Finite Group Databasebeta

← #7681635

Subgroups — #7681635

Order 512.

5277 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#60021C214yesmaximal, complemented
2#59977C214yesmaximal, complemented
3#59620C214yesmaximal, complemented
4#59403C214yesmaximal, complemented
5#44643C214yesmaximal, complemented
6#44632C214yesmaximal, complemented
7#44305C214yesmaximal, complemented
8#44158C214yesmaximal, complemented
9#39739C211yesmaximal, characteristic, complemented
10#39622C211yesmaximal, characteristic, complemented
11#38942C212yesmaximal, complemented
12#38937C212yesmaximal, complemented
13#38936C212yesmaximal, complemented
14#37953C212yesmaximal, complemented
15#37775C212yesmaximal, complemented
16#36493C212yesmaximal, complemented
17#36211C211yesmaximal, characteristic, complemented
18#36136C211yesmaximal, characteristic, complemented
19#35638C212yesmaximal, complemented
20#35571C212yesmaximal, complemented
21#35332C211yesmaximal, characteristic, complemented
22#35303C212yesmaximal, complemented
23#34889C212yesmaximal, complemented
24#34329C212yesmaximal, complemented
25#34220C212yesmaximal, complemented
26#34123C211yesmaximal, characteristic, complemented
27C4×#540C211yesmaximal, characteristic, complemented
28C2×#559C2212yes—
29C2×#541C2211yescharacteristic
30C2×#540C2211yescharacteristic
31C2×#540C2211yescharacteristic
32C2×#532C2212yes—
33C2×#529C2212yes—
34C2×#529C2212yes—
35C2×C4×#41C2211yescharacteristic
36#2859C2211yescharacteristic
37#2858C2211yescharacteristic
38#2856C2212yes—
39#2856C2212yes—
40#2850C2212yes—
41#2850C2212yes—
42#2850C2212yes—
43#2806C2214yes—
44#2792C2214yes—
45#2785C2214yes—
46#2784C2214yes—
47#2784C2214yes—
48#2781C2214yes—
49#2781C2214yes—
50#2781C2214yes—
51#2775C2214yes—
52#2775C2214yes—
53#2756C2214yes—
54#2756C2214yes—
55#2756C2214yes—
56#2756C2214yes—
57#2744C2214yes—
58#2733C2214yes—
59#2714C2214yes—
60#2705C2214yes—
61#2699C2214yes—
62#2699C2214yes—
63#2686C2214yes—
64#2682C2214yes—
65#2682C2214yes—
66#2673C2214yes—
67#2660C2212yes—
68#2657C2212yes—
69#2642C2211yescharacteristic
70#2641C2211yescharacteristic
71#2641C2212yes—
72#2640C2212yes—
73#2620C2212yes—
74#2611C2214yes—
75#2610C2214yes—
76#2610C2214yes—
77#2610C2214yes—
78#2609C2214yes—
79#2603C2214yes—
80#2603C2214yes—
81#2603C2214yes—
82#2602C2214yes—
83#2601C2214yes—
84#2586C2214yes—
85#2572C2214yes—
86#2572C2214yes—
87#2566C2214yes—
88#2559C2214yes—
89#2559C2214yes—
90#2559C2214yes—
91#2558C2214yes—
92#2558C2214yes—
93#2558C2214yes—
94#2557C2214yes—
95#2557C2214yes—
96#2555C2214yes—
97#2554C2214yes—
98#2554C2214yes—
99#2552C2212yes—
100#2550C2212yes—
101#2550C2212yes—
102#2545C2212yes—
103#2544C2212yes—
104#2543C2214yes—
105#2543C2214yes—
106#2543C2214yes—
107#2541C2212yes—
108#2541C2212yes—
109#2540C2212yes—
110#2540C2212yes—
111#2538C2212yes—
112#2537C2214yes—
113#2535C2212yes—
114#2535C2212yes—
115#2532C2214yes—
116#2529C2214yes—
117#2526C2214yes—
118#2521C2214yes—
119#2519C2214yes—
120#2518C2214yes—
121#2513C2214yes—
122#2512C2214yes—
123#2507C2214yes—
124#2500C2214yes—
125#2495C2214yes—
126#2492C2212yes—
127#2491C2212yes—
128#2490C2212yes—
129#2490C2212yes—
130#2490C2212yes—
131#2489C2212yes—
132#2479C2214yes—
133#2474C2214yes—
134#2471C2214yes—
135#2471C2214yes—
136#2471C2214yes—
137#2464C2214yes—
138#2464C2214yes—
139#2459C2214yes—
140#2456C2214yes—
141#2456C2214yes—
142#2456C2214yes—
143#2456C2214yes—
144#2456C2214yes—
145#2456C2214yes—
146#2448C2214yes—
147#2431C2214yes—
148#2431C2214yes—
149#2430C2214yes—
150#2430C2214yes—
151#2430C2214yes—
152#2429C2212yes—
153#2428C2214yes—
154#2428C2214yes—
155#2428C2212yes—
156#2428C2212yes—
157#2428C2212yes—
158#2427C2212yes—
159#2426C2212yes—
160#2420C2214yes—
161#2420C2214yes—
162#2420C2214yes—
163#2414C2214yes—
164#2414C2214yes—
165#2414C2214yes—
166#2395C2214yes—
167#2388C2214yes—
168#2374C2214yes—
169#2373C2214yes—
170#2373C2214yes—
171#2372C2214yes—
172#2367C2212yes—
173#2367C2212yes—
174#2366C2214yes—
175#2366C2212yes—
176#2363C2214yes—
177#2363C2214yes—
178#2363C2214yes—
179#2359C2214yes—
180#2359C2214yes—
181#2359C2214yes—
182#2357C2212yes—
183#2356C2212yes—
184#2356C2212yes—
185#2355C2212yes—
186#2354C2212yes—
187#2353C2212yes—
188#2353C2214yes—
189#2353C2212yes—
190#2353C2214yes—
191#2349C2214yes—
192#2349C2212yes—
193#2346C2214yes—
194#2346C2212yes—
195#2343C2212yes—
196#2343C2212yes—
197#2343C2214yes—
198#2339C2212yes—
199#2337C2214yes—
200#2335C2214yes—
201#2335C2214yes—
202#2333C2214yes—
203#2330C2211yescharacteristic
204#2330C2212yes—
205#2328C2212yes—
206#2328C2211yescharacteristic
207#2326C2212yes—
208#2326C2212yes—
209#2326C2212yes—
210#2324C2212yes—
211#2320C2212yes—
212#2319C2212yes—
213#2319C2212yes—
214#2314C2211yescharacteristic
215C4×#127C2211yescharacteristic
216C4×#125C2211yescharacteristic
217C4×#124C2212yes—
218C4×C22⋊Q8C2212yes—
219C4×C22⋊Q8C2212yes—
220C4×#123C2214yes—
221C4×#123C2214yes—
222C4×#121C2214yes—
223C4×#121C2214yes—
224C4×#121C2212yes—
225C4×#121C2212yes—
226C4×#121C2212yes—
227#2297C2214yes—
228#2295C2211yescharacteristic
229#2295C2211yescharacteristic
230#2290C2214yes—
231#2290C2212yes—
232#2290C2212yes—
233#2285C2212yes—
234#2283C2211yescharacteristic
235#2283C2212yes—
236#2276C2212yes—
237#2275C2212yes—
238C42×D4C2212yes—
239C42×D4C2211yescharacteristic
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×#376C2212yes—
243C22×#41C2311yescharacteristic
244C22×#41C2314yes—
245#559—216no—
246#541—44no—
247#540—28no—
248#540—44no—
249#532—48no—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2312yes—
252C2×#127C2311yescharacteristic
253C2×#127C2312yes—
254C2×#127C2311yescharacteristic
255C2×#127C2314yes—
256C2×#127C2312yes—
257#529—216no—
258#529—48no—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#125C2314yes—
263C2×#125C2311yescharacteristic
264C2×#125C2311yescharacteristic
265C2×#125C2312yes—
266C2×#125C2311yescharacteristic
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2314yes—
270C2×#124C2312yes—
271C2×#124C2314yes—
272C2×#124C2312yes—
273C2×#124C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C4×#41—28no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2312yes—
331C2×#117C2314yes—
332C2×#117C2311yescharacteristic
333C2×#117C2314yes—
334C2×#117C2314yes—
335C2×#117C2314yes—
336C22×C42C2311yescharacteristic
337C22×C42C2312yes—
338C22×C42C2312yes—
339C22×C42C2312yes—
340C22×C42C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
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#394C2314yes—
392#394C2314yes—
393#394C2314yes—
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#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#390C2312yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2314yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2312yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
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#388C2312yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2312yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2314yes—
531#387C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2312yes—
551#386C2312yes—
552#386C2312yes—
553#386C2312yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#385C2312yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2312yes—
575#385C2312yes—
576#385C2312yes—
577#385C2314yes—
578#385C2314yes—
579#384C2311yescharacteristic
580#384C2314yes—
581#384C2312yes—
582#384C2312yes—
583#383C2311yescharacteristic
584#383C2314yes—
585#383C2314yes—
586#383C2311yescharacteristic
587#383C2312yes—
588#383C2312yes—
589#382C2311yescharacteristic
590#382C2314yes—
591#382C2314yes—
592#382C2312yes—
593#382C2312yes—
594#382C2312yes—
595#382C2314yes—
596#382C2312yes—
597#382C2312yes—
598#381C2312yes—
599#381C2314yes—
600#381C2314yes—
601#381C2314yes—
602#381C2312yes—
603#381C2311yescharacteristic
604#381C2311yescharacteristic
605#380C2312yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2312yes—
610#380C2312yes—
611#380C2314yes—
612#380C2312yes—
613#380C2314yes—
614#380C2312yes—
615#380C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2311yescharacteristic
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2312yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664#376C2311yescharacteristic
665#376C2312yes—
666#376C2311yescharacteristic
667#376C2312yes—
668#376C2312yes—
669#376C2312yes—
670#376C2312yes—
671#376C2312yes—
672#376C2314yes—
673#376C2312yes—
674#376C2314yes—
675C2×#95C2312yes—
676C2×#95C2312yes—
677C2×#95C2314yes—
678C2×#95C2312yes—
679C2×#95C2312yes—
680C43C2311yescharacteristic
681C43C2311yescharacteristic
682C2×#41—24no—
683C2×#41—48no—
684C2×#41—44no—
685C2×#41—48no—
686C2×#41—84no—
687C22×Q8C2412yes—
688C22×Q8C2414yes—
689C22×Q8C2411yescharacteristic
690C22×D4C2411yescharacteristic
691C22×D4C2412yes—
692C22×D4C2412yes—
693C22×D4C2414yes—
694C22×D4C2412yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C22×D4C2414yes—
701C22×D4C2414yes—
702C22×D4C2414yes—
703C22×D4C2414yes—
704C22×D4C2414yes—
705C22×D4C2414yes—
706C23×C4C2411yescharacteristic
707C23×C4C2412yes—
708C23×C4C2412yes—
709C23×C4C2412yes—
710C23×C4C2412yes—
711C23×C4C2414yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2411yescharacteristic
715C23×C4C2411yescharacteristic
716C23×C4C2412yes—
717C23×C4C2414yes—
718C23×C4C2412yes—
719C23×C4C2412yes—
720C23×C4C2414yes—
721C23×C4C2414yes—
722C4⋊Q8—44no—
723C4⋊Q8—42no—
724#127—24no—
725#127—28no—
726#127—44no—
727#127—42no—
728#127—48no—
729#126—216no—
730#126—48no—
731#126—48no—
732#125—44no—
733#125—42no—
734#125—42no—
735#125—48no—
736#125#4118yescomplemented
737#124—216no—
738#124—28no—
739#124—28no—
740#124—28no—
741#124—48no—
742#124—44no—
743#124—84no—
744#123—216no—
745#123—216no—
746#123—216no—
747#123—216no—
748#123—48no—
749#123—48no—
750C22⋊Q8—28no—
751C22⋊Q8—44no—
752C22⋊Q8—44no—
753#121—28no—
754#121—216no—
755#121—28no—
756#121—48no—
757#121—48no—
758#121—48no—
759#121—48no—
760#121—44no—
761#121—44no—
762#121—44no—
763#121—44no—
764#121—48no—
765#121—48no—
766#121—84no—
767#121—84no—
768#121—84no—
769#121—84no—
770#121—84no—
771C4×Q8—24no—
772C4×Q8—28no—
773C4×Q8—28no—
774C4×Q8—28no—
775C4×Q8#4118yescomplemented
776C4×D4—28no—
777C4×D4—24no—
778C4×D4—28no—
779C4×D4—216no—
780C4×D4—28no—
781C4×D4—216no—
782C4×D4—24no—
783C4×D4—28no—
784C4×D4—28no—
785C4×D4—28no—
786C4×D4—28no—
787C4×D4—28no—
788C4×D4—48no—
789C4×D4—48no—
790C4×D4—44no—
791C4×D4—44no—
792C4×D4—84no—
793C4×D4—84no—
794C4×D4—84no—
795C4×D4—84no—
796C4×D4—84no—
797#117—28no—
798#117—24no—
799#117—216no—
800#117—24no—
801#117—24no—
802#117—48no—
803#117—84no—
804#117—84no—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
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×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C42—24no—
898C2×C42—28no—
899C2×C42—28no—
900C2×C42—28no—
901C2×C42—84no—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2411yescharacteristic
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2411yescharacteristic
959#95C2411yescharacteristic
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2411yescharacteristic
966#95C2411yescharacteristic
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990C24C2514yes—
991C24C2514yes—
992C24C2511yescharacteristic
993C24C2512yes—
994#41—416no—
995#41—832no—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—42no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—44no—
1003C2×Q8C2×#4114yes—
1004C2×D4—24no—
1005C2×D4—28no—
1006C2×D4—24no—
1007C2×D4—28no—
1008C2×D4—28no—
1009C2×D4—28no—
1010C2×D4—22no—
1011C2×D4—24no—
1012C2×D4—28no—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—28no—
1018C2×D4—28no—
1019C2×D4—28no—
1020C2×D4—28no—
1021C2×D4—24no—
1022C2×D4—24no—
1023C2×D4—44no—
1024C2×D4—42no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—22no—
1056C22×C4—24no—
1057C22×C4—22no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—22no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—22no—
1064C22×C4—28no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—24no—
1068C22×C4—28no—
1069C22×C4—28no—
1070C22×C4—28no—
1071C22×C4—28no—
1072C22×C4—24no—
1073C22×C4—28no—
1074C22×C4—44no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—42no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—44no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4C2511yescharacteristic
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2511yescharacteristic
1120C4⋊C4—24no—
1121C4⋊C4—22no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4C2×#4118yes—
1156C4⋊C4C2×#4114yes—
1157C4⋊C4C2×#41116yes—
1158C4⋊C4C2×#4118yes—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
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—24no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
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—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C42—22no—
1213C42—24no—
1214C42—22no—
1215C42—24no—
1216C42—24no—
1217C42—22no—
1218C42—24no—
1219C42—24no—
1220C42—22no—
1221C42—28no—
1222C42—28no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—22no—
1227C42—28no—
1228C42—42no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—42no—
1235C42—42no—
1236C42—42no—
1237C42—44no—
1238C42—44no—
1239C42C2×#4114yes—
1240C42C2×#4114yes—
1241C42C2×#4118yes—
1242C42H(5,𝔽2)14yes—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—24no—
1250C23—24no—
1251C23—24no—
1252C23—21no—
1253C23—24no—
1254C23—21no—
1255C23—21no—
1256C23—24no—
1257C23—24no—
1258C23—24no—
1259C23—24no—
1260C23—24no—
1261C23—24no—
1262C23—22no—
1263C23—22no—
1264C23—24no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23#58514yes—
1269C23C2611yescharacteristic
1270Q8—44no—
1271Q8—48no—
1272Q8—88no—
1273D4—28no—
1274D4—416no—
1275D4—48no—
1276D4—48no—
1277D4—48no—
1278D4—88no—
1279D4—88no—
1280D4—88no—
1281D4—88no—
1282D4—88no—
1283D4—88no—
1284D4—88no—
1285D4—88no—
1286D4—88no—
1287D4—164no—
1288D4—164no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—48no—
1345C2×C4—48no—
1346C2×C4—48no—
1347C2×C4—44no—
1348C2×C4—416no—
1349C2×C4—48no—
1350C2×C4—44no—
1351C2×C4—84no—
1352C2×C4—88no—
1353C2×C4—88no—
1354C2×C4—88no—
1355C2×C4—82no—
1356C2×C4—88no—
1357C2×C4—84no—
1358C2×C4—84no—
1359C2×C4—88no—
1360C2×C4C22×#4114yes—
1361C2×C4C22×#4114yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4112yes—
1364C2×C4C22×#4114yes—
1365C2×C4C22×#4118yes—
1366C2×C4C22×#4112yes—
1367C2×C4C22×#4112yes—
1368C2×C4C2×H(5,𝔽2)14yes—
1369C2×C4C2×H(5,𝔽2)12yes—
1370C22—24no—
1371C22—24no—
1372C22—24no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22—44no—
1381C22—42no—
1382C22—41no—
1383C22—44no—
1384C22—44no—
1385C22—44no—
1386C22—44no—
1387C22—41no—
1388C22—44no—
1389C22—44no—
1390C22—44no—
1391C22—44no—
1392C22—42no—
1393C22—41no—
1394C22—44no—
1395C22—44no—
1396C22C23×#4111yescharacteristic
1397C22C23×#4111yescharacteristic
1398C22C22×H(5,𝔽2)11yescharacteristic
1399C22C2×#58512yes—
1400C22H(7,𝔽2)12yes—
1401C4—24no—
1402C4—28no—
1403C4—22no—
1404C4—24no—
1405C4—22no—
1406C4—24no—
1407C4—24no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—41no—
1412C4—44no—
1413C4—41no—
1414C4—42no—
1415C4—44no—
1416C4—42no—
1417C4—44no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—41no—
1422C4—44no—
1423C4#348314yes—
1424C2—44no—
1425C2—84no—
1426C2—84no—
1427C2—81no—
1428C2C2×#348311yescharacteristic
1429C2#6281411yescharacteristic
1430C2#6285811yescharacteristic
1431C2#6292412yes—
1432C2#6300812yes—
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. #60021C2semidirect
2. #59977C2semidirect
3. #59620C2semidirect
4. #59403C2semidirect
5. #44643C2semidirect
6. #44632C2semidirect
7. #44305C2semidirect
8. #44158C2semidirect
9. #39739C2semidirect
10. #39622C2semidirect
11. #38942C2semidirect
12. #38937C2semidirect
13. #38936C2semidirect
14. #37953C2semidirect
15. #37775C2semidirect
16. #36493C2semidirect
17. #36211C2semidirect
18. #36136C2semidirect
19. #35638C2semidirect
20. #35571C2semidirect
21. #35332C2semidirect
22. #35303C2semidirect
23. #34889C2semidirect
24. #34329C2semidirect
25. #34220C2semidirect
26. #34123C2semidirect
27. C4×#540C2semidirect
736. #125#41semidirect
775. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#600212
#599772
#596202
#594032
#446432
#446322
#443052
#441582
#397392
#396222
#389422
#389372
#389362
#379532
#377752
#364932
#362112
#361362
#356382
#355712
#353322
#353032
#348892
#343292
#342202
#341232
C4×#5402