Finite Group Databasebeta

← #7642942

Subgroups — #7642942

Order 512.

4926 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39931C214yesmaximal, complemented
2#39930C214yesmaximal, complemented
3#39905C214yesmaximal, complemented
4#39904C214yesmaximal, complemented
5#39159C212yesmaximal, complemented
6#39158C212yesmaximal, complemented
7#39147C212yesmaximal, complemented
8#39146C212yesmaximal, complemented
9#38941C212yesmaximal, complemented
10#38940C212yesmaximal, complemented
11#38933C212yesmaximal, complemented
12#38932C212yesmaximal, complemented
13#36980C214yesmaximal, complemented
14#36730C214yesmaximal, complemented
15#36625C211yesmaximal, characteristic, complemented
16#36624C211yesmaximal, characteristic
17#35629C212yesmaximal, complemented
18#35620C212yesmaximal, complemented
19#35542C212yesmaximal, complemented
20#35516C212yesmaximal, complemented
21#35270C214yesmaximal, complemented
22#35180C211yesmaximal, characteristic, complemented
23#35167C211yesmaximal, characteristic, complemented
24#35080C214yesmaximal, complemented
25#34213C211yesmaximal, characteristic, complemented
26#34206C211yesmaximal, characteristic, complemented
27C2×#2283C211yesmaximal, characteristic, complemented
28C2×#544C2212yes—
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×#525C2212yes—
32C2×#520C2212yes—
33C23×C42C2211yescharacteristic
34#2857C2214yes—
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2856C2211yescharacteristic
42#2856C2211yescharacteristic
43#2855C2212yes—
44#2855C2212yes—
45#2854C2212yes—
46#2854C2212yes—
47#2851C2212yes—
48#2851C2212yes—
49#2850C2214yes—
50#2850C2212yes—
51#2850C2212yes—
52#2848C2212yes—
53#2848C2212yes—
54#2847C2212yes—
55#2847C2212yes—
56#2775C2218yescomplemented
57#2770C2218yescomplemented
58#2766C2218yescomplemented
59#2764C2218yescomplemented
60#2759C2218yescomplemented
61#2758C2218yescomplemented
62#2757C2218yescomplemented
63#2746C2218yes—
64#2745C2218yes—
65#2738C2218yes—
66#2737C2218yes—
67#2737C2218yescomplemented
68#2701C2218yes—
69#2700C2218yes—
70#2687C2218yes—
71#2686C2218yes—
72#2659C2214yes—
73#2653C2218yes—
74#2649C2218yes—
75#2647C2214yescomplemented
76#2645C2214yescomplemented
77#2644C2214yescomplemented
78#2640C2214yescomplemented
79#2639C2214yes—
80#2592C2214yescomplemented
81#2568C2212yescomplemented
82#2568C2214yescomplemented
83#2566C2214yescomplemented
84#2565C2214yescomplemented
85#2563C2214yes—
86#2563C2212yescomplemented
87#2563C2214yescomplemented
88#2562C2214yes—
89#2562C2214yes—
90#2562C2214yescomplemented
91#2552C2212yescomplemented
92#2552C2212yescomplemented
93#2551C2212yescomplemented
94#2551C2212yescomplemented
95#2550C2214yescomplemented
96#2550C2214yescomplemented
97#2548C2212yescomplemented
98#2547C2214yes—
99#2547C2212yescomplemented
100#2532C2218yescomplemented
101#2530C2218yescomplemented
102#2529C2218yescomplemented
103#2527C2218yescomplemented
104#2514C2214yescomplemented
105#2514C2214yescomplemented
106#2513C2214yescomplemented
107#2513C2214yescomplemented
108#2510C2218yes—
109#2510C2218yes—
110#2495C2214yes—
111#2495C2214yescomplemented
112#2495C2214yescomplemented
113#2494C2214yes—
114#2494C2214yescomplemented
115#2494C2214yescomplemented
116#2492C2214yes—
117#2492C2214yes—
118#2491C2214yes—
119#2491C2214yes—
120#2490C2214yes—
121#2489C2214yes—
122#2488C2218yes—
123#2487C2214yes—
124#2486C2214yes—
125#2485C2214yes—
126#2485C2214yes—
127#2472C2218yes—
128#2450C2218yes—
129#2450C2218yes—
130#2442C2214yescomplemented
131#2442C2214yescomplemented
132#2439C2214yescomplemented
133#2439C2214yescomplemented
134#2427C2214yes—
135#2426C2214yes—
136#2423C2214yes—
137#2423C2214yes—
138#2422C2214yes—
139#2422C2214yes—
140#2421C2214yes—
141#2420C2214yes—
142#2419C2218yes—
143#2418C2218yes—
144#2370C2214yescomplemented
145#2369C2212yescomplemented
146#2367C2214yescomplemented
147#2366C2212yescomplemented
148#2365C2212yescomplemented
149#2365C2212yescomplemented
150#2355C2212yescomplemented
151#2355C2214yescomplemented
152#2354C2212yescomplemented
153#2352C2214yescomplemented
154Q8×C4⋊C4C2212yescomplemented
155D4×C4⋊C4C2212yescomplemented
156#2337C2218yes—
157#2335C2218yes—
158#2331C2214yescomplemented
159#2329C2214yes—
160#2326C2214yescomplemented
161#2325C2214yes—
162#2320C2214yescomplemented
163#2319C2214yescomplemented
164#2317C2212yes—
165#2316C2212yes—
166#2311C2212yes—
167#2311C2212yes—
168#2311C2212yes—
169C4×C22⋊Q8C2214yes—
170C4×C22⋊Q8C2212yes—
171C4×C22⋊Q8C2212yes—
172C4×C22⋊Q8C2212yes—
173C4×C22⋊Q8C2212yes—
174C4×#121C2214yes—
175C4×#121C2212yes—
176C4×#121C2212yes—
177C4×#121C2212yes—
178C4×#121C2212yes—
179#2297C2212yes—
180#2296C2212yes—
181#2285C2211yescharacteristic
182#2285C2211yescharacteristic
183#2283C2212yes—
184#2283C2212yes—
185#2283C2212yes—
186#2283C2212yes—
187#2283C2212yes—
188#2283C2212yes—
189#2283C2212yes—
190#2283C2212yes—
191C2×#383C2212yes—
192C2×#382C2211yescharacteristic
193C2×#382C2211yescharacteristic
194#2280C2212yes—
195C2×#381C2212yes—
196C2×#380C2211yescharacteristic
197C2×#380C2211yescharacteristic
198#2274C2212yes—
199C2×C4×C4⋊C4C2211yescharacteristic
200C2×C4×C4⋊C4C2211yescharacteristic
201C2×C4×C22⋊C4C2212yes—
202C2×#376C2212yes—
203C22×#41C2312yes—
204C24×C4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C24×C4C2311yescharacteristic
207#544—48no—
208#533—28no—
209#532—28no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×#127C2311yescharacteristic
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#124C2312yes—
221C2×#124C2314yes—
222C2×#124C2318yes—
223#525—48no—
224C2×#123C2318yes—
225C2×#123C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2318yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#120C2314yes—
244#520—48no—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2318yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2314yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2314yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C42—28no—
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2311yescharacteristic
282#401C2318yes—
283#401C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#399C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#396C2318yes—
309#396C2318yes—
310#395C2318yes—
311#395C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#393C2318yes—
318#393C2318yes—
319#393C2318yes—
320#393C2318yes—
321#393C2318yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2314yes—
328#391C2318yes—
329#391C2318yes—
330#391C2312yes—
331#391C2312yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#390C2318yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2312yes—
343#390C2314yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2318yes—
361#389C2312yes—
362#389C2312yes—
363#389C2318yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2314yes—
373#389C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2314yes—
411#386C2314yes—
412#386C2314yes—
413#386C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#385C2314yes—
424#385C2314yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#384C2314yes—
429#384C2314yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#383C2318yes—
435#383C2318yes—
436#383C2314yes—
437#383C2314yes—
438#383C2314yes—
439#383C2314yes—
440#382C2318yes—
441#382C2312yes—
442#382C2314yes—
443#382C2314yes—
444#382C2312yes—
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2312yes—
452#382C2312yes—
453#381C2318yes—
454#381C2314yes—
455#381C2314yes—
456#381C2314yes—
457#381C2314yes—
458#381C2314yes—
459#380C2312yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2312yes—
469#380C2314yes—
470#380C2318yes—
471#380C2318yes—
472#380C2318yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489#380C2312yes—
490#380C2312yes—
491#380C2312yes—
492#379C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2318yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524#376C2314yes—
525#376C2314yes—
526#376C2314yes—
527#376C2314yes—
528C2×#95C2312yes—
529C2×#95C2312yes—
530C2×#95C2312yes—
531C2×#95C2312yes—
532C2×#95C2312yes—
533C2×#95C2312yes—
534C2×#95C2312yes—
535C2×#95C2312yes—
536C25C2411yescharacteristic
537C2×#41—28no—
538C2×#41—28no—
539C2×#41—28no—
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×Q8C2418yes—
544C22×D4C2412yes—
545C22×D4C2414yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C22×D4C2412yes—
550C23×C4—24no—
551C23×C4—24no—
552C23×C4—24no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—42no—
556C23×C4—42no—
557C23×C4—42no—
558C23×C4—42no—
559C23×C4C2414yes—
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2412yes—
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2418yes—
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C4⋊Q8—24no—
584C4⋊Q8—24no—
585C4⋊Q8—24no—
586C4⋊Q8—48no—
587C4⋊Q8—48no—
588C4⋊Q8—48no—
589#127—24no—
590#125—28no—
591#125—48no—
592#125—48no—
593#124—28no—
594#124—48no—
595#124—416no—
596#123—416no—
597#123—48no—
598C22⋊Q8—28no—
599C22⋊Q8—28no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—416no—
603C22⋊Q8—44no—
604C22⋊Q8—44no—
605C22⋊Q8—44no—
606C22⋊Q8—44no—
607#121—28no—
608#121—28no—
609#121—44no—
610#121—44no—
611#121—44no—
612#121—44no—
613#121—44no—
614#121—44no—
615#120—48no—
616C4×Q8—28no—
617C4×Q8—28no—
618C4×Q8—48no—
619C4×Q8—48no—
620C4×D4—28no—
621C4×D4—28no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—48no—
626C4×D4—416no—
627#117—28no—
628#117—28no—
629#117—28no—
630#117—48no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—48no—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2418yes—
678C2×C22⋊C4—44no—
679C2×C22⋊C4—44no—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C42—24no—
709C2×C42—24no—
710C2×C42—24no—
711C2×C42—24no—
712C2×C42—24no—
713C2×C42—24no—
714C2×C42—24no—
715C2×C42—24no—
716C2×C42—24no—
717C2×C42—24no—
718C2×C42—24no—
719C2×C42—44no—
720C2×C42—44no—
721C2×C42#4118yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2418yes—
740C2×C42C2418yes—
741C2×C42C2418yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2418yes—
778#95C2418yes—
779#95C2414yes—
780#95C2418yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2418yes—
787#95C2418yes—
788#95C2418yes—
789#95C2418yes—
790#95C2418yes—
791#95C2418yes—
792C24—22no—
793C24—22no—
794C24—22no—
795C24—22no—
796C24—22no—
797C24—41no—
798C24—41no—
799C24C2514yes—
800C24C2511yescharacteristic
801C24C2511yescharacteristic
802C24C2511yescharacteristic
803#41—432no—
804C2×Q8—24no—
805C2×Q8—24no—
806C2×Q8—24no—
807C2×Q8—24no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—24no—
811C2×Q8—42no—
812C2×Q8—42no—
813C2×Q8—48no—
814C2×Q8—48no—
815C2×Q8—48no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—28no—
862C22×C4—28no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—28no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—416no—
902C22×C4—416no—
903C22×C4—416no—
904C22×C4C2×#4114yes—
905C22×C4C2×#4114yes—
906C22×C4C2×#4114yes—
907C22×C4H(5,𝔽2)14yes—
908C22×C42−1+414yes—
909C22×C4C2514yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2514yes—
920C22×C4C2514yes—
921C22×C4C2514yes—
922C22×C4C2514yes—
923C22×C4C2514yes—
924C22×C4C2514yes—
925C22×C4C2514yes—
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—48no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—48no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—48no—
969C4⋊C4—48no—
970C4⋊C4—48no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—48no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—28no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—48no—
986C22⋊C4—48no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—22no—
1006C42—22no—
1007C42—22no—
1008C42—22no—
1009C42—22no—
1010C42—22no—
1011C42—22no—
1012C42—22no—
1013C42—22no—
1014C42—28no—
1015C42—28no—
1016C42—28no—
1017C42—28no—
1018C42—28no—
1019C42—44no—
1020C42—44no—
1021C42—48no—
1022C42—48no—
1023C42—48no—
1024C42C2×#4114yes—
1025C42C2×#4114yes—
1026C42C2×#4114yes—
1027C42C2×#4114yes—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—28no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—44no—
1053C23—44no—
1054C23—44no—
1055C23—44no—
1056C23—44no—
1057C23—44no—
1058C23C22×#4112yes—
1059C23C2×H(5,𝔽2)12yes—
1060C23C2×2−1+412yes—
1061C23#58512yes—
1062C23#58512yes—
1063C23C2611yescharacteristic
1064Q8—48no—
1065Q8—48no—
1066Q8—84no—
1067Q8—168no—
1068D4—416no—
1069D4—48no—
1070D4—48no—
1071D4—84no—
1072D4—88no—
1073D4—88no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—28no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—44no—
1133C2×C4—44no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—44no—
1140C2×C4—44no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—44no—
1145C2×C4—44no—
1146C2×C4—416no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—84no—
1150C2×C4—84no—
1151C2×C4—84no—
1152C2×C4—84no—
1153C2×C4—168no—
1154C2×C4#542116yes—
1155C2×C4C22×#4112yes—
1156C2×C4C22×#4112yes—
1157C2×C4C22×#4112yes—
1158C2×C4C22×#4112yes—
1159C2×C4C22×#4112yes—
1160C2×C4C22×#4112yes—
1161C2×C4C2×H(5,𝔽2)12yes—
1162C2×C4C2×H(5,𝔽2)12yes—
1163C2×C4C2×2−1+412yes—
1164C2×C4C2×2−1+412yes—
1165C2×C4#58512yes—
1166C2×C4#58512yes—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—22no—
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—416no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—44no—
1192C22—44no—
1193C22—44no—
1194C22—44no—
1195C22C2×#54214yes—
1196C22C23×#4111yescharacteristic
1197C22C22×H(5,𝔽2)11yescharacteristic
1198C22C22×2−1+411yescharacteristic
1199C22C2×#58511yescharacteristic
1200C22C2×#58511yescharacteristic
1201C22C2×#58511yescharacteristic
1202C22C2×#58511yescharacteristic
1203C4—22no—
1204C4—22no—
1205C4—22no—
1206C4—41no—
1207C4—41no—
1208C4—44no—
1209C4—41no—
1210C4—41no—
1211C4—44no—
1212C4—44no—
1213C4—44no—
1214C4—44no—
1215C4—44no—
1216C4—44no—
1217C4—44no—
1218C4—44no—
1219C4—44no—
1220C4—41no—
1221C4—41no—
1222C4—44no—
1223C4C2×#54214yes—
1224C4C2×#54214yes—
1225C4#349314yes—
1226C2—24no—
1227C2—42no—
1228C2—42no—
1229C2—84no—
1230C2C22×#54211yescharacteristic
1231C2C2×#349311yescharacteristic
1232C2#6281411yescharacteristic
1233C2#6283011yescharacteristic
1234C2#6283011yescharacteristic
1235C2#6283111yescharacteristic
1236C2#6283111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39931C2semidirect
2. #39930C2semidirect
3. #39905C2semidirect
4. #39904C2semidirect
5. #39159C2semidirect
6. #39158C2semidirect
7. #39147C2semidirect
8. #39146C2semidirect
9. #38941C2semidirect
10. #38940C2semidirect
11. #38933C2semidirect
12. #38932C2semidirect
13. #36980C2semidirect
14. #36730C2semidirect
15. #36625C2semidirect
17. #35629C2semidirect
18. #35620C2semidirect
19. #35542C2semidirect
20. #35516C2semidirect
21. #35270C2semidirect
22. #35180C2semidirect
23. #35167C2semidirect
24. #35080C2semidirect
25. #34213C2semidirect
26. #34206C2semidirect
27. C2×#2283C2semidirect
56. #2775C22semidirect
57. #2770C22semidirect
58. #2766C22semidirect
59. #2764C22semidirect
60. #2759C22semidirect
61. #2758C22semidirect
62. #2757C22semidirect
67. #2737C22semidirect
75. #2647C22semidirect
76. #2645C22semidirect
77. #2644C22semidirect
78. #2640C22semidirect
80. #2592C22semidirect
81. #2568C22semidirect
82. #2568C22semidirect
83. #2566C22semidirect
84. #2565C22semidirect
86. #2563C22semidirect
87. #2563C22semidirect
90. #2562C22semidirect
91. #2552C22semidirect
92. #2552C22semidirect
93. #2551C22semidirect
94. #2551C22semidirect
95. #2550C22semidirect
96. #2550C22semidirect
97. #2548C22semidirect
99. #2547C22semidirect
100. #2532C22semidirect
101. #2530C22semidirect
102. #2529C22semidirect
103. #2527C22semidirect
104. #2514C22semidirect
105. #2514C22semidirect
106. #2513C22semidirect
107. #2513C22semidirect
111. #2495C22semidirect
112. #2495C22semidirect
114. #2494C22semidirect
115. #2494C22semidirect
130. #2442C22semidirect
131. #2442C22semidirect
132. #2439C22semidirect
133. #2439C22semidirect
144. #2370C22semidirect
145. #2369C22semidirect
146. #2367C22semidirect
147. #2366C22semidirect
148. #2365C22semidirect
149. #2365C22semidirect
150. #2355C22semidirect
151. #2355C22semidirect
152. #2354C22semidirect
153. #2352C22semidirect
154. Q8×C4⋊C4C22semidirect
155. D4×C4⋊C4C22semidirect
158. #2331C22semidirect
160. #2326C22semidirect
162. #2320C22semidirect
163. #2319C22semidirect

Maximal subgroups

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

subgroupindex
#399312
#399302
#399052
#399042
#391592
#391582
#391472
#391462
#389412
#389402
#389332
#389322
#369802
#367302
#366252
#366242
#356292
#356202
#355422
#355162
#352702
#351802
#351672
#350802
#342132
#342062
C2×#22832