Finite Group Databasebeta

← #7656035

Subgroups — #7656035

Order 512.

5150 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41696C214yesmaximal, complemented
2#41693C214yesmaximal, complemented
3#41057C214yesmaximal, complemented
4#41052C214yesmaximal, complemented
5#40670C214yesmaximal, complemented
6#40667C214yesmaximal, complemented
7#39252C214yesmaximal, complemented
8#38223C214yesmaximal, complemented
9#38120C214yesmaximal, complemented
10#37460C212yesmaximal, complemented
11#37459C212yesmaximal, complemented
12#37439C212yesmaximal, complemented
13#36221C214yesmaximal, complemented
14#35965C214yesmaximal, complemented
15#35953C214yesmaximal, complemented
16#35051C211yesmaximal, characteristic, complemented
17#35022C212yesmaximal, complemented
18#34570C212yesmaximal, complemented
19C2×#2646C211yesmaximal, characteristic, complemented
20#34233C212yesmaximal, complemented
21C2×#2364C211yesmaximal, characteristic, complemented
22C2×#553C2214yescomplemented
23C2×#525C2212yes—
24C22×#121C2211yescharacteristic
25C22×C4×D4C2212yes—
26#2852C2214yes—
27#2849C2214yes—
28#2847C2214yes—
29#2837C2214yescomplemented
30#2836C2214yescomplemented
31#2831C2214yescomplemented
32#2828C2214yescomplemented
33#2813C2214yes—
34#2813C2214yes—
35#2797C2214yescomplemented
36#2781C2214yescomplemented
37#2779C2214yescomplemented
38#2778C2214yescomplemented
39#2773C2214yescomplemented
40#2767C2214yescomplemented
41#2766C2214yescomplemented
42#2761C2214yescomplemented
43#2757C2214yescomplemented
44#2753C2214yescomplemented
45#2753C2214yescomplemented
46#2749C2214yescomplemented
47#2749C2214yescomplemented
48#2747C2214yescomplemented
49#2743C2214yescomplemented
50#2741C2214yescomplemented
51#2738C2214yescomplemented
52#2738C2214yescomplemented
53#2714C2214yescomplemented
54#2703C2214yescomplemented
55#2701C2214yescomplemented
56#2691C2214yescomplemented
57#2688C2214yescomplemented
58#2688C2214yescomplemented
59#2664C2214yescomplemented
60#2661C2214yescomplemented
61#2659C2211yescharacteristic
62#2656C2214yes—
63#2656C2211yescharacteristic
64#2654C2214yescomplemented
65#2653C2214yescomplemented
66#2652C2214yescomplemented
67#2651C2214yescomplemented
68#2650C2214yescomplemented
69#2649C2214yescomplemented
70#2649C2214yescomplemented
71#2648C2214yescomplemented
72#2646C2211yescharacteristic
73#2646C2214yes—
74#2646C2212yes—
75#2646C2211yescharacteristic
76#2646C2214yescomplemented
77#2646C2214yescomplemented
78#2643C2214yes—
79#2639C2212yes—
80#2639C2214yes—
81#2637C2214yescomplemented
82#2635C2214yescomplemented
83#2626C2212yes—
84#2626C2212yes—
85#2624C2214yes—
86#2622C2214yes—
87#2617C2212yes—
88#2617C2212yes—
89#2615C2214yes—
90#2611C2214yescomplemented
91#2603C2214yescomplemented
92#2603C2214yescomplemented
93#2602C2214yescomplemented
94#2600C2214yescomplemented
95#2598C2214yescomplemented
96#2597C2214yescomplemented
97#2591C2214yescomplemented
98#2579C2214yescomplemented
99#2573C2214yescomplemented
100#2572C2214yescomplemented
101#2564C2214yescomplemented
102#2559C2214yescomplemented
103#2554C2214yescomplemented
104#2554C2214yescomplemented
105#2553C2214yescomplemented
106#2553C2214yescomplemented
107#2543C2214yescomplemented
108#2543C2214yescomplemented
109#2543C2214yescomplemented
110#2543C2214yescomplemented
111#2533C2214yescomplemented
112#2533C2214yescomplemented
113#2530C2214yescomplemented
114#2526C2214yescomplemented
115#2519C2214yescomplemented
116#2519C2214yescomplemented
117#2516C2214yescomplemented
118#2516C2214yescomplemented
119#2515C2214yescomplemented
120#2510C2214yescomplemented
121#2505C2214yes—
122#2504C2214yescomplemented
123#2498C2214yescomplemented
124#2498C2214yescomplemented
125#2493C2214yescomplemented
126#2487C2214yes—
127#2481C2214yescomplemented
128#2480C2214yes—
129#2480C2214yes—
130#2473C2214yes—
131#2469C2214yescomplemented
132#2468C2214yescomplemented
133#2464C2214yescomplemented
134#2464C2214yescomplemented
135#2464C2214yescomplemented
136#2460C2214yescomplemented
137#2458C2214yescomplemented
138#2457C2214yescomplemented
139#2456C2214yescomplemented
140#2444C2214yes—
141#2444C2214yescomplemented
142#2444C2214yescomplemented
143#2444C2214yescomplemented
144#2444C2214yescomplemented
145#2443C2214yes—
146#2443C2214yescomplemented
147#2430C2214yescomplemented
148#2424C2214yes—
149#2424C2214yes—
150#2416C2214yes—
151#2416C2214yes—
152#2416C2214yescomplemented
153#2410C2214yes—
154#2410C2214yes—
155#2408C2214yes—
156#2401C2214yescomplemented
157#2398C2214yescomplemented
158#2395C2214yescomplemented
159C2×#400C2214yescomplemented
160#2392C2214yescomplemented
161C2×#398C2214yescomplemented
162#2364C2214yes—
163#2364C2214yes—
164#2364C2214yes—
165#2364C2214yes—
166#2364C2214yescomplemented
167#2361C2212yescomplemented
168#2361C2214yescomplemented
169#2361C2212yescomplemented
170#2360C2212yescomplemented
171#2360C2212yescomplemented
172#2358C2214yes—
173#2358C2214yes—
174#2353C2214yes—
175#2353C2214yescomplemented
176#2349C2214yes—
177#2347C2212yescomplemented
178#2346C2212yescomplemented
179#2341C2212yescomplemented
180#2339C2212yescomplemented
181#2335C2214yescomplemented
182#2335C2214yescomplemented
183#2325C2214yes—
184#2321C2214yes—
185#2318C2214yes—
186#2318C2214yescomplemented
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191C4×#120C2214yes—
192#2290C2214yes—
193C2×#388C2212yes—
194C2×#387C2212yes—
195C2×#386C2212yes—
196C2×#386C2212yes—
197C2×#385C2214yes—
198C2×#380C2212yes—
199#2275C2214yescomplemented
200C2×C4×C22⋊C4C2212yes—
201C2×C4×C22⋊C4C2211yescharacteristic
202C22×#95C2211yescharacteristic
203C22×#41C2312yes—
204C23×D4C2312yes—
205C23×D4C2311yescharacteristic
206C24×C4C2312yes—
207C24×C4C2312yes—
208C24×C4C2311yescharacteristic
209#553—416no—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#126C2314yes—
213C2×#125C2314yes—
214#525—216no—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×#121—28no—
222C2×#121C2314yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#120C2314yes—
238C2×#120C2314yes—
239C2×#120C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×D4—48no—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C22⋊C4C2311yescharacteristic
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2314yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274#401C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#399C2314yes—
295#399C2314yes—
296#399C2314yes—
297#399C2314yes—
298#399C2314yes—
299#399C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#395C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#393C2314yes—
365#393C2314yes—
366#393C2314yes—
367#392C2314yes—
368#392C2314yes—
369#392C2314yes—
370#392C2314yes—
371#392C2314yes—
372#392C2314yes—
373#392C2314yes—
374#392C2314yes—
375#392C2314yes—
376#392C2314yes—
377#392C2314yes—
378#391C2312yes—
379#391C2312yes—
380#390C2312yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2312yes—
386#390C2314yes—
387#390C2314yes—
388#390C2314yes—
389#390C2314yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2312yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#386C2314yes—
459#386C2314yes—
460#386C2314yes—
461#386C2314yes—
462#386C2314yes—
463#386C2314yes—
464#386C2314yes—
465#386C2314yes—
466#386C2314yes—
467#386C2314yes—
468#386C2314yes—
469#386C2314yes—
470#386C2314yes—
471#386C2314yes—
472#386C2314yes—
473#386C2314yes—
474#386C2314yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#383C2314yes—
519#383C2314yes—
520#383C2314yes—
521#382C2314yes—
522#382C2314yes—
523#382C2314yes—
524#381C2314yes—
525#381C2314yes—
526#381C2314yes—
527#381C2314yes—
528#381C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2312yes—
536#380C2312yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2312yes—
541#380C2312yes—
542#379C2314yes—
543#379C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2312yes—
550C4×C4⋊C4C2312yes—
551C4×C4⋊C4C2314yes—
552C4×C22⋊C4C2314yes—
553C4×C22⋊C4C2314yes—
554C4×C22⋊C4C2314yes—
555C4×C22⋊C4C2314yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2312yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2312yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2314yes—
570#376C2314yes—
571#376C2314yes—
572C2×#95C2314yes—
573C2×#95C2312yes—
574C2×#95C2314yes—
575C2×#95C2312yes—
576C2×#95C2314yes—
577C2×#95C2312yes—
578C2×#95C2314yes—
579C2×#95C2314yes—
580C2×#95C2314yes—
581C2×#95C2311yescharacteristic
582C2×#95C2311yescharacteristic
583C2×#95C2312yes—
584C25C2411yescharacteristic
585C25C2412yes—
586C2×#41—28no—
587C2×#41—82no—
588C2×#41—82no—
589C22×Q8C2412yes—
590C22×D4—28no—
591C22×D4—24no—
592C22×D4—44no—
593C22×D4—44no—
594C22×D4—82no—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C22×D4C2412yes—
600C22×D4C2414yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2414yes—
604C22×D4C2414yes—
605C22×D4C2414yes—
606C22×D4C2414yes—
607C23×C4—44no—
608C23×C4—44no—
609C23×C4—44no—
610C23×C4—44no—
611C23×C4—82no—
612C23×C4—82no—
613C23×C4—82no—
614C23×C4#4118yes—
615C23×C4C2412yes—
616C23×C4C2412yes—
617C23×C4C2412yes—
618C23×C4C2414yes—
619C23×C4C2414yes—
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2414yes—
623C23×C4C2414yes—
624C23×C4C2414yes—
625C23×C4C2414yes—
626C23×C4C2414yes—
627C23×C4C2414yes—
628C23×C4C2414yes—
629C23×C4C2411yescharacteristic
630C23×C4C2412yes—
631C23×C4C2411yescharacteristic
632C23×C4C2412yes—
633#126—48no—
634#126—48no—
635#126—84no—
636#125—48no—
637#123—216no—
638#123—48no—
639#123—48no—
640#123—84no—
641C22⋊Q8—28no—
642C22⋊Q8—28no—
643#121—216no—
644#121—216no—
645#121—28no—
646#121—28no—
647#121—48no—
648#121—48no—
649#121—48no—
650#121—48no—
651#121—48no—
652#121—48no—
653#121—48no—
654#121—84no—
655#121—84no—
656#121—84no—
657#121—84no—
658#120—216no—
659#120—48no—
660#120—48no—
661C4×Q8—82no—
662C4×Q8—82no—
663C4×D4—216no—
664C4×D4—216no—
665C4×D4—216no—
666C4×D4—216no—
667C4×D4—48no—
668C4×D4—48no—
669C4×D4—48no—
670C4×D4—48no—
671C4×D4—48no—
672C4×D4—48no—
673C4×D4—48no—
674C4×D4—82no—
675C4×D4—82no—
676C4×D4—84no—
677#117—28no—
678#117—48no—
679C2×C4⋊C4—24no—
680C2×C4⋊C4—44no—
681C2×C4⋊C4—48no—
682C2×C4⋊C4—82no—
683C2×C4⋊C4—82no—
684C2×C4⋊C4—84no—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C22⋊C4—28no—
720C2×C22⋊C4—24no—
721C2×C22⋊C4—44no—
722C2×C22⋊C4—42no—
723C2×C22⋊C4—48no—
724C2×C22⋊C4—44no—
725C2×C22⋊C4—82no—
726C2×C22⋊C4C2411yescharacteristic
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2411yescharacteristic
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C42—44no—
778C2×C42—82no—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2414yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2412yes—
791C2×C42C2412yes—
792#95C2414yes—
793#95C2412yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2412yes—
799#95C2414yes—
800#95C2412yes—
801#95C2414yes—
802#95C2412yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842C24—22no—
843C24—24no—
844C24—22no—
845C24—24no—
846C24—24no—
847C24—24no—
848C24—42no—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—42no—
853C24C2×#4114yes—
854C24C2514yes—
855C24C2514yes—
856C24C2511yescharacteristic
857C24C2511yescharacteristic
858C24C2511yescharacteristic
859#41—816no—
860C2×Q8—24no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×D4—28no—
864C2×D4—28no—
865C2×D4—28no—
866C2×D4—28no—
867C2×D4—28no—
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—28no—
873C2×D4—28no—
874C2×D4—24no—
875C2×D4—28no—
876C2×D4—44no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—432no—
900C2×D4—88no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—28no—
905C22×C4—28no—
906C22×C4—24no—
907C22×C4—28no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—28no—
911C22×C4—28no—
912C22×C4—28no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—42no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—88no—
950C22×C4—816no—
951C22×C4—816no—
952C22×C4C2×#4114yes—
953C22×C4C2×#4114yes—
954C22×C4C2×#4118yes—
955C22×C4C2×#4118yes—
956C22×C4C2512yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C4⋊C4—28no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—44no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C22⋊C4—28no—
1007C22⋊C4—28no—
1008C22⋊C4—28no—
1009C22⋊C4—22no—
1010C22⋊C4—24no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—24no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—41no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—41no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4H(5,𝔽2)14yes—
1057C42—28no—
1058C42—28no—
1059C42—28no—
1060C42—44no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—42no—
1065C42—44no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C23—21no—
1071C23—22no—
1072C23—21no—
1073C23—22no—
1074C23—22no—
1075C23—21no—
1076C23—22no—
1077C23—21no—
1078C23—22no—
1079C23—28no—
1080C23—28no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23—24no—
1091C23—24no—
1092C23—24no—
1093C23—24no—
1094C23—24no—
1095C23—44no—
1096C23—48no—
1097C23—48no—
1098C23—48no—
1099C23—48no—
1100C23—48no—
1101C23—84no—
1102C23—84no—
1103C23—84no—
1104C23—84no—
1105C23C22×#4112yes—
1106C23C22×#4112yes—
1107C23C22×#4112yes—
1108C23C2×H(5,𝔽2)12yes—
1109C23#58512yes—
1110C23#58514yes—
1111C23C2611yescharacteristic
1112Q8—48no—
1113D4—48no—
1114D4—416no—
1115D4—416no—
1116D4—416no—
1117D4—416no—
1118D4—88no—
1119D4—88no—
1120D4—88no—
1121D4—88no—
1122D4—164no—
1123D4—164no—
1124D4—164no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—48no—
1171C2×C4—44no—
1172C2×C4—44no—
1173C2×C4—48no—
1174C2×C4—48no—
1175C2×C4—48no—
1176C2×C4—48no—
1177C2×C4—88no—
1178C2×C4—88no—
1179C2×C4—88no—
1180C2×C4—88no—
1181C2×C4—84no—
1182C2×C4—88no—
1183C2×C4—88no—
1184C2×C4—84no—
1185C2×C4—88no—
1186C2×C4—88no—
1187C2×C4—164no—
1188C2×C4C22×#4114yes—
1189C2×C4C22×#4114yes—
1190C2×C4C2×H(5,𝔽2)14yes—
1191C22—22no—
1192C22—22no—
1193C22—22no—
1194C22—24no—
1195C22—24no—
1196C22—22no—
1197C22—24no—
1198C22—24no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—416no—
1203C22—42no—
1204C22—42no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—816no—
1220C22#346014yes—
1221C22#351214yes—
1222C22C23×#4111yescharacteristic
1223C22C22×H(5,𝔽2)11yescharacteristic
1224C22C2×#58512yes—
1225C22C2×#58511yescharacteristic
1226C22H(7,𝔽2)12yes—
1227C4—24no—
1228C4—24no—
1229C4—24no—
1230C4—44no—
1231C4—44no—
1232C4—42no—
1233C4—44no—
1234C4—44no—
1235C4—44no—
1236C4—44no—
1237C4—44no—
1238C4—44no—
1239C4—42no—
1240C4—42no—
1241C4—44no—
1242C4—44no—
1243C2—24no—
1244C2—24no—
1245C2—42no—
1246C2—84no—
1247C2—84no—
1248C2C2×#346011yescharacteristic
1249C2C2×#351211yescharacteristic
1250C2#6284411yescharacteristic
1251C2#6289612yes—
1252C2#6296312yes—
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. #41696C2semidirect
2. #41693C2semidirect
3. #41057C2semidirect
4. #41052C2semidirect
5. #40670C2semidirect
6. #40667C2semidirect
7. #39252C2semidirect
8. #38223C2semidirect
9. #38120C2semidirect
10. #37460C2semidirect
11. #37459C2semidirect
12. #37439C2semidirect
13. #36221C2semidirect
14. #35965C2semidirect
15. #35953C2semidirect
16. #35051C2semidirect
17. #35022C2semidirect
18. #34570C2semidirect
19. C2×#2646C2semidirect
20. #34233C2semidirect
21. C2×#2364C2semidirect
22. C2×#553C22semidirect
29. #2837C22semidirect
30. #2836C22semidirect
31. #2831C22semidirect
32. #2828C22semidirect
35. #2797C22semidirect
36. #2781C22semidirect
37. #2779C22semidirect
38. #2778C22semidirect
39. #2773C22semidirect
40. #2767C22semidirect
41. #2766C22semidirect
42. #2761C22semidirect
43. #2757C22semidirect
44. #2753C22semidirect
45. #2753C22semidirect
46. #2749C22semidirect
47. #2749C22semidirect
48. #2747C22semidirect
49. #2743C22semidirect
50. #2741C22semidirect
51. #2738C22semidirect
52. #2738C22semidirect
53. #2714C22semidirect
54. #2703C22semidirect
55. #2701C22semidirect
56. #2691C22semidirect
57. #2688C22semidirect
58. #2688C22semidirect
59. #2664C22semidirect
60. #2661C22semidirect
64. #2654C22semidirect
65. #2653C22semidirect
66. #2652C22semidirect
67. #2651C22semidirect
68. #2650C22semidirect
69. #2649C22semidirect
70. #2649C22semidirect
71. #2648C22semidirect
76. #2646C22semidirect
77. #2646C22semidirect
81. #2637C22semidirect
82. #2635C22semidirect
90. #2611C22semidirect
91. #2603C22semidirect
92. #2603C22semidirect
93. #2602C22semidirect
94. #2600C22semidirect
95. #2598C22semidirect
96. #2597C22semidirect
97. #2591C22semidirect
98. #2579C22semidirect
99. #2573C22semidirect
100. #2572C22semidirect
101. #2564C22semidirect
102. #2559C22semidirect
103. #2554C22semidirect
104. #2554C22semidirect
105. #2553C22semidirect
106. #2553C22semidirect
107. #2543C22semidirect
108. #2543C22semidirect
109. #2543C22semidirect
110. #2543C22semidirect
111. #2533C22semidirect
112. #2533C22semidirect
113. #2530C22semidirect
114. #2526C22semidirect
115. #2519C22semidirect
116. #2519C22semidirect
117. #2516C22semidirect
118. #2516C22semidirect
119. #2515C22semidirect
120. #2510C22semidirect
122. #2504C22semidirect
123. #2498C22semidirect
124. #2498C22semidirect
125. #2493C22semidirect
127. #2481C22semidirect
131. #2469C22semidirect
132. #2468C22semidirect
133. #2464C22semidirect
134. #2464C22semidirect
135. #2464C22semidirect
136. #2460C22semidirect
137. #2458C22semidirect
138. #2457C22semidirect
139. #2456C22semidirect
141. #2444C22semidirect
142. #2444C22semidirect
143. #2444C22semidirect
144. #2444C22semidirect
146. #2443C22semidirect
147. #2430C22semidirect
152. #2416C22semidirect
156. #2401C22semidirect
157. #2398C22semidirect
158. #2395C22semidirect
159. C2×#400C22semidirect
160. #2392C22semidirect
161. C2×#398C22semidirect
166. #2364C22semidirect
167. #2361C22semidirect
168. #2361C22semidirect
169. #2361C22semidirect
170. #2360C22semidirect
171. #2360C22semidirect
175. #2353C22semidirect
177. #2347C22semidirect
178. #2346C22semidirect
179. #2341C22semidirect
180. #2339C22semidirect
181. #2335C22semidirect
182. #2335C22semidirect
186. #2318C22semidirect
199. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#416962
#416932
#410572
#410522
#406702
#406672
#392522
#382232
#381202
#374602
#374592
#374392
#362212
#359652
#359532
#350512
#350222
#345702
C2×#26462
#342332
C2×#23642