Finite Group Databasebeta

← #7652530

Subgroups — #7652530

Order 512.

4542 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42983C211yesmaximal, characteristic, complemented
2#42977C211yesmaximal, characteristic
3#42699C212yesmaximal, complemented
4#42695C211yesmaximal, characteristic, complemented
5#42523C212yesmaximal, complemented
6#42522C211yesmaximal, characteristic, complemented
7#40881C214yesmaximal, complemented
8#40872C214yesmaximal, complemented
9#40835C214yesmaximal, complemented
10#40824C214yesmaximal, complemented
11#40160C214yesmaximal, complemented
12#40034C212yesmaximal, complemented
13#40026C212yesmaximal, complemented
14#39206C214yesmaximal, complemented
15#39203C212yesmaximal, complemented
16#39198C212yesmaximal, complemented
17#38592C214yesmaximal, complemented
18#38587C214yesmaximal, complemented
19#35615C212yesmaximal, complemented
20#35562C212yesmaximal, complemented
21#35536C212yesmaximal, complemented
22#35331C211yesmaximal, characteristic, complemented
23#35188C212yesmaximal, complemented
24#34954C212yesmaximal, complemented
25#34882C211yesmaximal, characteristic, complemented
26#34285C212yesmaximal, complemented
27#34255C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×#518C2211yescharacteristic
30#2866C2214yescomplemented
31#2865C2214yescomplemented
32#2862C2211yescharacteristic, complemented
33#2858C2211yescharacteristic, complemented
34#2850C2212yes—
35#2837C2214yescomplemented
36#2834C2212yes—
37#2832C2214yescomplemented
38#2830C2212yes—
39#2828C2212yes—
40#2826C2212yes—
41#2803C2214yes—
42#2803C2214yes—
43#2803C2214yescomplemented
44#2798C2214yescomplemented
45#2798C2214yescomplemented
46#2797C2214yes—
47#2796C2214yes—
48#2795C2212yescomplemented
49#2791C2214yescomplemented
50#2789C2212yescomplemented
51#2782C2214yes—
52#2781C2214yescomplemented
53#2769C2212yescomplemented
54#2754C2214yescomplemented
55#2754C2214yescomplemented
56#2753C2214yescomplemented
57#2750C2214yes—
58#2746C2214yescomplemented
59#2741C2214yescomplemented
60#2737C2214yescomplemented
61#2736C2212yes—
62#2735C2214yes—
63#2735C2212yes—
64#2723C2214yes—
65#2717C2214yescomplemented
66#2711C2214yescomplemented
67#2710C2214yes—
68#2702C2214yescomplemented
69#2701C2214yescomplemented
70#2700C2214yescomplemented
71#2692C2214yescomplemented
72#2687C2214yescomplemented
73#2680C2212yescomplemented
74#2678C2214yes—
75#2670C2212yes—
76#2668C2212yes—
77#2663C2214yescomplemented
78#2661C2214yes—
79#2654C2214yescomplemented
80#2653C2214yescomplemented
81#2652C2214yes—
82#2651C2214yes—
83#2651C2214yescomplemented
84#2650C2214yescomplemented
85#2650C2214yescomplemented
86#2648C2214yescomplemented
87#2640C2212yescomplemented
88#2632C2214yescomplemented
89#2630C2214yes—
90#2625C2214yescomplemented
91#2622C2214yes—
92#2621C2211yescharacteristic
93#2619C2211yescharacteristic
94#2596C2214yescomplemented
95#2593C2212yes—
96#2593C2214yescomplemented
97#2593C2214yescomplemented
98#2592C2212yes—
99#2592C2212yes—
100#2586C2212yescomplemented
101#2585C2212yescomplemented
102#2582C2212yescomplemented
103#2581C2212yescomplemented
104#2580C2212yescomplemented
105#2578C2214yescomplemented
106#2577C2214yescomplemented
107#2576C2214yescomplemented
108#2575C2214yescomplemented
109#2575C2214yescomplemented
110#2574C2212yes—
111#2574C2214yescomplemented
112#2573C2214yescomplemented
113#2571C2212yescomplemented
114#2571C2212yescomplemented
115#2570C2212yescomplemented
116#2570C2212yescomplemented
117#2563C2212yes—
118#2560C2214yescomplemented
119#2560C2214yescomplemented
120#2559C2214yescomplemented
121#2557C2214yes—
122#2557C2214yes—
123#2557C2214yescomplemented
124#2556C2212yes—
125#2555C2212yes—
126#2548C2212yes—
127#2548C2212yes—
128#2548C2212yes—
129#2545C2212yes—
130#2544C2212yes—
131#2544C2212yes—
132#2544C2212yes—
133#2542C2212yes—
134#2541C2212yes—
135#2538C2212yescomplemented
136#2523C2212yes—
137#2522C2212yes—
138#2521C2214yescomplemented
139#2520C2212yescomplemented
140#2518C2214yescomplemented
141#2518C2214yescomplemented
142#2514C2212yescomplemented
143#2513C2212yes—
144#2513C2212yes—
145#2513C2212yes—
146#2513C2212yes—
147#2513C2212yescomplemented
148#2513C2214yescomplemented
149#2512C2212yescomplemented
150#2511C2212yescomplemented
151#2510C2214yescomplemented
152#2500C2212yes—
153#2499C2212yes—
154#2489C2214yescomplemented
155#2488C2214yescomplemented
156#2477C2214yescomplemented
157#2476C2214yescomplemented
158#2476C2214yescomplemented
159#2472C2214yes—
160#2472C2214yes—
161#2472C2214yes—
162#2471C2214yescomplemented
163#2471C2214yescomplemented
164#2470C2214yescomplemented
165#2467C2214yes—
166#2467C2214yes—
167#2467C2214yescomplemented
168#2465C2212yes—
169#2463C2212yes—
170#2463C2214yes—
171#2463C2214yes—
172#2462C2212yescomplemented
173#2459C2214yescomplemented
174#2458C2214yescomplemented
175#2448C2212yes—
176#2448C2212yes—
177#2448C2214yescomplemented
178#2448C2212yescomplemented
179#2447C2212yescomplemented
180#2446C2212yescomplemented
181#2445C2212yes—
182#2445C2212yes—
183#2445C2212yescomplemented
184#2444C2214yescomplemented
185#2435C2212yes—
186#2433C2212yes—
187#2425C2214yescomplemented
188#2421C2214yescomplemented
189#2418C2214yes—
190#2418C2214yes—
191#2418C2214yes—
192#2399C2211yescharacteristic, complemented
193#2399C2211yescharacteristic, complemented
194#2396C2211yescharacteristic
195#2396C2211yescharacteristic
196#2395C2214yescomplemented
197#2395C2214yescomplemented
198#2374C2214yes—
199#2369C2212yescomplemented
200#2368C2214yescomplemented
201#2367C2212yescomplemented
202#2367C2212yescomplemented
203#2365C2212yescomplemented
204#2363C2212yes—
205#2362C2212yes—
206#2362C2214yescomplemented
207#2361C2212yes—
208#2360C2212yes—
209#2359C2214yes—
210#2357C2214yes—
211#2354C2214yes—
212#2342C2214yes—
213#2342C2214yes—
214#2337C2214yes—
215#2334C2214yescomplemented
216#2334C2214yescomplemented
217#2333C2214yescomplemented
218#2328C2212yes—
219#2328C2211yescharacteristic, complemented
220#2327C2211yescharacteristic, complemented
221#2326C2212yes—
222#2323C2214yescomplemented
223#2321C2214yes—
224#2320C2212yescomplemented
225#2319C2212yes—
226#2319C2212yes—
227#2317C2211yescharacteristic
228#2309C2211yescharacteristic
229C4×#127C2212yes—
230C4×#125C2212yescomplemented
231C4×#126C2214yescomplemented
232C4×#124C2212yes—
233C4×#124C2214yes—
234C4×#124C2212yescomplemented
235C4×#124C2214yescomplemented
236C4×C22⋊Q8C2212yes—
237#2298C2212yes—
238#2296C2211yescharacteristic
239#2295C2211yescharacteristic, complemented
240#2295C2212yescomplemented
241#2293C2212yes—
242#2293C2212yes—
243#2293C2214yescomplemented
244#2293C2212yescomplemented
245C2×#390C2211yescharacteristic
246#2275C2212yescomplemented
247#2274C2211yescharacteristic
248C42×Q8C2211yescharacteristic, complemented
249C42×Q8C2212yescomplemented
250C4×#117C2211yescharacteristic
251C23×D4C2311yescharacteristic
252#542—216no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×#127C2312yes—
256C2×#127C2312yes—
257C2×#127C2311yescharacteristic
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2312yes—
261C2×#124C2314yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283#518—28no—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×#117C2311yescharacteristic
302C2×#117C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2314yes—
305C2×#117C2314yes—
306C2×#117C2314yes—
307C2×#117C2311yescharacteristic
308C22×C4⋊C4C2311yescharacteristic
309C22×C22⋊C4C2314yes—
310C22×C22⋊C4C2314yes—
311C22×C42C2311yescharacteristic
312#401C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2311yescharacteristic
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2311yescharacteristic
326#399C2311yescharacteristic
327#399C2314yes—
328#399C2314yes—
329#399C2311yescharacteristic
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#398C2312yes—
335#398C2312yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2314yes—
340#398C2314yes—
341#398C2312yes—
342#398C2314yes—
343#398C2312yes—
344#398C2312yes—
345#398C2312yes—
346#398C2312yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2312yes—
361#397C2314yes—
362#397C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2312yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2312yes—
378#395C2312yes—
379#395C2314yes—
380#395C2311yescharacteristic
381#395C2312yes—
382#395C2312yes—
383#395C2311yescharacteristic
384#395C2312yes—
385#394C2312yes—
386#394C2312yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2311yescharacteristic
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2311yescharacteristic
418#392C2312yes—
419#392C2314yes—
420#392C2314yes—
421#392C2312yes—
422#392C2314yes—
423#392C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#390C2314yes—
441#390C2314yes—
442#390C2312yes—
443#390C2312yes—
444#390C2314yes—
445#390C2314yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2312yes—
462#390C2314yes—
463#390C2312yes—
464#390C2314yes—
465#390C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2312yes—
496#388C2312yes—
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#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#387C2312yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2312yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#385C2312yes—
597#385C2312yes—
598#385C2314yes—
599#385C2312yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#384C2312yes—
611#384C2312yes—
612#384C2312yes—
613#383C2314yes—
614#383C2314yes—
615#382C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2311yescharacteristic
619#382C2311yescharacteristic
620#382C2312yes—
621#382C2314yes—
622#382C2314yes—
623#382C2312yes—
624#382C2314yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#379C2312yes—
635#379C2312yes—
636#379C2314yes—
637#379C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684#376C2311yescharacteristic
685#376C2311yescharacteristic
686#376C2312yes—
687C2×#95C2314yes—
688C43C2314yes—
689C43C2311yescharacteristic
690C43C2312yes—
691C43C2311yescharacteristic
692C25C2412yes—
693C22×Q8C2412yes—
694C22×Q8C2411yescharacteristic
695C22×Q8C2414yes—
696C22×Q8C2411yescharacteristic
697C22×Q8C2412yes—
698C22×D4—24no—
699C22×D4—42no—
700C22×D4—42no—
701C22×D4C2412yes—
702C22×D4C2412yes—
703C22×D4C2412yes—
704C22×D4C2414yes—
705C22×D4C2414yes—
706C22×D4C2414yes—
707C22×D4C2414yes—
708C22×D4C2414yes—
709C22×D4C2412yes—
710C22×D4C2412yes—
711C23×C4C2411yescharacteristic
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C23×C4C2412yes—
716C23×C4C2412yes—
717C23×C4C2414yes—
718C23×C4C2414yes—
719C4⋊Q8—28no—
720C4⋊Q8—42no—
721#127—42no—
722#127—44no—
723#127—44no—
724#126—216no—
725#126—48no—
726#125—44no—
727#124—216no—
728#124—28no—
729#124—44no—
730#124—44no—
731#124—44no—
732#124—48no—
733#124—84no—
734#123—216no—
735#123—84no—
736#123—84no—
737#123—84no—
738C22⋊Q8—28no—
739C22⋊Q8—216no—
740C22⋊Q8—44no—
741C22⋊Q8—48no—
742C22⋊Q8—84no—
743C22⋊Q8—84no—
744#121—28no—
745#121—48no—
746#121—84no—
747#120—48no—
748#120—84no—
749C4×Q8—28no—
750C4×Q8—44no—
751C4×Q8—42no—
752C4×Q8—42no—
753C4×Q8—44no—
754C4×Q8—44no—
755C4×Q8—44no—
756C4×Q8—84no—
757C4×D4—216no—
758C4×D4—28no—
759C4×D4—28no—
760C4×D4—28no—
761C4×D4—48no—
762C4×D4—44no—
763C4×D4—44no—
764C4×D4—84no—
765C4×D4—84no—
766#117—24no—
767#117—42no—
768#117—42no—
769#117—84no—
770#117—84no—
771#117—84no—
772#117#4118yes—
773C2×C4⋊C4—42no—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C22⋊C4—216no—
826C2×C22⋊C4—84no—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C42—42no—
880C2×C42C2412yes—
881C2×C42C2411yescharacteristic
882C2×C42C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2411yescharacteristic
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2411yescharacteristic
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2411yescharacteristic
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976C24—24no—
977C24—42no—
978C24—42no—
979C24—44no—
980C24—44no—
981C24C2514yes—
982C24C2514yes—
983C24C2511yescharacteristic
984C2×Q8—24no—
985C2×Q8—28no—
986C2×Q8—24no—
987C2×Q8—24no—
988C2×Q8—24no—
989C2×Q8—41no—
990C2×Q8—42no—
991C2×Q8—41no—
992C2×Q8—44no—
993C2×Q8—44no—
994C2×Q8—42no—
995C2×Q8—42no—
996C2×Q8—42no—
997C2×D4—28no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—24no—
1005C2×D4—28no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—416no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—42no—
1024C2×D4—42no—
1025C2×D4—44no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4C2×#4114yes—
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—42no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—41no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—41no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4C2×#4118yes—
1124C22⋊C4—24no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—24no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—41no—
1140C22⋊C4—41no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—42no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4C2×#4118yes—
1176C42—24no—
1177C42—28no—
1178C42—22no—
1179C42—22no—
1180C42—22no—
1181C42—22no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—42no—
1188C42—42no—
1189C42—42no—
1190C42—42no—
1191C42—44no—
1192C42—42no—
1193C42—44no—
1194C42—42no—
1195C42—44no—
1196C42—44no—
1197C42—42no—
1198C42—42no—
1199C42—44no—
1200C42—44no—
1201C42—44no—
1202C42—42no—
1203C42—44no—
1204C42C2×#4114yes—
1205C42C2×#4114yes—
1206C23—22no—
1207C23—21no—
1208C23—21no—
1209C23—22no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—48no—
1225C23—88no—
1226C23—162no—
1227C23—162no—
1228C23—164no—
1229C23C22×#4112yes—
1230C23C2611yescharacteristic
1231Q8—44no—
1232Q8—48no—
1233Q8—88no—
1234Q8—82no—
1235Q8—84no—
1236D4—48no—
1237D4—48no—
1238D4—48no—
1239D4—88no—
1240D4—88no—
1241D4—88no—
1242D4—162no—
1243D4—162no—
1244D4—164no—
1245D4—164no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—28no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—88no—
1309C2×C4—88no—
1310C2×C4—88no—
1311C2×C4—84no—
1312C2×C4—162no—
1313C2×C4—164no—
1314C2×C4—164no—
1315C2×C4C22×#4114yes—
1316C2×C4C22×#4112yes—
1317C2×C4C22×#4114yes—
1318C2×C4C22×#4112yes—
1319C2×C4#58514yes—
1320C2×C4#58512yes—
1321C2×C4#58512yes—
1322C22—24no—
1323C22—22no—
1324C22—41no—
1325C22—41no—
1326C22—42no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—44no—
1334C22—44no—
1335C22—44no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—168no—
1342C22C23×#4111yescharacteristic
1343C22C2×#58512yes—
1344C22C2×#58511yescharacteristic
1345C22C2×#58511yescharacteristic
1346C22H(7,𝔽2)12yes—
1347C4—24no—
1348C4—24no—
1349C4—24no—
1350C4—22no—
1351C4—44no—
1352C4—44no—
1353C4—44no—
1354C4—42no—
1355C4—41no—
1356C4—41no—
1357C4—44no—
1358C4—42no—
1359C4—42no—
1360C4—41no—
1361C4—41no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—44no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4#345514yes—
1371C2—42no—
1372C2—84no—
1373C2—84no—
1374C2C2×#345511yescharacteristic
1375C2#6282911yescharacteristic
1376C2#6288511yescharacteristic
1377C2#6296612yes—
1378C2#6301012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42977C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42983C2semidirect
3. #42699C2semidirect
4. #42695C2semidirect
5. #42523C2semidirect
6. #42522C2semidirect
7. #40881C2semidirect
8. #40872C2semidirect
9. #40835C2semidirect
10. #40824C2semidirect
11. #40160C2semidirect
12. #40034C2semidirect
13. #40026C2semidirect
14. #39206C2semidirect
15. #39203C2semidirect
16. #39198C2semidirect
17. #38592C2semidirect
18. #38587C2semidirect
19. #35615C2semidirect
20. #35562C2semidirect
21. #35536C2semidirect
22. #35331C2semidirect
23. #35188C2semidirect
24. #34954C2semidirect
25. #34882C2semidirect
26. #34285C2semidirect
27. #34255C2semidirect
30. #2866C22semidirect
31. #2865C22semidirect
32. #2862C22semidirect
33. #2858C22semidirect
35. #2837C22semidirect
37. #2832C22semidirect
43. #2803C22semidirect
44. #2798C22semidirect
45. #2798C22semidirect
48. #2795C22semidirect
49. #2791C22semidirect
50. #2789C22semidirect
52. #2781C22semidirect
53. #2769C22semidirect
54. #2754C22semidirect
55. #2754C22semidirect
56. #2753C22semidirect
58. #2746C22semidirect
59. #2741C22semidirect
60. #2737C22semidirect
65. #2717C22semidirect
66. #2711C22semidirect
68. #2702C22semidirect
69. #2701C22semidirect
70. #2700C22semidirect
71. #2692C22semidirect
72. #2687C22semidirect
73. #2680C22semidirect
77. #2663C22semidirect
79. #2654C22semidirect
80. #2653C22semidirect
83. #2651C22semidirect
84. #2650C22semidirect
85. #2650C22semidirect
86. #2648C22semidirect
87. #2640C22semidirect
88. #2632C22semidirect
90. #2625C22semidirect
94. #2596C22semidirect
96. #2593C22semidirect
97. #2593C22semidirect
100. #2586C22semidirect
101. #2585C22semidirect
102. #2582C22semidirect
103. #2581C22semidirect
104. #2580C22semidirect
105. #2578C22semidirect
106. #2577C22semidirect
107. #2576C22semidirect
108. #2575C22semidirect
109. #2575C22semidirect
111. #2574C22semidirect
112. #2573C22semidirect
113. #2571C22semidirect
114. #2571C22semidirect
115. #2570C22semidirect
116. #2570C22semidirect
118. #2560C22semidirect
119. #2560C22semidirect
120. #2559C22semidirect
123. #2557C22semidirect
135. #2538C22semidirect
138. #2521C22semidirect
139. #2520C22semidirect
140. #2518C22semidirect
141. #2518C22semidirect
142. #2514C22semidirect
147. #2513C22semidirect
148. #2513C22semidirect
149. #2512C22semidirect
150. #2511C22semidirect
151. #2510C22semidirect
154. #2489C22semidirect
155. #2488C22semidirect
156. #2477C22semidirect
157. #2476C22semidirect
158. #2476C22semidirect
162. #2471C22semidirect
163. #2471C22semidirect
164. #2470C22semidirect
167. #2467C22semidirect
172. #2462C22semidirect
173. #2459C22semidirect
174. #2458C22semidirect
177. #2448C22semidirect
178. #2448C22semidirect
179. #2447C22semidirect
180. #2446C22semidirect
183. #2445C22semidirect
184. #2444C22semidirect
187. #2425C22semidirect
188. #2421C22semidirect
192. #2399C22semidirect
193. #2399C22semidirect
196. #2395C22semidirect
197. #2395C22semidirect
199. #2369C22semidirect
200. #2368C22semidirect
201. #2367C22semidirect
202. #2367C22semidirect
203. #2365C22semidirect
206. #2362C22semidirect
215. #2334C22semidirect
216. #2334C22semidirect
217. #2333C22semidirect
219. #2328C22semidirect
220. #2327C22semidirect
222. #2323C22semidirect
224. #2320C22semidirect
230. C4×#125C22semidirect
231. C4×#126C22semidirect
234. C4×#124C22semidirect
235. C4×#124C22semidirect
239. #2295C22semidirect
240. #2295C22semidirect
243. #2293C22semidirect
244. #2293C22semidirect
246. #2275C22semidirect
248. C42×Q8C22semidirect
249. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#429832
#429772
#426992
#426952
#425232
#425222
#408812
#408722
#408352
#408242
#401602
#400342
#400262
#392062
#392032
#391982
#385922
#385872
#356152
#355622
#355362
#353312
#351882
#349542
#348822
#342852
#342552