Finite Group Databasebeta

← #8196954

Subgroups — #8196954

Order 512.

5294 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59952C212yesmaximal, complemented
2#59935C212yesmaximal, complemented
3#59217C212yesmaximal, complemented
4#59125C212yesmaximal, complemented
5#58965C214yesmaximal, complemented
6#58799C214yesmaximal, complemented
7#53005C212yesmaximal, complemented
8#52957C212yesmaximal, complemented
9#51930C214yesmaximal, complemented
10#47568C214yesmaximal, complemented
11#46152C212yesmaximal, complemented
12#46084C212yesmaximal, complemented
13#45244C212yesmaximal, complemented
14#44914C212yesmaximal, complemented
15#42923C214yesmaximal, complemented
16#42643C214yesmaximal, complemented
17#39950C214yesmaximal, complemented
18#39471C212yesmaximal, complemented
19#39340C212yesmaximal, complemented
20#39191C214yesmaximal, complemented
21#36315C212yesmaximal, complemented
22#36272C212yesmaximal, complemented
23#35279C211yesmaximal, characteristic, complemented
24#34977C211yesmaximal, characteristic, complemented
25#34977C211yesmaximal, characteristic, complemented
26C2×#552C2214yes—
27C2×#548C2214yes—
28C2×#547C2212yes—
29C2×#537C2214yes—
30C2×#532C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34#2861C2214yes—
35#2859C2214yes—
36#2857C2212yes—
37#2857C2212yes—
38#2844C2214yes—
39#2832C2218yes—
40#2828C2214yes—
41#2824C2214yes—
42#2813C2218yes—
43#2809C2214yes—
44#2785C2214yes—
45#2784C2214yes—
46#2782C2214yes—
47#2781C2218yes—
48#2763C2214yes—
49#2753C2218yes—
50#2753C2218yes—
51#2753C2218yes—
52#2733C2214yes—
53#2723C2218yes—
54#2720C2218yes—
55#2720C2218yes—
56#2714C2218yes—
57#2711C2218yes—
58#2711C2218yes—
59#2710C2218yes—
60#2703C2218yes—
61#2696C2218yes—
62#2683C2214yes—
63#2676C2218yes—
64#2675C2214yes—
65#2674C2218yes—
66#2673C2218yes—
67#2672C2218yes—
68#2671C2218yes—
69#2662C2218yes—
70#2661C2218yes—
71#2628C2212yes—
72#2628C2212yes—
73#2624C2218yes—
74#2616C2214yes—
75#2615C2214yes—
76#2612C2214yes—
77#2611C2218yes—
78#2610C2218yes—
79#2610C2212yes—
80#2610C2212yes—
81#2610C2212yes—
82#2610C2212yes—
83#2603C2218yes—
84#2574C2218yes—
85#2568C2212yes—
86#2567C2211yescharacteristic
87#2567C2212yes—
88#2567C2211yescharacteristic
89#2563C2211yescharacteristic
90#2563C2211yescharacteristic
91#2563C2212yes—
92#2562C2214yes—
93#2555C2214yes—
94#2553C2218yes—
95#2552C2212yes—
96#2548C2211yescharacteristic
97#2548C2211yescharacteristic
98#2547C2212yes—
99#2542C2212yes—
100#2542C2212yes—
101#2541C2211yescharacteristic
102#2541C2211yescharacteristic
103#2540C2214yes—
104#2537C2214yes—
105#2537C2214yes—
106#2537C2212yes—
107#2531C2218yes—
108#2529C2218yes—
109#2500C2218yes—
110#2500C2212yes—
111#2500C2212yes—
112#2497C2218yes—
113#2497C2214yes—
114#2497C2214yes—
115#2496C2214yes—
116#2492C2214yes—
117#2491C2214yes—
118#2490C2214yes—
119#2489C2214yes—
120#2489C2214yes—
121#2487C2212yes—
122#2487C2214yes—
123#2487C2212yes—
124#2485C2214yes—
125#2485C2214yes—
126#2476C2218yes—
127#2463C2214yes—
128#2443C2218yes—
129#2440C2214yes—
130#2440C2214yes—
131#2432C2214yes—
132#2431C2214yes—
133#2431C2212yes—
134#2431C2212yes—
135#2429C2214yes—
136#2428C2218yes—
137#2428C2214yes—
138#2426C2214yes—
139#2422C2214yes—
140#2417C2214yes—
141#2416C2214yes—
142#2416C2214yes—
143#2416C2214yes—
144#2415C2214yes—
145#2414C2212yes—
146#2414C2212yes—
147#2414C2214yes—
148#2414C2212yes—
149#2414C2212yes—
150#2409C2214yes—
151#2409C2212yes—
152#2409C2212yes—
153#2407C2214yes—
154#2407C2214yes—
155#2388C2212yes—
156#2388C2212yes—
157#2388C2212yes—
158#2388C2212yes—
159#2379C2214yes—
160#2372C2214yes—
161#2365C2212yes—
162#2363C2214yes—
163#2360C2214yes—
164#2354C2214yes—
165#2354C2212yes—
166D4×C4⋊C4C2214yes—
167D4×C4⋊C4C2212yes—
168#2346C2214yes—
169#2345C2214yes—
170#2324C2218yes—
171#2317C2212yes—
172#2311C2214yes—
173#2311C2212yes—
174C4×#127C2212yes—
175C4×#127C2212yes—
176C4×#124C2212yes—
177C4×#124C2212yes—
178C4×#121C2212yes—
179C4×#121C2212yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182#2295C2214yes—
183#2293C2214yes—
184#2285C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2312yes—
189C22×#41C2312yes—
190C22×#41C2314yes—
191C23×Q8C2312yes—
192#552—416no—
193#548—416no—
194#547—48no—
195#537—416no—
196#532—44no—
197#532—44no—
198C2×C4⋊Q8—44no—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×#127C2312yes—
206C2×#127C2312yes—
207C2×#127C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#126C2318yes—
210C2×#125C2314yes—
211C2×#125C2318yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2314yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#124C2318yes—
218C2×#123C2318yes—
219C2×#123C2318yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2318yes—
230C2×#121C2312yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2318yes—
234C2×#121C2312yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2318yes—
240C2×#121C2318yes—
241C2×#121C2318yes—
242C2×#121C2312yes—
243C4×#41—44no—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2318yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C2×#117C2311yescharacteristic
267C2×#117C2318yes—
268C2×#117C2312yes—
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278#400C2318yes—
279#400C2314yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#399C2318yes—
285#399C2314yes—
286#399C2318yes—
287#399C2314yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#395C2312yes—
301#395C2312yes—
302#395C2314yes—
303#395C2314yes—
304#395C2312yes—
305#395C2312yes—
306#395C2318yes—
307#395C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2312yes—
311#394C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2312yes—
319#394C2312yes—
320#394C2312yes—
321#394C2314yes—
322#394C2314yes—
323#394C2314yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#393C2312yes—
330#393C2312yes—
331#393C2314yes—
332#393C2312yes—
333#393C2312yes—
334#393C2314yes—
335#393C2318yes—
336#393C2318yes—
337#392C2312yes—
338#392C2318yes—
339#392C2318yes—
340#392C2314yes—
341#392C2312yes—
342#392C2312yes—
343#392C2312yes—
344#392C2318yes—
345#392C2318yes—
346#392C2314yes—
347#392C2314yes—
348#392C2314yes—
349#392C2318yes—
350#391C2314yes—
351#391C2318yes—
352#391C2312yes—
353#391C2312yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#390C2312yes—
359#390C2312yes—
360#390C2314yes—
361#390C2314yes—
362#390C2312yes—
363#390C2314yes—
364#390C2314yes—
365#390C2312yes—
366#390C2314yes—
367#390C2318yes—
368#390C2312yes—
369#390C2318yes—
370#390C2312yes—
371#390C2314yes—
372#390C2318yes—
373#390C2312yes—
374#390C2318yes—
375#390C2312yes—
376#390C2312yes—
377#390C2314yes—
378#390C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2318yes—
392#389C2314yes—
393#389C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2314yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#388C2314yes—
407#388C2318yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#386C2314yes—
423#386C2318yes—
424#386C2314yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2314yes—
431#386C2314yes—
432#386C2314yes—
433#386C2314yes—
434#386C2318yes—
435#385C2314yes—
436#385C2314yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#384C2312yes—
445#384C2312yes—
446#384C2314yes—
447#384C2312yes—
448#384C2314yes—
449#384C2314yes—
450#382C2314yes—
451#382C2312yes—
452#382C2312yes—
453#382C2318yes—
454#382C2318yes—
455#382C2312yes—
456#380C2312yes—
457#380C2312yes—
458#380C2314yes—
459#380C2314yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2318yes—
470#380C2318yes—
471#380C2314yes—
472#380C2314yes—
473#380C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495#376C2318yes—
496#376C2312yes—
497#376C2312yes—
498C43C2312yes—
499C43C2312yes—
500C2×#41—24no—
501C2×#41—42no—
502C2×#41—44no—
503C2×#41—44no—
504C2×#41—48no—
505C2×#41—48no—
506C2×#41—42no—
507C2×#41—48no—
508C2×#41—48no—
509C2×#41—48no—
510C22×Q8—44no—
511C22×Q8—48no—
512C22×Q8C2414yes—
513C22×Q8C2412yes—
514C22×Q8C2414yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×D4C2412yes—
518C22×D4C2412yes—
519C22×D4C2414yes—
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2414yes—
524C22×D4C2414yes—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2414yes—
528C22×D4C2414yes—
529C22×D4C2418yes—
530C22×D4C2418yes—
531C22×D4C2412yes—
532C22×D4C2414yes—
533C22×D4C2412yes—
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2414yes—
537C23×C4C2414yes—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2418yes—
546C23×C4C2414yes—
547C23×C4C2418yes—
548C4⋊Q8—28no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—42no—
552C4⋊Q8—42no—
553C4⋊Q8—44no—
554#127—42no—
555#127—42no—
556#127—44no—
557#127—44no—
558#126—416no—
559#125—416no—
560#125—48no—
561#124—28no—
562#124—28no—
563#124—44no—
564#124—44no—
565#124—416no—
566#124—48no—
567#123—416no—
568#123—416no—
569C22⋊Q8—216no—
570C22⋊Q8—416no—
571C22⋊Q8—416no—
572C22⋊Q8—48no—
573C22⋊Q8—48no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576#121—28no—
577#121—28no—
578#121—44no—
579#121—44no—
580#121—416no—
581#121—416no—
582#121—416no—
583#121—416no—
584#121—48no—
585#121—44no—
586#121—44no—
587#121—44no—
588#121—44no—
589#121—48no—
590#121—416no—
591#121—48no—
592C4×Q8—216no—
593C4×Q8—42no—
594C4×Q8—42no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—48no—
598C4×D4—416no—
599C4×D4—48no—
600C4×D4—48no—
601C4×D4—42no—
602C4×D4—42no—
603C4×D4—42no—
604C4×D4—42no—
605C4×D4—42no—
606C4×D4—42no—
607C4×D4—44no—
608C4×D4—44no—
609C4×D4—48no—
610C4×D4—48no—
611#117—28no—
612#117—42no—
613#117—42no—
614#117—42no—
615#117—416no—
616#117—44no—
617#117—48no—
618#117—44no—
619C2×C4⋊C4—216no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—48no—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2412yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2411yescharacteristic
671C2×C22⋊C4C2411yescharacteristic
672C2×C22⋊C4C2411yescharacteristic
673C2×C22⋊C4C2411yescharacteristic
674C2×C22⋊C4C2411yescharacteristic
675C2×C22⋊C4C2411yescharacteristic
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C42—24no—
700C2×C42—24no—
701C2×C42—24no—
702C2×C42C2414yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2418yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2418yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723#95C2414yes—
724#95C2418yes—
725#95C2412yes—
726#95C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2412yes—
730#95C2412yes—
731#95C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751C24C2511yescharacteristic
752C24C2514yes—
753C24C2514yes—
754C24C2511yescharacteristic
755C24C2511yescharacteristic
756#41—416no—
757#41—816no—
758#41—816no—
759#41—832no—
760C2×Q8—28no—
761C2×Q8—28no—
762C2×Q8—28no—
763C2×Q8—41no—
764C2×Q8—41no—
765C2×Q8—44no—
766C2×Q8—48no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—816no—
772C2×Q82−1+414yes—
773C2×D4—28no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—28no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—28no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—41no—
791C2×D4—41no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—41no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—48no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—48no—
807C2×D4—48no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—48no—
820C2×D4—48no—
821C2×D4—48no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—24no—
836C22×C4—28no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—24no—
843C22×C4—28no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—24no—
847C22×C4—216no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—44no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4C2511yescharacteristic
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2518yes—
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C22×C4C2518yes—
868C22×C4C2514yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2514yes—
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C4⋊C4—28no—
878C4⋊C4—216no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—216no—
885C4⋊C4—216no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4H(5,𝔽2)18yes—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—216no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—41no—
927C22⋊C4—41no—
928C22⋊C4—41no—
929C22⋊C4—41no—
930C22⋊C4—41no—
931C22⋊C4—41no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—22no—
962C42—28no—
963C42—216no—
964C42—28no—
965C42—24no—
966C42—24no—
967C42—28no—
968C42—44no—
969C42—44no—
970C42—48no—
971C42—42no—
972C42—42no—
973C42H(5,𝔽2)14yes—
974C23—21no—
975C23—22no—
976C23—21no—
977C23—22no—
978C23—22no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—22no—
985C23—24no—
986C23—21no—
987C23—21no—
988C23—24no—
989C23—24no—
990C23—21no—
991C23—21no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—22no—
999C23—24no—
1000C23—21no—
1001C23—21no—
1002C23#58512yes—
1003C23C2611yescharacteristic
1004Q8—44no—
1005Q8—416no—
1006Q8—88no—
1007Q8—84no—
1008Q8—84no—
1009D4—416no—
1010D4—44no—
1011D4—44no—
1012D4—44no—
1013D4—48no—
1014D4—48no—
1015D4—88no—
1016D4—84no—
1017D4—84no—
1018D4—88no—
1019D4—88no—
1020D4—84no—
1021D4—88no—
1022D4—88no—
1023D4—84no—
1024D4—816no—
1025D4—168no—
1026C2×C4—28no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—24no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—24no—
1036C2×C4—21no—
1037C2×C4—24no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—28no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—28no—
1052C2×C4—24no—
1053C2×C4—28no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—28no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—28no—
1064C2×C4—28no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—416no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—416no—
1079C2×C4—44no—
1080C2×C4—816no—
1081C2×C4—88no—
1082C2×C4—816no—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×H(5,𝔽2)18yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×H(5,𝔽2)14yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4C2×2−1+412yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4#58514yes—
1092C22—24no—
1093C22—22no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—44no—
1099C22—41no—
1100C22—44no—
1101C22—44no—
1102C22—41no—
1103C22—41no—
1104C22—44no—
1105C22—44no—
1106C22—44no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—42no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—42no—
1116C22—44no—
1117C22—41no—
1118C22—41no—
1119C22—44no—
1120C22—44no—
1121C22C22×H(5,𝔽2)11yescharacteristic
1122C22C22×H(5,𝔽2)12yes—
1123C22C22×2−1+411yescharacteristic
1124C22C2×#58512yes—
1125C22C2×#58511yescharacteristic
1126C4—28no—
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—22no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—44no—
1135C4—41no—
1136C4—44no—
1137C4—41no—
1138C4—41no—
1139C4—48no—
1140C4—48no—
1141C4—44no—
1142C4—44no—
1143C4—44no—
1144C4#354914yes—
1145C4#355114yes—
1146C2—42no—
1147C2—81no—
1148C2—84no—
1149C2—81no—
1150C2—84no—
1151C2C2×#355111yescharacteristic
1152C2C2×#354911yescharacteristic
1153C2#6281911yescharacteristic
1154C2#6301812yes—
1155C2#6303912yes—
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. #59952C2semidirect
2. #59935C2semidirect
3. #59217C2semidirect
4. #59125C2semidirect
5. #58965C2semidirect
6. #58799C2semidirect
7. #53005C2semidirect
8. #52957C2semidirect
9. #51930C2semidirect
10. #47568C2semidirect
11. #46152C2semidirect
12. #46084C2semidirect
13. #45244C2semidirect
14. #44914C2semidirect
15. #42923C2semidirect
16. #42643C2semidirect
17. #39950C2semidirect
18. #39471C2semidirect
19. #39340C2semidirect
20. #39191C2semidirect
21. #36315C2semidirect
22. #36272C2semidirect
23. #35279C2semidirect
24. #34977C2semidirect
25. #34977C2semidirect

Maximal subgroups

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

subgroupindex
#599522
#599352
#592172
#591252
#589652
#587992
#530052
#529572
#519302
#475682
#461522
#460842
#452442
#449142
#429232
#426432
#399502
#394712
#393402
#391912
#363152
#362722
#352792
#349772