Finite Group Databasebeta

← #7654853

Subgroups — #7654853

Order 512.

4770 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42934C214yesmaximal, complemented
2#42055C218yesmaximal, complemented
3#39608C212yesmaximal, complemented
4#39544C214yesmaximal, complemented
5#39480C212yesmaximal, complemented
6#39149C212yesmaximal, complemented
7#39043C214yesmaximal, complemented
8#38940C212yesmaximal, complemented
9#38200C214yesmaximal, complemented
10#37749C214yesmaximal, complemented
11#37642C211yesmaximal, characteristic, complemented
12#37631C212yesmaximal, complemented
13#36586C212yesmaximal, complemented
14#36480C212yesmaximal, complemented
15#36301C212yesmaximal, complemented
16#36133C212yesmaximal, complemented
17#35828C214yesmaximal, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35279C211yesmaximal, characteristic, complemented
20#35196C212yesmaximal, complemented
21#35187C212yesmaximal, complemented
22#34976C211yesmaximal, characteristic
23#34929C212yesmaximal, complemented
24#34216C211yesmaximal, characteristic, complemented
25#34129C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27C2×#536C2212yes—
28C2×#533C2214yes—
29C22×C4⋊Q8C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2864C2214yes—
33#2863C2214yes—
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2855C2214yes—
39#2850C2214yes—
40#2844C2214yes—
41#2838C2218yes—
42#2776C2218yes—
43#2775C2218yes—
44#2763C2218yes—
45#2762C2218yes—
46#2746C2218yes—
47#2745C2218yes—
48#2739C2218yes—
49#2737C2218yes—
50#2696C2218yes—
51#2694C2218yes—
52#2692C2218yes—
53#2690C2218yes—
54#2655C2218yes—
55#2650C2218yes—
56#2649C2218yes—
57#2645C2214yes—
58#2640C2214yes—
59#2628C2214yes—
60#2628C2214yes—
61#2628C2214yes—
62#2628C2214yes—
63#2628C2214yes—
64#2625C2214yes—
65#2621C2214yes—
66#2609C2214yes—
67#2605C2218yes—
68#2596C2218yes—
69#2582C2211yescharacteristic
70#2575C2218yes—
71#2572C2218yes—
72#2571C2212yes—
73#2571C2212yes—
74#2571C2212yes—
75#2570C2214yes—
76#2568C2212yes—
77#2567C2212yes—
78#2563C2214yes—
79#2563C2212yes—
80#2556C2218yes—
81#2551C2212yes—
82#2551C2212yes—
83#2551C2212yes—
84#2547C2212yes—
85#2547C2212yes—
86#2546C2212yes—
87#2546C2212yes—
88#2542C2212yes—
89#2538C2211yescharacteristic
90#2538C2211yescharacteristic
91#2537C2211yescharacteristic
92#2527C2218yes—
93#2524C2218yes—
94#2516C2218yes—
95#2514C2214yes—
96#2514C2214yes—
97#2510C2218yes—
98#2509C2214yes—
99#2508C2214yes—
100#2506C2214yes—
101#2506C2214yes—
102#2497C2214yes—
103#2497C2214yes—
104#2495C2214yes—
105#2494C2214yes—
106#2494C2214yes—
107#2494C2214yes—
108#2492C2214yes—
109#2492C2214yes—
110#2487C2214yes—
111#2487C2214yes—
112#2486C2214yes—
113#2486C2214yes—
114#2485C2214yes—
115#2485C2212yes—
116#2485C2212yes—
117#2477C2218yes—
118#2471C2218yes—
119#2465C2218yes—
120#2462C2218yes—
121#2458C2218yes—
122#2452C2214yes—
123#2451C2214yes—
124#2448C2214yes—
125#2446C2214yes—
126#2440C2214yes—
127#2439C2214yes—
128#2438C2218yes—
129#2429C2214yes—
130#2426C2214yes—
131#2421C2214yes—
132#2420C2214yes—
133#2409C2214yes—
134#2407C2212yes—
135#2407C2212yes—
136#2396C2218yes—
137#2392C2214yes—
138#2369C2212yes—
139#2369C2212yes—
140#2365C2212yes—
141#2365C2214yes—
142#2365C2212yes—
143#2355C2211yescharacteristic
144#2355C2211yescharacteristic
145#2354C2211yescharacteristic
146#2354C2212yes—
147#2354C2211yescharacteristic
148#2354C2212yes—
149#2352C2212yes—
150#2352C2212yes—
151#2352C2214yes—
152Q8×C4⋊C4C2211yescharacteristic
153Q8×C4⋊C4C2211yescharacteristic
154D4×C4⋊C4C2211yescharacteristic
155D4×C4⋊C4C2211yescharacteristic
156#2347C2212yes—
157#2347C2214yes—
158#2346C2214yes—
159#2346C2212yes—
160#2345C2214yes—
161#2344C2214yes—
162#2343C2214yes—
163#2341C2212yes—
164Q8×C22⋊C4C2214yes—
165#2339C2212yes—
166#2331C2214yes—
167#2327C2214yes—
168#2324C2214yes—
169#2320C2214yes—
170#2317C2212yes—
171#2316C2212yes—
172#2314C2214yes—
173#2311C2212yes—
174#2310C2212yes—
175C4×C4⋊Q8C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×#121C2212yes—
182C4×#121C2212yes—
183#2295C2212yes—
184#2293C2214yes—
185#2293C2214yes—
186#2293C2212yes—
187#2290C2214yes—
188#2285C2211yescharacteristic
189#2285C2211yescharacteristic
190#2285C2211yescharacteristic
191#2285C2212yes—
192#2283C2212yes—
193#2274C2212yes—
194C42×Q8C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×Q8C2312yes—
202#536—48no—
203#533—416no—
204C2×C4⋊Q8—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×#125C2318yes—
214C2×#124C2314yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2318yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C4×#41—28no—
226C4×#41—28no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2318yes—
235C2×C4×Q8C2312yes—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2311yescharacteristic
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2311yescharacteristic
257C2×#117C2312yes—
258C2×#117C2318yes—
259C2×#117C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C42C2312yes—
265C22×C42C2312yes—
266C22×C42C2314yes—
267C22×C42C2311yescharacteristic
268#401C2318yes—
269#401C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2318yes—
282#399C2318yes—
283#399C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#397C2314yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#396C2314yes—
298#396C2314yes—
299#396C2318yes—
300#396C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#394C2314yes—
307#394C2314yes—
308#394C2314yes—
309#394C2318yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#393C2318yes—
315#392C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2318yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2312yes—
328#391C2312yes—
329#391C2318yes—
330#391C2318yes—
331#391C2312yes—
332#391C2312yes—
333#390C2314yes—
334#390C2318yes—
335#390C2312yes—
336#390C2312yes—
337#390C2314yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#388C2318yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2318yes—
409#387C2314yes—
410#387C2318yes—
411#387C2314yes—
412#386C2318yes—
413#386C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#385C2314yes—
425#385C2318yes—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2314yes—
429#384C2312yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2312yes—
435#383C2318yes—
436#383C2318yes—
437#383C2314yes—
438#382C2314yes—
439#382C2318yes—
440#382C2314yes—
441#382C2312yes—
442#382C2314yes—
443#382C2314yes—
444#382C2312yes—
445#382C2312yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#381C2318yes—
450#381C2318yes—
451#381C2314yes—
452#380C2314yes—
453#380C2312yes—
454#380C2312yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2314yes—
461#380C2318yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2314yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518#376C2314yes—
519#376C2312yes—
520#376C2314yes—
521C2×#95C2314yes—
522C43C2312yes—
523C43C2314yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—42no—
529C2×#41—42no—
530C22×Q8—28no—
531C22×Q8—44no—
532C22×Q8—44no—
533C22×Q8C2414yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2414yes—
537C22×Q8C2418yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C22×D4C2414yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2414yes—
554C23×C4C2414yes—
555C4⋊Q8—216no—
556C4⋊Q8—28no—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559C4⋊Q8—28no—
560C4⋊Q8—48no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563#125—416no—
564#124—48no—
565#123—416no—
566C22⋊Q8—28no—
567C22⋊Q8—416no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C22⋊Q8—48no—
571C22⋊Q8—44no—
572C22⋊Q8—48no—
573#121—28no—
574#121—44no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—24no—
580C4×Q8—416no—
581C4×Q8—48no—
582C4×Q8—44no—
583C4×Q8—48no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—28no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—44no—
594C4×D4—48no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—28no—
599#117—28no—
600#117—28no—
601#117—48no—
602#117—44no—
603#117—44no—
604#117—44no—
605#117—416no—
606#117—42no—
607#117—44no—
608C2×C4⋊C4—28no—
609C2×C4⋊C4—28no—
610C2×C4⋊C4—28no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C42—28no—
692C2×C42—28no—
693C2×C42—48no—
694C2×C42#4118yes—
695C2×C42C2412yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2418yes—
712C2×C42C2412yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#95C2412yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2412yes—
727#95C2412yes—
728#95C2414yes—
729#95C2412yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766C24C2512yes—
767C24C2511yescharacteristic
768C24C2512yes—
769#41—416no—
770#41—416no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—28no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—28no—
779C2×Q8—22no—
780C2×Q8—48no—
781C2×Q8—44no—
782C2×Q8—48no—
783C2×Q8—48no—
784C2×Q8—44no—
785C2×Q8—816no—
786C2×Q8H(5,𝔽2)14yes—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—28no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D42−1+414yes—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—28no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—44no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4C2×#4114yes—
836C22×C4C2×#4114yes—
837C22×C4C2×#4114yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2518yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—216no—
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—216no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—22no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—22no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—44no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C42−1+414yes—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—28no—
922C22⋊C4—24no—
923C22⋊C4—28no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—42no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—28no—
948C42—28no—
949C42—24no—
950C42—28no—
951C42—24no—
952C42—24no—
953C42—28no—
954C42—28no—
955C42—24no—
956C42—44no—
957C42—44no—
958C42—42no—
959C42—44no—
960C42—48no—
961C42—44no—
962C42—48no—
963C42C2×#4114yes—
964C42C2×#4114yes—
965C42C2×#4114yes—
966C42C2×#4114yes—
967C23—22no—
968C23—22no—
969C23—21no—
970C23—21no—
971C23—22no—
972C23—21no—
973C23—21no—
974C23—22no—
975C23—21no—
976C23—22no—
977C23—22no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23C22×#4112yes—
987C23C2×2−1+414yes—
988C23C2611yescharacteristic
989Q8—28no—
990Q8—416no—
991Q8—44no—
992Q8—88no—
993Q8—816no—
994D4—28no—
995D4—48no—
996D4—48no—
997D4—44no—
998D4—88no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—28no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—28no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—48no—
1058C2×C4—416no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C2×H(5,𝔽2)14yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×2−1+414yes—
1075C2×C4C2×2−1+412yes—
1076C2×C4C2×2−1+412yes—
1077C2×C4#58512yes—
1078C2×C4#58512yes—
1079C2×C4#58512yes—
1080C22—24no—
1081C22—24no—
1082C22—22no—
1083C22—22no—
1084C22—24no—
1085C22—22no—
1086C22—41no—
1087C22—42no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22C23×#4111yescharacteristic
1102C22C22×H(5,𝔽2)11yescharacteristic
1103C22C22×2−1+411yescharacteristic
1104C22C22×2−1+411yescharacteristic
1105C22C2×#58511yescharacteristic
1106C22C2×#58511yescharacteristic
1107C22C2×#58511yescharacteristic
1108C4—24no—
1109C4—22no—
1110C4—24no—
1111C4—22no—
1112C4—22no—
1113C4—44no—
1114C4—42no—
1115C4—44no—
1116C4—44no—
1117C4—44no—
1118C4—42no—
1119C4—44no—
1120C4—42no—
1121C4—44no—
1122C4—42no—
1123C4—48no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4#346114yes—
1129C4#349414yes—
1130C4#349514yes—
1131C2—44no—
1132C2—42no—
1133C2—82no—
1134C2C2×#346111yescharacteristic
1135C2C2×#349411yescharacteristic
1136C2C2×#349511yescharacteristic
1137C2#6301611yescharacteristic
1138C2#6302211yescharacteristic
1139C2#6302511yescharacteristic
1140C2#6303411yescharacteristic
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. #42934C2semidirect
2. #42055C2semidirect
3. #39608C2semidirect
4. #39544C2semidirect
5. #39480C2semidirect
6. #39149C2semidirect
7. #39043C2semidirect
8. #38940C2semidirect
9. #38200C2semidirect
10. #37749C2semidirect
11. #37642C2semidirect
12. #37631C2semidirect
13. #36586C2semidirect
14. #36480C2semidirect
15. #36301C2semidirect
16. #36133C2semidirect
17. #35828C2semidirect
18. #35316C2semidirect
19. #35279C2semidirect
20. #35196C2semidirect
21. #35187C2semidirect
23. #34929C2semidirect
24. #34216C2semidirect
25. #34129C2semidirect
26. #34127C2semidirect

Maximal subgroups

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

subgroupindex
#429342
#420552
#396082
#395442
#394802
#391492
#390432
#389402
#382002
#377492
#376422
#376312
#365862
#364802
#363012
#361332
#358282
#353162
#352792
#351962
#351872
#349762
#349292
#342162
#341292
#341272