Finite Group Databasebeta

← #7654848

Subgroups — #7654848

Order 512.

4980 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42939C214yesmaximal, complemented
2#42062C218yesmaximal, complemented
3#39642C212yesmaximal, complemented
4#39435C214yesmaximal, complemented
5#39385C212yesmaximal, complemented
6#39200C212yesmaximal, complemented
7#39076C214yesmaximal, complemented
8#38985C212yesmaximal, complemented
9#38260C214yesmaximal, complemented
10#37783C214yesmaximal, complemented
11#37640C211yesmaximal, characteristic
12#37628C212yesmaximal, complemented
13#36563C212yesmaximal, complemented
14#36454C212yesmaximal, complemented
15#36300C212yesmaximal, complemented
16#36134C212yesmaximal, complemented
17#35745C214yesmaximal, complemented
18#35317C211yesmaximal, characteristic
19#35281C211yesmaximal, characteristic, complemented
20#35209C212yesmaximal, complemented
21#35176C212yesmaximal, complemented
22#34978C211yesmaximal, characteristic, complemented
23#34929C212yesmaximal, complemented
24#34216C211yesmaximal, characteristic, complemented
25#34155C211yesmaximal, characteristic
26#34154C211yesmaximal, characteristic, complemented
27C2×#541C2214yes—
28C2×#536C2212yes—
29C2×#536C2212yes—
30C2×#533C2211yescharacteristic
31C2×#533C2214yes—
32C2×#532C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34#2868C2212yes—
35#2868C2212yes—
36#2862C2212yes—
37#2860C2214yes—
38#2859C2214yes—
39#2858C2212yes—
40#2857C2214yes—
41#2855C2214yes—
42#2836C2218yes—
43#2820C2214yes—
44#2773C2218yes—
45#2754C2218yes—
46#2721C2218yes—
47#2721C2218yes—
48#2715C2218yes—
49#2713C2218yes—
50#2713C2218yes—
51#2707C2218yes—
52#2700C2218yes—
53#2695C2218yes—
54#2694C2218yes—
55#2687C2218yes—
56#2667C2218yes—
57#2664C2218yes—
58#2660C2214yes—
59#2658C2214yes—
60#2654C2218yes—
61#2647C2214yes—
62#2644C2214yes—
63#2625C2214yes—
64#2624C2214yes—
65#2621C2214yes—
66#2620C2214yes—
67#2616C2214yes—
68#2612C2214yes—
69#2592C2214yes—
70#2582C2214yes—
71#2575C2218yes—
72#2571C2211yescharacteristic
73#2567C2212yes—
74#2567C2212yes—
75#2567C2212yes—
76#2558C2218yes—
77#2556C2218yes—
78#2553C2218yes—
79#2552C2214yes—
80#2552C2211yescharacteristic
81#2552C2211yescharacteristic
82#2552C2214yes—
83#2552C2214yes—
84#2551C2211yescharacteristic
85#2550C2218yes—
86#2548C2212yes—
87#2547C2212yes—
88#2546C2212yes—
89#2546C2212yes—
90#2542C2212yes—
91#2542C2212yes—
92#2542C2212yes—
93#2542C2212yes—
94#2542C2212yes—
95#2538C2212yes—
96#2538C2212yes—
97#2538C2214yes—
98#2522C2218yes—
99#2521C2218yes—
100#2519C2218yes—
101#2517C2218yes—
102#2513C2214yes—
103#2512C2214yes—
104#2512C2214yes—
105#2512C2214yes—
106#2511C2214yes—
107#2511C2214yes—
108#2507C2214yes—
109#2507C2214yes—
110#2506C2214yes—
111#2506C2214yes—
112#2502C2214yes—
113#2501C2214yes—
114#2501C2214yes—
115#2492C2214yes—
116#2489C2214yes—
117#2474C2218yes—
118#2470C2218yes—
119#2458C2218yes—
120#2454C2214yes—
121#2452C2214yes—
122#2451C2218yes—
123#2448C2214yes—
124#2447C2214yes—
125#2441C2212yes—
126#2441C2218yes—
127#2441C2212yes—
128#2439C2212yes—
129#2439C2212yes—
130#2434C2214yes—
131#2429C2214yes—
132#2429C2214yes—
133#2429C2214yes—
134#2429C2214yes—
135#2423C2214yes—
136#2423C2218yes—
137#2421C2214yes—
138#2396C2218yes—
139#2396C2214yes—
140#2372C2214yes—
141#2371C2214yes—
142#2369C2212yes—
143#2369C2211yescharacteristic
144#2369C2211yescharacteristic
145#2369C2212yes—
146#2367C2214yes—
147#2366C2211yescharacteristic
148#2366C2211yescharacteristic
149#2365C2211yescharacteristic
150#2365C2212yes—
151#2365C2211yescharacteristic
152#2365C2212yes—
153#2365C2211yescharacteristic
154#2365C2211yescharacteristic
155#2363C2212yes—
156#2363C2212yes—
157#2363C2212yes—
158#2363C2212yes—
159#2362C2212yes—
160#2362C2212yes—
161#2362C2212yes—
162#2362C2212yes—
163#2355C2214yes—
164#2354C2214yes—
165Q8×C4⋊C4C2214yes—
166#2345C2214yes—
167Q8×C22⋊C4C2214yes—
168#2331C2214yes—
169#2330C2214yes—
170#2323C2214yes—
171#2319C2214yes—
172#2317C2212yes—
173#2317C2212yes—
174#2316C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2214yes—
179C4×C4⋊Q8C2212yes—
180C4×#125C2212yes—
181C4×#125C2212yes—
182C4×C22⋊Q8C2214yes—
183#2298C2214yes—
184#2297C2214yes—
185#2295C2212yes—
186#2295C2212yes—
187#2293C2212yes—
188#2293C2212yes—
189#2293C2214yes—
190#2285C2211yescharacteristic
191#2274C2212yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×D4C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C4×#117C2211yescharacteristic
199C22×#41C2312yes—
200C23×Q8C2312yes—
201#541—416no—
202#536—48no—
203#536—48no—
204#533—28no—
205#533—416no—
206#532—28no—
207C2×C4⋊Q8—28no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2314yes—
221C2×#127C2311yescharacteristic
222C2×#126C2318yes—
223C2×#126C2318yes—
224C2×#125C2312yes—
225C2×#125C2312yes—
226C2×#125C2312yes—
227C2×#125C2318yes—
228C2×#125C2318yes—
229C2×#125C2318yes—
230C2×#124C2312yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#124C2314yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2318yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2318yes—
256C2×C4×Q8C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2312yes—
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2312yes—
271C2×#117C2314yes—
272C2×#117C2318yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C42C2314yes—
276C22×C42C2311yescharacteristic
277#400C2314yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#399C2318yes—
283#399C2318yes—
284#399C2318yes—
285#399C2318yes—
286#399C2314yes—
287#399C2318yes—
288#399C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2314yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2314yes—
313#396C2314yes—
314#396C2318yes—
315#396C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2314yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#393C2318yes—
324#393C2314yes—
325#391C2318yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2318yes—
335#391C2318yes—
336#391C2312yes—
337#391C2314yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2314yes—
342#391C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2312yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2312yes—
354#390C2312yes—
355#390C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2318yes—
380#389C2312yes—
381#389C2318yes—
382#389C2318yes—
383#389C2312yes—
384#389C2318yes—
385#389C2312yes—
386#389C2318yes—
387#389C2318yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2318yes—
410#388C2318yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2318yes—
431#386C2314yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2312yes—
443#384C2314yes—
444#384C2314yes—
445#384C2314yes—
446#384C2314yes—
447#384C2314yes—
448#384C2314yes—
449#384C2314yes—
450#384C2314yes—
451#384C2314yes—
452#382C2312yes—
453#382C2312yes—
454#382C2312yes—
455#382C2314yes—
456#382C2314yes—
457#382C2318yes—
458#381C2318yes—
459#380C2318yes—
460#380C2318yes—
461#380C2314yes—
462#380C2312yes—
463#380C2312yes—
464#380C2318yes—
465#380C2314yes—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518#376C2314yes—
519#376C2312yes—
520#376C2312yes—
521#376C2312yes—
522C43C2312yes—
523C43C2312yes—
524C43C2312yes—
525C43C2314yes—
526C2×#41—28no—
527C2×#41—44no—
528C2×#41—44no—
529C22×Q8—28no—
530C22×Q8—44no—
531C22×Q8—44no—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2414yes—
535C22×Q8C2414yes—
536C22×Q8C2414yes—
537C22×Q8C2412yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2412yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2414yes—
548C23×C4C2414yes—
549C4⋊Q8—28no—
550C4⋊Q8—28no—
551C4⋊Q8—28no—
552C4⋊Q8—28no—
553C4⋊Q8—28no—
554C4⋊Q8—28no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—48no—
559C4⋊Q8—48no—
560C4⋊Q8—48no—
561C4⋊Q8—48no—
562#127—24no—
563#126—416no—
564#126—416no—
565#125—28no—
566#125—28no—
567#125—28no—
568#125—416no—
569#125—416no—
570#125—416no—
571#124—28no—
572#124—48no—
573#124—48no—
574#124—48no—
575#123—416no—
576#123—416no—
577C22⋊Q8—28no—
578C22⋊Q8—28no—
579C22⋊Q8—216no—
580C22⋊Q8—216no—
581C22⋊Q8—416no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586#121—28no—
587#121—28no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—28no—
592C4×Q8—28no—
593C4×Q8—48no—
594C4×Q8—44no—
595C4×Q8—48no—
596C4×Q8—416no—
597C4×Q8—48no—
598C4×D4—28no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—28no—
603C4×D4—44no—
604#117—28no—
605#117—24no—
606#117—24no—
607#117—24no—
608#117—24no—
609#117—24no—
610#117—44no—
611#117—48no—
612#117—416no—
613#117—42no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—28no—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C42—48no—
698C2×C42#4118yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2418yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2418yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#95C2412yes—
732#95C2412yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773C24C2514yes—
774C24C2511yescharacteristic
775#41—816no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—28no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—28no—
788C2×Q8—24no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—816no—
795C2×D4—28no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—42no—
806C2×D4—42no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4C2×#4114yes—
826C22×C4C2×#4114yes—
827C22×C4C2×#4114yes—
828C22×C4C2514yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2518yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—216no—
872C4⋊C4—216no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4H(5,𝔽2)14yes—
905C4⋊C4H(5,𝔽2)14yes—
906C4⋊C42−1+414yes—
907C4⋊C42−1+414yes—
908C4⋊C42−1+414yes—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—216no—
915C22⋊C4—216no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—44no—
923C22⋊C4—42no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C42—28no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—28no—
939C42—24no—
940C42—24no—
941C42—28no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—28no—
950C42—24no—
951C42—24no—
952C42—28no—
953C42—24no—
954C42—24no—
955C42—44no—
956C42—44no—
957C42—42no—
958C42—48no—
959C42—44no—
960C42—48no—
961C42C2×#4114yes—
962C42C2×#4114yes—
963C42C2×#4114yes—
964C42C2×#4114yes—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23C22×#4112yes—
979C23C2611yescharacteristic
980Q8—416no—
981Q8—48no—
982Q8—48no—
983Q8—416no—
984Q8—88no—
985Q8—84no—
986D4—48no—
987D4—48no—
988D4—84no—
989D4—88no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—28no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—28no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—28no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—416no—
1049C2×C4—416no—
1050C2×C4—88no—
1051C2×C4—88no—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C2×H(5,𝔽2)14yes—
1059C2×C4C2×H(5,𝔽2)14yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×2−1+414yes—
1063C2×C4C2×2−1+414yes—
1064C2×C4C2×2−1+414yes—
1065C2×C4C2×2−1+412yes—
1066C2×C4C2×2−1+412yes—
1067C2×C4C2×2−1+412yes—
1068C2×C4#58512yes—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22C23×#4111yescharacteristic
1084C22C22×H(5,𝔽2)11yescharacteristic
1085C22C22×H(5,𝔽2)11yescharacteristic
1086C22C22×2−1+411yescharacteristic
1087C22C22×2−1+411yescharacteristic
1088C22C22×2−1+411yescharacteristic
1089C22C2×#58511yescharacteristic
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—24no—
1094C4—24no—
1095C4—22no—
1096C4—22no—
1097C4—22no—
1098C4—42no—
1099C4—44no—
1100C4—42no—
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—44no—
1107C4—44no—
1108C4—48no—
1109C4—44no—
1110C4—44no—
1111C4#346114yes—
1112C4#350814yes—
1113C4#350914yes—
1114C2—42no—
1115C2—84no—
1116C2C2×#346111yescharacteristic
1117C2C2×#350811yescharacteristic
1118C2C2×#350911yescharacteristic
1119C2#6301311yescharacteristic
1120C2#6301611yescharacteristic
1121C2#6303711yescharacteristic
1122C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42939C2semidirect
2. #42062C2semidirect
3. #39642C2semidirect
4. #39435C2semidirect
5. #39385C2semidirect
6. #39200C2semidirect
7. #39076C2semidirect
8. #38985C2semidirect
9. #38260C2semidirect
10. #37783C2semidirect
12. #37628C2semidirect
13. #36563C2semidirect
14. #36454C2semidirect
15. #36300C2semidirect
16. #36134C2semidirect
17. #35745C2semidirect
19. #35281C2semidirect
20. #35209C2semidirect
21. #35176C2semidirect
22. #34978C2semidirect
23. #34929C2semidirect
24. #34216C2semidirect
26. #34154C2semidirect

Maximal subgroups

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

subgroupindex
#429392
#420622
#396422
#394352
#393852
#392002
#390762
#389852
#382602
#377832
#376402
#376282
#365632
#364542
#363002
#361342
#357452
#353172
#352812
#352092
#351762
#349782
#349292
#342162
#341552
#341542