Finite Group Databasebeta

← #7678970

Subgroups — #7678970

Order 512.

4634 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59904C212yesmaximal, complemented
2#59567C212yesmaximal, complemented
3#59355C214yesmaximal, complemented
4#59347C214yesmaximal, complemented
5#59330C212yesmaximal, complemented
6#59064C212yesmaximal
7#45436C211yesmaximal, characteristic, complemented
8#45431C211yesmaximal, characteristic, complemented
9#45231C211yesmaximal, characteristic, complemented
10#45221C211yesmaximal, characteristic, complemented
11#45221C211yesmaximal, characteristic, complemented
12#45137C211yesmaximal, characteristic, complemented
13#45083C211yesmaximal, characteristic, complemented
14#44947C211yesmaximal, characteristic, complemented
15#43519C214yesmaximal, complemented
16#43517C214yesmaximal, complemented
17#40312C214yesmaximal, complemented
18#38712C214yesmaximal, complemented
19#38418C214yesmaximal, complemented
20#36358C214yesmaximal, complemented
21#35656C212yesmaximal, complemented
22#35632C212yesmaximal, complemented
23#35206C212yesmaximal, complemented
24#35200C211yesmaximal, characteristic, complemented
25#34979C211yesmaximal, characteristic, complemented
26#34878C211yesmaximal, characteristic, complemented
27#34329C212yesmaximal, complemented
28#34221C211yesmaximal, characteristic, complemented
29#34195C211yesmaximal, characteristic, complemented
30#34123C211yesmaximal, characteristic, complemented
31#34070C211yesmaximal, characteristic
32C2×#559C2212yes—
33C2×#533C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37#2855C2214yes—
38#2851C2214yes—
39#2851C2214yes—
40#2782C2214yes—
41#2770C2214yes—
42#2770C2214yes—
43#2769C2214yes—
44#2769C2214yes—
45#2764C2214yes—
46#2762C2214yes—
47#2758C2214yes—
48#2750C2214yes—
49#2748C2214yes—
50#2747C2214yes—
51#2747C2214yes—
52#2747C2214yes—
53#2747C2214yes—
54#2746C2214yes—
55#2738C2214yes—
56#2728C2214yes—
57#2717C2214yes—
58#2717C2214yes—
59#2708C2214yes—
60#2708C2214yes—
61#2692C2214yes—
62#2690C2214yes—
63#2690C2214yes—
64#2652C2214yes—
65#2652C2214yes—
66#2638C2212yes—
67#2638C2212yes—
68#2612C2212yes—
69#2612C2214yes—
70#2612C2212yes—
71#2612C2214yes—
72#2611C2212yes—
73#2611C2214yes—
74#2611C2212yes—
75#2606C2212yes—
76#2605C2212yes—
77#2605C2214yes—
78#2599C2212yes—
79#2599C2212yes—
80#2590C2214yes—
81#2588C2214yes—
82#2581C2212yes—
83#2580C2212yes—
84#2578C2214yes—
85#2578C2214yes—
86#2577C2214yes—
87#2577C2214yes—
88#2576C2214yes—
89#2575C2214yes—
90#2575C2214yes—
91#2573C2214yes—
92#2570C2212yes—
93#2570C2212yes—
94#2569C2214yes—
95#2569C2212yes—
96#2569C2214yes—
97#2568C2212yes—
98#2568C2212yes—
99#2568C2211yescharacteristic
100#2568C2212yes—
101#2567C2211yescharacteristic
102#2564C2214yes—
103#2563C2211yescharacteristic
104#2552C2212yes—
105#2549C2212yes—
106#2547C2212yes—
107#2547C2211yescharacteristic
108#2547C2211yescharacteristic
109#2547C2212yes—
110#2546C2212yes—
111#2546C2211yescharacteristic
112#2546C2211yescharacteristic
113#2542C2211yescharacteristic
114#2538C2212yes—
115#2533C2214yes—
116#2533C2214yes—
117#2533C2214yes—
118#2530C2214yes—
119#2530C2214yes—
120#2530C2214yes—
121#2530C2214yes—
122#2528C2214yes—
123#2528C2214yes—
124#2528C2214yes—
125#2527C2214yes—
126#2527C2214yes—
127#2527C2214yes—
128#2524C2214yes—
129#2524C2214yes—
130#2523C2214yes—
131#2520C2214yes—
132#2520C2214yes—
133#2517C2214yes—
134#2515C2214yes—
135#2515C2214yes—
136#2515C2214yes—
137#2514C2212yes—
138#2514C2212yes—
139#2511C2212yes—
140#2511C2212yes—
141#2511C2212yes—
142#2511C2212yes—
143#2505C2214yes—
144#2505C2214yes—
145#2499C2212yes—
146#2499C2212yes—
147#2495C2214yes—
148#2493C2214yes—
149#2493C2214yes—
150#2493C2214yes—
151#2489C2214yes—
152#2485C2214yes—
153#2477C2214yes—
154#2450C2214yes—
155#2447C2212yes—
156#2447C2214yes—
157#2447C2212yes—
158#2447C2212yes—
159#2447C2212yes—
160#2446C2212yes—
161#2446C2212yes—
162#2438C2214yes—
163#2438C2212yes—
164#2438C2212yes—
165#2432C2212yes—
166#2432C2212yes—
167#2427C2214yes—
168#2420C2214yes—
169#2419C2214yes—
170#2419C2214yes—
171#2419C2214yes—
172#2419C2214yes—
173#2415C2214yes—
174#2402C2211yescharacteristic
175#2402C2211yescharacteristic
176#2399C2211yescharacteristic
177#2399C2211yescharacteristic
178#2395C2212yes—
179#2395C2212yes—
180#2374C2214yes—
181#2372C2214yes—
182#2371C2214yes—
183#2371C2214yes—
184#2368C2214yes—
185#2368C2214yes—
186#2367C2212yes—
187#2367C2212yes—
188#2366C2212yes—
189#2359C2214yes—
190#2357C2212yes—
191#2356C2212yes—
192#2356C2211yescharacteristic
193#2356C2211yescharacteristic
194#2356C2211yescharacteristic
195#2356C2211yescharacteristic
196#2356C2214yes—
197#2355C2212yes—
198#2354C2212yes—
199#2353C2214yes—
200#2353C2212yes—
201#2353C2212yes—
202#2353C2212yes—
203#2353C2212yes—
204#2349C2214yes—
205#2349C2211yescharacteristic
206#2349C2211yescharacteristic
207#2349C2211yescharacteristic
208#2349C2211yescharacteristic
209#2347C2212yes—
210#2346C2212yes—
211#2343C2214yes—
212#2343C2214yes—
213#2343C2214yes—
214#2343C2214yes—
215#2339C2212yes—
216#2339C2212yes—
217#2337C2214yes—
218#2335C2214yes—
219#2331C2211yescharacteristic
220#2331C2211yescharacteristic
221#2328C2211yescharacteristic
222#2328C2211yescharacteristic
223#2327C2211yescharacteristic
224#2327C2211yescharacteristic
225#2327C2212yes—
226#2327C2211yescharacteristic
227#2327C2211yescharacteristic
228#2326C2211yescharacteristic
229#2326C2211yescharacteristic
230#2326C2211yescharacteristic
231#2326C2211yescharacteristic
232#2326C2212yes—
233#2325C2214yes—
234#2325C2214yes—
235#2320C2212yes—
236#2320C2212yes—
237#2318C2214yes—
238C4×C4⋊Q8C2212yes—
239C4×#124C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2214yes—
244C4×C22⋊Q8C2212yes—
245C4×#123C2214yes—
246#2297C2211yescharacteristic
247#2297C2211yescharacteristic
248#2295C2212yes—
249#2295C2212yes—
250#2295C2212yes—
251#2290C2214yes—
252#2290C2214yes—
253#2290C2214yes—
254#2290C2214yes—
255#2285C2211yescharacteristic
256#2283C2212yes—
257#2283C2211yescharacteristic
258#2283C2211yescharacteristic
259#2283C2212yes—
260C2×#383C2212yes—
261#2276C2212yes—
262#2275C2212yes—
263C42×D4C2212yes—
264C4×#117C2211yescharacteristic
265C2×#376C2212yes—
266C2×#376C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269#559—216no—
270#533—28no—
271#532—28no—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×#127C2311yescharacteristic
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#124C2311yescharacteristic
281C2×#124C2311yescharacteristic
282C2×#124C2312yes—
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×#121C2314yes—
294C4×#41—28no—
295C4×#41—28no—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2314yes—
327C2×#117C2312yes—
328C22×C42C2312yes—
329C22×C42C2312yes—
330C22×C42C2311yescharacteristic
331C22×C42C2314yes—
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334#401C2314yes—
335#401C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#399C2312yes—
364#399C2314yes—
365#399C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#396C2314yes—
407#396C2314yes—
408#395C2312yes—
409#395C2312yes—
410#395C2312yes—
411#395C2314yes—
412#395C2312yes—
413#395C2312yes—
414#395C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#393C2312yes—
420#393C2312yes—
421#393C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2311yescharacteristic
427#391C2311yescharacteristic
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#390C2312yes—
452#390C2311yescharacteristic
453#390C2312yes—
454#390C2311yescharacteristic
455#390C2311yescharacteristic
456#390C2311yescharacteristic
457#390C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
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#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2312yes—
508#387C2312yes—
509#387C2312yes—
510#387C2312yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2312yes—
519#387C2312yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2312yes—
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#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2312yes—
579#385C2312yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2312yes—
604#384C2312yes—
605#384C2312yes—
606#384C2311yescharacteristic
607#384C2311yescharacteristic
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#383C2314yes—
614#383C2312yes—
615#383C2311yescharacteristic
616#383C2311yescharacteristic
617#383C2312yes—
618#383C2312yes—
619#383C2312yes—
620#383C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2314yes—
624#382C2314yes—
625#382C2314yes—
626#382C2311yescharacteristic
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#382C2311yescharacteristic
631#382C2311yescharacteristic
632#382C2311yescharacteristic
633#382C2312yes—
634#381C2314yes—
635#381C2312yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2311yescharacteristic
642#381C2311yescharacteristic
643#381C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2314yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711#376C2311yescharacteristic
712#376C2312yes—
713#376C2311yescharacteristic
714#376C2311yescharacteristic
715#376C2311yescharacteristic
716#376C2314yes—
717#376C2312yes—
718#376C2314yes—
719#376C2312yes—
720#376C2312yes—
721#376C2312yes—
722#376C2312yes—
723#376C2312yes—
724#376C2311yescharacteristic
725#376C2311yescharacteristic
726#376C2314yes—
727#376C2312yes—
728#376C2314yes—
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2312yes—
732C2×#95C2314yes—
733C2×#95C2312yes—
734C2×#95C2314yes—
735C2×#95C2314yes—
736C2×#95C2312yes—
737C2×#95C2312yes—
738C43C2312yes—
739C2×#41—24no—
740C2×#41—24no—
741C2×#41—24no—
742C2×#41—24no—
743C2×#41—42no—
744C2×#41—42no—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2412yes—
750C22×Q8C2412yes—
751C22×D4C2412yes—
752C22×D4C2412yes—
753C22×D4C2411yescharacteristic
754C22×D4C2411yescharacteristic
755C22×D4C2414yes—
756C23×C4C2412yes—
757C23×C4C2412yes—
758C23×C4C2411yescharacteristic
759C23×C4C2414yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2412yes—
764C23×C4C2412yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2414yes—
768C23×C4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C4⋊Q8—24no—
772C4⋊Q8—24no—
773C4⋊Q8—24no—
774C4⋊Q8—44no—
775C4⋊Q8—44no—
776#127#4118yes—
777#125—28no—
778#125—48no—
779#124—24no—
780#124—24no—
781#124—28no—
782#124—28no—
783#124—216no—
784#123—216no—
785#123—216no—
786C22⋊Q8—28no—
787C22⋊Q8—28no—
788C22⋊Q8—48no—
789C22⋊Q8—44no—
790C22⋊Q8—44no—
791C22⋊Q8—48no—
792#121—216no—
793C4×Q8—24no—
794C4×Q8—24no—
795C4×Q8—24no—
796C4×Q8—24no—
797C4×Q8—28no—
798C4×Q8—28no—
799C4×Q8—28no—
800C4×Q8—28no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×D4—216no—
804C4×D4—28no—
805C4×D4—28no—
806C4×D4—216no—
807C4×D4—28no—
808C4×D4—28no—
809C4×D4—28no—
810C4×D4—28no—
811C4×D4—24no—
812C4×D4—24no—
813C4×D4—24no—
814C4×D4—24no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—48no—
818#117—24no—
819#117—24no—
820#117—28no—
821#117—28no—
822#117—28no—
823#117—44no—
824#117—48no—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C42—28no—
913C2×C42—28no—
914C2×C42—24no—
915C2×C42—48no—
916C2×C42—42no—
917C2×C42#4118yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952#95C2412yes—
953#95C2411yescharacteristic
954#95C2411yescharacteristic
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2411yescharacteristic
959#95C2411yescharacteristic
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2411yescharacteristic
984#95C2411yescharacteristic
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2411yescharacteristic
991#95C2411yescharacteristic
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040C24C2512yes—
1041C24C2512yes—
1042C24C2511yescharacteristic
1043#41—416no—
1044#41—416no—
1045C2×Q8—22no—
1046C2×Q8—22no—
1047C2×Q8—24no—
1048C2×Q8—24no—
1049C2×Q8—22no—
1050C2×Q8—22no—
1051C2×Q8—24no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—22no—
1055C2×Q8—22no—
1056C2×Q8—24no—
1057C2×Q8—42no—
1058C2×Q8—42no—
1059C2×Q8—44no—
1060C2×Q8—42no—
1061C2×Q8—42no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—24no—
1065C2×D4—24no—
1066C2×D4—22no—
1067C2×D4—22no—
1068C2×D4—22no—
1069C2×D4—22no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4C2×#4114yes—
1075C2×D4C2×#4114yes—
1076C2×D4C2×#41116yes—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—28no—
1082C22×C4—28no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—28no—
1091C22×C4—44no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—44no—
1102C22×C4—42no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—42no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4C2×#4114yes—
1114C22×C4C2×#4114yes—
1115C22×C4C2×#4114yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C4⋊C4—22no—
1145C4⋊C4—22no—
1146C4⋊C4—22no—
1147C4⋊C4—22no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—28no—
1157C4⋊C4—28no—
1158C4⋊C4—28no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—24no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—24no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C42—24no—
1232C42—24no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—24no—
1237C42—24no—
1238C42—22no—
1239C42—28no—
1240C42—28no—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—28no—
1245C42—22no—
1246C42—22no—
1247C42—24no—
1248C42—24no—
1249C42—44no—
1250C42—42no—
1251C42—44no—
1252C42—42no—
1253C42—42no—
1254C42—44no—
1255C42—44no—
1256C42—42no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42C2×#4114yes—
1261C42C2×#4114yes—
1262C42C2×#4114yes—
1263C42C2×#4114yes—
1264C42C2×#4114yes—
1265C23—22no—
1266C23—22no—
1267C23—21no—
1268C23—22no—
1269C23—24no—
1270C23—24no—
1271C23—22no—
1272C23—22no—
1273C23—21no—
1274C23—22no—
1275C23—24no—
1276C23—24no—
1277C23C22×#4114yes—
1278C23C22×#4114yes—
1279C23C22×#4112yes—
1280C23C2611yescharacteristic
1281Q8—48no—
1282Q8—44no—
1283Q8—44no—
1284Q8—84no—
1285Q8—84no—
1286Q8—84no—
1287D4—28no—
1288D4—28no—
1289D4—416no—
1290D4—48no—
1291D4—48no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—28no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—44no—
1360C2×C4—44no—
1361C2×C4—48no—
1362C2×C4—48no—
1363C2×C4—48no—
1364C2×C4—84no—
1365C2×C4—84no—
1366C2×C4—84no—
1367C2×C4—84no—
1368C2×C4—88no—
1369C2×C4—88no—
1370C2×C4—88no—
1371C2×C4—84no—
1372C2×C4—164no—
1373C2×C4C22×#4112yes—
1374C2×C4C22×#4112yes—
1375C2×C4C22×#4114yes—
1376C2×C4C22×#4112yes—
1377C2×C4C22×#4112yes—
1378C2×C4C22×#4112yes—
1379C2×C4C22×#4112yes—
1380C2×C4C22×#4112yes—
1381C2×C4#58514yes—
1382C2×C4#58512yes—
1383C22—28no—
1384C22—28no—
1385C22—22no—
1386C22—22no—
1387C22—22no—
1388C22—24no—
1389C22—24no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—44no—
1396C22—42no—
1397C22—44no—
1398C22C23×#4111yescharacteristic
1399C22C23×#4111yescharacteristic
1400C22C2×#58512yes—
1401C22C2×#58511yescharacteristic
1402C222−1+612yes—
1403C4—24no—
1404C4—22no—
1405C4—22no—
1406C4—22no—
1407C4—22no—
1408C4—24no—
1409C4—22no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4—44no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—44no—
1430C4#347514yes—
1431C2—44no—
1432C2—44no—
1433C2—42no—
1434C2C2×#347511yescharacteristic
1435C2#6281511yescharacteristic
1436C2#6286011yescharacteristic
1437C2#6294012yes—
1438C2#6299112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59904C2semidirect
2. #59567C2semidirect
3. #59355C2semidirect
4. #59347C2semidirect
5. #59330C2semidirect
7. #45436C2semidirect
8. #45431C2semidirect
9. #45231C2semidirect
10. #45221C2semidirect
11. #45221C2semidirect
12. #45137C2semidirect
13. #45083C2semidirect
14. #44947C2semidirect
15. #43519C2semidirect
16. #43517C2semidirect
17. #40312C2semidirect
18. #38712C2semidirect
19. #38418C2semidirect
20. #36358C2semidirect
21. #35656C2semidirect
22. #35632C2semidirect
23. #35206C2semidirect
24. #35200C2semidirect
25. #34979C2semidirect
26. #34878C2semidirect
27. #34329C2semidirect
28. #34221C2semidirect
29. #34195C2semidirect
30. #34123C2semidirect

Maximal subgroups

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

subgroupindex
#599042
#595672
#593552
#593472
#593302
#590642
#454362
#454312
#452312
#452212
#451372
#450832
#449472
#435192
#435172
#403122
#387122
#384182
#363582
#356562
#356322
#352062
#352002
#349792
#348782
#343292
#342212
#341952
#341232
#340702