Finite Group Databasebeta

← #7679790

Subgroups — #7679790

Order 512.

5208 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59677C214yesmaximal, complemented
2#59308C214yesmaximal, complemented
3#59303C212yesmaximal, complemented
4#59302C212yesmaximal, complemented
5#59257C212yesmaximal, complemented
6#59212C212yesmaximal, complemented
7#45160C214yesmaximal, complemented
8#45158C214yesmaximal, complemented
9#43580C218yesmaximal, complemented
10#39285C214yesmaximal, complemented
11#39284C214yesmaximal, complemented
12#39149C212yesmaximal, complemented
13#39148C212yesmaximal, complemented
14#36460C212yesmaximal, complemented
15#36449C212yesmaximal, complemented
16#35618C212yesmaximal, complemented
17#35564C212yesmaximal, complemented
18#35273C211yesmaximal, characteristic, complemented
19#35267C212yesmaximal, complemented
20C2×#2571C211yesmaximal, characteristic, complemented
21#34937C211yesmaximal, characteristic, complemented
22#34208C212yesmaximal, complemented
23#34206C211yesmaximal, characteristic, complemented
24#34183C211yesmaximal, characteristic, complemented
25#34121C211yesmaximal, characteristic, complemented
26C4×#537C211yesmaximal, characteristic, complemented
27C2×#537C2211yescharacteristic
28C2×#537C2212yes—
29C2×#532C2211yescharacteristic
30C2×#532C2212yes—
31C2×#520C2212yes—
32C2×#520C2212yes—
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2863C2214yes—
36#2860C2214yes—
37#2857C2212yes—
38#2856C2212yes—
39#2800C2218yes—
40#2795C2218yes—
41#2793C2218yes—
42#2779C2218yes—
43#2778C2218yes—
44#2776C2218yes—
45#2772C2218yes—
46#2753C2218yes—
47#2750C2218yes—
48#2749C2218yes—
49#2739C2218yes—
50#2688C2218yes—
51#2645C2214yes—
52#2644C2214yes—
53#2620C2214yes—
54#2608C2218yes—
55#2595C2218yes—
56#2591C2218yes—
57#2578C2218yes—
58#2576C2218yes—
59#2573C2218yes—
60#2571C2212yes—
61#2571C2212yes—
62#2571C2214yes—
63#2571C2214yes—
64#2571C2212yes—
65#2571C2212yes—
66#2570C2214yes—
67#2559C2218yes—
68#2559C2218yes—
69#2548C2211yescharacteristic
70#2547C2211yescharacteristic
71#2546C2211yescharacteristic
72#2545C2212yes—
73#2544C2212yes—
74#2543C2214yes—
75#2543C2218yes—
76#2541C2211yescharacteristic
77#2538C2212yes—
78#2538C2212yes—
79#2537C2212yes—
80#2537C2212yes—
81#2535C2214yes—
82#2530C2218yes—
83#2526C2218yes—
84#2518C2218yes—
85#2512C2214yes—
86#2510C2218yes—
87#2509C2214yes—
88#2504C2214yes—
89#2504C2214yes—
90#2503C2214yes—
91#2500C2214yes—
92#2500C2214yes—
93#2499C2214yes—
94#2497C2214yes—
95#2497C2214yes—
96#2496C2214yes—
97#2495C2214yes—
98#2495C2214yes—
99#2494C2214yes—
100#2494C2214yes—
101#2485C2214yes—
102#2481C2218yes—
103#2481C2218yes—
104#2444C2218yes—
105#2444C2218yes—
106#2429C2214yes—
107#2428C2214yes—
108#2427C2214yes—
109#2426C2214yes—
110#2421C2214yes—
111#2421C2214yes—
112#2420C2214yes—
113#2420C2214yes—
114#2420C2214yes—
115#2417C2214yes—
116#2416C2212yes—
117#2416C2218yes—
118#2416C2214yes—
119#2416C2214yes—
120#2416C2214yes—
121#2416C2214yes—
122#2416C2212yes—
123#2415C2214yes—
124#2414C2214yes—
125C2×#400C2214yes—
126#2392C2214yes—
127#2367C2214yes—
128#2366C2212yes—
129#2365C2212yes—
130#2364C2218yes—
131#2364C2218yes—
132#2363C2214yes—
133#2357C2212yes—
134#2357C2214yes—
135#2356C2212yes—
136#2355C2211yescharacteristic
137#2355C2211yescharacteristic
138#2354C2211yescharacteristic
139#2354C2211yescharacteristic
140#2354C2212yes—
141#2353C2214yes—
142#2352C2212yes—
143#2352C2212yes—
144#2352C2214yes—
145#2352C2214yes—
146#2352C2214yes—
147#2352C2214yes—
148#2352C2214yes—
149#2352C2214yes—
150Q8×C4⋊C4C2212yes—
151Q8×C4⋊C4C2212yes—
152D4×C4⋊C4C2214yes—
153D4×C4⋊C4C2214yes—
154D4×C4⋊C4C2212yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2212yes—
157#2345C2214yes—
158#2328C2214yes—
159#2327C2214yes—
160#2325C2214yes—
161#2325C2214yes—
162#2324C2212yes—
163#2324C2212yes—
164#2323C2212yes—
165#2323C2212yes—
166#2317C2212yes—
167#2317C2214yes—
168#2316C2211yescharacteristic
169#2311C2211yescharacteristic
170#2311C2211yescharacteristic
171#2311C2212yes—
172#2311C2212yes—
173C4×#124C2214yes—
174C4×#124C2214yes—
175C4×C22⋊Q8C2212yes—
176C4×C22⋊Q8C2212yes—
177C4×#121C2214yes—
178C4×#121C2214yes—
179C4×#121C2212yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182C4×#121C2212yes—
183#2298C2214yes—
184#2297C2212yes—
185#2297C2212yes—
186C2×#389C2212yes—
187C2×#389C2212yes—
188#2285C2211yescharacteristic
189#2285C2212yes—
190C2×#384C2211yescharacteristic
191C2×#384C2212yes—
192#2283C2212yes—
193C2×#382C2212yes—
194C2×#382C2212yes—
195C4×#117C2212yes—
196C4×#117C2212yes—
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2312yes—
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202#537—28no—
203#537—48no—
204#532—216no—
205#532—28no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127C2312yes—
209C2×#127C2311yescharacteristic
210C2×#126C2318yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×#121C2312yes—
219C2×#121C2312yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2312yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2312yes—
229C2×#121C2318yes—
230C2×#121C2312yes—
231C2×#121C2318yes—
232C2×#121C2314yes—
233#520—48no—
234#520—48no—
235C4×#41—28no—
236C4×#41—28no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2318yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2318yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2314yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2314yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284C22×C42C2312yes—
285C22×C42C2312yes—
286C22×C42C2311yescharacteristic
287#401C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#400C2318yes—
296#400C2318yes—
297#398C2318yes—
298#398C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2314yes—
311#396C2318yes—
312#396C2318yes—
313#396C2314yes—
314#396C2318yes—
315#394C2314yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2314yes—
321#394C2314yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#392C2314yes—
326#392C2318yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#390C2312yes—
336#390C2312yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2318yes—
341#390C2314yes—
342#390C2314yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2314yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#389C2312yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#388C2314yes—
373#388C2318yes—
374#388C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2318yes—
382#388C2314yes—
383#388C2318yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#386C2314yes—
412#386C2318yes—
413#386C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2314yes—
418#386C2318yes—
419#386C2314yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2314yes—
425#386C2318yes—
426#386C2314yes—
427#386C2314yes—
428#386C2318yes—
429#386C2314yes—
430#386C2314yes—
431#386C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2314yes—
437#385C2314yes—
438#384C2314yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2312yes—
443#384C2314yes—
444#384C2311yescharacteristic
445#384C2314yes—
446#384C2311yescharacteristic
447#383C2318yes—
448#383C2314yes—
449#382C2312yes—
450#382C2314yes—
451#382C2318yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#382C2314yes—
457#382C2312yes—
458#382C2314yes—
459#382C2312yes—
460#381C2318yes—
461#381C2318yes—
462#381C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2312yes—
474#380C2312yes—
475#380C2318yes—
476#380C2314yes—
477#380C2312yes—
478#380C2314yes—
479#380C2314yes—
480#380C2312yes—
481#380C2312yes—
482#380C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
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⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520#376C2314yes—
521C2×#95C2312yes—
522C2×#95C2312yes—
523C2×#95C2314yes—
524C2×#95C2314yes—
525C2×#95C2314yes—
526C43C2314yes—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41—28no—
530C2×#41—28no—
531C2×#41—24no—
532C2×#41—24no—
533C2×#41—28no—
534C2×#41—24no—
535C2×#41#4118yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2412yes—
538C22×Q8C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2414yes—
542C22×D4C2411yescharacteristic
543C22×D4C2412yes—
544C22×D4C2412yes—
545C22×D4C2411yescharacteristic
546C22×D4C2414yes—
547C22×D4C2414yes—
548C22×D4C2412yes—
549C22×D4C2414yes—
550C22×D4C2418yes—
551C23×C4C2412yes—
552C23×C4C2414yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2411yescharacteristic
556C23×C4C2412yes—
557C23×C4C2414yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2418yes—
565C23×C4C2418yes—
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C4⋊Q8—28no—
569C4⋊Q8—24no—
570#127—28no—
571#127—24no—
572#126—88no—
573#124—28no—
574#124—28no—
575#124—28no—
576C22⋊Q8—28no—
577C22⋊Q8—28no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580#121—216no—
581#121—216no—
582#121—28no—
583#121—216no—
584#121—28no—
585#121—28no—
586#121—28no—
587#121—48no—
588#121—44no—
589#121—44no—
590#121—48no—
591#121—48no—
592#121—416no—
593#121—88no—
594#121—84no—
595C4×Q8—24no—
596C4×Q8—24no—
597C4×Q8—24no—
598C4×Q8—24no—
599C4×Q8—48no—
600C4×Q8—48no—
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—24no—
610C4×D4—24no—
611C4×D4—28no—
612C4×D4—28no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—48no—
617C4×D4—416no—
618C4×D4—416no—
619#117—24no—
620#117—24no—
621#117—28no—
622#117—28no—
623#117—28no—
624#117—44no—
625#117—44no—
626#117—48no—
627#117—48no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—28no—
631C2×C4⋊C4—48no—
632C2×C4⋊C4—44no—
633C2×C4⋊C4—42no—
634C2×C4⋊C4—42no—
635C2×C4⋊C4—48no—
636C2×C4⋊C4—48no—
637C2×C4⋊C4—82no—
638C2×C4⋊C4—84no—
639C2×C4⋊C4—84no—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C42—28no—
720C2×C42—28no—
721C2×C42—28no—
722C2×C42—44no—
723C2×C42#4118yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2418yes—
737C2×C42C2418yes—
738C2×C42C2414yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747#95C2412yes—
748#95C2418yes—
749#95C2418yes—
750#95C2412yes—
751#95C2414yes—
752#95C2414yes—
753#95C2412yes—
754#95C2412yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2418yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2418yes—
782#95C2414yes—
783#95C2418yes—
784#95C2418yes—
785C24C2512yes—
786C24C2514yes—
787C24C2512yes—
788C24C2511yescharacteristic
789#41—232no—
790#41—416no—
791#41—432no—
792C2×Q8—22no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—22no—
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8C2×#4114yes—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—24no—
807C2×D4—28no—
808C2×D4—24no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—22no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—24no—
821C2×D4—22no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—44no—
832C2×D4—48no—
833C2×D4—48no—
834C2×D4—48no—
835C2×D4C2×#4118yes—
836C2×D4C2×#4114yes—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—24no—
853C22×C4—28no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—41no—
861C22×C4—42no—
862C22×C4—41no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—44no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—44no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4C2×#4114yes—
883C22×C4C2×#4118yes—
884C22×C4C2×#4114yes—
885C22×C4C2×#4114yes—
886C22×C4C2×#4114yes—
887C22×C4H(5,𝔽2)14yes—
888C22×C4C2512yes—
889C22×C4C2512yes—
890C22×C4C2514yes—
891C22×C4C2512yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C22×C4C2514yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2514yes—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2512yes—
901C22×C4C2518yes—
902C22×C4C2514yes—
903C22×C4C2511yescharacteristic
904C22×C4C2511yescharacteristic
905C22×C4C2511yescharacteristic
906C22×C4C2512yes—
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—22no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—24no—
926C4⋊C4—28no—
927C4⋊C4—24no—
928C4⋊C4—28no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—28no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—24no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—44no—
941C4⋊C4—48no—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C4⋊C4—42no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—48no—
948C4⋊C4—48no—
949C4⋊C4—48no—
950C4⋊C4—42no—
951C4⋊C4—44no—
952C4⋊C4—48no—
953C4⋊C4—44no—
954C22⋊C4—24no—
955C22⋊C4—24no—
956C22⋊C4—28no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—24no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—28no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—48no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—48no—
984C22⋊C4—48no—
985C22⋊C4—44no—
986C22⋊C4—48no—
987C22⋊C4—48no—
988C22⋊C4—44no—
989C42—24no—
990C42—24no—
991C42—24no—
992C42—24no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—28no—
1000C42—28no—
1001C42—44no—
1002C42—44no—
1003C42—44no—
1004C42—44no—
1005C42—48no—
1006C42—48no—
1007C42—44no—
1008C42C2×#4114yes—
1009C42C2×#4114yes—
1010C42C2×#4114yes—
1011C42C2×#4114yes—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—22no—
1028C23—22no—
1029C23—24no—
1030C23—24no—
1031C23—22no—
1032C23—24no—
1033C23—22no—
1034C23—22no—
1035C23—24no—
1036C23C22×#4114yes—
1037C23C22×#4112yes—
1038C23C22×#4112yes—
1039C23C2×H(5,𝔽2)12yes—
1040C23C2611yescharacteristic
1041Q8—28no—
1042Q8—44no—
1043Q8—48no—
1044D4—216no—
1045D4—28no—
1046D4—48no—
1047D4—416no—
1048D4—44no—
1049D4—48no—
1050D4—48no—
1051D4—84no—
1052D4—88no—
1053D4—88no—
1054D4—88no—
1055D4—168no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—216no—
1065C2×C4—28no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—28no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—28no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—28no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—44no—
1112C2×C4—48no—
1113C2×C4—416no—
1114C2×C4—48no—
1115C2×C4—48no—
1116C2×C4—48no—
1117C2×C4—84no—
1118C2×C4—84no—
1119C2×C4—84no—
1120C2×C4—84no—
1121C2×C4—84no—
1122C2×C4—88no—
1123C2×C4—168no—
1124C2×C4—168no—
1125C2×C4#553116yes—
1126C2×C4C22×#4112yes—
1127C2×C4C22×#4112yes—
1128C2×C4C22×#4112yes—
1129C2×C4C22×#4114yes—
1130C2×C4C22×#4112yes—
1131C2×C4C22×#4112yes—
1132C2×C4C22×#4112yes—
1133C2×C4C22×#4112yes—
1134C2×C4C22×#4112yes—
1135C2×C4C2×H(5,𝔽2)12yes—
1136C2×C4C2×H(5,𝔽2)12yes—
1137C2×C4#58512yes—
1138C2×C4#58512yes—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—44no—
1154C22—44no—
1155C22—42no—
1156C22—42no—
1157C22—44no—
1158C22—42no—
1159C22—44no—
1160C22—44no—
1161C22—42no—
1162C22—42no—
1163C22—44no—
1164C22—42no—
1165C22—44no—
1166C22C2×#55314yes—
1167C22C23×#4111yescharacteristic
1168C22C23×#4111yescharacteristic
1169C22C22×H(5,𝔽2)11yescharacteristic
1170C22C2×#58511yescharacteristic
1171C22C2×#58511yescharacteristic
1172C22H(7,𝔽2)11yescharacteristic
1173C222−1+611yescharacteristic
1174C4—22no—
1175C4—22no—
1176C4—22no—
1177C4—24no—
1178C4—42no—
1179C4—44no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—44no—
1188C4—44no—
1189C4—42no—
1190C4—44no—
1191C4—48no—
1192C4—44no—
1193C4C2×#55314yes—
1194C4C2×#55314yes—
1195C4#351214yes—
1196C2—24no—
1197C2—44no—
1198C2—82no—
1199C2—84no—
1200C2C22×#55311yescharacteristic
1201C2C2×#351211yescharacteristic
1202C2#6285611yescharacteristic
1203C2#6293111yescharacteristic
1204C2#6296111yescharacteristic
1205C2#6299411yescharacteristic
1206C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59677C2semidirect
2. #59308C2semidirect
3. #59303C2semidirect
4. #59302C2semidirect
5. #59257C2semidirect
6. #59212C2semidirect
7. #45160C2semidirect
8. #45158C2semidirect
9. #43580C2semidirect
10. #39285C2semidirect
11. #39284C2semidirect
12. #39149C2semidirect
13. #39148C2semidirect
14. #36460C2semidirect
15. #36449C2semidirect
16. #35618C2semidirect
17. #35564C2semidirect
18. #35273C2semidirect
19. #35267C2semidirect
20. C2×#2571C2semidirect
21. #34937C2semidirect
22. #34208C2semidirect
23. #34206C2semidirect
24. #34183C2semidirect
25. #34121C2semidirect
26. C4×#537C2semidirect

Maximal subgroups

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

subgroupindex
#596772
#593082
#593032
#593022
#592572
#592122
#451602
#451582
#435802
#392852
#392842
#391492
#391482
#364602
#364492
#356182
#355642
#352732
#352672
C2×#25712
#349372
#342082
#342062
#341832
#341212
C4×#5372