Finite Group Databasebeta

← #7664906

Subgroups — #7664906

Order 512.

5088 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39506C212yesmaximal, complemented
2#39505C212yesmaximal, complemented
3#38943C212yesmaximal, complemented
4#38941C212yesmaximal, complemented
5#38939C214yesmaximal, complemented
6#38289C214yesmaximal, complemented
7#38284C214yesmaximal, complemented
8#38281C218yesmaximal, complemented
9#37955C214yesmaximal, complemented
10#37952C214yesmaximal, complemented
11#36302C212yesmaximal, complemented
12#36288C212yesmaximal, complemented
13#36257C214yesmaximal, complemented
14#36194C212yesmaximal, complemented
15#36174C212yesmaximal, complemented
16#35312C212yesmaximal, complemented
17#35308C212yesmaximal, complemented
18#35275C211yesmaximal, characteristic, complemented
19#35273C211yesmaximal, characteristic
20#35178C211yesmaximal, characteristic, complemented
21#35158C212yesmaximal, complemented
22#34141C211yesmaximal, characteristic, complemented
23#34121C211yesmaximal, characteristic, complemented
24C2×#2355C211yesmaximal, characteristic, complemented
25C4×#536C211yesmaximal, characteristic, complemented
26#34060C212yesmaximal, complemented
27C2×#544C2212yes—
28C2×#537C2212yes—
29C2×#536C2211yescharacteristic
30C2×#536C2212yes—
31C2×#532C2211yescharacteristic
32C2×C4×#41C2212yes—
33C2×C4×#41C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2868C2212yes—
36#2862C2214yes—
37#2861C2214yes—
38#2859C2212yes—
39#2857C2212yes—
40#2857C2214yes—
41#2856C2212yes—
42#2854C2214yes—
43#2850C2214yes—
44#2850C2218yes—
45#2795C2218yes—
46#2785C2218yes—
47#2783C2218yes—
48#2783C2218yes—
49#2781C2218yes—
50#2775C2218yes—
51#2769C2218yes—
52#2744C2218yes—
53#2744C2218yes—
54#2737C2218yes—
55#2731C2218yes—
56#2686C2218yes—
57#2660C2214yes—
58#2642C2214yes—
59#2640C2214yes—
60#2639C2218yes—
61#2621C2214yes—
62#2620C2214yes—
63#2620C2214yes—
64#2618C2214yes—
65#2612C2218yes—
66#2593C2218yes—
67#2574C2218yes—
68#2574C2218yes—
69#2571C2214yes—
70#2563C2214yes—
71#2552C2212yes—
72#2552C2212yes—
73#2551C2212yes—
74#2551C2212yes—
75#2548C2212yes—
76#2546C2212yes—
77#2545C2214yes—
78#2538C2212yes—
79#2538C2212yes—
80#2538C2212yes—
81#2538C2212yes—
82#2537C2212yes—
83#2537C2212yes—
84#2536C2214yes—
85#2531C2218yes—
86#2529C2218yes—
87#2526C2218yes—
88#2518C2218yes—
89#2513C2214yes—
90#2513C2214yes—
91#2508C2214yes—
92#2508C2214yes—
93#2500C2214yes—
94#2497C2214yes—
95#2497C2218yes—
96#2495C2214yes—
97#2492C2214yes—
98#2492C2214yes—
99#2492C2214yes—
100#2492C2214yes—
101#2491C2214yes—
102#2491C2214yes—
103#2491C2214yes—
104#2490C2214yes—
105#2490C2214yes—
106#2489C2214yes—
107#2489C2214yes—
108#2489C2214yes—
109#2489C2214yes—
110#2488C2218yes—
111#2488C2218yes—
112#2476C2218yes—
113#2474C2218yes—
114#2440C2214yes—
115#2440C2214yes—
116#2439C2214yes—
117#2439C2218yes—
118#2429C2214yes—
119#2429C2214yes—
120#2427C2214yes—
121#2427C2214yes—
122#2425C2218yes—
123#2425C2218yes—
124#2420C2214yes—
125#2416C2214yes—
126#2416C2214yes—
127#2369C2214yes—
128#2367C2212yes—
129#2367C2212yes—
130#2366C2211yescharacteristic
131#2366C2211yescharacteristic
132#2365C2211yescharacteristic
133#2365C2211yescharacteristic
134#2364C2214yes—
135#2363C2214yes—
136#2361C2212yes—
137#2361C2212yes—
138#2357C2212yes—
139#2356C2212yes—
140#2355C2212yes—
141#2355C2214yes—
142#2355C2212yes—
143#2355C2212yes—
144#2355C2214yes—
145#2355C2212yes—
146#2355C2211yescharacteristic
147#2355C2211yescharacteristic
148#2354C2211yescharacteristic
149#2354C2211yescharacteristic
150#2354C2214yes—
151#2353C2214yes—
152#2352C2212yes—
153#2352C2212yes—
154#2346C2214yes—
155#2327C2212yes—
156#2326C2212yes—
157#2323C2212yes—
158#2323C2212yes—
159#2322C2214yes—
160#2320C2214yes—
161#2319C2214yes—
162#2318C2218yes—
163#2317C2211yescharacteristic
164#2317C2212yes—
165#2314C2214yes—
166#2314C2214yes—
167#2311C2212yes—
168#2311C2212yes—
169#2311C2211yescharacteristic
170#2310C2211yescharacteristic
171C4×C4⋊Q8C2212yes—
172C4×#124C2212yes—
173C4×C22⋊Q8C2212yes—
174C4×C22⋊Q8C2212yes—
175C4×#123C2214yes—
176#2298C2214yes—
177#2297C2212yes—
178#2297C2212yes—
179#2295C2214yes—
180C2×#391C2212yes—
181#2293C2214yes—
182#2293C2212yes—
183#2290C2218yes—
184#2290C2214yes—
185C2×#387C2214yes—
186#2285C2214yes—
187#2285C2211yescharacteristic
188C2×#384C2211yescharacteristic
189#2283C2214yes—
190#2283C2212yes—
191C2×#382C2212yes—
192C42×D4C2212yes—
193C4×#117C2212yes—
194C4×#117C2211yescharacteristic
195C4×#117C2212yes—
196C2×C4×C4⋊C4C2212yes—
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C22×#41C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202#544—48no—
203#537—48no—
204#536—28no—
205#536—48no—
206#532—28no—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×#127C2311yescharacteristic
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#124C2318yes—
221C2×#123C2314yes—
222C2×#123C2318yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2314yes—
233C2×#121C2318yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C4×#41—216no—
238C4×#41—28no—
239C2×C4×Q8—28no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2312yes—
263C2×#117C2314yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2318yes—
268C2×#117C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C42C2314yes—
277C22×C42C2312yes—
278C22×C42C2312yes—
279C22×C42C2312yes—
280C22×C42C2314yes—
281C22×C42C2311yescharacteristic
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#395C2318yes—
306#395C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2318yes—
326#391C2318yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2318yes—
332#391C2314yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2318yes—
342#390C2312yes—
343#390C2314yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2312yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#386C2314yes—
425#385C2314yes—
426#385C2318yes—
427#385C2314yes—
428#385C2314yes—
429#385C2314yes—
430#385C2314yes—
431#384C2312yes—
432#384C2314yes—
433#384C2314yes—
434#384C2312yes—
435#384C2311yescharacteristic
436#384C2312yes—
437#384C2311yescharacteristic
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#383C2318yes—
442#383C2314yes—
443#382C2312yes—
444#382C2314yes—
445#382C2312yes—
446#382C2314yes—
447#382C2318yes—
448#382C2318yes—
449#382C2318yes—
450#382C2318yes—
451#382C2312yes—
452#382C2314yes—
453#382C2318yes—
454#382C2312yes—
455#381C2314yes—
456#381C2318yes—
457#381C2314yes—
458#380C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2318yes—
468#380C2312yes—
469#380C2314yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517#376C2314yes—
518#376C2312yes—
519#376C2318yes—
520#376C2314yes—
521C2×#95C2314yes—
522C2×#95C2312yes—
523C2×#95C2314yes—
524C2×#95C2314yes—
525C43C2312yes—
526C43C2314yes—
527C2×#41—28no—
528C2×#41—24no—
529C2×#41—28no—
530C2×#41—24no—
531C2×#41—28no—
532C2×#41—24no—
533C22×Q8—24no—
534C22×Q8—24no—
535C22×Q8—24no—
536C22×Q8C2412yes—
537C22×Q8C2411yescharacteristic
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2418yes—
541C22×D4C2412yes—
542C22×D4C2414yes—
543C22×D4C2412yes—
544C22×D4C2411yescharacteristic
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2418yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2414yes—
554C23×C4C2411yescharacteristic
555C23×C4C2414yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2414yes—
559C23×C4C2412yes—
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C4⋊Q8—24no—
563C4⋊Q8—28no—
564C4⋊Q8—48no—
565C4⋊Q8—48no—
566C4⋊Q8—48no—
567C4⋊Q8—48no—
568C4⋊Q8—84no—
569#127—24no—
570#125—48no—
571#125—48no—
572#124—28no—
573#124—28no—
574#124—48no—
575#124—88no—
576#123—216no—
577#123—416no—
578C22⋊Q8—28no—
579C22⋊Q8—28no—
580C22⋊Q8—416no—
581C22⋊Q8—48no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585#121—28no—
586#121—28no—
587#121—48no—
588#121—48no—
589#121—48no—
590#121—416no—
591#121—84no—
592C4×Q8—28no—
593C4×Q8—28no—
594C4×Q8—28no—
595C4×Q8—28no—
596C4×Q8—28no—
597C4×Q8—28no—
598C4×Q8—24no—
599C4×Q8—24no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—28no—
603C4×D4—28no—
604C4×D4—28no—
605C4×D4—216no—
606C4×D4—216no—
607C4×D4—24no—
608C4×D4—24no—
609C4×D4—28no—
610C4×D4—28no—
611C4×D4—44no—
612#117—24no—
613#117—28no—
614#117—24no—
615#117—28no—
616#117—216no—
617#117—28no—
618#117—44no—
619#117—88no—
620#117#4118yes—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—28no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4—82no—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2412yes—
704C2×C42—28no—
705C2×C42—28no—
706C2×C42—216no—
707C2×C42—28no—
708C2×C42—84no—
709C2×C42#4118yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2412yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2418yes—
729C2×C42C2418yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2414yes—
733C2×C42C2412yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738#95C2412yes—
739#95C2412yes—
740#95C2418yes—
741#95C2418yes—
742#95C2412yes—
743#95C2418yes—
744#95C2412yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2414yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780C24C2512yes—
781C24C2514yes—
782C24C2511yescharacteristic
783#41—432no—
784#41—416no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—22no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—22no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—48no—
798C2×Q8—48no—
799C2×Q8—48no—
800C2×Q8—416no—
801C2×D4—24no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—28no—
807C2×D4—24no—
808C2×D4—22no—
809C2×D4—24no—
810C2×D4—22no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—48no—
820C2×D4—48no—
821C2×D4—48no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—24no—
835C22×C4—28no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—24no—
843C22×C4—28no—
844C22×C4—24no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—41no—
848C22×C4—44no—
849C22×C4—41no—
850C22×C4—42no—
851C22×C4—44no—
852C22×C4—42no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—42no—
856C22×C4—44no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4C2×#4114yes—
860C22×C4C2×#4114yes—
861C22×C4C2×#4114yes—
862C22×C4C2×#4114yes—
863C22×C4H(5,𝔽2)14yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2514yes—
870C22×C4C2514yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2512yes—
876C22×C4C2518yes—
877C22×C4C2514yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2511yescharacteristic
883C22×C4C2512yes—
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4—24no—
908C4⋊C4—22no—
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—28no—
913C4⋊C4—24no—
914C4⋊C4—42no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—42no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—42no—
930C4⋊C4C2×#4114yes—
931C4⋊C4C2×#4114yes—
932C4⋊C42−1+414yes—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—28no—
936C22⋊C4—24no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—24no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4C2×#4118yes—
963C42—24no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—28no—
968C42—24no—
969C42—28no—
970C42—24no—
971C42—24no—
972C42—28no—
973C42—28no—
974C42—28no—
975C42—24no—
976C42—28no—
977C42—24no—
978C42—24no—
979C42—48no—
980C42—48no—
981C42—42no—
982C42—44no—
983C42—44no—
984C42—44no—
985C42—42no—
986C42C2×#4114yes—
987C42C2×#4118yes—
988C42C2×#4114yes—
989C42C2×#4114yes—
990C42C2×#4114yes—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—22no—
996C23—24no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—22no—
1005C23—24no—
1006C23—22no—
1007C23—22no—
1008C23—24no—
1009C23C22×#4112yes—
1010C23C22×#4112yes—
1011C23C2×H(5,𝔽2)12yes—
1012C23C2611yescharacteristic
1013Q8—48no—
1014Q8—48no—
1015Q8—44no—
1016Q8—48no—
1017Q8—168no—
1018D4—416no—
1019D4—48no—
1020D4—48no—
1021D4—44no—
1022D4—48no—
1023D4—84no—
1024D4—168no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—28no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—28no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—28no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—28no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—44no—
1081C2×C4—416no—
1082C2×C4—48no—
1083C2×C4—48no—
1084C2×C4—48no—
1085C2×C4—48no—
1086C2×C4—416no—
1087C2×C4—48no—
1088C2×C4—88no—
1089C2×C4—84no—
1090C2×C4—84no—
1091C2×C4—88no—
1092C2×C4#555116yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C22×#4114yes—
1096C2×C4C22×#4114yes—
1097C2×C4C22×#4112yes—
1098C2×C4C22×#4112yes—
1099C2×C4C22×#4112yes—
1100C2×C4C22×#4112yes—
1101C2×C4C22×#4112yes—
1102C2×C4C22×#4112yes—
1103C2×C4C2×H(5,𝔽2)12yes—
1104C2×C4C2×H(5,𝔽2)12yes—
1105C2×C4C2×2−1+414yes—
1106C2×C4C2×2−1+412yes—
1107C2×C4#58512yes—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—44no—
1115C22—42no—
1116C22—44no—
1117C22—42no—
1118C22—42no—
1119C22—44no—
1120C22—42no—
1121C22—44no—
1122C22—44no—
1123C22—42no—
1124C22—42no—
1125C22—44no—
1126C22—42no—
1127C22—44no—
1128C22C2×#55514yes—
1129C22C23×#4111yescharacteristic
1130C22C23×#4111yescharacteristic
1131C22C22×H(5,𝔽2)11yescharacteristic
1132C22C22×2−1+411yescharacteristic
1133C22C2×#58511yescharacteristic
1134C22H(7,𝔽2)11yescharacteristic
1135C222−1+611yescharacteristic
1136C4—24no—
1137C4—24no—
1138C4—24no—
1139C4—22no—
1140C4—22no—
1141C4—22no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—44no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4—42no—
1150C4—48no—
1151C4—44no—
1152C4—42no—
1153C4—44no—
1154C4—42no—
1155C4—44no—
1156C4#346114yes—
1157C4C2×#55514yes—
1158C4C2×#55514yes—
1159C2—24no—
1160C2—84no—
1161C2—82no—
1162C2C2×#346111yescharacteristic
1163C2C22×#55511yescharacteristic
1164C2#6285611yescharacteristic
1165C2#6294611yescharacteristic
1166C2#6296111yescharacteristic
1167C2#6300011yescharacteristic
1168C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35273C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39506C2semidirect
2. #39505C2semidirect
3. #38943C2semidirect
4. #38941C2semidirect
5. #38939C2semidirect
6. #38289C2semidirect
7. #38284C2semidirect
8. #38281C2semidirect
9. #37955C2semidirect
10. #37952C2semidirect
11. #36302C2semidirect
12. #36288C2semidirect
13. #36257C2semidirect
14. #36194C2semidirect
15. #36174C2semidirect
16. #35312C2semidirect
17. #35308C2semidirect
18. #35275C2semidirect
20. #35178C2semidirect
21. #35158C2semidirect
22. #34141C2semidirect
23. #34121C2semidirect
24. C2×#2355C2semidirect
25. C4×#536C2semidirect
26. #34060C2semidirect

Maximal subgroups

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

subgroupindex
#395062
#395052
#389432
#389412
#389392
#382892
#382842
#382812
#379552
#379522
#363022
#362882
#362572
#361942
#361742
#353122
#353082
#352752
#352732
#351782
#351582
#341412
#341212
C2×#23552
C4×#5362
#340602