Finite Group Databasebeta

← #7712560

Subgroups — #7712560

Order 512.

4608 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59289C214yesmaximal, complemented
2#59111C214yesmaximal, complemented
3#46158C212yesmaximal, complemented
4#46157C212yesmaximal, complemented
5#46023C212yesmaximal, complemented
6#46022C212yesmaximal, complemented
7#39791C214yesmaximal, complemented
8#39788C214yesmaximal, complemented
9#39637C212yesmaximal, complemented
10#39512C212yesmaximal, complemented
11#39509C212yesmaximal, complemented
12#39504C212yesmaximal
13#39496C212yesmaximal, complemented
14#39487C212yesmaximal
15#37884C214yesmaximal, complemented
16#37549C212yesmaximal
17#37328C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19C2×#2859C211yesmaximal, characteristic, complemented
20#36574C212yesmaximal, complemented
21#36210C212yesmaximal, complemented
22#36189C212yesmaximal, complemented
23#36181C212yesmaximal, complemented
24#35294C212yesmaximal, complemented
25#35284C212yesmaximal, complemented
26#34378C212yesmaximal, complemented
27C4×#529C211yesmaximal, characteristic
28C2×#552C2214yes—
29C2×#533C2212yes—
30C2×#529C2211yescharacteristic
31C22×#125C2212yes—
32#2868C2211yescharacteristic
33#2868C2211yescharacteristic
34#2862C2212yes—
35#2859C2212yes—
36#2859C2212yes—
37#2859C2212yes—
38#2859C2212yes—
39#2859C2212yes—
40#2859C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2859C2212yes—
44#2859C2212yes—
45#2859C2212yes—
46#2859C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2822C2214yes—
54#2820C2214yes—
55#2810C2214yes—
56#2809C2214yes—
57#2808C2214yes—
58#2806C2214yes—
59#2805C2214yes—
60#2805C2214yes—
61#2802C2218yes—
62#2783C2218yes—
63#2776C2218yes—
64#2773C2218yes—
65#2772C2218yes—
66#2767C2218yes—
67#2766C2218yes—
68#2762C2218yes—
69#2754C2218yes—
70#2727C2214yes—
71#2726C2214yes—
72#2725C2218yes—
73#2725C2218yes—
74#2719C2218yes—
75#2664C2218yes—
76#2647C2214yes—
77#2629C2214yes—
78#2629C2214yes—
79#2628C2214yes—
80#2627C2214yes—
81#2618C2214yes—
82#2596C2218yes—
83#2585C2218yes—
84#2584C2214yes—
85#2584C2214yes—
86#2581C2214yes—
87#2570C2214yes—
88#2570C2214yes—
89#2570C2214yes—
90#2565C2214yes—
91#2562C2214yes—
92#2550C2214yes—
93#2550C2214yes—
94#2514C2214yes—
95#2511C2214yes—
96#2509C2214yes—
97#2509C2214yes—
98#2509C2214yes—
99#2508C2214yes—
100#2508C2214yes—
101#2507C2214yes—
102#2507C2214yes—
103#2507C2214yes—
104#2506C2214yes—
105#2506C2214yes—
106#2503C2214yes—
107#2499C2214yes—
108#2498C2218yes—
109#2497C2214yes—
110#2497C2214yes—
111#2497C2214yes—
112#2496C2214yes—
113#2496C2214yes—
114#2495C2214yes—
115#2494C2214yes—
116#2494C2214yes—
117#2493C2218yes—
118#2488C2218yes—
119#2487C2214yes—
120#2486C2214yes—
121#2486C2214yes—
122#2485C2214yes—
123#2469C2218yes—
124#2453C2214yes—
125#2453C2218yes—
126#2453C2214yes—
127#2446C2214yes—
128#2446C2214yes—
129#2442C2214yes—
130#2441C2214yes—
131#2441C2214yes—
132#2441C2214yes—
133#2439C2214yes—
134#2439C2214yes—
135#2438C2218yes—
136#2429C2214yes—
137#2429C2214yes—
138#2423C2214yes—
139#2421C2214yes—
140#2417C2214yes—
141#2415C2214yes—
142#2413C2218yes—
143#2382C2214yes—
144#2382C2214yes—
145#2370C2214yes—
146#2370C2214yes—
147#2370C2214yes—
148#2362C2214yes—
149#2360C2214yes—
150#2352C2214yes—
151#2351C2214yes—
152#2347C2214yes—
153#2345C2214yes—
154#2344C2214yes—
155#2344C2214yes—
156#2344C2218yes—
157#2336C2218yes—
158#2331C2214yes—
159#2330C2214yes—
160#2330C2214yes—
161#2316C2214yes—
162#2314C2214yes—
163#2313C2214yes—
164C4×C4⋊Q8C2212yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2212yes—
167C4×C4⋊Q8C2212yes—
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×#125C2211yescharacteristic
171C4×#125C2211yescharacteristic
172C4×#126C2212yes—
173C4×#126C2212yes—
174C4×#124C2211yescharacteristic
175C4×#124C2211yescharacteristic
176C4×C22⋊Q8C2211yescharacteristic
177C4×C22⋊Q8C2211yescharacteristic
178C4×#123C2212yes—
179C4×#123C2212yes—
180C4×#121C2211yescharacteristic
181C4×#121C2211yescharacteristic
182#2298C2212yes—
183#2295C2211yescharacteristic
184#2293C2211yescharacteristic
185C2×#389C2212yes—
186C2×#389C2212yes—
187C2×#389C2212yes—
188C2×#389C2212yes—
189#2290C2212yes—
190#2285C2212yes—
191#2285C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194C2×#384C2211yescharacteristic
195C2×#384C2211yescharacteristic
196#2283C2211yescharacteristic
197C2×#382C2212yes—
198C42×Q8C2211yescharacteristic
199C42×D4C2212yes—
200C42×D4C2211yescharacteristic
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203#552—416no—
204#533—48no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211#529—28no—
212C2×#126C2312yes—
213C2×#126C2318yes—
214C2×#125—216no—
215C2×#125C2311yescharacteristic
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2318yes—
224C2×#124C2311yescharacteristic
225C2×#123C2312yes—
226C2×#123C2318yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×#121C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2318yes—
249C2×#117C2314yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2312yes—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268#401C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2318yes—
282#399C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#395C2318yes—
305#395C2318yes—
306#394C2318yes—
307#393C2318yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2318yes—
316#391C2318yes—
317#391C2314yes—
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2314yes—
348#389C2318yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2318yes—
376#388C2312yes—
377#388C2312yes—
378#388C2312yes—
379#388C2312yes—
380#388C2312yes—
381#388C2312yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2312yes—
390#388C2312yes—
391#387C2312yes—
392#387C2312yes—
393#387C2312yes—
394#387C2312yes—
395#387C2312yes—
396#387C2312yes—
397#387C2312yes—
398#387C2312yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#386C2318yes—
423#386C2312yes—
424#386C2312yes—
425#385C2318yes—
426#385C2312yes—
427#385C2312yes—
428#384C2312yes—
429#384C2312yes—
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#383C2312yes—
445#383C2318yes—
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#382C2314yes—
449#382C2314yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#382C2314yes—
457#382C2314yes—
458#382C2318yes—
459#381C2318yes—
460#381C2312yes—
461#381C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2311yescharacteristic
467#380C2314yes—
468#380C2311yescharacteristic
469#380C2318yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2318yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521#376C2312yes—
522#376C2312yes—
523C2×#95C2314yes—
524C2×#95C2314yes—
525C43C2311yescharacteristic
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2312yes—
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C22×Q8C2414yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2414yes—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C23×C4C2414yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2414yes—
550C23×C4C2411yescharacteristic
551C4⋊Q8—28no—
552C4⋊Q8—28no—
553C4⋊Q8—44no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557#126—28no—
558#126—416no—
559#125—216no—
560#125—216no—
561#125—216no—
562#125—216no—
563#125—24no—
564#125—48no—
565#125—48no—
566#125—48no—
567#125—416no—
568#124—24no—
569#123—28no—
570#123—416no—
571C22⋊Q8—24no—
572C22⋊Q8—216no—
573C22⋊Q8—48no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576#121—24no—
577C4×Q8—24no—
578C4×Q8—42no—
579C4×Q8—42no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—48no—
583C4×Q8—48no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—24no—
588C4×D4—42no—
589C4×D4—42no—
590#117—28no—
591#117—28no—
592#117—48no—
593#117—416no—
594#117—48no—
595#117—48no—
596C2×C4⋊C4—28no—
597C2×C4⋊C4—216no—
598C2×C4⋊C4—216no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—28no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4—44no—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C42—24no—
677C2×C42—24no—
678C2×C42—24no—
679C2×C42—28no—
680C2×C42—24no—
681C2×C42—42no—
682C2×C42—42no—
683C2×C42#4118yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2412yes—
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2418yes—
712C2×C42C2418yes—
713C2×C42C2418yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2412yes—
731#95C2412yes—
732#95C2412yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2418yes—
748#95C2418yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770C24C2512yes—
771C24C2511yescharacteristic
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—28no—
776C2×Q8—28no—
777C2×Q8—41no—
778C2×Q8—41no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—22no—
785C2×D4—41no—
786C2×D4—41no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—28no—
796C22×C4—22no—
797C22×C4—28no—
798C22×C4—22no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4C2×#4114yes—
819C22×C4C2×#4114yes—
820C22×C4C2×#4114yes—
821C22×C4H(5,𝔽2)14yes—
822C22×C42−1+414yes—
823C22×C4C2511yescharacteristic
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2518yes—
831C22×C4C2518yes—
832C22×C4C2512yes—
833C22×C4C2518yes—
834C22×C4C2518yes—
835C22×C4C2512yes—
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C4⋊C4—216no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—216no—
852C4⋊C4—216no—
853C4⋊C4—216no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—22no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—216no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—216no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—24no—
911C22⋊C4—24no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C42—24no—
921C42—22no—
922C42—22no—
923C42—22no—
924C42—22no—
925C42—24no—
926C42—22no—
927C42—22no—
928C42—22no—
929C42—22no—
930C42—22no—
931C42—22no—
932C42—22no—
933C42—22no—
934C42—22no—
935C42—22no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—24no—
946C42—24no—
947C42—41no—
948C42—41no—
949C42—41no—
950C42—41no—
951C42—48no—
952C42—48no—
953C42—48no—
954C42—48no—
955C42—48no—
956C42C2×#4114yes—
957C42C2×#4114yes—
958C42C2×#4114yes—
959C42C2×#4114yes—
960C422−1+414yes—
961C422−1+414yes—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23C22×#4112yes—
974C23C2×H(5,𝔽2)12yes—
975C23C2×2−1+412yes—
976C23C2611yescharacteristic
977Q8—44no—
978Q8—416no—
979Q8—88no—
980D4—44no—
981D4—48no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—28no—
1001C2×C4—28no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—28no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—28no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—28no—
1042C2×C4—22no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—416no—
1047C2×C4—48no—
1048C2×C4—48no—
1049C2×C4—48no—
1050C2×C4—88no—
1051C2×C4C22×#4112yes—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C2×H(5,𝔽2)12yes—
1058C2×C4C2×H(5,𝔽2)12yes—
1059C2×C4C2×2−1+412yes—
1060C2×C4C2×2−1+412yes—
1061C2×C4C2×2−1+412yes—
1062C2×C4C2×2−1+412yes—
1063C2×C4C2×2−1+412yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4C2×2−1+412yes—
1066C2×C4C2×2−1+412yes—
1067C2×C4#58512yes—
1068C2×C4#58512yes—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22#351114yes—
1083C22C23×#4111yescharacteristic
1084C22C22×H(5,𝔽2)11yescharacteristic
1085C22C22×2−1+411yescharacteristic
1086C22C22×2−1+411yescharacteristic
1087C22C22×2−1+411yescharacteristic
1088C22C2×#58511yescharacteristic
1089C22C2×#58511yescharacteristic
1090C4—22no—
1091C4—22no—
1092C4—22no—
1093C4—22no—
1094C4—22no—
1095C4—22no—
1096C4—22no—
1097C4—22no—
1098C4—22no—
1099C4—42no—
1100C4—48no—
1101C4—42no—
1102C4—48no—
1103C4—42no—
1104C4—42no—
1105C4—48no—
1106C4—42no—
1107C4—42no—
1108C4—41no—
1109C4—48no—
1110C4—42no—
1111C4—41no—
1112C4#350914yes—
1113C4#355914yes—
1114C4#356314yes—
1115C2—24no—
1116C2—82no—
1117C2C2×#355911yescharacteristic
1118C2C2×#356311yescharacteristic
1119C2C2×#351111yescharacteristic
1120C2C2×#350911yescharacteristic
1121C2#6281511yescharacteristic
1122C2#6283511yescharacteristic
1123C2#6283711yescharacteristic
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. #59289C2semidirect
2. #59111C2semidirect
3. #46158C2semidirect
4. #46157C2semidirect
5. #46023C2semidirect
6. #46022C2semidirect
7. #39791C2semidirect
8. #39788C2semidirect
9. #39637C2semidirect
10. #39512C2semidirect
11. #39509C2semidirect
13. #39496C2semidirect
15. #37884C2semidirect
17. #37328C2semidirect
18. #36645C2semidirect
19. C2×#2859C2semidirect
20. #36574C2semidirect
21. #36210C2semidirect
22. #36189C2semidirect
23. #36181C2semidirect
24. #35294C2semidirect
25. #35284C2semidirect
26. #34378C2semidirect

Maximal subgroups

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

subgroupindex
#592892
#591112
#461582
#461572
#460232
#460222
#397912
#397882
#396372
#395122
#395092
#395042
#394962
#394872
#378842
#375492
#373282
#366452
C2×#28592
#365742
#362102
#361892
#361812
#352942
#352842
#343782
C4×#5292