Finite Group Databasebeta

← #7652548

Subgroups — #7652548

Order 512.

4730 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42983C211yesmaximal, characteristic, complemented
2#42982C211yesmaximal, characteristic
3#42830C212yesmaximal, complemented
4#42829C212yesmaximal, complemented
5#42818C211yesmaximal, characteristic, complemented
6#42807C211yesmaximal, characteristic, complemented
7#42418C214yesmaximal, complemented
8#42400C214yesmaximal, complemented
9#42381C214yesmaximal, complemented
10#42355C214yesmaximal, complemented
11#40236C214yesmaximal, complemented
12#40098C212yesmaximal, complemented
13#39914C212yesmaximal, complemented
14#39310C214yesmaximal, complemented
15#39226C212yesmaximal, complemented
16#39123C212yesmaximal, complemented
17#38891C214yesmaximal, complemented
18#38752C214yesmaximal, complemented
19#35658C212yesmaximal, complemented
20#35586C212yesmaximal, complemented
21#35523C212yesmaximal, complemented
22#35324C211yesmaximal, characteristic, complemented
23#35246C212yesmaximal, complemented
24#34879C211yesmaximal, characteristic, complemented
25#34708C212yesmaximal, complemented
26#34291C212yesmaximal, complemented
27#34211C211yesmaximal, characteristic, complemented
28C2×D4×Q8C2212yes—
29C2×#529C2212yes—
30C22×#124C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#518C2211yescharacteristic
33C22×C4×Q8C2212yescomplemented
34#2864C2211yescharacteristic, complemented
35#2862C2211yescharacteristic, complemented
36#2855C2212yes—
37#2853C2214yescomplemented
38#2853C2214yescomplemented
39#2841C2212yes—
40#2836C2214yescomplemented
41#2831C2214yescomplemented
42#2830C2212yes—
43#2830C2212yes—
44#2817C2212yes—
45#2809C2212yescomplemented
46#2807C2214yescomplemented
47#2806C2214yescomplemented
48#2804C2214yescomplemented
49#2799C2212yescomplemented
50#2796C2214yescomplemented
51#2788C2214yescomplemented
52#2787C2214yescomplemented
53#2783C2214yescomplemented
54#2781C2214yescomplemented
55#2781C2214yescomplemented
56#2775C2214yescomplemented
57#2773C2214yescomplemented
58#2765C2214yescomplemented
59#2759C2214yescomplemented
60#2746C2214yes—
61#2744C2214yes—
62#2744C2214yescomplemented
63#2738C2214yes—
64#2736C2212yes—
65#2735C2214yes—
66#2735C2212yes—
67#2735C2212yes—
68#2734C2212yescomplemented
69#2731C2214yes—
70#2731C2214yes—
71#2730C2214yes—
72#2730C2214yes—
73#2729C2214yescomplemented
74#2728C2212yescomplemented
75#2715C2214yescomplemented
76#2708C2214yescomplemented
77#2695C2214yes—
78#2695C2214yescomplemented
79#2684C2214yes—
80#2668C2212yes—
81#2667C2214yes—
82#2665C2214yescomplemented
83#2655C2214yescomplemented
84#2654C2214yescomplemented
85#2654C2214yescomplemented
86#2653C2214yescomplemented
87#2653C2214yescomplemented
88#2652C2214yescomplemented
89#2651C2214yes—
90#2648C2214yes—
91#2645C2212yescomplemented
92#2638C2214yes—
93#2637C2214yescomplemented
94#2637C2214yescomplemented
95#2628C2211yescharacteristic
96#2626C2214yes—
97#2621C2211yescharacteristic
98#2607C2212yes—
99#2600C2212yes—
100#2600C2214yes—
101#2599C2214yescomplemented
102#2599C2214yescomplemented
103#2596C2214yescomplemented
104#2596C2214yescomplemented
105#2594C2214yescomplemented
106#2593C2212yes—
107#2592C2212yes—
108#2590C2214yescomplemented
109#2588C2214yescomplemented
110#2582C2212yescomplemented
111#2579C2214yescomplemented
112#2579C2214yescomplemented
113#2577C2214yescomplemented
114#2577C2214yescomplemented
115#2576C2214yescomplemented
116#2575C2214yes—
117#2575C2214yescomplemented
118#2574C2214yescomplemented
119#2574C2212yescomplemented
120#2574C2214yescomplemented
121#2573C2212yescomplemented
122#2572C2212yes—
123#2571C2212yescomplemented
124#2565C2212yescomplemented
125#2565C2212yescomplemented
126#2561C2214yes—
127#2559C2214yescomplemented
128#2555C2212yes—
129#2553C2212yes—
130#2553C2214yescomplemented
131#2545C2212yes—
132#2545C2212yes—
133#2545C2212yes—
134#2534C2214yes—
135#2534C2214yes—
136#2532C2214yescomplemented
137#2532C2214yescomplemented
138#2531C2214yescomplemented
139#2530C2214yescomplemented
140#2529C2214yescomplemented
141#2528C2214yescomplemented
142#2527C2214yes—
143#2527C2214yescomplemented
144#2525C2214yescomplemented
145#2524C2212yescomplemented
146#2522C2214yescomplemented
147#2521C2214yescomplemented
148#2515C2212yes—
149#2515C2214yescomplemented
150#2514C2212yescomplemented
151#2513C2212yes—
152#2513C2212yes—
153#2507C2212yescomplemented
154#2504C2212yes—
155#2502C2212yescomplemented
156#2496C2212yescomplemented
157#2491C2212yes—
158#2485C2214yes—
159#2482C2214yes—
160#2481C2214yescomplemented
161#2480C2214yes—
162#2469C2214yescomplemented
163#2468C2214yescomplemented
164#2468C2212yescomplemented
165#2466C2214yes—
166#2458C2214yescomplemented
167#2457C2212yes—
168#2455C2214yes—
169#2454C2212yes—
170#2453C2212yescomplemented
171#2451C2212yescomplemented
172#2448C2212yes—
173#2448C2212yes—
174#2448C2212yes—
175#2447C2212yes—
176#2447C2214yescomplemented
177#2446C2212yescomplemented
178#2443C2214yescomplemented
179#2442C2212yescomplemented
180#2441C2212yes—
181#2436C2212yes—
182#2436C2212yes—
183#2435C2212yes—
184#2434C2212yescomplemented
185#2427C2212yes—
186#2426C2212yes—
187#2426C2212yes—
188#2422C2212yes—
189#2421C2212yescomplemented
190#2421C2212yescomplemented
191#2418C2214yes—
192#2416C2212yes—
193#2415C2212yes—
194#2409C2212yescomplemented
195#2408C2212yes—
196#2402C2211yescharacteristic, complemented
197#2398C2211yescharacteristic, complemented
198#2398C2214yescomplemented
199#2396C2211yescharacteristic
200#2396C2214yescomplemented
201#2392C2211yescharacteristic
202#2367C2214yes—
203#2367C2214yes—
204#2365C2212yescomplemented
205#2365C2214yescomplemented
206#2362C2214yes—
207#2362C2212yes—
208#2360C2212yescomplemented
209#2360C2214yescomplemented
210#2352C2214yes—
211#2352C2212yes—
212#2351C2212yescomplemented
213#2342C2214yes—
214#2342C2214yes—
215Q8×C22⋊C4C2212yes—
216Q8×C22⋊C4C2212yescomplemented
217#2337C2214yescomplemented
218#2335C2214yescomplemented
219#2334C2214yescomplemented
220#2331C2211yescharacteristic, complemented
221#2327C2212yescomplemented
222#2327C2214yescomplemented
223#2327C2211yescharacteristic, complemented
224#2326C2212yes—
225#2326C2212yes—
226#2326C2212yes—
227#2323C2214yes—
228#2323C2212yes—
229#2321C2214yes—
230#2319C2212yes—
231#2310C2211yescharacteristic
232#2309C2211yescharacteristic
233C4×#126C2212yescomplemented
234C4×#124C2212yes—
235C4×#124C2212yes—
236C4×C22⋊Q8C2212yescomplemented
237C4×C22⋊Q8C2214yescomplemented
238C4×#123C2212yes—
239C4×#121C2212yes—
240C4×#121C2214yescomplemented
241#2295C2211yescharacteristic, complemented
242#2295C2212yescomplemented
243#2290C2214yes—
244#2290C2212yes—
245#2290C2214yescomplemented
246#2285C2211yescharacteristic
247#2283C2212yescomplemented
248#2276C2212yescomplemented
249C42×D4C2211yescharacteristic, complemented
250C4×#117C2211yescharacteristic
251C23×Q8C2312yes—
252C23×Q8C2311yescharacteristic
253C23×D4C2311yescharacteristic
254D4×Q8—216no—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2314yes—
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259#529—48no—
260C2×#126C2312yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#125C2312yes—
264C2×#124—28no—
265C2×#124C2312yes—
266C2×#124C2314yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2314yes—
270C2×#124C2312yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#120C2314yes—
283#519—44no—
284#518—44no—
285C2×C4×Q8—48no—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2314yes—
305C2×C4×D4C2312yes—
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2314yes—
311C2×#117C2314yes—
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2314yes—
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318C22×C42C2314yes—
319#401C2314yes—
320#401C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2311yescharacteristic
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#399C2312yes—
339#399C2314yes—
340#399C2311yescharacteristic
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2314yes—
352#398C2311yescharacteristic
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2312yes—
365#397C2314yes—
366#397C2314yes—
367#397C2311yescharacteristic
368#397C2312yes—
369#397C2314yes—
370#397C2312yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#396C2312yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2312yes—
400#395C2314yes—
401#395C2314yes—
402#395C2311yescharacteristic
403#395C2314yes—
404#395C2312yes—
405#395C2314yes—
406#394C2312yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2311yescharacteristic
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#393C2314yes—
420#393C2314yes—
421#393C2311yescharacteristic
422#393C2312yes—
423#393C2314yes—
424#393C2314yes—
425#393C2312yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#392C2311yescharacteristic
430#392C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2314yes—
449#391C2312yes—
450#391C2314yes—
451#391C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#388C2312yes—
483#388C2312yes—
484#388C2312yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2312yes—
490#388C2312yes—
491#388C2314yes—
492#388C2312yes—
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#388C2312yes—
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#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#386C2312yes—
575#386C2312yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2312yes—
587#386C2314yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#385C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#384C2312yes—
610#384C2312yes—
611#383C2312yes—
612#383C2312yes—
613#383C2312yes—
614#383C2314yes—
615#382C2311yescharacteristic
616#382C2312yes—
617#382C2314yes—
618#382C2312yes—
619#382C2312yes—
620#382C2314yes—
621#382C2312yes—
622#382C2314yes—
623#382C2311yescharacteristic
624#381C2312yes—
625#381C2314yes—
626#381C2312yes—
627#381C2312yes—
628#381C2312yes—
629#381C2312yes—
630#381C2314yes—
631#381C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2312yes—
644#379C2314yes—
645#379C2314yes—
646#379C2312yes—
647#379C2312yes—
648#379C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2312yes—
689#376C2312yes—
690#376C2311yescharacteristic
691#376C2311yescharacteristic
692#376C2314yes—
693#376C2314yes—
694C43C2311yescharacteristic
695C43C2311yescharacteristic
696C25C2412yes—
697C22×Q8—28no—
698C22×Q8—44no—
699C22×Q8—42no—
700C22×Q8—42no—
701C22×Q8—44no—
702C22×Q8#4118yes—
703C22×Q8C2412yes—
704C22×Q8C2412yes—
705C22×Q8C2414yes—
706C22×Q8C2411yescharacteristic
707C22×Q8C2412yes—
708C22×Q8C2412yes—
709C22×D4—24no—
710C22×D4—42no—
711C22×D4—42no—
712C22×D4C2412yes—
713C22×D4C2412yes—
714C22×D4C2411yescharacteristic
715C22×D4C2412yes—
716C22×D4C2414yes—
717C22×D4C2414yes—
718C23×C4C2412yes—
719C23×C4C2412yes—
720C23×C4C2411yescharacteristic
721C23×C4C2412yes—
722C23×C4C2414yes—
723C23×C4C2412yes—
724C23×C4C2414yes—
725C23×C4C2414yes—
726C23×C4C2414yes—
727C23×C4C2412yes—
728C4⋊Q8—28no—
729C4⋊Q8—216no—
730C4⋊Q8—42no—
731C4⋊Q8—42no—
732#126—48no—
733#126—48no—
734#126—44no—
735#125—44no—
736#124—28no—
737#124—28no—
738#124—216no—
739#124—44no—
740#124—44no—
741#124—48no—
742#123—48no—
743#123—44no—
744#123—48no—
745C22⋊Q8—28no—
746C22⋊Q8—216no—
747C22⋊Q8—28no—
748C22⋊Q8—216no—
749C22⋊Q8—44no—
750#121—48no—
751#121—44no—
752#121—44no—
753#120—48no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—28no—
757C4×Q8—48no—
758C4×Q8—42no—
759C4×Q8—48no—
760C4×Q8—48no—
761C4×Q8—44no—
762C4×Q8—44no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×D4—28no—
766C4×D4—216no—
767C4×D4—28no—
768C4×D4—44no—
769C4×D4—42no—
770C4×D4—48no—
771C4×D4—48no—
772C4×D4—44no—
773C4×D4—48no—
774#117—24no—
775#117—42no—
776#117—48no—
777#117—48no—
778#117—42no—
779#117—42no—
780C2×C4⋊C4—44no—
781C2×C4⋊C4—48no—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C22⋊C4—216no—
835C2×C22⋊C4—48no—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2411yescharacteristic
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C42—24no—
885C2×C42—28no—
886C2×C42—48no—
887C2×C42C2412yes—
888C2×C42C2411yescharacteristic
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2414yes—
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2411yescharacteristic
935#95C2411yescharacteristic
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2411yescharacteristic
975#95C2411yescharacteristic
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987C24—24no—
988C24—42no—
989C24—42no—
990C24—44no—
991C24—44no—
992C24C2514yes—
993C24C2511yescharacteristic
994C24C2512yes—
995C2×Q8—28no—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—42no—
1002C2×Q8—44no—
1003C2×Q8—42no—
1004C2×Q8—44no—
1005C2×Q8—41no—
1006C2×Q8—42no—
1007C2×Q8—44no—
1008C2×Q8—42no—
1009C2×Q8—416no—
1010C2×Q8—432no—
1011C2×Q8C2×#4118yes—
1012C2×Q8C2×#4118yes—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—28no—
1017C2×D4—28no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—24no—
1022C2×D4—42no—
1023C2×D4—41no—
1024C2×D4—42no—
1025C2×D4—42no—
1026C2×D4—416no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—28no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4C2×#4114yes—
1060C22×C4C2×#4118yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2514yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—41no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—41no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C22⋊C4—28no—
1138C22⋊C4—24no—
1139C22⋊C4—28no—
1140C22⋊C4—24no—
1141C22⋊C4—28no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C22⋊C4—28no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C22⋊C4—44no—
1160C22⋊C4—42no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—42no—
1164C22⋊C4—41no—
1165C22⋊C4—41no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C42—24no—
1186C42—22no—
1187C42—22no—
1188C42—28no—
1189C42—24no—
1190C42—24no—
1191C42—24no—
1192C42—24no—
1193C42—28no—
1194C42—28no—
1195C42—22no—
1196C42—22no—
1197C42—22no—
1198C42—24no—
1199C42—44no—
1200C42—44no—
1201C42—42no—
1202C42—42no—
1203C42—42no—
1204C42—44no—
1205C42—42no—
1206C42—44no—
1207C42—42no—
1208C42—44no—
1209C42—44no—
1210C42—44no—
1211C42—42no—
1212C42H(5,𝔽2)14yes—
1213C23—22no—
1214C23—21no—
1215C23—22no—
1216C23—22no—
1217C23—21no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—24no—
1230C23—48no—
1231C23—88no—
1232C23—162no—
1233C23—162no—
1234C23—164no—
1235C23C22×#4112yes—
1236C23#58514yes—
1237C23C2611yescharacteristic
1238Q8—216no—
1239Q8—48no—
1240Q8—416no—
1241Q8—48no—
1242Q8—82no—
1243Q8—162no—
1244D4—48no—
1245D4—48no—
1246D4—44no—
1247D4—48no—
1248D4—88no—
1249D4—88no—
1250C2×C4—24no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—28no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—48no—
1314C2×C4—48no—
1315C2×C4—416no—
1316C2×C4—48no—
1317C2×C4—84no—
1318C2×C4—88no—
1319C2×C4—84no—
1320C2×C4—88no—
1321C2×C4—164no—
1322C2×C4C22×#4112yes—
1323C2×C4C22×#4118yes—
1324C2×C4C22×#4112yes—
1325C2×C4C2×H(5,𝔽2)14yes—
1326C2×C4C2×H(5,𝔽2)12yes—
1327C2×C4#58512yes—
1328C22—24no—
1329C22—24no—
1330C22—24no—
1331C22—22no—
1332C22—24no—
1333C22—42no—
1334C22—41no—
1335C22—42no—
1336C22—41no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—168no—
1348C22C23×#4111yescharacteristic
1349C22C22×H(5,𝔽2)11yescharacteristic
1350C22C2×#58512yes—
1351C22C2×#58511yescharacteristic
1352C222−1+612yes—
1353C4—22no—
1354C4—28no—
1355C4—24no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—41no—
1363C4—44no—
1364C4—41no—
1365C4—41no—
1366C4—42no—
1367C4—41no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—44no—
1374C4—44no—
1375C4—42no—
1376C4#345914yes—
1377C2—44no—
1378C2—42no—
1379C2—84no—
1380C2C2×#345911yescharacteristic
1381C2#6282911yescharacteristic
1382C2#6289111yescharacteristic
1383C2#6295412yes—
1384C2#6300512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42982C2
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. #42830C2semidirect
4. #42829C2semidirect
5. #42818C2semidirect
6. #42807C2semidirect
7. #42418C2semidirect
8. #42400C2semidirect
9. #42381C2semidirect
10. #42355C2semidirect
11. #40236C2semidirect
12. #40098C2semidirect
13. #39914C2semidirect
14. #39310C2semidirect
15. #39226C2semidirect
16. #39123C2semidirect
17. #38891C2semidirect
18. #38752C2semidirect
19. #35658C2semidirect
20. #35586C2semidirect
21. #35523C2semidirect
22. #35324C2semidirect
23. #35246C2semidirect
24. #34879C2semidirect
25. #34708C2semidirect
26. #34291C2semidirect
27. #34211C2semidirect
33. C22×C4×Q8C22semidirect
34. #2864C22semidirect
35. #2862C22semidirect
37. #2853C22semidirect
38. #2853C22semidirect
40. #2836C22semidirect
41. #2831C22semidirect
45. #2809C22semidirect
46. #2807C22semidirect
47. #2806C22semidirect
48. #2804C22semidirect
49. #2799C22semidirect
50. #2796C22semidirect
51. #2788C22semidirect
52. #2787C22semidirect
53. #2783C22semidirect
54. #2781C22semidirect
55. #2781C22semidirect
56. #2775C22semidirect
57. #2773C22semidirect
58. #2765C22semidirect
59. #2759C22semidirect
62. #2744C22semidirect
68. #2734C22semidirect
73. #2729C22semidirect
74. #2728C22semidirect
75. #2715C22semidirect
76. #2708C22semidirect
78. #2695C22semidirect
82. #2665C22semidirect
83. #2655C22semidirect
84. #2654C22semidirect
85. #2654C22semidirect
86. #2653C22semidirect
87. #2653C22semidirect
88. #2652C22semidirect
91. #2645C22semidirect
93. #2637C22semidirect
94. #2637C22semidirect
101. #2599C22semidirect
102. #2599C22semidirect
103. #2596C22semidirect
104. #2596C22semidirect
105. #2594C22semidirect
108. #2590C22semidirect
109. #2588C22semidirect
110. #2582C22semidirect
111. #2579C22semidirect
112. #2579C22semidirect
113. #2577C22semidirect
114. #2577C22semidirect
115. #2576C22semidirect
117. #2575C22semidirect
118. #2574C22semidirect
119. #2574C22semidirect
120. #2574C22semidirect
121. #2573C22semidirect
123. #2571C22semidirect
124. #2565C22semidirect
125. #2565C22semidirect
127. #2559C22semidirect
130. #2553C22semidirect
136. #2532C22semidirect
137. #2532C22semidirect
138. #2531C22semidirect
139. #2530C22semidirect
140. #2529C22semidirect
141. #2528C22semidirect
143. #2527C22semidirect
144. #2525C22semidirect
145. #2524C22semidirect
146. #2522C22semidirect
147. #2521C22semidirect
149. #2515C22semidirect
150. #2514C22semidirect
153. #2507C22semidirect
155. #2502C22semidirect
156. #2496C22semidirect
160. #2481C22semidirect
162. #2469C22semidirect
163. #2468C22semidirect
164. #2468C22semidirect
166. #2458C22semidirect
170. #2453C22semidirect
171. #2451C22semidirect
176. #2447C22semidirect
177. #2446C22semidirect
178. #2443C22semidirect
179. #2442C22semidirect
184. #2434C22semidirect
189. #2421C22semidirect
190. #2421C22semidirect
194. #2409C22semidirect
196. #2402C22semidirect
197. #2398C22semidirect
198. #2398C22semidirect
200. #2396C22semidirect
204. #2365C22semidirect
205. #2365C22semidirect
208. #2360C22semidirect
209. #2360C22semidirect
212. #2351C22semidirect
216. Q8×C22⋊C4C22semidirect
217. #2337C22semidirect
218. #2335C22semidirect
219. #2334C22semidirect
220. #2331C22semidirect
221. #2327C22semidirect
222. #2327C22semidirect
223. #2327C22semidirect
233. C4×#126C22semidirect
236. C4×C22⋊Q8C22semidirect
237. C4×C22⋊Q8C22semidirect
240. C4×#121C22semidirect
241. #2295C22semidirect
242. #2295C22semidirect
245. #2290C22semidirect
247. #2283C22semidirect
248. #2276C22semidirect
249. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#429832
#429822
#428302
#428292
#428182
#428072
#424182
#424002
#423812
#423552
#402362
#400982
#399142
#393102
#392262
#391232
#388912
#387522
#356582
#355862
#355232
#353242
#352462
#348792
#347082
#342912
#342112