Finite Group Databasebeta

← #7674979

Subgroups — #7674979

Order 512.

4572 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59766C212yesmaximal, complemented
2#59718C212yesmaximal, complemented
3#59715C212yesmaximal, complemented
4#59669C212yesmaximal, complemented
5#59664C212yesmaximal, complemented
6#59631C212yesmaximal, complemented
7#59246C212yesmaximal, complemented
8#59209C212yesmaximal, complemented
9#44672C214yesmaximal, complemented
10#44614C214yesmaximal, complemented
11#43809C214yesmaximal, complemented
12#43794C214yesmaximal, complemented
13#39512C212yesmaximal, complemented
14#39512C211yesmaximal, characteristic, complemented
15#39376C212yesmaximal
16#39376C211yesmaximal, characteristic
17#39122C212yesmaximal, complemented
18#38270C214yesmaximal, complemented
19#36599C211yesmaximal, characteristic, complemented
20#36561C211yesmaximal, characteristic
21#36256C212yesmaximal, complemented
22#35461C214yesmaximal, complemented
23#35104C212yesmaximal, complemented
24#35015C211yesmaximal, characteristic, complemented
25#34780C212yesmaximal, complemented
26#34332C212yesmaximal, complemented
27#34278C212yesmaximal
28C2×#2370C211yesmaximal, characteristic, complemented
29C4×#539C211yesmaximal, characteristic
30C2×#554C2212yes—
31C2×#539C2211yescharacteristic
32C2×#539C2212yes—
33C22×#125C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2855C2212yes—
39#2851C2214yes—
40#2810C2212yes—
41#2810C2214yes—
42#2805C2214yes—
43#2805C2212yes—
44#2794C2214yes—
45#2791C2214yes—
46#2787C2214yes—
47#2776C2214yes—
48#2776C2214yes—
49#2776C2214yes—
50#2776C2214yes—
51#2774C2214yes—
52#2771C2214yes—
53#2770C2214yes—
54#2745C2214yes—
55#2726C2214yes—
56#2726C2212yes—
57#2724C2212yes—
58#2724C2214yes—
59#2719C2214yes—
60#2719C2214yes—
61#2690C2214yes—
62#2690C2214yes—
63#2689C2214yes—
64#2689C2214yes—
65#2689C2214yes—
66#2646C2212yes—
67#2627C2212yes—
68#2627C2212yes—
69#2627C2214yes—
70#2627C2212yes—
71#2606C2214yes—
72#2606C2214yes—
73#2605C2214yes—
74#2605C2214yes—
75#2599C2214yes—
76#2590C2214yes—
77#2590C2214yes—
78#2588C2214yes—
79#2588C2214yes—
80#2585C2214yes—
81#2585C2214yes—
82#2581C2212yes—
83#2581C2214yes—
84#2577C2214yes—
85#2575C2214yes—
86#2575C2214yes—
87#2573C2214yes—
88#2570C2212yes—
89#2570C2214yes—
90#2570C2214yes—
91#2570C2214yes—
92#2569C2214yes—
93#2564C2214yes—
94#2556C2214yes—
95#2552C2211yescharacteristic
96#2551C2211yescharacteristic
97#2550C2214yes—
98#2550C2214yes—
99#2550C2212yes—
100#2550C2212yes—
101#2546C2211yescharacteristic
102#2542C2211yescharacteristic
103#2533C2214yes—
104#2533C2214yes—
105#2533C2214yes—
106#2530C2214yes—
107#2528C2214yes—
108#2528C2214yes—
109#2528C2214yes—
110#2528C2214yes—
111#2527C2214yes—
112#2524C2214yes—
113#2524C2214yes—
114#2524C2214yes—
115#2523C2214yes—
116#2520C2214yes—
117#2517C2214yes—
118#2515C2214yes—
119#2514C2214yes—
120#2514C2212yes—
121#2514C2212yes—
122#2511C2212yes—
123#2511C2212yes—
124#2511C2212yes—
125#2509C2212yes—
126#2508C2212yes—
127#2507C2212yes—
128#2506C2212yes—
129#2506C2212yes—
130#2506C2214yes—
131#2506C2212yes—
132#2505C2214yes—
133#2503C2214yes—
134#2503C2212yes—
135#2496C2214yes—
136#2496C2212yes—
137#2495C2212yes—
138#2494C2212yes—
139#2493C2214yes—
140#2493C2214yes—
141#2493C2214yes—
142#2493C2214yes—
143#2492C2212yes—
144#2489C2212yes—
145#2489C2212yes—
146#2489C2212yes—
147#2489C2212yes—
148#2486C2214yes—
149#2486C2212yes—
150#2486C2214yes—
151#2486C2212yes—
152#2484C2214yes—
153#2475C2214yes—
154#2473C2214yes—
155#2462C2214yes—
156#2453C2212yes—
157#2453C2212yes—
158#2452C2212yes—
159#2451C2212yes—
160#2446C2214yes—
161#2446C2212yes—
162#2446C2212yes—
163#2446C2212yes—
164#2442C2212yes—
165#2442C2212yes—
166#2442C2212yes—
167#2440C2212yes—
168#2440C2214yes—
169#2419C2214yes—
170#2419C2214yes—
171#2419C2214yes—
172#2417C2212yes—
173#2402C2214yes—
174#2401C2214yes—
175#2374C2214yes—
176#2373C2214yes—
177#2373C2214yes—
178#2371C2214yes—
179#2370C2212yes—
180#2370C2214yes—
181#2370C2212yes—
182#2370C2212yes—
183#2370C2214yes—
184#2370C2212yes—
185#2370C2214yes—
186#2370C2214yes—
187#2370C2212yes—
188#2370C2212yes—
189#2369C2212yes—
190#2368C2214yes—
191#2365C2211yescharacteristic
192#2365C2211yescharacteristic
193#2362C2214yes—
194#2360C2212yes—
195#2360C2212yes—
196#2360C2214yes—
197#2360C2212yes—
198#2360C2214yes—
199#2360C2212yes—
200#2359C2214yes—
201#2356C2212yes—
202#2355C2211yescharacteristic
203Q8×C4⋊C4C2212yes—
204D4×C4⋊C4C2214yes—
205D4×C4⋊C4C2212yes—
206D4×C4⋊C4C2211yescharacteristic
207#2345C2212yes—
208#2345C2212yes—
209#2344C2212yes—
210#2336C2212yes—
211#2335C2212yes—
212#2334C2212yes—
213#2332C2212yes—
214#2330C2214yes—
215#2329C2214yes—
216#2329C2214yes—
217#2329C2211yescharacteristic
218#2329C2212yes—
219#2325C2211yescharacteristic
220#2322C2212yes—
221#2322C2214yes—
222#2318C2212yes—
223#2313C2211yescharacteristic
224#2313C2212yes—
225#2313C2212yes—
226C4×C4⋊Q8C2212yes—
227C4×#125C2212yes—
228C4×#125C2212yes—
229C4×#126C2212yes—
230C4×C22⋊Q8C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2211yescharacteristic
235C4×C22⋊Q8C2212yes—
236C4×#123C2212yes—
237C4×#123C2212yes—
238C4×#123C2214yes—
239C4×#121C2211yescharacteristic
240C4×#121C2212yes—
241#2295C2212yes—
242#2295C2212yes—
243C2×#389C2212yes—
244C2×#389C2211yescharacteristic
245C2×#389C2211yescharacteristic
246C2×#389C2212yes—
247#2290C2214yes—
248C2×#387C2212yes—
249C2×#387C2212yes—
250#2283C2214yes—
251#2283C2212yes—
252#2275C2214yes—
253C42×D4C2212yes—
254C2×C4×C4⋊C4C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259#554—216no—
260#539—28no—
261#539—216no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×#126C2312yes—
268C2×#126C2314yes—
269C2×#125—28no—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#123C2312yes—
279C2×#123C2314yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×#117C2314yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2314yes—
318C22×C4⋊C4C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2312yes—
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2312yes—
324C22×C42C2312yes—
325C22×C42C2312yes—
326#401C2314yes—
327#401C2314yes—
328#401C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#399C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#396C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#393C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2314yes—
402#391C2312yes—
403#391C2312yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2311yescharacteristic
408#391C2312yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#390C2311yescharacteristic
420#390C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2314yes—
426#389C2312yes—
427#389C2312yes—
428#389C2314yes—
429#389C2314yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2311yescharacteristic
453#389C2312yes—
454#389C2314yes—
455#389C2311yescharacteristic
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#388C2312yes—
476#388C2312yes—
477#388C2312yes—
478#388C2312yes—
479#388C2314yes—
480#388C2312yes—
481#388C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2312yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#387C2312yes—
491#387C2312yes—
492#387C2312yes—
493#387C2312yes—
494#387C2312yes—
495#387C2312yes—
496#387C2312yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2312yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2312yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2312yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2312yes—
542#387C2312yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
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#386C2312yes—
567#386C2314yes—
568#386C2312yes—
569#386C2312yes—
570#385C2314yes—
571#385C2314yes—
572#385C2312yes—
573#385C2314yes—
574#385C2314yes—
575#385C2312yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2312yes—
580#385C2312yes—
581#385C2314yes—
582#385C2314yes—
583#385C2312yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#384C2312yes—
591#384C2312yes—
592#384C2311yescharacteristic
593#384C2312yes—
594#384C2314yes—
595#384C2311yescharacteristic
596#383C2312yes—
597#383C2314yes—
598#383C2314yes—
599#383C2314yes—
600#383C2314yes—
601#383C2314yes—
602#382C2312yes—
603#382C2312yes—
604#382C2314yes—
605#382C2314yes—
606#382C2314yes—
607#382C2312yes—
608#382C2314yes—
609#382C2312yes—
610#382C2314yes—
611#381C2312yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#381C2312yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#381C2314yes—
620#380C2312yes—
621#380C2314yes—
622#380C2311yescharacteristic
623#380C2312yes—
624#380C2312yes—
625#380C2311yescharacteristic
626#380C2314yes—
627#380C2314yes—
628#380C2312yes—
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2314yes—
635#380C2312yes—
636#380C2312yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703#376C2314yes—
704#376C2314yes—
705#376C2314yes—
706#376C2314yes—
707C2×#95C2312yes—
708C2×#95C2311yescharacteristic
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2314yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C43C2312yes—
716C22×Q8C2412yes—
717C22×Q8C2411yescharacteristic
718C22×Q8C2412yes—
719C22×Q8C2414yes—
720C22×D4C2412yes—
721C22×D4C2411yescharacteristic
722C23×C4C2411yescharacteristic
723C23×C4C2412yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2411yescharacteristic
727C23×C4C2411yescharacteristic
728C23×C4C2412yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2412yes—
732C23×C4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2411yescharacteristic
738C4⋊Q8—28no—
739C4⋊Q8—42no—
740C4⋊Q8—42no—
741C4⋊Q8—82no—
742C4⋊Q8—82no—
743#126—28no—
744#126—216no—
745#125—28no—
746#125—216no—
747#125—28no—
748#125—28no—
749#125—216no—
750#125—216no—
751#125—28no—
752#125—84no—
753#123—28no—
754#123—216no—
755#123—28no—
756#123—216no—
757C22⋊Q8—24no—
758C22⋊Q8—28no—
759C22⋊Q8—216no—
760C22⋊Q8—28no—
761C22⋊Q8—216no—
762C22⋊Q8—28no—
763C22⋊Q8—28no—
764C22⋊Q8—28no—
765C22⋊Q8—216no—
766#121#4118yes—
767C4×Q8—28no—
768C4×Q8—42no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—82no—
772C4×Q8—84no—
773C4×D4—28no—
774C4×D4—216no—
775C4×D4—216no—
776C4×D4—28no—
777C4×D4—28no—
778C4×D4—42no—
779C4×D4—82no—
780#117—84no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—24no—
785C2×C4⋊C4—28no—
786C2×C4⋊C4—24no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—42no—
790C2×C4⋊C4—44no—
791C2×C4⋊C4—82no—
792C2×C4⋊C4—84no—
793C2×C4⋊C4#4118yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C42—24no—
889C2×C42—28no—
890C2×C42—42no—
891C2×C42—44no—
892C2×C42—42no—
893C2×C42—82no—
894C2×C42—82no—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2512yes—
1009C24C2511yescharacteristic
1010C2×Q8—24no—
1011C2×Q8—22no—
1012C2×Q8—24no—
1013C2×Q8—28no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—41no—
1017C2×Q8—44no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—41no—
1021C2×Q8—44no—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—41no—
1025C2×D4—41no—
1026C2×D4C2×#4118yes—
1027C2×D4C2×#4114yes—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—24no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—24no—
1040C22×C4—28no—
1041C22×C4—24no—
1042C22×C4—22no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—28no—
1048C22×C4—24no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—42no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—41no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—41no—
1060C22×C4—42no—
1061C22×C4—41no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—41no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—41no—
1072C22×C4C2×#4114yes—
1073C22×C4C2×#4114yes—
1074C22×C4C2×#4118yes—
1075C22×C42−1+414yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—22no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—41no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—41no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—41no—
1171C4⋊C4C2×#4114yes—
1172C4⋊C4C2×#4118yes—
1173C4⋊C4C2×#4114yes—
1174C4⋊C4C2×#4114yes—
1175C4⋊C42−1+414yes—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—28no—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—28no—
1186C22⋊C4—24no—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—28no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4C2×#4118yes—
1197C42—24no—
1198C42—24no—
1199C42—28no—
1200C42—24no—
1201C42—24no—
1202C42—28no—
1203C42—28no—
1204C42—28no—
1205C42—24no—
1206C42—24no—
1207C42—24no—
1208C42—22no—
1209C42—24no—
1210C42—22no—
1211C42—42no—
1212C42—42no—
1213C42—41no—
1214C42—41no—
1215C42—42no—
1216C42—44no—
1217C42—42no—
1218C42—42no—
1219C42—44no—
1220C42—42no—
1221C42—42no—
1222C42—44no—
1223C42—42no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—42no—
1230C23—21no—
1231C23—21no—
1232C23—21no—
1233C23—21no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23C22×#4114yes—
1241C23C22×#4112yes—
1242C23C22×#4112yes—
1243C23C2×2−1+412yes—
1244C23C2611yescharacteristic
1245Q8—48no—
1246Q8—82no—
1247Q8—84no—
1248Q8—88no—
1249D4—216no—
1250D4—44no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—28no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—44no—
1323C2×C4—48no—
1324C2×C4—44no—
1325C2×C4—48no—
1326C2×C4—44no—
1327C2×C4—44no—
1328C2×C4—48no—
1329C2×C4—48no—
1330C2×C4—88no—
1331C2×C4—84no—
1332C2×C4—82no—
1333C2×C4—84no—
1334C2×C4—84no—
1335C2×C4—88no—
1336C2×C4—82no—
1337C2×C4C22×#4114yes—
1338C2×C4C22×#4112yes—
1339C2×C4C22×#4114yes—
1340C2×C4C22×#4114yes—
1341C2×C4C22×#4112yes—
1342C2×C4C22×#4112yes—
1343C2×C4C22×#4112yes—
1344C2×C4C2×2−1+414yes—
1345C2×C4C2×2−1+414yes—
1346C2×C4C2×2−1+412yes—
1347C2×C4#58512yes—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—22no—
1354C22—24no—
1355C22—24no—
1356C22—24no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22#348214yes—
1362C22C23×#4111yescharacteristic
1363C22C23×#4111yescharacteristic
1364C22C22×2−1+411yescharacteristic
1365C22C22×2−1+411yescharacteristic
1366C22C2×#58511yescharacteristic
1367C22H(7,𝔽2)11yescharacteristic
1368C222−1+611yescharacteristic
1369C4—22no—
1370C4—22no—
1371C4—22no—
1372C4—24no—
1373C4—24no—
1374C4—24no—
1375C4—24no—
1376C4—24no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—44no—
1381C4—42no—
1382C4—44no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—42no—
1389C4—41no—
1390C4—41no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4#350714yes—
1396C2—24no—
1397C2—44no—
1398C2C2×#348211yescharacteristic
1399C2C2×#350711yescharacteristic
1400C2#6284711yescharacteristic
1401C2#6290411yescharacteristic
1402C2#6294511yescharacteristic
1403C2#6299211yescharacteristic
1404C2#6300111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59766C2semidirect
2. #59718C2semidirect
3. #59715C2semidirect
4. #59669C2semidirect
5. #59664C2semidirect
6. #59631C2semidirect
7. #59246C2semidirect
8. #59209C2semidirect
9. #44672C2semidirect
10. #44614C2semidirect
11. #43809C2semidirect
12. #43794C2semidirect
13. #39512C2semidirect
14. #39512C2semidirect
17. #39122C2semidirect
18. #38270C2semidirect
19. #36599C2semidirect
21. #36256C2semidirect
22. #35461C2semidirect
23. #35104C2semidirect
24. #35015C2semidirect
25. #34780C2semidirect
26. #34332C2semidirect
28. C2×#2370C2semidirect

Maximal subgroups

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

subgroupindex
#597662
#597182
#597152
#596692
#596642
#596312
#592462
#592092
#446722
#446142
#438092
#437942
#395122
#393762
#391222
#382702
#365992
#365612
#362562
#354612
#351042
#350152
#347802
#343322
#342782
C2×#23702
C4×#5392