Finite Group Databasebeta

← #7671970

Subgroups — #7671970

Order 512.

5586 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59863C211yesmaximal, characteristic, complemented
3#59821C211yesmaximal, characteristic, complemented
4#59815C211yesmaximal, characteristic, complemented
5#59677C214yesmaximal, complemented
6#59640C212yesmaximal, complemented
7#59429C212yesmaximal, complemented
8#59303C212yesmaximal, complemented
9#59125C212yesmaximal, complemented
10#40020C214yesmaximal, complemented
11#39828C214yesmaximal, complemented
12#39783C214yesmaximal, complemented
13#38487C214yesmaximal, complemented
14#36631C211yesmaximal, characteristic, complemented
15#36606C214yesmaximal, complemented
16#36579C212yesmaximal, complemented
17#36576C212yesmaximal, complemented
18#36477C212yesmaximal, complemented
19#36419C212yesmaximal, complemented
20#36374C214yesmaximal, complemented
21#35597C214yesmaximal, complemented
22#35238C212yesmaximal, complemented
23#35196C212yesmaximal, complemented
24#34316C212yesmaximal, complemented
25#34243C212yesmaximal, complemented
26C4×#532C211yesmaximal, characteristic, complemented
27C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#550C2212yes—
30C2×#548C2214yes—
31C2×#547C2212yes—
32C2×#532C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2212yes—
35C2×C4×#41C2212yes—
36C22×C4×Q8C2212yes—
37#2861C2212yes—
38#2860C2212yes—
39#2860C2212yes—
40#2859C2211yescharacteristic
41#2858C2211yescharacteristic
42#2857C2211yescharacteristic
43#2856C2211yescharacteristic
44#2856C2214yes—
45#2855C2214yes—
46#2854C2212yes—
47#2854C2212yes—
48#2850C2214yes—
49#2850C2212yes—
50#2850C2214yes—
51#2808C2214yes—
52#2805C2214yes—
53#2803C2218yes—
54#2800C2218yes—
55#2795C2218yes—
56#2788C2218yes—
57#2779C2218yes—
58#2727C2214yes—
59#2682C2214yes—
60#2674C2218yes—
61#2662C2218yes—
62#2649C2218yes—
63#2608C2218yes—
64#2595C2218yes—
65#2593C2218yes—
66#2592C2214yes—
67#2592C2214yes—
68#2591C2218yes—
69#2587C2218yes—
70#2581C2214yes—
71#2581C2214yes—
72#2571C2212yes—
73#2570C2214yes—
74#2568C2212yes—
75#2567C2212yes—
76#2566C2214yes—
77#2563C2212yes—
78#2559C2218yes—
79#2559C2218yes—
80#2548C2212yes—
81#2548C2214yes—
82#2548C2212yes—
83#2547C2212yes—
84#2544C2214yes—
85#2544C2214yes—
86#2542C2212yes—
87#2541C2212yes—
88#2538C2214yes—
89#2538C2212yes—
90#2538C2212yes—
91#2537C2212yes—
92#2516C2218yes—
93#2513C2214yes—
94#2512C2214yes—
95#2511C2214yes—
96#2509C2214yes—
97#2500C2214yes—
98#2500C2214yes—
99#2497C2214yes—
100#2497C2214yes—
101#2497C2214yes—
102#2491C2214yes—
103#2485C2214yes—
104#2481C2218yes—
105#2477C2218yes—
106#2474C2218yes—
107#2469C2218yes—
108#2465C2218yes—
109#2459C2218yes—
110#2448C2214yes—
111#2445C2214yes—
112#2444C2218yes—
113#2443C2218yes—
114#2440C2214yes—
115#2432C2214yes—
116#2430C2218yes—
117#2429C2214yes—
118#2426C2218yes—
119#2426C2214yes—
120#2421C2214yes—
121#2420C2214yes—
122#2416C2214yes—
123#2416C2214yes—
124#2416C2218yes—
125#2416C2214yes—
126#2416C2214yes—
127#2415C2214yes—
128#2409C2214yes—
129#2407C2214yes—
130#2374C2218yes—
131#2370C2214yes—
132#2367C2214yes—
133#2367C2214yes—
134#2365C2212yes—
135#2364C2218yes—
136#2363C2214yes—
137#2362C2214yes—
138#2359C2218yes—
139#2357C2214yes—
140#2355C2212yes—
141#2355C2212yes—
142#2354C2212yes—
143#2354C2212yes—
144#2354C2212yes—
145#2352C2214yes—
146#2352C2214yes—
147Q8×C4⋊C4C2212yes—
148Q8×C4⋊C4C2212yes—
149D4×C4⋊C4C2214yes—
150D4×C4⋊C4C2212yes—
151#2345C2214yes—
152#2341C2214yes—
153#2335C2218yes—
154#2334C2218yes—
155#2324C2214yes—
156#2324C2214yes—
157#2314C2214yes—
158C4×C4⋊Q8C2211yescharacteristic
159C4×C4⋊Q8C2212yes—
160C4×C4⋊Q8C2211yescharacteristic
161C4×C4⋊Q8C2211yescharacteristic
162C4×C4⋊Q8C2212yes—
163C4×C4⋊Q8C2212yes—
164C4×C4⋊Q8C2212yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2211yescharacteristic
167C4×C4⋊Q8C2212yes—
168C4×C4⋊Q8C2211yescharacteristic
169C4×C4⋊Q8C2211yescharacteristic
170C4×C4⋊Q8C2211yescharacteristic
171C4×#127C2211yescharacteristic
172C4×#127C2211yescharacteristic
173C4×#127C2211yescharacteristic
174C4×#124C2212yes—
175C4×#124C2212yes—
176C4×#124C2212yes—
177C4×C22⋊Q8C2214yes—
178C4×C22⋊Q8C2214yes—
179C4×#121C2212yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182C4×#121C2212yes—
183C4×#121C2214yes—
184C4×#121C2212yes—
185C4×#121C2212yes—
186#2297C2214yes—
187#2297C2212yes—
188C2×#391C2212yes—
189#2293C2212yes—
190#2293C2212yes—
191#2293C2212yes—
192#2293C2212yes—
193C2×#389C2212yes—
194C2×#389C2212yes—
195#2285C2211yescharacteristic
196C2×#384C2211yescharacteristic
197#2274C2214yes—
198C42×D4C2212yes—
199C42×D4C2212yes—
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C22×#41C2314yes—
204C22×#41C2312yes—
205C23×Q8C2312yes—
206#556—48no—
207#550—48no—
208#548—416no—
209#547—216no—
210#532—28no—
211C2×C4⋊Q8—28no—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2314yes—
222#529—216no—
223C2×#126C2314yes—
224C2×#126C2318yes—
225C2×#125C2312yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2318yes—
232C2×#123C2318yes—
233C2×#123C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2314yes—
245C2×#121C2318yes—
246C2×#121C2314yes—
247C2×#121C2312yes—
248C2×#121C2318yes—
249C2×#121C2318yes—
250C4×#41—48no—
251C2×C4×Q8—48no—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2318yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2314yes—
282C2×#117C2312yes—
283C2×#117C2314yes—
284C22×C4⋊C4C2314yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2314yes—
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2314yes—
296C22×C42C2314yes—
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300#400C2318yes—
301#400C2318yes—
302#400C2318yes—
303#400C2318yes—
304#400C2318yes—
305#399C2318yes—
306#398C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#395C2318yes—
318#395C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#393C2318yes—
330#393C2318yes—
331#392C2318yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#391C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2318yes—
359#390C2318yes—
360#390C2314yes—
361#390C2314yes—
362#390C2318yes—
363#390C2314yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2312yes—
368#390C2312yes—
369#390C2312yes—
370#390C2312yes—
371#390C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2314yes—
383#389C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2314yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2314yes—
420#388C2314yes—
421#388C2318yes—
422#388C2314yes—
423#388C2318yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2314yes—
446#386C2314yes—
447#386C2318yes—
448#386C2318yes—
449#386C2314yes—
450#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#386C2314yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#384C2311yescharacteristic
466#384C2312yes—
467#384C2312yes—
468#384C2312yes—
469#384C2311yescharacteristic
470#384C2314yes—
471#384C2314yes—
472#382C2314yes—
473#382C2314yes—
474#382C2314yes—
475#382C2312yes—
476#382C2312yes—
477#381C2318yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2318yes—
483#380C2314yes—
484#380C2312yes—
485#380C2312yes—
486#380C2314yes—
487#380C2312yes—
488#380C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2318yes—
509C4×C4⋊C4C2318yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2318yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2318yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2318yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2314yes—
529C2×#95C2314yes—
530C2×#95C2314yes—
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C43C2311yescharacteristic
537C43C2311yescharacteristic
538C43C2311yescharacteristic
539C2×#41—216no—
540C2×#41—28no—
541C2×#41—44no—
542C2×#41—44no—
543C2×#41—48no—
544C2×#41—48no—
545C22×Q8—28no—
546C22×Q8—28no—
547C22×Q8—44no—
548C22×Q8C2412yes—
549C22×Q8C2412yes—
550C22×Q8C2414yes—
551C22×Q8C2412yes—
552C22×Q8C2412yes—
553C22×D4C2414yes—
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2414yes—
558C22×D4C2412yes—
559C22×D4C2412yes—
560C22×D4C2412yes—
561C22×D4C2418yes—
562C22×D4C2418yes—
563C23×C4C2411yescharacteristic
564C23×C4C2414yes—
565C23×C4C2414yes—
566C23×C4C2411yescharacteristic
567C23×C4C2414yes—
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C23×C4C2414yes—
574C23×C4C2418yes—
575C23×C4C2414yes—
576C23×C4C2414yes—
577C4⋊Q8—28no—
578C4⋊Q8—28no—
579C4⋊Q8—28no—
580C4⋊Q8—24no—
581C4⋊Q8—24no—
582C4⋊Q8—24no—
583C4⋊Q8#4118yescomplemented
584#127—24no—
585#127—24no—
586#127—48no—
587#126—216no—
588#126—416no—
589#125—28no—
590#124—28no—
591#124—28no—
592#124—28no—
593#124—48no—
594#124—48no—
595#124—416no—
596#123—216no—
597#123—232no—
598C22⋊Q8—216no—
599C22⋊Q8—28no—
600C22⋊Q8—416no—
601C22⋊Q8—48no—
602C22⋊Q8—48no—
603#121—28no—
604#121—28no—
605#121—28no—
606#121—28no—
607#121—216no—
608#121—416no—
609#121—48no—
610#121—48no—
611#121—44no—
612#121—416no—
613#121—416no—
614C4×Q8—28no—
615C4×Q8—28no—
616C4×Q8—28no—
617C4×Q8—48no—
618C4×Q8—44no—
619C4×Q8—48no—
620C4×Q8—44no—
621C4×Q8—44no—
622C4×Q8—44no—
623C4×Q8—48no—
624C4×Q8—48no—
625C4×D4—216no—
626C4×D4—216no—
627C4×D4—28no—
628C4×D4—28no—
629C4×D4—28no—
630C4×D4—28no—
631C4×D4—28no—
632C4×D4—28no—
633C4×D4—28no—
634C4×D4—44no—
635C4×D4—44no—
636C4×D4—48no—
637C4×D4—44no—
638C4×D4—44no—
639C4×D4—48no—
640C4×D4—416no—
641#117—216no—
642#117—48no—
643#117—44no—
644#117—48no—
645#117—48no—
646C2×C4⋊C4—28no—
647C2×C4⋊C4—28no—
648C2×C4⋊C4—216no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—44no—
651C2×C4⋊C4—48no—
652C2×C4⋊C4—44no—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C42—24no—
731C2×C42—24no—
732C2×C42—24no—
733C2×C42—24no—
734C2×C42—48no—
735C2×C42—48no—
736C2×C42—42no—
737C2×C42—42no—
738C2×C42#4118yescomplemented
739C2×C42C2411yescharacteristic
740C2×C42C2414yes—
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2414yes—
746C2×C42C2414yes—
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2414yes—
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2414yes—
759C2×C42C2418yes—
760C2×C42C2418yes—
761C2×C42C2418yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2411yescharacteristic
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796#95C2414yes—
797#95C2414yes—
798#95C2418yes—
799#95C2414yes—
800#95C2418yes—
801#95C2418yes—
802#95C2418yes—
803#95C2418yes—
804#95C2414yes—
805#95C2414yes—
806#95C2418yes—
807#95C2418yes—
808C24C2514yes—
809C24C2514yes—
810C24C2511yescharacteristic
811#41—432no—
812#41—832no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—28no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—24no—
820C2×Q8—24no—
821C2×Q8—28no—
822C2×Q8—24no—
823C2×Q8—24no—
824C2×Q8—44no—
825C2×Q8—42no—
826C2×Q8—42no—
827C2×Q8—432no—
828C2×Q8C2×#4118yes—
829C2×D4—28no—
830C2×D4—28no—
831C2×D4—28no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—28no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—216no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—48no—
854C2×D4—48no—
855C2×D4—42no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4—48no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—28no—
872C22×C4—22no—
873C22×C4—28no—
874C22×C4—28no—
875C22×C4—28no—
876C22×C4—28no—
877C22×C4—28no—
878C22×C4—28no—
879C22×C4—22no—
880C22×C4—28no—
881C22×C4—28no—
882C22×C4—22no—
883C22×C4—28no—
884C22×C4—216no—
885C22×C4—28no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—44no—
897C22×C4C2×#4114yes—
898C22×C4C2×#4114yes—
899C22×C4C2×#4114yes—
900C22×C4H(5,𝔽2)14yes—
901C22×C4C2511yescharacteristic
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2511yescharacteristic
908C22×C4C2514yes—
909C22×C4C2514yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2514yes—
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C4⋊C4—24no—
926C4⋊C4—216no—
927C4⋊C4—28no—
928C4⋊C4—28no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—28no—
938C4⋊C4—24no—
939C4⋊C4—28no—
940C4⋊C4—24no—
941C4⋊C4—28no—
942C4⋊C4—24no—
943C4⋊C4—28no—
944C4⋊C4—24no—
945C4⋊C4—28no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—44no—
954C4⋊C4—42no—
955C4⋊C4—44no—
956C4⋊C4—42no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—44no—
963C4⋊C4—42no—
964C4⋊C4—48no—
965C4⋊C4—48no—
966C4⋊C4—48no—
967C4⋊C4—42no—
968C4⋊C4—48no—
969C4⋊C4C2×#4118yes—
970C4⋊C4C2×#4118yes—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—28no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—216no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—48no—
989C22⋊C4—44no—
990C22⋊C4—48no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—44no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—28no—
1006C42—22no—
1007C42—22no—
1008C42—22no—
1009C42—22no—
1010C42—22no—
1011C42—22no—
1012C42—22no—
1013C42—28no—
1014C42—28no—
1015C42—28no—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—22no—
1020C42—22no—
1021C42—41no—
1022C42—41no—
1023C42—41no—
1024C42—41no—
1025C42—41no—
1026C42—41no—
1027C42—44no—
1028C42—44no—
1029C42—44no—
1030C42—44no—
1031C42—48no—
1032C42—48no—
1033C42—48no—
1034C42C2×#4114yes—
1035C42C2×#4114yes—
1036C42C2×#4114yes—
1037C42C2×#4114yes—
1038C42C2×#4114yes—
1039C42H(5,𝔽2)14yes—
1040C422−1+414yes—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23—24no—
1059C23C22×#4112yes—
1060C23C2×H(5,𝔽2)12yes—
1061C23#58512yes—
1062C23C2611yescharacteristic
1063Q8—216no—
1064Q8—416no—
1065Q8—48no—
1066Q8—48no—
1067Q8—48no—
1068D4—48no—
1069D4—416no—
1070D4—416no—
1071D4—48no—
1072D4—48no—
1073D4—48no—
1074D4—48no—
1075D4—84no—
1076D4—816no—
1077D4—168no—
1078C2×C4—28no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—28no—
1100C2×C4—28no—
1101C2×C4—28no—
1102C2×C4—28no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—21no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—416no—
1139C2×C4—416no—
1140C2×C4—416no—
1141C2×C4—416no—
1142C2×C4—88no—
1143C2×C4—816no—
1144C2×C4—88no—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4112yes—
1147C2×C4C22×#4112yes—
1148C2×C4C22×#4112yes—
1149C2×C4C22×#4112yes—
1150C2×C4C22×#4118yes—
1151C2×C4C22×#4112yes—
1152C2×C4C22×#4112yes—
1153C2×C4C22×#4112yes—
1154C2×C4C22×#4112yes—
1155C2×C4C2×H(5,𝔽2)12yes—
1156C2×C4C2×H(5,𝔽2)12yes—
1157C2×C4C2×H(5,𝔽2)12yes—
1158C2×C4C2×H(5,𝔽2)12yes—
1159C2×C4C2×H(5,𝔽2)12yes—
1160C2×C4C2×2−1+412yes—
1161C2×C4C2×2−1+412yes—
1162C2×C4C2×2−1+412yes—
1163C2×C4#58512yes—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—44no—
1171C22—44no—
1172C22—44no—
1173C22—44no—
1174C22—44no—
1175C22—44no—
1176C22—44no—
1177C22—44no—
1178C22—44no—
1179C22—44no—
1180C22—44no—
1181C22—44no—
1182C22—44no—
1183C22—44no—
1184C22#350614yes—
1185C22C23×#4111yescharacteristic
1186C22C23×#4111yescharacteristic
1187C22C22×H(5,𝔽2)11yescharacteristic
1188C22C22×H(5,𝔽2)11yescharacteristic
1189C22C22×2−1+411yescharacteristic
1190C22C2×#58511yescharacteristic
1191C22C2×#58511yescharacteristic
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—28no—
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—22no—
1200C4—22no—
1201C4—22no—
1202C4—44no—
1203C4—44no—
1204C4—44no—
1205C4—44no—
1206C4—44no—
1207C4—41no—
1208C4—44no—
1209C4—44no—
1210C4—41no—
1211C4—44no—
1212C4—44no—
1213C4#348014yes—
1214C4#351114yes—
1215C4#351914yes—
1216C2—24no—
1217C2—84no—
1218C2—84no—
1219C2C2×#348011yescharacteristic
1220C2C2×#350611yescharacteristic
1221C2C2×#351911yescharacteristic
1222C2#6278811yescharacteristic
1223C2C2×#351111yescharacteristic
1224C2#6283011yescharacteristic
1225C2#6283511yescharacteristic
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. #59870C2semidirect
2. #59863C2semidirect
3. #59821C2semidirect
4. #59815C2semidirect
5. #59677C2semidirect
6. #59640C2semidirect
7. #59429C2semidirect
8. #59303C2semidirect
9. #59125C2semidirect
10. #40020C2semidirect
11. #39828C2semidirect
12. #39783C2semidirect
13. #38487C2semidirect
14. #36631C2semidirect
15. #36606C2semidirect
16. #36579C2semidirect
17. #36576C2semidirect
18. #36477C2semidirect
19. #36419C2semidirect
20. #36374C2semidirect
21. #35597C2semidirect
22. #35238C2semidirect
23. #35196C2semidirect
24. #34316C2semidirect
25. #34243C2semidirect
26. C4×#532C2semidirect
27. C2×C4×C4⋊Q8C2semidirect
583. C4⋊Q8#41semidirect
738. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#598702
#598632
#598212
#598152
#596772
#596402
#594292
#593032
#591252
#400202
#398282
#397832
#384872
#366312
#366062
#365792
#365762
#364772
#364192
#363742
#355972
#352382
#351962
#343162
#342432
C4×#5322
C2×C4×C4⋊Q82