Finite Group Databasebeta

← #7699585

Subgroups — #7699585

Order 512.

7415 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C212yesmaximal, complemented
2#59817C211yesmaximal, characteristic, complemented
3#59654C212yesmaximal, complemented
4#59498C214yesmaximal, complemented
5#59178C218yesmaximal, complemented
6#59098C214yesmaximal, complemented
7#59066C212yesmaximal, complemented
8#59042C212yesmaximal, complemented
9#59037C214yesmaximal, complemented
10#36560C211yesmaximal, characteristic, complemented
11#36505C212yesmaximal, complemented
12#36473C212yesmaximal, complemented
13#36443C214yesmaximal, complemented
14#36404C212yesmaximal, complemented
15#36270C212yesmaximal, complemented
16#36232C214yesmaximal, complemented
17#36134C211yesmaximal, characteristic, complemented
18#36133C212yesmaximal, complemented
19#36127C211yesmaximal, characteristic, complemented
20#36114C212yesmaximal, complemented
21#36113C214yesmaximal, complemented
22C4×#556C211yesmaximal, characteristic, complemented
23C4×D4×Q8C212yesmaximal, complemented
24C4×#550C211yesmaximal, characteristic, complemented
25C4×#547C211yesmaximal, characteristic, complemented
26#34141C212yesmaximal, complemented
27#3482—232no—
28C2×#557C2212yes—
29C2×#556C2214yes—
30C2×#556C2211yescharacteristic
31C2×#552C2218yes—
32C2×#552C2214yes—
33C2×#550C2211yescharacteristic
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2212yes—
36C2×#548C2214yes—
37C2×#547C2211yescharacteristic
38C2×#547C2212yes—
39C2×#547C2214yes—
40C2×#533C2214yes—
41C2×#533C2212yes—
42C2×#532C2212yes—
43C2×#529C2218yes—
44C2×#529C2214yes—
45C2×C4×#41C2212yes—
46C2×C4×#41C2214yes—
47C2×C4×#41C2212yes—
48C22×C4×Q8C2214yes—
49#2868C2211yescharacteristic
50#2860C2214yes—
51#2859C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2855C2214yes—
55#2852C2218yes—
56#2851C2214yes—
57#2690C2218yes—
58#2687C2218yes—
59#2683C2214yes—
60#2681C2218yes—
61#2671C2218yes—
62#2604C2218yes—
63#2601C2218yes—
64#2599C2218yes—
65#2568C2212yes—
66#2565C2214yes—
67#2562C2214yes—
68#2558C2218yes—
69#2552C2212yes—
70#2551C2212yes—
71#2547C2212yes—
72#2546C2212yes—
73#2546C2212yes—
74#2542C2212yes—
75#2538C2212yes—
76#2538C2212yes—
77#2538C2212yes—
78#2537C2212yes—
79#2537C2212yes—
80#2536C2214yes—
81#2536C2214yes—
82#2521C2218yes—
83#2506C2214yes—
84#2506C2214yes—
85#2506C2214yes—
86#2496C2214yes—
87#2492C2214yes—
88#2491C2214yes—
89#2477C2218yes—
90#2476C2218yes—
91#2475C2218yes—
92#2473C2218yes—
93#2470C2218yes—
94#2470C2218yes—
95#2468C2218yes—
96#2466C2218yes—
97#2462C2218yes—
98#2461C2218yes—
99#2460C2218yes—
100#2459C2218yes—
101#2458C2218yes—
102#2457C2218yes—
103#2452C2214yes—
104#2452C2214yes—
105#2451C2214yes—
106#2446C2214yes—
107#2445C2214yes—
108#2443C2218yes—
109#2441C2214yes—
110#2440C2214yes—
111#2438C2218yes—
112#2432C2214yes—
113#2432C2214yes—
114#2429C2214yes—
115#2428C2214yes—
116#2427C2214yes—
117#2423C2214yes—
118#2422C2214yes—
119#2422C2214yes—
120#2422C2214yes—
121#2421C2214yes—
122#2420C2214yes—
123#2415C2214yes—
124#2409C2214yes—
125#2409C2214yes—
126#2407C2214yes—
127#2407C2214yes—
128#2373C2214yes—
129#2367C2214yes—
130#2367C2214yes—
131#2367C2212yes—
132#2366C2212yes—
133#2366C2211yescharacteristic
134#2366C2212yes—
135#2365C2214yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2212yes—
139#2365C2211yescharacteristic
140#2365C2211yescharacteristic
141#2364C2218yes—
142#2363C2214yes—
143#2363C2212yes—
144#2362C2214yes—
145#2362C2212yes—
146#2362C2212yes—
147#2361C2214yes—
148#2361C2212yes—
149#2361C2214yes—
150#2360C2218yes—
151#2360C2214yes—
152#2359C2214yes—
153#2356C2212yes—
154#2355C2211yescharacteristic
155#2354C2212yes—
156#2354C2211yescharacteristic
157#2354C2212yes—
158#2354C2211yescharacteristic
159#2354C2211yescharacteristic
160#2352C2214yes—
161Q8×C4⋊C4C2212yes—
162Q8×C4⋊C4C2211yescharacteristic
163D4×C4⋊C4C2211yescharacteristic
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2214yes—
167#2347C2212yes—
168#2344C2214yes—
169#2344C2212yes—
170#2341C2212yes—
171Q8×C22⋊C4C2214yes—
172#2339C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2214yes—
176C4×C4⋊Q8C2211yescharacteristic
177C4×#127C2212yes—
178C4×#127C2211yescharacteristic
179C4×#126C2214yes—
180C4×#124C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2218yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2214yes—
185C4×#123C2214yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188C4×#121C2214yes—
189#2297C2214yes—
190#2293C2214yes—
191#2290C2218yes—
192C42×Q8C2211yescharacteristic
193C42×Q8C2212yes—
194C42×D4C2214yes—
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2312yes—
201C22×#41C2312yes—
202C22×#41C2314yes—
203C23×Q8C2314yes—
204#557—216no—
205#556—232no—
206#556D4116yescomplemented
207#552—264no—
208#552—232no—
209#550—28no—
210D4×Q8—216no—
211D4×Q8—216no—
212#548—232no—
213#547—28no—
214#547—232no—
215#547—216no—
216#533—216no—
217#533—232no—
218#532—216no—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#127C2312yes—
228C2×#127C2311yescharacteristic
229#529—264no—
230#529—232no—
231C2×#126C2318yes—
232C2×#126C2318yes—
233C2×#126C2314yes—
234C2×#125C2314yes—
235C2×#125C2318yes—
236C2×#125C2314yes—
237C2×#125C2318yes—
238C2×#124C2314yes—
239C2×#124C2318yes—
240C2×#124C2312yes—
241C2×#123C2314yes—
242C2×#123C2318yes—
243C2×#123C2318yes—
244C2×#123C2318yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2318yes—
252C2×C22⋊Q8C2318yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#121C2318yes—
263C4×#41—216no—
264C4×#41—216no—
265C4×#41—232no—
266C2×C4×Q8—232no—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2318yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2318yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2318yes—
297C2×C4×D4C2318yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×#117C2318yes—
307C2×#117C2314yes—
308C2×#117C2318yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2314yes—
312C2×#117C2314yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2314yes—
318C22×C4⋊C4C2318yes—
319C22×C42C2314yes—
320C22×C42C2318yes—
321C22×C42C2314yes—
322C22×C42C2312yes—
323C22×C42C2312yes—
324#400C2318yes—
325#400C2318yes—
326#400C2318yes—
327#399C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#397C2318yes—
334#397C2318yes—
335#397C2318yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#395C2318yes—
340#395C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#393C2318yes—
349#393C2318yes—
350#392C2318yes—
351#391C2312yes—
352#391C2314yes—
353#391C2318yes—
354#391C2312yes—
355#391C2314yes—
356#391C2314yes—
357#391C2312yes—
358#391C2318yes—
359#391C2314yes—
360#391C2314yes—
361#391C2312yes—
362#391C2312yes—
363#390C2314yes—
364#390C2312yes—
365#390C2314yes—
366#390C2312yes—
367#390C2312yes—
368#390C2312yes—
369#390C2312yes—
370#390C2312yes—
371#390C2314yes—
372#390C2312yes—
373#390C2314yes—
374#390C2312yes—
375#390C2314yes—
376#390C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2312yes—
381#389C2314yes—
382#389C2318yes—
383#389C2312yes—
384#389C2314yes—
385#389C2312yes—
386#389C2312yes—
387#389C2314yes—
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2314yes—
397#389C2314yes—
398#389C2318yes—
399#389C2314yes—
400#389C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2318yes—
408#388C2318yes—
409#388C2314yes—
410#388C2318yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2314yes—
418#388C2318yes—
419#388C2314yes—
420#388C2318yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2314yes—
431#387C2318yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2318yes—
436#387C2318yes—
437#386C2314yes—
438#386C2314yes—
439#386C2314yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2314yes—
445#386C2314yes—
446#386C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2314yes—
455#385C2318yes—
456#385C2314yes—
457#385C2318yes—
458#385C2314yes—
459#384C2311yescharacteristic
460#384C2312yes—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2312yes—
464#384C2314yes—
465#384C2312yes—
466#384C2312yes—
467#384C2312yes—
468#383C2314yes—
469#382C2314yes—
470#382C2312yes—
471#381C2314yes—
472#381C2318yes—
473#380C2312yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2318yes—
479#380C2312yes—
480#380C2314yes—
481#380C2312yes—
482#380C2314yes—
483#380C2312yes—
484#380C2314yes—
485#380C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2318yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2311yescharacteristic
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2318yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2318yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2318yes—
532C4×C22⋊C4C2314yes—
533C4×C22⋊C4C2314yes—
534C4×C22⋊C4C2314yes—
535C4×C22⋊C4C2318yes—
536#376C2314yes—
537C2×#95C2314yes—
538C43C2314yes—
539C43C2311yescharacteristic
540C43C2312yes—
541C2×#41—28no—
542C2×#41—28no—
543C2×#41—28no—
544C2×#41—216no—
545C2×#41—28no—
546C2×#41—216no—
547C2×#41—48no—
548C2×#41—44no—
549C2×#41—44no—
550C22×Q8—216no—
551C22×Q8—216no—
552C22×Q8—48no—
553C22×Q8C2414yes—
554C22×Q8C2418yes—
555C22×Q8C2412yes—
556C22×Q8C2411yescharacteristic
557C22×Q8C2412yes—
558C22×D4C2411yescharacteristic
559C22×D4C2418yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2411yescharacteristic
563C22×D4C2412yes—
564C22×D4C2412yes—
565C22×D4C2414yes—
566C22×D4C2412yes—
567C23×C4C2412yes—
568C23×C4C2414yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2418yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2418yes—
576C23×C4C2412yes—
577C23×C4C2414yes—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C4⋊Q8—216no—
581C4⋊Q8—216no—
582C4⋊Q8—216no—
583C4⋊Q8—28no—
584C4⋊Q8—28no—
585C4⋊Q8—44no—
586C4⋊Q8C2×D418yes—
587C4⋊Q8#4118yescomplemented
588#127—28no—
589#127#4118yescomplemented
590#126—232no—
591#126—232no—
592#126C2×D4132yes—
593#125—232no—
594#125—216no—
595#125—232no—
596#125—216no—
597#124—216no—
598#124—232no—
599#124C2×D4116yes—
600#123—232no—
601#123—216no—
602#123—232no—
603#123—232no—
604C22⋊Q8—216no—
605C22⋊Q8—216no—
606C22⋊Q8—28no—
607C22⋊Q8—216no—
608C22⋊Q8—216no—
609C22⋊Q8—232no—
610C22⋊Q8—216no—
611C22⋊Q8—232no—
612C22⋊Q8—232no—
613C22⋊Q8—48no—
614C22⋊Q8C2×D4116yes—
615#121—216no—
616#121—216no—
617#121—216no—
618#121—28no—
619#121—216no—
620#121—28no—
621#121—232no—
622C4×Q8—216no—
623C4×Q8—28no—
624C4×Q8—28no—
625C4×Q8—232no—
626C4×Q8—216no—
627C4×Q8—216no—
628C4×Q8—216no—
629C4×Q8—232no—
630C4×Q8—28no—
631C4×Q8—28no—
632C4×Q8—24no—
633C4×Q8—44no—
634C4×Q8—42no—
635C4×Q8C2×D4116yes—
636C4×Q8C2×D418yes—
637C4×D4—28no—
638C4×D4—216no—
639C4×D4—216no—
640C4×D4—28no—
641C4×D4—216no—
642C4×D4—28no—
643C4×D4—216no—
644C4×D4—216no—
645C4×D4—216no—
646C4×D4—28no—
647C4×D4—24no—
648C4×D4—216no—
649C4×D4—232no—
650C4×D4—232no—
651C4×D4—28no—
652C4×D4—216no—
653C4×D4—24no—
654C4×D4—24no—
655C4×D4—28no—
656C4×D4—24no—
657C4×D4—42no—
658C4×D4—44no—
659C4×D4—48no—
660C4×D4C2×D418yes—
661#117—28no—
662#117—216no—
663#117—28no—
664#117—216no—
665#117—216no—
666#117—232no—
667#117—232no—
668#117—44no—
669#117C2×D4116yes—
670C2×C4⋊C4—232no—
671C2×C4⋊C4—216no—
672C2×C4⋊C4—28no—
673C2×C4⋊C4—28no—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2418yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2418yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2412yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C42—216no—
755C2×C42—216no—
756C2×C42—232no—
757C2×C42—28no—
758C2×C42—28no—
759C2×C42C2414yes—
760C2×C42C2412yes—
761C2×C42C2414yes—
762C2×C42C2418yes—
763C2×C42C2414yes—
764C2×C42C2411yescharacteristic
765C2×C42C2414yes—
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2412yes—
769C2×C42C2418yes—
770C2×C42C2412yes—
771C2×C42C2414yes—
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2414yes—
775C2×C42C2412yes—
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778C2×C42C2412yes—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2412yes—
782C2×C42C2411yescharacteristic
783C2×C42C2414yes—
784C2×C42C2412yes—
785C2×C42C2414yes—
786C2×C42C2411yescharacteristic
787C2×C42C2412yes—
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790#95C2412yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2412yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2412yes—
799#95C2412yes—
800#95C2412yes—
801#95C2414yes—
802#95C2418yes—
803#95C2414yes—
804#95C2412yes—
805#95C2412yes—
806#95C2418yes—
807#95C2414yes—
808#95C2414yes—
809#95C2418yes—
810#95C2414yes—
811#95C2418yes—
812#95C2414yes—
813#95C2414yes—
814#95C2412yes—
815#95C2414yes—
816#95C2412yes—
817#95C2418yes—
818#95C2418yes—
819#95C2414yes—
820#95C2414yes—
821#95C2418yes—
822#95C2418yes—
823#95C2418yes—
824C24C2512yes—
825C24C2512yes—
826C24C2514yes—
827#41—464no—
828#41—432no—
829#41—432no—
830C2×Q8—24no—
831C2×Q8—216no—
832C2×Q8—28no—
833C2×Q8—24no—
834C2×Q8—22no—
835C2×Q8—216no—
836C2×Q8—28no—
837C2×Q8—24no—
838C2×Q8—22no—
839C2×Q8—24no—
840C2×Q8—28no—
841C2×Q8—48no—
842C2×Q8—464no—
843C2×Q8C22×D418yes—
844C2×Q8C22×D414yes—
845C2×Q8C2×#4118yes—
846C2×D4—216no—
847C2×D4—28no—
848C2×D4—216no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—24no—
852C2×D4—28no—
853C2×D4—24no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—28no—
858C2×D4—24no—
859C2×D4—22no—
860C2×D4—22no—
861C2×D4—24no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—48no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4C22×D414yes—
870C2×D4C2×#4118yes—
871C2×D4C2×#4118yes—
872C2×D4C2×#4118yes—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—28no—
876C22×C4—28no—
877C22×C4—216no—
878C22×C4—28no—
879C22×C4—28no—
880C22×C4—28no—
881C22×C4—216no—
882C22×C4—216no—
883C22×C4—28no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—28no—
890C22×C4—24no—
891C22×C4—216no—
892C22×C4—28no—
893C22×C4—24no—
894C22×C4—28no—
895C22×C4—24no—
896C22×C4—28no—
897C22×C4—24no—
898C22×C4—28no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—44no—
903C22×C4—42no—
904C22×C4—44no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4C22×D418yes—
912C22×C4C2512yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2512yes—
916C22×C4C2511yescharacteristic
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2514yes—
922C22×C4C2518yes—
923C22×C4C2512yes—
924C22×C4C2512yes—
925C22×C4C2511yescharacteristic
926C22×C4C2514yes—
927C22×C4C2512yes—
928C22×C4C2511yescharacteristic
929C22×C4C2514yes—
930C22×C4C2511yescharacteristic
931C22×C4C2512yes—
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C4⋊C4—28no—
936C4⋊C4—216no—
937C4⋊C4—28no—
938C4⋊C4—216no—
939C4⋊C4—216no—
940C4⋊C4—28no—
941C4⋊C4—28no—
942C4⋊C4—216no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—216no—
946C4⋊C4—216no—
947C4⋊C4—216no—
948C4⋊C4—28no—
949C4⋊C4—22no—
950C4⋊C4—28no—
951C4⋊C4—22no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—22no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—22no—
958C4⋊C4—28no—
959C4⋊C4—24no—
960C4⋊C4—216no—
961C4⋊C4—28no—
962C4⋊C4—24no—
963C4⋊C4—22no—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—44no—
970C4⋊C4—42no—
971C4⋊C4—44no—
972C4⋊C4—48no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4C22×D414yes—
976C4⋊C4C22×D4116yes—
977C4⋊C4C22×D414yes—
978C4⋊C4C22×D418yes—
979C4⋊C4C22×D418yes—
980C4⋊C4C22×D418yes—
981C4⋊C4C2×#4118yes—
982C4⋊C4C2×#4118yes—
983C4⋊C42−1+414yes—
984C22⋊C4—28no—
985C22⋊C4—216no—
986C22⋊C4—28no—
987C22⋊C4—216no—
988C22⋊C4—216no—
989C22⋊C4—28no—
990C22⋊C4—216no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—28no—
994C22⋊C4—216no—
995C22⋊C4—24no—
996C22⋊C4—216no—
997C22⋊C4—28no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—24no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—48no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—42no—
1010C22⋊C4—44no—
1011C22⋊C4—48no—
1012C22⋊C4C22×D418yes—
1013C22⋊C4C22×D4116yes—
1014C22⋊C4C22×D4116yes—
1015C42—28no—
1016C42—24no—
1017C42—24no—
1018C42—24no—
1019C42—28no—
1020C42—28no—
1021C42—216no—
1022C42—28no—
1023C42—28no—
1024C42—216no—
1025C42—24no—
1026C42—24no—
1027C42—24no—
1028C42—24no—
1029C42—28no—
1030C42—24no—
1031C42—22no—
1032C42—22no—
1033C42—24no—
1034C42—22no—
1035C42—42no—
1036C42—41no—
1037C42—44no—
1038C42—44no—
1039C42—42no—
1040C42—44no—
1041C42C22×D4116yes—
1042C42C22×D414yes—
1043C42C22×D418yes—
1044C42C2×#4114yes—
1045C42C2×#4114yes—
1046C23—24no—
1047C23—24no—
1048C23—22no—
1049C23—22no—
1050C23—24no—
1051C23—22no—
1052C23—24no—
1053C23—22no—
1054C23—22no—
1055C23—24no—
1056C23—22no—
1057C23—24no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23C23×D414yes—
1066C23C22×#4118yes—
1067C23C2611yescharacteristic
1068Q8—216no—
1069Q8—216no—
1070Q8—28no—
1071Q8—432no—
1072Q8—416no—
1073D4—28no—
1074D4—216no—
1075D4—216no—
1076D4—48no—
1077D4—416no—
1078D4—416no—
1079D4—432no—
1080D4—44no—
1081D4—88no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—216no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—28no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—28no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—28no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—416no—
1135C2×C4—48no—
1136C2×C4—432no—
1137C2×C4—416no—
1138C2×C4—432no—
1139C2×C4—416no—
1140C2×C4—416no—
1141C2×C4—416no—
1142C2×C4—48no—
1143C2×C4—48no—
1144C2×C4—48no—
1145C2×C4—84no—
1146C2×C4C23×D414yes—
1147C2×C4C23×D414yes—
1148C2×C4C23×D412yes—
1149C2×C4C23×D418yes—
1150C2×C4C23×D414yes—
1151C2×C4C23×D412yes—
1152C2×C4C23×D412yes—
1153C2×C4C22×#4112yes—
1154C2×C4C22×#4112yes—
1155C2×C4C22×#4118yes—
1156C2×C4C22×#4112yes—
1157C2×C4C22×#4112yes—
1158C2×C4C22×#4112yes—
1159C2×C4C22×#4112yes—
1160C2×C4C2×2−1+414yes—
1161C2×C4C2×2−1+412yes—
1162C2×C4#58512yes—
1163C2×C4#58512yes—
1164C22—28no—
1165C22—24no—
1166C22—24no—
1167C22—28no—
1168C22—24no—
1169C22—28no—
1170C22—42no—
1171C22—44no—
1172C22—44no—
1173C22—42no—
1174C22—44no—
1175C22—42no—
1176C22—44no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22C24×D411yescharacteristic
1186C22C23×#4111yescharacteristic
1187C22C23×#4111yescharacteristic
1188C22C22×2−1+411yescharacteristic
1189C22C2×#58511yescharacteristic
1190C22C2×#58511yescharacteristic
1191C222−1+611yescharacteristic
1192C4—22no—
1193C4—24no—
1194C4—24no—
1195C4—22no—
1196C4—22no—
1197C4—24no—
1198C4—28no—
1199C4—24no—
1200C4—28no—
1201C4—42no—
1202C4—42no—
1203C4—44no—
1204C4—44no—
1205C4—42no—
1206C4—41no—
1207C4—42no—
1208C4—42no—
1209C4—48no—
1210C4—44no—
1211C4—42no—
1212C4D4×#4114yes—
1213C4D4×#4114yes—
1214C4#348214yescomplemented
1215C2—48no—
1216C2—44no—
1217C2—82no—
1218C2C2×D4×#4111yescharacteristic
1219C2C2×D4×#4111yescharacteristic
1220C2C2×#348211yescharacteristic
1221C2#6299111yescharacteristic
1222C2D4×2−1+411yescharacteristic
1223C2#6300711yescharacteristic
1224C2#6303411yescharacteristic
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×#3482C2semidirect
2. #59817C2semidirect
3. #59654C2semidirect
4. #59498C2semidirect
5. #59178C2semidirect
6. #59098C2semidirect
7. #59066C2semidirect
8. #59042C2semidirect
9. #59037C2semidirect
10. #36560C2semidirect
11. #36505C2semidirect
12. #36473C2semidirect
13. #36443C2semidirect
14. #36404C2semidirect
15. #36270C2semidirect
16. #36232C2semidirect
17. #36134C2semidirect
18. #36133C2semidirect
19. #36127C2semidirect
20. #36114C2semidirect
21. #36113C2semidirect
22. C4×#556C2semidirect
23. C4×D4×Q8C2semidirect
24. C4×#550C2semidirect
25. C4×#547C2semidirect
26. #34141C2semidirect
206. #556D4semidirect
587. C4⋊Q8#41semidirect
589. #127#41semidirect
1214. C4#3482semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
#598172
#596542
#594982
#591782
#590982
#590662
#590422
#590372
#365602
#365052
#364732
#364432
#364042
#362702
#362322
#361342
#361332
#361272
#361142
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C4×#5562
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C4×#5472
#341412