Finite Group Databasebeta

← #7688351

Subgroups — #7688351

Order 512.

4911 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59961C214yesmaximal, complemented
2#59821C212yesmaximal, complemented
3#59821C211yesmaximal, characteristic, complemented
4#59719C214yesmaximal, complemented
5#59646C212yesmaximal
6#59227C212yesmaximal, complemented
7#45133C214yesmaximal, complemented
8#44618C218yesmaximal, complemented
9#40128C214yesmaximal, complemented
10#40123C214yesmaximal, complemented
11#39506C212yesmaximal, complemented
12#39139C212yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36559C211yesmaximal, characteristic, complemented
15#36447C212yesmaximal, complemented
16#36312C212yesmaximal, complemented
17#36272C212yesmaximal, complemented
18#36270C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#35773C214yesmaximal, complemented
21#34954C212yesmaximal, complemented
22#34934C211yesmaximal, characteristic
23#34322C212yesmaximal, complemented
24#34242C212yesmaximal, complemented
25C4×#557C211yesmaximal, characteristic, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#557C2211yescharacteristic
28C2×#556C2212yes—
29C2×#556C2211yescharacteristic
30C2×#554C2212yes—
31C2×#552C2214yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2860C2214yes—
35#2859C2212yes—
36#2859C2214yes—
37#2859C2212yes—
38#2857C2212yes—
39#2808C2218yes—
40#2803C2218yes—
41#2785C2218yes—
42#2783C2218yes—
43#2783C2218yes—
44#2781C2218yes—
45#2775C2218yes—
46#2727C2214yes—
47#2727C2218yes—
48#2721C2218yes—
49#2694C2218yes—
50#2663C2218yes—
51#2621C2214yes—
52#2611C2218yes—
53#2602C2218yes—
54#2601C2218yes—
55#2593C2218yes—
56#2582C2212yes—
57#2571C2214yes—
58#2571C2212yes—
59#2567C2212yes—
60#2566C2214yes—
61#2563C2212yes—
62#2563C2212yes—
63#2562C2214yes—
64#2560C2218yes—
65#2558C2218yes—
66#2556C2218yes—
67#2554C2214yes—
68#2553C2218yes—
69#2552C2214yes—
70#2552C2212yes—
71#2552C2211yescharacteristic
72#2550C2214yes—
73#2548C2211yescharacteristic
74#2548C2212yes—
75#2548C2214yes—
76#2542C2212yes—
77#2542C2214yes—
78#2541C2211yescharacteristic
79#2538C2212yes—
80#2538C2212yes—
81#2538C2212yes—
82#2538C2212yes—
83#2538C2211yescharacteristic
84#2536C2214yes—
85#2532C2218yes—
86#2529C2218yes—
87#2529C2218yes—
88#2519C2218yes—
89#2513C2214yes—
90#2513C2214yes—
91#2513C2214yes—
92#2512C2212yes—
93#2512C2218yes—
94#2512C2214yes—
95#2508C2214yes—
96#2508C2218yes—
97#2508C2214yes—
98#2507C2214yes—
99#2506C2214yes—
100#2506C2218yes—
101#2500C2214yes—
102#2499C2218yes—
103#2497C2214yes—
104#2496C2214yes—
105#2492C2214yes—
106#2490C2212yes—
107#2490C2214yes—
108#2489C2214yes—
109#2489C2214yes—
110#2452C2214yes—
111#2452C2214yes—
112#2451C2214yes—
113#2448C2214yes—
114#2448C2214yes—
115#2448C2214yes—
116#2448C2214yes—
117#2445C2212yes—
118#2445C2214yes—
119#2439C2214yes—
120#2426C2212yes—
121#2423C2214yes—
122#2422C2214yes—
123#2415C2214yes—
124#2415C2214yes—
125#2415C2214yes—
126#2395C2218yes—
127#2392C2214yes—
128#2373C2218yes—
129#2373C2218yes—
130#2373C2214yes—
131#2370C2212yes—
132#2370C2214yes—
133#2369C2212yes—
134#2369C2212yes—
135#2367C2214yes—
136#2367C2212yes—
137#2365C2211yescharacteristic
138#2365C2211yescharacteristic
139#2365C2212yes—
140#2363C2214yes—
141#2362C2212yes—
142#2362C2214yes—
143#2360C2214yes—
144#2356C2212yes—
145#2355C2212yes—
146#2355C2212yes—
147#2355C2211yescharacteristic
148#2355C2211yescharacteristic
149#2355C2212yes—
150#2354C2214yes—
151#2354C2212yes—
152#2354C2212yes—
153#2354C2211yescharacteristic
154#2352C2214yes—
155#2351C2214yes—
156#2351C2212yes—
157Q8×C4⋊C4C2214yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163#2347C2212yes—
164#2346C2214yes—
165#2346C2214yes—
166#2335C2218yes—
167#2334C2218yes—
168#2323C2214yes—
169#2314C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×#127C2212yes—
175C4×#127C2211yescharacteristic
176C4×#127C2212yes—
177C4×#125C2214yes—
178C4×#125C2214yes—
179C4×#125C2212yes—
180C4×#126C2214yes—
181C4×#124C2214yes—
182C4×#124C2212yes—
183C4×#124C2214yes—
184C4×C22⋊Q8C2212yes—
185C4×#121C2212yes—
186#2295C2214yes—
187#2293C2212yes—
188#2293C2214yes—
189#2293C2214yes—
190#2285C2212yes—
191#2274C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×Q8C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#557—28no—
200#556—216no—
201#556—28no—
202#554—48no—
203#552—416no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#127C2312yes—
212#529—216no—
213C2×#126C2314yes—
214C2×#126C2318yes—
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2318yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2311yescharacteristic
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2318yes—
269C2×#117C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C42C2312yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#399C2318yes—
277#399C2318yes—
278#399C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2314yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2314yes—
298#396C2314yes—
299#395C2318yes—
300#394C2314yes—
301#394C2318yes—
302#394C2314yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2314yes—
307#394C2318yes—
308#393C2318yes—
309#393C2318yes—
310#392C2314yes—
311#391C2318yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2318yes—
322#390C2318yes—
323#390C2314yes—
324#390C2312yes—
325#390C2314yes—
326#390C2312yes—
327#390C2312yes—
328#390C2314yes—
329#390C2312yes—
330#390C2312yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2318yes—
335#390C2312yes—
336#390C2314yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2312yes—
351#389C2314yes—
352#389C2312yes—
353#389C2314yes—
354#389C2312yes—
355#389C2314yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2312yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2318yes—
369#389C2314yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2312yes—
376#389C2312yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2314yes—
422#386C2318yes—
423#386C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2314yes—
428#384C2312yes—
429#384C2311yescharacteristic
430#384C2312yes—
431#384C2312yes—
432#384C2311yescharacteristic
433#384C2312yes—
434#384C2311yescharacteristic
435#384C2312yes—
436#384C2314yes—
437#384C2312yes—
438#384C2314yes—
439#384C2318yes—
440#383C2314yes—
441#382C2312yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2314yes—
447#382C2318yes—
448#382C2318yes—
449#382C2318yes—
450#382C2312yes—
451#380C2312yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2318yes—
517C4×C22⋊C4C2312yes—
518#376C2318yes—
519#376C2314yes—
520C43C2314yes—
521C43C2312yes—
522C43C2314yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2412yes—
529C22×Q8C2414yes—
530C22×D4C2412yes—
531C22×D4C2411yescharacteristic
532C22×D4C2412yes—
533C22×D4C2412yes—
534C22×D4C2414yes—
535C22×D4C2414yes—
536C23×C4C2414yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2418yes—
540C23×C4C2412yes—
541C4⋊Q8—24no—
542C4⋊Q8—28no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—44no—
546C4⋊Q8#4118yes—
547#127—24no—
548#127—44no—
549#126—216no—
550#126—216no—
551#126—232no—
552#126—416no—
553#125—28no—
554#125—28no—
555#125—216no—
556#125—416no—
557#125—48no—
558#125—48no—
559#124—28no—
560#124—216no—
561#124—28no—
562#123—216no—
563#123—416no—
564C22⋊Q8—28no—
565C22⋊Q8—216no—
566C22⋊Q8—28no—
567C22⋊Q8—416no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C22⋊Q8—48no—
571#121—28no—
572#121—44no—
573C4×Q8—216no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—28no—
580C4×Q8—24no—
581C4×Q8—28no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—44no—
585C4×Q8—44no—
586C4×Q8—48no—
587C4×Q8—42no—
588C4×Q8#4118yes—
589C4×D4—28no—
590C4×D4—216no—
591C4×D4—28no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—48no—
595C4×D4—48no—
596C4×D4—42no—
597C4×D4—48no—
598C4×D4—48no—
599C4×D4—44no—
600#117—216no—
601#117—28no—
602#117—28no—
603#117—216no—
604#117—416no—
605#117—48no—
606C2×C4⋊C4—216no—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C42—28no—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694C2×C42C2414yes—
695C2×C42C2418yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2414yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2414yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2418yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2411yescharacteristic
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#95C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2412yes—
746#95C2414yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764C24C2514yes—
765C24C2512yes—
766C2×Q8—24no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—24no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8C2×#4118yes—
780C2×Q8C2×#4114yes—
781C2×D4—24no—
782C2×D4—22no—
783C2×D4—24no—
784C2×D4—28no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—24no—
804C22×C4—28no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—216no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2511yescharacteristic
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2518yes—
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C4⋊C4—24no—
839C4⋊C4—22no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—22no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—22no—
847C4⋊C4—28no—
848C4⋊C4—216no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—216no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—22no—
870C4⋊C4—28no—
871C4⋊C4—22no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—44no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—42no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—42no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4C2×#4118yes—
890C4⋊C4C2×#4114yes—
891C4⋊C4C2×#4118yes—
892C4⋊C4C2×#4118yes—
893C4⋊C4H(5,𝔽2)14yes—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—216no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—24no—
902C22⋊C4—28no—
903C22⋊C4—216no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—24no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—42no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C42—24no—
922C42—24no—
923C42—24no—
924C42—28no—
925C42—216no—
926C42—28no—
927C42—24no—
928C42—28no—
929C42—24no—
930C42—28no—
931C42—28no—
932C42—24no—
933C42—24no—
934C42—22no—
935C42—28no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—22no—
940C42—24no—
941C42—22no—
942C42—41no—
943C42—42no—
944C42—42no—
945C42—44no—
946C42—44no—
947C42—48no—
948C42—48no—
949C42—42no—
950C42—44no—
951C42—44no—
952C42C2×#4114yes—
953C42C2×#4118yes—
954C42C2×#4114yes—
955C422−1+414yes—
956C23—22no—
957C23—24no—
958C23—24no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—24no—
964C23—22no—
965C23—24no—
966C23—24no—
967C23—22no—
968C23—24no—
969C23—22no—
970C23C2611yescharacteristic
971Q8—28no—
972Q8—216no—
973Q8—48no—
974Q8—44no—
975Q8—164no—
976D4—48no—
977D4—48no—
978D4—44no—
979D4—48no—
980D4—88no—
981D4—88no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—21no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—28no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—22no—
1031C2×C4—28no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—48no—
1039C2×C4—416no—
1040C2×C4—48no—
1041C2×C4—84no—
1042C2×C4—816no—
1043C2×C4C22×#4118yes—
1044C2×C4C22×#4114yes—
1045C2×C4C22×#4112yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4114yes—
1048C2×C4C22×#4112yes—
1049C2×C4C22×#4112yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4112yes—
1052C2×C4C2×H(5,𝔽2)14yes—
1053C2×C4C2×H(5,𝔽2)12yes—
1054C2×C4C2×2−1+412yes—
1055C2×C4C2×2−1+412yes—
1056C2×C4C2×2−1+412yes—
1057C2×C4#58512yes—
1058C2×C4#58512yes—
1059C22—42no—
1060C22—44no—
1061C22—42no—
1062C22—44no—
1063C22—44no—
1064C22—42no—
1065C22—42no—
1066C22—44no—
1067C22—42no—
1068C22—44no—
1069C22—44no—
1070C22—42no—
1071C22—44no—
1072C22—42no—
1073C22C23×#4111yescharacteristic
1074C22C23×#4111yescharacteristic
1075C22C22×H(5,𝔽2)11yescharacteristic
1076C22C22×2−1+411yescharacteristic
1077C22C2×#58511yescharacteristic
1078C22C2×#58511yescharacteristic
1079C222−1+611yescharacteristic
1080C4—22no—
1081C4—22no—
1082C4—24no—
1083C4—24no—
1084C4—24no—
1085C4—28no—
1086C4—22no—
1087C4—42no—
1088C4—44no—
1089C4—42no—
1090C4—42no—
1091C4—48no—
1092C4—42no—
1093C4—41no—
1094C4—42no—
1095C4—42no—
1096C4—44no—
1097C4—42no—
1098C4—44no—
1099C4—44no—
1100C4—42no—
1101C4#348314yes—
1102C4#350714yes—
1103C4#351514yes—
1104C2—82no—
1105C2—84no—
1106C2C2×#348311yescharacteristic
1107C2C2×#350711yescharacteristic
1108C2C2×#351511yescharacteristic
1109C2#6291311yescharacteristic
1110C2#6300711yescharacteristic
1111C2#6300911yescharacteristic
1112C2#6302111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59961C2semidirect
2. #59821C2semidirect
3. #59821C2semidirect
4. #59719C2semidirect
6. #59227C2semidirect
7. #45133C2semidirect
8. #44618C2semidirect
9. #40128C2semidirect
10. #40123C2semidirect
11. #39506C2semidirect
12. #39139C2semidirect
13. #36563C2semidirect
14. #36559C2semidirect
15. #36447C2semidirect
16. #36312C2semidirect
17. #36272C2semidirect
18. #36270C2semidirect
19. #36194C2semidirect
20. #35773C2semidirect
21. #34954C2semidirect
23. #34322C2semidirect
24. #34242C2semidirect
25. C4×#557C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#599612
#598212
#597192
#596462
#592272
#451332
#446182
#401282
#401232
#395062
#391392
#365632
#365592
#364472
#363122
#362722
#362702
#361942
#357732
#349542
#349342
#343222
#342422
C4×#5572
C4×#5562