Finite Group Databasebeta

← #7986718

Subgroups — #7986718

Order 512.

7307 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3547C212yesmaximal, complemented
2#59822C211yesmaximal, characteristic, complemented
3#59680C212yesmaximal, complemented
4#59080C212yesmaximal, complemented
5#59050C212yesmaximal, complemented
6#51900C218yesmaximal, complemented
7#45484C214yesmaximal, complemented
8#45245C214yesmaximal, complemented
9#44973C214yesmaximal, complemented
10#42646C214yesmaximal, complemented
11#42643C214yesmaximal, complemented
12#39369C212yesmaximal, complemented
13#39351C214yesmaximal, complemented
14#39343C212yesmaximal, complemented
15#39340C212yesmaximal, complemented
16#39124C212yesmaximal, complemented
17Q8×#127C211yesmaximal, characteristic, complemented
18#36187C212yesmaximal, complemented
19#36186C212yesmaximal, complemented
20#36134C211yesmaximal, characteristic, complemented
21#36127C211yesmaximal, characteristic, complemented
22#35171C212yesmaximal, complemented
23#35166C212yesmaximal, complemented
24#34934C211yesmaximal, characteristic, complemented
25#34925C211yesmaximal, characteristic, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27#3547—232no—
28C2×#562C2218yes—
29C2×#555C2214yes—
30C2×#555C2212yes—
31C2×#554C2211yescharacteristic
32C2×#553C2214yes—
33C2×#552C2214yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2212yes—
36C2×D4×Q8C2212yes—
37C2×#548C2214yes—
38C2×#547C2212yes—
39C2×#544C2214yes—
40C2×#542C2218yes—
41C2×#540C2214yes—
42C2×#537C2214yes—
43C2×#537C2214yes—
44C2×#536C2214yes—
45C2×#533C2212yes—
46C2×#532C2212yes—
47C2×#532C2212yes—
48C2×#532C2212yes—
49C2×#529C2212yes—
50#2868C2211yescharacteristic
51#2868C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2856C2214yes—
55#2856C2214yes—
56#2854C2214yes—
57#2813C2218yes—
58#2733C2214yes—
59#2730C2218yes—
60#2723C2218yes—
61#2723C2218yes—
62#2720C2218yes—
63#2714C2218yes—
64#2711C2218yes—
65#2696C2218yes—
66#2681C2218yes—
67#2677C2218yes—
68#2676C2218yes—
69#2676C2218yes—
70#2674C2218yes—
71#2672C2218yes—
72#2672C2218yes—
73#2672C2218yes—
74#2671C2218yes—
75#2661C2218yes—
76#2656C2218yes—
77#2628C2214yes—
78#2624C2218yes—
79#2616C2214yes—
80#2563C2214yes—
81#2555C2214yes—
82#2554C2214yes—
83#2552C2212yes—
84#2552C2211yescharacteristic
85#2551C2211yescharacteristic
86#2551C2214yes—
87#2548C2211yescharacteristic
88#2548C2214yes—
89#2547C2212yes—
90#2542C2212yes—
91#2542C2212yes—
92#2542C2214yes—
93#2542C2212yes—
94#2542C2214yes—
95#2542C2212yes—
96#2542C2214yes—
97#2542C2214yes—
98#2541C2211yescharacteristic
99#2541C2214yes—
100#2541C2212yes—
101#2541C2211yescharacteristic
102#2541C2212yes—
103#2541C2211yescharacteristic
104#2540C2214yes—
105#2540C2214yes—
106#2540C2218yes—
107#2538C2212yes—
108#2538C2211yescharacteristic
109#2537C2212yes—
110#2537C2212yes—
111#2537C2211yescharacteristic
112#2537C2214yes—
113#2537C2212yes—
114#2535C2214yes—
115#2519C2218yes—
116#2512C2214yes—
117#2512C2212yes—
118#2506C2214yes—
119#2500C2218yes—
120#2498C2218yes—
121#2491C2214yes—
122#2491C2214yes—
123#2491C2218yes—
124#2491C2212yes—
125#2491C2212yes—
126#2490C2214yes—
127#2490C2212yes—
128#2489C2214yes—
129#2464C2218yes—
130#2463C2218yes—
131#2456C2218yes—
132#2452C2214yes—
133#2452C2218yes—
134#2448C2218yes—
135#2445C2214yes—
136#2445C2212yes—
137#2441C2214yes—
138#2441C2214yes—
139#2440C2214yes—
140#2436C2214yes—
141#2432C2214yes—
142#2429C2214yes—
143#2428C2214yes—
144#2428C2214yes—
145#2428C2212yes—
146#2428C2212yes—
147#2426C2212yes—
148#2426C2214yes—
149#2423C2214yes—
150#2422C2214yes—
151#2422C2214yes—
152#2422C2214yes—
153#2417C2214yes—
154#2416C2214yes—
155#2415C2214yes—
156#2414C2214yes—
157#2414C2214yes—
158#2414C2214yes—
159#2409C2214yes—
160#2407C2214yes—
161#2392C2214yes—
162#2388C2214yes—
163#2370C2212yes—
164#2369C2211yescharacteristic
165#2368C2214yes—
166#2366C2214yes—
167#2365C2212yes—
168#2362C2214yes—
169#2360C2212yes—
170#2355C2211yescharacteristic
171#2354C2212yes—
172#2354C2212yes—
173#2354C2214yes—
174#2354C2212yes—
175Q8×C4⋊C4C2212yes—
176#2349C2212yes—
177D4×C4⋊C4C2212yes—
178D4×C4⋊C4C2212yes—
179D4×C4⋊C4C2211yescharacteristic
180#2345C2212yes—
181#2324C2214yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×#127C2211yescharacteristic
184C4×#127C2212yes—
185C4×#127C2212yes—
186C4×#127C2211yescharacteristic
187C4×#125C2212yes—
188C4×C22⋊Q8C2214yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191C4×#121C2212yes—
192C4×#121C2212yes—
193#2293C2212yes—
194#2285C2214yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2212yes—
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2314yes—
201C22×#41C2314yes—
202C23×Q8C2314yes—
203#562—264no—
204#555—216no—
205#555—232no—
206#554D4116yescomplemented
207#553—232no—
208#552—232no—
209D4×Q8—216no—
210D4×Q8—48no—
211D4×Q8—48no—
212#548—232no—
213#547—216no—
214#544—232no—
215#542—264no—
216#540—232no—
217#537—232no—
218#537—416no—
219#536—232no—
220#533—216no—
221#532—216no—
222#532—48no—
223#532—48no—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2318yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#127C2311yescharacteristic
236C2×#127C2312yes—
237C2×#127C2312yes—
238C2×#127C2314yes—
239C2×#127C2312yes—
240#529—216no—
241C2×#126C2314yes—
242C2×#126C2318yes—
243C2×#125C2312yes—
244C2×#125C2314yes—
245C2×#125C2318yes—
246C2×#125C2312yes—
247C2×#124C2312yes—
248C2×#124C2314yes—
249C2×#124C2318yes—
250C2×#124C2318yes—
251C2×#124C2318yes—
252C2×#124C2314yes—
253C2×#124C2314yes—
254C2×#123C2318yes—
255C2×#123C2318yes—
256C2×#123C2314yes—
257C2×#123C2318yes—
258C2×#123C2318yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2318yes—
265C2×C22⋊Q8C2318yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2318yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2318yes—
271C2×C22⋊Q8C2318yes—
272C2×C22⋊Q8C2318yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×#121C2318yes—
276C2×#121C2318yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2318yes—
284C2×#121C2312yes—
285C2×#121C2318yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2312yes—
292C2×#121C2318yes—
293C2×#121C2318yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2318yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2318yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2314yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2314yes—
333C2×#117C2318yes—
334C22×C4⋊C4C2314yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C42C2312yes—
338C22×C42C2312yes—
339C22×C42C2314yes—
340#400C2318yes—
341#399C2318yes—
342#399C2318yes—
343#399C2318yes—
344#399C2318yes—
345#399C2318yes—
346#399C2318yes—
347#398C2314yes—
348#398C2318yes—
349#398C2318yes—
350#397C2314yes—
351#397C2318yes—
352#397C2318yes—
353#397C2318yes—
354#396C2314yes—
355#396C2314yes—
356#396C2318yes—
357#396C2318yes—
358#396C2318yes—
359#395C2318yes—
360#395C2318yes—
361#395C2314yes—
362#394C2318yes—
363#394C2318yes—
364#394C2318yes—
365#394C2314yes—
366#394C2318yes—
367#394C2318yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2318yes—
374#394C2318yes—
375#394C2318yes—
376#394C2318yes—
377#394C2318yes—
378#393C2318yes—
379#393C2318yes—
380#393C2318yes—
381#393C2314yes—
382#392C2314yes—
383#392C2314yes—
384#392C2314yes—
385#392C2314yes—
386#392C2318yes—
387#392C2318yes—
388#392C2318yes—
389#392C2318yes—
390#392C2318yes—
391#391C2312yes—
392#391C2314yes—
393#391C2314yes—
394#391C2312yes—
395#391C2314yes—
396#390C2314yes—
397#390C2312yes—
398#390C2314yes—
399#390C2312yes—
400#390C2312yes—
401#390C2314yes—
402#390C2312yes—
403#390C2312yes—
404#390C2314yes—
405#390C2312yes—
406#390C2312yes—
407#390C2314yes—
408#390C2312yes—
409#390C2318yes—
410#390C2312yes—
411#390C2318yes—
412#390C2314yes—
413#390C2312yes—
414#390C2318yes—
415#390C2314yes—
416#390C2314yes—
417#390C2318yes—
418#390C2312yes—
419#390C2318yes—
420#390C2318yes—
421#390C2312yes—
422#390C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2314yes—
428#389C2312yes—
429#389C2314yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2318yes—
435#389C2314yes—
436#389C2312yes—
437#389C2318yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2318yes—
459#387C2318yes—
460#387C2314yes—
461#386C2318yes—
462#386C2318yes—
463#386C2318yes—
464#386C2318yes—
465#386C2318yes—
466#386C2314yes—
467#386C2314yes—
468#386C2314yes—
469#385C2318yes—
470#385C2314yes—
471#385C2318yes—
472#385C2318yes—
473#385C2314yes—
474#385C2314yes—
475#385C2318yes—
476#384C2311yescharacteristic
477#384C2312yes—
478#384C2311yescharacteristic
479#384C2312yes—
480#384C2311yescharacteristic
481#384C2314yes—
482#384C2314yes—
483#384C2312yes—
484#384C2312yes—
485#384C2314yes—
486#384C2312yes—
487#384C2314yes—
488#382C2312yes—
489#382C2318yes—
490#380C2312yes—
491#380C2314yes—
492#380C2314yes—
493#380C2314yes—
494#380C2314yes—
495#380C2312yes—
496#380C2314yes—
497#380C2314yes—
498#380C2314yes—
499#380C2314yes—
500#380C2314yes—
501#380C2312yes—
502#380C2318yes—
503#380C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2311yescharacteristic
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2311yescharacteristic
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2318yes—
520C4×C4⋊C4C2311yescharacteristic
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2311yescharacteristic
523C4×C4⋊C4C2312yes—
524C4×C4⋊C4C2314yes—
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2311yescharacteristic
527C4×C4⋊C4C2311yescharacteristic
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2314yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2312yes—
534C4×C22⋊C4C2312yes—
535C4×C22⋊C4C2314yes—
536C4×C22⋊C4C2312yes—
537C4×C22⋊C4C2314yes—
538C4×C22⋊C4C2312yes—
539C2×#95C2314yes—
540C43C2312yes—
541C43C2311yescharacteristic
542C2×#41—216no—
543C2×#41—216no—
544C2×#41—48no—
545C2×#41—48no—
546C2×#41—48no—
547C2×#41—48no—
548C22×Q8—216no—
549C22×Q8—48no—
550C22×Q8—48no—
551C22×Q8C2414yes—
552C22×Q8C2411yescharacteristic
553C22×Q8C2418yes—
554C22×Q8C2414yes—
555C22×Q8C2412yes—
556C22×D4C2412yes—
557C22×D4C2412yes—
558C22×D4C2411yescharacteristic
559C22×D4C2412yes—
560C22×D4C2412yes—
561C22×D4C2411yescharacteristic
562C22×D4C2412yes—
563C22×D4C2412yes—
564C22×D4C2414yes—
565C22×D4C2418yes—
566C22×D4C2414yes—
567C22×D4C2414yes—
568C22×D4C2418yes—
569C22×D4C2414yes—
570C22×D4C2414yes—
571C22×D4C2414yes—
572C22×D4C2414yes—
573C22×D4C2418yes—
574C23×C4C2414yes—
575C23×C4C2412yes—
576C23×C4C2414yes—
577C23×C4C2412yes—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2418yes—
581C23×C4C2414yes—
582C23×C4C2418yes—
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2414yes—
586C4⋊Q8—28no—
587C4⋊Q8—232no—
588C4⋊Q8—28no—
589C4⋊Q8—216no—
590C4⋊Q8—28no—
591C4⋊Q8—44no—
592C4⋊Q8—48no—
593C4⋊Q8—48no—
594C4⋊Q8—44no—
595C4⋊Q8C2×D418yes—
596#127—28no—
597#127—24no—
598#127—24no—
599#127—44no—
600#127—48no—
601#127—44no—
602#126—216no—
603#126—232no—
604#125—28no—
605#125—216no—
606#125—232no—
607#125C2×D4116yes—
608#124—28no—
609#124—232no—
610#124—216no—
611#124—232no—
612#124—232no—
613#124—48no—
614#124—48no—
615#123—232no—
616#123—216no—
617#123—232no—
618#123—232no—
619#123—232no—
620C22⋊Q8—28no—
621C22⋊Q8—216no—
622C22⋊Q8—216no—
623C22⋊Q8—216no—
624C22⋊Q8—232no—
625C22⋊Q8—216no—
626C22⋊Q8—232no—
627C22⋊Q8—232no—
628C22⋊Q8—216no—
629C22⋊Q8—416no—
630C22⋊Q8—416no—
631C22⋊Q8—416no—
632C22⋊Q8—48no—
633C22⋊Q8—48no—
634C22⋊Q8C2×D4116yes—
635C22⋊Q8C2×D4132yes—
636#121—28no—
637#121—216no—
638#121—232no—
639#121—232no—
640#121—28no—
641#121—28no—
642#121—216no—
643#121—232no—
644#121—216no—
645#121—28no—
646#121—216no—
647#121—232no—
648#121—48no—
649#121—416no—
650#121—416no—
651#121—44no—
652#121—44no—
653#121—48no—
654#121—44no—
655#121—44no—
656#121—48no—
657#121—48no—
658#121—48no—
659#121—416no—
660C4×Q8—216no—
661C4×Q8—216no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—44no—
665C4×Q8C2×D418yes—
666C4×D4—216no—
667C4×D4—232no—
668C4×D4—28no—
669C4×D4—216no—
670C4×D4—28no—
671C4×D4—216no—
672C4×D4—24no—
673C4×D4—28no—
674C4×D4—24no—
675C4×D4—28no—
676C4×D4—24no—
677C4×D4—48no—
678C4×D4—44no—
679C4×D4—42no—
680C4×D4—42no—
681C4×D4—48no—
682C4×D4—48no—
683C4×D4—48no—
684C4×D4—44no—
685C4×D4—48no—
686C4×D4—48no—
687C4×D4—44no—
688C4×D4C2×D418yes—
689C4×D4C2×D4116yes—
690#117—232no—
691#117—216no—
692#117—216no—
693#117—216no—
694#117—216no—
695C2×C4⋊C4—216no—
696C2×C4⋊C4—28no—
697C2×C4⋊C4C2×D4116yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2418yes—
720C2×C4⋊C4C2418yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2418yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2418yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2418yes—
766C2×C22⋊C4C2418yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2418yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2418yes—
778C2×C22⋊C4C2418yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2418yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C42—28no—
786C2×C42—28no—
787C2×C42—48no—
788C2×C42C2418yes—
789C2×C42C2418yes—
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2411yescharacteristic
793C2×C42C2412yes—
794C2×C42C2411yescharacteristic
795C2×C42C2412yes—
796C2×C42C2412yes—
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2411yescharacteristic
801C2×C42C2412yes—
802C2×C42C2414yes—
803C2×C42C2412yes—
804C2×C42C2411yescharacteristic
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2412yes—
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812#95C2412yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2412yes—
817#95C2412yes—
818#95C2414yes—
819#95C2412yes—
820#95C2412yes—
821#95C2414yes—
822#95C2414yes—
823#95C2412yes—
824#95C2412yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2412yes—
830#95C2412yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2414yes—
835#95C2414yes—
836#95C2418yes—
837#95C2418yes—
838C24C2514yes—
839C24C2512yes—
840C24C2514yes—
841C24C2512yes—
842#41—832no—
843#41—832no—
844C2×Q8—28no—
845C2×Q8—216no—
846C2×Q8—28no—
847C2×Q8—22no—
848C2×Q8—22no—
849C2×Q8—28no—
850C2×Q8—28no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—44no—
854C2×Q8—48no—
855C2×Q8—48no—
856C2×Q8—44no—
857C2×Q8—832no—
858C2×Q8C22×D414yes—
859C2×Q8C22×D418yes—
860C2×D4—28no—
861C2×D4—216no—
862C2×D4—28no—
863C2×D4—28no—
864C2×D4—24no—
865C2×D4—24no—
866C2×D4—28no—
867C2×D4—216no—
868C2×D4—28no—
869C2×D4—24no—
870C2×D4—22no—
871C2×D4—24no—
872C2×D4—24no—
873C2×D4—24no—
874C2×D4—24no—
875C2×D4—28no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—24no—
882C2×D4—22no—
883C2×D4—22no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—48no—
898C2×D4—44no—
899C2×D4—48no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—48no—
906C2×D4—44no—
907C2×D4—48no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—48no—
911C2×D4—48no—
912C2×D4—48no—
913C2×D4C22×D414yes—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—28no—
919C22×C4—28no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—28no—
923C22×C4—28no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—28no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—216no—
933C22×C4—216no—
934C22×C4—24no—
935C22×C4—28no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—48no—
940C22×C4—48no—
941C22×C4—48no—
942C22×C4—44no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—48no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4C22×D418yes—
949C22×C4C22×D4116yes—
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2511yescharacteristic
958C22×C4C2514yes—
959C22×C4C2512yes—
960C22×C4C2518yes—
961C22×C4C2514yes—
962C22×C4C2511yescharacteristic
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C4⋊C4—28no—
973C4⋊C4—216no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—216no—
978C4⋊C4—28no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—216no—
982C4⋊C4—216no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—22no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—22no—
993C4⋊C4—216no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—24no—
997C4⋊C4—22no—
998C4⋊C4—24no—
999C4⋊C4—22no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—42no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—42no—
1006C4⋊C4—44no—
1007C4⋊C4—42no—
1008C4⋊C4—48no—
1009C4⋊C4—48no—
1010C4⋊C4—44no—
1011C4⋊C4C22×D414yes—
1012C4⋊C4C22×D414yes—
1013C4⋊C4C22×D418yes—
1014C4⋊C4C22×D4116yes—
1015C4⋊C4C22×D418yes—
1016C4⋊C4C22×D4116yes—
1017C4⋊C4C22×D418yes—
1018C4⋊C4H(5,𝔽2)14yes—
1019C22⋊C4—28no—
1020C22⋊C4—216no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—216no—
1024C22⋊C4—216no—
1025C22⋊C4—216no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—216no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—24no—
1033C22⋊C4—28no—
1034C22⋊C4—216no—
1035C22⋊C4—28no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—28no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—42no—
1044C22⋊C4—44no—
1045C22⋊C4—42no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C22⋊C4—44no—
1051C22⋊C4—48no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4C22×D418yes—
1058C22⋊C4C22×D4116yes—
1059C42—24no—
1060C42—24no—
1061C42—24no—
1062C42—216no—
1063C42—216no—
1064C42—24no—
1065C42—24no—
1066C42—24no—
1067C42—24no—
1068C42—22no—
1069C42—24no—
1070C42—24no—
1071C42—28no—
1072C42—24no—
1073C42—22no—
1074C42—22no—
1075C42—44no—
1076C42—44no—
1077C42—41no—
1078C42—42no—
1079C42C22×D414yes—
1080C42C22×D418yes—
1081C42H(5,𝔽2)14yes—
1082C422−1+414yes—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—24no—
1091C23—24no—
1092C23—24no—
1093C23—24no—
1094C23—22no—
1095C23—24no—
1096C23—22no—
1097C23—24no—
1098C23—22no—
1099C23—24no—
1100C23—24no—
1101C23—24no—
1102C23—22no—
1103C23—24no—
1104C23—22no—
1105C23—24no—
1106C23—24no—
1107C23—24no—
1108C23—22no—
1109C23—24no—
1110C23C23×D414yes—
1111C23C2611yescharacteristic
1112Q8—28no—
1113Q8—48no—
1114Q8—416no—
1115Q8—816no—
1116Q8—88no—
1117D4—28no—
1118D4—48no—
1119D4—48no—
1120D4—48no—
1121D4—48no—
1122D4—48no—
1123D4—44no—
1124D4—48no—
1125D4—88no—
1126D4—816no—
1127D4—88no—
1128D4—88no—
1129D4—88no—
1130D4—88no—
1131D4—88no—
1132D4—816no—
1133D4—88no—
1134D4—168no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—24no—
1151C2×C4—216no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—28no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—28no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—28no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—416no—
1186C2×C4—48no—
1187C2×C4—416no—
1188C2×C4—416no—
1189C2×C4—48no—
1190C2×C4—48no—
1191C2×C4—84no—
1192C2×C4—88no—
1193C2×C4—84no—
1194C2×C4—816no—
1195C2×C4—816no—
1196C2×C4C23×D418yes—
1197C2×C4C23×D412yes—
1198C2×C4C23×D414yes—
1199C2×C4C23×D414yes—
1200C2×C4C23×D414yes—
1201C2×C4C23×D412yes—
1202C2×C4C23×D412yes—
1203C2×C4C2×H(5,𝔽2)12yes—
1204C2×C4C2×H(5,𝔽2)14yes—
1205C2×C4C2×H(5,𝔽2)12yes—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4C2×H(5,𝔽2)12yes—
1208C2×C4C2×2−1+412yes—
1209C2×C4C2×2−1+412yes—
1210C2×C4C2×2−1+412yes—
1211C2×C4#58512yes—
1212C2×C4#58512yes—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—44no—
1226C22—42no—
1227C22—44no—
1228C22—44no—
1229C22—42no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—42no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—44no—
1239C22—42no—
1240C22—44no—
1241C22C24×D411yescharacteristic
1242C22C22×H(5,𝔽2)11yescharacteristic
1243C22C22×H(5,𝔽2)11yescharacteristic
1244C22C22×2−1+411yescharacteristic
1245C22C2×#58511yescharacteristic
1246C22C2×#58511yescharacteristic
1247C222−1+611yescharacteristic
1248C4—24no—
1249C4—28no—
1250C4—22no—
1251C4—24no—
1252C4—24no—
1253C4—24no—
1254C4—22no—
1255C4—22no—
1256C4—42no—
1257C4—42no—
1258C4—41no—
1259C4—44no—
1260C4—42no—
1261C4—44no—
1262C4—42no—
1263C4—44no—
1264C4—48no—
1265C4—42no—
1266C4—42no—
1267C4#349714yes—
1268C4#349814yes—
1269C4#354714yescomplemented
1270C2—44no—
1271C2—82no—
1272C2—84no—
1273C2—84no—
1274C2C2×#354711yescharacteristic
1275C2C2×#349711yescharacteristic
1276C2C2×#349811yescharacteristic
1277C2#6291311yescharacteristic
1278C2#6292511yescharacteristic
1279C2#6298811yescharacteristic
1280C2#6302411yescharacteristic
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×#3547C2semidirect
2. #59822C2semidirect
3. #59680C2semidirect
4. #59080C2semidirect
5. #59050C2semidirect
6. #51900C2semidirect
7. #45484C2semidirect
8. #45245C2semidirect
9. #44973C2semidirect
10. #42646C2semidirect
11. #42643C2semidirect
12. #39369C2semidirect
13. #39351C2semidirect
14. #39343C2semidirect
15. #39340C2semidirect
16. #39124C2semidirect
17. Q8×#127C2semidirect
18. #36187C2semidirect
19. #36186C2semidirect
20. #36134C2semidirect
21. #36127C2semidirect
22. #35171C2semidirect
23. #35166C2semidirect
24. #34934C2semidirect
25. #34925C2semidirect
26. C4×#554C2semidirect
206. #554D4semidirect
1269. C4#3547semidirect

Maximal subgroups

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

subgroupindex
C2×#35472
#598222
#596802
#590802
#590502
#519002
#454842
#452452
#449732
#426462
#426432
#393692
#393512
#393432
#393402
#391242
Q8×#1272
#361872
#361862
#361342
#361272
#351712
#351662
#349342
#349252
C4×#5542