Finite Group Databasebeta

← #7739327

Subgroups — #7739327

Order 512.

5026 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59322C212yesmaximal, complemented
2#59312C212yesmaximal, complemented
3#59249C212yesmaximal, complemented
4#59234C212yesmaximal, complemented
5#51558C218yesmaximal, complemented
6#44978C214yesmaximal, complemented
7#44971C214yesmaximal, complemented
8#44920C214yesmaximal, complemented
9#44917C214yesmaximal, complemented
10#39609C212yesmaximal, complemented
11#39377C212yesmaximal, complemented
12#39350C212yesmaximal, complemented
13#39192C212yesmaximal, complemented
14#37342C214yesmaximal, complemented
15#36563C212yesmaximal, complemented
16#36481C212yesmaximal, complemented
17#36299C212yesmaximal, complemented
18#36272C212yesmaximal, complemented
19#35606C214yesmaximal, complemented
20#35280C211yesmaximal, characteristic, complemented
21#35275C211yesmaximal, characteristic, complemented
22#34979C211yesmaximal, characteristic, complemented
23#34976C211yesmaximal, characteristic
24#34374C211yesmaximal, characteristic, complemented
25#34183C211yesmaximal, characteristic, complemented
26#34129C211yesmaximal, characteristic, complemented
27C2×#552C2214yes—
28C2×#544C2212yes—
29C2×#542C2214yes—
30C2×#533C2211yescharacteristic
31C2×#520C2212yes—
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34#2868C2212yes—
35#2863C2214yes—
36#2859C2212yes—
37#2859C2214yes—
38#2857C2212yes—
39#2857C2212yes—
40#2796C2218yes—
41#2792C2218yes—
42#2775C2218yes—
43#2774C2218yes—
44#2772C2218yes—
45#2770C2218yes—
46#2767C2218yes—
47#2742C2218yes—
48#2725C2218yes—
49#2723C2218yes—
50#2721C2218yes—
51#2718C2218yes—
52#2717C2218yes—
53#2698C2218yes—
54#2690C2218yes—
55#2674C2218yes—
56#2660C2214yes—
57#2629C2214yes—
58#2628C2214yes—
59#2625C2214yes—
60#2611C2214yes—
61#2611C2218yes—
62#2609C2214yes—
63#2606C2218yes—
64#2602C2218yes—
65#2583C2218yes—
66#2582C2212yes—
67#2582C2211yescharacteristic
68#2582C2212yes—
69#2568C2211yescharacteristic
70#2567C2214yes—
71#2567C2214yes—
72#2553C2218yes—
73#2552C2212yes—
74#2552C2214yes—
75#2552C2212yes—
76#2551C2212yes—
77#2551C2212yes—
78#2550C2218yes—
79#2547C2214yes—
80#2547C2211yescharacteristic
81#2546C2211yescharacteristic
82#2542C2211yescharacteristic
83#2538C2211yescharacteristic
84#2538C2212yes—
85#2538C2212yes—
86#2538C2211yescharacteristic
87#2537C2211yescharacteristic
88#2522C2218yes—
89#2515C2218yes—
90#2513C2214yes—
91#2512C2214yes—
92#2511C2214yes—
93#2509C2214yes—
94#2509C2214yes—
95#2507C2214yes—
96#2507C2218yes—
97#2507C2214yes—
98#2501C2214yes—
99#2499C2212yes—
100#2496C2214yes—
101#2496C2214yes—
102#2496C2214yes—
103#2495C2214yes—
104#2492C2214yes—
105#2491C2214yes—
106#2489C2214yes—
107#2486C2214yes—
108#2485C2212yes—
109#2485C2212yes—
110#2478C2218yes—
111#2475C2218yes—
112#2474C2218yes—
113#2468C2218yes—
114#2461C2218yes—
115#2451C2214yes—
116#2451C2214yes—
117#2447C2214yes—
118#2441C2214yes—
119#2440C2214yes—
120#2440C2214yes—
121#2440C2214yes—
122#2440C2214yes—
123#2432C2212yes—
124#2429C2214yes—
125#2423C2214yes—
126#2423C2214yes—
127#2422C2214yes—
128#2421C2214yes—
129#2417C2214yes—
130#2417C2214yes—
131#2415C2218yes—
132#2415C2214yes—
133#2415C2212yes—
134#2415C2212yes—
135#2413C2218yes—
136#2407C2212yes—
137#2407C2212yes—
138#2395C2214yes—
139#2392C2214yes—
140#2382C2214yes—
141#2370C2214yes—
142#2369C2214yes—
143#2365C2212yes—
144#2365C2212yes—
145#2360C2214yes—
146#2360C2214yes—
147#2355C2212yes—
148#2355C2212yes—
149#2355C2214yes—
150#2354C2211yescharacteristic
151#2354C2212yes—
152#2354C2211yescharacteristic
153#2354C2212yes—
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2212yes—
157Q8×C4⋊C4C2211yescharacteristic
158Q8×C4⋊C4C2211yescharacteristic
159Q8×C4⋊C4C2212yes—
160D4×C4⋊C4C2214yes—
161D4×C4⋊C4C2214yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164#2347C2214yes—
165#2346C2214yes—
166#2346C2212yes—
167#2344C2214yes—
168#2341C2212yes—
169#2323C2214yes—
170#2323C2214yes—
171#2323C2214yes—
172#2317C2214yes—
173#2317C2212yes—
174#2317C2212yes—
175#2316C2212yes—
176#2314C2214yes—
177#2311C2212yes—
178C4×C4⋊Q8C2214yes—
179C4×C4⋊Q8C2212yes—
180C4×#124C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×#121C2212yes—
186C4×#121C2212yes—
187#2293C2214yes—
188#2293C2214yes—
189#2293C2212yes—
190#2285C2211yescharacteristic
191#2285C2211yescharacteristic
192#2285C2212yes—
193#2285C2212yes—
194C2×#384C2212yes—
195C2×#384C2211yescharacteristic
196C42×Q8C2212yes—
197C4×#117C2212yes—
198C4×#117C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201#552—416no—
202#544—48no—
203#542—416no—
204#533—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×#126C2318yes—
213C2×#126C2318yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2318yes—
217C2×#125C2314yes—
218C2×#124C2312yes—
219C2×#124C2318yes—
220C2×#123C2318yes—
221C2×#123C2318yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234#520—48no—
235C4×#41—28no—
236C4×#41—28no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2318yes—
258C2×C4×D4C2314yes—
259C2×#117C2312yes—
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2311yescharacteristic
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C2×#117C2318yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2314yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2311yescharacteristic
282#400C2314yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#399C2314yes—
289#399C2318yes—
290#399C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2318yes—
311#397C2318yes—
312#396C2314yes—
313#396C2314yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#395C2318yes—
321#395C2318yes—
322#394C2314yes—
323#394C2318yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#394C2314yes—
328#393C2318yes—
329#392C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2314yes—
333#391C2312yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#391C2312yes—
339#391C2314yes—
340#391C2314yes—
341#391C2312yes—
342#391C2318yes—
343#391C2318yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#389C2318yes—
353#389C2318yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2318yes—
386#389C2314yes—
387#389C2318yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2318yes—
408#388C2318yes—
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#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#386C2318yes—
427#386C2314yes—
428#386C2314yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2314yes—
434#385C2314yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#384C2314yes—
443#384C2314yes—
444#384C2314yes—
445#384C2312yes—
446#384C2314yes—
447#384C2314yes—
448#384C2312yes—
449#384C2311yescharacteristic
450#384C2312yes—
451#384C2312yes—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2312yes—
456#384C2314yes—
457#383C2318yes—
458#382C2312yes—
459#382C2314yes—
460#382C2312yes—
461#382C2314yes—
462#382C2314yes—
463#382C2314yes—
464#382C2318yes—
465#382C2312yes—
466#381C2318yes—
467#380C2314yes—
468#380C2314yes—
469#380C2312yes—
470#380C2312yes—
471#380C2318yes—
472#380C2312yes—
473#380C2312yes—
474#380C2314yes—
475#380C2314yes—
476#380C2312yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2312yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2318yes—
489C4×C4⋊C4C2318yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522#376C2314yes—
523#376C2312yes—
524C43C2314yes—
525C43C2312yes—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41—24no—
530C2×#41—24no—
531C2×#41—42no—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2418yes—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2418yes—
552C23×C4C2414yes—
553C4⋊Q8—28no—
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8—48no—
557C4⋊Q8—48no—
558C4⋊Q8—48no—
559C4⋊Q8—48no—
560#126—416no—
561#126—416no—
562#125—216no—
563#125—28no—
564#125—48no—
565#125—416no—
566#124—28no—
567#124—416no—
568#123—416no—
569#123—416no—
570C22⋊Q8—28no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—28no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—416no—
577C22⋊Q8—416no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580#121—28no—
581#121—44no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—24no—
587C4×Q8—28no—
588C4×Q8—28no—
589C4×Q8—44no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×D4—216no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—28no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—48no—
603C4×D4—416no—
604#117—24no—
605#117—24no—
606#117—28no—
607#117—24no—
608#117—28no—
609#117—24no—
610#117—28no—
611#117—28no—
612#117—28no—
613#117—44no—
614#117—48no—
615#117—44no—
616#117—416no—
617#117—48no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—48no—
623C2×C4⋊C4—48no—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C42—28no—
712C2×C42—28no—
713C2×C42#4118yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2412yes—
732C2×C42C2418yes—
733C2×C42C2418yes—
734C2×C42C2418yes—
735C2×C42C2414yes—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#95C2412yes—
741#95C2414yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778C24C2512yes—
779C24C2511yescharacteristic
780C24C2512yes—
781#41—232no—
782#41—416no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—48no—
794C2×Q8—48no—
795C2×Q8—48no—
796C2×Q82−1+414yes—
797C2×Q82−1+414yes—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—28no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—24no—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4H(5,𝔽2)14yes—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—24no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—216no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—42no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4C2×#4114yes—
844C22×C4C2×#4114yes—
845C22×C4C2×#4114yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2518yes—
858C22×C4C2514yes—
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—22no—
887C4⋊C4—216no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—216no—
891C4⋊C4—24no—
892C4⋊C4—22no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—28no—
904C4⋊C4—24no—
905C4⋊C4—42no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—42no—
916C4⋊C4—44no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4H(5,𝔽2)14yes—
927C4⋊C42−1+414yes—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—28no—
931C22⋊C4—216no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—24no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—28no—
963C42—28no—
964C42—24no—
965C42—28no—
966C42—24no—
967C42—28no—
968C42—24no—
969C42—28no—
970C42—28no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—48no—
975C42—48no—
976C42—44no—
977C42—48no—
978C42C2×#4114yes—
979C42C2×#4114yes—
980C42C2×#4114yes—
981C42C2×#4114yes—
982C23—22no—
983C23—21no—
984C23—22no—
985C23—21no—
986C23—22no—
987C23—22no—
988C23—21no—
989C23—21no—
990C23—22no—
991C23—21no—
992C23—22no—
993C23—21no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23C22×#4112yes—
1002C23C2×H(5,𝔽2)14yes—
1003C23C2611yescharacteristic
1004Q8—28no—
1005Q8—28no—
1006Q8—48no—
1007Q8—48no—
1008Q8—168no—
1009D4—216no—
1010D4—28no—
1011D4—48no—
1012D4—44no—
1013D4—88no—
1014C2×C4—216no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—28no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—28no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—28no—
1071C2×C4—48no—
1072C2×C4—48no—
1073C2×C4—48no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—816no—
1077C2×C4—164no—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C22×#4112yes—
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4112yes—
1084C2×C4C2×H(5,𝔽2)14yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×2−1+414yes—
1088C2×C4C2×2−1+414yes—
1089C2×C4C2×2−1+414yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4#58512yes—
1094C22—24no—
1095C22—22no—
1096C22—24no—
1097C22—24no—
1098C22—22no—
1099C22—22no—
1100C22—41no—
1101C22—42no—
1102C22—41no—
1103C22—41no—
1104C22—42no—
1105C22—41no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22C23×#4111yescharacteristic
1116C22C22×H(5,𝔽2)11yescharacteristic
1117C22C22×H(5,𝔽2)11yescharacteristic
1118C22C22×2−1+411yescharacteristic
1119C22C22×2−1+411yescharacteristic
1120C22C22×2−1+411yescharacteristic
1121C22C2×#58511yescharacteristic
1122C4—22no—
1123C4—24no—
1124C4—24no—
1125C4—24no—
1126C4—22no—
1127C4—22no—
1128C4—24no—
1129C4—44no—
1130C4—48no—
1131C4—44no—
1132C4—42no—
1133C4—42no—
1134C4—44no—
1135C4—44no—
1136C4—44no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—44no—
1141C4—42no—
1142C4#349214yes—
1143C4#349514yes—
1144C4#351114yes—
1145C2—44no—
1146C2—42no—
1147C2—82no—
1148C2C2×#349211yescharacteristic
1149C2C2×#351111yescharacteristic
1150C2C2×#349511yescharacteristic
1151C2#6301411yescharacteristic
1152C2#6303211yescharacteristic
1153C2#6303711yescharacteristic
1154C2#6303711yescharacteristic
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. #59322C2semidirect
2. #59312C2semidirect
3. #59249C2semidirect
4. #59234C2semidirect
5. #51558C2semidirect
6. #44978C2semidirect
7. #44971C2semidirect
8. #44920C2semidirect
9. #44917C2semidirect
10. #39609C2semidirect
11. #39377C2semidirect
12. #39350C2semidirect
13. #39192C2semidirect
14. #37342C2semidirect
15. #36563C2semidirect
16. #36481C2semidirect
17. #36299C2semidirect
18. #36272C2semidirect
19. #35606C2semidirect
20. #35280C2semidirect
21. #35275C2semidirect
22. #34979C2semidirect
24. #34374C2semidirect
25. #34183C2semidirect
26. #34129C2semidirect

Maximal subgroups

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

subgroupindex
#593222
#593122
#592492
#592342
#515582
#449782
#449712
#449202
#449172
#396092
#393772
#393502
#391922
#373422
#365632
#364812
#362992
#362722
#356062
#352802
#352752
#349792
#349762
#343742
#341832
#341292