Finite Group Databasebeta

← #7683856

Subgroups — #7683856

Order 512.

6124 conjugacy classes of subgroups.

The subgroup lattice has 1434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60047C212yesmaximal, complemented
2#59991C214yesmaximal, complemented
3#59948C212yesmaximal, complemented
4#59819C212yesmaximal, complemented
5#59798C212yesmaximal, complemented
6#59182C212yesmaximal, complemented
7#59160C212yesmaximal, complemented
8#59151C211yesmaximal, characteristic, complemented
9#59135C211yesmaximal, characteristic, complemented
10#59115C214yesmaximal, complemented
11#59084C212yesmaximal, complemented
12#44377C214yesmaximal, complemented
13#44265C214yesmaximal, complemented
14#44223C214yesmaximal, complemented
15#44181C214yesmaximal, complemented
16#43938C214yesmaximal, complemented
17#43913C214yesmaximal, complemented
18#35397C212yesmaximal, complemented
19#35393C214yesmaximal, complemented
20#34738C212yesmaximal, complemented
21C2×#2432C211yesmaximal, characteristic, complemented
22#34296C214yesmaximal, complemented
23#34277C212yesmaximal, complemented
24C23×#41C2211yescharacteristic
25C2×Q82C2211yescharacteristic, complemented
26C2×#555C2212yescomplemented
27C2×#555C2211yescharacteristic, complemented
28C2×#551C2214yes—
29C2×#539C2212yes—
30C2×#538C2212yes—
31C2×#532C2212yes—
32C2×#532C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C2×#525C2212yes—
36C22×C22⋊Q8C2211yescharacteristic
37#2809C2212yescomplemented
38#2803C2214yescomplemented
39#2803C2214yescomplemented
40#2795C2214yescomplemented
41#2785C2214yescomplemented
42#2781C2214yescomplemented
43#2775C2214yescomplemented
44#2756C2214yescomplemented
45#2734C2212yescomplemented
46#2734C2212yescomplemented
47#2733C2212yescomplemented
48#2733C2214yescomplemented
49#2733C2212yescomplemented
50#2732C2212yescomplemented
51#2731C2212yescomplemented
52#2731C2212yescomplemented
53#2731C2214yescomplemented
54#2731C2212yescomplemented
55#2731C2212yescomplemented
56#2730C2214yescomplemented
57#2727C2212yescomplemented
58#2727C2214yescomplemented
59#2714C2214yescomplemented
60#2705C2214yescomplemented
61#2705C2214yescomplemented
62#2686C2214yescomplemented
63#2686C2214yescomplemented
64#2682C2214yescomplemented
65#2682C2212yescomplemented
66#2673C2214yescomplemented
67#2612C2214yescomplemented
68#2611C2214yescomplemented
69#2610C2214yescomplemented
70#2610C2214yescomplemented
71#2603C2214yescomplemented
72#2602C2214yescomplemented
73#2601C2214yescomplemented
74#2593C2214yescomplemented
75#2574C2214yescomplemented
76#2567C2212yescomplemented
77#2566C2214yescomplemented
78#2564C2214yescomplemented
79#2563C2212yescomplemented
80#2561C2212yes—
81#2560C2214yescomplemented
82#2560C2214yescomplemented
83#2559C2214yescomplemented
84#2558C2214yescomplemented
85#2556C2214yescomplemented
86#2556C2214yescomplemented
87#2556C2214yescomplemented
88#2555C2214yescomplemented
89#2554C2214yescomplemented
90#2554C2214yescomplemented
91#2554C2214yescomplemented
92#2553C2214yescomplemented
93#2551C2214yescomplemented
94#2548C2214yescomplemented
95#2539C2214yes—
96#2539C2212yes—
97#2534C2214yes—
98#2532C2214yescomplemented
99#2526C2214yescomplemented
100#2518C2214yescomplemented
101#2500C2214yescomplemented
102#2491C2214yescomplemented
103#2491C2214yescomplemented
104#2491C2214yescomplemented
105#2488C2214yes—
106#2479C2214yescomplemented
107#2479C2214yescomplemented
108#2476C2214yescomplemented
109#2474C2214yescomplemented
110#2474C2214yescomplemented
111#2474C2214yescomplemented
112#2472C2214yes—
113#2467C2214yescomplemented
114#2464C2214yescomplemented
115#2461C2214yescomplemented
116#2461C2214yescomplemented
117#2461C2214yescomplemented
118#2459C2214yescomplemented
119#2456C2214yescomplemented
120#2452C2214yescomplemented
121#2452C2214yescomplemented
122#2452C2214yescomplemented
123#2451C2214yescomplemented
124#2445C2214yescomplemented
125#2440C2214yes—
126#2439C2214yescomplemented
127#2439C2214yescomplemented
128#2436C2212yes—
129#2436C2212yes—
130#2435C2212yes—
131#2434C2212yes—
132#2434C2212yes—
133#2433C2212yes—
134#2432C2212yes—
135#2432C2214yes—
136#2432C2212yes—
137#2432C2214yes—
138#2432C2212yes—
139#2432C2212yes—
140#2432C2212yes—
141#2432C2212yes—
142#2432C2214yescomplemented
143#2431C2212yes—
144#2431C2212yes—
145#2430C2214yes—
146#2430C2214yes—
147#2430C2214yescomplemented
148#2428C2214yescomplemented
149#2426C2214yescomplemented
150#2426C2214yescomplemented
151#2425C2214yes—
152#2424C2214yes—
153#2422C2214yescomplemented
154#2416C2214yes—
155#2414C2214yescomplemented
156#2413C2214yes—
157#2411C2214yes—
158#2410C2214yes—
159#2410C2214yes—
160#2388C2214yes—
161#2388C2214yes—
162C2×#394C2214yes—
163#2374C2214yescomplemented
164#2373C2214yescomplemented
165#2373C2214yescomplemented
166#2373C2214yescomplemented
167#2373C2214yescomplemented
168#2372C2212yescomplemented
169#2372C2212yescomplemented
170#2372C2214yescomplemented
171#2369C2211yescharacteristic, complemented
172#2369C2212yescomplemented
173#2369C2211yescharacteristic, complemented
174#2368C2214yescomplemented
175#2367C2214yescomplemented
176#2367C2214yescomplemented
177#2364C2214yescomplemented
178#2363C2214yescomplemented
179#2363C2214yescomplemented
180#2360C2214yes—
181#2359C2214yes—
182#2359C2214yescomplemented
183#2359C2214yescomplemented
184#2359C2214yescomplemented
185#2358C2214yes—
186#2352C2214yes—
187#2349C2214yescomplemented
188#2343C2214yes—
189#2343C2214yescomplemented
190#2342C2214yes—
191#2342C2214yes—
192#2337C2214yescomplemented
193#2335C2214yescomplemented
194#2334C2214yescomplemented
195#2334C2214yescomplemented
196#2329C2212yes—
197#2325C2212yes—
198#2322C2214yes—
199#2321C2214yes—
200#2312C2212yes—
201C4×C22⋊Q8C2212yes—
202C4×C22⋊Q8C2214yescomplemented
203C4×#123C2214yescomplemented
204C4×#121C2212yes—
205C4×#120C2214yes—
206C4×#120C2214yes—
207#2297C2212yes—
208#2297C2212yes—
209#2296C2214yescomplemented
210C2×#391C2211yescharacteristic
211C2×#390C2211yescharacteristic
212#2290C2214yes—
213#2290C2214yescomplemented
214C2×#385C2214yes—
215#2275C2214yes—
216#2274C2212yes—
217C2×C4×C22⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2212yes—
219C22×#41—44no—
220C22×#41—44no—
221C22×#41—44no—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2312yes—
227C23×Q8C2311yescharacteristic
228C23×Q8C2311yescharacteristic
229C23×D4C2311yescharacteristic
230C23×D4C2312yes—
231C24×C4C2311yescharacteristic
232C24×C4C2312yes—
233Q82—44no—
234#555—48no—
235#555—44no—
236#551—232no—
237#539—48no—
238#538—216no—
239#532—48no—
240#532—48no—
241C2×C4⋊Q8—44no—
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2312yes—
252C2×#127C2312yes—
253C2×#127C2312yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#125C2314yes—
259C2×#124—44no—
260C2×#124C2314yes—
261C2×#124C2314yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2314yes—
271C2×#124C2312yes—
272C2×#124C2312yes—
273#525—48no—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×C22⋊Q8—44no—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×#121C2312yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#120C2314yes—
303C2×#120C2314yes—
304C2×#120C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×#117C2314yes—
319C2×#117C2314yes—
320C2×#117C2314yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2314yes—
326C22×C4⋊C4C2311yescharacteristic
327C22×C22⋊C4C2312yes—
328C22×C22⋊C4C2314yes—
329C22×C22⋊C4C2314yes—
330C22×C22⋊C4C2312yes—
331C22×C22⋊C4C2314yes—
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2312yes—
335C22×C42C2312yes—
336#400C2314yes—
337#400C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#392C2314yes—
399#392C2314yes—
400#392C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#391C2312yes—
412#391C2314yes—
413#391C2312yes—
414#391C2314yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2312yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#384C2314yes—
566#383C2314yes—
567#382C2314yes—
568#382C2314yes—
569#382C2314yes—
570#381C2314yes—
571#381C2314yes—
572#380C2314yes—
573#380C2314yes—
574#380C2314yes—
575#380C2312yes—
576#380C2312yes—
577#380C2314yes—
578#379C2314yes—
579#379C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2312yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2314yes—
622#376C2314yes—
623#376C2314yes—
624#376C2314yes—
625C2×#95C2314yes—
626C2×#95C2312yes—
627C2×#95C2314yes—
628C2×#95C2314yes—
629C25C2412yes—
630C25C2411yescharacteristic
631C2×#41—28no—
632C2×#41—28no—
633C2×#41—44no—
634C2×#41—44no—
635C2×#41—44no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—44no—
639C2×#41—44no—
640C2×#41—44no—
641C2×#41—44no—
642C2×#41—44no—
643C2×#41—44no—
644C2×#41—44no—
645C2×#41—44no—
646C2×#41—464no—
647C22×Q8—24no—
648C22×Q8—42no—
649C22×Q8—42no—
650C22×Q8—42no—
651C22×Q8—42no—
652C22×Q8—42no—
653C22×Q8C2412yes—
654C22×Q8C2411yescharacteristic
655C22×Q8C2412yes—
656C22×Q8C2411yescharacteristic
657C22×Q8C2412yes—
658C22×Q8C2411yescharacteristic
659C22×Q8C2412yes—
660C22×Q8C2412yes—
661C22×Q8C2411yescharacteristic
662C22×D4—24no—
663C22×D4—42no—
664C22×D4—44no—
665C22×D4—42no—
666C22×D4—44no—
667C22×D4—44no—
668C22×D4C2414yes—
669C22×D4C2414yes—
670C22×D4C2412yes—
671C22×D4C2412yes—
672C22×D4C2414yes—
673C22×D4C2414yes—
674C22×D4C2414yes—
675C22×D4C2412yes—
676C22×D4C2414yes—
677C22×D4C2412yes—
678C22×D4C2412yes—
679C22×D4C2411yescharacteristic
680C22×D4C2412yes—
681C22×D4C2414yes—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2411yescharacteristic
685C23×C4—24no—
686C23×C4—28no—
687C23×C4—42no—
688C23×C4—42no—
689C23×C4—44no—
690C23×C4—44no—
691C23×C4C2412yes—
692C23×C4C2411yescharacteristic
693C23×C4C2412yes—
694C23×C4C2414yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2414yes—
705C23×C4C2414yes—
706C23×C4C2412yes—
707C23×C4C2412yes—
708C23×C4C2411yescharacteristic
709C4⋊Q8—24no—
710C4⋊Q8—24no—
711C4⋊Q8—28no—
712C4⋊Q8—42no—
713C4⋊Q8—42no—
714C4⋊Q8—48no—
715C4⋊Q8—44no—
716C4⋊Q8—44no—
717C4⋊Q8—48no—
718C4⋊Q8—44no—
719#127—44no—
720#127—44no—
721#126—216no—
722#126—216no—
723#126—216no—
724#126—48no—
725#125—48no—
726#124—216no—
727#124—216no—
728#124—28no—
729#124—28no—
730#124—44no—
731#124—44no—
732#124—44no—
733#124—44no—
734#124—44no—
735#124—48no—
736#124—44no—
737#124—44no—
738#124—44no—
739#123—216no—
740#123—216no—
741#123—216no—
742#123—216no—
743#123—48no—
744#123—48no—
745#123—48no—
746C22⋊Q8—216no—
747C22⋊Q8—44no—
748C22⋊Q8—44no—
749C22⋊Q8—44no—
750C22⋊Q8—48no—
751C22⋊Q8—44no—
752C22⋊Q8—44no—
753C22⋊Q8—48no—
754C22⋊Q8#41116yescomplemented
755#121—216no—
756#121—28no—
757#121—216no—
758#121—44no—
759#121—48no—
760#121—48no—
761#121—48no—
762#121—48no—
763#121—44no—
764#121—48no—
765#121—44no—
766#120—216no—
767#120—216no—
768#120—48no—
769C4×Q8—48no—
770C4×Q8—44no—
771C4×D4—216no—
772C4×D4—216no—
773C4×D4—216no—
774C4×D4—216no—
775C4×D4—44no—
776C4×D4—48no—
777C4×D4—48no—
778C4×D4—48no—
779C4×D4—48no—
780C4×D4—48no—
781C4×D4—48no—
782#117—216no—
783#117—216no—
784#117—44no—
785#117—48no—
786#117—48no—
787#117—48no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—48no—
790C2×C4⋊C4—42no—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C22⋊C4—28no—
830C2×C22⋊C4—216no—
831C2×C22⋊C4—216no—
832C2×C22⋊C4—48no—
833C2×C22⋊C4—44no—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C42—42no—
884C2×C42—42no—
885C2×C42—44no—
886C2×C42—44no—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2411yescharacteristic
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949C24—22no—
950C24—24no—
951C24—28no—
952C24—24no—
953C24—24no—
954C24—42no—
955C24—41no—
956C24—41no—
957C24—44no—
958C24—42no—
959C24C2512yes—
960C24C2512yes—
961C24C2514yes—
962C24C2512yes—
963C24C2511yescharacteristic
964#41—432no—
965#41—432no—
966#41—432no—
967#41—432no—
968#41—816no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—22no—
972C2×Q8—24no—
973C2×Q8—22no—
974C2×Q8—24no—
975C2×Q8—22no—
976C2×Q8—42no—
977C2×Q8—41no—
978C2×Q8—41no—
979C2×Q8—41no—
980C2×Q8—42no—
981C2×Q8—41no—
982C2×Q8—42no—
983C2×Q8—41no—
984C2×Q8—42no—
985C2×Q8—41no—
986C2×Q8—42no—
987C2×Q8—41no—
988C2×Q8—41no—
989C2×Q8—42no—
990C2×Q8—42no—
991C2×Q8—42no—
992C2×Q8—42no—
993C2×Q8—42no—
994C2×Q8—416no—
995C2×Q8—88no—
996C2×Q8C2×#4118yescomplemented
997C2×Q8H(5,𝔽2)14yes—
998C2×D4—28no—
999C2×D4—28no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—24no—
1005C2×D4—28no—
1006C2×D4—28no—
1007C2×D4—28no—
1008C2×D4—28no—
1009C2×D4—28no—
1010C2×D4—24no—
1011C2×D4—24no—
1012C2×D4—24no—
1013C2×D4—22no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—42no—
1017C2×D4—41no—
1018C2×D4—41no—
1019C2×D4—42no—
1020C2×D4—42no—
1021C2×D4—41no—
1022C2×D4—42no—
1023C2×D4—41no—
1024C2×D4—42no—
1025C2×D4—42no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—42no—
1029C2×D4—44no—
1030C2×D4—416no—
1031C2×D4—44no—
1032C2×D4—42no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—42no—
1038C2×D4—44no—
1039C2×D4—42no—
1040C2×D4—44no—
1041C2×D4—42no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—42no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—432no—
1050C2×D4H(5,𝔽2)14yes—
1051C22×C4—24no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—28no—
1058C22×C4—28no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—28no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—28no—
1075C22×C4—28no—
1076C22×C4—28no—
1077C22×C4—28no—
1078C22×C4—42no—
1079C22×C4—41no—
1080C22×C4—41no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—44no—
1090C22×C4—42no—
1091C22×C4—44no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—42no—
1102C22×C4—416no—
1103C22×C4—432no—
1104C22×C4C2×#4118yes—
1105C22×C4H(5,𝔽2)14yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2514yes—
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2512yes—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4C2×#41116yescomplemented
1161C4⋊C4C2×#4118yescomplemented
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4C2×#41116yes—
1211C42—28no—
1212C42—28no—
1213C42—28no—
1214C42—28no—
1215C42—24no—
1216C42—24no—
1217C42—22no—
1218C42—24no—
1219C42—22no—
1220C42—28no—
1221C42—44no—
1222C42—44no—
1223C42—42no—
1224C42—42no—
1225C42—42no—
1226C42—42no—
1227C42—44no—
1228C42—44no—
1229C42—42no—
1230C42—44no—
1231C42—42no—
1232C42—42no—
1233C42—44no—
1234C42—42no—
1235C23—21no—
1236C23—21no—
1237C23—22no—
1238C23—24no—
1239C23—22no—
1240C23—22no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—24no—
1256C23—24no—
1257C23—24no—
1258C23—24no—
1259C23—48no—
1260C23—416no—
1261C23—44no—
1262C23—44no—
1263C23—48no—
1264C23—44no—
1265C23—88no—
1266C23—84no—
1267C23—84no—
1268C23—84no—
1269C23C22×#4114yes—
1270C23C2×H(5,𝔽2)14yes—
1271C23C2×H(5,𝔽2)12yes—
1272C23C2611yescharacteristic
1273Q8—44no—
1274Q8—48no—
1275Q8—48no—
1276Q8—44no—
1277Q8—82no—
1278Q8—84no—
1279Q8—82no—
1280Q8—84no—
1281Q8—162no—
1282D4—44no—
1283D4—416no—
1284D4—48no—
1285D4—48no—
1286D4—48no—
1287D4—44no—
1288D4—48no—
1289D4—48no—
1290D4—416no—
1291D4—84no—
1292D4—88no—
1293D4—88no—
1294D4—88no—
1295D4—84no—
1296D4—88no—
1297D4—88no—
1298D4—162no—
1299C2×C4—28no—
1300C2×C4—216no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—44no—
1348C2×C4—48no—
1349C2×C4—48no—
1350C2×C4—48no—
1351C2×C4—48no—
1352C2×C4—416no—
1353C2×C4—48no—
1354C2×C4—48no—
1355C2×C4—48no—
1356C2×C4—48no—
1357C2×C4—88no—
1358C2×C4—88no—
1359C2×C4—88no—
1360C2×C4—88no—
1361C2×C4—84no—
1362C2×C4—84no—
1363C2×C4C22×#4114yes—
1364C2×C4C22×#4118yes—
1365C2×C4C22×#4118yes—
1366C2×C4C22×#4114yes—
1367C2×C4C2×H(5,𝔽2)12yes—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4C2×H(5,𝔽2)14yes—
1370C2×C4C2×H(5,𝔽2)14yes—
1371C22—24no—
1372C22—24no—
1373C22—22no—
1374C22—22no—
1375C22—28no—
1376C22—24no—
1377C22—44no—
1378C22—42no—
1379C22—42no—
1380C22—44no—
1381C22—44no—
1382C22—44no—
1383C22—44no—
1384C22—44no—
1385C22—44no—
1386C22—44no—
1387C22—44no—
1388C22—42no—
1389C22—42no—
1390C22—44no—
1391C22—42no—
1392C22—44no—
1393C22—42no—
1394C22—44no—
1395C22—42no—
1396C22—42no—
1397C22—816no—
1398C22—88no—
1399C22#348314yes—
1400C22C23×#4112yes—
1401C22C22×H(5,𝔽2)11yescharacteristic
1402C22C22×H(5,𝔽2)11yescharacteristic
1403C22C22×H(5,𝔽2)11yescharacteristic
1404C222−1+612yes—
1405C4—24no—
1406C4—24no—
1407C4—28no—
1408C4—28no—
1409C4—24no—
1410C4—24no—
1411C4—22no—
1412C4—22no—
1413C4—44no—
1414C4—44no—
1415C4—44no—
1416C4—42no—
1417C4—44no—
1418C4—42no—
1419C4—42no—
1420C4—44no—
1421C4—44no—
1422C4—44no—
1423C2—24no—
1424C2—44no—
1425C2—84no—
1426C2—82no—
1427C2—82no—
1428C2C2×#348311yescharacteristic
1429C2#6281711yescharacteristic
1430C2#6288611yescharacteristic
1431C2#6298412yes—
1432C2#6298512yes—
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. #60047C2semidirect
2. #59991C2semidirect
3. #59948C2semidirect
4. #59819C2semidirect
5. #59798C2semidirect
6. #59182C2semidirect
7. #59160C2semidirect
8. #59151C2semidirect
9. #59135C2semidirect
10. #59115C2semidirect
11. #59084C2semidirect
12. #44377C2semidirect
13. #44265C2semidirect
14. #44223C2semidirect
15. #44181C2semidirect
16. #43938C2semidirect
17. #43913C2semidirect
18. #35397C2semidirect
19. #35393C2semidirect
20. #34738C2semidirect
21. C2×#2432C2semidirect
22. #34296C2semidirect
23. #34277C2semidirect
25. C2×Q82C22semidirect
26. C2×#555C22semidirect
27. C2×#555C22semidirect
37. #2809C22semidirect
38. #2803C22semidirect
39. #2803C22semidirect
40. #2795C22semidirect
41. #2785C22semidirect
42. #2781C22semidirect
43. #2775C22semidirect
44. #2756C22semidirect
45. #2734C22semidirect
46. #2734C22semidirect
47. #2733C22semidirect
48. #2733C22semidirect
49. #2733C22semidirect
50. #2732C22semidirect
51. #2731C22semidirect
52. #2731C22semidirect
53. #2731C22semidirect
54. #2731C22semidirect
55. #2731C22semidirect
56. #2730C22semidirect
57. #2727C22semidirect
58. #2727C22semidirect
59. #2714C22semidirect
60. #2705C22semidirect
61. #2705C22semidirect
62. #2686C22semidirect
63. #2686C22semidirect
64. #2682C22semidirect
65. #2682C22semidirect
66. #2673C22semidirect
67. #2612C22semidirect
68. #2611C22semidirect
69. #2610C22semidirect
70. #2610C22semidirect
71. #2603C22semidirect
72. #2602C22semidirect
73. #2601C22semidirect
74. #2593C22semidirect
75. #2574C22semidirect
76. #2567C22semidirect
77. #2566C22semidirect
78. #2564C22semidirect
79. #2563C22semidirect
81. #2560C22semidirect
82. #2560C22semidirect
83. #2559C22semidirect
84. #2558C22semidirect
85. #2556C22semidirect
86. #2556C22semidirect
87. #2556C22semidirect
88. #2555C22semidirect
89. #2554C22semidirect
90. #2554C22semidirect
91. #2554C22semidirect
92. #2553C22semidirect
93. #2551C22semidirect
94. #2548C22semidirect
98. #2532C22semidirect
99. #2526C22semidirect
100. #2518C22semidirect
101. #2500C22semidirect
102. #2491C22semidirect
103. #2491C22semidirect
104. #2491C22semidirect
106. #2479C22semidirect
107. #2479C22semidirect
108. #2476C22semidirect
109. #2474C22semidirect
110. #2474C22semidirect
111. #2474C22semidirect
113. #2467C22semidirect
114. #2464C22semidirect
115. #2461C22semidirect
116. #2461C22semidirect
117. #2461C22semidirect
118. #2459C22semidirect
119. #2456C22semidirect
120. #2452C22semidirect
121. #2452C22semidirect
122. #2452C22semidirect
123. #2451C22semidirect
124. #2445C22semidirect
126. #2439C22semidirect
127. #2439C22semidirect
142. #2432C22semidirect
147. #2430C22semidirect
148. #2428C22semidirect
149. #2426C22semidirect
150. #2426C22semidirect
153. #2422C22semidirect
155. #2414C22semidirect
163. #2374C22semidirect
164. #2373C22semidirect
165. #2373C22semidirect
166. #2373C22semidirect
167. #2373C22semidirect
168. #2372C22semidirect
169. #2372C22semidirect
170. #2372C22semidirect
171. #2369C22semidirect
172. #2369C22semidirect
173. #2369C22semidirect
174. #2368C22semidirect
175. #2367C22semidirect
176. #2367C22semidirect
177. #2364C22semidirect
178. #2363C22semidirect
179. #2363C22semidirect
182. #2359C22semidirect
183. #2359C22semidirect
184. #2359C22semidirect
187. #2349C22semidirect
189. #2343C22semidirect
192. #2337C22semidirect
193. #2335C22semidirect
194. #2334C22semidirect
195. #2334C22semidirect
202. C4×C22⋊Q8C22semidirect
203. C4×#123C22semidirect
209. #2296C22semidirect
213. #2290C22semidirect
754. C22⋊Q8#41semidirect
996. C2×Q8C2×#41semidirect
1160. C4⋊C4C2×#41semidirect
1161. C4⋊C4C2×#41semidirect

Maximal subgroups

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

subgroupindex
#600472
#599912
#599482
#598192
#597982
#591822
#591602
#591512
#591352
#591152
#590842
#443772
#442652
#442232
#441812
#439382
#439132
#353972
#353932
#347382
C2×#24322
#342962
#342772