Finite Group Databasebeta

← #7656606

Subgroups — #7656606

Order 512.

4420 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42704C212yesmaximal, complemented
2#42703C212yesmaximal, complemented
3#42700C212yesmaximal, complemented
4#42699C212yesmaximal, complemented
5#41765C214yesmaximal, complemented
6#41761C214yesmaximal, complemented
7#41758C214yesmaximal, complemented
8#41754C214yesmaximal, complemented
9#39796C212yesmaximal, complemented
10#39767C211yesmaximal, characteristic
11#39668C212yesmaximal, complemented
12#39639C211yesmaximal, characteristic, complemented
13#38982C212yesmaximal, complemented
14#38221C214yesmaximal, complemented
15#37615C212yesmaximal, complemented
16#37525C214yesmaximal, complemented
17#36587C211yesmaximal, characteristic
18#36552C211yesmaximal, characteristic, complemented
19#36255C212yesmaximal, complemented
20#35974C212yesmaximal, complemented
21#35958C212yesmaximal, complemented
22#35934C212yesmaximal, complemented
23#35860C212yesmaximal, complemented
24#35103C211yesmaximal, characteristic
25#35098C212yesmaximal, complemented
26#34595C211yesmaximal, characteristic, complemented
27#34584C212yesmaximal, complemented
28#34230C212yesmaximal, complemented
29C2×#2369C211yesmaximal, characteristic, complemented
30C22×C4⋊Q8C2211yescharacteristic
31C2×#529C2212yes—
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2852C2214yes—
35#2851C2212yes—
36#2850C2212yes—
37#2850C2212yes—
38#2839C2214yes—
39#2838C2214yes—
40#2837C2214yes—
41#2836C2214yes—
42#2821C2214yes—
43#2821C2214yes—
44#2809C2212yes—
45#2808C2212yes—
46#2802C2214yes—
47#2796C2214yes—
48#2787C2214yes—
49#2783C2214yes—
50#2777C2214yes—
51#2764C2214yes—
52#2763C2214yes—
53#2762C2214yes—
54#2762C2214yes—
55#2759C2214yes—
56#2758C2214yes—
57#2755C2214yes—
58#2754C2214yes—
59#2726C2212yes—
60#2724C2212yes—
61#2704C2214yes—
62#2702C2214yes—
63#2700C2214yes—
64#2698C2214yes—
65#2692C2214yes—
66#2690C2214yes—
67#2689C2214yes—
68#2689C2214yes—
69#2687C2214yes—
70#2667C2214yes—
71#2666C2212yes—
72#2666C2212yes—
73#2666C2214yes—
74#2666C2212yes—
75#2666C2212yes—
76#2664C2214yes—
77#2663C2214yes—
78#2660C2212yes—
79#2660C2212yes—
80#2659C2211yescharacteristic
81#2659C2211yescharacteristic
82#2655C2214yes—
83#2655C2214yes—
84#2654C2214yes—
85#2654C2214yes—
86#2652C2214yes—
87#2651C2214yes—
88#2650C2214yes—
89#2649C2214yes—
90#2646C2212yes—
91#2646C2212yes—
92#2643C2214yes—
93#2640C2212yes—
94#2640C2212yes—
95#2639C2212yes—
96#2627C2211yescharacteristic
97#2627C2211yescharacteristic
98#2627C2212yes—
99#2623C2214yes—
100#2623C2214yes—
101#2621C2214yes—
102#2621C2214yes—
103#2618C2212yes—
104#2618C2212yes—
105#2612C2214yes—
106#2605C2214yes—
107#2601C2214yes—
108#2601C2214yes—
109#2597C2214yes—
110#2594C2214yes—
111#2592C2212yes—
112#2590C2214yes—
113#2589C2214yes—
114#2586C2214yes—
115#2585C2214yes—
116#2582C2212yes—
117#2581C2212yes—
118#2580C2212yes—
119#2577C2214yes—
120#2573C2214yes—
121#2571C2212yes—
122#2571C2211yescharacteristic
123#2570C2212yes—
124#2570C2212yes—
125#2570C2212yes—
126#2568C2212yes—
127#2568C2212yes—
128#2568C2211yescharacteristic
129#2566C2212yes—
130#2565C2212yes—
131#2560C2214yes—
132#2556C2214yes—
133#2556C2214yes—
134#2553C2214yes—
135#2552C2212yes—
136#2552C2211yescharacteristic
137#2549C2214yes—
138#2548C2211yescharacteristic
139#2545C2212yes—
140#2544C2212yes—
141#2542C2212yes—
142#2542C2212yes—
143#2538C2212yes—
144#2532C2214yes—
145#2532C2214yes—
146#2532C2214yes—
147#2527C2214yes—
148#2525C2214yes—
149#2524C2214yes—
150#2522C2214yes—
151#2521C2214yes—
152#2520C2214yes—
153#2520C2214yes—
154#2519C2214yes—
155#2516C2214yes—
156#2515C2214yes—
157#2514C2212yes—
158#2514C2212yes—
159#2513C2212yes—
160#2513C2212yes—
161#2513C2212yes—
162#2512C2212yes—
163#2512C2212yes—
164#2511C2212yes—
165#2511C2212yes—
166#2510C2214yes—
167#2508C2212yes—
168#2505C2214yes—
169#2504C2212yes—
170#2504C2212yes—
171#2502C2212yes—
172#2502C2212yes—
173#2488C2214yes—
174#2481C2214yes—
175#2478C2214yes—
176#2477C2214yes—
177#2473C2214yes—
178#2465C2214yes—
179#2453C2212yes—
180#2450C2214yes—
181#2450C2214yes—
182#2449C2214yes—
183#2448C2212yes—
184#2447C2212yes—
185#2447C2212yes—
186#2446C2212yes—
187#2445C2212yes—
188#2444C2214yes—
189#2443C2214yes—
190#2438C2214yes—
191#2409C2214yes—
192#2409C2214yes—
193#2402C2212yes—
194#2402C2214yes—
195#2402C2212yes—
196#2401C2214yes—
197#2399C2212yes—
198#2399C2212yes—
199#2396C2214yes—
200#2395C2214yes—
201#2370C2212yes—
202#2370C2212yes—
203#2369C2212yes—
204#2369C2214yes—
205#2369C2214yes—
206#2369C2212yes—
207#2369C2212yes—
208#2369C2212yes—
209#2367C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2366C2211yescharacteristic
213#2365C2211yescharacteristic
214#2361C2212yes—
215#2361C2212yes—
216#2360C2212yes—
217#2360C2212yes—
218#2357C2212yes—
219#2356C2212yes—
220#2355C2212yes—
221#2355C2212yes—
222#2355C2211yescharacteristic
223#2354C2212yes—
224#2353C2214yes—
225Q8×C4⋊C4C2211yescharacteristic
226#2349C2214yes—
227#2347C2214yes—
228#2343C2214yes—
229#2334C2214yes—
230#2334C2214yes—
231#2329C2212yes—
232#2325C2212yes—
233#2325C2212yes—
234#2325C2212yes—
235#2320C2212yes—
236#2319C2212yes—
237#2318C2214yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2211yescharacteristic
241C4×C22⋊Q8C2211yescharacteristic
242C4×#123C2214yes—
243C4×#123C2214yes—
244C4×#121C2212yes—
245C2×#391C2212yes—
246C2×#391C2212yes—
247C2×#389C2211yescharacteristic
248C2×#389C2211yescharacteristic
249C2×#389C2212yes—
250#2290C2214yes—
251#2283C2212yes—
252#2276C2212yes—
253#2275C2212yes—
254C2×C4×C4⋊C4C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2312yes—
260C2×C4⋊Q8—28no—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×#127C2311yescharacteristic
266#529—216no—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2312yes—
304C2×#117C2314yes—
305C2×#117C2314yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2312yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2312yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2312yes—
466#391C2311yescharacteristic
467#391C2311yescharacteristic
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2311yescharacteristic
510#389C2311yescharacteristic
511#389C2312yes—
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#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
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#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2312yes—
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#385C2312yes—
608#385C2312yes—
609#385C2314yes—
610#384C2311yescharacteristic
611#384C2311yescharacteristic
612#384C2312yes—
613#384C2312yes—
614#384C2312yes—
615#384C2312yes—
616#383C2312yes—
617#383C2312yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#383C2314yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2314yes—
629#382C2312yes—
630#382C2314yes—
631#382C2312yes—
632#382C2312yes—
633#382C2314yes—
634#381C2314yes—
635#381C2314yes—
636#381C2314yes—
637#381C2312yes—
638#381C2312yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2311yescharacteristic
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2311yescharacteristic
648#380C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2314yes—
705#376C2314yes—
706C2×#95C2312yes—
707C2×#95C2311yescharacteristic
708C2×#95C2311yescharacteristic
709C2×#95C2312yes—
710C2×#95C2314yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C22×Q8—28no—
715C22×Q8—82no—
716C22×Q8—82no—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2414yes—
721C22×Q8C2414yes—
722C22×Q8C2412yes—
723C22×D4C2414yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2411yescharacteristic
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C4⋊Q8—216no—
742C4⋊Q8—28no—
743C4⋊Q8—28no—
744C4⋊Q8—42no—
745#127—42no—
746#126—216no—
747#126—84no—
748#126—84no—
749#125—28no—
750#125—82no—
751#125—84no—
752#124—28no—
753#124—44no—
754#124—82no—
755#123—216no—
756#123—84no—
757C22⋊Q8—28no—
758C22⋊Q8—24no—
759C22⋊Q8—24no—
760C22⋊Q8—44no—
761C22⋊Q8—84no—
762C22⋊Q8—84no—
763C22⋊Q8—84no—
764C22⋊Q8—84no—
765C22⋊Q8—84no—
766#121—28no—
767#121—28no—
768#121—44no—
769C4×Q8—28no—
770C4×Q8—28no—
771C4×Q8—44no—
772C4×Q8—42no—
773C4×Q8—42no—
774C4×Q8—44no—
775C4×Q8—82no—
776C4×D4—216no—
777C4×D4—28no—
778C4×D4—28no—
779C4×D4—44no—
780C4×D4—48no—
781C4×D4—48no—
782C4×D4—82no—
783#117—216no—
784#117—84no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—24no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—24no—
790C2×C4⋊C4—42no—
791C2×C4⋊C4—42no—
792C2×C4⋊C4—82no—
793C2×C4⋊C4—82no—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C42—42no—
895C2×C42—42no—
896C2×C42—44no—
897C2×C42—82no—
898C2×C42—82no—
899C2×C42#4118yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2412yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005C24C2514yes—
1006C24C2511yescharacteristic
1007C2×Q8—24no—
1008C2×Q8—28no—
1009C2×Q8—28no—
1010C2×Q8—24no—
1011C2×Q8—22no—
1012C2×Q8—22no—
1013C2×Q8—24no—
1014C2×Q8—41no—
1015C2×Q8—41no—
1016C2×Q8—41no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—44no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—41no—
1025C2×Q8—816no—
1026C2×D4—28no—
1027C2×D4—28no—
1028C2×D4—28no—
1029C2×D4—24no—
1030C2×D4—24no—
1031C2×D4—24no—
1032C2×D4—24no—
1033C2×D4—42no—
1034C2×D4—42no—
1035C2×D4—42no—
1036C2×D4—42no—
1037C2×D4—42no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—24no—
1050C22×C4—28no—
1051C22×C4—28no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4114yes—
1078C22×C4C2×#4114yes—
1079C22×C42−1+414yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—22no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—41no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C42−1+414yes—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C42—28no—
1208C42—24no—
1209C42—24no—
1210C42—28no—
1211C42—24no—
1212C42—22no—
1213C42—22no—
1214C42—24no—
1215C42—24no—
1216C42—41no—
1217C42—41no—
1218C42—44no—
1219C42—42no—
1220C42—44no—
1221C42—44no—
1222C42—42no—
1223C42—42no—
1224C42—42no—
1225C42—42no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42C2×#4118yes—
1233C42C2×#4118yes—
1234C23—21no—
1235C23—21no—
1236C23—21no—
1237C23—21no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23C22×#4112yes—
1246C23C2×2−1+412yes—
1247C23#58512yes—
1248C23C2611yescharacteristic
1249Q8—44no—
1250Q8—48no—
1251Q8—82no—
1252Q8—88no—
1253Q8—88no—
1254Q8—84no—
1255D4—416no—
1256D4—48no—
1257D4—84no—
1258D4—162no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—28no—
1272C2×C4—28no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—44no—
1334C2×C4—44no—
1335C2×C4—48no—
1336C2×C4—44no—
1337C2×C4—48no—
1338C2×C4—48no—
1339C2×C4—88no—
1340C2×C4—88no—
1341C2×C4—82no—
1342C2×C4—84no—
1343C2×C4—82no—
1344C2×C4—164no—
1345C2×C4C22×#4114yes—
1346C2×C4C22×#4114yes—
1347C2×C4C22×#4112yes—
1348C2×C4C22×#4112yes—
1349C2×C4C2×2−1+414yes—
1350C2×C4C2×2−1+412yes—
1351C2×C4C2×2−1+412yes—
1352C2×C4C2×2−1+412yes—
1353C2×C4#58512yes—
1354C22—22no—
1355C22—22no—
1356C22—22no—
1357C22—22no—
1358C22—22no—
1359C22—22no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—44no—
1367C22#350714yes—
1368C22C23×#4111yescharacteristic
1369C22C22×2−1+411yescharacteristic
1370C22C22×2−1+411yescharacteristic
1371C22C2×#58511yescharacteristic
1372C22C2×#58511yescharacteristic
1373C22H(7,𝔽2)11yescharacteristic
1374C22H(7,𝔽2)11yescharacteristic
1375C4—24no—
1376C4—24no—
1377C4—22no—
1378C4—22no—
1379C4—22no—
1380C4—24no—
1381C4—44no—
1382C4—44no—
1383C4—42no—
1384C4—42no—
1385C4—44no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—41no—
1390C4—44no—
1391C4—41no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4#346114yes—
1402C2—24no—
1403C2—84no—
1404C2C2×#346111yescharacteristic
1405C2C2×#350711yescharacteristic
1406C2#6285511yescharacteristic
1407C2#6290211yescharacteristic
1408C2#6291011yescharacteristic
1409C2#6294311yescharacteristic
1410C2#6294811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42704C2semidirect
2. #42703C2semidirect
3. #42700C2semidirect
4. #42699C2semidirect
5. #41765C2semidirect
6. #41761C2semidirect
7. #41758C2semidirect
8. #41754C2semidirect
9. #39796C2semidirect
11. #39668C2semidirect
12. #39639C2semidirect
13. #38982C2semidirect
14. #38221C2semidirect
15. #37615C2semidirect
16. #37525C2semidirect
18. #36552C2semidirect
19. #36255C2semidirect
20. #35974C2semidirect
21. #35958C2semidirect
22. #35934C2semidirect
23. #35860C2semidirect
25. #35098C2semidirect
26. #34595C2semidirect
27. #34584C2semidirect
28. #34230C2semidirect
29. C2×#2369C2semidirect

Maximal subgroups

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

subgroupindex
#427042
#427032
#427002
#426992
#417652
#417612
#417582
#417542
#397962
#397672
#396682
#396392
#389822
#382212
#376152
#375252
#365872
#365522
#362552
#359742
#359582
#359342
#358602
#351032
#350982
#345952
#345842
#342302
C2×#23692