Finite Group Databasebeta

← #7739334

Subgroups — #7739334

Order 512.

4730 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59258C212yesmaximal, complemented
2#59245C212yesmaximal, complemented
3#59242C212yesmaximal, complemented
4#59230C212yesmaximal, complemented
5#51563C218yesmaximal, complemented
6#45162C214yesmaximal, complemented
7#45157C214yesmaximal, complemented
8#45128C214yesmaximal, complemented
9#45003C214yesmaximal, complemented
10#39761C212yesmaximal, complemented
11#39159C212yesmaximal, complemented
12#38976C212yesmaximal, complemented
13#38940C212yesmaximal, complemented
14#37338C214yesmaximal, complemented
15#36599C212yesmaximal, complemented
16#36464C212yesmaximal, complemented
17#36194C212yesmaximal, complemented
18#36186C212yesmaximal, complemented
19#35608C214yesmaximal, complemented
20#35280C211yesmaximal, characteristic, complemented
21#35275C211yesmaximal, characteristic, complemented
22#34979C211yesmaximal, characteristic, complemented
23#34976C211yesmaximal, characteristic
24#34374C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27C2×#552C2214yes—
28C2×#544C2212yes—
29C2×#533C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2868C2212yes—
33#2859C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2857C2214yes—
37#2854C2214yes—
38#2793C2218yes—
39#2788C2218yes—
40#2787C2218yes—
41#2784C2218yes—
42#2779C2218yes—
43#2778C2218yes—
44#2775C2218yes—
45#2766C2218yes—
46#2758C2218yes—
47#2745C2218yes—
48#2737C2218yes—
49#2719C2218yes—
50#2716C2218yes—
51#2702C2218yes—
52#2696C2218yes—
53#2695C2218yes—
54#2660C2214yes—
55#2645C2214yes—
56#2640C2214yes—
57#2629C2214yes—
58#2611C2214yes—
59#2609C2214yes—
60#2588C2218yes—
61#2585C2218yes—
62#2582C2211yescharacteristic
63#2582C2212yes—
64#2582C2212yes—
65#2578C2218yes—
66#2577C2218yes—
67#2574C2218yes—
68#2571C2214yes—
69#2569C2218yes—
70#2568C2214yes—
71#2568C2211yescharacteristic
72#2563C2214yes—
73#2563C2214yes—
74#2558C2218yes—
75#2552C2212yes—
76#2552C2212yes—
77#2551C2212yes—
78#2551C2212yes—
79#2547C2211yescharacteristic
80#2546C2211yescharacteristic
81#2542C2211yescharacteristic
82#2538C2211yescharacteristic
83#2538C2212yes—
84#2538C2211yescharacteristic
85#2538C2212yes—
86#2537C2211yescharacteristic
87#2524C2218yes—
88#2519C2218yes—
89#2518C2218yes—
90#2514C2214yes—
91#2514C2214yes—
92#2512C2214yes—
93#2511C2214yes—
94#2511C2214yes—
95#2509C2214yes—
96#2508C2214yes—
97#2506C2214yes—
98#2506C2214yes—
99#2499C2212yes—
100#2499C2214yes—
101#2498C2218yes—
102#2497C2214yes—
103#2497C2218yes—
104#2496C2214yes—
105#2495C2214yes—
106#2495C2214yes—
107#2492C2214yes—
108#2492C2214yes—
109#2492C2214yes—
110#2492C2214yes—
111#2489C2218yes—
112#2489C2214yes—
113#2485C2212yes—
114#2485C2214yes—
115#2485C2212yes—
116#2477C2218yes—
117#2475C2218yes—
118#2446C2214yes—
119#2442C2214yes—
120#2440C2214yes—
121#2440C2214yes—
122#2439C2214yes—
123#2439C2214yes—
124#2439C2218yes—
125#2432C2212yes—
126#2426C2214yes—
127#2422C2214yes—
128#2421C2214yes—
129#2417C2214yes—
130#2417C2214yes—
131#2417C2214yes—
132#2415C2212yes—
133#2415C2212yes—
134#2407C2212yes—
135#2407C2212yes—
136#2395C2214yes—
137#2392C2214yes—
138#2382C2214yes—
139#2370C2214yes—
140#2369C2214yes—
141#2365C2212yes—
142#2365C2212yes—
143#2363C2214yes—
144#2362C2214yes—
145#2355C2212yes—
146#2355C2212yes—
147#2355C2212yes—
148#2355C2211yescharacteristic
149#2355C2211yescharacteristic
150#2355C2212yes—
151#2354C2212yes—
152#2354C2212yes—
153#2354C2214yes—
154#2352C2214yes—
155#2352C2212yes—
156#2352C2212yes—
157#2352C2214yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2211yescharacteristic
162#2347C2212yes—
163#2347C2214yes—
164#2345C2214yes—
165#2343C2214yes—
166#2339C2212yes—
167#2331C2214yes—
168#2323C2214yes—
169#2323C2214yes—
170#2320C2214yes—
171#2317C2212yes—
172#2316C2212yes—
173#2314C2214yes—
174#2314C2214yes—
175#2311C2212yes—
176#2311C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×#124C2212yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×#121C2212yes—
185C4×#121C2212yes—
186#2295C2212yes—
187#2290C2214yes—
188#2285C2214yes—
189#2285C2211yescharacteristic
190#2285C2211yescharacteristic
191#2285C2212yes—
192#2285C2212yes—
193C2×#384C2211yescharacteristic
194#2283C2212yes—
195#2274C2212yes—
196C42×D4C2212yes—
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201#552—416no—
202#544—48no—
203#533—28no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×#126C2318yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#125C2318yes—
216C2×#124C2312yes—
217C2×#123C2318yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2318yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C4×#41—28no—
230C4×#41—28no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2314yes—
260C2×#117C2314yes—
261C2×#117C2318yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C42C2312yes—
268C22×C42C2312yes—
269C22×C42C2314yes—
270C22×C42C2311yescharacteristic
271#401C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#399C2314yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2314yes—
293#397C2314yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2314yes—
299#397C2318yes—
300#396C2318yes—
301#396C2314yes—
302#396C2314yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#395C2318yes—
307#395C2318yes—
308#394C2314yes—
309#394C2314yes—
310#394C2314yes—
311#394C2314yes—
312#394C2314yes—
313#394C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#392C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2312yes—
324#391C2314yes—
325#391C2318yes—
326#391C2318yes—
327#391C2312yes—
328#391C2318yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2312yes—
334#391C2318yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2318yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2312yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2314yes—
356#389C2318yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2318yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2318yes—
378#388C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2318yes—
384#388C2314yes—
385#388C2318yes—
386#388C2314yes—
387#388C2314yes—
388#388C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#386C2318yes—
414#386C2318yes—
415#386C2314yes—
416#386C2314yes—
417#386C2318yes—
418#386C2314yes—
419#386C2314yes—
420#385C2314yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#384C2312yes—
429#384C2312yes—
430#384C2314yes—
431#384C2314yes—
432#384C2314yes—
433#384C2311yescharacteristic
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#384C2314yes—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#383C2318yes—
442#383C2318yes—
443#383C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2318yes—
447#382C2312yes—
448#382C2312yes—
449#382C2314yes—
450#382C2312yes—
451#382C2318yes—
452#382C2314yes—
453#382C2312yes—
454#382C2312yes—
455#381C2314yes—
456#380C2312yes—
457#380C2312yes—
458#380C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2318yes—
467#380C2312yes—
468#380C2312yes—
469#380C2318yes—
470#380C2312yes—
471#380C2312yes—
472#380C2314yes—
473#380C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2318yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521#376C2312yes—
522C2×#95C2314yes—
523C43C2312yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41—42no—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2418yes—
535C22×D4C2411yescharacteristic
536C22×D4C2412yes—
537C22×D4C2411yescharacteristic
538C22×D4C2412yes—
539C22×D4C2414yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2414yes—
545C23×C4C2412yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2414yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C4⋊Q8—24no—
553C4⋊Q8—24no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—48no—
557C4⋊Q8—48no—
558C4⋊Q8—44no—
559#126—416no—
560#125—216no—
561#125—28no—
562#125—48no—
563#125—416no—
564#124—44no—
565#123—416no—
566C22⋊Q8—28no—
567C22⋊Q8—28no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—416no—
571C22⋊Q8—48no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—48no—
575#121—28no—
576#121—44no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—24no—
580C4×Q8—24no—
581C4×Q8—28no—
582C4×Q8—28no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—44no—
595C4×D4—48no—
596#117—24no—
597#117—24no—
598#117—28no—
599#117—24no—
600#117—24no—
601#117—28no—
602#117—28no—
603#117—44no—
604#117—44no—
605#117—48no—
606#117—48no—
607#117—416no—
608C2×C4⋊C4—28no—
609C2×C4⋊C4—28no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C42—28no—
695C2×C42—28no—
696C2×C42—48no—
697C2×C42#4118yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2418yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2412yes—
728#95C2412yes—
729#95C2412yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767C24C2512yes—
768C24C2511yescharacteristic
769C24C2512yes—
770#41—416no—
771#41—416no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—48no—
785C2×Q8—48no—
786C2×Q8—48no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—28no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D42−1+414yes—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—28no—
826C22×C4—44no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4C2×#4114yes—
836C22×C4C2×#4114yes—
837C22×C4C2×#4114yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2518yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—22no—
879C4⋊C4—28no—
880C4⋊C4—216no—
881C4⋊C4—216no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4H(5,𝔽2)14yes—
914C4⋊C42−1+414yes—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—28no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—28no—
949C42—24no—
950C42—28no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—28no—
955C42—24no—
956C42—24no—
957C42—44no—
958C42—44no—
959C42—48no—
960C42—48no—
961C42—48no—
962C42—48no—
963C42C2×#4114yes—
964C42C2×#4114yes—
965C42C2×#4114yes—
966C42C2×#4114yes—
967C23—22no—
968C23—21no—
969C23—22no—
970C23—21no—
971C23—22no—
972C23—21no—
973C23—22no—
974C23—21no—
975C23—22no—
976C23—22no—
977C23—21no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23C22×#4112yes—
987C23C2×2−1+414yes—
988C23C2611yescharacteristic
989Q8—48no—
990Q8—44no—
991Q8—44no—
992Q8—48no—
993Q8—168no—
994D4—28no—
995D4—48no—
996D4—48no—
997D4—44no—
998D4—88no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—28no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—28no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—28no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—416no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—88no—
1065C2×C4—164no—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C2×H(5,𝔽2)14yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×2−1+414yes—
1075C2×C4C2×2−1+412yes—
1076C2×C4C2×2−1+412yes—
1077C2×C4#58512yes—
1078C2×C4#58512yes—
1079C2×C4#58512yes—
1080C22—24no—
1081C22—22no—
1082C22—24no—
1083C22—22no—
1084C22—22no—
1085C22—24no—
1086C22—41no—
1087C22—42no—
1088C22—41no—
1089C22—42no—
1090C22—41no—
1091C22—41no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22C23×#4111yescharacteristic
1102C22C22×H(5,𝔽2)11yescharacteristic
1103C22C22×2−1+411yescharacteristic
1104C22C22×2−1+411yescharacteristic
1105C22C2×#58511yescharacteristic
1106C22C2×#58511yescharacteristic
1107C22C2×#58511yescharacteristic
1108C4—24no—
1109C4—24no—
1110C4—22no—
1111C4—22no—
1112C4—22no—
1113C4—44no—
1114C4—44no—
1115C4—44no—
1116C4—42no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4—48no—
1121C4—44no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—44no—
1126C4—42no—
1127C4—42no—
1128C4#349314yes—
1129C4#349514yes—
1130C4#351114yes—
1131C2—44no—
1132C2—42no—
1133C2—82no—
1134C2C2×#349311yescharacteristic
1135C2C2×#351111yescharacteristic
1136C2C2×#349511yescharacteristic
1137C2#6301311yescharacteristic
1138C2#6302511yescharacteristic
1139C2#6303211yescharacteristic
1140C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34976C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59258C2semidirect
2. #59245C2semidirect
3. #59242C2semidirect
4. #59230C2semidirect
5. #51563C2semidirect
6. #45162C2semidirect
7. #45157C2semidirect
8. #45128C2semidirect
9. #45003C2semidirect
10. #39761C2semidirect
11. #39159C2semidirect
12. #38976C2semidirect
13. #38940C2semidirect
14. #37338C2semidirect
15. #36599C2semidirect
16. #36464C2semidirect
17. #36194C2semidirect
18. #36186C2semidirect
19. #35608C2semidirect
20. #35280C2semidirect
21. #35275C2semidirect
22. #34979C2semidirect
24. #34374C2semidirect
25. #34188C2semidirect
26. #34127C2semidirect

Maximal subgroups

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

subgroupindex
#592582
#592452
#592422
#592302
#515632
#451622
#451572
#451282
#450032
#397612
#391592
#389762
#389402
#373382
#365992
#364642
#361942
#361862
#356082
#352802
#352752
#349792
#349762
#343742
#341882
#341272