. #2681C22semidirect
87. #2680C22semidirect
90. #2677C22semidirect
93. #2676C22semidirect
94. #2674C22semidirect
97. #2673C22semidirect
98. #2672C22semidirect
102. #2667C22semidirect
103. #2653C22semidirect
104. #2653C22semidirect
105. #2651C22semidirect
106. #2650C22semidirect
107. #2643C22semidirect
110. #2632C22semidirect
113. #2618C22semidirect
119. #2594C22semidirect
120. #2593C22semidirect
121. #2591C22semidirect
122. #2589C22semidirect
123. #2583C22semidirect
124. #2582C22semidirect
125. #2576C22semidirect
126. #2576C22semidirect
129. #2560C22semidirect
130. #2559C22semidirect
131. #2557C22semidirect
132. #2557C22semidirect
134. #2551C22semidirect
135. #2544C22semidirect
138. #2532C22semidirect
140. #2514C22semidirect
141. #2505C22semidirect
148. #2492C22semidirect
149. #2481C22semidirect
151. #2477C22semidirect
152. #2474C22semidirect
156. #2465C22semidirect
161. #2461C22semidirect
162. #2461C22semidirect
163. #2459C22semidirect
164. #2459C22semidirect
165. #2458C22semidirect
167. #2449C22semidirect
168. #2449C22semidirect
169. #2449C22semidirect
172. #2445C22semidirect
174. #2443C22semidirect
175. #2443C22semidirect
176. #2440C22semidirect
177. #2432C22semidirect
178. #2431C22semidirect
181. #2429C22semidirect
184. #2425C22semidirect
188. #2413C22semidirect
191. #2409C22semidirect
192. #2407C22semidirect
193. #2406C22semidirect
195. #2399C22semidirect
196. #2392C22semidirect
198. C2×#395C22semidirect
200. #2379C22semidirect
201. #2374C22semidirect
202. #2365C22semidirect
204. #2359C22semidirect
205. #2359C22semidirect
207. #2355C22semidirect
208. #2353C22semidirect
210. #2332C22semidirect
211. #2324C22semidirect

Maximal subgroups

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

subgroupindex
#592482
#588012
#574882
#535342
#534902
#524142
#520052
#504462
#502852
#476582
#467582
#463572
#462322
#452412
#447582
#440792
#430112
#413052
#411682
#394202
#387622
#357402
#355312