Finite Group Databasebeta

← #7987092

Subgroups — #7987092

Order 512.

6955 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3544C212yesmaximal, complemented
2#59823C211yesmaximal, characteristic, complemented
3#59444C212yesmaximal, complemented
4#59258C212yesmaximal, complemented
5#59136C212yesmaximal, complemented
6#51538C218yesmaximal, complemented
7#45485C214yesmaximal, complemented
8#45016C214yesmaximal, complemented
9#44971C214yesmaximal, complemented
10#42428C214yesmaximal, complemented
11#42423C214yesmaximal, complemented
12#39369C212yesmaximal, complemented
13#39351C212yesmaximal, complemented
14#39343C214yesmaximal, complemented
15#39125C212yesmaximal, complemented
16#38922C212yesmaximal, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18#36187C211yesmaximal, characteristic, complemented
19#36127C212yesmaximal, complemented
20#36126C212yesmaximal, complemented
21D4×C4⋊Q8C211yesmaximal, characteristic, complemented
22#35170C212yesmaximal, complemented
23#35167C212yesmaximal, complemented
24#34934C211yesmaximal, characteristic, complemented
25#34932C211yesmaximal, characteristic, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27#3544—232no—
28C2×#563C2218yes—
29C2×Q82C2212yes—
30C2×#555C2212yes—
31C2×#554C2212yes—
32C2×#554C2211yescharacteristic
33C2×#552C2214yes—
34C2×#552C2214yes—
35C2×D4×Q8C2212yes—
36C2×#547C2214yes—
37C2×#547C2214yes—
38C2×#544C2214yes—
39C2×#544C2214yes—
40C2×#542C2214yes—
41C2×#542C2214yes—
42C2×#536C2218yes—
43C2×#532C2214yes—
44C22×C4⋊Q8C2212yes—
45C2×#529C2212yes—
46C2×#529C2212yes—
47#2868C2211yescharacteristic
48#2868C2212yes—
49#2857C2212yes—
50#2857C2214yes—
51#2857C2214yes—
52#2856C2212yes—
53#2854C2214yes—
54#2814C2218yes—
55#2732C2214yes—
56#2729C2218yes—
57#2725C2218yes—
58#2723C2218yes—
59#2720C2218yes—
60#2716C2218yes—
61#2715C2218yes—
62#2695C2218yes—
63#2695C2218yes—
64#2694C2218yes—
65#2690C2218yes—
66#2677C2218yes—
67#2674C2218yes—
68#2674C2218yes—
69#2672C2218yes—
70#2672C2218yes—
71#2672C2218yes—
72#2663C2218yes—
73#2659C2218yes—
74#2628C2214yes—
75#2624C2214yes—
76#2616C2218yes—
77#2567C2212yes—
78#2567C2214yes—
79#2563C2212yes—
80#2554C2214yes—
81#2553C2214yes—
82#2552C2214yes—
83#2552C2211yescharacteristic
84#2552C2212yes—
85#2552C2211yescharacteristic
86#2551C2212yes—
87#2551C2212yes—
88#2551C2212yes—
89#2551C2214yes—
90#2551C2214yes—
91#2551C2214yes—
92#2551C2212yes—
93#2550C2214yes—
94#2550C2218yes—
95#2550C2214yes—
96#2548C2211yescharacteristic
97#2547C2214yes—
98#2547C2211yescharacteristic
99#2546C2212yes—
100#2542C2211yescharacteristic
101#2542C2212yes—
102#2542C2214yes—
103#2541C2211yescharacteristic
104#2538C2212yes—
105#2538C2211yescharacteristic
106#2538C2214yes—
107#2537C2214yes—
108#2537C2211yescharacteristic
109#2537C2212yes—
110#2537C2212yes—
111#2536C2214yes—
112#2521C2218yes—
113#2512C2214yes—
114#2512C2212yes—
115#2506C2214yes—
116#2500C2214yes—
117#2496C2214yes—
118#2496C2212yes—
119#2492C2214yes—
120#2491C2214yes—
121#2491C2214yes—
122#2491C2214yes—
123#2491C2214yes—
124#2490C2212yes—
125#2489C2212yes—
126#2485C2214yes—
127#2479C2218yes—
128#2475C2218yes—
129#2461C2218yes—
130#2454C2214yes—
131#2452C2214yes—
132#2452C2214yes—
133#2448C2214yes—
134#2445C2214yes—
135#2445C2212yes—
136#2442C2214yes—
137#2441C2214yes—
138#2440C2214yes—
139#2440C2214yes—
140#2440C2214yes—
141#2434C2214yes—
142#2432C2218yes—
143#2430C2218yes—
144#2427C2214yes—
145#2427C2212yes—
146#2426C2212yes—
147#2422C2218yes—
148#2422C2214yes—
149#2422C2214yes—
150#2422C2212yes—
151#2421C2214yes—
152#2417C2214yes—
153#2417C2214yes—
154#2416C2214yes—
155#2415C2214yes—
156#2415C2218yes—
157#2409C2218yes—
158#2395C2214yes—
159#2392C2214yes—
160#2370C2212yes—
161#2369C2211yescharacteristic
162#2368C2214yes—
163#2366C2212yes—
164#2361C2214yes—
165#2360C2212yes—
166#2355C2211yescharacteristic
167#2354C2212yes—
168#2354C2214yes—
169#2354C2212yes—
170Q8×C4⋊C4C2212yes—
171Q8×C4⋊C4C2212yes—
172#2349C2212yes—
173D4×C4⋊C4C2214yes—
174D4×C4⋊C4C2211yescharacteristic
175D4×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177D4×C4⋊C4C2212yes—
178#2345C2212yes—
179#2323C2214yes—
180#2316C2214yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×#127C2212yes—
185C4×#127C2211yescharacteristic
186C4×#125C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2214yes—
190C4×#121C2212yes—
191C4×#121C2212yes—
192#2293C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C42×D4C2211yescharacteristic
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2318yes—
201C23×Q8C2314yes—
202#563—264no—
203Q82—216no—
204#555—216no—
205#554—216no—
206#554D4116yescomplemented
207#552—232no—
208#552—232no—
209D4×Q8—48no—
210#547—232no—
211#547—232no—
212#544—232no—
213#544—232no—
214#542—232no—
215#542—232no—
216#536—264no—
217#532—416no—
218C2×C4⋊Q8—216no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2318yes—
226C2×C4⋊Q8C2318yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#127C2312yes—
236#529—216no—
237#529—216no—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2318yes—
241C2×#126C2318yes—
242C2×#125C2312yes—
243C2×#125C2312yes—
244C2×#125C2318yes—
245C2×#125C2314yes—
246C2×#125C2318yes—
247C2×#125C2312yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#124C2318yes—
251C2×#124C2318yes—
252C2×#124C2318yes—
253C2×#123C2318yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2318yes—
257C2×#123C2318yes—
258C2×#123C2318yes—
259C2×C22⋊Q8C2318yes—
260C2×C22⋊Q8C2318yes—
261C2×C22⋊Q8C2318yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2318yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2318yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2318yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2318yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2318yes—
282C2×#121C2314yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2318yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×#117C2314yes—
309C2×#117C2314yes—
310C2×#117C2314yes—
311C2×#117C2314yes—
312C2×#117C2318yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2312yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2314yes—
321#400C2318yes—
322#400C2314yes—
323#400C2318yes—
324#399C2318yes—
325#399C2318yes—
326#399C2314yes—
327#399C2318yes—
328#398C2314yes—
329#398C2314yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#397C2318yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2318yes—
341#397C2318yes—
342#397C2318yes—
343#396C2314yes—
344#396C2314yes—
345#396C2318yes—
346#396C2318yes—
347#396C2318yes—
348#396C2318yes—
349#395C2318yes—
350#395C2318yes—
351#395C2318yes—
352#395C2318yes—
353#395C2318yes—
354#395C2318yes—
355#395C2318yes—
356#394C2314yes—
357#394C2314yes—
358#394C2318yes—
359#394C2318yes—
360#394C2318yes—
361#394C2318yes—
362#394C2318yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2318yes—
367#394C2318yes—
368#393C2318yes—
369#393C2318yes—
370#393C2318yes—
371#392C2314yes—
372#391C2314yes—
373#391C2312yes—
374#391C2312yes—
375#391C2312yes—
376#391C2318yes—
377#391C2318yes—
378#391C2314yes—
379#391C2312yes—
380#391C2314yes—
381#390C2312yes—
382#390C2314yes—
383#390C2312yes—
384#390C2312yes—
385#390C2314yes—
386#390C2312yes—
387#390C2312yes—
388#390C2314yes—
389#390C2312yes—
390#390C2314yes—
391#390C2314yes—
392#390C2314yes—
393#390C2312yes—
394#390C2314yes—
395#390C2312yes—
396#390C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2312yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2318yes—
408#389C2318yes—
409#389C2312yes—
410#389C2314yes—
411#389C2318yes—
412#389C2318yes—
413#389C2314yes—
414#389C2314yes—
415#389C2318yes—
416#389C2314yes—
417#389C2312yes—
418#389C2312yes—
419#389C2318yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2314yes—
434#388C2318yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2318yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2318yes—
445#387C2314yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2314yes—
450#386C2314yes—
451#385C2314yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2314yes—
458#385C2314yes—
459#385C2318yes—
460#385C2314yes—
461#384C2312yes—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#384C2312yes—
466#384C2314yes—
467#384C2312yes—
468#384C2312yes—
469#384C2314yes—
470#384C2314yes—
471#384C2314yes—
472#384C2312yes—
473#384C2312yes—
474#384C2312yes—
475#382C2312yes—
476#382C2314yes—
477#382C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2318yes—
481#380C2318yes—
482#380C2312yes—
483#380C2312yes—
484#380C2314yes—
485#380C2312yes—
486#380C2312yes—
487#380C2314yes—
488#380C2314yes—
489#380C2314yes—
490#380C2312yes—
491#380C2314yes—
492#380C2318yes—
493#380C2318yes—
494#380C2314yes—
495#380C2314yes—
496#380C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2311yescharacteristic
522C4×C4⋊C4C2311yescharacteristic
523C4×C4⋊C4C2311yescharacteristic
524C4×C4⋊C4C2311yescharacteristic
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2314yes—
534C4×C22⋊C4C2312yes—
535C4×C22⋊C4C2312yes—
536C2×#95C2314yes—
537C43C2312yes—
538C43C2311yescharacteristic
539C2×#41—232no—
540C2×#41—416no—
541C2×#41—88no—
542C22×Q8—216no—
543C22×Q8—48no—
544C22×Q8—84no—
545C22×Q8C2412yes—
546C22×Q8C2411yescharacteristic
547C22×Q8C2418yes—
548C22×Q8C2418yes—
549C22×Q8C2414yes—
550C22×Q8C2412yes—
551C22×D4C2412yes—
552C22×D4C2412yes—
553C22×D4C2414yes—
554C22×D4C2414yes—
555C22×D4C2414yes—
556C22×D4C2411yescharacteristic
557C22×D4C2411yescharacteristic
558C22×D4C2412yes—
559C22×D4C2418yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2414yes—
563C23×C4C2412yes—
564C23×C4C2418yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2418yes—
568C23×C4C2414yes—
569C23×C4C2412yes—
570C23×C4C2414yes—
571C4⋊Q8—216no—
572C4⋊Q8—216no—
573C4⋊Q8—216no—
574C4⋊Q8—232no—
575C4⋊Q8—232no—
576C4⋊Q8—216no—
577C4⋊Q8—28no—
578C4⋊Q8—216no—
579C4⋊Q8—24no—
580C4⋊Q8—48no—
581C4⋊Q8—48no—
582C4⋊Q8—44no—
583C4⋊Q8—82no—
584C4⋊Q8—84no—
585C4⋊Q8C2×D418yes—
586#127—28no—
587#127—24no—
588#126—216no—
589#126—232no—
590#126—216no—
591#126—232no—
592#125—28no—
593#125—28no—
594#125—216no—
595#125—232no—
596#125—232no—
597#125C2×D4116yes—
598#124—28no—
599#124—28no—
600#124—232no—
601#124—232no—
602#124—416no—
603#123—232no—
604#123—216no—
605#123—232no—
606#123—216no—
607#123—232no—
608#123—232no—
609C22⋊Q8—28no—
610C22⋊Q8—232no—
611C22⋊Q8—232no—
612C22⋊Q8—232no—
613C22⋊Q8—28no—
614C22⋊Q8—232no—
615C22⋊Q8—216no—
616C22⋊Q8—232no—
617C22⋊Q8—48no—
618C22⋊Q8—416no—
619C22⋊Q8—48no—
620C22⋊Q8—44no—
621C22⋊Q8—88no—
622C22⋊Q8C2×D4132yes—
623C22⋊Q8C2×D4116yes—
624#121—28no—
625#121—216no—
626#121—28no—
627#121—216no—
628#121—28no—
629#121—28no—
630#121—416no—
631#121—48no—
632#121—84no—
633C4×Q8—216no—
634C4×Q8—24no—
635C4×Q8—28no—
636C4×Q8—216no—
637C4×Q8—24no—
638C4×Q8—44no—
639C4×Q8C2×D418yes—
640C4×D4—216no—
641C4×D4—24no—
642C4×D4—216no—
643C4×D4—216no—
644C4×D4—216no—
645C4×D4—28no—
646C4×D4—24no—
647C4×D4—24no—
648C4×D4—24no—
649C4×D4—28no—
650C4×D4—44no—
651C4×D4—42no—
652C4×D4—48no—
653C4×D4—48no—
654C4×D4—44no—
655C4×D4—416no—
656C4×D4C2×D418yes—
657C4×D4C2×D4116yes—
658#117—216no—
659#117—216no—
660#117—232no—
661#117—216no—
662#117—216no—
663C2×C4⋊C4—216no—
664C2×C4⋊C4—216no—
665C2×C4⋊C4—216no—
666C2×C4⋊C4—28no—
667C2×C4⋊C4C2×D4116yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2418yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2418yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2418yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2412yes—
757C2×C42—28no—
758C2×C42—28no—
759C2×C42—48no—
760C2×C42C2418yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
763C2×C42C2414yes—
764C2×C42C2418yes—
765C2×C42C2412yes—
766C2×C42C2411yescharacteristic
767C2×C42C2414yes—
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2412yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2411yescharacteristic
780C2×C42C2412yes—
781C2×C42C2412yes—
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785#95C2412yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2412yes—
790#95C2414yes—
791#95C2414yes—
792#95C2412yes—
793#95C2412yes—
794#95C2414yes—
795#95C2412yes—
796#95C2412yes—
797#95C2412yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2412yes—
803#95C2412yes—
804#95C2418yes—
805#95C2414yes—
806#95C2418yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2418yes—
812#95C2418yes—
813#95C2414yes—
814#95C2418yes—
815#95C2418yes—
816#95C2418yes—
817C24C2514yes—
818C24C2512yes—
819C24C2512yes—
820#41—864no—
821C2×Q8—24no—
822C2×Q8—216no—
823C2×Q8—216no—
824C2×Q8—28no—
825C2×Q8—22no—
826C2×Q8—22no—
827C2×Q8—24no—
828C2×Q8—24no—
829C2×Q8—42no—
830C2×Q8—42no—
831C2×Q8—48no—
832C2×Q8—44no—
833C2×Q8—48no—
834C2×Q8—48no—
835C2×Q8—44no—
836C2×Q8—48no—
837C2×Q8—832no—
838C2×Q8C22×D414yes—
839C2×Q8C22×D418yes—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—28no—
843C2×D4—28no—
844C2×D4—216no—
845C2×D4—24no—
846C2×D4—28no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—24no—
852C2×D4—28no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—42no—
862C2×D4—48no—
863C2×D4—42no—
864C2×D4—48no—
865C2×D4C22×D414yes—
866C2×D4H(5,𝔽2)14yes—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—216no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—216no—
875C22×C4—28no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—28no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—28no—
885C22×C4—216no—
886C22×C4—24no—
887C22×C4—28no—
888C22×C4—44no—
889C22×C4—42no—
890C22×C4—48no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—48no—
894C22×C4—44no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—48no—
898C22×C4C22×D418yes—
899C22×C4C22×D4116yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2514yes—
905C22×C4C2511yescharacteristic
906C22×C4C2514yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2518yes—
911C22×C4C2514yes—
912C22×C4C2512yes—
913C22×C4C2512yes—
914C22×C4C2511yescharacteristic
915C22×C4C2512yes—
916C22×C4C2514yes—
917C22×C4C2511yescharacteristic
918C22×C4C2512yes—
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—216no—
927C4⋊C4—216no—
928C4⋊C4—216no—
929C4⋊C4—24no—
930C4⋊C4—216no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—216no—
939C4⋊C4—216no—
940C4⋊C4—28no—
941C4⋊C4—22no—
942C4⋊C4—24no—
943C4⋊C4—28no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—22no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—22no—
955C4⋊C4—24no—
956C4⋊C4—42no—
957C4⋊C4—44no—
958C4⋊C4—48no—
959C4⋊C4—44no—
960C4⋊C4—42no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—48no—
964C4⋊C4—48no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—48no—
969C4⋊C4—44no—
970C4⋊C4—42no—
971C4⋊C4C22×D418yes—
972C4⋊C4C22×D418yes—
973C4⋊C4C22×D414yes—
974C4⋊C4C22×D4116yes—
975C4⋊C4C22×D414yes—
976C4⋊C4C22×D4116yes—
977C4⋊C4C22×D418yes—
978C4⋊C42−1+414yes—
979C22⋊C4—28no—
980C22⋊C4—216no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—216no—
984C22⋊C4—24no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—216no—
990C22⋊C4—28no—
991C22⋊C4—216no—
992C22⋊C4—28no—
993C22⋊C4—28no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—42no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—48no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—44no—
1008C22⋊C4—48no—
1009C22⋊C4—44no—
1010C22⋊C4C22×D4116yes—
1011C22⋊C4C22×D418yes—
1012C42—24no—
1013C42—24no—
1014C42—24no—
1015C42—216no—
1016C42—28no—
1017C42—216no—
1018C42—24no—
1019C42—28no—
1020C42—22no—
1021C42—24no—
1022C42—24no—
1023C42—24no—
1024C42—24no—
1025C42—22no—
1026C42—24no—
1027C42—24no—
1028C42—22no—
1029C42—44no—
1030C42—44no—
1031C42—41no—
1032C42—42no—
1033C42C22×D414yes—
1034C42C22×D418yes—
1035C422−1+414yes—
1036C422−1+414yes—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23C23×D414yes—
1057C23C2×H(5,𝔽2)14yes—
1058C23C2611yescharacteristic
1059Q8—28no—
1060Q8—48no—
1061Q8—48no—
1062Q8—816no—
1063Q8—88no—
1064Q8—816no—
1065D4—28no—
1066D4—28no—
1067D4—416no—
1068D4—416no—
1069D4—416no—
1070D4—48no—
1071D4—48no—
1072D4—84no—
1073D4—816no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—24no—
1090C2×C4—216no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—28no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—28no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—28no—
1126C2×C4—24no—
1127C2×C4—416no—
1128C2×C4—48no—
1129C2×C4—432no—
1130C2×C4—48no—
1131C2×C4—416no—
1132C2×C4—48no—
1133C2×C4—48no—
1134C2×C4—88no—
1135C2×C4—84no—
1136C2×C4—816no—
1137C2×C4C23×D414yes—
1138C2×C4C23×D414yes—
1139C2×C4C23×D412yes—
1140C2×C4C23×D414yes—
1141C2×C4C23×D418yes—
1142C2×C4C23×D412yes—
1143C2×C4C23×D412yes—
1144C2×C4C2×H(5,𝔽2)12yes—
1145C2×C4C2×2−1+412yes—
1146C2×C4C2×2−1+414yes—
1147C2×C4C2×2−1+412yes—
1148C2×C4C2×2−1+412yes—
1149C2×C4C2×2−1+412yes—
1150C2×C4C2×2−1+412yes—
1151C2×C4C2×2−1+412yes—
1152C2×C4C2×2−1+412yes—
1153C2×C4#58512yes—
1154C22—24no—
1155C22—24no—
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—24no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—44no—
1169C22—44no—
1170C22—44no—
1171C22—44no—
1172C22—44no—
1173C22—44no—
1174C22—44no—
1175C22C24×D411yescharacteristic
1176C22C22×H(5,𝔽2)11yescharacteristic
1177C22C22×2−1+411yescharacteristic
1178C22C22×2−1+411yescharacteristic
1179C22C22×2−1+411yescharacteristic
1180C22C2×#58511yescharacteristic
1181C22H(7,𝔽2)11yescharacteristic
1182C4—28no—
1183C4—24no—
1184C4—22no—
1185C4—24no—
1186C4—24no—
1187C4—24no—
1188C4—22no—
1189C4—22no—
1190C4—48no—
1191C4—42no—
1192C4—44no—
1193C4—42no—
1194C4—41no—
1195C4—44no—
1196C4—42no—
1197C4—44no—
1198C4—44no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4#349714yes—
1203C4#349914yes—
1204C4#354414yescomplemented
1205C2—44no—
1206C2—44no—
1207C2—84no—
1208C2C2×#354411yescharacteristic
1209C2C2×#349711yescharacteristic
1210C2C2×#349911yescharacteristic
1211C2#6292911yescharacteristic
1212C2#6294311yescharacteristic
1213C2D4×H(5,𝔽2)11yescharacteristic
1214C2#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×#3544C2semidirect
2. #59823C2semidirect
3. #59444C2semidirect
4. #59258C2semidirect
5. #59136C2semidirect
6. #51538C2semidirect
7. #45485C2semidirect
8. #45016C2semidirect
9. #44971C2semidirect
10. #42428C2semidirect
11. #42423C2semidirect
12. #39369C2semidirect
13. #39351C2semidirect
14. #39343C2semidirect
15. #39125C2semidirect
16. #38922C2semidirect
17. Q8×C4⋊Q8C2semidirect
18. #36187C2semidirect
19. #36127C2semidirect
20. #36126C2semidirect
21. D4×C4⋊Q8C2semidirect
22. #35170C2semidirect
23. #35167C2semidirect
24. #34934C2semidirect
25. #34932C2semidirect
26. C4×#554C2semidirect
206. #554D4semidirect
1204. C4#3544semidirect

Maximal subgroups

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

subgroupindex
C2×#35442
#598232
#594442
#592582
#591362
#515382
#454852
#450162
#449712
#424282
#424232
#393692
#393512
#393432
#391252
#389222
Q8×C4⋊Q82
#361872
#361272
#361262
D4×C4⋊Q82
#351702
#351672
#349342
#349322
C4×#5542