Finite Group Databasebeta

← #7739333

Subgroups — #7739333

Order 512.

4450 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59257C212yesmaximal, complemented
2#59256C212yesmaximal, complemented
3#59242C212yesmaximal, complemented
4#59214C212yesmaximal, complemented
5#51561C218yesmaximal, complemented
6#45161C214yesmaximal, complemented
7#45158C214yesmaximal, complemented
8#45129C214yesmaximal, complemented
9#45127C214yesmaximal, complemented
10#39762C212yesmaximal, complemented
11#39156C212yesmaximal, complemented
12#38978C212yesmaximal, complemented
13#38943C212yesmaximal, complemented
14#37406C214yesmaximal, complemented
15#36586C212yesmaximal, complemented
16#36477C212yesmaximal, complemented
17#36177C212yesmaximal, complemented
18#36174C212yesmaximal, complemented
19#35647C214yesmaximal, complemented
20#35286C211yesmaximal, characteristic, complemented
21#35280C211yesmaximal, characteristic, complemented
22#34979C211yesmaximal, characteristic, complemented
23#34976C211yesmaximal, characteristic
24#34374C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27C2×#533C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30#2859C2212yes—
31#2859C2212yes—
32#2857C2212yes—
33#2857C2212yes—
34#2855C2214yes—
35#2850C2214yes—
36#2787C2218yes—
37#2780C2218yes—
38#2779C2218yes—
39#2778C2218yes—
40#2777C2218yes—
41#2777C2218yes—
42#2776C2218yes—
43#2776C2218yes—
44#2772C2218yes—
45#2770C2218yes—
46#2769C2218yes—
47#2750C2218yes—
48#2749C2218yes—
49#2744C2218yes—
50#2741C2218yes—
51#2740C2218yes—
52#2647C2214yes—
53#2644C2214yes—
54#2642C2214yes—
55#2629C2214yes—
56#2611C2214yes—
57#2609C2214yes—
58#2608C2218yes—
59#2596C2218yes—
60#2587C2218yes—
61#2587C2218yes—
62#2582C2212yes—
63#2582C2211yescharacteristic
64#2582C2212yes—
65#2578C2218yes—
66#2576C2218yes—
67#2573C2218yes—
68#2571C2214yes—
69#2571C2212yes—
70#2571C2212yes—
71#2570C2214yes—
72#2568C2211yescharacteristic
73#2566C2214yes—
74#2552C2212yes—
75#2552C2212yes—
76#2547C2211yescharacteristic
77#2546C2211yescharacteristic
78#2542C2211yescharacteristic
79#2538C2211yescharacteristic
80#2538C2212yes—
81#2538C2214yes—
82#2538C2212yes—
83#2538C2211yescharacteristic
84#2537C2211yescharacteristic
85#2533C2218yes—
86#2530C2218yes—
87#2528C2218yes—
88#2526C2218yes—
89#2524C2218yes—
90#2518C2218yes—
91#2514C2214yes—
92#2514C2214yes—
93#2514C2214yes—
94#2514C2214yes—
95#2514C2214yes—
96#2510C2218yes—
97#2509C2214yes—
98#2509C2214yes—
99#2509C2214yes—
100#2508C2214yes—
101#2503C2214yes—
102#2499C2212yes—
103#2499C2214yes—
104#2499C2214yes—
105#2497C2214yes—
106#2497C2214yes—
107#2495C2214yes—
108#2495C2218yes—
109#2495C2214yes—
110#2495C2214yes—
111#2494C2214yes—
112#2493C2218yes—
113#2490C2214yes—
114#2489C2214yes—
115#2489C2214yes—
116#2487C2214yes—
117#2485C2212yes—
118#2485C2212yes—
119#2448C2214yes—
120#2442C2214yes—
121#2442C2214yes—
122#2441C2214yes—
123#2432C2212yes—
124#2429C2214yes—
125#2421C2214yes—
126#2420C2214yes—
127#2417C2214yes—
128#2417C2214yes—
129#2415C2212yes—
130#2415C2212yes—
131#2415C2214yes—
132#2407C2212yes—
133#2407C2212yes—
134#2395C2214yes—
135#2392C2214yes—
136#2382C2214yes—
137#2370C2214yes—
138#2365C2212yes—
139#2365C2212yes—
140#2363C2214yes—
141#2360C2214yes—
142#2357C2214yes—
143#2356C2214yes—
144#2355C2212yes—
145#2355C2212yes—
146#2355C2212yes—
147#2355C2211yescharacteristic
148#2355C2211yescharacteristic
149#2355C2212yes—
150#2354C2212yes—
151#2354C2212yes—
152#2352C2214yes—
153#2352C2212yes—
154#2352C2212yes—
155#2352C2214yes—
156#2352C2214yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159D4×C4⋊C4C2211yescharacteristic
160D4×C4⋊C4C2211yescharacteristic
161#2347C2212yes—
162#2347C2214yes—
163#2346C2214yes—
164#2343C2214yes—
165#2339C2212yes—
166#2330C2214yes—
167#2323C2214yes—
168#2323C2214yes—
169#2320C2214yes—
170#2317C2212yes—
171#2316C2212yes—
172#2316C2212yes—
173#2314C2214yes—
174#2314C2214yes—
175#2311C2212yes—
176#2311C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×#124C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×#121C2212yes—
185C4×#121C2212yes—
186#2295C2212yes—
187#2290C2214yes—
188#2285C2211yescharacteristic
189#2285C2211yescharacteristic
190#2285C2212yes—
191#2285C2212yes—
192C2×#384C2211yescharacteristic
193#2283C2212yes—
194#2283C2214yes—
195#2274C2212yes—
196C42×D4C2212yes—
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201#533—28no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×#125C2312yes—
206C2×#125C2314yes—
207C2×#125C2314yes—
208C2×#124C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C4×#41—28no—
220C4×#41—28no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2312yes—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2312yes—
244C2×#117C2311yescharacteristic
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C2×#117C2311yescharacteristic
249C2×#117C2314yes—
250C2×#117C2314yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C42C2312yes—
257C22×C42C2312yes—
258C22×C42C2314yes—
259C22×C42C2311yescharacteristic
260#401C2318yes—
261#401C2318yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#399C2318yes—
276#399C2314yes—
277#398C2318yes—
278#398C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#397C2318yes—
285#397C2314yes—
286#397C2314yes—
287#397C2314yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2314yes—
292#397C2318yes—
293#397C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2314yes—
298#396C2318yes—
299#396C2314yes—
300#396C2318yes—
301#394C2314yes—
302#394C2314yes—
303#394C2314yes—
304#394C2314yes—
305#394C2314yes—
306#394C2318yes—
307#392C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#390C2312yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2312yes—
328#390C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2312yes—
332#389C2314yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2312yes—
349#389C2314yes—
350#389C2318yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2314yes—
356#389C2312yes—
357#389C2318yes—
358#389C2318yes—
359#389C2312yes—
360#389C2312yes—
361#389C2314yes—
362#389C2312yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2314yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2314yes—
409#386C2314yes—
410#386C2318yes—
411#386C2318yes—
412#386C2314yes—
413#386C2314yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2314yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#384C2312yes—
424#384C2314yes—
425#384C2312yes—
426#384C2314yes—
427#384C2312yes—
428#384C2312yes—
429#384C2312yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#383C2318yes—
435#383C2318yes—
436#383C2314yes—
437#383C2318yes—
438#383C2318yes—
439#382C2314yes—
440#382C2312yes—
441#382C2312yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2312yes—
446#382C2318yes—
447#382C2314yes—
448#382C2314yes—
449#382C2318yes—
450#382C2312yes—
451#382C2312yes—
452#381C2318yes—
453#381C2314yes—
454#381C2318yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2312yes—
461#380C2318yes—
462#380C2318yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2314yes—
473#380C2314yes—
474#380C2312yes—
475#380C2312yes—
476#380C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2318yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517#376C2314yes—
518#376C2312yes—
519#376C2318yes—
520C2×#95C2314yes—
521C43C2312yes—
522C2×#41—24no—
523C2×#41—24no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2412yes—
534C22×D4C2411yescharacteristic
535C22×D4C2412yes—
536C22×D4C2414yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C4⋊Q8—24no—
550C4⋊Q8—24no—
551C4⋊Q8—44no—
552#125—28no—
553#125—48no—
554#125—48no—
555#124—44no—
556C22⋊Q8—28no—
557C22⋊Q8—28no—
558C22⋊Q8—48no—
559C22⋊Q8—48no—
560C22⋊Q8—44no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563C22⋊Q8—44no—
564#121—28no—
565#121—44no—
566C4×Q8—24no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—28no—
571C4×Q8—28no—
572C4×Q8—48no—
573C4×Q8—48no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—28no—
577C4×D4—28no—
578C4×D4—28no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—44no—
584C4×D4—48no—
585#117—24no—
586#117—24no—
587#117—28no—
588#117—28no—
589#117—28no—
590#117—44no—
591#117—44no—
592#117—42no—
593#117—42no—
594#117—48no—
595#117—48no—
596C2×C4⋊C4—44no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4—44no—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C42—28no—
682C2×C42—28no—
683C2×C42—48no—
684C2×C42#4118yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2418yes—
701C2×C42C2418yes—
702C2×C42C2418yes—
703C2×C42C2418yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#95C2412yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756C24C2512yes—
757C24C2511yescharacteristic
758C24C2512yes—
759#41—416no—
760#41—416no—
761C2×Q8—22no—
762C2×Q8—22no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—28no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D42−1+414yes—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—24no—
795C22×C4—28no—
796C22×C4—24no—
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—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4C2×#4114yes—
822C22×C4C2×#4114yes—
823C22×C4C2×#4114yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2512yes—
838C22×C4C2518yes—
839C22×C4C2514yes—
840C22×C4C2512yes—
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2511yescharacteristic
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—28no—
934C42—24no—
935C42—24no—
936C42—28no—
937C42—28no—
938C42—24no—
939C42—24no—
940C42—44no—
941C42—44no—
942C42—42no—
943C42—42no—
944C42—48no—
945C42—48no—
946C42—48no—
947C42—48no—
948C42C2×#4114yes—
949C42C2×#4114yes—
950C42C2×#4114yes—
951C42C2×#4114yes—
952C23—22no—
953C23—21no—
954C23—21no—
955C23—22no—
956C23—22no—
957C23—21no—
958C23—22no—
959C23—21no—
960C23—22no—
961C23—22no—
962C23—21no—
963C23—21no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23C22×#4112yes—
972C23C2×2−1+414yes—
973C23C2611yescharacteristic
974Q8—48no—
975Q8—44no—
976Q8—44no—
977Q8—48no—
978D4—28no—
979D4—48no—
980D4—48no—
981D4—44no—
982D4—88no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—28no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—48no—
1049C2×C4—88no—
1050C2×C4—88no—
1051C2×C4—164no—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C2×2−1+412yes—
1059C2×C4#58512yes—
1060C2×C4#58512yes—
1061C2×C4#58512yes—
1062C2×C4#58512yes—
1063C2×C4#58512yes—
1064C22—24no—
1065C22—24no—
1066C22—22no—
1067C22—22no—
1068C22—24no—
1069C22—22no—
1070C22—41no—
1071C22—41no—
1072C22—42no—
1073C22—41no—
1074C22—42no—
1075C22—41no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22C23×#4111yescharacteristic
1086C22C22×2−1+411yescharacteristic
1087C22C2×#58511yescharacteristic
1088C22C2×#58511yescharacteristic
1089C22C2×#58511yescharacteristic
1090C22C2×#58511yescharacteristic
1091C22C2×#58511yescharacteristic
1092C4—22no—
1093C4—22no—
1094C4—22no—
1095C4—42no—
1096C4—44no—
1097C4—42no—
1098C4—44no—
1099C4—44no—
1100C4—44no—
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—44no—
1105C4—42no—
1106C4—48no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—44no—
1112C4#349314yes—
1113C4#349514yes—
1114C4#351214yes—
1115C2—44no—
1116C2—42no—
1117C2—82no—
1118C2C2×#349311yescharacteristic
1119C2C2×#349511yescharacteristic
1120C2C2×#351211yescharacteristic
1121C2#6302511yescharacteristic
1122C2#6302511yescharacteristic
1123C2#6303111yescharacteristic
1124C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34976C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59257C2semidirect
2. #59256C2semidirect
3. #59242C2semidirect
4. #59214C2semidirect
5. #51561C2semidirect
6. #45161C2semidirect
7. #45158C2semidirect
8. #45129C2semidirect
9. #45127C2semidirect
10. #39762C2semidirect
11. #39156C2semidirect
12. #38978C2semidirect
13. #38943C2semidirect
14. #37406C2semidirect
15. #36586C2semidirect
16. #36477C2semidirect
17. #36177C2semidirect
18. #36174C2semidirect
19. #35647C2semidirect
20. #35286C2semidirect
21. #35280C2semidirect
22. #34979C2semidirect
24. #34374C2semidirect
25. #34188C2semidirect
26. #34127C2semidirect

Maximal subgroups

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

subgroupindex
#592572
#592562
#592422
#592142
#515612
#451612
#451582
#451292
#451272
#397622
#391562
#389782
#389432
#374062
#365862
#364772
#361772
#361742
#356472
#352862
#352802
#349792
#349762
#343742
#341882
#341272