Finite Group Databasebeta

← #7739349

Subgroups — #7739349

Order 512.

5064 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59321C212yesmaximal, complemented
2#59314C212yesmaximal, complemented
3#59248C212yesmaximal, complemented
4#59235C212yesmaximal, complemented
5#51559C218yesmaximal, complemented
6#45372C214yesmaximal, complemented
7#45331C214yesmaximal, complemented
8#45109C214yesmaximal, complemented
9#44988C214yesmaximal, complemented
10#39633C212yesmaximal, complemented
11#39146C212yesmaximal, complemented
12#38976C212yesmaximal, complemented
13#38933C212yesmaximal, complemented
14#37347C214yesmaximal, complemented
15#36561C212yesmaximal, complemented
16#36453C212yesmaximal, complemented
17#36134C212yesmaximal, complemented
18#36133C212yesmaximal, complemented
19#35526C214yesmaximal, 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#34127C211yesmaximal, characteristic, complemented
27C2×#554C2214yes—
28C2×#544C2212yes—
29C2×#533C2211yescharacteristic
30C2×#533C2214yes—
31C2×#520C2212yes—
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34#2868C2212yes—
35#2859C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2214yes—
39#2855C2214yes—
40#2791C2218yes—
41#2790C2218yes—
42#2789C2218yes—
43#2787C2218yes—
44#2770C2218yes—
45#2766C2218yes—
46#2766C2218yes—
47#2746C2218yes—
48#2746C2218yes—
49#2744C2218yes—
50#2738C2218yes—
51#2729C2218yes—
52#2728C2218yes—
53#2720C2218yes—
54#2719C2218yes—
55#2690C2218yes—
56#2660C2214yes—
57#2647C2214yes—
58#2645C2214yes—
59#2629C2214yes—
60#2611C2214yes—
61#2609C2218yes—
62#2609C2214yes—
63#2599C2218yes—
64#2598C2218yes—
65#2582C2211yescharacteristic
66#2582C2212yes—
67#2582C2212yes—
68#2576C2218yes—
69#2568C2211yescharacteristic
70#2565C2214yes—
71#2564C2218yes—
72#2562C2214yes—
73#2556C2218yes—
74#2552C2214yes—
75#2552C2212yes—
76#2552C2212yes—
77#2551C2212yes—
78#2551C2212yes—
79#2547C2211yescharacteristic
80#2546C2211yescharacteristic
81#2542C2214yes—
82#2542C2211yescharacteristic
83#2538C2211yescharacteristic
84#2538C2212yes—
85#2538C2212yes—
86#2538C2211yescharacteristic
87#2537C2211yescharacteristic
88#2536C2218yes—
89#2514C2214yes—
90#2514C2214yes—
91#2511C2214yes—
92#2508C2214yes—
93#2506C2214yes—
94#2506C2214yes—
95#2506C2214yes—
96#2502C2214yes—
97#2499C2212yes—
98#2497C2214yes—
99#2494C2214yes—
100#2494C2214yes—
101#2494C2214yes—
102#2492C2214yes—
103#2492C2214yes—
104#2489C2214yes—
105#2487C2214yes—
106#2485C2212yes—
107#2485C2212yes—
108#2473C2218yes—
109#2463C2218yes—
110#2462C2218yes—
111#2460C2218yes—
112#2460C2218yes—
113#2452C2214yes—
114#2451C2214yes—
115#2449C2218yes—
116#2446C2214yes—
117#2442C2214yes—
118#2441C2218yes—
119#2440C2214yes—
120#2440C2214yes—
121#2440C2214yes—
122#2440C2214yes—
123#2438C2218yes—
124#2432C2212yes—
125#2429C2218yes—
126#2427C2214yes—
127#2423C2214yes—
128#2423C2214yes—
129#2423C2214yes—
130#2420C2214yes—
131#2417C2214yes—
132#2417C2214yes—
133#2417C2214yes—
134#2415C2212yes—
135#2415C2212yes—
136#2407C2212yes—
137#2407C2212yes—
138#2395C2214yes—
139#2392C2214yes—
140#2382C2214yes—
141#2365C2214yes—
142#2365C2212yes—
143#2365C2214yes—
144#2365C2212yes—
145#2361C2214yes—
146#2360C2214yes—
147#2355C2212yes—
148#2355C2212yes—
149#2355C2211yescharacteristic
150#2355C2211yescharacteristic
151#2354C2214yes—
152#2352C2212yes—
153#2352C2212yes—
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2212yes—
157Q8×C4⋊C4C2212yes—
158D4×C4⋊C4C2214yes—
159D4×C4⋊C4C2214yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2211yescharacteristic
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164#2347C2212yes—
165#2345C2214yes—
166#2344C2214yes—
167#2343C2214yes—
168#2339C2212yes—
169#2326C2214yes—
170#2323C2214yes—
171#2323C2214yes—
172#2320C2214yes—
173#2317C2212yes—
174#2317C2214yes—
175#2317C2212yes—
176#2316C2212yes—
177#2314C2214yes—
178#2311C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×#124C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×#121C2212yes—
186C4×#121C2214yes—
187C4×#121C2212yes—
188#2295C2212yes—
189#2290C2214yes—
190#2285C2211yescharacteristic
191#2285C2211yescharacteristic
192#2285C2212yes—
193C2×#384C2212yes—
194C2×#384C2211yescharacteristic
195#2283C2212yes—
196C42×D4C2212yes—
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201#554—416no—
202#544—48no—
203#533—28no—
204#533—416no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#125C2318yes—
216C2×#125C2318yes—
217C2×#124C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232#520—48no—
233C4×#41—28no—
234C4×#41—28no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2318yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2314yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2318yes—
259C2×#117C2312yes—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2312yes—
263C2×#117C2311yescharacteristic
264C2×#117C2312yes—
265C2×#117C2311yescharacteristic
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2318yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C42C2312yes—
279C22×C42C2312yes—
280C22×C42C2314yes—
281C22×C42C2311yescharacteristic
282#401C2318yes—
283#401C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#399C2314yes—
293#399C2318yes—
294#399C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#397C2318yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2314yes—
317#396C2314yes—
318#396C2318yes—
319#395C2318yes—
320#395C2318yes—
321#395C2318yes—
322#394C2318yes—
323#394C2314yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#394C2314yes—
328#393C2318yes—
329#392C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#391C2318yes—
345#391C2318yes—
346#390C2314yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2318yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2312yes—
373#389C2314yes—
374#389C2318yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#386C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2314yes—
424#386C2314yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2314yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#384C2312yes—
440#384C2314yes—
441#384C2314yes—
442#384C2312yes—
443#384C2314yes—
444#384C2314yes—
445#384C2314yes—
446#384C2311yescharacteristic
447#384C2312yes—
448#384C2312yes—
449#384C2312yes—
450#384C2311yescharacteristic
451#384C2314yes—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2314yes—
455#383C2318yes—
456#383C2314yes—
457#382C2312yes—
458#382C2312yes—
459#382C2314yes—
460#382C2312yes—
461#382C2314yes—
462#382C2314yes—
463#382C2318yes—
464#382C2312yes—
465#382C2312yes—
466#381C2318yes—
467#381C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2318yes—
474#380C2314yes—
475#380C2312yes—
476#380C2312yes—
477#380C2318yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2312yes—
482#380C2318yes—
483#380C2314yes—
484#380C2312yes—
485#380C2314yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4C2314yes—
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—
524C2×#95C2314yes—
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×D4C2414yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2414yes—
553C23×C4C2418yes—
554C23×C4C2414yes—
555C4⋊Q8—28no—
556C4⋊Q8—216no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—48no—
560C4⋊Q8—48no—
561C4⋊Q8—48no—
562#125—28no—
563#125—48no—
564#125—48no—
565#125—416no—
566#125—416no—
567#124—28no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—416no—
574C22⋊Q8—416no—
575C22⋊Q8—416no—
576C22⋊Q8—44no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579C22⋊Q8—416no—
580#121—28no—
581#121—28no—
582C4×Q8—216no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—24no—
587C4×Q8—28no—
588C4×Q8—28no—
589C4×Q8—416no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—44no—
602C4×D4—48no—
603C4×D4—416no—
604C4×D4—48no—
605C4×D4—416no—
606#117—24no—
607#117—24no—
608#117—28no—
609#117—24no—
610#117—24no—
611#117—28no—
612#117—28no—
613#117—44no—
614#117—48no—
615#117—44no—
616#117—416no—
617C2×C4⋊C4—28no—
618C2×C4⋊C4—28no—
619C2×C4⋊C4—48no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4—44no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—48no—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C42—28no—
709C2×C42—28no—
710C2×C42—48no—
711C2×C42#4118yes—
712C2×C42C2418yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2418yes—
729C2×C42C2418yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778C24C2511yescharacteristic
779C24C2512yes—
780C24C2512yes—
781#41—232no—
782#41—416no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—216no—
790C2×Q8—22no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×Q8H(5,𝔽2)14yes—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—44no—
810C2×D4—42no—
811C2×D42−1+414yes—
812C2×D42−1+414yes—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—22no—
816C22×C4—24no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—28no—
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—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—44no—
840C22×C4—42no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—48no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—48no—
848C22×C4—44no—
849C22×C4C2×#4114yes—
850C22×C4C2×#4114yes—
851C22×C4C2×#4114yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2514yes—
864C22×C4C2518yes—
865C22×C4C2514yes—
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—216no—
893C4⋊C4—28no—
894C4⋊C4—22no—
895C4⋊C4—28no—
896C4⋊C4—216no—
897C4⋊C4—28no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—28no—
910C4⋊C4—24no—
911C4⋊C4—42no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—48no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—48no—
930C4⋊C4H(5,𝔽2)14yes—
931C4⋊C42−1+414yes—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—24no—
948C22⋊C4—28no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—28no—
965C42—24no—
966C42—28no—
967C42—24no—
968C42—216no—
969C42—28no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—44no—
975C42—44no—
976C42—48no—
977C42—48no—
978C42C2×#4114yes—
979C42C2×#4114yes—
980C42C2×#4114yes—
981C42C2×#4114yes—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—21no—
986C23—22no—
987C23—22no—
988C23—21no—
989C23—22no—
990C23—22no—
991C23—21no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—21no—
1000C23C22×#4112yes—
1001C23C2×2−1+414yes—
1002C23C2×2−1+414yes—
1003C23C2611yescharacteristic
1004Q8—28no—
1005Q8—48no—
1006Q8—44no—
1007Q8—48no—
1008Q8—816no—
1009D4—216no—
1010D4—28no—
1011D4—28no—
1012D4—416no—
1013D4—48no—
1014C2×C4—216no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—28no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—28no—
1071C2×C4—22no—
1072C2×C4—416no—
1073C2×C4—48no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—88no—
1079C2×C4—168no—
1080C2×C4—164no—
1081C2×C4C22×#4112yes—
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4112yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4112yes—
1087C2×C4C2×H(5,𝔽2)14yes—
1088C2×C4C2×H(5,𝔽2)14yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×2−1+414yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4C2×2−1+412yes—
1094C2×C4C2×2−1+412yes—
1095C2×C4#58512yes—
1096C22—24no—
1097C22—24no—
1098C22—24no—
1099C22—22no—
1100C22—24no—
1101C22—24no—
1102C22—22no—
1103C22—22no—
1104C22—24no—
1105C22—42no—
1106C22—41no—
1107C22—42no—
1108C22—42no—
1109C22—41no—
1110C22—41no—
1111C22—42no—
1112C22—41no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22C23×#4111yescharacteristic
1118C22C22×H(5,𝔽2)11yescharacteristic
1119C22C22×H(5,𝔽2)11yescharacteristic
1120C22C22×2−1+411yescharacteristic
1121C22C22×2−1+411yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22C2×#58511yescharacteristic
1124C4—24no—
1125C4—24no—
1126C4—22no—
1127C4—24no—
1128C4—22no—
1129C4—22no—
1130C4—44no—
1131C4—48no—
1132C4—44no—
1133C4—42no—
1134C4—44no—
1135C4—44no—
1136C4—42no—
1137C4—44no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—44no—
1142C4—42no—
1143C4—42no—
1144C4#349214yes—
1145C4#349514yes—
1146C4#351114yes—
1147C2—44no—
1148C2—44no—
1149C2—42no—
1150C2C2×#349211yescharacteristic
1151C2C2×#351111yescharacteristic
1152C2C2×#349511yescharacteristic
1153C2#6301411yescharacteristic
1154C2#6301611yescharacteristic
1155C2#6301611yescharacteristic
1156C2#6303211yescharacteristic
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. #59321C2semidirect
2. #59314C2semidirect
3. #59248C2semidirect
4. #59235C2semidirect
5. #51559C2semidirect
6. #45372C2semidirect
7. #45331C2semidirect
8. #45109C2semidirect
9. #44988C2semidirect
10. #39633C2semidirect
11. #39146C2semidirect
12. #38976C2semidirect
13. #38933C2semidirect
14. #37347C2semidirect
15. #36561C2semidirect
16. #36453C2semidirect
17. #36134C2semidirect
18. #36133C2semidirect
19. #35526C2semidirect
20. #35280C2semidirect
21. #35275C2semidirect
22. #34979C2semidirect
24. #34374C2semidirect
25. #34183C2semidirect
26. #34127C2semidirect

Maximal subgroups

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

subgroupindex
#593212
#593142
#592482
#592352
#515592
#453722
#453312
#451092
#449882
#396332
#391462
#389762
#389332
#373472
#365612
#364532
#361342
#361332
#355262
#352802
#352752
#349792
#349762
#343742
#341832
#341272