Finite Group Databasebeta

← #7654831

Subgroups — #7654831

Order 512.

5692 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#42989C214yesmaximal, complemented
2#42079C218yesmaximal, complemented
3#39560C214yesmaximal, complemented
4#39505C212yesmaximal, complemented
5#39191C212yesmaximal, complemented
6#39158C212yesmaximal, complemented
7#39052C214yesmaximal, complemented
8#38942C212yesmaximal, complemented
9#37780C214yesmaximal, complemented
10#37756C214yesmaximal, complemented
11#37639C211yesmaximal, characteristic, complemented
12#37625C212yesmaximal, complemented
13#36551C212yesmaximal, complemented
14#36453C212yesmaximal, complemented
15#36127C212yesmaximal, complemented
16#36126C212yesmaximal, complemented
17#35682C214yesmaximal, complemented
18#35275C211yesmaximal, characteristic, complemented
19#35273C211yesmaximal, characteristic, complemented
20#35207C212yesmaximal, complemented
21#35177C212yesmaximal, complemented
22#34977C211yesmaximal, characteristic, complemented
23#34925C212yesmaximal, complemented
24#34207C211yesmaximal, characteristic, complemented
25#34155C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27C2×#547C2214yes—
28C2×#544C2212yes—
29C2×#537C2212yes—
30C2×#532C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#532C2214yes—
33C2×#532C2214yes—
34C2×#520C2212yes—
35C2×C4×#41C2211yescharacteristic
36#2868C2212yes—
37#2859C2212yes—
38#2857C2214yes—
39#2857C2212yes—
40#2856C2212yes—
41#2855C2214yes—
42#2854C2214yes—
43#2851C2214yes—
44#2829C2218yes—
45#2819C2214yes—
46#2795C2218yes—
47#2778C2218yes—
48#2759C2218yes—
49#2756C2218yes—
50#2753C2218yes—
51#2731C2218yes—
52#2730C2218yes—
53#2711C2218yes—
54#2700C2218yes—
55#2699C2218yes—
56#2688C2218yes—
57#2676C2218yes—
58#2665C2218yes—
59#2660C2214yes—
60#2653C2218yes—
61#2644C2214yes—
62#2641C2214yes—
63#2630C2218yes—
64#2624C2214yes—
65#2620C2214yes—
66#2620C2214yes—
67#2619C2214yes—
68#2615C2214yes—
69#2615C2214yes—
70#2610C2214yes—
71#2602C2218yes—
72#2589C2218yes—
73#2576C2218yes—
74#2567C2211yescharacteristic
75#2563C2212yes—
76#2563C2212yes—
77#2563C2211yescharacteristic
78#2555C2218yes—
79#2552C2212yes—
80#2552C2212yes—
81#2551C2212yes—
82#2551C2212yes—
83#2548C2211yescharacteristic
84#2547C2214yes—
85#2541C2212yes—
86#2541C2212yes—
87#2541C2211yescharacteristic
88#2538C2212yes—
89#2538C2212yes—
90#2537C2212yes—
91#2537C2212yes—
92#2537C2212yes—
93#2537C2214yes—
94#2537C2212yes—
95#2509C2214yes—
96#2500C2214yes—
97#2500C2212yes—
98#2497C2214yes—
99#2497C2214yes—
100#2494C2214yes—
101#2494C2214yes—
102#2494C2214yes—
103#2492C2214yes—
104#2491C2214yes—
105#2491C2214yes—
106#2491C2214yes—
107#2490C2214yes—
108#2487C2214yes—
109#2485C2214yes—
110#2465C2218yes—
111#2463C2218yes—
112#2461C2218yes—
113#2460C2218yes—
114#2458C2218yes—
115#2456C2218yes—
116#2454C2214yes—
117#2452C2214yes—
118#2450C2218yes—
119#2445C2214yes—
120#2440C2214yes—
121#2440C2214yes—
122#2439C2214yes—
123#2432C2218yes—
124#2431C2212yes—
125#2430C2218yes—
126#2428C2214yes—
127#2428C2214yes—
128#2427C2214yes—
129#2422C2218yes—
130#2422C2214yes—
131#2422C2214yes—
132#2420C2214yes—
133#2416C2214yes—
134#2416C2214yes—
135#2416C2214yes—
136#2414C2214yes—
137#2414C2212yes—
138#2414C2212yes—
139#2407C2218yes—
140#2388C2218yes—
141#2388C2214yes—
142#2372C2214yes—
143#2369C2211yescharacteristic
144#2369C2211yescharacteristic
145#2366C2211yescharacteristic
146#2366C2211yescharacteristic
147#2363C2212yes—
148#2363C2212yes—
149#2363C2212yes—
150#2363C2212yes—
151#2361C2214yes—
152#2361C2214yes—
153#2361C2214yes—
154#2355C2211yescharacteristic
155#2355C2211yescharacteristic
156#2354C2212yes—
157#2354C2212yes—
158#2352C2212yes—
159#2352C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2211yescharacteristic
163D4×C4⋊C4C2214yes—
164D4×C4⋊C4C2212yes—
165#2347C2212yes—
166#2345C2214yes—
167#2343C2214yes—
168#2339C2212yes—
169#2331C2214yes—
170#2326C2214yes—
171#2324C2214yes—
172#2319C2214yes—
173#2317C2212yes—
174#2314C2214yes—
175#2311C2212yes—
176#2311C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×#127C2212yes—
179C4×#127C2212yes—
180C4×#124C2212yes—
181C4×#121C2212yes—
182C4×#121C2212yes—
183C4×#121C2214yes—
184C4×#121C2214yes—
185#2297C2214yes—
186#2295C2212yes—
187#2293C2212yes—
188#2293C2212yes—
189#2290C2214yes—
190#2285C2211yescharacteristic
191C2×#384C2211yescharacteristic
192#2283C2212yes—
193C42×D4C2212yes—
194C42×D4C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201C22×#41C2312yes—
202C22×#41C2318yes—
203#547—416no—
204#544—48no—
205#537—48no—
206#532—28no—
207#532—28no—
208#532—416no—
209#532—416no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×#127C2311yescharacteristic
217C2×#127C2312yes—
218C2×#127C2311yescharacteristic
219C2×#127C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2318yes—
226C2×#124C2318yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2318yes—
233C2×#121C2314yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2318yes—
248C2×#121C2318yes—
249C2×#121C2318yes—
250#520—48no—
251C4×#41—28no—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2314yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2318yes—
274C2×C4×D4C2318yes—
275C2×C4×D4C2318yes—
276C2×C4×D4C2312yes—
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2312yes—
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2314yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C42C2312yes—
293C22×C42C2314yes—
294C22×C42C2314yes—
295C22×C42C2311yescharacteristic
296#401C2318yes—
297#400C2318yes—
298#400C2318yes—
299#399C2318yes—
300#398C2318yes—
301#398C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#395C2314yes—
313#395C2318yes—
314#395C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2314yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2314yes—
330#394C2318yes—
331#393C2318yes—
332#393C2318yes—
333#393C2314yes—
334#393C2318yes—
335#393C2318yes—
336#392C2318yes—
337#392C2318yes—
338#392C2318yes—
339#392C2314yes—
340#392C2318yes—
341#392C2314yes—
342#392C2318yes—
343#392C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2312yes—
347#391C2318yes—
348#391C2318yes—
349#391C2314yes—
350#391C2312yes—
351#391C2312yes—
352#391C2314yes—
353#390C2312yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2312yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2318yes—
365#390C2312yes—
366#390C2314yes—
367#390C2314yes—
368#390C2314yes—
369#390C2312yes—
370#390C2312yes—
371#390C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2312yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2318yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2314yes—
423#387C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2314yes—
430#386C2314yes—
431#386C2314yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#386C2314yes—
437#386C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2314yes—
445#385C2314yes—
446#385C2318yes—
447#384C2312yes—
448#384C2312yes—
449#384C2314yes—
450#384C2314yes—
451#384C2312yes—
452#384C2312yes—
453#384C2311yescharacteristic
454#384C2312yes—
455#384C2311yescharacteristic
456#384C2314yes—
457#383C2314yes—
458#382C2314yes—
459#382C2312yes—
460#382C2312yes—
461#382C2314yes—
462#382C2312yes—
463#382C2312yes—
464#381C2318yes—
465#381C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2318yes—
477#380C2312yes—
478#380C2314yes—
479#380C2318yes—
480#380C2314yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522#376C2314yes—
523#376C2312yes—
524#376C2312yes—
525C2×#95C2314yes—
526C43C2312yes—
527C43C2312yes—
528C2×#41—24no—
529C2×#41—24no—
530C2×#41—28no—
531C2×#41—28no—
532C2×#41—44no—
533C2×#41—44no—
534C2×#41—44no—
535C2×#41—416no—
536C2×#41—44no—
537C2×#41—416no—
538C2×#41—42no—
539C2×#41—416no—
540C22×Q8C2411yescharacteristic
541C22×Q8C2412yes—
542C22×Q8C2418yes—
543C22×Q8C2412yes—
544C22×D4C2412yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2414yes—
549C22×D4C2412yes—
550C22×D4C2414yes—
551C22×D4C2411yescharacteristic
552C22×D4C2414yes—
553C22×D4C2412yes—
554C22×D4C2418yes—
555C22×D4C2414yes—
556C22×D4C2412yes—
557C22×D4C2418yes—
558C22×D4C2418yes—
559C23×C4C2412yes—
560C23×C4C2414yes—
561C23×C4C2414yes—
562C23×C4C2412yes—
563C23×C4C2414yes—
564C23×C4C2412yes—
565C23×C4C2414yes—
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2418yes—
570C23×C4C2414yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C4⋊Q8—216no—
574C4⋊Q8—24no—
575C4⋊Q8—24no—
576C4⋊Q8—48no—
577C4⋊Q8—48no—
578C4⋊Q8—48no—
579#127—28no—
580#127—24no—
581#127—24no—
582#127—48no—
583#125—48no—
584#125—48no—
585#124—28no—
586#124—28no—
587#124—44no—
588#124—416no—
589#124—416no—
590#123—416no—
591#123—416no—
592C22⋊Q8—48no—
593C22⋊Q8—416no—
594C22⋊Q8—416no—
595C22⋊Q8—48no—
596#121—216no—
597#121—28no—
598#121—28no—
599#121—28no—
600#121—28no—
601#121—28no—
602#121—28no—
603#121—416no—
604#121—416no—
605#121—416no—
606#121—48no—
607#121—48no—
608#121—48no—
609#121—48no—
610#121—48no—
611#121—48no—
612#121—48no—
613C4×Q8—24no—
614C4×Q8—24no—
615C4×Q8—48no—
616C4×D4—28no—
617C4×D4—28no—
618C4×D4—28no—
619C4×D4—28no—
620C4×D4—28no—
621C4×D4—28no—
622C4×D4—24no—
623C4×D4—24no—
624C4×D4—28no—
625C4×D4—28no—
626C4×D4—28no—
627C4×D4—28no—
628C4×D4—44no—
629C4×D4—44no—
630C4×D4—48no—
631C4×D4—48no—
632C4×D4—48no—
633C4×D4—48no—
634C4×D4—48no—
635C4×D4—416no—
636C4×D4—416no—
637C4×D4—416no—
638#117—24no—
639#117—24no—
640#117—24no—
641#117—24no—
642#117—28no—
643#117—48no—
644#117—44no—
645#117—42no—
646#117—48no—
647C2×C4⋊C4—216no—
648C2×C4⋊C4—28no—
649C2×C4⋊C4—44no—
650C2×C4⋊C4—44no—
651C2×C4⋊C4—44no—
652C2×C4⋊C4—44no—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C42—28no—
734C2×C42—48no—
735C2×C42—48no—
736C2×C42#4118yescomplemented
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2414yes—
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2412yes—
751C2×C42C2412yes—
752C2×C42C2418yes—
753C2×C42C2412yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#95C2412yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2412yes—
770#95C2412yes—
771#95C2412yes—
772#95C2412yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2418yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2418yes—
789#95C2414yes—
790#95C2418yes—
791#95C2418yes—
792#95C2418yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796C24C2514yes—
797C24C2514yes—
798C24C2511yescharacteristic
799C24C2512yes—
800#41—416no—
801#41—432no—
802#41—816no—
803#41—864no—
804C2×Q8—22no—
805C2×Q8—24no—
806C2×Q8—24no—
807C2×Q8—22no—
808C2×Q8—216no—
809C2×Q8—22no—
810C2×Q8—42no—
811C2×Q8—42no—
812C2×Q8—42no—
813C2×Q8—48no—
814C2×Q8—48no—
815C2×Q8—42no—
816C2×D4—24no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—24no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—216no—
823C2×D4—22no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—28no—
835C2×D4—24no—
836C2×D4—28no—
837C2×D4—24no—
838C2×D4—22no—
839C2×D4—24no—
840C2×D4—24no—
841C2×D4—42no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—44no—
848C2×D4—48no—
849C2×D4—42no—
850C2×D4—44no—
851C2×D4—48no—
852C2×D4—48no—
853C2×D4—48no—
854C2×D4—48no—
855C2×D4—48no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4—42no—
859C2×D4—44no—
860C2×D4H(5,𝔽2)14yes—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—28no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—28no—
873C22×C4—28no—
874C22×C4—24no—
875C22×C4—28no—
876C22×C4—28no—
877C22×C4—24no—
878C22×C4—28no—
879C22×C4—28no—
880C22×C4—28no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—28no—
884C22×C4—28no—
885C22×C4—216no—
886C22×C4—28no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—42no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4C2×#4114yes—
901C22×C4C2×#4114yes—
902C22×C4C2×#4114yes—
903C22×C4C2512yes—
904C22×C4C2512yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2512yes—
915C22×C4C2518yes—
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—28no—
934C4⋊C4—216no—
935C4⋊C4—24no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—28no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—24no—
942C4⋊C4—216no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—24no—
946C4⋊C4—22no—
947C4⋊C4—24no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—44no—
957C4⋊C4—48no—
958C4⋊C4—44no—
959C4⋊C4—48no—
960C4⋊C4—48no—
961C4⋊C4—48no—
962C4⋊C4—48no—
963C4⋊C4H(5,𝔽2)14yes—
964C4⋊C4H(5,𝔽2)14yes—
965C4⋊C42−1+414yes—
966C22⋊C4—24no—
967C22⋊C4—28no—
968C22⋊C4—216no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—28no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—24no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—42no—
986C22⋊C4—48no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C42—24no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—24no—
1011C42—28no—
1012C42—24no—
1013C42—24no—
1014C42—24no—
1015C42—24no—
1016C42—24no—
1017C42—24no—
1018C42—24no—
1019C42—24no—
1020C42—44no—
1021C42—44no—
1022C42—44no—
1023C42—44no—
1024C42—42no—
1025C42—48no—
1026C42C2×#4114yes—
1027C42C2×#4114yes—
1028C42C2×#4114yes—
1029C42C2×#4114yes—
1030C23—22no—
1031C23—21no—
1032C23—21no—
1033C23—22no—
1034C23—22no—
1035C23—21no—
1036C23—21no—
1037C23—22no—
1038C23—22no—
1039C23—21no—
1040C23—22no—
1041C23—21no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23C22×#4112yes—
1057C23C2×H(5,𝔽2)14yes—
1058C23C2611yescharacteristic
1059Q8—48no—
1060Q8—44no—
1061Q8—816no—
1062Q8—84no—
1063D4—28no—
1064D4—416no—
1065D4—416no—
1066D4—48no—
1067D4—48no—
1068D4—416no—
1069D4—48no—
1070D4—48no—
1071D4—48no—
1072D4—48no—
1073D4—84no—
1074D4—816no—
1075D4—88no—
1076D4—816no—
1077D4—816no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—28no—
1091C2×C4—28no—
1092C2×C4—28no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—28no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—28no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—416no—
1133C2×C4—48no—
1134C2×C4—416no—
1135C2×C4—48no—
1136C2×C4—416no—
1137C2×C4—416no—
1138C2×C4—48no—
1139C2×C4—88no—
1140C2×C4—816no—
1141C2×C4—88no—
1142C2×C4—164no—
1143C2×C4C22×#4112yes—
1144C2×C4C22×#4112yes—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4112yes—
1147C2×C4C22×#4112yes—
1148C2×C4C22×#4112yes—
1149C2×C4C2×H(5,𝔽2)14yes—
1150C2×C4C2×H(5,𝔽2)14yes—
1151C2×C4C2×H(5,𝔽2)12yes—
1152C2×C4C2×H(5,𝔽2)12yes—
1153C2×C4C2×H(5,𝔽2)12yes—
1154C2×C4C2×2−1+414yes—
1155C2×C4C2×2−1+412yes—
1156C2×C4#58512yes—
1157C2×C4#58512yes—
1158C22—24no—
1159C22—24no—
1160C22—22no—
1161C22—24no—
1162C22—22no—
1163C22—22no—
1164C22—41no—
1165C22—41no—
1166C22—42no—
1167C22—41no—
1168C22—41no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
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—44no—
1185C22—44no—
1186C22C23×#4111yescharacteristic
1187C22C22×H(5,𝔽2)11yescharacteristic
1188C22C22×H(5,𝔽2)11yescharacteristic
1189C22C22×H(5,𝔽2)11yescharacteristic
1190C22C22×2−1+411yescharacteristic
1191C22C2×#58511yescharacteristic
1192C22C2×#58511yescharacteristic
1193C4—24no—
1194C4—24no—
1195C4—24no—
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—44no—
1200C4—48no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—44no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—44no—
1209C4—42no—
1210C4—42no—
1211C4—44no—
1212C4#346014yes—
1213C4#349414yes—
1214C4#351114yes—
1215C2—44no—
1216C2—42no—
1217C2—84no—
1218C2—84no—
1219C2C2×#346011yescharacteristic
1220C2C2×#349411yescharacteristic
1221C2C2×#351111yescharacteristic
1222C2#6301111yescharacteristic
1223C2#6301311yescharacteristic
1224C2#6302211yescharacteristic
1225C2#6303911yescharacteristic
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. #42989C2semidirect
2. #42079C2semidirect
3. #39560C2semidirect
4. #39505C2semidirect
5. #39191C2semidirect
6. #39158C2semidirect
7. #39052C2semidirect
8. #38942C2semidirect
9. #37780C2semidirect
10. #37756C2semidirect
11. #37639C2semidirect
12. #37625C2semidirect
13. #36551C2semidirect
14. #36453C2semidirect
15. #36127C2semidirect
16. #36126C2semidirect
17. #35682C2semidirect
18. #35275C2semidirect
19. #35273C2semidirect
20. #35207C2semidirect
21. #35177C2semidirect
22. #34977C2semidirect
23. #34925C2semidirect
24. #34207C2semidirect
25. #34155C2semidirect
26. #34127C2semidirect
736. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#429892
#420792
#395602
#395052
#391912
#391582
#390522
#389422
#377802
#377562
#376392
#376252
#365512
#364532
#361272
#361262
#356822
#352752
#352732
#352072
#351772
#349772
#349252
#342072
#341552
#341272