Finite Group Databasebeta

← #8429481

Subgroups — #8429481

Order 512.

4529 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C212yesmaximal, complemented
2#59828C211yesmaximal, characteristic, complemented
3#59245C212yesmaximal, complemented
4#59055C212yesmaximal, complemented
5#55301C218yesmaximal, complemented
6#53130C214yesmaximal, complemented
7#53107C214yesmaximal, complemented
8#53070C214yesmaximal, complemented
9#42840C214yesmaximal, complemented
10#42708C214yesmaximal, complemented
11#42621C214yesmaximal, complemented
12#39727C212yesmaximal, complemented
13#39609C212yesmaximal, complemented
14#39599C212yesmaximal, complemented
15#39200C212yesmaximal, complemented
16#39200C212yesmaximal, complemented
17#39139C212yesmaximal, complemented
18#37641C212yesmaximal, complemented
19#37627C212yesmaximal
20#37622C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22#36188C211yesmaximal, characteristic, complemented
23#36134C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic
25#34929C211yesmaximal, characteristic, complemented
26#34929C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#556C2212yes—
29C2×#533C2212yes—
30C2×#533C2212yes—
31C2×#533C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2862C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2839C2218yes—
38#2837C2218yes—
39#2836C2218yes—
40#2832C2218yes—
41#2831C2218yes—
42#2822C2218yes—
43#2814C2218yes—
44#2806C2218yes—
45#2800C2218yes—
46#2798C2218yes—
47#2791C2218yes—
48#2788C2218yes—
49#2774C2218yes—
50#2773C2218yes—
51#2773C2218yes—
52#2754C2218yes—
53#2754C2218yes—
54#2742C2218yes—
55#2726C2214yes—
56#2726C2218yes—
57#2725C2218yes—
58#2721C2218yes—
59#2721C2218yes—
60#2704C2218yes—
61#2702C2218yes—
62#2694C2218yes—
63#2664C2218yes—
64#2654C2218yes—
65#2651C2218yes—
66#2629C2214yes—
67#2628C2214yes—
68#2625C2218yes—
69#2625C2214yes—
70#2625C2214yes—
71#2625C2214yes—
72#2624C2214yes—
73#2621C2214yes—
74#2621C2214yes—
75#2620C2214yes—
76#2592C2214yes—
77#2592C2214yes—
78#2588C2218yes—
79#2584C2214yes—
80#2584C2214yes—
81#2582C2214yes—
82#2582C2214yes—
83#2582C2214yes—
84#2582C2214yes—
85#2582C2212yes—
86#2582C2212yes—
87#2571C2212yes—
88#2570C2214yes—
89#2568C2212yes—
90#2568C2214yes—
91#2568C2212yes—
92#2567C2214yes—
93#2556C2214yes—
94#2556C2214yes—
95#2553C2214yes—
96#2552C2212yes—
97#2552C2214yes—
98#2552C2211yescharacteristic
99#2552C2212yes—
100#2551C2211yescharacteristic
101#2551C2211yescharacteristic
102#2547C2211yescharacteristic
103#2547C2212yes—
104#2547C2212yes—
105#2546C2211yescharacteristic
106#2546C2214yes—
107#2546C2212yes—
108#2546C2211yescharacteristic
109#2542C2211yescharacteristic
110#2542C2212yes—
111#2542C2211yescharacteristic
112#2542C2211yescharacteristic
113#2542C2214yes—
114#2538C2212yes—
115#2538C2211yescharacteristic
116#2538C2211yescharacteristic
117#2537C2211yescharacteristic
118#2536C2214yes—
119#2511C2214yes—
120#2511C2214yes—
121#2511C2214yes—
122#2509C2214yes—
123#2507C2218yes—
124#2506C2212yes—
125#2506C2214yes—
126#2506C2212yes—
127#2499C2214yes—
128#2497C2214yes—
129#2496C2214yes—
130#2496C2212yes—
131#2496C2214yes—
132#2492C2214yes—
133#2492C2214yes—
134#2492C2212yes—
135#2492C2212yes—
136#2490C2214yes—
137#2489C2212yes—
138#2479C2218yes—
139#2453C2214yes—
140#2452C2212yes—
141#2452C2212yes—
142#2451C2214yes—
143#2448C2214yes—
144#2448C2214yes—
145#2446C2214yes—
146#2446C2214yes—
147#2441C2214yes—
148#2439C2214yes—
149#2429C2214yes—
150#2429C2214yes—
151#2429C2214yes—
152#2429C2212yes—
153#2429C2212yes—
154#2427C2212yes—
155#2426C2214yes—
156#2423C2214yes—
157#2423C2214yes—
158#2423C2214yes—
159#2423C2214yes—
160#2422C2212yes—
161#2415C2214yes—
162#2415C2214yes—
163#2396C2214yes—
164#2396C2214yes—
165#2395C2214yes—
166#2369C2214yes—
167#2365C2212yes—
168#2365C2212yes—
169#2365C2212yes—
170#2365C2212yes—
171#2365C2212yes—
172#2362C2214yes—
173#2355C2212yes—
174#2355C2212yes—
175#2354C2212yes—
176Q8×C4⋊C4C2212yes—
177Q8×C4⋊C4C2212yes—
178Q8×C4⋊C4C2214yes—
179#2323C2214yes—
180#2323C2214yes—
181#2323C2214yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2211yescharacteristic
186C4×C4⋊Q8C2211yescharacteristic
187C4×C4⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191C4×#121C2212yes—
192#2293C2212yes—
193#2293C2212yes—
194#2285C2212yes—
195#2285C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199#557—48no—
200#556—48no—
201#533—48no—
202#533—48no—
203#533—48no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217#529—48no—
218C2×#126C2314yes—
219C2×#126C2318yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#124C2312yes—
227C2×#124C2314yes—
228C2×#123C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2314yes—
265C2×C4×D4C2311yescharacteristic
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C22×C42C2312yes—
272C22×C42C2312yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2318yes—
280#400C2318yes—
281#400C2314yes—
282#400C2314yes—
283#400C2318yes—
284#400C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2314yes—
289#399C2314yes—
290#399C2314yes—
291#399C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2314yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#397C2314yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2314yes—
322#397C2314yes—
323#396C2318yes—
324#396C2318yes—
325#396C2314yes—
326#396C2318yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2318yes—
331#395C2318yes—
332#395C2318yes—
333#395C2314yes—
334#395C2314yes—
335#394C2314yes—
336#394C2318yes—
337#394C2318yes—
338#394C2314yes—
339#394C2318yes—
340#393C2314yes—
341#393C2314yes—
342#393C2318yes—
343#393C2318yes—
344#391C2314yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2312yes—
353#391C2318yes—
354#391C2314yes—
355#391C2314yes—
356#391C2318yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2318yes—
361#391C2314yes—
362#391C2312yes—
363#391C2318yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2312yes—
368#390C2312yes—
369#390C2312yes—
370#390C2312yes—
371#390C2314yes—
372#390C2318yes—
373#390C2312yes—
374#390C2312yes—
375#389C2312yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2318yes—
390#389C2318yes—
391#389C2314yes—
392#389C2312yes—
393#389C2318yes—
394#389C2318yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2318yes—
401#389C2318yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2318yes—
406#389C2312yes—
407#389C2318yes—
408#389C2314yes—
409#389C2318yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2318yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2314yes—
427#388C2314yes—
428#388C2318yes—
429#388C2318yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2314yes—
442#387C2314yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2314yes—
449#386C2314yes—
450#385C2314yes—
451#385C2314yes—
452#385C2314yes—
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2312yes—
457#384C2312yes—
458#384C2312yes—
459#384C2314yes—
460#384C2312yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2314yes—
465#384C2318yes—
466#384C2312yes—
467#382C2314yes—
468#382C2314yes—
469#382C2314yes—
470#382C2314yes—
471#382C2314yes—
472#380C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480#380C2314yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2318yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2311yescharacteristic
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2414yes—
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C4⋊Q8—28no—
542C4⋊Q8—24no—
543C4⋊Q8—28no—
544C4⋊Q8—24no—
545C4⋊Q8—24no—
546C4⋊Q8—28no—
547C4⋊Q8—44no—
548C4⋊Q8—44no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552C4⋊Q8—44no—
553C4⋊Q8—48no—
554#126—48no—
555#126—416no—
556#125—44no—
557#125—48no—
558#125—48no—
559#125—48no—
560#125—48no—
561#125—416no—
562#124—44no—
563#124—48no—
564#123—48no—
565C22⋊Q8—28no—
566C22⋊Q8—28no—
567C22⋊Q8—28no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C22⋊Q8—48no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—48no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579#121—44no—
580#121—44no—
581C4×Q8—24no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—28no—
586C4×Q8—28no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—42no—
601C4×D4—48no—
602#117—48no—
603#117—48no—
604#117—48no—
605#117—48no—
606#117—48no—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C42—28no—
696C2×C42—28no—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2411yescharacteristic
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2412yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765C24C2512yes—
766C24C2512yes—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—28no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—28no—
782C2×Q8—28no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4C2511yescharacteristic
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2518yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C42−1+414yes—
902C4⋊C42−1+414yes—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—42no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—28no—
936C42—28no—
937C42—28no—
938C42—22no—
939C42—22no—
940C42—24no—
941C42—24no—
942C42—22no—
943C42—24no—
944C42—41no—
945C42—42no—
946C42—48no—
947C42—48no—
948C42—48no—
949C42—48no—
950C42H(5,𝔽2)14yes—
951C42H(5,𝔽2)14yes—
952C422−1+414yes—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23C2611yescharacteristic
968Q8—48no—
969Q8—44no—
970Q8—48no—
971Q8—48no—
972Q8—416no—
973Q8—88no—
974Q8—88no—
975D4—44no—
976D4—44no—
977D4—88no—
978C2×C4—22no—
979C2×C4—21no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—28no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—28no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—48no—
1037C2×C4—48no—
1038C2×C4—48no—
1039C2×C4—48no—
1040C2×C4—48no—
1041C2×C4—84no—
1042C2×C4C2×H(5,𝔽2)12yes—
1043C2×C4C2×H(5,𝔽2)12yes—
1044C2×C4C2×H(5,𝔽2)12yes—
1045C2×C4C2×H(5,𝔽2)12yes—
1046C2×C4C2×H(5,𝔽2)12yes—
1047C2×C4C2×H(5,𝔽2)12yes—
1048C2×C4C2×2−1+414yes—
1049C2×C4C2×2−1+412yes—
1050C2×C4C2×2−1+414yes—
1051C2×C4C2×2−1+412yes—
1052C2×C4C2×2−1+412yes—
1053C2×C4C2×2−1+412yes—
1054C2×C4C2×2−1+412yes—
1055C2×C4#58512yes—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22C22×H(5,𝔽2)11yescharacteristic
1071C22C22×H(5,𝔽2)11yescharacteristic
1072C22C22×2−1+411yescharacteristic
1073C22C22×2−1+411yescharacteristic
1074C22C22×2−1+411yescharacteristic
1075C22C2×#58511yescharacteristic
1076C222−1+611yescharacteristic
1077C4—24no—
1078C4—22no—
1079C4—24no—
1080C4—22no—
1081C4—22no—
1082C4—42no—
1083C4—48no—
1084C4—42no—
1085C4—42no—
1086C4—44no—
1087C4—42no—
1088C4—44no—
1089C4—42no—
1090C4—44no—
1091C4—41no—
1092C4—44no—
1093C4—42no—
1094C4—42no—
1095C4—44no—
1096C4—44no—
1097C4—42no—
1098C4#354814yes—
1099C4#355014yes—
1100C4#355414yes—
1101C2—82no—
1102C2—82no—
1103C2C2×#355411yescharacteristic
1104C2C2×#354811yescharacteristic
1105C2C2×#355011yescharacteristic
1106C2#6294211yescharacteristic
1107C2#6294711yescharacteristic
1108C2#6296011yescharacteristic
1109C2#6303211yescharacteristic
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. #59828C2semidirect
3. #59245C2semidirect
4. #59055C2semidirect
5. #55301C2semidirect
6. #53130C2semidirect
7. #53107C2semidirect
8. #53070C2semidirect
9. #42840C2semidirect
10. #42708C2semidirect
11. #42621C2semidirect
12. #39727C2semidirect
13. #39609C2semidirect
14. #39599C2semidirect
15. #39200C2semidirect
16. #39200C2semidirect
17. #39139C2semidirect
18. #37641C2semidirect
20. #37622C2semidirect
21. #36598C2semidirect
22. #36188C2semidirect
23. #36134C2semidirect
25. #34929C2semidirect
26. #34929C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598282
#592452
#590552
#553012
#531302
#531072
#530702
#428402
#427082
#426212
#397272
#396092
#395992
#392002
#391392
#376412
#376272
#376222
#365982
#361882
#361342
#349322
#349292