Finite Group Databasebeta

← #7655930

Subgroups — #7655930

Order 512.

6930 conjugacy classes of subgroups.

The subgroup lattice has 1147 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C212yesmaximal, complemented
2#42311C214yesmaximal, complemented
3#42310C214yesmaximal, complemented
4#41384C214yesmaximal, complemented
5#41375C214yesmaximal, complemented
6#40504C214yesmaximal, complemented
7#40495C214yesmaximal, complemented
8#39610C214yesmaximal, complemented
9#37866C214yesmaximal, complemented
10#37860C214yesmaximal, complemented
11#37557C212yesmaximal, complemented
12#37447C212yesmaximal, complemented
13#37442C212yesmaximal, complemented
14#36183C214yesmaximal, complemented
15#36021C214yesmaximal, complemented
16#35740C214yesmaximal, complemented
17#35119C211yesmaximal, characteristic, complemented
18#35051C211yesmaximal, characteristic, complemented
19#35011C211yesmaximal, characteristic, complemented
20#34642C211yesmaximal, characteristic, complemented
21#34575C211yesmaximal, characteristic, complemented
22C2×#2659C211yesmaximal, characteristic, complemented
23C2×#2353C211yesmaximal, characteristic, complemented
24#3520—232no—
25C2×#556C2212yes—
26C2×#554C2214yes—
27C2×#552C2212yes—
28C2×#552C2212yes—
29C2×#551C2214yes—
30C2×#551C2214yes—
31C2×D4×Q8C2212yes—
32C2×#548C2212yes—
33C2×#548C2212yes—
34C2×#547C2212yes—
35C2×#547C2212yes—
36C2×#546C2214yes—
37C2×#542C2214yes—
38C2×#539C2214yes—
39C2×#539C2214yes—
40C2×#533C2212yes—
41C2×#529C2212yes—
42C2×#525C2212yes—
43C2×#525C2212yes—
44C22×C22⋊Q8C2212yes—
45C22×C22⋊Q8C2212yes—
46C2×#520C2214yes—
47C22×C4×D4C2211yescharacteristic
48#2857C2214yes—
49#2854C2214yes—
50#2847C2214yes—
51#2821C2214yescomplemented
52#2821C2214yescomplemented
53#2817C2214yescomplemented
54#2816C2214yescomplemented
55#2814C2214yescomplemented
56#2814C2214yescomplemented
57#2720C2218yescomplemented
58#2718C2218yescomplemented
59#2717C2218yes—
60#2713C2218yescomplemented
61#2708C2218yes—
62#2706C2218yescomplemented
63#2698C2218yescomplemented
64#2692C2218yescomplemented
65#2686C2218yes—
66#2680C2218yescomplemented
67#2677C2218yescomplemented
68#2671C2218yes—
69#2663C2214yescomplemented
70#2661C2214yescomplemented
71#2660C2214yescomplemented
72#2660C2214yescomplemented
73#2659C2211yescharacteristic
74#2659C2211yescharacteristic
75#2659C2212yes—
76#2659C2214yes—
77#2659C2212yes—
78#2659C2212yes—
79#2659C2214yes—
80#2659C2211yescharacteristic
81#2659C2214yescomplemented
82#2659C2214yescomplemented
83#2656C2211yescharacteristic
84#2639C2212yes—
85#2639C2212yes—
86#2639C2212yes—
87#2638C2214yescomplemented
88#2638C2214yescomplemented
89#2634C2214yescomplemented
90#2634C2214yescomplemented
91#2633C2214yescomplemented
92#2632C2214yescomplemented
93#2627C2214yescomplemented
94#2625C2214yescomplemented
95#2623C2214yescomplemented
96#2618C2214yescomplemented
97#2617C2214yes—
98#2616C2214yescomplemented
99#2614C2214yescomplemented
100#2611C2214yescomplemented
101#2610C2214yescomplemented
102#2604C2214yescomplemented
103#2603C2214yescomplemented
104#2599C2214yescomplemented
105#2599C2214yescomplemented
106#2583C2214yescomplemented
107#2583C2214yescomplemented
108#2564C2218yes—
109#2564C2218yes—
110#2564C2214yescomplemented
111#2553C2218yescomplemented
112#2543C2214yescomplemented
113#2521C2218yescomplemented
114#2502C2214yescomplemented
115#2501C2214yescomplemented
116#2498C2218yes—
117#2498C2214yescomplemented
118#2496C2214yescomplemented
119#2496C2214yescomplemented
120#2491C2214yescomplemented
121#2488C2218yescomplemented
122#2486C2214yescomplemented
123#2484C2214yescomplemented
124#2478C2218yescomplemented
125#2474C2218yescomplemented
126#2473C2218yescomplemented
127#2468C2218yescomplemented
128#2465C2218yescomplemented
129#2462C2218yescomplemented
130#2461C2218yescomplemented
131#2449C2218yescomplemented
132#2443C2218yes—
133#2440C2214yescomplemented
134#2434C2214yescomplemented
135#2430C2218yes—
136#2430C2214yescomplemented
137#2422C2214yescomplemented
138#2419C2218yes—
139#2417C2218yes—
140#2412C2218yes—
141#2412C2218yes—
142#2409C2214yescomplemented
143#2406C2218yes—
144#2406C2214yescomplemented
145#2399C2214yescomplemented
146#2399C2214yescomplemented
147#2395C2214yescomplemented
148C2×#398C2214yescomplemented
149#2388C2214yescomplemented
150C2×#395C2214yescomplemented
151#2361C2214yescomplemented
152#2359C2218yescomplemented
153#2353C2214yes—
154#2353C2214yes—
155#2353C2214yes—
156#2353C2214yes—
157#2344C2214yescomplemented
158#2325C2214yes—
159#2325C2214yes—
160#2315C2214yes—
161C4×#121C2214yes—
162C2×#388C2212yes—
163C2×#387C2212yes—
164C2×#386C2212yes—
165#2285C2214yes—
166C2×#383C2211yescharacteristic
167C2×#381C2211yescharacteristic
168C2×#380C2214yes—
169C2×#380C2211yescharacteristic
170C2×C4×C22⋊C4C2211yescharacteristic
171C2×C4×C22⋊C4C2212yes—
172C2×#376C2211yescharacteristic
173C22×#95C2211yescharacteristic
174C22×#41C2314yes—
175C22×#41C2312yes—
176C22×#41C2312yes—
177C23×Q8C2312yes—
178C23×Q8C2312yes—
179C23×D4C2311yescharacteristic
180C24×C4C2312yes—
181C24×C4C2311yescharacteristic
182C24×C4C2311yescharacteristic
183#556—216no—
184#554—232no—
185#552—216no—
186#552—216no—
187#551—232no—
188#551—232no—
189D4×Q8—216no—
190#548—216no—
191#548—216no—
192#547—216no—
193#547—216no—
194#546—232no—
195#542—232no—
196#539—232no—
197#539—232no—
198#533—216no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203#529—216no—
204C2×#126C2314yes—
205C2×#126C2314yes—
206C2×#126C2314yes—
207C2×#126C2314yes—
208C2×#126C2314yes—
209C2×#125C2312yes—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#124C2312yes—
214C2×#124C2314yes—
215C2×#124C2314yes—
216C2×#124C2314yes—
217#525—216no—
218#525—216no—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×C22⋊Q8—216no—
231C2×C22⋊Q8—216no—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2318yes—
252C2×#121C2312yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#121C2312yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259C2×#121C2314yes—
260C2×#121C2314yes—
261C2×#120C2314yes—
262C2×#120C2314yes—
263#520—232no—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2314yes—
269C2×C4×D4D4116yescomplemented
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×#117C2314yes—
285C2×#117C2314yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C22×C4⋊C4C2314yes—
291C22×C4⋊C4C2314yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2314yes—
295C22×C4⋊C4C2314yes—
296C22×C4⋊C4C2314yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2311yescharacteristic
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2314yes—
302C22×C22⋊C4C2312yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C42C2312yes—
307C22×C42C2312yes—
308C22×C42C2311yescharacteristic
309#400C2318yes—
310#400C2314yes—
311#400C2314yes—
312#400C2318yes—
313#400C2318yes—
314#400C2314yes—
315#399C2318yes—
316#399C2318yes—
317#399C2314yes—
318#399C2318yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2318yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2318yes—
329#398C2318yes—
330#398C2314yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#397C2318yes—
336#397C2318yes—
337#397C2314yes—
338#397C2314yes—
339#397C2318yes—
340#397C2314yes—
341#397C2318yes—
342#397C2318yes—
343#397C2318yes—
344#396C2318yes—
345#396C2318yes—
346#395C2318yes—
347#395C2314yes—
348#395C2314yes—
349#395C2318yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2318yes—
358#395C2318yes—
359#395C2318yes—
360#395C2318yes—
361#394C2314yes—
362#394C2314yes—
363#394C2318yes—
364#394C2318yes—
365#394C2314yes—
366#394C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2318yes—
370#393C2318yes—
371#393C2318yes—
372#393C2314yes—
373#393C2314yes—
374#393C2314yes—
375#392C2314yes—
376#392C2318yes—
377#391C2318yes—
378#391C2318yes—
379#390C2314yes—
380#390C2314yes—
381#390C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#389C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#384C2314yes—
432#384C2314yes—
433#384C2314yes—
434#383C2314yes—
435#383C2314yes—
436#382C2318yes—
437#381C2314yes—
438#381C2318yes—
439#381C2314yes—
440#381C2318yes—
441#380C2318yes—
442#380C2318yes—
443#380C2318yes—
444#380C2314yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2318yes—
451#380C2314yes—
452#380C2318yes—
453#380C2314yes—
454#380C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2318yes—
458C4×C4⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2318yes—
466#376C2314yes—
467#376C2314yes—
468C2×#95C2312yes—
469C2×#95C2312yes—
470C2×#95C2314yes—
471C2×#95C2312yes—
472C2×#95C2312yes—
473C2×#95C2314yes—
474C2×#95C2318yes—
475C2×#95C2311yescharacteristic
476C2×#95C2311yescharacteristic
477C2×#95C2311yescharacteristic
478C2×#95C2311yescharacteristic
479C2×#95C2312yes—
480C25C2411yescharacteristic
481C25C2411yescharacteristic
482C2×#41—216no—
483C2×#41—28no—
484C2×#41—28no—
485C2×#41—48no—
486C2×#41—48no—
487C2×#41—84no—
488C2×#41—84no—
489C22×Q8—28no—
490C22×Q8—28no—
491C22×Q8—84no—
492C22×Q8—84no—
493C22×Q8C2414yes—
494C22×Q8C2412yes—
495C22×Q8C2412yes—
496C22×Q8C2412yes—
497C22×Q8C2414yes—
498C22×Q8C2414yes—
499C22×D4—42no—
500C22×D4—42no—
501C22×D4C2×D418yes—
502C22×D4C2414yes—
503C22×D4C2414yes—
504C22×D4C2412yes—
505C22×D4C2414yes—
506C22×D4C2412yes—
507C22×D4C2414yes—
508C22×D4C2414yes—
509C22×D4C2414yes—
510C22×D4C2412yes—
511C23×C4—28no—
512C23×C4—44no—
513C23×C4—82no—
514C23×C4—82no—
515C23×C4—82no—
516C23×C4C2×D418yes—
517C23×C4C2×D418yes—
518C23×C4C2414yes—
519C23×C4C2414yes—
520C23×C4C2411yescharacteristic
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2414yes—
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2412yes—
527C23×C4C2414yes—
528C23×C4C2414yes—
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2411yescharacteristic
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2411yescharacteristic
539C23×C4C2412yes—
540C4⋊Q8—216no—
541C4⋊Q8—28no—
542C4⋊Q8—28no—
543C4⋊Q8—84no—
544#126—216no—
545#126—216no—
546#126—216no—
547#126—216no—
548#126—216no—
549#125—216no—
550#125—216no—
551#125—28no—
552#125—216no—
553#124—216no—
554#124—216no—
555#124—216no—
556#124—28no—
557#123—216no—
558#123—216no—
559#123—216no—
560#123—216no—
561#123—216no—
562#123—216no—
563#123—216no—
564#123—216no—
565#123—216no—
566#123—416no—
567#123—88no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—216no—
572C22⋊Q8—216no—
573C22⋊Q8—28no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—216no—
578C22⋊Q8—216no—
579C22⋊Q8—28no—
580C22⋊Q8—28no—
581C22⋊Q8—216no—
582C22⋊Q8—216no—
583C22⋊Q8—216no—
584C22⋊Q8—216no—
585C22⋊Q8—216no—
586C22⋊Q8—216no—
587C22⋊Q8—88no—
588#121—216no—
589#121—216no—
590#121—216no—
591#121—28no—
592#121—28no—
593#121—28no—
594#121—216no—
595#121—48no—
596#121—84no—
597#120—216no—
598#120—216no—
599C4×Q8—216no—
600C4×Q8—216no—
601C4×Q8—28no—
602C4×Q8—28no—
603C4×Q8—28no—
604C4×D4—216no—
605C4×D4—216no—
606C4×D4—216no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—216no—
611C4×D4—216no—
612C4×D4—28no—
613C4×D4—84no—
614C4×D4C2×D4116yes—
615C4×D4C2×D4116yes—
616C4×D4C2×D4116yes—
617C4×D4C2×D4116yes—
618#117—28no—
619#117—28no—
620#117—216no—
621#117—216no—
622#117—216no—
623#117—216no—
624C2×C4⋊C4—216no—
625C2×C4⋊C4—216no—
626C2×C4⋊C4—28no—
627C2×C4⋊C4—28no—
628C2×C4⋊C4—216no—
629C2×C4⋊C4—48no—
630C2×C4⋊C4—84no—
631C2×C4⋊C4—82no—
632C2×C4⋊C4C2×D418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C22⋊C4—216no—
673C2×C22⋊C4—216no—
674C2×C22⋊C4—28no—
675C2×C22⋊C4—44no—
676C2×C22⋊C4—82no—
677C2×C22⋊C4C2×D418yes—
678C2×C22⋊C4C2×D418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2411yescharacteristic
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2411yescharacteristic
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2411yescharacteristic
712C2×C22⋊C4C2411yescharacteristic
713C2×C42—28no—
714C2×C42—82no—
715C2×C42C2×D418yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753C24—24no—
754C24—22no—
755C24—22no—
756C24—24no—
757C24—42no—
758C24—42no—
759C24—41no—
760C24—41no—
761C24C22×D414yes—
762C24C22×D414yes—
763C24C2514yes—
764C24C2512yes—
765C24C2511yescharacteristic
766C24C2511yescharacteristic
767C24C2511yescharacteristic
768#41—464no—
769#41—816no—
770#41—816no—
771C2×Q8—28no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—28no—
776C2×Q8—28no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—44no—
782C2×Q8—48no—
783C2×Q8—48no—
784C2×Q8—816no—
785C2×Q8—816no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—216no—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—24no—
797C2×D4—28no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—48no—
806C2×D4—48no—
807C2×D4—416no—
808C2×D4C22×D418yes—
809C2×D4C22×D418yes—
810C22×C4—24no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—44no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—42no—
854C22×C4—88no—
855C22×C4—88no—
856C22×C4—816no—
857C22×C4C22×D414yes—
858C22×C4C22×D414yes—
859C22×C4C22×D414yes—
860C22×C4C22×D414yes—
861C22×C4C22×D414yes—
862C22×C4C22×D418yes—
863C22×C4C22×D418yes—
864C22×C4C22×D418yes—
865C22×C4C22×D418yes—
866C22×C42−1+418yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2514yes—
871C22×C4C2514yes—
872C22×C4C2514yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2512yes—
884C22×C4C2514yes—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—24no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4C22×D418yes—
923C4⋊C4C22×D418yes—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—216no—
943C22⋊C4—216no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4C22×D414yes—
953C22⋊C4C22×D418yes—
954C22⋊C4C22×D414yes—
955C22⋊C4C22×D418yes—
956C22⋊C4C22×D414yes—
957C22⋊C4C22×D414yes—
958C42—28no—
959C42—28no—
960C42—28no—
961C42—28no—
962C42—28no—
963C42—28no—
964C42—28no—
965C42—44no—
966C42—44no—
967C42C22×D418yes—
968C42C22×D418yes—
969C23—22no—
970C23—21no—
971C23—21no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—22no—
976C23—21no—
977C23—21no—
978C23—22no—
979C23—22no—
980C23—24no—
981C23—22no—
982C23—28no—
983C23—28no—
984C23—28no—
985C23—24no—
986C23—28no—
987C23—24no—
988C23—24no—
989C23—28no—
990C23—44no—
991C23—44no—
992C23—44no—
993C23—48no—
994C23—48no—
995C23—84no—
996C23—84no—
997C23C23×D412yes—
998C23C23×D414yes—
999C23C23×D412yes—
1000C23C23×D412yes—
1001C23C2×2−1+414yes—
1002C23#58512yes—
1003C23#58512yes—
1004C23C2611yescharacteristic
1005Q8—48no—
1006Q8—48no—
1007Q8—48no—
1008Q8—416no—
1009Q8—88no—
1010Q8—88no—
1011D4—216no—
1012D4—48no—
1013D4—48no—
1014D4—416no—
1015D4—416no—
1016D4—416no—
1017D4—88no—
1018D4—88no—
1019D4—88no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—28no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—28no—
1056C2×C4—28no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—44no—
1066C2×C4—416no—
1067C2×C4—416no—
1068C2×C4—416no—
1069C2×C4—416no—
1070C2×C4—88no—
1071C2×C4—88no—
1072C2×C4—88no—
1073C2×C4—84no—
1074C2×C4—84no—
1075C2×C4—84no—
1076C2×C4—88no—
1077C2×C4—88no—
1078C2×C4C23×D412yes—
1079C2×C4C23×D412yes—
1080C2×C4C23×D414yes—
1081C2×C4C23×D414yes—
1082C2×C4C23×D412yes—
1083C2×C4C23×D414yes—
1084C2×C4C23×D412yes—
1085C2×C4C2×2−1+418yes—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—24no—
1090C22—24no—
1091C22—22no—
1092C22—24no—
1093C22—24no—
1094C22—22no—
1095C22—24no—
1096C22—24no—
1097C22—22no—
1098C22—24no—
1099C22—22no—
1100C22—416no—
1101C22—42no—
1102C22—44no—
1103C22—42no—
1104C22—44no—
1105C22—44no—
1106C22—44no—
1107C22—48no—
1108C22—44no—
1109C22—48no—
1110C22—88no—
1111C22#344914yes—
1112C22#349914yes—
1113C22C24×D411yescharacteristic
1114C22C22×2−1+412yes—
1115C22C2×#58511yescharacteristic
1116C22C2×#58511yescharacteristic
1117C22H(7,𝔽2)12yes—
1118C4—22no—
1119C4—22no—
1120C4—24no—
1121C4—22no—
1122C4—24no—
1123C4—22no—
1124C4—28no—
1125C4—24no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—44no—
1130C4—44no—
1131C4—44no—
1132C4—44no—
1133C4—44no—
1134C4—44no—
1135C4—44no—
1136C2—24no—
1137C2—24no—
1138C2—42no—
1139C2—44no—
1140C2—84no—
1141C2C2×#344911yescharacteristic
1142C2C2×#349911yescharacteristic
1143C2#6284211yescharacteristic
1144C2#6290312yes—
1145C2#6295812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3520C2semidirect
2. #42311C2semidirect
3. #42310C2semidirect
4. #41384C2semidirect
5. #41375C2semidirect
6. #40504C2semidirect
7. #40495C2semidirect
8. #39610C2semidirect
9. #37866C2semidirect
10. #37860C2semidirect
11. #37557C2semidirect
12. #37447C2semidirect
13. #37442C2semidirect
14. #36183C2semidirect
15. #36021C2semidirect
16. #35740C2semidirect
17. #35119C2semidirect
18. #35051C2semidirect
19. #35011C2semidirect
20. #34642C2semidirect
21. #34575C2semidirect
22. C2×#2659C2semidirect
23. C2×#2353C2semidirect
51. #2821C22semidirect
52. #2821C22semidirect
53. #2817C22semidirect
54. #2816C22semidirect
55. #2814C22semidirect
56. #2814C22semidirect
57. #2720C22semidirect
58. #2718C22semidirect
60. #2713C22semidirect
62. #2706C22semidirect
63. #2698C22semidirect
64. #2692C22semidirect
66. #2680C22semidirect
67. #2677C22semidirect
69. #2663C22semidirect
70. #2661C22semidirect
71. #2660C22semidirect
72. #2660C22semidirect
81. #2659C22semidirect
82. #2659C22semidirect
87. #2638C22semidirect
88. #2638C22semidirect
89. #2634C22semidirect
90. #2634C22semidirect
91. #2633C22semidirect
92. #2632C22semidirect
93. #2627C22semidirect
94. #2625C22semidirect
95. #2623C22semidirect
96. #2618C22semidirect
98. #2616C22semidirect
99. #2614C22semidirect
100. #2611C22semidirect
101. #2610C22semidirect
102. #2604C22semidirect
103. #2603C22semidirect
104. #2599C22semidirect
105. #2599C22semidirect
106. #2583C22semidirect
107. #2583C22semidirect
110. #2564C22semidirect
111. #2553C22semidirect
112. #2543C22semidirect
113. #2521C22semidirect
114. #2502C22semidirect
115. #2501C22semidirect
117. #2498C22semidirect
118. #2496C22semidirect
119. #2496C22semidirect
120. #2491C22semidirect
121. #2488C22semidirect
122. #2486C22semidirect
123. #2484C22semidirect
124. #2478C22semidirect
125. #2474C22semidirect
126. #2473C22semidirect
127. #2468C22semidirect
128. #2465C22semidirect
129. #2462C22semidirect
130. #2461C22semidirect
131. #2449C22semidirect
133. #2440C22semidirect
134. #2434C22semidirect
136. #2430C22semidirect
137. #2422C22semidirect
142. #2409C22semidirect
144. #2406C22semidirect
145. #2399C22semidirect
146. #2399C22semidirect
147. #2395C22semidirect
148. C2×#398C22semidirect
149. #2388C22semidirect
150. C2×#395C22semidirect
151. #2361C22semidirect
152. #2359C22semidirect
157. #2344C22semidirect
269. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
#423112
#423102
#413842
#413752
#405042
#404952
#396102
#378662
#378602
#375572
#374472
#374422
#361832
#360212
#357402
#351192
#350512
#350112
#346422
#345752
C2×#26592
C2×#23532