Finite Group Databasebeta

← #8429410

Subgroups — #8429410

Order 512.

4249 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59666C212yesmaximal, complemented
3#59243C212yesmaximal, complemented
4#59065C212yesmaximal, complemented
5#55303C218yesmaximal, complemented
6#53111C214yesmaximal, complemented
7#53077C214yesmaximal, complemented
8#53029C214yesmaximal, complemented
9#42861C214yesmaximal, complemented
10#42692C214yesmaximal, complemented
11#42461C214yesmaximal, complemented
12#39727C212yesmaximal, complemented
13#39515C212yesmaximal, complemented
14#39481C212yesmaximal, complemented
15#39203C212yesmaximal, complemented
16#38943C212yesmaximal, complemented
17#38933C212yesmaximal, complemented
18#37635C212yesmaximal, complemented
19#37627C212yesmaximal
20#37624C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22#36188C211yesmaximal, characteristic, complemented
23#36134C211yesmaximal, characteristic, complemented
24#34943C211yesmaximal, characteristic
25#34941C211yesmaximal, characteristic, complemented
26#34929C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#533C2212yes—
29C2×#533C2212yes—
30#2868C2211yescharacteristic
31#2862C2212yes—
32#2857C2212yes—
33#2857C2212yes—
34#2841C2218yes—
35#2837C2218yes—
36#2837C2218yes—
37#2836C2218yes—
38#2836C2218yes—
39#2830C2218yes—
40#2817C2218yes—
41#2806C2214yes—
42#2802C2218yes—
43#2802C2218yes—
44#2798C2218yes—
45#2798C2218yes—
46#2786C2218yes—
47#2775C2218yes—
48#2773C2218yes—
49#2772C2218yes—
50#2769C2218yes—
51#2766C2218yes—
52#2759C2218yes—
53#2754C2218yes—
54#2744C2218yes—
55#2741C2218yes—
56#2738C2218yes—
57#2725C2218yes—
58#2723C2218yes—
59#2702C2218yes—
60#2666C2218yes—
61#2660C2214yes—
62#2655C2218yes—
63#2651C2218yes—
64#2647C2214yes—
65#2642C2214yes—
66#2634C2218yes—
67#2629C2214yes—
68#2628C2214yes—
69#2625C2214yes—
70#2625C2214yes—
71#2624C2214yes—
72#2620C2214yes—
73#2594C2218yes—
74#2592C2214yes—
75#2584C2214yes—
76#2582C2214yes—
77#2582C2212yes—
78#2582C2214yes—
79#2581C2214yes—
80#2581C2214yes—
81#2574C2214yes—
82#2572C2214yes—
83#2571C2211yescharacteristic
84#2571C2214yes—
85#2571C2212yes—
86#2570C2214yes—
87#2570C2214yes—
88#2568C2212yes—
89#2568C2212yes—
90#2567C2211yescharacteristic
91#2567C2212yes—
92#2565C2214yes—
93#2563C2211yescharacteristic
94#2563C2211yescharacteristic
95#2563C2211yescharacteristic
96#2556C2214yes—
97#2552C2212yes—
98#2552C2211yescharacteristic
99#2552C2212yes—
100#2552C2212yes—
101#2551C2211yescharacteristic
102#2550C2214yes—
103#2547C2212yes—
104#2547C2212yes—
105#2546C2211yescharacteristic
106#2542C2212yes—
107#2542C2211yescharacteristic
108#2538C2212yes—
109#2538C2211yescharacteristic
110#2538C2211yescharacteristic
111#2537C2211yescharacteristic
112#2536C2214yes—
113#2520C2218yes—
114#2514C2214yes—
115#2513C2214yes—
116#2513C2214yes—
117#2511C2214yes—
118#2508C2214yes—
119#2508C2212yes—
120#2507C2214yes—
121#2507C2214yes—
122#2506C2212yes—
123#2499C2214yes—
124#2499C2214yes—
125#2499C2214yes—
126#2497C2214yes—
127#2497C2212yes—
128#2496C2214yes—
129#2496C2214yes—
130#2495C2214yes—
131#2495C2212yes—
132#2495C2212yes—
133#2494C2214yes—
134#2494C2214yes—
135#2492C2212yes—
136#2490C2214yes—
137#2489C2214yes—
138#2489C2214yes—
139#2469C2218yes—
140#2454C2212yes—
141#2452C2212yes—
142#2448C2214yes—
143#2446C2214yes—
144#2441C2214yes—
145#2441C2214yes—
146#2439C2214yes—
147#2429C2214yes—
148#2429C2214yes—
149#2429C2212yes—
150#2426C2214yes—
151#2423C2214yes—
152#2423C2214yes—
153#2423C2214yes—
154#2423C2212yes—
155#2421C2214yes—
156#2420C2212yes—
157#2420C2212yes—
158#2415C2214yes—
159#2415C2214yes—
160#2398C2214yes—
161#2396C2214yes—
162#2396C2214yes—
163#2370C2214yes—
164#2369C2212yes—
165#2365C2212yes—
166#2365C2212yes—
167#2365C2212yes—
168#2365C2212yes—
169#2365C2212yes—
170#2355C2212yes—
171#2355C2212yes—
172#2354C2212yes—
173#2354C2214yes—
174#2351C2214yes—
175Q8×C4⋊C4C2212yes—
176Q8×C4⋊C4C2212yes—
177#2323C2214yes—
178#2320C2214yes—
179#2314C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×#125C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2293C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194#2283C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199#556—48no—
200#533—48no—
201#533—48no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#126C2318yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#124C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2314yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2314yes—
248C2×#117C2314yes—
249C2×#117C2314yes—
250C2×#117C2314yes—
251C22×C42C2312yes—
252C22×C42C2312yes—
253#401C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2314yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#399C2314yes—
269#399C2318yes—
270#399C2318yes—
271#399C2318yes—
272#399C2314yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2314yes—
278#398C2318yes—
279#398C2314yes—
280#398C2314yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2314yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#396C2314yes—
302#396C2314yes—
303#396C2318yes—
304#396C2314yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#395C2314yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2314yes—
314#394C2314yes—
315#394C2314yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#393C2314yes—
320#393C2314yes—
321#393C2314yes—
322#393C2314yes—
323#393C2318yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2314yes—
339#391C2318yes—
340#391C2318yes—
341#391C2314yes—
342#391C2314yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2318yes—
347#390C2312yes—
348#390C2314yes—
349#390C2312yes—
350#390C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2314yes—
369#389C2312yes—
370#389C2318yes—
371#389C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2312yes—
376#389C2314yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2314yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2318yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#388C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2314yes—
428#386C2314yes—
429#386C2314yes—
430#385C2314yes—
431#385C2314yes—
432#384C2311yescharacteristic
433#384C2312yes—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2314yes—
437#384C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#383C2314yes—
446#383C2314yes—
447#383C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2312yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#382C2318yes—
457#382C2312yes—
458#382C2314yes—
459#382C2318yes—
460#381C2314yes—
461#381C2314yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2312yes—
478#380C2312yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2318yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520C43C2312yes—
521C43C2311yescharacteristic
522C22×Q8C2412yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2414yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2414yes—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2414yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C4⋊Q8—24no—
538C4⋊Q8—28no—
539C4⋊Q8—24no—
540C4⋊Q8—28no—
541C4⋊Q8—24no—
542C4⋊Q8—44no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—44no—
546#126—416no—
547#125—48no—
548#125—44no—
549#125—48no—
550#125—48no—
551#124—48no—
552C22⋊Q8—48no—
553C22⋊Q8—44no—
554C22⋊Q8—44no—
555C22⋊Q8—48no—
556C22⋊Q8—44no—
557C22⋊Q8—44no—
558C22⋊Q8—48no—
559C22⋊Q8—48no—
560C22⋊Q8—48no—
561#121—44no—
562#121—44no—
563C4×Q8—24no—
564C4×Q8—28no—
565C4×Q8—24no—
566C4×Q8—44no—
567C4×Q8—44no—
568C4×Q8—48no—
569C4×Q8—48no—
570C4×Q8—42no—
571C4×Q8—48no—
572C4×Q8—48no—
573C4×Q8—48no—
574C4×Q8—48no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—42no—
580C4×D4—42no—
581C4×D4—48no—
582#117—48no—
583#117—48no—
584#117—48no—
585#117—48no—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C42—28no—
670C2×C42—28no—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2411yescharacteristic
676C2×C42C2414yes—
677C2×C42C2411yescharacteristic
678C2×C42C2412yes—
679C2×C42C2411yescharacteristic
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2418yes—
688C2×C42C2418yes—
689C2×C42C2412yes—
690C2×C42C2418yes—
691C2×C42C2418yes—
692C2×C42C2411yescharacteristic
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2412yes—
716#95C2414yes—
717#95C2414yes—
718#95C2412yes—
719#95C2412yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745C24C2512yes—
746C24C2512yes—
747C2×Q8—24no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—28no—
751C2×Q8—22no—
752C2×Q8—24no—
753C2×Q8—28no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—28no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—44no—
761C2×Q8—42no—
762C2×Q8—44no—
763C2×Q8—42no—
764C2×Q8—44no—
765C2×D4—22no—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2512yes—
801C22×C4C2518yes—
802C22×C4C2512yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2512yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2514yes—
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—22no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—42no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—42no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—28no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—28no—
910C42—22no—
911C42—28no—
912C42—22no—
913C42—22no—
914C42—24no—
915C42—41no—
916C42—42no—
917C42—48no—
918C42—48no—
919C42—42no—
920C42—48no—
921C42—48no—
922C42H(5,𝔽2)14yes—
923C422−1+414yes—
924C422−1+414yes—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23C2611yescharacteristic
940Q8—48no—
941Q8—48no—
942Q8—44no—
943Q8—416no—
944Q8—84no—
945Q8—88no—
946D4—44no—
947D4—44no—
948D4—88no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—28no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—28no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—48no—
1010C2×C4—48no—
1011C2×C4—48no—
1012C2×C4—48no—
1013C2×C4—84no—
1014C2×C4—84no—
1015C2×C4C2×H(5,𝔽2)12yes—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×H(5,𝔽2)12yes—
1018C2×C4C2×2−1+412yes—
1019C2×C4C2×2−1+412yes—
1020C2×C4C2×2−1+412yes—
1021C2×C4C2×2−1+412yes—
1022C2×C4C2×2−1+412yes—
1023C2×C4C2×2−1+412yes—
1024C2×C4#58512yes—
1025C2×C4#58512yes—
1026C2×C4#58512yes—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22C22×H(5,𝔽2)11yescharacteristic
1042C22C22×2−1+411yescharacteristic
1043C22C22×2−1+411yescharacteristic
1044C22C2×#58511yescharacteristic
1045C22C2×#58511yescharacteristic
1046C22C2×#58511yescharacteristic
1047C222−1+611yescharacteristic
1048C4—22no—
1049C4—22no—
1050C4—22no—
1051C4—42no—
1052C4—48no—
1053C4—42no—
1054C4—42no—
1055C4—44no—
1056C4—42no—
1057C4—42no—
1058C4—41no—
1059C4—42no—
1060C4—44no—
1061C4—44no—
1062C4—42no—
1063C4—44no—
1064C4—44no—
1065C4—42no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4#354714yes—
1070C4#355414yes—
1071C4#355514yes—
1072C2—82no—
1073C2—82no—
1074C2C2×#355411yescharacteristic
1075C2C2×#354711yescharacteristic
1076C2C2×#355511yescharacteristic
1077C2#6292511yescharacteristic
1078C2#6293211yescharacteristic
1079C2#6295911yescharacteristic
1080C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59666C2semidirect
3. #59243C2semidirect
4. #59065C2semidirect
5. #55303C2semidirect
6. #53111C2semidirect
7. #53077C2semidirect
8. #53029C2semidirect
9. #42861C2semidirect
10. #42692C2semidirect
11. #42461C2semidirect
12. #39727C2semidirect
13. #39515C2semidirect
14. #39481C2semidirect
15. #39203C2semidirect
16. #38943C2semidirect
17. #38933C2semidirect
18. #37635C2semidirect
20. #37624C2semidirect
21. #36598C2semidirect
22. #36188C2semidirect
23. #36134C2semidirect
25. #34941C2semidirect
26. #34929C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#596662
#592432
#590652
#553032
#531112
#530772
#530292
#428612
#426922
#424612
#397272
#395152
#394812
#392032
#389432
#389332
#376352
#376272
#376242
#365982
#361882
#361342
#349432
#349412
#349292