Finite Group Databasebeta

← #7671986

Subgroups — #7671986

Order 512.

4866 conjugacy classes of subgroups.

The subgroup lattice has 1117 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59871C211yesmaximal, characteristic, complemented
3#59870C211yesmaximal, characteristic, complemented
4#59832C211yesmaximal, characteristic, complemented
5#59667C212yesmaximal, complemented
6#59663C214yesmaximal
7#59456C212yesmaximal, complemented
8#59321C212yesmaximal
9#59151C212yesmaximal
10#39975C214yesmaximal, complemented
11#39703C214yesmaximal, complemented
12#39653C214yesmaximal, complemented
13#38446C214yesmaximal
14#36635C211yesmaximal, characteristic
15#36564C212yesmaximal
16#36552C212yesmaximal
17#36545C214yesmaximal
18#36466C212yesmaximal, complemented
19#36286C212yesmaximal, complemented
20#36280C214yesmaximal
21#35582C214yesmaximal, complemented
22#35239C212yesmaximal
23#35208C212yesmaximal, complemented
24#34335C212yesmaximal, complemented
25#34235C212yesmaximal
26C4×#533C211yesmaximal, characteristic
27C2×C4×C4⋊Q8C211yesmaximal, characteristic
28C2×Q82C2212yes—
29C2×#557C2214yes—
30C2×#533C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C22×C4×Q8C2212yes—
33#2864C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2863C2214yes—
37#2862C2211yescharacteristic
38#2859C2211yescharacteristic
39#2859C2214yes—
40#2857C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2214yes—
43#2855C2212yes—
44#2855C2212yes—
45#2851C2212yes—
46#2851C2214yes—
47#2806C2214yes—
48#2806C2214yes—
49#2805C2214yes—
50#2802C2218yes—
51#2791C2218yes—
52#2755C2218yes—
53#2755C2218yes—
54#2734C2218yes—
55#2734C2214yes—
56#2713C2218yes—
57#2666C2218yes—
58#2666C2218yes—
59#2612C2218yes—
60#2606C2218yes—
61#2605C2218yes—
62#2590C2218yes—
63#2588C2218yes—
64#2586C2218yes—
65#2585C2218yes—
66#2584C2218yes—
67#2584C2214yes—
68#2584C2214yes—
69#2584C2214yes—
70#2582C2214yes—
71#2582C2214yes—
72#2582C2212yes—
73#2581C2214yes—
74#2581C2214yes—
75#2571C2212yes—
76#2570C2214yes—
77#2568C2212yes—
78#2567C2212yes—
79#2567C2212yes—
80#2567C2212yes—
81#2565C2214yes—
82#2552C2212yes—
83#2552C2212yes—
84#2552C2214yes—
85#2552C2212yes—
86#2552C2212yes—
87#2551C2214yes—
88#2551C2214yes—
89#2551C2212yes—
90#2551C2212yes—
91#2550C2214yes—
92#2550C2218yes—
93#2549C2218yes—
94#2546C2214yes—
95#2511C2214yes—
96#2511C2214yes—
97#2511C2214yes—
98#2509C2214yes—
99#2508C2214yes—
100#2507C2214yes—
101#2507C2214yes—
102#2507C2214yes—
103#2507C2214yes—
104#2506C2214yes—
105#2506C2214yes—
106#2505C2218yes—
107#2502C2214yes—
108#2473C2218yes—
109#2473C2218yes—
110#2462C2218yes—
111#2462C2218yes—
112#2462C2218yes—
113#2453C2214yes—
114#2453C2214yes—
115#2451C2214yes—
116#2451C2214yes—
117#2451C2214yes—
118#2451C2214yes—
119#2451C2214yes—
120#2446C2218yes—
121#2442C2214yes—
122#2440C2214yes—
123#2440C2214yes—
124#2438C2218yes—
125#2434C2218yes—
126#2369C2212yes—
127#2369C2214yes—
128#2369C2212yes—
129#2365C2214yes—
130#2365C2212yes—
131#2365C2212yes—
132#2365C2218yes—
133#2365C2212yes—
134#2365C2212yes—
135#2365C2212yes—
136#2360C2214yes—
137#2360C2214yes—
138#2360C2218yes—
139#2360C2214yes—
140#2356C2214yes—
141#2355C2212yes—
142#2355C2214yes—
143#2355C2214yes—
144#2351C2214yes—
145#2351C2214yes—
146Q8×C4⋊C4C2212yes—
147Q8×C4⋊C4C2212yes—
148Q8×C4⋊C4C2212yes—
149#2345C2214yes—
150#2343C2218yes—
151#2336C2218yes—
152#2331C2218yes—
153#2331C2214yes—
154#2330C2214yes—
155#2320C2214yes—
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2212yes—
158C4×C4⋊Q8C2212yes—
159C4×C4⋊Q8C2211yescharacteristic
160C4×C4⋊Q8C2211yescharacteristic
161C4×C4⋊Q8C2211yescharacteristic
162C4×C4⋊Q8C2214yes—
163C4×C4⋊Q8C2212yes—
164C4×C4⋊Q8C2211yescharacteristic
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2211yescharacteristic
167C4×C4⋊Q8C2211yescharacteristic
168C4×C4⋊Q8C2211yescharacteristic
169C4×C4⋊Q8C2211yescharacteristic
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×#125C2212yes—
174C4×#125C2212yes—
175C4×#125C2212yes—
176C4×C22⋊Q8C2212yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184#2296C2212yes—
185#2295C2212yes—
186#2295C2212yes—
187#2295C2214yes—
188#2295C2212yes—
189#2295C2212yes—
190C2×#391C2212yes—
191C2×#389C2212yes—
192C2×#389C2212yes—
193#2285C2211yescharacteristic
194C2×#384C2211yescharacteristic
195#2283C2212yes—
196#2276C2214yes—
197C42×Q8C2212yes—
198C42×Q8C2212yes—
199C4×#117C2212yes—
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2312yes—
204Q82—216no—
205#557—416no—
206#533Q8116yescomplemented
207C2×C4⋊Q8—28no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2318yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2318yes—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#125C2318yes—
227C2×#125C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C4×Q8—48no—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2318yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2314yes—
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#395C2318yes—
294#395C2318yes—
295#395C2318yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#391C2312yes—
303#391C2314yes—
304#391C2312yes—
305#391C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2318yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2318yes—
322#391C2318yes—
323#391C2314yes—
324#391C2312yes—
325#391C2318yes—
326#391C2318yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2318yes—
332#391C2312yes—
333#391C2318yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2312yes—
344#389C2314yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2318yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2312yes—
379#389C2318yes—
380#389C2318yes—
381#389C2314yes—
382#389C2318yes—
383#389C2318yes—
384#389C2314yes—
385#389C2318yes—
386#389C2318yes—
387#389C2314yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2312yes—
392#389C2318yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
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#387C2314yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#384C2312yes—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2312yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2314yes—
449#384C2314yes—
450#384C2314yes—
451#384C2314yes—
452#384C2314yes—
453#383C2318yes—
454#383C2314yes—
455#382C2312yes—
456#382C2312yes—
457#382C2314yes—
458#382C2314yes—
459#382C2312yes—
460#382C2318yes—
461#382C2318yes—
462#382C2312yes—
463#381C2314yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469#380C2318yes—
470#380C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2318yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2318yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2318yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C22⋊C4C2318yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521#376C2314yes—
522#376C2318yes—
523#376C2314yes—
524C2×#95C2314yes—
525C2×#95C2314yes—
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2314yes—
535C22×Q8—28no—
536C22×Q8—44no—
537C22×Q8—44no—
538C22×Q8C2412yes—
539C22×Q8C2414yes—
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×Q8C2418yes—
544C22×Q8C2412yes—
545C22×Q8C2412yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2414yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2414yes—
555C4⋊Q8—28no—
556C4⋊Q8—232no—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559C4⋊Q8—216no—
560C4⋊Q8—216no—
561C4⋊Q8—24no—
562C4⋊Q8—24no—
563C4⋊Q8—24no—
564C4⋊Q8—48no—
565C4⋊Q8—416no—
566C4⋊Q8C2×Q818yescomplemented
567C4⋊Q8C2×Q818yescomplemented
568C4⋊Q8#4118yes—
569#125—28no—
570#125—48no—
571#125—48no—
572#125—416no—
573#125—416no—
574#125C2×Q8116yescomplemented
575C22⋊Q8—28no—
576C22⋊Q8—416no—
577C22⋊Q8—44no—
578C22⋊Q8C2×Q8116yes—
579C22⋊Q8C2×Q8116yes—
580C4×Q8—216no—
581C4×Q8—216no—
582C4×Q8—28no—
583C4×Q8—28no—
584C4×Q8—216no—
585C4×Q8—28no—
586C4×Q8—28no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—44no—
590C4×Q8—44no—
591C4×Q8—44no—
592C4×Q8—416no—
593C4×Q8—48no—
594C4×Q8—44no—
595C4×Q8—48no—
596C4×Q8—48no—
597C4×Q8—48no—
598C4×Q8C2×Q8116yescomplemented
599C4×Q8C2×Q8116yescomplemented
600#117—44no—
601#117C2×Q8116yes—
602C2×C4⋊C4—28no—
603C2×C4⋊C4—28no—
604C2×C4⋊C4—28no—
605C2×C4⋊C4—44no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C42—24no—
677C2×C42—24no—
678C2×C42—24no—
679C2×C42—24no—
680C2×C42—48no—
681C2×C42—42no—
682C2×C42—42no—
683C2×C42C2×Q818yes—
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2414yes—
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2418yes—
709C2×C42C2418yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2414yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774C24C2511yescharacteristic
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—28no—
778C2×Q8—24no—
779C2×Q8—216no—
780C2×Q8—24no—
781C2×Q8—28no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—44no—
791C2×Q8—42no—
792C2×Q8—48no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—48no—
796C2×Q8—432no—
797C2×Q8C22×Q818yes—
798C2×Q8C22×Q818yes—
799C2×Q8C2×#4118yes—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—44no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4C22×Q814yes—
824C22×C4C22×Q814yes—
825C22×C4C22×Q814yes—
826C22×C42−1+414yes—
827C22×C4C2514yes—
828C22×C4C2511yescharacteristic
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2514yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—216no—
858C4⋊C4—28no—
859C4⋊C4—216no—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—44no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—42no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4C22×Q818yes—
910C4⋊C4C22×Q818yes—
911C4⋊C4C22×Q8116yes—
912C4⋊C4C22×Q8116yes—
913C4⋊C4C22×Q818yes—
914C4⋊C4C22×Q818yes—
915C4⋊C4C2×#4118yes—
916C4⋊C4C2×#4118yes—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4C22×Q8116yes—
921C42—22no—
922C42—22no—
923C42—22no—
924C42—216no—
925C42—28no—
926C42—28no—
927C42—22no—
928C42—22no—
929C42—22no—
930C42—28no—
931C42—28no—
932C42—28no—
933C42—22no—
934C42—22no—
935C42—22no—
936C42—22no—
937C42—22no—
938C42—22no—
939C42—22no—
940C42—28no—
941C42—22no—
942C42—22no—
943C42—28no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—41no—
948C42—41no—
949C42—41no—
950C42—44no—
951C42—44no—
952C42—44no—
953C42—44no—
954C42—48no—
955C42—48no—
956C42—48no—
957C42C22×Q814yes—
958C42C22×Q814yes—
959C42C22×Q814yes—
960C42C22×Q814yes—
961C42C22×Q8116yes—
962C42C2×#4114yes—
963C42H(5,𝔽2)14yes—
964C422−1+414yes—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23C23×Q812yes—
970C23C2×2−1+412yes—
971C23#58512yes—
972C23C2611yescharacteristic
973Q8—216no—
974Q8—216no—
975Q8—48no—
976Q8—416no—
977Q8—48no—
978Q8—48no—
979Q8—816no—
980Q8—84no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—24no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—28no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—21no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—416no—
1046C2×C4—88no—
1047C2×C4C23×Q812yes—
1048C2×C4C23×Q812yes—
1049C2×C4C23×Q812yes—
1050C2×C4C23×Q812yes—
1051C2×C4C23×Q818yes—
1052C2×C4C23×Q818yes—
1053C2×C4C23×Q812yes—
1054C2×C4C23×Q812yes—
1055C2×C4C22×#4118yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C2×H(5,𝔽2)12yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
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—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22#350214yes—
1075C22C24×Q811yescharacteristic
1076C22C23×#4111yescharacteristic
1077C22C22×H(5,𝔽2)11yescharacteristic
1078C22C22×2−1+411yescharacteristic
1079C22C22×2−1+411yescharacteristic
1080C22C2×#58511yescharacteristic
1081C22C2×#58511yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—28no—
1085C4—22no—
1086C4—22no—
1087C4—22no—
1088C4—22no—
1089C4—28no—
1090C4—22no—
1091C4—22no—
1092C4—22no—
1093C4—28no—
1094C4—44no—
1095C4—44no—
1096C4—44no—
1097C4—44no—
1098C4—44no—
1099C4—41no—
1100C4—44no—
1101C4—44no—
1102C4—41no—
1103C4—44no—
1104C4—44no—
1105C4Q8×#4114yes—
1106C4#350314yes—
1107C4#352314yes—
1108C2—24no—
1109C2C2×Q8×#4111yescharacteristic
1110C2#6277311yescharacteristic
1111C2C2×#350211yescharacteristic
1112C2C2×#352311yescharacteristic
1113C2C2×#350311yescharacteristic
1114C2#6283111yescharacteristic
1115C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59871C2semidirect
3. #59870C2semidirect
4. #59832C2semidirect
5. #59667C2semidirect
7. #59456C2semidirect
10. #39975C2semidirect
11. #39703C2semidirect
12. #39653C2semidirect
18. #36466C2semidirect
19. #36286C2semidirect
21. #35582C2semidirect
23. #35208C2semidirect
24. #34335C2semidirect
206. #533Q8semidirect
566. C4⋊Q8C2×Q8semidirect
567. C4⋊Q8C2×Q8semidirect
574. #125C2×Q8semidirect
598. C4×Q8C2×Q8semidirect
599. C4×Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598712
#598702
#598322
#596672
#596632
#594562
#593212
#591512
#399752
#397032
#396532
#384462
#366352
#365642
#365522
#365452
#364662
#362862
#362802
#355822
#352392
#352082
#343352
#342352
C4×#5332
C2×C4×C4⋊Q82