Finite Group Databasebeta

← #7631627

Subgroups — #7631627

Order 512.

7128 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C212yesmaximal, complemented
2#36561C212yesmaximal, complemented
3#36560C212yesmaximal, complemented
4#36473C212yesmaximal, complemented
5#36469C212yesmaximal, complemented
6#36272C212yesmaximal, complemented
7#36271C212yesmaximal, complemented
8#36188C212yesmaximal, complemented
9#36186C212yesmaximal, complemented
10#35959C214yesmaximal, complemented
11#35938C214yesmaximal, complemented
12#35834C214yesmaximal, complemented
13#35773C214yesmaximal, complemented
14#35628C212yesmaximal, complemented
15#35621C212yesmaximal, complemented
16#35464C218yesmaximal, complemented
17#35317C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35008C214yesmaximal, complemented
20#34938C211yesmaximal, characteristic, complemented
21#34937C211yesmaximal, characteristic
22#34763C214yesmaximal, complemented
23#34266C212yesmaximal, complemented
24#34206C211yesmaximal, characteristic, complemented
25C2×#2365C211yesmaximal, characteristic, complemented
26C4×#520C211yesmaximal, characteristic, complemented
27#3507—232no—
28C2×#559C2214yes—
29C2×#557C2214yes—
30C2×#556C2214yes—
31C2×#556C2214yes—
32C2×#556C2214yes—
33C2×#554C2214yes—
34C2×#552C2214yes—
35C2×#552C2214yes—
36C2×#539C2218yes—
37C2×#536C2212yes—
38C2×#536C2212yes—
39C2×#536C2212yes—
40C2×#533C2212yes—
41C2×#532C2212yes—
42C2×#532C2211yescharacteristic
43C22×C4⋊Q8C2211yescharacteristic
44C2×#529C2218yes—
45C2×#520C2211yescharacteristic
46C2×#520C2212yes—
47C2×#520C2211yescharacteristic
48C2×C4×#41C2211yescharacteristic
49C22×C4×Q8C2212yes—
50#2868C2212yes—
51#2860C2214yes—
52#2859C2214yes—
53#2858C2212yes—
54#2857C2212yes—
55#2857C2214yes—
56#2857C2212yes—
57#2854C2214yes—
58#2664C2218yes—
59#2663C2218yes—
60#2658C2214yes—
61#2621C2214yes—
62#2611C2218yes—
63#2604C2218yes—
64#2602C2218yes—
65#2601C2218yes—
66#2592C2214yes—
67#2592C2214yes—
68#2568C2214yes—
69#2568C2214yes—
70#2565C2218yes—
71#2564C2218yes—
72#2560C2218yes—
73#2557C2218yes—
74#2556C2218yes—
75#2556C2218yes—
76#2553C2218yes—
77#2553C2218yes—
78#2552C2211yescharacteristic
79#2552C2211yescharacteristic
80#2551C2211yescharacteristic
81#2551C2211yescharacteristic
82#2550C2212yes—
83#2550C2212yes—
84#2549C2214yes—
85#2548C2211yescharacteristic
86#2547C2214yes—
87#2547C2211yescharacteristic
88#2547C2212yes—
89#2547C2212yes—
90#2546C2214yes—
91#2546C2212yes—
92#2546C2211yescharacteristic
93#2546C2212yes—
94#2545C2214yes—
95#2545C2212yes—
96#2544C2214yes—
97#2544C2212yes—
98#2543C2214yes—
99#2542C2212yes—
100#2542C2212yes—
101#2542C2212yes—
102#2542C2212yes—
103#2541C2211yescharacteristic
104#2521C2218yes—
105#2521C2218yes—
106#2519C2218yes—
107#2519C2218yes—
108#2512C2214yes—
109#2506C2214yes—
110#2506C2218yes—
111#2506C2214yes—
112#2501C2214yes—
113#2501C2214yes—
114#2499C2218yes—
115#2498C2218yes—
116#2496C2214yes—
117#2496C2218yes—
118#2496C2214yes—
119#2492C2214yes—
120#2492C2214yes—
121#2491C2214yes—
122#2489C2214yes—
123#2489C2214yes—
124#2488C2218yes—
125#2488C2218yes—
126#2486C2214yes—
127#2486C2214yes—
128#2452C2214yes—
129#2440C2212yes—
130#2440C2212yes—
131#2425C2218yes—
132#2425C2218yes—
133#2422C2214yes—
134#2417C2214yes—
135#2417C2214yes—
136#2416C2212yes—
137#2416C2212yes—
138#2415C2214yes—
139#2415C2214yes—
140#2399C2214yes—
141#2396C2218yes—
142#2395C2218yes—
143#2392C2214yes—
144#2367C2214yes—
145#2367C2214yes—
146#2367C2214yes—
147#2366C2212yes—
148#2365C2212yes—
149#2365C2212yes—
150#2365C2214yes—
151#2365C2212yes—
152#2365C2212yes—
153#2365C2214yes—
154#2365C2214yes—
155#2365C2212yes—
156#2365C2214yes—
157#2362C2214yes—
158#2362C2214yes—
159#2360C2214yes—
160#2360C2214yes—
161#2354C2212yes—
162#2352C2214yes—
163D4×C4⋊C4C2212yes—
164#2325C2214yes—
165#2322C2218yes—
166#2311C2212yes—
167#2310C2212yes—
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2214yes—
171C4×#123C2218yes—
172C4×#121C2212yes—
173C4×#121C2214yes—
174C4×#121C2212yes—
175C4×#121C2214yes—
176#2297C2212yes—
177#2296C2212yes—
178C2×#391C2212yes—
179#2293C2214yes—
180C2×#389C2212yes—
181C2×#387C2214yes—
182#2285C2214yes—
183#2285C2211yescharacteristic
184#2276C2212yes—
185#2275C2212yes—
186#2275C2214yes—
187#2274C2211yescharacteristic
188#2274C2212yes—
189#2274C2211yescharacteristic
190#2274C2212yes—
191C42×Q8C2212yes—
192C42×D4C2212yes—
193C42×D4C2214yes—
194C4×#117C2212yes—
195C4×#117C2211yescharacteristic
196C2×C4×C4⋊C4C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2312yes—
201C22×#41C2311yescharacteristic
202C23×Q8C2312yes—
203#559—232no—
204#557—232no—
205#556—232no—
206#556—232no—
207#556—232no—
208#554—232no—
209#552—232no—
210#552—232no—
211#539—264no—
212#536—216no—
213#536—216no—
214#536—216no—
215#533—216no—
216#532—216no—
217#532—28no—
218C2×C4⋊Q8—28no—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2312yes—
232C2×#127C2311yescharacteristic
233C2×#127C2312yes—
234#529—264no—
235C2×#126C2318yes—
236C2×#126C2318yes—
237C2×#126C2318yes—
238C2×#126C2318yes—
239C2×#125C2318yes—
240C2×#125C2318yes—
241C2×#125C2312yes—
242C2×#125C2312yes—
243C2×#125C2318yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2312yes—
247C2×#124C2318yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#124C2314yes—
251C2×#123C2318yes—
252C2×#123C2318yes—
253C2×#123C2318yes—
254C2×#123C2318yes—
255C2×#123C2318yes—
256C2×C22⋊Q8C2318yes—
257C2×C22⋊Q8C2318yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×#121C2312yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272#520—28no—
273#520—216no—
274#520D4116yescomplemented
275C4×#41—28no—
276C2×C4×Q8—216no—
277C2×C4×Q8C2318yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×D4C2318yes—
290C2×C4×D4C2318yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C2×#117C2318yes—
308C2×#117C2314yes—
309C2×#117C2312yes—
310C2×#117C2318yes—
311C2×#117C2312yes—
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2311yescharacteristic
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2314yes—
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2312yes—
325C22×C42C2312yes—
326C22×C42C2314yes—
327C22×C42C2312yes—
328C22×C42C2314yes—
329C22×C42C2312yes—
330C22×C42C2311yescharacteristic
331#400C2318yes—
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#399C2318yes—
336#399C2318yes—
337#399C2318yes—
338#399C2318yes—
339#398C2318yes—
340#398C2314yes—
341#398C2318yes—
342#398C2318yes—
343#398C2314yes—
344#398C2318yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#397C2318yes—
349#397C2318yes—
350#397C2318yes—
351#397C2318yes—
352#397C2314yes—
353#397C2318yes—
354#397C2318yes—
355#396C2318yes—
356#396C2318yes—
357#396C2314yes—
358#396C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#394C2314yes—
364#394C2318yes—
365#394C2318yes—
366#394C2314yes—
367#394C2314yes—
368#393C2318yes—
369#393C2318yes—
370#392C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2318yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2312yes—
380#391C2312yes—
381#391C2314yes—
382#391C2314yes—
383#391C2318yes—
384#391C2314yes—
385#391C2314yes—
386#390C2314yes—
387#390C2314yes—
388#390C2312yes—
389#390C2312yes—
390#390C2314yes—
391#390C2314yes—
392#390C2314yes—
393#390C2314yes—
394#390C2312yes—
395#390C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2318yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2318yes—
406#389C2318yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2312yes—
414#389C2318yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2314yes—
432#388C2318yes—
433#388C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#386C2318yes—
444#386C2314yes—
445#386C2318yes—
446#386C2318yes—
447#386C2314yes—
448#386C2318yes—
449#386C2314yes—
450#386C2314yes—
451#385C2318yes—
452#385C2318yes—
453#385C2314yes—
454#385C2318yes—
455#385C2314yes—
456#384C2312yes—
457#384C2314yes—
458#384C2312yes—
459#384C2314yes—
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#384C2314yes—
463#384C2314yes—
464#382C2318yes—
465#382C2318yes—
466#382C2312yes—
467#381C2318yes—
468#380C2314yes—
469#380C2318yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473#380C2314yes—
474#380C2312yes—
475#380C2314yes—
476#380C2314yes—
477#380C2312yes—
478#380C2318yes—
479#380C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2318yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2311yescharacteristic
515C4×C4⋊C4C2311yescharacteristic
516C4×C4⋊C4C2311yescharacteristic
517C4×C4⋊C4C2311yescharacteristic
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2318yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2318yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2314yes—
533#376C2314yes—
534#376C2312yes—
535C2×#95C2314yes—
536C2×#95C2312yes—
537C2×#95C2314yes—
538C2×#95C2314yes—
539C2×#95C2312yes—
540C43C2312yes—
541C43C2314yes—
542C2×#41—28no—
543C2×#41—24no—
544C2×#41—24no—
545C2×#41—28no—
546C2×#41—28no—
547C2×#41C2×D418yes—
548C22×Q8—28no—
549C22×Q8—28no—
550C22×Q8—28no—
551C22×Q8C2414yes—
552C22×Q8C2414yes—
553C22×Q8C2412yes—
554C22×Q8C2414yes—
555C22×Q8C2411yescharacteristic
556C22×Q8C2414yes—
557C22×D4C2412yes—
558C22×D4C2414yes—
559C22×D4C2412yes—
560C22×D4C2414yes—
561C22×D4C2412yes—
562C22×D4C2411yescharacteristic
563C22×D4C2414yes—
564C22×D4C2412yes—
565C23×C4C2414yes—
566C23×C4C2414yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2411yescharacteristic
571C23×C4C2412yes—
572C23×C4C2418yes—
573C23×C4C2412yes—
574C23×C4C2414yes—
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2414yes—
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C4⋊Q8—28no—
581C4⋊Q8—216no—
582C4⋊Q8—28no—
583C4⋊Q8—28no—
584C4⋊Q8—28no—
585C4⋊Q8—216no—
586C4⋊Q8—28no—
587C4⋊Q8—28no—
588C4⋊Q8—28no—
589C4⋊Q8—28no—
590C4⋊Q8—24no—
591C4⋊Q8—216no—
592C4⋊Q8—44no—
593#127—28no—
594#127—24no—
595#126—232no—
596#126—232no—
597#126—232no—
598#126—232no—
599#125—232no—
600#125—28no—
601#125—28no—
602#125—232no—
603#125—232no—
604#124—28no—
605#124—28no—
606#124—216no—
607#124—232no—
608#124—216no—
609#124—28no—
610#124—216no—
611#123—232no—
612#123—232no—
613#123—232no—
614#123—232no—
615#123—232no—
616C22⋊Q8—216no—
617C22⋊Q8—216no—
618C22⋊Q8—232no—
619C22⋊Q8—216no—
620C22⋊Q8—216no—
621C22⋊Q8—232no—
622C22⋊Q8—216no—
623C22⋊Q8—216no—
624C22⋊Q8—216no—
625C22⋊Q8—216no—
626#121—216no—
627#121—216no—
628#121—28no—
629#121—28no—
630#121—28no—
631#121—44no—
632C4×Q8—216no—
633C4×Q8—216no—
634C4×Q8—216no—
635C4×Q8—216no—
636C4×Q8—216no—
637C4×Q8—232no—
638C4×Q8—216no—
639C4×Q8—216no—
640C4×Q8—24no—
641C4×Q8—24no—
642C4×Q8—28no—
643C4×Q8C2×D4116yes—
644C4×D4—232no—
645C4×D4—232no—
646C4×D4—216no—
647C4×D4—216no—
648C4×D4—28no—
649C4×D4—28no—
650C4×D4—216no—
651C4×D4—216no—
652C4×D4—24no—
653C4×D4—24no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—28no—
657C4×D4—48no—
658C4×D4C2×D4132yes—
659C4×D4C2×D4116yes—
660#117—28no—
661#117—232no—
662#117—24no—
663#117—216no—
664#117—28no—
665#117—232no—
666#117—28no—
667#117C2×D418yes—
668#117C2×D4116yes—
669#117#4118yes—
670C2×C4⋊C4—216no—
671C2×C4⋊C4—24no—
672C2×C4⋊C4—28no—
673C2×C4⋊C4—28no—
674C2×C4⋊C4—216no—
675C2×C4⋊C4—28no—
676C2×C4⋊C4—24no—
677C2×C4⋊C4—42no—
678C2×C4⋊C4C2×D418yes—
679C2×C4⋊C4C2×D4116yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2418yes—
713C2×C4⋊C4C2418yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2418yes—
716C2×C4⋊C4C2418yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2418yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2412yes—
760C2×C42—216no—
761C2×C42—28no—
762C2×C42—28no—
763C2×C42—44no—
764C2×C42—48no—
765C2×C42#4118yes—
766C2×C42C2418yes—
767C2×C42C2418yes—
768C2×C42C2412yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2418yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2414yes—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2414yes—
786C2×C42C2414yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2412yes—
790C2×C42C2411yescharacteristic
791C2×C42C2412yes—
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795#95C2414yes—
796#95C2412yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2418yes—
801#95C2412yes—
802#95C2412yes—
803#95C2418yes—
804#95C2412yes—
805#95C2412yes—
806#95C2418yes—
807#95C2418yes—
808#95C2412yes—
809#95C2414yes—
810#95C2414yes—
811#95C2412yes—
812#95C2412yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2418yes—
819#95C2418yes—
820#95C2418yes—
821#95C2414yes—
822#95C2414yes—
823#95C2418yes—
824#95C2418yes—
825#95C2418yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829C24C2514yes—
830C24C2512yes—
831C24C2511yescharacteristic
832#41—232no—
833#41—432no—
834C2×Q8—28no—
835C2×Q8—28no—
836C2×Q8—28no—
837C2×Q8—24no—
838C2×Q8—28no—
839C2×Q8—22no—
840C2×Q8—22no—
841C2×Q8—28no—
842C2×Q8—28no—
843C2×Q8—24no—
844C2×Q8—28no—
845C2×Q8—28no—
846C2×Q8—24no—
847C2×Q8—28no—
848C2×Q8—44no—
849C2×Q8—44no—
850C2×Q8—44no—
851C2×Q8—432no—
852C2×Q8C22×D414yes—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—28no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—28no—
860C2×D4—24no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—24no—
866C2×D4—24no—
867C2×D4—28no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—44no—
875C2×D4C22×D418yes—
876C2×D4C22×D414yes—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—28no—
883C22×C4—28no—
884C22×C4—28no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—28no—
888C22×C4—24no—
889C22×C4—28no—
890C22×C4—28no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—216no—
895C22×C4—24no—
896C22×C4—28no—
897C22×C4—42no—
898C22×C4—44no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—42no—
902C22×C4—44no—
903C22×C4—42no—
904C22×C4—44no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—48no—
908C22×C4—44no—
909C22×C4—48no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4C22×D418yes—
915C22×C4C22×D418yes—
916C22×C4C22×D4116yes—
917C22×C4C22×D414yes—
918C22×C4C2×#4114yes—
919C22×C4C2×#4114yes—
920C22×C4C2×#4114yes—
921C22×C4C2×#4114yes—
922C22×C4C2512yes—
923C22×C4C2512yes—
924C22×C4C2514yes—
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2518yes—
931C22×C4C2514yes—
932C22×C4C2514yes—
933C22×C4C2512yes—
934C22×C4C2512yes—
935C22×C4C2512yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2512yes—
939C22×C4C2511yescharacteristic
940C22×C4C2512yes—
941C22×C4C2512yes—
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C4⋊C4—24no—
946C4⋊C4—216no—
947C4⋊C4—216no—
948C4⋊C4—216no—
949C4⋊C4—24no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—216no—
953C4⋊C4—216no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—28no—
958C4⋊C4—28no—
959C4⋊C4—216no—
960C4⋊C4—216no—
961C4⋊C4—28no—
962C4⋊C4—24no—
963C4⋊C4—28no—
964C4⋊C4—24no—
965C4⋊C4—28no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—216no—
976C4⋊C4—216no—
977C4⋊C4—24no—
978C4⋊C4—22no—
979C4⋊C4—28no—
980C4⋊C4—24no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—24no—
984C4⋊C4—42no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—44no—
990C4⋊C4C22×D418yes—
991C4⋊C4C22×D414yes—
992C4⋊C4C22×D418yes—
993C4⋊C4C22×D4116yes—
994C4⋊C4C22×D414yes—
995C4⋊C4C2×#4114yes—
996C4⋊C4C2×#4114yes—
997C4⋊C42−1+414yes—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—216no—
1001C22⋊C4—28no—
1002C22⋊C4—216no—
1003C22⋊C4—24no—
1004C22⋊C4—28no—
1005C22⋊C4—216no—
1006C22⋊C4—216no—
1007C22⋊C4—28no—
1008C22⋊C4—216no—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—216no—
1015C22⋊C4—216no—
1016C22⋊C4—28no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—48no—
1020C22⋊C4—48no—
1021C22⋊C4—44no—
1022C22⋊C4C22×D418yes—
1023C22⋊C4C22×D4116yes—
1024C22⋊C4C2×#4118yes—
1025C42—216no—
1026C42—24no—
1027C42—24no—
1028C42—216no—
1029C42—24no—
1030C42—24no—
1031C42—216no—
1032C42—28no—
1033C42—24no—
1034C42—24no—
1035C42—24no—
1036C42—28no—
1037C42—24no—
1038C42—28no—
1039C42—24no—
1040C42—44no—
1041C42—44no—
1042C42—44no—
1043C42—42no—
1044C42—44no—
1045C42—42no—
1046C42—44no—
1047C42C22×D4116yes—
1048C42C22×D418yes—
1049C42C2×#4114yes—
1050C42C2×#4114yes—
1051C42C2×#4114yes—
1052C42C2×#4114yes—
1053C42C2×#4118yes—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—24no—
1065C23—24no—
1066C23—24no—
1067C23—24no—
1068C23—24no—
1069C23—24no—
1070C23—24no—
1071C23C23×D414yes—
1072C23C23×D412yes—
1073C23C22×#4112yes—
1074C23C22×#4112yes—
1075C23C2611yescharacteristic
1076Q8—28no—
1077Q8—416no—
1078Q8—416no—
1079Q8—416no—
1080Q8—48no—
1081Q8—88no—
1082D4—216no—
1083D4—28no—
1084D4—416no—
1085D4—416no—
1086D4—48no—
1087D4—48no—
1088D4—84no—
1089D4—88no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—22no—
1110C2×C4—216no—
1111C2×C4—28no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—28no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—28no—
1124C2×C4—24no—
1125C2×C4—28no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—48no—
1143C2×C4—416no—
1144C2×C4—44no—
1145C2×C4—48no—
1146C2×C4—416no—
1147C2×C4—416no—
1148C2×C4—48no—
1149C2×C4—816no—
1150C2×C4—88no—
1151C2×C4—84no—
1152C2×C4—84no—
1153C2×C4—84no—
1154C2×C4#532116yes—
1155C2×C4C23×D418yes—
1156C2×C4C23×D414yes—
1157C2×C4C23×D414yes—
1158C2×C4C23×D414yes—
1159C2×C4C23×D412yes—
1160C2×C4C23×D412yes—
1161C2×C4C22×#4112yes—
1162C2×C4C22×#4114yes—
1163C2×C4C22×#4112yes—
1164C2×C4C22×#4112yes—
1165C2×C4C22×#4114yes—
1166C2×C4C22×#4112yes—
1167C2×C4C22×#4112yes—
1168C2×C4C22×#4112yes—
1169C2×C4C22×#4112yes—
1170C2×C4C22×#4112yes—
1171C2×C4C2×2−1+414yes—
1172C2×C4C2×2−1+412yes—
1173C2×C4#58512yes—
1174C22—22no—
1175C22—22no—
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—22no—
1180C22—24no—
1181C22—24no—
1182C22—24no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—44no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—44no—
1192C22—44no—
1193C22—44no—
1194C22C2×#53214yes—
1195C22C24×D411yescharacteristic
1196C22C23×#4111yescharacteristic
1197C22C23×#4111yescharacteristic
1198C22C22×2−1+411yescharacteristic
1199C22C2×#58511yescharacteristic
1200C222−1+611yescharacteristic
1201C222−1+611yescharacteristic
1202C4—28no—
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—24no—
1207C4—24no—
1208C4—22no—
1209C4—22no—
1210C4—22no—
1211C4—24no—
1212C4—44no—
1213C4—42no—
1214C4—42no—
1215C4—44no—
1216C4—42no—
1217C4—44no—
1218C4—42no—
1219C4—42no—
1220C4—44no—
1221C4—48no—
1222C4C2×#53214yes—
1223C4C2×#53214yes—
1224C4#350714yescomplemented
1225C2—24no—
1226C2—44no—
1227C2—84no—
1228C2C22×#53211yescharacteristic
1229C2C2×#350711yescharacteristic
1230C2#6286011yescharacteristic
1231C2#6298811yescharacteristic
1232C2#6299511yescharacteristic
1233C2D4×2−1+411yescharacteristic
1234C2#6300111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3507C2semidirect
2. #36561C2semidirect
3. #36560C2semidirect
4. #36473C2semidirect
5. #36469C2semidirect
6. #36272C2semidirect
7. #36271C2semidirect
8. #36188C2semidirect
9. #36186C2semidirect
10. #35959C2semidirect
11. #35938C2semidirect
12. #35834C2semidirect
13. #35773C2semidirect
14. #35628C2semidirect
15. #35621C2semidirect
16. #35464C2semidirect
17. #35317C2semidirect
18. #35316C2semidirect
19. #35008C2semidirect
20. #34938C2semidirect
22. #34763C2semidirect
23. #34266C2semidirect
24. #34206C2semidirect
25. C2×#2365C2semidirect
26. C4×#520C2semidirect
274. #520D4semidirect
1224. C4#3507semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
#365612
#365602
#364732
#364692
#362722
#362712
#361882
#361862
#359592
#359382
#358342
#357732
#356282
#356212
#354642
#353172
#353162
#350082
#349382
#349372
#347632
#342662
#342062
C2×#23652
C4×#5202