Finite Group Databasebeta

← #7688534

Subgroups — #7688534

Order 512.

5269 conjugacy classes of subgroups.

The subgroup lattice has 1135 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#59697C214yesmaximal, complemented
3#59639C212yesmaximal, complemented
4#59418C212yesmaximal, complemented
5#59321C212yesmaximal, complemented
6#59098C214yesmaximal, complemented
7#45147C214yesmaximal, complemented
8#44410C218yesmaximal, complemented
9#40226C214yesmaximal, complemented
10#40079C214yesmaximal, complemented
11#39726C212yesmaximal, complemented
12#39488C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36593C211yesmaximal, characteristic, complemented
15#36508C212yesmaximal, complemented
16#36406C212yesmaximal, complemented
17#36302C212yesmaximal, complemented
18#36179C211yesmaximal, characteristic
19#36134C212yesmaximal, complemented
20#35745C214yesmaximal, complemented
21#34929C212yesmaximal, complemented
22#34929C211yesmaximal, characteristic, complemented
23#34316C212yesmaximal, complemented
24#34214C212yesmaximal, complemented
25C4×#559C211yesmaximal, characteristic, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#559C2211yescharacteristic
28C2×#557C2212yes—
29C2×#556C2211yescharacteristic
30C2×#556C2212yes—
31C2×#547C2212yes—
32C2×#547C2212yes—
33C2×#547C2212yes—
34C2×#533C2212yes—
35C2×#533C2214yes—
36#2868C2212yes—
37#2868C2211yescharacteristic
38#2862C2212yes—
39#2861C2214yes—
40#2857C2214yes—
41#2856C2212yes—
42#2798C2218yes—
43#2791C2218yes—
44#2777C2218yes—
45#2738C2218yes—
46#2727C2214yes—
47#2718C2218yes—
48#2718C2218yes—
49#2707C2218yes—
50#2707C2218yes—
51#2687C2218yes—
52#2681C2218yes—
53#2654C2218yes—
54#2620C2214yes—
55#2596C2218yes—
56#2592C2214yes—
57#2582C2212yes—
58#2571C2212yes—
59#2570C2214yes—
60#2568C2212yes—
61#2565C2214yes—
62#2558C2218yes—
63#2558C2218yes—
64#2556C2218yes—
65#2556C2214yes—
66#2553C2218yes—
67#2553C2218yes—
68#2552C2212yes—
69#2552C2214yes—
70#2552C2214yes—
71#2552C2214yes—
72#2552C2212yes—
73#2551C2211yescharacteristic
74#2548C2212yes—
75#2546C2212yes—
76#2546C2211yescharacteristic
77#2546C2214yes—
78#2545C2214yes—
79#2542C2212yes—
80#2542C2212yes—
81#2542C2211yescharacteristic
82#2542C2212yes—
83#2542C2212yes—
84#2538C2211yescharacteristic
85#2538C2212yes—
86#2538C2214yes—
87#2531C2218yes—
88#2522C2218yes—
89#2519C2218yes—
90#2519C2218yes—
91#2513C2214yes—
92#2512C2214yes—
93#2511C2214yes—
94#2511C2214yes—
95#2506C2214yes—
96#2506C2212yes—
97#2502C2214yes—
98#2501C2214yes—
99#2501C2214yes—
100#2501C2214yes—
101#2500C2214yes—
102#2499C2214yes—
103#2492C2212yes—
104#2492C2214yes—
105#2490C2214yes—
106#2476C2218yes—
107#2473C2218yes—
108#2470C2218yes—
109#2458C2218yes—
110#2452C2214yes—
111#2452C2212yes—
112#2448C2214yes—
113#2446C2214yes—
114#2442C2214yes—
115#2441C2218yes—
116#2432C2214yes—
117#2432C2214yes—
118#2429C2214yes—
119#2429C2214yes—
120#2429C2212yes—
121#2429C2214yes—
122#2429C2214yes—
123#2427C2214yes—
124#2427C2214yes—
125#2426C2214yes—
126#2423C2218yes—
127#2421C2214yes—
128#2415C2214yes—
129#2396C2214yes—
130#2396C2218yes—
131#2374C2218yes—
132#2374C2214yes—
133#2373C2214yes—
134#2367C2212yes—
135#2367C2212yes—
136#2367C2212yes—
137#2366C2211yescharacteristic
138#2365C2212yes—
139#2365C2211yescharacteristic
140#2363C2214yes—
141#2362C2214yes—
142#2362C2212yes—
143#2362C2214yes—
144#2360C2214yes—
145#2360C2214yes—
146#2360C2214yes—
147#2360C2218yes—
148#2357C2212yes—
149#2357C2212yes—
150#2356C2212yes—
151#2355C2214yes—
152#2355C2211yescharacteristic
153#2355C2211yescharacteristic
154#2355C2211yescharacteristic
155#2355C2212yes—
156#2355C2212yes—
157#2354C2211yescharacteristic
158#2354C2212yes—
159#2354C2214yes—
160Q8×C4⋊C4C2214yes—
161Q8×C4⋊C4C2212yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164#2347C2212yes—
165#2345C2214yes—
166#2341C2214yes—
167#2335C2218yes—
168#2330C2218yes—
169#2324C2214yes—
170#2317C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2214yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2214yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×#127C2211yescharacteristic
179C4×#126C2214yes—
180C4×#124C2212yes—
181C4×#124C2212yes—
182C4×#124C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×#123C2214yes—
187#2297C2214yes—
188#2293C2212yes—
189#2293C2214yes—
190C2×#384C2212yes—
191#2274C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2314yes—
200#559—28no—
201#557—48no—
202#556—28no—
203#556—48no—
204#547—216no—
205#547—48no—
206#547—48no—
207#533—216no—
208#533—416no—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2312yes—
219C2×#127C2311yescharacteristic
220C2×#126C2314yes—
221C2×#126C2318yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2318yes—
225C2×#125C2318yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#124C2314yes—
230C2×#123C2318yes—
231C2×#123C2314yes—
232C2×#123C2318yes—
233C2×#123C2318yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2318yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2318yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2312yes—
273C2×C4×D4C2311yescharacteristic
274C2×#117C2312yes—
275C2×#117C2314yes—
276C2×#117C2312yes—
277C2×#117C2314yes—
278C2×#117C2318yes—
279C22×C4⋊C4C2314yes—
280C22×C4⋊C4C2314yes—
281C22×C4⋊C4C2314yes—
282C22×C42C2312yes—
283C22×C42C2314yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2314yes—
288#400C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2314yes—
292#399C2318yes—
293#399C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2314yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2314yes—
311#396C2314yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#395C2314yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#393C2318yes—
322#393C2314yes—
323#391C2312yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2312yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#391C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2318yes—
344#390C2318yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2314yes—
349#390C2314yes—
350#390C2312yes—
351#390C2314yes—
352#390C2312yes—
353#390C2314yes—
354#390C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2318yes—
358#389C2318yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#389C2312yes—
378#389C2314yes—
379#389C2318yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2318yes—
394#388C2314yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2318yes—
407#388C2318yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#387C2318yes—
422#387C2314yes—
423#387C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2314yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2314yes—
433#385C2318yes—
434#385C2314yes—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2314yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2314yes—
443#384C2314yes—
444#384C2312yes—
445#384C2314yes—
446#384C2314yes—
447#384C2314yes—
448#384C2312yes—
449#384C2314yes—
450#384C2314yes—
451#383C2314yes—
452#382C2312yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#382C2312yes—
457#382C2312yes—
458#381C2314yes—
459#380C2312yes—
460#380C2318yes—
461#380C2314yes—
462#380C2318yes—
463#380C2318yes—
464#380C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2314yes—
523#376C2314yes—
524C43C2314yes—
525C43C2311yescharacteristic
526C43C2312yes—
527C43C2312yes—
528C2×#41—216no—
529C2×#41—48no—
530C2×#41—48no—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2414yes—
535C22×Q8C2414yes—
536C22×Q8C2411yescharacteristic
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2411yescharacteristic
540C22×D4C2412yes—
541C22×D4C2418yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2418yes—
548C23×C4C2414yes—
549C4⋊Q8—28no—
550C4⋊Q8—28no—
551C4⋊Q8—28no—
552C4⋊Q8—28no—
553C4⋊Q8—24no—
554C4⋊Q8—28no—
555C4⋊Q8—24no—
556C4⋊Q8—48no—
557C4⋊Q8—44no—
558C4⋊Q8—48no—
559#127—24no—
560#126—216no—
561#126—416no—
562#125—216no—
563#125—48no—
564#125—416no—
565#125—416no—
566#124—28no—
567#124—28no—
568#124—28no—
569#124—48no—
570#123—216no—
571#123—232no—
572#123—416no—
573#123—416no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—216no—
578C22⋊Q8—216no—
579C22⋊Q8—216no—
580C22⋊Q8—28no—
581C22⋊Q8—416no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585#121—216no—
586#121—48no—
587#121—48no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—24no—
591C4×Q8—24no—
592C4×Q8—216no—
593C4×Q8—28no—
594C4×Q8—24no—
595C4×Q8—24no—
596C4×Q8—28no—
597C4×Q8—24no—
598C4×Q8—48no—
599C4×Q8—416no—
600C4×Q8—48no—
601C4×Q8—48no—
602C4×Q8—48no—
603C4×Q8#4118yescomplemented
604C4×D4—28no—
605C4×D4—24no—
606C4×D4—28no—
607C4×D4—28no—
608C4×D4—28no—
609C4×D4—28no—
610C4×D4—24no—
611C4×D4—28no—
612C4×D4—44no—
613C4×D4#4118yes—
614#117—28no—
615#117—28no—
616#117—216no—
617#117—416no—
618#117—48no—
619C2×C4⋊C4—216no—
620C2×C4⋊C4—48no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2412yes—
705C2×C42—28no—
706C2×C42—48no—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2411yescharacteristic
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2418yes—
728C2×C42C2418yes—
729C2×C42C2418yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2412yes—
735C2×C42C2414yes—
736C2×C42C2412yes—
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2412yes—
746#95C2412yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2412yes—
752#95C2414yes—
753#95C2418yes—
754#95C2412yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774#95C2418yes—
775#95C2414yes—
776#95C2414yes—
777#95C2418yes—
778C24C2514yes—
779C24C2512yes—
780#41—832no—
781C2×Q8—22no—
782C2×Q8—28no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—28no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—28no—
791C2×Q8—24no—
792C2×Q8—28no—
793C2×Q8—28no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—24no—
797C2×Q8—44no—
798C2×Q8C2×#4114yes—
799C2×D4—216no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—42no—
810C2×D4—48no—
811C2×D4—48no—
812C2×D4—42no—
813C2×D4C2×#4114yes—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—216no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—44no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4C2×#4118yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2518yes—
846C22×C4C2514yes—
847C22×C4C2511yescharacteristic
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—216no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—22no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—216no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—22no—
884C4⋊C4—28no—
885C4⋊C4—24no—
886C4⋊C4—22no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—42no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4C2×#4114yes—
910C4⋊C4C2×#4114yes—
911C4⋊C4C2×#4118yes—
912C4⋊C4H(5,𝔽2)14yes—
913C4⋊C42−1+414yes—
914C4⋊C42−1+414yes—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—216no—
923C22⋊C4—28no—
924C22⋊C4—216no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4C2×#4118yes—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—28no—
946C42—28no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—28no—
952C42—22no—
953C42—28no—
954C42—24no—
955C42—28no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—22no—
960C42—22no—
961C42—24no—
962C42—44no—
963C42—44no—
964C42—41no—
965C42—42no—
966C42—42no—
967C42—44no—
968C42—48no—
969C42—48no—
970C42—48no—
971C42C2×#4114yes—
972C42C2×#4118yes—
973C42C2×#4114yes—
974C42H(5,𝔽2)14yes—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23C22×#4114yes—
989C23C2611yescharacteristic
990Q8—28no—
991Q8—416no—
992Q8—44no—
993Q8—48no—
994Q8—416no—
995Q8—48no—
996D4—28no—
997D4—48no—
998D4—48no—
999D4—84no—
1000D4—816no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—216no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—28no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—28no—
1041C2×C4—28no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—48no—
1057C2×C4—416no—
1058C2×C4—416no—
1059C2×C4—48no—
1060C2×C4—88no—
1061C2×C4—816no—
1062C2×C4C22×#4112yes—
1063C2×C4C22×#4114yes—
1064C2×C4C22×#4114yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4114yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C2×H(5,𝔽2)14yes—
1072C2×C4C2×H(5,𝔽2)12yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×H(5,𝔽2)12yes—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×2−1+414yes—
1077C2×C4C2×2−1+414yes—
1078C2×C4C2×2−1+412yes—
1079C2×C4C2×2−1+412yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—44no—
1092C22—44no—
1093C22—44no—
1094C22C23×#4111yescharacteristic
1095C22C23×#4111yescharacteristic
1096C22C22×H(5,𝔽2)11yescharacteristic
1097C22C22×H(5,𝔽2)11yescharacteristic
1098C22C22×2−1+411yescharacteristic
1099C22C22×2−1+411yescharacteristic
1100C222−1+611yescharacteristic
1101C4—22no—
1102C4—24no—
1103C4—24no—
1104C4—22no—
1105C4—24no—
1106C4—24no—
1107C4—24no—
1108C4—22no—
1109C4—24no—
1110C4—42no—
1111C4—44no—
1112C4—42no—
1113C4—41no—
1114C4—44no—
1115C4—48no—
1116C4—44no—
1117C4—42no—
1118C4—44no—
1119C4—44no—
1120C4—42no—
1121C4—42no—
1122C4#348214yes—
1123C4#350814yes—
1124C4#351114yes—
1125C2—44no—
1126C2—84no—
1127C2C2×#348211yescharacteristic
1128C2C2×#350811yescharacteristic
1129C2C2×#351111yescharacteristic
1130C2#6294611yescharacteristic
1131C2#6298511yescharacteristic
1132C2#6300111yescharacteristic
1133C2#6301611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36179C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59697C2semidirect
3. #59639C2semidirect
4. #59418C2semidirect
5. #59321C2semidirect
6. #59098C2semidirect
7. #45147C2semidirect
8. #44410C2semidirect
9. #40226C2semidirect
10. #40079C2semidirect
11. #39726C2semidirect
12. #39488C2semidirect
13. #36598C2semidirect
14. #36593C2semidirect
15. #36508C2semidirect
16. #36406C2semidirect
17. #36302C2semidirect
19. #36134C2semidirect
20. #35745C2semidirect
21. #34929C2semidirect
22. #34929C2semidirect
23. #34316C2semidirect
24. #34214C2semidirect
25. C4×#559C2semidirect
26. C4×#556C2semidirect
603. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598212
#596972
#596392
#594182
#593212
#590982
#451472
#444102
#402262
#400792
#397262
#394882
#365982
#365932
#365082
#364062
#363022
#361792
#361342
#357452
#349292
#343162
#342142
C4×#5592
C4×#5562