Finite Group Databasebeta

← #7688551

Subgroups — #7688551

Order 512.

7211 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C212yesmaximal, complemented
2#59823C211yesmaximal, characteristic, complemented
3#59444C212yesmaximal, complemented
4#59312C212yesmaximal, complemented
5#59312C214yesmaximal, complemented
6#59052C212yesmaximal, complemented
7#59047C214yesmaximal, complemented
8#45217C214yesmaximal, complemented
9#43497C218yesmaximal, complemented
10#39385C212yesmaximal, complemented
11#39384C214yesmaximal, complemented
12#39139C212yesmaximal, complemented
13#39134C214yesmaximal, complemented
14#36596C212yesmaximal, complemented
15#36593C211yesmaximal, characteristic, complemented
16#36259C212yesmaximal, complemented
17#36179C212yesmaximal, complemented
18#36179C211yesmaximal, characteristic, complemented
19#36134C211yesmaximal, characteristic, complemented
20#36117C212yesmaximal, complemented
21#36020C214yesmaximal, complemented
22#34934C211yesmaximal, characteristic, complemented
23C2×#2552C212yesmaximal, complemented
24#34308C212yesmaximal, complemented
25C4×#554C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic, complemented
27#3515—232no—
28C2×#557C2212yes—
29C2×#554C2212yes—
30C2×#554C2211yescharacteristic
31C2×#553C2214yes—
32C2×#552C2214yes—
33C2×#552C2214yes—
34C2×#552C2218yes—
35C2×#547C2212yes—
36C2×#547C2212yes—
37C2×#547C2214yes—
38C2×#547C2211yescharacteristic
39C2×#547C2214yes—
40C2×#547C2212yes—
41C2×#541C2214yes—
42C2×#539C2218yes—
43C2×#533C2212yes—
44C2×#529C2214yes—
45C2×#529C2212yes—
46C22×#125C2214yes—
47C2×#520C2214yes—
48C2×C4×#41C2212yes—
49#2868C2211yescharacteristic
50#2868C2212yes—
51#2857C2212yes—
52#2856C2212yes—
53#2856C2214yes—
54#2854C2214yes—
55#2732C2218yes—
56#2732C2214yes—
57#2727C2218yes—
58#2721C2218yes—
59#2721C2218yes—
60#2721C2218yes—
61#2721C2218yes—
62#2721C2218yes—
63#2694C2218yes—
64#2694C2218yes—
65#2694C2218yes—
66#2621C2214yes—
67#2618C2218yes—
68#2554C2214yes—
69#2554C2218yes—
70#2552C2212yes—
71#2552C2214yes—
72#2552C2211yescharacteristic
73#2552C2218yes—
74#2552C2214yes—
75#2552C2212yes—
76#2552C2214yes—
77#2552C2214yes—
78#2552C2212yes—
79#2552C2214yes—
80#2552C2214yes—
81#2552C2212yes—
82#2552C2214yes—
83#2548C2211yescharacteristic
84#2546C2214yes—
85#2546C2212yes—
86#2543C2218yes—
87#2542C2212yes—
88#2542C2212yes—
89#2542C2212yes—
90#2542C2214yes—
91#2542C2214yes—
92#2542C2212yes—
93#2542C2212yes—
94#2541C2211yescharacteristic
95#2538C2212yes—
96#2538C2211yescharacteristic
97#2538C2212yes—
98#2538C2214yes—
99#2536C2214yes—
100#2512C2214yes—
101#2512C2214yes—
102#2512C2212yes—
103#2512C2214yes—
104#2501C2214yes—
105#2501C2214yes—
106#2501C2218yes—
107#2501C2214yes—
108#2501C2214yes—
109#2501C2218yes—
110#2501C2214yes—
111#2490C2212yes—
112#2490C2214yes—
113#2486C2214yes—
114#2486C2218yes—
115#2479C2218yes—
116#2479C2218yes—
117#2454C2214yes—
118#2454C2214yes—
119#2448C2214yes—
120#2445C2214yes—
121#2445C2212yes—
122#2441C2214yes—
123#2441C2218yes—
124#2441C2214yes—
125#2429C2214yes—
126#2429C2214yes—
127#2429C2214yes—
128#2426C2212yes—
129#2425C2218yes—
130#2425C2218yes—
131#2425C2218yes—
132#2423C2214yes—
133#2423C2214yes—
134#2423C2218yes—
135#2417C2214yes—
136#2417C2214yes—
137#2416C2214yes—
138#2415C2214yes—
139#2413C2218yes—
140#2413C2218yes—
141#2413C2218yes—
142#2392C2214yes—
143C2×#398C2218yes—
144#2370C2212yes—
145#2369C2211yescharacteristic
146#2368C2214yes—
147#2366C2212yes—
148#2365C2212yes—
149#2365C2211yescharacteristic
150#2363C2214yes—
151#2362C2212yes—
152#2361C2214yes—
153#2361C2212yes—
154#2360C2214yes—
155#2360C2212yes—
156#2359C2218yes—
157#2359C2214yes—
158#2355C2211yescharacteristic
159#2354C2214yes—
160#2354C2212yes—
161#2354C2211yescharacteristic
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2212yes—
165#2349C2212yes—
166D4×C4⋊C4C2211yescharacteristic
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2211yescharacteristic
169#2345C2212yes—
170#2344C2214yes—
171#2344C2212yes—
172#2339C2214yes—
173#2339C2212yes—
174#2323C2214yes—
175#2322C2218yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×#127C2212yes—
180C4×#127C2211yescharacteristic
181C4×#125C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2214yes—
185C4×#123C2214yes—
186C4×#121C2214yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2293C2212yes—
190C2×#389C2214yes—
191C2×#389C2214yes—
192C2×#384C2214yes—
193C2×#384C2212yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2312yes—
201C22×#41C2314yes—
202#557—216no—
203#554—216no—
204#554D4116yescomplemented
205#553—232no—
206#552—232no—
207#552—264no—
208#552—232no—
209#547—232no—
210#547—216no—
211#547—216no—
212#547—28no—
213#547—416no—
214#547—48no—
215#541—232no—
216#539—264no—
217#533—216no—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#127C2312yes—
227#529—232no—
228#529—216no—
229C2×#126C2318yes—
230C2×#126C2314yes—
231C2×#126C2318yes—
232C2×#126C2318yes—
233C2×#125—232no—
234C2×#125C2312yes—
235C2×#125C2314yes—
236C2×#125C2318yes—
237C2×#125C2318yes—
238C2×#125C2314yes—
239C2×#125C2314yes—
240C2×#125C2318yes—
241C2×#125C2318yes—
242C2×#125C2312yes—
243C2×#124C2312yes—
244C2×#123C2318yes—
245C2×#123C2314yes—
246C2×#123C2318yes—
247C2×#123C2318yes—
248C2×#123C2318yes—
249C2×#123C2314yes—
250C2×#123C2318yes—
251C2×#123C2318yes—
252C2×#123C2318yes—
253C2×#123C2318yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2318yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2312yes—
270C2×#121C2318yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2318yes—
274C2×#121C2314yes—
275#520—232no—
276C4×#41—216no—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4C2312yes—
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2318yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2314yes—
297C2×C4×D4C2318yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×#117C2314yes—
308C2×#117C2314yes—
309C2×#117C2318yes—
310C2×#117C2312yes—
311C2×#117C2314yes—
312C2×#117C2318yes—
313C22×C4⋊C4C2318yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2318yes—
319C22×C4⋊C4C2314yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2318yes—
323C22×C4⋊C4C2312yes—
324C22×C42C2314yes—
325C22×C42C2312yes—
326C22×C42C2312yes—
327C22×C42C2314yes—
328#399C2318yes—
329#399C2318yes—
330#399C2318yes—
331#399C2318yes—
332#399C2318yes—
333#399C2318yes—
334#399C2318yes—
335#399C2318yes—
336#399C2318yes—
337#398C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2314yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#397C2318yes—
350#397C2318yes—
351#397C2314yes—
352#397C2318yes—
353#396C2318yes—
354#396C2318yes—
355#396C2318yes—
356#396C2318yes—
357#396C2314yes—
358#396C2314yes—
359#396C2318yes—
360#396C2318yes—
361#394C2314yes—
362#394C2318yes—
363#394C2314yes—
364#394C2314yes—
365#394C2318yes—
366#392C2314yes—
367#391C2314yes—
368#391C2312yes—
369#391C2312yes—
370#391C2314yes—
371#391C2312yes—
372#391C2312yes—
373#391C2314yes—
374#390C2312yes—
375#390C2312yes—
376#390C2314yes—
377#390C2314yes—
378#390C2312yes—
379#390C2312yes—
380#390C2312yes—
381#390C2312yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2314yes—
386#390C2318yes—
387#390C2314yes—
388#390C2318yes—
389#390C2314yes—
390#390C2312yes—
391#390C2312yes—
392#390C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2314yes—
401#389C2318yes—
402#389C2312yes—
403#389C2314yes—
404#389C2314yes—
405#389C2312yes—
406#389C2314yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2318yes—
412#389C2318yes—
413#389C2318yes—
414#389C2318yes—
415#389C2314yes—
416#389C2314yes—
417#389C2318yes—
418#389C2318yes—
419#389C2314yes—
420#389C2318yes—
421#389C2312yes—
422#389C2312yes—
423#388C2314yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2314yes—
429#388C2318yes—
430#388C2318yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2318yes—
435#388C2314yes—
436#388C2318yes—
437#387C2314yes—
438#387C2314yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#386C2318yes—
449#386C2318yes—
450#386C2314yes—
451#386C2314yes—
452#386C2318yes—
453#386C2318yes—
454#386C2314yes—
455#385C2314yes—
456#385C2318yes—
457#385C2318yes—
458#385C2314yes—
459#385C2314yes—
460#385C2314yes—
461#385C2314yes—
462#384C2312yes—
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#384C2311yescharacteristic
466#384C2312yes—
467#384C2314yes—
468#384C2314yes—
469#384C2312yes—
470#384C2314yes—
471#384C2314yes—
472#384C2312yes—
473#384C2312yes—
474#384C2314yes—
475#384C2314yes—
476#384C2318yes—
477#384C2314yes—
478#384C2318yes—
479#384C2314yes—
480#384C2314yes—
481#382C2312yes—
482#381C2318yes—
483#381C2314yes—
484#380C2314yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2314yes—
489#380C2314yes—
490#380C2314yes—
491#380C2318yes—
492#380C2318yes—
493#380C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2311yescharacteristic
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2311yescharacteristic
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2311yescharacteristic
523C4×C4⋊C4C2311yescharacteristic
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2314yes—
531C4×C22⋊C4C2312yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2318yes—
534C4×C22⋊C4C2314yes—
535C4×C22⋊C4C2312yes—
536C2×#95C2314yes—
537C2×#95C2318yes—
538C2×#95C2314yes—
539C43C2312yes—
540C43C2311yescharacteristic
541C2×#41—28no—
542C2×#41—216no—
543C2×#41—28no—
544C2×#41—216no—
545C2×#41—28no—
546C2×#41—216no—
547C22×Q8C2414yes—
548C22×Q8C2412yes—
549C22×Q8C2411yescharacteristic
550C22×Q8C2412yes—
551C22×D4C2412yes—
552C22×D4C2411yescharacteristic
553C22×D4C2412yes—
554C22×D4C2418yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2412yes—
559C22×D4C2411yescharacteristic
560C23×C4C2418yes—
561C23×C4C2414yes—
562C23×C4C2414yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2414yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2414yes—
570C23×C4C2418yes—
571C23×C4C2412yes—
572C23×C4C2414yes—
573C4⋊Q8—28no—
574C4⋊Q8—216no—
575C4⋊Q8—28no—
576C4⋊Q8—24no—
577C4⋊Q8—44no—
578C4⋊Q8—48no—
579C4⋊Q8C2×D418yes—
580#127—24no—
581#127—44no—
582#126—232no—
583#126—216no—
584#126—232no—
585#126—232no—
586#125—28no—
587#125—216no—
588#125—232no—
589#125—232no—
590#125—216no—
591#125—216no—
592#125—232no—
593#125—232no—
594#125C2×D4116yes—
595#124—28no—
596#123—216no—
597#123—232no—
598#123—232no—
599#123—232no—
600#123—232no—
601#123—232no—
602#123—216no—
603#123—416no—
604#123—416no—
605#123—416no—
606C22⋊Q8—28no—
607C22⋊Q8—216no—
608C22⋊Q8—232no—
609C22⋊Q8—216no—
610C22⋊Q8—216no—
611C22⋊Q8—216no—
612C22⋊Q8—216no—
613C22⋊Q8—28no—
614C22⋊Q8—48no—
615C22⋊Q8—48no—
616C22⋊Q8—48no—
617C22⋊Q8C2×D4116yes—
618C22⋊Q8C2×D4132yes—
619#121—216no—
620#121—232no—
621#121—216no—
622#121—28no—
623#121—28no—
624#121—28no—
625#121—416no—
626#121—48no—
627C4×Q8—216no—
628C4×Q8—216no—
629C4×Q8—28no—
630C4×Q8—216no—
631C4×Q8—24no—
632C4×Q8—28no—
633C4×Q8—216no—
634C4×Q8—24no—
635C4×Q8—44no—
636C4×Q8C2×D418yes—
637C4×D4—28no—
638C4×D4—28no—
639C4×D4—24no—
640C4×D4—216no—
641C4×D4—232no—
642C4×D4—216no—
643C4×D4—216no—
644C4×D4—232no—
645C4×D4—216no—
646C4×D4—28no—
647C4×D4—28no—
648C4×D4—24no—
649C4×D4—24no—
650C4×D4—48no—
651C4×D4—42no—
652C4×D4—44no—
653C4×D4—48no—
654C4×D4C2×D418yes—
655C4×D4C2×D4116yes—
656C4×D4#4118yes—
657#117—28no—
658#117—232no—
659#117—216no—
660#117—216no—
661#117—232no—
662#117—216no—
663C2×C4⋊C4—232no—
664C2×C4⋊C4—216no—
665C2×C4⋊C4—232no—
666C2×C4⋊C4—28no—
667C2×C4⋊C4—216no—
668C2×C4⋊C4—216no—
669C2×C4⋊C4—28no—
670C2×C4⋊C4—44no—
671C2×C4⋊C4—48no—
672C2×C4⋊C4—416no—
673C2×C4⋊C4C2×D4116yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2418yes—
713C2×C4⋊C4C2418yes—
714C2×C4⋊C4C2418yes—
715C2×C4⋊C4C2418yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2418yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C42—216no—
764C2×C42—28no—
765C2×C42—28no—
766C2×C42—48no—
767C2×C42C2414yes—
768C2×C42C2412yes—
769C2×C42C2418yes—
770C2×C42C2418yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2411yescharacteristic
774C2×C42C2414yes—
775C2×C42C2411yescharacteristic
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2411yescharacteristic
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2412yes—
786C2×C42C2411yescharacteristic
787C2×C42C2412yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2412yes—
791C2×C42C2411yescharacteristic
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794#95C2412yes—
795#95C2414yes—
796#95C2412yes—
797#95C2418yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2418yes—
805#95C2418yes—
806#95C2414yes—
807#95C2412yes—
808#95C2412yes—
809#95C2414yes—
810#95C2414yes—
811#95C2412yes—
812#95C2412yes—
813#95C2412yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2412yes—
818#95C2412yes—
819#95C2414yes—
820#95C2418yes—
821#95C2418yes—
822#95C2414yes—
823#95C2414yes—
824C24C2512yes—
825C24C2514yes—
826C24C2512yes—
827#41—432no—
828#41—464no—
829C2×Q8—24no—
830C2×Q8—28no—
831C2×Q8—28no—
832C2×Q8—24no—
833C2×Q8—28no—
834C2×Q8—24no—
835C2×Q8—22no—
836C2×Q8—22no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8C22×D414yes—
840C2×Q8C22×D418yes—
841C2×D4—28no—
842C2×D4—216no—
843C2×D4—216no—
844C2×D4—28no—
845C2×D4—28no—
846C2×D4—216no—
847C2×D4—24no—
848C2×D4—28no—
849C2×D4—22no—
850C2×D4—24no—
851C2×D4—22no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—28no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—22no—
859C2×D4—44no—
860C2×D4—42no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—42no—
865C2×D4C22×D414yes—
866C2×D4C2×#4114yes—
867C2×D4H(5,𝔽2)14yes—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—28no—
873C22×C4—216no—
874C22×C4—216no—
875C22×C4—28no—
876C22×C4—28no—
877C22×C4—24no—
878C22×C4—216no—
879C22×C4—28no—
880C22×C4—28no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—28no—
884C22×C4—28no—
885C22×C4—24no—
886C22×C4—28no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—28no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—216no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—42no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—48no—
903C22×C4—44no—
904C22×C4C22×D418yes—
905C22×C4C22×D4116yes—
906C22×C4C2×#4118yes—
907C22×C4C2512yes—
908C22×C4C2512yes—
909C22×C4C2512yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2512yes—
913C22×C4C2511yescharacteristic
914C22×C4C2512yes—
915C22×C4C2518yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2512yes—
919C22×C4C2512yes—
920C22×C4C2511yescharacteristic
921C22×C4C2512yes—
922C22×C4C2514yes—
923C22×C4C2511yescharacteristic
924C22×C4C2512yes—
925C22×C4C2511yescharacteristic
926C22×C4C2512yes—
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C4⋊C4—24no—
931C4⋊C4—216no—
932C4⋊C4—28no—
933C4⋊C4—24no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—216no—
937C4⋊C4—216no—
938C4⋊C4—216no—
939C4⋊C4—216no—
940C4⋊C4—216no—
941C4⋊C4—216no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—216no—
947C4⋊C4—22no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—216no—
953C4⋊C4—28no—
954C4⋊C4—24no—
955C4⋊C4—22no—
956C4⋊C4—24no—
957C4⋊C4—28no—
958C4⋊C4—24no—
959C4⋊C4—22no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—24no—
965C4⋊C4—44no—
966C4⋊C4—42no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—48no—
970C4⋊C4—48no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—42no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—42no—
977C4⋊C4—48no—
978C4⋊C4—44no—
979C4⋊C4C22×D418yes—
980C4⋊C4C22×D414yes—
981C4⋊C4C22×D418yes—
982C4⋊C4C22×D4116yes—
983C4⋊C4C22×D414yes—
984C4⋊C4C22×D4116yes—
985C4⋊C4C22×D418yes—
986C4⋊C4C2×#4114yes—
987C4⋊C42−1+414yes—
988C22⋊C4—28no—
989C22⋊C4—24no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—28no—
994C22⋊C4—28no—
995C22⋊C4—216no—
996C22⋊C4—216no—
997C22⋊C4—216no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—24no—
1001C22⋊C4—28no—
1002C22⋊C4—216no—
1003C22⋊C4—28no—
1004C22⋊C4—24no—
1005C22⋊C4—28no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—48no—
1009C22⋊C4—42no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—48no—
1014C22⋊C4—48no—
1015C22⋊C4—48no—
1016C22⋊C4C22×D4116yes—
1017C22⋊C4C22×D418yes—
1018C22⋊C4C2×#4118yes—
1019C42—24no—
1020C42—28no—
1021C42—24no—
1022C42—24no—
1023C42—28no—
1024C42—28no—
1025C42—216no—
1026C42—216no—
1027C42—24no—
1028C42—22no—
1029C42—24no—
1030C42—24no—
1031C42—24no—
1032C42—24no—
1033C42—22no—
1034C42—24no—
1035C42—24no—
1036C42—28no—
1037C42—22no—
1038C42—44no—
1039C42—44no—
1040C42—41no—
1041C42—42no—
1042C42C22×D414yes—
1043C42C22×D418yes—
1044C42C2×#4114yes—
1045C422−1+414yes—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—24no—
1051C23—22no—
1052C23—24no—
1053C23—22no—
1054C23—22no—
1055C23—24no—
1056C23—22no—
1057C23—24no—
1058C23—22no—
1059C23—24no—
1060C23—24no—
1061C23—22no—
1062C23—22no—
1063C23—24no—
1064C23C23×D414yes—
1065C23C22×#4114yes—
1066C23C2×H(5,𝔽2)14yes—
1067C23C2611yescharacteristic
1068Q8—28no—
1069Q8—48no—
1070Q8—48no—
1071Q8—416no—
1072D4—416no—
1073D4—432no—
1074D4—48no—
1075D4—44no—
1076D4—48no—
1077D4—88no—
1078D4—88no—
1079D4—84no—
1080D4#550116yes—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—24no—
1099C2×C4—216no—
1100C2×C4—216no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—28no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—28no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—28no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—21no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—416no—
1135C2×C4—416no—
1136C2×C4—48no—
1137C2×C4—416no—
1138C2×C4—432no—
1139C2×C4—48no—
1140C2×C4—416no—
1141C2×C4—48no—
1142C2×C4—816no—
1143C2×C4—84no—
1144C2×C4—88no—
1145C2×C4C23×D414yes—
1146C2×C4C23×D414yes—
1147C2×C4C23×D412yes—
1148C2×C4C23×D418yes—
1149C2×C4C23×D414yes—
1150C2×C4C23×D412yes—
1151C2×C4C23×D412yes—
1152C2×C4C22×#4112yes—
1153C2×C4C22×#4114yes—
1154C2×C4C22×#4112yes—
1155C2×C4C22×#4112yes—
1156C2×C4C2×H(5,𝔽2)12yes—
1157C2×C4C2×2−1+412yes—
1158C2×C4C2×2−1+414yes—
1159C2×C4C2×2−1+412yes—
1160C2×C4C2×2−1+412yes—
1161C2×C4C2×2−1+412yes—
1162C2×C4#58512yes—
1163C22—24no—
1164C22—24no—
1165C22—24no—
1166C22—24no—
1167C22—24no—
1168C22—24no—
1169C22—44no—
1170C22—42no—
1171C22—44no—
1172C22—42no—
1173C22—42no—
1174C22—44no—
1175C22—42no—
1176C22—44no—
1177C22—42no—
1178C22—44no—
1179C22—44no—
1180C22—42no—
1181C22—44no—
1182C22—42no—
1183C22C2×#55018yes—
1184C22C24×D411yescharacteristic
1185C22C23×#4111yescharacteristic
1186C22C22×H(5,𝔽2)11yescharacteristic
1187C22C22×2−1+411yescharacteristic
1188C22C22×2−1+411yescharacteristic
1189C22C2×#58511yescharacteristic
1190C222−1+611yescharacteristic
1191C4—24no—
1192C4—28no—
1193C4—22no—
1194C4—22no—
1195C4—24no—
1196C4—24no—
1197C4—24no—
1198C4—24no—
1199C4—22no—
1200C4—44no—
1201C4—42no—
1202C4—41no—
1203C4—44no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—44no—
1209C4—44no—
1210C4—48no—
1211C4C2×#55014yes—
1212C4#349914yes—
1213C4#351514yescomplemented
1214C2—28no—
1215C2—84no—
1216C2—82no—
1217C2C22×#55011yescharacteristic
1218C2C2×#351511yescharacteristic
1219C2C2×#349911yescharacteristic
1220C2#6291511yescharacteristic
1221C2#6298811yescharacteristic
1222C2#6300111yescharacteristic
1223C2#6301311yescharacteristic
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×#3515C2semidirect
2. #59823C2semidirect
3. #59444C2semidirect
4. #59312C2semidirect
5. #59312C2semidirect
6. #59052C2semidirect
7. #59047C2semidirect
8. #45217C2semidirect
9. #43497C2semidirect
10. #39385C2semidirect
11. #39384C2semidirect
12. #39139C2semidirect
13. #39134C2semidirect
14. #36596C2semidirect
15. #36593C2semidirect
16. #36259C2semidirect
17. #36179C2semidirect
18. #36179C2semidirect
19. #36134C2semidirect
20. #36117C2semidirect
21. #36020C2semidirect
22. #34934C2semidirect
23. C2×#2552C2semidirect
24. #34308C2semidirect
25. C4×#554C2semidirect
26. C4×#547C2semidirect
204. #554D4semidirect
1213. C4#3515semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
#598232
#594442
#593122
#590522
#590472
#452172
#434972
#393852
#393842
#391392
#391342
#365962
#365932
#362592
#361792
#361342
#361172
#360202
#349342
C2×#25522
#343082
C4×#5542
C4×#5472