Finite Group Databasebeta

← #7688394

Subgroups — #7688394

Order 512.

5071 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59822C211yesmaximal, characteristic
2#59679C214yesmaximal, complemented
3#59659C212yesmaximal, complemented
4#59640C212yesmaximal, complemented
5#59426C212yesmaximal, complemented
6#59118C214yesmaximal, complemented
7#45314C214yesmaximal, complemented
8#44068C218yesmaximal, complemented
9#40021C214yesmaximal, complemented
10#39213C214yesmaximal, complemented
11#39201C212yesmaximal, complemented
12#39194C212yesmaximal, complemented
13#36594C211yesmaximal, characteristic, complemented
14#36590C212yesmaximal, complemented
15#36563C211yesmaximal, characteristic, complemented
16#36559C211yesmaximal, characteristic, complemented
17#36496C212yesmaximal, complemented
18#36416C212yesmaximal, complemented
19#36114C212yesmaximal, complemented
20#35722C214yesmaximal, complemented
21#34954C211yesmaximal, characteristic, complemented
22#34934C212yesmaximal, complemented
23#34321C212yesmaximal, complemented
24#34317C212yesmaximal, complemented
25C4×Q82C211yesmaximal, characteristic, complemented
26C4×#559C211yesmaximal, characteristic, complemented
27C2×#559C2211yescharacteristic
28C2×Q82C2211yescharacteristic
29C2×#556C2212yes—
30C2×#555C2212yes—
31C2×#554C2212yes—
32C2×#529C2214yes—
33#2868C2211yescharacteristic
34#2861C2214yes—
35#2859C2212yes—
36#2859C2212yes—
37#2858C2212yes—
38#2851C2214yes—
39#2803C2218yes—
40#2801C2218yes—
41#2800C2218yes—
42#2800C2218yes—
43#2759C2218yes—
44#2757C2218yes—
45#2733C2214yes—
46#2731C2218yes—
47#2718C2218yes—
48#2712C2218yes—
49#2710C2218yes—
50#2653C2218yes—
51#2624C2214yes—
52#2594C2218yes—
53#2593C2214yes—
54#2592C2214yes—
55#2589C2218yes—
56#2587C2218yes—
57#2582C2212yes—
58#2582C2211yescharacteristic
59#2580C2214yes—
60#2571C2211yescharacteristic
61#2567C2212yes—
62#2566C2214yes—
63#2566C2214yes—
64#2563C2212yes—
65#2554C2218yes—
66#2552C2212yes—
67#2550C2214yes—
68#2548C2214yes—
69#2548C2214yes—
70#2548C2211yescharacteristic
71#2548C2211yescharacteristic
72#2547C2212yes—
73#2545C2218yes—
74#2545C2214yes—
75#2544C2214yes—
76#2541C2212yes—
77#2541C2212yes—
78#2538C2212yes—
79#2538C2212yes—
80#2538C2212yes—
81#2538C2212yes—
82#2537C2212yes—
83#2525C2218yes—
84#2514C2214yes—
85#2513C2212yes—
86#2513C2214yes—
87#2513C2212yes—
88#2512C2218yes—
89#2512C2214yes—
90#2512C2214yes—
91#2512C2214yes—
92#2507C2214yes—
93#2500C2214yes—
94#2496C2214yes—
95#2494C2214yes—
96#2494C2214yes—
97#2491C2214yes—
98#2491C2214yes—
99#2490C2214yes—
100#2479C2218yes—
101#2470C2218yes—
102#2469C2218yes—
103#2466C2218yes—
104#2466C2218yes—
105#2461C2218yes—
106#2461C2218yes—
107#2459C2218yes—
108#2452C2214yes—
109#2452C2214yes—
110#2451C2214yes—
111#2448C2212yes—
112#2448C2212yes—
113#2447C2218yes—
114#2445C2214yes—
115#2441C2214yes—
116#2439C2214yes—
117#2439C2214yes—
118#2426C2214yes—
119#2426C2214yes—
120#2426C2214yes—
121#2422C2214yes—
122#2421C2214yes—
123#2420C2214yes—
124#2414C2214yes—
125#2414C2214yes—
126#2395C2214yes—
127#2392C2218yes—
128#2374C2214yes—
129#2370C2214yes—
130#2369C2212yes—
131#2369C2211yescharacteristic
132#2369C2214yes—
133#2369C2212yes—
134#2369C2212yes—
135#2367C2212yes—
136#2367C2218yes—
137#2367C2212yes—
138#2366C2211yescharacteristic
139#2363C2214yes—
140#2362C2214yes—
141#2362C2214yes—
142#2362C2218yes—
143#2361C2214yes—
144#2361C2214yes—
145#2357C2214yes—
146#2357C2212yes—
147#2357C2212yes—
148#2355C2211yescharacteristic
149#2355C2214yes—
150#2355C2211yescharacteristic
151#2355C2212yes—
152#2354C2212yes—
153#2354C2212yes—
154#2354C2212yes—
155#2354C2212yes—
156Q8×C4⋊C4C2212yes—
157Q8×C4⋊C4C2211yescharacteristic
158Q8×C4⋊C4C2211yescharacteristic
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2212yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163#2347C2214yes—
164#2347C2214yes—
165#2344C2214yes—
166#2337C2218yes—
167#2332C2218yes—
168#2324C2214yes—
169#2323C2214yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2214yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×#127C2214yes—
177C4×#127C2212yes—
178C4×#127C2211yescharacteristic
179C4×#127C2211yescharacteristic
180C4×#125C2214yes—
181C4×#124C2212yes—
182C4×#124C2212yes—
183C4×#124C2212yes—
184C4×#124C2212yes—
185C4×#123C2214yes—
186C4×#121C2214yes—
187#2296C2214yes—
188#2293C2212yes—
189#2293C2214yes—
190#2293C2212yes—
191#2274C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2212yes—
198C42×D4C2212yes—
199#559—28no—
200Q82—28no—
201#556—48no—
202#555—216no—
203#554—216no—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2314yes—
214#529—416no—
215C2×#126C2318yes—
216C2×#126C2318yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#124C2318yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2318yes—
227C2×#123C2314yes—
228C2×#123C2318yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2318yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2318yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C2×#117C2318yes—
272C2×#117C2314yes—
273C22×C4⋊C4C2314yes—
274C22×C42C2314yes—
275#401C2318yes—
276#400C2314yes—
277#400C2318yes—
278#399C2318yes—
279#399C2314yes—
280#398C2314yes—
281#398C2318yes—
282#398C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2314yes—
287#397C2314yes—
288#397C2314yes—
289#397C2318yes—
290#397C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2318yes—
298#395C2318yes—
299#394C2314yes—
300#394C2314yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2318yes—
312#392C2318yes—
313#392C2318yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2318yes—
326#391C2318yes—
327#391C2312yes—
328#390C2312yes—
329#390C2314yes—
330#390C2312yes—
331#390C2312yes—
332#390C2314yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2312yes—
337#390C2318yes—
338#390C2314yes—
339#390C2318yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2318yes—
345#390C2314yes—
346#390C2314yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2318yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2312yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2318yes—
376#389C2314yes—
377#389C2314yes—
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2318yes—
415#388C2314yes—
416#388C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2314yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#384C2311yescharacteristic
439#384C2314yes—
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2311yescharacteristic
443#384C2312yes—
444#384C2312yes—
445#384C2312yes—
446#384C2314yes—
447#384C2312yes—
448#384C2312yes—
449#383C2318yes—
450#382C2312yes—
451#382C2314yes—
452#382C2312yes—
453#382C2312yes—
454#382C2314yes—
455#382C2312yes—
456#381C2318yes—
457#381C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C43C2314yes—
521C43C2311yescharacteristic
522C43C2312yes—
523C43C2312yes—
524C43C2312yes—
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2414yes—
529C22×Q8C2414yes—
530C22×Q8C2412yes—
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2412yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2418yes—
537C22×D4C2412yes—
538C22×D4C2418yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2418yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C4⋊Q8—216no—
545C4⋊Q8—28no—
546C4⋊Q8—28no—
547C4⋊Q8—28no—
548C4⋊Q8—44no—
549C4⋊Q8—82no—
550C4⋊Q8#4118yes—
551#127—24no—
552#127—24no—
553#127—48no—
554#126—416no—
555#126—416no—
556#125—216no—
557#125—48no—
558#124—232no—
559#124—28no—
560#124—28no—
561#124—28no—
562#124—48no—
563#124—44no—
564#124—88no—
565#124—84no—
566#123—216no—
567#123—416no—
568C22⋊Q8—216no—
569C22⋊Q8—216no—
570C22⋊Q8—232no—
571#121—216no—
572#121—216no—
573#121—48no—
574#121—48no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—24no—
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—48no—
585C4×Q8—44no—
586C4×Q8—48no—
587C4×Q8—44no—
588C4×Q8—42no—
589C4×Q8—42no—
590C4×Q8—84no—
591C4×Q8#4118yes—
592C4×D4—28no—
593C4×D4—216no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—28no—
599C4×D4—416no—
600C4×D4—44no—
601C4×D4—44no—
602C4×D4—48no—
603C4×D4—44no—
604C4×D4—44no—
605C4×D4—88no—
606C4×D4—84no—
607#117—216no—
608#117—216no—
609#117—48no—
610#117—416no—
611#117—48no—
612C2×C4⋊C4—216no—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C42—48no—
696C2×C42C2414yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2418yes—
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2414yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2418yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#95C2414yes—
732#95C2412yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2412yes—
751#95C2414yes—
752#95C2412yes—
753#95C2412yes—
754#95C2414yes—
755#95C2412yes—
756#95C2412yes—
757#95C2414yes—
758#95C2414yes—
759#95C2412yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767C24C2514yes—
768C24C2514yes—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—28no—
773C2×Q8—28no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—44no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8C2×#4114yes—
785C2×Q8C2×#4118yes—
786C2×Q8H(5,𝔽2)14yes—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—216no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—48no—
805C2×D4—42no—
806C2×D4—48no—
807C2×D4—48no—
808C2×D4—42no—
809C2×D4—48no—
810C2×D4—48no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—216no—
818C22×C4—28no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—48no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—48no—
825C22×C4—44no—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2518yes—
838C22×C4C2512yes—
839C22×C4C2511yescharacteristic
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2511yescharacteristic
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C4⋊C4—216no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—216no—
865C4⋊C4—22no—
866C4⋊C4—28no—
867C4⋊C4—216no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—42no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—42no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—42no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4C2×#4114yes—
898C4⋊C4C2×#4118yes—
899C4⋊C4C2×#4118yes—
900C4⋊C4C2×#4118yes—
901C22⋊C4—216no—
902C22⋊C4—216no—
903C22⋊C4—28no—
904C22⋊C4—216no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—216no—
913C22⋊C4—28no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C42—216no—
933C42—24no—
934C42—28no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—28no—
940C42—22no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—22no—
947C42—24no—
948C42—22no—
949C42—24no—
950C42—28no—
951C42—44no—
952C42—44no—
953C42—48no—
954C42—42no—
955C42—44no—
956C42—42no—
957C42—42no—
958C42—44no—
959C42—42no—
960C42—48no—
961C42—42no—
962C42—41no—
963C42C2×#4114yes—
964C42C2×#4118yes—
965C42C2×#4114yes—
966C422−1+414yes—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23C2611yescharacteristic
982Q8—28no—
983Q8—28no—
984Q8—48no—
985Q8—44no—
986Q8—88no—
987Q8—88no—
988D4—48no—
989D4—48no—
990D4—48no—
991D4—48no—
992D4—48no—
993D4—84no—
994D4—816no—
995D4—816no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—21no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—28no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—28no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—416no—
1053C2×C4—416no—
1054C2×C4—88no—
1055C2×C4—816no—
1056C2×C4—88no—
1057C2×C4C22×#4118yes—
1058C2×C4C22×#4114yes—
1059C2×C4C22×#4112yes—
1060C2×C4C22×#4112yes—
1061C2×C4C22×#4114yes—
1062C2×C4C22×#4112yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C2×H(5,𝔽2)14yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×2−1+412yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4C2×2−1+412yes—
1071C2×C4#58512yes—
1072C2×C4#58512yes—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22C23×#4111yescharacteristic
1088C22C23×#4111yescharacteristic
1089C22C22×H(5,𝔽2)11yescharacteristic
1090C22C22×2−1+411yescharacteristic
1091C22C2×#58511yescharacteristic
1092C22C2×#58511yescharacteristic
1093C22H(7,𝔽2)11yescharacteristic
1094C4—24no—
1095C4—22no—
1096C4—28no—
1097C4—22no—
1098C4—24no—
1099C4—22no—
1100C4—24no—
1101C4—42no—
1102C4—48no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—41no—
1107C4—42no—
1108C4—42no—
1109C4—44no—
1110C4—44no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—44no—
1115C4#348014yes—
1116C4#351814yes—
1117C4#352214yes—
1118C2—84no—
1119C2—84no—
1120C2C2×#348011yescharacteristic
1121C2C2×#352211yescharacteristic
1122C2C2×#351811yescharacteristic
1123C2#6292611yescharacteristic
1124C2#6298611yescharacteristic
1125C2#6299211yescharacteristic
1126C2#6302211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59822C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59679C2semidirect
3. #59659C2semidirect
4. #59640C2semidirect
5. #59426C2semidirect
6. #59118C2semidirect
7. #45314C2semidirect
8. #44068C2semidirect
9. #40021C2semidirect
10. #39213C2semidirect
11. #39201C2semidirect
12. #39194C2semidirect
13. #36594C2semidirect
14. #36590C2semidirect
15. #36563C2semidirect
16. #36559C2semidirect
17. #36496C2semidirect
18. #36416C2semidirect
19. #36114C2semidirect
20. #35722C2semidirect
21. #34954C2semidirect
22. #34934C2semidirect
23. #34321C2semidirect
24. #34317C2semidirect
25. C4×Q82C2semidirect
26. C4×#559C2semidirect

Maximal subgroups

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

subgroupindex
#598222
#596792
#596592
#596402
#594262
#591182
#453142
#440682
#400212
#392132
#392012
#391942
#365942
#365902
#365632
#365592
#364962
#364162
#361142
#357222
#349542
#349342
#343212
#343172
C4×Q822
C4×#5592