Finite Group Databasebeta

← #7715985

Subgroups — #7715985

Order 512.

4492 conjugacy classes of subgroups.

The subgroup lattice has 1445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50616C214yesmaximal, complemented
2#50548C214yesmaximal, complemented
3#49510C214yesmaximal, complemented
4#49418C214yesmaximal, complemented
5#45341C212yesmaximal, complemented
6#45331C212yesmaximal, complemented
7#45235C212yesmaximal, complemented
8#45210C212yesmaximal, complemented
9#45170C212yesmaximal, complemented
10#45122C212yesmaximal, complemented
11#44984C212yesmaximal, complemented
12#44977C212yesmaximal, complemented
13#39799C212yesmaximal, complemented
14#39751C211yesmaximal, characteristic, complemented
15#39679C212yesmaximal, complemented
16#39614C211yesmaximal, characteristic, complemented
17#39477C212yesmaximal, complemented
18#39477C214yesmaximal, complemented
19#36782C214yesmaximal, complemented
20#36586C211yesmaximal, characteristic, complemented
21#36552C211yesmaximal, characteristic, complemented
22#36546C212yesmaximal, complemented
23#35231C212yesmaximal, complemented
24#35014C211yesmaximal, characteristic, complemented
25#35012C212yesmaximal, complemented
26#34996C212yesmaximal
27#34570C211yesmaximal, characteristic
28#34464C212yesmaximal, complemented
29C2×#2345C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C23×C4⋊C4C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2852C2214yes—
35#2851C2214yes—
36#2851C2212yes—
37#2850C2212yes—
38#2848C2214yes—
39#2848C2212yes—
40#2809C2214yescomplemented
41#2805C2212yescomplemented
42#2805C2214yescomplemented
43#2802C2214yescomplemented
44#2789C2214yescomplemented
45#2787C2214yes—
46#2787C2214yes—
47#2787C2214yes—
48#2787C2214yescomplemented
49#2786C2214yescomplemented
50#2783C2214yescomplemented
51#2783C2214yescomplemented
52#2781C2214yes—
53#2781C2214yes—
54#2781C2214yes—
55#2779C2214yes—
56#2779C2214yes—
57#2779C2214yes—
58#2776C2214yescomplemented
59#2776C2214yescomplemented
60#2775C2214yescomplemented
61#2774C2214yescomplemented
62#2772C2214yescomplemented
63#2770C2214yes—
64#2770C2214yes—
65#2770C2214yes—
66#2769C2214yescomplemented
67#2766C2214yescomplemented
68#2766C2214yescomplemented
69#2762C2214yescomplemented
70#2762C2214yescomplemented
71#2755C2214yescomplemented
72#2747C2214yescomplemented
73#2744C2214yescomplemented
74#2726C2212yescomplemented
75#2726C2212yescomplemented
76#2725C2214yescomplemented
77#2719C2214yescomplemented
78#2704C2214yescomplemented
79#2690C2214yescomplemented
80#2689C2214yescomplemented
81#2683C2212yescomplemented
82#2659C2212yes—
83#2659C2212yes—
84#2655C2214yescomplemented
85#2654C2214yescomplemented
86#2653C2212yes—
87#2652C2212yes—
88#2649C2212yes—
89#2648C2212yes—
90#2646C2211yescharacteristic
91#2646C2212yes—
92#2643C2212yes—
93#2639C2211yescharacteristic
94#2626C2211yescharacteristic
95#2626C2212yes—
96#2622C2212yes—
97#2622C2214yes—
98#2617C2211yescharacteristic
99#2599C2214yescomplemented
100#2596C2214yescomplemented
101#2594C2214yescomplemented
102#2590C2214yescomplemented
103#2590C2214yescomplemented
104#2589C2214yes—
105#2587C2214yes—
106#2584C2212yescomplemented
107#2583C2214yes—
108#2581C2214yescomplemented
109#2579C2214yes—
110#2574C2214yes—
111#2574C2214yes—
112#2571C2211yescharacteristic, complemented
113#2568C2211yescharacteristic, complemented
114#2562C2212yes—
115#2562C2214yes—
116#2556C2214yes—
117#2556C2214yes—
118#2552C2211yescharacteristic, complemented
119#2550C2212yescomplemented
120#2547C2211yescharacteristic, complemented
121#2536C2214yes—
122#2536C2212yes—
123#2524C2214yescomplemented
124#2524C2214yescomplemented
125#2523C2214yes—
126#2522C2214yes—
127#2522C2214yes—
128#2519C2214yescomplemented
129#2518C2214yes—
130#2518C2214yes—
131#2517C2214yes—
132#2514C2212yescomplemented
133#2514C2212yescomplemented
134#2511C2212yescomplemented
135#2510C2214yes—
136#2510C2214yes—
137#2510C2214yes—
138#2508C2212yescomplemented
139#2508C2212yescomplemented
140#2508C2214yescomplemented
141#2506C2212yescomplemented
142#2506C2212yescomplemented
143#2505C2214yes—
144#2505C2214yes—
145#2505C2214yes—
146#2502C2212yes—
147#2497C2212yes—
148#2496C2212yescomplemented
149#2495C2214yes—
150#2495C2212yes—
151#2494C2214yes—
152#2494C2212yes—
153#2494C2212yescomplemented
154#2492C2212yes—
155#2489C2212yes—
156#2489C2214yes—
157#2489C2212yescomplemented
158#2487C2212yes—
159#2485C2212yes—
160#2485C2214yes—
161#2474C2214yescomplemented
162#2473C2214yes—
163#2473C2214yes—
164#2467C2214yes—
165#2466C2214yes—
166#2465C2214yes—
167#2465C2214yes—
168#2462C2214yescomplemented
169#2460C2214yes—
170#2459C2214yes—
171#2453C2212yescomplemented
172#2451C2212yescomplemented
173#2449C2214yes—
174#2449C2214yes—
175#2448C2212yescomplemented
176#2442C2212yes—
177#2442C2214yes—
178#2440C2212yes—
179#2440C2212yes—
180#2440C2212yescomplemented
181#2429C2212yes—
182#2429C2212yescomplemented
183#2423C2212yes—
184#2421C2214yes—
185#2421C2212yes—
186#2417C2212yes—
187#2417C2214yes—
188#2417C2212yes—
189#2417C2212yes—
190#2417C2212yescomplemented
191#2415C2212yes—
192#2415C2214yes—
193#2401C2212yes—
194#2398C2212yes—
195#2395C2212yes—
196#2392C2212yes—
197#2382C2214yescomplemented
198#2378C2214yescomplemented
199#2365C2212yescomplemented
200#2365C2211yescharacteristic, complemented
201#2365C2211yescharacteristic, complemented
202#2362C2212yescomplemented
203#2360C2212yes—
204#2360C2212yes—
205#2360C2214yes—
206#2360C2212yes—
207#2355C2212yescomplemented
208#2354C2211yescharacteristic, complemented
209#2352C2214yes—
210#2352C2212yes—
211#2351C2212yescomplemented
212Q8×C4⋊C4C2211yescharacteristic, complemented
213D4×C4⋊C4C2212yes—
214D4×C4⋊C4C2212yes—
215#2347C2212yescomplemented
216#2345C2214yes—
217#2345C2212yes—
218#2345C2212yes—
219#2345C2212yes—
220#2345C2214yes—
221#2345C2212yes—
222#2345C2212yes—
223#2344C2212yescomplemented
224#2336C2214yescomplemented
225#2331C2212yescomplemented
226#2330C2212yescomplemented
227#2329C2212yes—
228#2329C2212yes—
229#2329C2214yes—
230#2325C2212yes—
231#2323C2212yescomplemented
232#2323C2214yescomplemented
233#2323C2212yescomplemented
234#2320C2212yescomplemented
235#2320C2212yescomplemented
236#2318C2214yes—
237#2316C2212yescomplemented
238#2314C2212yescomplemented
239#2312C2214yes—
240#2312C2212yes—
241C4×C22⋊Q8C2211yescharacteristic
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×#121C2211yescharacteristic
246C4×#120C2212yes—
247C4×#120C2214yes—
248C2×#389C2211yescharacteristic
249C2×#389C2211yescharacteristic
250#2290C2212yes—
251C2×#387C2212yes—
252C2×#387C2212yes—
253C2×#380C2211yescharacteristic
254C2×#380C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C22⋊C4C2211yescharacteristic
258C2×C4×C22⋊C4C2212yes—
259C24×C4C2311yescharacteristic
260C24×C4C2312yes—
261#554—216no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×#126C2314yes—
266C2×#125C2314yes—
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#125C2312yes—
271C2×#124C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2311yescharacteristic
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×#121C2311yescharacteristic
285C2×#120C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2314yes—
303C22×C4⋊C4—28no—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2314yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2311yescharacteristic
315C22×C22⋊C4C2312yes—
316C22×C22⋊C4C2311yescharacteristic
317C22×C22⋊C4C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2312yes—
321C22×C42C2312yes—
322#401C2314yes—
323#401C2312yes—
324#401C2314yes—
325#401C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#397C2312yes—
377#397C2314yes—
378#397C2314yes—
379#397C2312yes—
380#397C2312yes—
381#397C2312yes—
382#397C2312yes—
383#397C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#396C2312yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#396C2312yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#394C2312yes—
412#394C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2312yes—
416#394C2312yes—
417#394C2312yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#393C2312yes—
423#393C2314yes—
424#393C2312yes—
425#392C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2311yescharacteristic
442#391C2314yes—
443#390C2312yes—
444#390C2311yescharacteristic
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2311yescharacteristic
487#389C2311yescharacteristic
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
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#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#386C2312yes—
577#386C2314yes—
578#386C2312yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2312yes—
583#386C2312yes—
584#386C2312yes—
585#386C2312yes—
586#386C2314yes—
587#386C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2312yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2312yes—
607#385C2312yes—
608#385C2312yes—
609#385C2312yes—
610#385C2314yes—
611#385C2314yes—
612#384C2312yes—
613#384C2311yescharacteristic
614#384C2312yes—
615#384C2311yescharacteristic
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2314yes—
626#382C2314yes—
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#382C2314yes—
631#382C2314yes—
632#381C2314yes—
633#380C2312yes—
634#380C2314yes—
635#380C2312yes—
636#380C2312yes—
637#380C2314yes—
638#380C2312yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2314yes—
647#380C2314yes—
648#380C2312yes—
649#380C2314yes—
650#380C2312yes—
651#380C2311yescharacteristic
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2311yescharacteristic
660#379C2314yes—
661#379C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706#376C2312yes—
707C2×#95C2312yes—
708C2×#95C2312yes—
709C2×#95C2311yescharacteristic
710C2×#95C2311yescharacteristic
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C25C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2414yes—
718C22×Q8C2412yes—
719C22×D4C2412yes—
720C22×D4C2412yes—
721C22×D4C2412yes—
722C22×D4C2411yescharacteristic
723C23×C4—24no—
724C23×C4—28no—
725C23×C4—42no—
726C23×C4—42no—
727C23×C4—82no—
728C23×C4—82no—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2411yescharacteristic
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2412yes—
744C23×C4C2411yescharacteristic
745C4⋊Q8—28no—
746C4⋊Q8—42no—
747C4⋊Q8—42no—
748#126—84no—
749#125—216no—
750#125—44no—
751#125—82no—
752#125—84no—
753#125—84no—
754#124—82no—
755C22⋊Q8—216no—
756C22⋊Q8—28no—
757C22⋊Q8—24no—
758C22⋊Q8—28no—
759C22⋊Q8—216no—
760C22⋊Q8—28no—
761C22⋊Q8—44no—
762C22⋊Q8—44no—
763C22⋊Q8—44no—
764C22⋊Q8—84no—
765C22⋊Q8—84no—
766C22⋊Q8—84no—
767#121—24no—
768#120—28no—
769C4×Q8—28no—
770C4×Q8—42no—
771C4×Q8—44no—
772C4×Q8—44no—
773C4×Q8—82no—
774C4×Q8—82no—
775C4×Q8—84no—
776C4×D4—216no—
777C4×D4—28no—
778C4×D4—42no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4—84no—
782C4×D4—84no—
783#117—44no—
784#117—44no—
785#117—84no—
786C2×C4⋊C4—24no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4—216no—
791C2×C4⋊C4—28no—
792C2×C4⋊C4—42no—
793C2×C4⋊C4—42no—
794C2×C4⋊C4—82no—
795C2×C4⋊C4—82no—
796C2×C4⋊C4#4118yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C22⋊C4—28no—
866C2×C22⋊C4—24no—
867C2×C22⋊C4—24no—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C42—42no—
907C2×C42—42no—
908C2×C42—82no—
909C2×C42—82no—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24—22no—
1009C24—22no—
1010C24—41no—
1011C24—41no—
1012C24—41no—
1013C24—41no—
1014C242−1+414yes—
1015C24C2512yes—
1016C24C2512yes—
1017C24C2511yescharacteristic
1018C2×Q8—24no—
1019C2×Q8—28no—
1020C2×Q8—22no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—41no—
1025C2×Q8—41no—
1026C2×Q8—44no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—42no—
1030C2×D4—24no—
1031C2×D4—24no—
1032C2×D4—24no—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—22no—
1036C2×D4—42no—
1037C2×D4—42no—
1038C2×D4—42no—
1039C2×D4—42no—
1040C2×D4—41no—
1041C2×D4—41no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—22no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—28no—
1059C22×C4—28no—
1060C22×C4—28no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—41no—
1074C22×C4—41no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—41no—
1080C22×C4—41no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—416no—
1088C22×C4—816no—
1089C22×C4C2×#4114yes—
1090C22×C4C2×#4118yes—
1091C22×C42−1+414yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2514yes—
1109C22×C4C2514yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2514yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2514yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—22no—
1131C4⋊C4—22no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—22no—
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—41no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—41no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4C2×#4118yes—
1185C4⋊C4C2×#4118yes—
1186C22⋊C4—28no—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C42—28no—
1225C42—24no—
1226C42—24no—
1227C42—22no—
1228C42—22no—
1229C42—24no—
1230C42—24no—
1231C42—41no—
1232C42—41no—
1233C42—42no—
1234C42—42no—
1235C42—42no—
1236C42—42no—
1237C42—42no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C23—21no—
1249C23—21no—
1250C23—21no—
1251C23—21no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—28no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—44no—
1267C23—44no—
1268C23—44no—
1269C23—44no—
1270C23—44no—
1271C23—44no—
1272C23C22×#4112yes—
1273C23C2×2−1+414yes—
1274C23C2×2−1+412yes—
1275C23C2×2−1+412yes—
1276C23C2611yescharacteristic
1277Q8—44no—
1278Q8—48no—
1279Q8—88no—
1280Q8—84no—
1281D4—48no—
1282D4—48no—
1283D4—48no—
1284D4—82no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—28no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—21no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—21no—
1357C2×C4—48no—
1358C2×C4—44no—
1359C2×C4—48no—
1360C2×C4—44no—
1361C2×C4—44no—
1362C2×C4—48no—
1363C2×C4—48no—
1364C2×C4—48no—
1365C2×C4—88no—
1366C2×C4—88no—
1367C2×C4—88no—
1368C2×C4—82no—
1369C2×C4—82no—
1370C2×C4—84no—
1371C2×C4—84no—
1372C2×C4C22×#4118yes—
1373C2×C4C22×#4112yes—
1374C2×C4C22×#4112yes—
1375C2×C4C2×2−1+412yes—
1376C2×C4C2×2−1+412yes—
1377C2×C4#58512yes—
1378C2×C4#58512yes—
1379C22—22no—
1380C22—22no—
1381C22—22no—
1382C22—22no—
1383C22—22no—
1384C22—22no—
1385C22—24no—
1386C22—24no—
1387C22—24no—
1388C22—416no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22#352314yes—
1401C22C23×#4111yescharacteristic
1402C22C22×2−1+411yescharacteristic
1403C22C22×2−1+411yescharacteristic
1404C22C2×#58511yescharacteristic
1405C22C2×#58511yescharacteristic
1406C22H(7,𝔽2)11yescharacteristic
1407C22H(7,𝔽2)11yescharacteristic
1408C4—22no—
1409C4—28no—
1410C4—22no—
1411C4—22no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—41no—
1422C4—41no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—44no—
1430C4—42no—
1431C4—44no—
1432C4—42no—
1433C4#349314yes—
1434C2—24no—
1435C2—44no—
1436C2—82no—
1437C2C2×#349311yescharacteristic
1438C2C2×#352311yescharacteristic
1439C2#6284611yescharacteristic
1440C2#6290211yescharacteristic
1441C2#6290211yescharacteristic
1442C2#6290211yescharacteristic
1443C2#6292611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2617C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50616C2semidirect
2. #50548C2semidirect
3. #49510C2semidirect
4. #49418C2semidirect
5. #45341C2semidirect
6. #45331C2semidirect
7. #45235C2semidirect
8. #45210C2semidirect
9. #45170C2semidirect
10. #45122C2semidirect
11. #44984C2semidirect
12. #44977C2semidirect
13. #39799C2semidirect
14. #39751C2semidirect
15. #39679C2semidirect
16. #39614C2semidirect
17. #39477C2semidirect
18. #39477C2semidirect
19. #36782C2semidirect
20. #36586C2semidirect
21. #36552C2semidirect
22. #36546C2semidirect
23. #35231C2semidirect
24. #35014C2semidirect
25. #35012C2semidirect
28. #34464C2semidirect
29. C2×#2345C2semidirect
40. #2809C22semidirect
41. #2805C22semidirect
42. #2805C22semidirect
43. #2802C22semidirect
44. #2789C22semidirect
48. #2787C22semidirect
49. #2786C22semidirect
50. #2783C22semidirect
51. #2783C22semidirect
58. #2776C22semidirect
59. #2776C22semidirect
60. #2775C22semidirect
61. #2774C22semidirect
62. #2772C22semidirect
66. #2769C22semidirect
67. #2766C22semidirect
68. #2766C22semidirect
69. #2762C22semidirect
70. #2762C22semidirect
71. #2755C22semidirect
72. #2747C22semidirect
73. #2744C22semidirect
74. #2726C22semidirect
75. #2726C22semidirect
76. #2725C22semidirect
77. #2719C22semidirect
78. #2704C22semidirect
79. #2690C22semidirect
80. #2689C22semidirect
81. #2683C22semidirect
84. #2655C22semidirect
85. #2654C22semidirect
99. #2599C22semidirect
100. #2596C22semidirect
101. #2594C22semidirect
102. #2590C22semidirect
103. #2590C22semidirect
106. #2584C22semidirect
108. #2581C22semidirect
112. #2571C22semidirect
113. #2568C22semidirect
118. #2552C22semidirect
119. #2550C22semidirect
120. #2547C22semidirect
123. #2524C22semidirect
124. #2524C22semidirect
128. #2519C22semidirect
132. #2514C22semidirect
133. #2514C22semidirect
134. #2511C22semidirect
138. #2508C22semidirect
139. #2508C22semidirect
140. #2508C22semidirect
141. #2506C22semidirect
142. #2506C22semidirect
148. #2496C22semidirect
153. #2494C22semidirect
157. #2489C22semidirect
161. #2474C22semidirect
168. #2462C22semidirect
171. #2453C22semidirect
172. #2451C22semidirect
175. #2448C22semidirect
180. #2440C22semidirect
182. #2429C22semidirect
190. #2417C22semidirect
197. #2382C22semidirect
198. #2378C22semidirect
199. #2365C22semidirect
200. #2365C22semidirect
201. #2365C22semidirect
202. #2362C22semidirect
207. #2355C22semidirect
208. #2354C22semidirect
211. #2351C22semidirect
212. Q8×C4⋊C4C22semidirect
215. #2347C22semidirect
223. #2344C22semidirect
224. #2336C22semidirect
225. #2331C22semidirect
226. #2330C22semidirect
231. #2323C22semidirect
232. #2323C22semidirect
233. #2323C22semidirect
234. #2320C22semidirect
235. #2320C22semidirect
237. #2316C22semidirect
238. #2314C22semidirect

Maximal subgroups

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

subgroupindex
#506162
#505482
#495102
#494182
#453412
#453312
#452352
#452102
#451702
#451222
#449842
#449772
#397992
#397512
#396792
#396142
#394772
#367822
#365862
#365522
#365462
#352312
#350142
#350122
#349962
#345702
#344642
C2×#23452