Finite Group Databasebeta

← #7739372

Subgroups — #7739372

Order 512.

4910 conjugacy classes of subgroups.

The subgroup lattice has 1187 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59257C212yesmaximal, complemented
2#59227C212yesmaximal, complemented
3#59213C212yesmaximal, complemented
4#59212C212yesmaximal, complemented
5#51766C218yesmaximal, complemented
6#45160C214yesmaximal, complemented
7#45125C214yesmaximal, complemented
8#45092C214yesmaximal, complemented
9#45024C214yesmaximal, complemented
10#39763C212yesmaximal, complemented
11#39157C212yesmaximal, complemented
12#38977C212yesmaximal, complemented
13#38942C212yesmaximal, complemented
14#37361C214yesmaximal, complemented
15#36587C212yesmaximal, complemented
16#36468C212yesmaximal, complemented
17#36176C212yesmaximal, complemented
18#36174C212yesmaximal, complemented
19#35588C214yesmaximal, complemented
20#35286C211yesmaximal, characteristic, complemented
21#35273C211yesmaximal, characteristic, complemented
22#34977C211yesmaximal, characteristic, complemented
23#34976C211yesmaximal, characteristic, complemented
24#34368C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27C2×#553C2214yes—
28C2×#537C2212yes—
29C2×#532C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2859C2212yes—
33#2859C2212yes—
34#2857C2212yes—
35#2856C2212yes—
36#2854C2214yes—
37#2850C2214yes—
38#2800C2218yes—
39#2800C2218yes—
40#2781C2218yes—
41#2778C2218yes—
42#2778C2218yes—
43#2765C2218yes—
44#2762C2218yes—
45#2756C2218yes—
46#2753C2218yes—
47#2750C2218yes—
48#2739C2218yes—
49#2708C2218yes—
50#2703C2218yes—
51#2699C2218yes—
52#2689C2218yes—
53#2688C2218yes—
54#2647C2214yes—
55#2645C2214yes—
56#2641C2214yes—
57#2620C2214yes—
58#2610C2214yes—
59#2609C2214yes—
60#2602C2218yes—
61#2597C2218yes—
62#2595C2218yes—
63#2582C2211yescharacteristic
64#2578C2218yes—
65#2573C2218yes—
66#2571C2212yes—
67#2571C2212yes—
68#2571C2214yes—
69#2567C2211yescharacteristic
70#2563C2211yescharacteristic
71#2562C2214yes—
72#2559C2218yes—
73#2559C2218yes—
74#2552C2212yes—
75#2552C2212yes—
76#2548C2211yescharacteristic
77#2541C2211yescharacteristic
78#2538C2212yes—
79#2538C2211yescharacteristic
80#2538C2211yescharacteristic
81#2538C2212yes—
82#2537C2214yes—
83#2537C2212yes—
84#2537C2212yes—
85#2537C2211yescharacteristic
86#2535C2214yes—
87#2532C2218yes—
88#2531C2218yes—
89#2529C2218yes—
90#2526C2218yes—
91#2518C2218yes—
92#2513C2214yes—
93#2513C2214yes—
94#2513C2214yes—
95#2509C2214yes—
96#2508C2214yes—
97#2504C2214yes—
98#2503C2214yes—
99#2500C2212yes—
100#2500C2214yes—
101#2496C2214yes—
102#2496C2214yes—
103#2495C2214yes—
104#2495C2214yes—
105#2494C2214yes—
106#2494C2214yes—
107#2490C2214yes—
108#2489C2214yes—
109#2489C2214yes—
110#2488C2218yes—
111#2486C2214yes—
112#2485C2212yes—
113#2485C2212yes—
114#2485C2214yes—
115#2485C2214yes—
116#2468C2218yes—
117#2447C2214yes—
118#2444C2218yes—
119#2442C2214yes—
120#2442C2214yes—
121#2442C2214yes—
122#2431C2212yes—
123#2428C2214yes—
124#2420C2218yes—
125#2420C2214yes—
126#2420C2214yes—
127#2416C2214yes—
128#2416C2214yes—
129#2415C2214yes—
130#2415C2214yes—
131#2414C2214yes—
132#2414C2212yes—
133#2414C2212yes—
134#2407C2212yes—
135#2407C2212yes—
136#2392C2214yes—
137#2388C2214yes—
138#2379C2214yes—
139#2369C2212yes—
140#2366C2212yes—
141#2363C2214yes—
142#2361C2214yes—
143#2357C2214yes—
144#2355C2212yes—
145#2355C2211yescharacteristic
146#2355C2211yescharacteristic
147#2355C2212yes—
148#2354C2212yes—
149#2354C2212yes—
150#2354C2212yes—
151#2354C2212yes—
152#2352C2214yes—
153#2352C2214yes—
154#2352C2214yes—
155#2352C2212yes—
156#2352C2212yes—
157#2352C2214yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2211yescharacteristic
162#2347C2212yes—
163#2346C2214yes—
164#2346C2214yes—
165#2343C2214yes—
166#2339C2212yes—
167#2330C2214yes—
168#2324C2214yes—
169#2324C2214yes—
170#2319C2214yes—
171#2317C2212yes—
172#2316C2212yes—
173#2314C2214yes—
174#2311C2214yes—
175#2311C2212yes—
176#2311C2212yes—
177C4×#127C2212yes—
178C4×#124C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×#121C2214yes—
182C4×#121C2212yes—
183C4×#121C2212yes—
184C4×#121C2212yes—
185C4×#121C2212yes—
186#2295C2212yes—
187#2290C2214yes—
188#2285C2211yescharacteristic
189#2285C2211yescharacteristic
190#2285C2212yes—
191#2285C2212yes—
192C2×#384C2211yescharacteristic
193#2283C2214yes—
194#2283C2212yes—
195#2274C2212yes—
196C42×D4C2212yes—
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201C22×#41C2311yescharacteristic
202#553—416no—
203#537—48no—
204#532—28no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×#127C2311yescharacteristic
207C2×#127C2312yes—
208C2×#126C2318yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#123C2318yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×#121C2312yes—
219C2×#121C2312yes—
220C2×#121C2314yes—
221C2×#121C2312yes—
222C2×#121C2314yes—
223C2×#121C2312yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×#121C2318yes—
229C2×#121C2318yes—
230C4×#41—28no—
231C4×#41—28no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2318yes—
253C2×C4×D4C2314yes—
254C2×#117C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2311yescharacteristic
258C2×#117C2312yes—
259C2×#117C2314yes—
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2311yescharacteristic
263C2×#117C2314yes—
264C2×#117C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2314yes—
274C22×C42C2311yescharacteristic
275#401C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#397C2318yes—
289#397C2314yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#396C2318yes—
299#396C2314yes—
300#396C2314yes—
301#396C2318yes—
302#395C2314yes—
303#394C2318yes—
304#394C2314yes—
305#394C2318yes—
306#394C2314yes—
307#394C2314yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2314yes—
315#394C2314yes—
316#394C2318yes—
317#393C2314yes—
318#392C2318yes—
319#392C2314yes—
320#392C2314yes—
321#392C2314yes—
322#392C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2318yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#390C2312yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2318yes—
336#390C2314yes—
337#390C2314yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2318yes—
343#390C2314yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2312yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2314yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2314yes—
416#386C2314yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2314yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2314yes—
428#385C2318yes—
429#385C2314yes—
430#385C2314yes—
431#385C2314yes—
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2312yes—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#383C2318yes—
443#383C2314yes—
444#382C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2312yes—
448#382C2314yes—
449#382C2318yes—
450#382C2314yes—
451#382C2314yes—
452#382C2318yes—
453#382C2312yes—
454#382C2314yes—
455#382C2312yes—
456#381C2318yes—
457#381C2314yes—
458#381C2318yes—
459#381C2318yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2318yes—
473#380C2318yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480#380C2314yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2312yes—
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⋊C4C2312yes—
519#376C2314yes—
520#376C2312yes—
521#376C2318yes—
522C2×#95C2314yes—
523C43C2312yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—28no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—42no—
531C2×#41—42no—
532C2×#41—42no—
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2412yes—
542C22×D4C2418yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2412yes—
546C22×D4C2414yes—
547C22×D4C2414yes—
548C23×C4C2412yes—
549C23×C4C2414yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2414yes—
558C23×C4C2412yes—
559C23×C4C2414yes—
560C23×C4C2418yes—
561C23×C4C2414yes—
562C4⋊Q8—24no—
563#127—24no—
564#127—44no—
565#126—416no—
566#125—48no—
567#125—48no—
568#124—28no—
569#124—44no—
570#123—416no—
571C22⋊Q8—48no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—48no—
575#121—216no—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—416no—
580#121—416no—
581#121—48no—
582#121—48no—
583#121—44no—
584#121—44no—
585#121—44no—
586#121—48no—
587C4×Q8—24no—
588C4×Q8—24no—
589C4×Q8—24no—
590C4×Q8—24no—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—48no—
603C4×D4—48no—
604C4×D4—44no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—416no—
609#117—24no—
610#117—24no—
611#117—28no—
612#117—28no—
613#117—44no—
614#117—44no—
615#117—42no—
616#117—42no—
617#117—48no—
618#117—48no—
619#117—48no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—44no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4—48no—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C42—28no—
709C2×C42—28no—
710C2×C42—48no—
711C2×C42#4118yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2418yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2418yes—
728C2×C42C2418yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735#95C2412yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773C24C2512yes—
774C24C2514yes—
775C24C2511yescharacteristic
776C24C2512yes—
777#41—416no—
778#41—416no—
779#41—816no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—28no—
793C2×D4—216no—
794C2×D4—28no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—22no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—42no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—48no—
818C2×D4—44no—
819C2×D4—48no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4H(5,𝔽2)14yes—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—24no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—28no—
840C22×C4—28no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—28no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—48no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4C2×#4114yes—
865C22×C4C2×#4114yes—
866C22×C4C2×#4114yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2514yes—
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2514yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2514yes—
880C22×C4C2512yes—
881C22×C4C2518yes—
882C22×C4C2512yes—
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—48no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—44no—
928C4⋊C4—48no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—216no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—28no—
980C42—28no—
981C42—24no—
982C42—24no—
983C42—44no—
984C42—44no—
985C42—42no—
986C42—42no—
987C42—48no—
988C42—48no—
989C42—48no—
990C42C2×#4114yes—
991C42C2×#4114yes—
992C42C2×#4114yes—
993C42C2×#4114yes—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—21no—
1006C23—22no—
1007C23—24no—
1008C23—22no—
1009C23—24no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—22no—
1017C23—22no—
1018C23—24no—
1019C23—22no—
1020C23C22×#4112yes—
1021C23C2×H(5,𝔽2)14yes—
1022C23C2611yescharacteristic
1023Q8—44no—
1024Q8—44no—
1025Q8—84no—
1026D4—28no—
1027D4—48no—
1028D4—48no—
1029D4—48no—
1030D4—44no—
1031D4—48no—
1032D4—84no—
1033D4—816no—
1034D4—88no—
1035D4—88no—
1036D4—88no—
1037D4—88no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—28no—
1045C2×C4—28no—
1046C2×C4—28no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—28no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—28no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—28no—
1095C2×C4—48no—
1096C2×C4—48no—
1097C2×C4—48no—
1098C2×C4—48no—
1099C2×C4—416no—
1100C2×C4—48no—
1101C2×C4—48no—
1102C2×C4—88no—
1103C2×C4—88no—
1104C2×C4—164no—
1105C2×C4—168no—
1106C2×C4C22×#4112yes—
1107C2×C4C22×#4112yes—
1108C2×C4C22×#4112yes—
1109C2×C4C22×#4112yes—
1110C2×C4C22×#4112yes—
1111C2×C4C22×#4112yes—
1112C2×C4C2×H(5,𝔽2)12yes—
1113C2×C4#58512yes—
1114C2×C4#58512yes—
1115C2×C4#58512yes—
1116C2×C4#58512yes—
1117C2×C4#58512yes—
1118C22—24no—
1119C22—24no—
1120C22—22no—
1121C22—22no—
1122C22—24no—
1123C22—22no—
1124C22—41no—
1125C22—41no—
1126C22—42no—
1127C22—41no—
1128C22—41no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22—44no—
1135C22—42no—
1136C22—42no—
1137C22—44no—
1138C22—42no—
1139C22—44no—
1140C22—42no—
1141C22—44no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—44no—
1146C22C23×#4111yescharacteristic
1147C22C22×H(5,𝔽2)11yescharacteristic
1148C22C2×#58511yescharacteristic
1149C22C2×#58511yescharacteristic
1150C22C2×#58511yescharacteristic
1151C22C2×#58511yescharacteristic
1152C22C2×#58511yescharacteristic
1153C4—22no—
1154C4—22no—
1155C4—22no—
1156C4—48no—
1157C4—42no—
1158C4—42no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—44no—
1170C4—42no—
1171C4—42no—
1172C4#349314yes—
1173C4#349414yes—
1174C4#351214yes—
1175C2—44no—
1176C2—42no—
1177C2—84no—
1178C2—82no—
1179C2C2×#349311yescharacteristic
1180C2C2×#349411yescharacteristic
1181C2C2×#351211yescharacteristic
1182C2#6302111yescharacteristic
1183C2#6302411yescharacteristic
1184C2#6303111yescharacteristic
1185C2#6303111yescharacteristic
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. #59257C2semidirect
2. #59227C2semidirect
3. #59213C2semidirect
4. #59212C2semidirect
5. #51766C2semidirect
6. #45160C2semidirect
7. #45125C2semidirect
8. #45092C2semidirect
9. #45024C2semidirect
10. #39763C2semidirect
11. #39157C2semidirect
12. #38977C2semidirect
13. #38942C2semidirect
14. #37361C2semidirect
15. #36587C2semidirect
16. #36468C2semidirect
17. #36176C2semidirect
18. #36174C2semidirect
19. #35588C2semidirect
20. #35286C2semidirect
21. #35273C2semidirect
22. #34977C2semidirect
23. #34976C2semidirect
24. #34368C2semidirect
25. #34188C2semidirect
26. #34127C2semidirect

Maximal subgroups

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

subgroupindex
#592572
#592272
#592132
#592122
#517662
#451602
#451252
#450922
#450242
#397632
#391572
#389772
#389422
#373612
#365872
#364682
#361762
#361742
#355882
#352862
#352732
#349772
#349762
#343682
#341882
#341272