Finite Group Databasebeta

← #7656034

Subgroups — #7656034

Order 512.

4526 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42184C214yesmaximal, complemented
2#42182C214yesmaximal, complemented
3#40635C214yesmaximal, complemented
4#40630C214yesmaximal, complemented
5#40620C214yesmaximal, complemented
6#40617C214yesmaximal, complemented
7#39175C214yesmaximal, complemented
8#38102C214yesmaximal, complemented
9#38096C214yesmaximal
10#37562C212yesmaximal, complemented
11#37478C212yesmaximal, complemented
12#37477C212yesmaximal, complemented
13#36319C214yesmaximal, complemented
14#35962C214yesmaximal, complemented
15#35951C214yesmaximal, complemented
16#35120C211yesmaximal, characteristic, complemented
17#35052C211yesmaximal, characteristic, complemented
18#35020C211yesmaximal, characteristic, complemented
19#34638C211yesmaximal, characteristic, complemented
20#34578C211yesmaximal, characteristic, complemented
21C2×#2646C211yesmaximal, characteristic, complemented
22#34194C212yesmaximal
23C2×#2353C211yesmaximal, characteristic
24C22×C4×D4C2211yescharacteristic
25#2855C2214yes—
26#2851C2214yes—
27#2848C2214yes—
28#2843C2214yescomplemented
29#2843C2214yescomplemented
30#2841C2214yescomplemented
31#2841C2214yescomplemented
32#2841C2214yescomplemented
33#2841C2214yescomplemented
34#2807C2214yescomplemented
35#2805C2214yescomplemented
36#2804C2214yes—
37#2802C2214yescomplemented
38#2791C2214yescomplemented
39#2790C2214yescomplemented
40#2788C2214yescomplemented
41#2788C2214yescomplemented
42#2784C2214yes—
43#2780C2214yes—
44#2780C2214yes—
45#2780C2214yes—
46#2774C2214yescomplemented
47#2768C2214yescomplemented
48#2755C2214yescomplemented
49#2755C2214yescomplemented
50#2748C2214yes—
51#2742C2214yescomplemented
52#2732C2214yes—
53#2729C2214yescomplemented
54#2726C2214yescomplemented
55#2713C2214yescomplemented
56#2704C2214yescomplemented
57#2692C2214yes—
58#2667C2214yescomplemented
59#2667C2214yescomplemented
60#2666C2214yescomplemented
61#2666C2214yescomplemented
62#2666C2214yescomplemented
63#2666C2214yescomplemented
64#2665C2214yescomplemented
65#2665C2214yescomplemented
66#2659C2212yes—
67#2659C2212yes—
68#2659C2212yes—
69#2659C2214yescomplemented
70#2647C2214yescomplemented
71#2647C2214yescomplemented
72#2646C2214yes—
73#2646C2211yescharacteristic
74#2646C2211yescharacteristic
75#2646C2212yes—
76#2646C2214yes—
77#2646C2211yescharacteristic
78#2646C2212yes—
79#2646C2211yescharacteristic
80#2646C2212yes—
81#2646C2214yescomplemented
82#2646C2214yescomplemented
83#2646C2214yescomplemented
84#2629C2214yescomplemented
85#2628C2214yescomplemented
86#2627C2214yescomplemented
87#2627C2214yescomplemented
88#2626C2214yes—
89#2612C2214yescomplemented
90#2612C2214yescomplemented
91#2606C2214yescomplemented
92#2606C2214yescomplemented
93#2605C2214yescomplemented
94#2605C2214yescomplemented
95#2590C2214yescomplemented
96#2589C2214yescomplemented
97#2589C2214yescomplemented
98#2589C2214yescomplemented
99#2588C2214yescomplemented
100#2587C2214yescomplemented
101#2587C2214yescomplemented
102#2587C2214yescomplemented
103#2585C2214yescomplemented
104#2585C2214yescomplemented
105#2583C2214yescomplemented
106#2579C2214yes—
107#2574C2214yescomplemented
108#2574C2214yescomplemented
109#2569C2214yes—
110#2569C2214yes—
111#2569C2214yescomplemented
112#2569C2214yescomplemented
113#2569C2214yescomplemented
114#2564C2214yes—
115#2556C2214yescomplemented
116#2556C2214yescomplemented
117#2549C2214yes—
118#2549C2214yes—
119#2549C2214yescomplemented
120#2549C2214yescomplemented
121#2522C2214yescomplemented
122#2522C2214yescomplemented
123#2522C2214yescomplemented
124#2520C2214yescomplemented
125#2511C2214yescomplemented
126#2505C2214yescomplemented
127#2497C2214yescomplemented
128#2492C2214yescomplemented
129#2487C2214yes—
130#2473C2214yescomplemented
131#2465C2214yescomplemented
132#2462C2214yescomplemented
133#2450C2214yes—
134#2450C2214yes—
135#2450C2214yes—
136#2449C2214yes—
137#2446C2214yescomplemented
138#2442C2214yes—
139#2442C2214yescomplemented
140#2442C2214yescomplemented
141#2442C2214yescomplemented
142#2440C2214yes—
143#2440C2214yescomplemented
144#2438C2214yes—
145#2438C2214yes—
146#2438C2214yescomplemented
147#2438C2214yescomplemented
148#2438C2214yescomplemented
149#2438C2214yescomplemented
150#2437C2214yes—
151#2437C2214yes—
152#2437C2214yes—
153#2437C2214yes—
154#2417C2214yes—
155#2402C2214yescomplemented
156#2402C2214yescomplemented
157#2396C2214yescomplemented
158#2396C2214yescomplemented
159C2×#400C2214yescomplemented
160C2×#398C2214yescomplemented
161#2368C2214yescomplemented
162#2368C2214yescomplemented
163#2360C2214yescomplemented
164#2354C2212yes—
165#2354C2212yes—
166#2353C2214yes—
167#2353C2214yes—
168#2353C2214yes—
169#2353C2214yes—
170#2352C2212yes—
171#2352C2212yes—
172#2352C2212yes—
173#2352C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176#2345C2214yes—
177#2345C2214yescomplemented
178#2342C2214yes—
179#2342C2214yes—
180D4×C22⋊C4C2214yes—
181#2329C2214yes—
182#2329C2214yes—
183#2319C2214yes—
184#2318C2214yes—
185#2318C2214yes—
186#2315C2214yes—
187C4×C22⋊Q8C2214yes—
188#2296C2214yes—
189C2×#388C2212yes—
190C2×#387C2212yes—
191C2×#386C2212yes—
192C2×#385C2214yes—
193#2285C2212yes—
194#2283C2212yes—
195C2×#383C2211yescharacteristic
196#2280C2212yes—
197#2280C2212yes—
198C2×#381C2211yescharacteristic
199C2×#380C2212yes—
200C2×#380C2211yescharacteristic
201C2×#380C2212yes—
202#2275C2214yes—
203C2×C4×C22⋊C4C2211yescharacteristic
204C2×C4×C22⋊C4C2212yes—
205C2×#376C2211yescharacteristic
206C22×#95C2211yescharacteristic
207C23×D4C2311yescharacteristic
208C24×C4C2312yes—
209C24×C4C2311yescharacteristic
210C24×C4C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×D4Q8116yescomplemented
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×#117C2314yes—
232C2×#117C2312yes—
233C2×#117C2312yes—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C22×C4⋊C4C2314yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4C2314yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2314yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2311yescharacteristic
250C22×C22⋊C4C2311yescharacteristic
251C22×C42C2312yes—
252C22×C42C2312yes—
253C22×C42C2311yescharacteristic
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#399C2314yes—
281#399C2314yes—
282#399C2314yes—
283#399C2314yes—
284#399C2314yes—
285#399C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#393C2314yes—
353#393C2314yes—
354#393C2314yes—
355#393C2314yes—
356#393C2314yes—
357#393C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#390C2314yes—
372#390C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#386C2314yes—
449#386C2314yes—
450#386C2314yes—
451#386C2314yes—
452#386C2314yes—
453#386C2314yes—
454#386C2314yes—
455#386C2314yes—
456#385C2314yes—
457#385C2314yes—
458#385C2314yes—
459#385C2314yes—
460#385C2314yes—
461#385C2314yes—
462#385C2314yes—
463#385C2314yes—
464#385C2314yes—
465#385C2314yes—
466#385C2314yes—
467#385C2314yes—
468#385C2314yes—
469#385C2314yes—
470#385C2314yes—
471#385C2314yes—
472#385C2314yes—
473#385C2314yes—
474#385C2314yes—
475#385C2314yes—
476#385C2314yes—
477#385C2314yes—
478#385C2314yes—
479#385C2314yes—
480#385C2314yes—
481#385C2314yes—
482#385C2314yes—
483#385C2314yes—
484#385C2314yes—
485#385C2314yes—
486#385C2314yes—
487#385C2314yes—
488#385C2314yes—
489#385C2314yes—
490#384C2312yes—
491#384C2312yes—
492#384C2314yes—
493#383C2314yes—
494#383C2314yes—
495#383C2314yes—
496#382C2314yes—
497#382C2314yes—
498#382C2314yes—
499#382C2312yes—
500#382C2312yes—
501#381C2314yes—
502#381C2314yes—
503#381C2314yes—
504#381C2314yes—
505#381C2314yes—
506#380C2314yes—
507#380C2314yes—
508#380C2314yes—
509#380C2314yes—
510#380C2314yes—
511#380C2314yes—
512#380C2314yes—
513#380C2312yes—
514#380C2312yes—
515#380C2312yes—
516#380C2314yes—
517#380C2314yes—
518#380C2314yes—
519#380C2314yes—
520#380C2314yes—
521#380C2314yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2312yes—
526#380C2312yes—
527#380C2312yes—
528#380C2312yes—
529#380C2314yes—
530#380C2314yes—
531#380C2312yes—
532#380C2314yes—
533#380C2314yes—
534#380C2312yes—
535#380C2312yes—
536#380C2312yes—
537#380C2312yes—
538#379C2314yes—
539#379C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2312yes—
551C4×C4⋊C4C2312yes—
552C4×C4⋊C4C2312yes—
553C4×C4⋊C4C2312yes—
554C4×C22⋊C4C2314yes—
555C4×C22⋊C4C2314yes—
556C4×C22⋊C4C2314yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2314yes—
559C4×C22⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569#376C2314yes—
570#376C2314yes—
571#376C2314yes—
572C2×#95C2314yes—
573C2×#95C2312yes—
574C2×#95C2312yes—
575C2×#95C2314yes—
576C2×#95C2314yes—
577C2×#95C2314yes—
578C2×#95C2312yes—
579C2×#95C2312yes—
580C2×#95C2314yes—
581C2×#95C2314yes—
582C2×#95C2311yescharacteristic
583C2×#95C2311yescharacteristic
584C2×#95C2311yescharacteristic
585C2×#95C2311yescharacteristic
586C2×#95C2312yes—
587C25C2411yescharacteristic
588C25C2411yescharacteristic
589C22×Q8C2414yes—
590C22×Q8C2414yes—
591C22×Q8C2414yes—
592C22×D4—42no—
593C22×D4—42no—
594C22×D4C2×Q818yes—
595C22×D4C2412yes—
596C22×D4C2412yes—
597C23×C4—44no—
598C23×C4—44no—
599C23×C4—82no—
600C23×C4—82no—
601C23×C4—82no—
602C23×C4C2×Q818yes—
603C23×C4C2×Q818yes—
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2412yes—
610C23×C4C2412yes—
611C23×C4C2414yes—
612C23×C4C2414yes—
613C23×C4C2414yes—
614C23×C4C2414yes—
615C23×C4C2411yescharacteristic
616C23×C4C2411yescharacteristic
617C23×C4C2412yes—
618C23×C4C2412yes—
619C23×C4C2411yescharacteristic
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2411yescharacteristic
623C4⋊Q8—84no—
624#125—84no—
625#125—84no—
626C22⋊Q8—48no—
627C22⋊Q8—48no—
628C22⋊Q8—48no—
629C22⋊Q8—48no—
630C22⋊Q8—48no—
631C22⋊Q8—48no—
632C22⋊Q8—84no—
633C22⋊Q8—84no—
634C22⋊Q8—84no—
635C4×Q8—84no—
636C4×D4—48no—
637C4×D4—48no—
638C4×D4C2×Q8116yes—
639C4×D4C2×Q8116yes—
640C4×D4C2×Q8116yes—
641C4×D4C2×Q8116yes—
642#117—48no—
643#117—82no—
644#117—82no—
645#117—82no—
646#117—82no—
647C2×C4⋊C4—48no—
648C2×C4⋊C4—82no—
649C2×C4⋊C4—82no—
650C2×C4⋊C4—82no—
651C2×C4⋊C4—82no—
652C2×C4⋊C4—84no—
653C2×C4⋊C4—82no—
654C2×C4⋊C4C2×Q818yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C22⋊C4—48no—
711C2×C22⋊C4—48no—
712C2×C22⋊C4—44no—
713C2×C22⋊C4—44no—
714C2×C22⋊C4—82no—
715C2×C22⋊C4C2×Q818yes—
716C2×C22⋊C4C2×Q818yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2411yescharacteristic
740C2×C22⋊C4C2411yescharacteristic
741C2×C22⋊C4C2411yescharacteristic
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2411yescharacteristic
744C2×C22⋊C4C2412yes—
745C2×C42—44no—
746C2×C42—82no—
747C2×C42C2×Q818yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2412yes—
761C2×C42C2412yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
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#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822C24—24no—
823C24—22no—
824C24—22no—
825C24—24no—
826C24—42no—
827C24—42no—
828C24—41no—
829C24—41no—
830C24C22×Q814yes—
831C24C22×Q814yes—
832C24C2512yes—
833C24C2511yescharacteristic
834C24C2511yescharacteristic
835C24C2511yescharacteristic
836C2×Q8—44no—
837C2×Q8—44no—
838C2×Q8—44no—
839C2×Q8—44no—
840C2×Q8—44no—
841C2×Q8—44no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—44no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—416no—
850C2×D4C22×Q818yes—
851C2×D4C22×Q818yes—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—28no—
857C22×C4—28no—
858C22×C4—28no—
859C22×C4—24no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—42no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—42no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—88no—
897C22×C4—88no—
898C22×C4—816no—
899C22×C4C22×Q814yes—
900C22×C4C22×Q814yes—
901C22×C4C22×Q814yes—
902C22×C4C22×Q814yes—
903C22×C4C22×Q814yes—
904C22×C4C22×Q818yes—
905C22×C4C22×Q818yes—
906C22×C4C22×Q818yes—
907C22×C4C22×Q818yes—
908C22×C4C2514yes—
909C22×C4C2514yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2514yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2514yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2514yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2512yes—
926C22×C4C2511yescharacteristic
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4C22×Q818yes—
981C4⋊C4C22×Q818yes—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4C22×Q818yes—
1005C22⋊C4C22×Q814yes—
1006C22⋊C4C22×Q814yes—
1007C22⋊C4C22×Q818yes—
1008C22⋊C4C22×Q814yes—
1009C22⋊C4C22×Q814yes—
1010C42—44no—
1011C42—44no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42—44no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C42—44no—
1020C42—44no—
1021C42—44no—
1022C42C22×Q818yes—
1023C42C22×Q818yes—
1024C23—22no—
1025C23—21no—
1026C23—21no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—21no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—21no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—28no—
1040C23—28no—
1041C23—28no—
1042C23—44no—
1043C23—44no—
1044C23—44no—
1045C23—48no—
1046C23—48no—
1047C23—84no—
1048C23—84no—
1049C23C23×Q814yes—
1050C23C23×Q812yes—
1051C23C23×Q812yes—
1052C23C23×Q812yes—
1053C23#58512yes—
1054C23#58512yes—
1055C23#58514yes—
1056C23C2611yescharacteristic
1057Q8—88no—
1058Q8—164no—
1059Q8—164no—
1060D4—216no—
1061D4—48no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—28no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—44no—
1110C2×C4—48no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—48no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—48no—
1118C2×C4—88no—
1119C2×C4—88no—
1120C2×C4—84no—
1121C2×C4—84no—
1122C2×C4—88no—
1123C2×C4—84no—
1124C2×C4—88no—
1125C2×C4—164no—
1126C2×C4—164no—
1127C2×C4C23×Q812yes—
1128C2×C4C23×Q812yes—
1129C2×C4C23×Q814yes—
1130C2×C4C23×Q814yes—
1131C2×C4C23×Q812yes—
1132C2×C4C23×Q814yes—
1133C2×C4C23×Q812yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—24no—
1138C22—24no—
1139C22—22no—
1140C22—24no—
1141C22—24no—
1142C22—22no—
1143C22—24no—
1144C22—22no—
1145C22—24no—
1146C22—24no—
1147C22—22no—
1148C22—416no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—88no—
1156C22#345814yes—
1157C22#350414yes—
1158C22C24×Q811yescharacteristic
1159C22C2×#58512yes—
1160C22C2×#58511yescharacteristic
1161C22C2×#58511yescharacteristic
1162C22H(7,𝔽2)12yes—
1163C4—22no—
1164C4—22no—
1165C4—24no—
1166C4—22no—
1167C4—22no—
1168C4—24no—
1169C4—24no—
1170C4—44no—
1171C4—44no—
1172C4—44no—
1173C4—44no—
1174C4—44no—
1175C4—44no—
1176C4—44no—
1177C4—44no—
1178C4—44no—
1179C4—44no—
1180C4—44no—
1181C4—44no—
1182C2—24no—
1183C2—24no—
1184C2—42no—
1185C2—44no—
1186C2C2×#345811yescharacteristic
1187C2C2×#350411yescharacteristic
1188C2#6284311yescharacteristic
1189C2#6290612yes—
1190C2#6296312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42184C2semidirect
2. #42182C2semidirect
3. #40635C2semidirect
4. #40630C2semidirect
5. #40620C2semidirect
6. #40617C2semidirect
7. #39175C2semidirect
8. #38102C2semidirect
10. #37562C2semidirect
11. #37478C2semidirect
12. #37477C2semidirect
13. #36319C2semidirect
14. #35962C2semidirect
15. #35951C2semidirect
16. #35120C2semidirect
17. #35052C2semidirect
18. #35020C2semidirect
19. #34638C2semidirect
20. #34578C2semidirect
21. C2×#2646C2semidirect
28. #2843C22semidirect
29. #2843C22semidirect
30. #2841C22semidirect
31. #2841C22semidirect
32. #2841C22semidirect
33. #2841C22semidirect
34. #2807C22semidirect
35. #2805C22semidirect
37. #2802C22semidirect
38. #2791C22semidirect
39. #2790C22semidirect
40. #2788C22semidirect
41. #2788C22semidirect
46. #2774C22semidirect
47. #2768C22semidirect
48. #2755C22semidirect
49. #2755C22semidirect
51. #2742C22semidirect
53. #2729C22semidirect
54. #2726C22semidirect
55. #2713C22semidirect
56. #2704C22semidirect
58. #2667C22semidirect
59. #2667C22semidirect
60. #2666C22semidirect
61. #2666C22semidirect
62. #2666C22semidirect
63. #2666C22semidirect
64. #2665C22semidirect
65. #2665C22semidirect
69. #2659C22semidirect
70. #2647C22semidirect
71. #2647C22semidirect
81. #2646C22semidirect
82. #2646C22semidirect
83. #2646C22semidirect
84. #2629C22semidirect
85. #2628C22semidirect
86. #2627C22semidirect
87. #2627C22semidirect
89. #2612C22semidirect
90. #2612C22semidirect
91. #2606C22semidirect
92. #2606C22semidirect
93. #2605C22semidirect
94. #2605C22semidirect
95. #2590C22semidirect
96. #2589C22semidirect
97. #2589C22semidirect
98. #2589C22semidirect
99. #2588C22semidirect
100. #2587C22semidirect
101. #2587C22semidirect
102. #2587C22semidirect
103. #2585C22semidirect
104. #2585C22semidirect
105. #2583C22semidirect
107. #2574C22semidirect
108. #2574C22semidirect
111. #2569C22semidirect
112. #2569C22semidirect
113. #2569C22semidirect
115. #2556C22semidirect
116. #2556C22semidirect
119. #2549C22semidirect
120. #2549C22semidirect
121. #2522C22semidirect
122. #2522C22semidirect
123. #2522C22semidirect
124. #2520C22semidirect
125. #2511C22semidirect
126. #2505C22semidirect
127. #2497C22semidirect
128. #2492C22semidirect
130. #2473C22semidirect
131. #2465C22semidirect
132. #2462C22semidirect
137. #2446C22semidirect
139. #2442C22semidirect
140. #2442C22semidirect
141. #2442C22semidirect
143. #2440C22semidirect
146. #2438C22semidirect
147. #2438C22semidirect
148. #2438C22semidirect
149. #2438C22semidirect
155. #2402C22semidirect
156. #2402C22semidirect
157. #2396C22semidirect
158. #2396C22semidirect
159. C2×#400C22semidirect
160. C2×#398C22semidirect
161. #2368C22semidirect
162. #2368C22semidirect
163. #2360C22semidirect
177. #2345C22semidirect
224. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#421842
#421822
#406352
#406302
#406202
#406172
#391752
#381022
#380962
#375622
#374782
#374772
#363192
#359622
#359512
#351202
#350522
#350202
#346382
#345782
C2×#26462
#341942
C2×#23532