Finite Group Databasebeta

← #7688396

Subgroups — #7688396

Order 512.

5421 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic
2#59764C214yesmaximal, complemented
3#59647C212yesmaximal, complemented
4#59418C212yesmaximal, complemented
5#59411C212yesmaximal, complemented
6#59076C214yesmaximal, complemented
7#45215C214yesmaximal, complemented
8#44173C218yesmaximal, complemented
9#40171C214yesmaximal, complemented
10#40165C214yesmaximal, complemented
11#39193C212yesmaximal, complemented
12#39192C212yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36559C211yesmaximal, characteristic, complemented
15#36559C211yesmaximal, characteristic, complemented
16#36299C212yesmaximal, complemented
17#36299C212yesmaximal, complemented
18#36290C212yesmaximal, complemented
19#36114C212yesmaximal, complemented
20#35724C214yesmaximal, complemented
21#34954C211yesmaximal, characteristic, complemented
22#34934C212yesmaximal, complemented
23#34313C212yesmaximal, complemented
24#34308C212yesmaximal, complemented
25C4×#557C211yesmaximal, characteristic, complemented
26C4×#559C211yesmaximal, characteristic, complemented
27C2×#559C2211yescharacteristic
28C2×#557C2211yescharacteristic
29C2×#554C2212yes—
30C2×#554C2212yes—
31C2×#550C2212yes—
32C2×#547C2212yes—
33C2×#529C2214yes—
34C2×#520C2214yes—
35#2868C2211yescharacteristic
36#2863C2214yes—
37#2859C2212yes—
38#2859C2212yes—
39#2859C2212yes—
40#2851C2214yes—
41#2797C2218yes—
42#2779C2218yes—
43#2772C2218yes—
44#2757C2218yes—
45#2751C2218yes—
46#2737C2218yes—
47#2725C2218yes—
48#2723C2218yes—
49#2707C2218yes—
50#2701C2218yes—
51#2682C2214yes—
52#2638C2218yes—
53#2625C2214yes—
54#2600C2218yes—
55#2593C2214yes—
56#2582C2212yes—
57#2582C2211yescharacteristic
58#2571C2211yescharacteristic
59#2567C2212yes—
60#2566C2214yes—
61#2566C2214yes—
62#2563C2212yes—
63#2563C2212yes—
64#2558C2218yes—
65#2554C2218yes—
66#2552C2212yes—
67#2550C2214yes—
68#2548C2211yescharacteristic
69#2548C2211yescharacteristic
70#2544C2214yes—
71#2541C2212yes—
72#2538C2212yes—
73#2538C2212yes—
74#2538C2212yes—
75#2538C2212yes—
76#2538C2212yes—
77#2537C2212yes—
78#2515C2218yes—
79#2515C2218yes—
80#2513C2214yes—
81#2513C2212yes—
82#2513C2212yes—
83#2512C2214yes—
84#2509C2214yes—
85#2509C2214yes—
86#2507C2214yes—
87#2507C2214yes—
88#2505C2218yes—
89#2504C2214yes—
90#2496C2214yes—
91#2495C2214yes—
92#2495C2214yes—
93#2490C2214yes—
94#2490C2214yes—
95#2488C2218yes—
96#2477C2218yes—
97#2475C2218yes—
98#2475C2218yes—
99#2473C2218yes—
100#2470C2218yes—
101#2466C2218yes—
102#2452C2214yes—
103#2452C2214yes—
104#2452C2214yes—
105#2452C2214yes—
106#2451C2214yes—
107#2449C2218yes—
108#2448C2212yes—
109#2448C2212yes—
110#2447C2214yes—
111#2447C2214yes—
112#2445C2214yes—
113#2445C2214yes—
114#2442C2214yes—
115#2442C2214yes—
116#2432C2214yes—
117#2429C2214yes—
118#2427C2214yes—
119#2426C2214yes—
120#2425C2218yes—
121#2422C2214yes—
122#2421C2214yes—
123#2421C2214yes—
124#2420C2214yes—
125#2416C2214yes—
126#2415C2218yes—
127#2407C2214yes—
128#2395C2214yes—
129#2392C2218yes—
130#2374C2214yes—
131#2370C2214yes—
132#2370C2212yes—
133#2369C2212yes—
134#2367C2212yes—
135#2367C2212yes—
136#2366C2211yescharacteristic
137#2366C2214yes—
138#2365C2211yescharacteristic
139#2365C2212yes—
140#2361C2214yes—
141#2361C2214yes—
142#2361C2218yes—
143#2360C2214yes—
144#2360C2214yes—
145#2359C2218yes—
146#2357C2212yes—
147#2357C2212yes—
148#2355C2211yescharacteristic
149#2355C2211yescharacteristic
150#2355C2211yescharacteristic
151#2355C2212yes—
152#2355C2212yes—
153#2351C2212yes—
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2211yescharacteristic
156#2349C2214yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2214yes—
160D4×C4⋊C4C2212yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163#2344C2214yes—
164#2344C2214yes—
165#2341C2214yes—
166#2339C2214yes—
167#2324C2214yes—
168#2324C2218yes—
169#2323C2214yes—
170#2322C2218yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×#127C2212yes—
175C4×#127C2214yes—
176C4×#127C2212yes—
177C4×#127C2211yescharacteristic
178C4×#127C2211yescharacteristic
179C4×#125C2214yes—
180C4×#125C2212yes—
181C4×#124C2212yes—
182C4×#124C2212yes—
183C4×#124C2212yes—
184C4×#124C2212yes—
185C4×#123C2214yes—
186C4×#121C2214yes—
187#2293C2212yes—
188#2293C2212yes—
189#2293C2214yes—
190#2293C2214yes—
191C2×#389C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2212yes—
198C42×D4C2212yes—
199C22×#41C2314yes—
200#559—28no—
201#557—28no—
202#554—48no—
203#554—48no—
204#550—216no—
205#547—216no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2314yes—
213C2×#127C2311yescharacteristic
214#529—416no—
215C2×#126C2318yes—
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#123C2318yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2318yes—
233C2×#121C2314yes—
234C2×#121C2318yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237#520—416no—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2318yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C2318yes—
273C2×#117C2314yes—
274C2×#117C2318yes—
275C2×#117C2318yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2318yes—
279C22×C4⋊C4C2314yes—
280C22×C42C2314yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#399C2314yes—
287#398C2314yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2314yes—
295#397C2318yes—
296#397C2314yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#395C2318yes—
309#394C2314yes—
310#394C2314yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#393C2318yes—
318#393C2318yes—
319#392C2318yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2318yes—
330#390C2314yes—
331#390C2312yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2312yes—
336#390C2318yes—
337#390C2314yes—
338#390C2318yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2312yes—
344#390C2314yes—
345#390C2312yes—
346#390C2318yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2318yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#388C2314yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2318yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2318yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2318yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#387C2314yes—
422#386C2318yes—
423#386C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2314yes—
441#384C2314yes—
442#384C2311yescharacteristic
443#384C2312yes—
444#384C2311yescharacteristic
445#384C2312yes—
446#384C2311yescharacteristic
447#384C2312yes—
448#384C2312yes—
449#384C2312yes—
450#383C2318yes—
451#382C2312yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2312yes—
456#382C2312yes—
457#382C2314yes—
458#382C2312yes—
459#382C2312yes—
460#381C2318yes—
461#381C2318yes—
462#381C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2318yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C2×#95C2318yes—
522C43C2312yes—
523C43C2314yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C43C2312yes—
527C2×#41—216no—
528C2×#41—216no—
529C2×#41—48no—
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×Q8C2412yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2414yes—
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2418yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2418yes—
542C22×D4C2412yes—
543C23×C4C2414yes—
544C23×C4C2414yes—
545C23×C4C2418yes—
546C23×C4C2414yes—
547C23×C4C2418yes—
548C23×C4C2414yes—
549C23×C4C2418yes—
550C4⋊Q8—28no—
551C4⋊Q8—44no—
552C4⋊Q8—44no—
553C4⋊Q8—44no—
554C4⋊Q8#4118yes—
555#127—216no—
556#127—24no—
557#127#4118yes—
558#126—416no—
559#125—216no—
560#125—28no—
561#125—48no—
562#125—48no—
563#125—48no—
564#124—28no—
565#124—28no—
566#124—28no—
567#124—44no—
568#123—216no—
569#123—232no—
570#123—416no—
571C22⋊Q8—216no—
572C22⋊Q8—216no—
573C22⋊Q8—416no—
574C22⋊Q8—416no—
575C22⋊Q8—48no—
576#121—216no—
577#121—232no—
578#121—216no—
579#121—48no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—28no—
584C4×Q8—28no—
585C4×Q8—24no—
586C4×Q8—28no—
587C4×Q8—24no—
588C4×Q8—24no—
589C4×Q8—24no—
590C4×Q8—24no—
591C4×Q8—24no—
592C4×Q8—24no—
593C4×Q8—42no—
594C4×Q8—48no—
595C4×D4—216no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—28no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—28no—
603C4×D4—416no—
604C4×D4—48no—
605C4×D4—44no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—48no—
610C4×D4—416no—
611C4×D4—48no—
612C4×D4—44no—
613C4×D4—44no—
614C4×D4—416no—
615#117—48no—
616#117—416no—
617#117—416no—
618C2×C4⋊C4—216no—
619C2×C4⋊C4—216no—
620C2×C4⋊C4—416no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C42—48no—
704C2×C42C2414yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2418yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2411yescharacteristic
732C2×C42C2412yes—
733C2×C42C2414yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2412yes—
757#95C2412yes—
758#95C2414yes—
759#95C2414yes—
760#95C2412yes—
761#95C2414yes—
762#95C2412yes—
763#95C2412yes—
764#95C2414yes—
765#95C2412yes—
766#95C2412yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775C24C2514yes—
776C24C2514yes—
777#41—464no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—22no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8C2×#4118yes—
792C2×Q8H(5,𝔽2)14yes—
793C2×D4—216no—
794C2×D4—216no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—216no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—48no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—48no—
813C2×D4—48no—
814C2×D4C2×#4118yes—
815C2×D4C2×#4118yes—
816C2×D4C2×#4118yes—
817C22×C4—216no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—216no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—216no—
827C22×C4—28no—
828C22×C4—48no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2511yescharacteristic
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2518yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C4⋊C4—24no—
863C4⋊C4—216no—
864C4⋊C4—24no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—216no—
880C4⋊C4—28no—
881C4⋊C4—22no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—216no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—24no—
894C4⋊C4—22no—
895C4⋊C4—28no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—42no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—42no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4C2×#4118yes—
912C4⋊C4C2×#4118yes—
913C4⋊C4H(5,𝔽2)14yes—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—216no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—216no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C42—24no—
944C42—24no—
945C42—28no—
946C42—28no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—28no—
953C42—28no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—22no—
958C42—22no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—22no—
964C42—44no—
965C42—44no—
966C42—41no—
967C42—42no—
968C42—42no—
969C42—42no—
970C42—44no—
971C42—48no—
972C42—42no—
973C42C2×#4114yes—
974C42C2×#4114yes—
975C422−1+414yes—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23C22×#4118yes—
990C23C2611yescharacteristic
991Q8—216no—
992Q8—28no—
993Q8—44no—
994Q8—44no—
995Q8—164no—
996D4—216no—
997D4—216no—
998D4—48no—
999D4—432no—
1000D4—48no—
1001D4—48no—
1002D4—48no—
1003D4—816no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—28no—
1041C2×C4—28no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—28no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—432no—
1062C2×C4—416no—
1063C2×C4—416no—
1064C2×C4—88no—
1065C2×C4—816no—
1066C2×C4—88no—
1067C2×C4—168no—
1068C2×C4C22×#4118yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C2×H(5,𝔽2)14yes—
1076C2×C4C2×H(5,𝔽2)14yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4C2×2−1+412yes—
1080C2×C4C2×2−1+412yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4#58512yes—
1083C22—28no—
1084C22—28no—
1085C22—28no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—44no—
1092C22—44no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—44no—
1097C22C23×#4111yescharacteristic
1098C22C23×#4111yescharacteristic
1099C22C22×H(5,𝔽2)11yescharacteristic
1100C22C22×H(5,𝔽2)11yescharacteristic
1101C22C22×2−1+411yescharacteristic
1102C22C2×#58511yescharacteristic
1103C222−1+611yescharacteristic
1104C4—22no—
1105C4—22no—
1106C4—24no—
1107C4—24no—
1108C4—22no—
1109C4—28no—
1110C4—42no—
1111C4—42no—
1112C4—44no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—48no—
1117C4—42no—
1118C4—41no—
1119C4—42no—
1120C4—44no—
1121C4—42no—
1122C4—42no—
1123C4—44no—
1124C4—42no—
1125C4#348114yes—
1126C4#351514yes—
1127C4#352214yes—
1128C2—48no—
1129C2—84no—
1130C2C2×#348111yescharacteristic
1131C2C2×#351511yescharacteristic
1132C2C2×#352211yescharacteristic
1133C2#6291311yescharacteristic
1134C2#6298411yescharacteristic
1135C2#6300711yescharacteristic
1136C2#6301411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59815C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59764C2semidirect
3. #59647C2semidirect
4. #59418C2semidirect
5. #59411C2semidirect
6. #59076C2semidirect
7. #45215C2semidirect
8. #44173C2semidirect
9. #40171C2semidirect
10. #40165C2semidirect
11. #39193C2semidirect
12. #39192C2semidirect
13. #36563C2semidirect
14. #36559C2semidirect
15. #36559C2semidirect
16. #36299C2semidirect
17. #36299C2semidirect
18. #36290C2semidirect
19. #36114C2semidirect
20. #35724C2semidirect
21. #34954C2semidirect
22. #34934C2semidirect
23. #34313C2semidirect
24. #34308C2semidirect
25. C4×#557C2semidirect
26. C4×#559C2semidirect

Maximal subgroups

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

subgroupindex
#598152
#597642
#596472
#594182
#594112
#590762
#452152
#441732
#401712
#401652
#391932
#391922
#365632
#365592
#362992
#362902
#361142
#357242
#349542
#349342
#343132
#343082
C4×#5572
C4×#5592