Finite Group Databasebeta

← #7641889

Subgroups — #7641889

Order 512.

5018 conjugacy classes of subgroups.

The subgroup lattice has 1441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37527C214yesmaximal, complemented
2#37527C214yesmaximal, complemented
3#37522C211yesmaximal, characteristic, complemented
4#37520C211yesmaximal, characteristic, complemented
5#37512C212yesmaximal, complemented
6#37481C211yesmaximal, characteristic, complemented
7#37469C214yesmaximal, complemented
8#37467C214yesmaximal, complemented
9#37455C211yesmaximal, characteristic, complemented
10#37445C212yesmaximal, complemented
11#35309C211yesmaximal, characteristic, complemented
12#35269C212yesmaximal, complemented
13#35259C211yesmaximal, characteristic, complemented
14#35205C212yesmaximal, complemented
15#35163C212yesmaximal, complemented
16#35161C212yesmaximal, complemented
17#35156C212yesmaximal, complemented
18#35072C214yesmaximal, complemented
19#35070C214yesmaximal, complemented
20#35049C214yesmaximal, complemented
21#35047C212yesmaximal, complemented
22#35045C212yesmaximal, complemented
23#35040C214yesmaximal, complemented
24#35038C212yesmaximal, complemented
25#35036C212yesmaximal, complemented
26C4×#525C212yesmaximal, complemented
27C4×#525C211yesmaximal, characteristic, complemented
28C2×#541C2211yescharacteristic, complemented
29C2×#540C2211yescharacteristic, complemented
30C2×#525C2211yescharacteristic
31C2×#525C2212yes—
32C2×C4×#41C2212yes—
33C2×C4×#41C2211yescharacteristic
34C23×C42C2211yescharacteristic
35#2866C2214yescomplemented
36#2865C2214yescomplemented
37#2864C2214yescomplemented
38#2863C2212yescomplemented
39#2861C2212yescomplemented
40#2860C2214yescomplemented
41#2860C2212yescomplemented
42#2859C2212yescomplemented
43#2857C2211yescharacteristic, complemented
44#2856C2211yescharacteristic, complemented
45#2855C2212yescomplemented
46#2854C2214yescomplemented
47#2854C2212yescomplemented
48#2853C2214yescomplemented
49#2852C2214yescomplemented
50#2851C2214yescomplemented
51#2851C2211yescharacteristic, complemented
52#2851C2211yescharacteristic, complemented
53#2842C2214yes—
54#2839C2214yescomplemented
55#2837C2214yescomplemented
56#2831C2214yescomplemented
57#2829C2214yescomplemented
58#2812C2214yes—
59#2812C2214yes—
60#2812C2214yes—
61#2667C2214yes—
62#2667C2214yes—
63#2663C2214yes—
64#2661C2214yes—
65#2652C2214yes—
66#2652C2214yes—
67#2652C2214yes—
68#2652C2214yes—
69#2649C2214yes—
70#2649C2214yes—
71#2649C2214yes—
72#2649C2214yes—
73#2648C2214yes—
74#2648C2214yes—
75#2648C2214yes—
76#2648C2214yes—
77#2638C2214yes—
78#2636C2214yes—
79#2636C2214yes—
80#2636C2214yes—
81#2636C2214yes—
82#2635C2214yes—
83#2635C2214yes—
84#2635C2214yes—
85#2633C2214yes—
86#2633C2214yes—
87#2630C2214yes—
88#2630C2214yes—
89#2630C2214yes—
90#2630C2214yes—
91#2630C2214yes—
92#2630C2214yes—
93#2629C2212yes—
94#2629C2211yescharacteristic
95#2629C2211yescharacteristic
96#2625C2212yes—
97#2624C2212yes—
98#2621C2211yescharacteristic
99#2620C2212yes—
100#2619C2211yescharacteristic
101#2616C2212yes—
102#2615C2212yes—
103#2608C2214yes—
104#2602C2214yes—
105#2602C2214yes—
106#2600C2214yes—
107#2596C2214yescomplemented
108#2595C2214yescomplemented
109#2590C2214yescomplemented
110#2587C2214yescomplemented
111#2585C2214yescomplemented
112#2578C2214yescomplemented
113#2575C2214yescomplemented
114#2574C2214yescomplemented
115#2559C2214yescomplemented
116#2558C2214yescomplemented
117#2554C2214yescomplemented
118#2553C2214yescomplemented
119#2533C2214yescomplemented
120#2530C2214yescomplemented
121#2529C2214yescomplemented
122#2526C2214yescomplemented
123#2525C2214yescomplemented
124#2522C2214yescomplemented
125#2519C2214yescomplemented
126#2518C2214yes—
127#2518C2214yes—
128#2518C2214yes—
129#2518C2214yes—
130#2517C2214yes—
131#2517C2214yes—
132#2515C2214yescomplemented
133#2512C2212yescomplemented
134#2511C2212yescomplemented
135#2509C2212yescomplemented
136#2508C2212yescomplemented
137#2500C2212yes—
138#2499C2212yes—
139#2497C2212yescomplemented
140#2496C2212yescomplemented
141#2490C2212yescomplemented
142#2489C2212yescomplemented
143#2485C2212yes—
144#2485C2212yes—
145#2479C2214yescomplemented
146#2476C2214yescomplemented
147#2475C2214yescomplemented
148#2470C2214yescomplemented
149#2468C2214yescomplemented
150#2467C2214yes—
151#2467C2214yes—
152#2467C2214yes—
153#2467C2214yes—
154#2466C2214yes—
155#2466C2214yes—
156#2466C2214yes—
157#2466C2214yes—
158#2464C2214yescomplemented
159#2462C2214yescomplemented
160#2460C2214yes—
161#2460C2214yes—
162#2460C2214yes—
163#2460C2214yes—
164#2458C2214yescomplemented
165#2456C2214yes—
166#2456C2214yes—
167#2456C2214yes—
168#2456C2214yes—
169#2455C2214yes—
170#2455C2214yes—
171#2454C2212yescomplemented
172#2453C2212yescomplemented
173#2446C2212yescomplemented
174#2445C2212yescomplemented
175#2441C2212yes—
176#2441C2212yes—
177#2441C2212yes—
178#2441C2212yes—
179#2432C2212yes—
180#2431C2212yes—
181#2427C2212yescomplemented
182#2426C2212yescomplemented
183#2423C2212yescomplemented
184#2422C2212yescomplemented
185#2415C2212yes—
186#2415C2212yes—
187#2414C2212yes—
188#2414C2212yes—
189#2407C2212yes—
190#2407C2212yes—
191#2336C2214yescomplemented
192#2335C2214yescomplemented
193#2335C2214yescomplemented
194#2335C2214yescomplemented
195#2334C2214yescomplemented
196#2334C2214yescomplemented
197#2334C2214yescomplemented
198#2333C2214yescomplemented
199#2330C2212yescomplemented
200#2326C2212yescomplemented
201#2324C2212yescomplemented
202#2323C2212yescomplemented
203#2320C2212yescomplemented
204#2319C2212yescomplemented
205#2314C2211yescharacteristic, complemented
206#2314C2211yescharacteristic, complemented
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C4×C22⋊Q8C2212yes—
210C4×C22⋊Q8C2212yes—
211C4×C22⋊Q8C2212yes—
212C4×C22⋊Q8C2212yes—
213C4×#123C2214yes—
214C4×#123C2214yes—
215C4×#123C2212yes—
216C4×#123C2212yes—
217C4×#121C2212yes—
218C4×#121C2212yes—
219C4×#121C2212yes—
220C4×#121C2212yes—
221C4×#121C2212yes—
222C4×#121C2212yes—
223C4×#120C2214yes—
224C4×#120C2212yes—
225C4×#120C2214yes—
226C4×#120C2212yes—
227#2297C2211yescharacteristic
228#2297C2212yes—
229#2296C2211yescharacteristic
230#2296C2212yes—
231#2290C2212yes—
232#2290C2212yes—
233#2290C2214yes—
234#2290C2214yes—
235#2280C2212yes—
236#2280C2211yescharacteristic
237C42×D4C2214yes—
238C42×D4C2212yes—
239C42×D4C2212yes—
240C42×D4C2214yes—
241C4×#117C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2312yes—
245C24×C4C2312yes—
246C24×C4C2311yescharacteristic
247#541—44no—
248#540—44no—
249C2×C4⋊Q8C2311yescharacteristic
250C2×#127C2311yescharacteristic
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2311yescharacteristic
258C2×#125C2311yescharacteristic
259C2×#125C2314yes—
260C2×#124C2312yes—
261#525—28no—
262#525—216no—
263C2×#123C2311yescharacteristic
264C2×#123C2311yescharacteristic
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#120C2311yescharacteristic
283C2×#120C2311yescharacteristic
284C2×#120C2314yes—
285C4×#41—44no—
286C4×#41—48no—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×#117C2311yescharacteristic
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2312yes—
313C2×#117C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2312yes—
318C22×C42—44no—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321C22×C42C2314yes—
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2312yes—
325C22×C42C2312yes—
326C22×C42C2312yes—
327C22×C42C2312yes—
328C22×C42C2311yescharacteristic
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#395C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#393C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#391C2311yescharacteristic
426#391C2311yescharacteristic
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#390C2311yescharacteristic
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2314yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2312yes—
445#390C2312yes—
446#390C2311yescharacteristic
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2314yes—
511#388C2312yes—
512#388C2314yes—
513#388C2312yes—
514#388C2312yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
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#387C2312yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2312yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2312yes—
568#386C2314yes—
569#386C2312yes—
570#386C2312yes—
571#386C2314yes—
572#386C2312yes—
573#386C2314yes—
574#386C2312yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2312yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#385C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2312yes—
599#384C2311yescharacteristic
600#384C2311yescharacteristic
601#384C2312yes—
602#384C2312yes—
603#383C2314yes—
604#383C2314yes—
605#382C2311yescharacteristic
606#382C2311yescharacteristic
607#382C2314yes—
608#382C2314yes—
609#382C2314yes—
610#382C2314yes—
611#381C2314yes—
612#381C2314yes—
613#381C2312yes—
614#381C2314yes—
615#380C2312yes—
616#380C2312yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2312yes—
621#380C2312yes—
622#380C2314yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#379C2312yes—
630#379C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677#376C2312yes—
678#376C2314yes—
679C43C2312yes—
680C43C2314yes—
681C25C2411yescharacteristic
682C2×#41—28no—
683C2×#41—24no—
684C2×#41—42no—
685C2×#41—42no—
686C2×#41—44no—
687C2×#41—44no—
688C22×Q8C2412yes—
689C22×Q8C2411yescharacteristic
690C22×D4C2412yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2412yes—
694C22×D4C2412yes—
695C22×D4C2414yes—
696C22×D4C2411yescharacteristic
697C22×D4C2411yescharacteristic
698C22×D4C2411yescharacteristic
699C22×D4C2414yes—
700C22×D4C2414yes—
701C22×D4C2414yes—
702C23×C4—42no—
703C23×C4—44no—
704C23×C4—44no—
705C23×C4—42no—
706C23×C4—44no—
707C23×C4#4118yes—
708C23×C4C2411yescharacteristic
709C23×C4C2411yescharacteristic
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2412yes—
713C23×C4C2412yes—
714C23×C4C2411yescharacteristic
715C23×C4C2414yes—
716C23×C4C2412yes—
717C23×C4C2414yes—
718C23×C4C2414yes—
719C23×C4C2412yes—
720C23×C4C2412yes—
721C23×C4C2412yes—
722C23×C4C2412yes—
723C23×C4C2411yescharacteristic
724C23×C4C2412yes—
725C4⋊Q8—42no—
726#127—42no—
727#126—48no—
728#126—48no—
729#126—48no—
730#126—48no—
731#125—44no—
732#125—48no—
733#125—42no—
734#125—42no—
735#125—48no—
736#124—44no—
737#123—24no—
738#123—24no—
739#123—216no—
740#123—48no—
741#123—48no—
742#123—48no—
743#123—48no—
744C22⋊Q8—28no—
745C22⋊Q8—28no—
746C22⋊Q8—28no—
747C22⋊Q8—44no—
748C22⋊Q8—44no—
749#121—28no—
750#121—28no—
751#121—28no—
752#121—48no—
753#121—48no—
754#121—44no—
755#121—44no—
756#120—24no—
757#120—24no—
758#120—216no—
759C4×Q8—28no—
760C4×Q8—44no—
761C4×Q8—44no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—216no—
765C4×D4—216no—
766C4×D4—28no—
767C4×D4—44no—
768C4×D4—44no—
769C4×D4—44no—
770C4×D4—44no—
771C4×D4—48no—
772C4×D4—48no—
773C4×D4—48no—
774C4×D4—48no—
775C4×D4—44no—
776C4×D4—48no—
777C4×D4—44no—
778C4×D4—44no—
779C4×D4—44no—
780C4×D4—48no—
781#117—28no—
782#117—24no—
783#117—24no—
784#117—24no—
785#117—42no—
786#117—42no—
787#117—48no—
788#117—44no—
789#117—44no—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2411yescharacteristic
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C42—28no—
891C2×C42—24no—
892C2×C42—42no—
893C2×C42—42no—
894C2×C42—48no—
895C2×C42—44no—
896C2×C42—44no—
897C2×C42—44no—
898C2×C42—44no—
899C2×C42—42no—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929#95C2412yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983C24—41no—
984C24—41no—
985C24—42no—
986C24—42no—
987C24C2×#4114yes—
988C24C2511yescharacteristic
989C24C2511yescharacteristic
990C24C2514yes—
991C24C2511yescharacteristic
992C24C2512yes—
993#41—432no—
994#41—416no—
995C2×Q8—22no—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—41no—
1000C2×Q8—41no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—28no—
1004C2×D4—28no—
1005C2×D4—28no—
1006C2×D4—22no—
1007C2×D4—22no—
1008C2×D4—22no—
1009C2×D4—24no—
1010C2×D4—24no—
1011C2×D4—24no—
1012C2×D4—41no—
1013C2×D4—44no—
1014C2×D4—41no—
1015C2×D4—41no—
1016C2×D4—42no—
1017C2×D4—44no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—42no—
1023C2×D4—44no—
1024C2×D4—41no—
1025C2×D4—41no—
1026C2×D4—44no—
1027C2×D4—41no—
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—
1037C22×C4—24no—
1038C22×C4—22no—
1039C22×C4—24no—
1040C22×C4—22no—
1041C22×C4—28no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—22no—
1056C22×C4—22no—
1057C22×C4—28no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—28no—
1061C22×C4—416no—
1062C22×C4—41no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—41no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—432no—
1086C22×C4C2×#4118yes—
1087C22×C4C2×#4114yes—
1088C22×C4C2×#4114yes—
1089C22×C4C2×#4118yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2511yescharacteristic
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—41no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C22⋊C4—28no—
1160C22⋊C4—22no—
1161C22⋊C4—22no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—42no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—42no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C42—28no—
1213C42—24no—
1214C42—24no—
1215C42—22no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—22no—
1220C42—22no—
1221C42—28no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—28no—
1226C42—42no—
1227C42—41no—
1228C42—42no—
1229C42—41no—
1230C42—44no—
1231C42—42no—
1232C42—42no—
1233C42—44no—
1234C42—44no—
1235C42—42no—
1236C42—44no—
1237C42—44no—
1238C42—42no—
1239C42—44no—
1240C42H(5,𝔽2)14yes—
1241C23—21no—
1242C23—22no—
1243C23—21no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—24no—
1252C23—21no—
1253C23—21no—
1254C23—21no—
1255C23—21no—
1256C23—24no—
1257C23—22no—
1258C23—24no—
1259C23—22no—
1260C23—24no—
1261C23—24no—
1262C23—21no—
1263C23—22no—
1264C23—24no—
1265C23—24no—
1266C23—22no—
1267C23—21no—
1268C23—44no—
1269C23—48no—
1270C23—48no—
1271C23—44no—
1272C23—44no—
1273C23C22×#4114yes—
1274C23C22×#4112yes—
1275C23C2611yescharacteristic
1276Q8—44no—
1277Q8—48no—
1278D4—44no—
1279D4—48no—
1280D4—416no—
1281D4—48no—
1282D4—416no—
1283D4—416no—
1284D4—44no—
1285D4—44no—
1286D4—48no—
1287D4—164no—
1288D4—164no—
1289D4—164no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—216no—
1301C2×C4—28no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—44no—
1351C2×C4—48no—
1352C2×C4—48no—
1353C2×C4—48no—
1354C2×C4—48no—
1355C2×C4—48no—
1356C2×C4—48no—
1357C2×C4—48no—
1358C2×C4—416no—
1359C2×C4—44no—
1360C2×C4—44no—
1361C2×C4—88no—
1362C2×C4—84no—
1363C2×C4—88no—
1364C2×C4—84no—
1365C2×C4C22×#4114yes—
1366C2×C4C22×#4112yes—
1367C2×C4C22×#4112yes—
1368C2×C4C2×H(5,𝔽2)14yes—
1369C2×C4C2×H(5,𝔽2)12yes—
1370C2×C4#58514yes—
1371C2×C4#58514yes—
1372C2×C4#58512yes—
1373C22—24no—
1374C22—22no—
1375C22—24no—
1376C22—24no—
1377C22—24no—
1378C22—416no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—41no—
1383C22—42no—
1384C22—41no—
1385C22—42no—
1386C22—42no—
1387C22—44no—
1388C22—44no—
1389C22—42no—
1390C22—41no—
1391C22—44no—
1392C22—41no—
1393C22—41no—
1394C22—44no—
1395C22—41no—
1396C22—44no—
1397C22—41no—
1398C22—41no—
1399C22—42no—
1400C22—44no—
1401C22—42no—
1402C22—44no—
1403C22C23×#4111yescharacteristic
1404C22C22×H(5,𝔽2)11yescharacteristic
1405C22C2×#58512yes—
1406C22C2×#58512yes—
1407C22C2×#58511yescharacteristic
1408C4—24no—
1409C4—24no—
1410C4—24no—
1411C4—24no—
1412C4—22no—
1413C4—42no—
1414C4—42no—
1415C4—44no—
1416C4—44no—
1417C4—42no—
1418C4—42no—
1419C4—44no—
1420C4—44no—
1421C4—42no—
1422C4—44no—
1423C4—41no—
1424C4—41no—
1425C4—42no—
1426C4—44no—
1427C4—42no—
1428C4—44no—
1429C4#345914yes—
1430C2—44no—
1431C2—42no—
1432C2—81no—
1433C2—84no—
1434C2—81no—
1435C2C2×#345911yescharacteristic
1436C2#6268612yes—
1437C2#6282112yes—
1438C2#6283911yescharacteristic
1439C2#6284011yescharacteristic
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. #37527C2semidirect
2. #37527C2semidirect
3. #37522C2semidirect
4. #37520C2semidirect
5. #37512C2semidirect
6. #37481C2semidirect
7. #37469C2semidirect
8. #37467C2semidirect
9. #37455C2semidirect
10. #37445C2semidirect
11. #35309C2semidirect
12. #35269C2semidirect
13. #35259C2semidirect
14. #35205C2semidirect
15. #35163C2semidirect
16. #35161C2semidirect
17. #35156C2semidirect
18. #35072C2semidirect
19. #35070C2semidirect
20. #35049C2semidirect
21. #35047C2semidirect
22. #35045C2semidirect
23. #35040C2semidirect
24. #35038C2semidirect
25. #35036C2semidirect
26. C4×#525C2semidirect
27. C4×#525C2semidirect
28. C2×#541C22semidirect
29. C2×#540C22semidirect
35. #2866C22semidirect
36. #2865C22semidirect
37. #2864C22semidirect
38. #2863C22semidirect
39. #2861C22semidirect
40. #2860C22semidirect
41. #2860C22semidirect
42. #2859C22semidirect
43. #2857C22semidirect
44. #2856C22semidirect
45. #2855C22semidirect
46. #2854C22semidirect
47. #2854C22semidirect
48. #2853C22semidirect
49. #2852C22semidirect
50. #2851C22semidirect
51. #2851C22semidirect
52. #2851C22semidirect
54. #2839C22semidirect
55. #2837C22semidirect
56. #2831C22semidirect
57. #2829C22semidirect
107. #2596C22semidirect
108. #2595C22semidirect
109. #2590C22semidirect
110. #2587C22semidirect
111. #2585C22semidirect
112. #2578C22semidirect
113. #2575C22semidirect
114. #2574C22semidirect
115. #2559C22semidirect
116. #2558C22semidirect
117. #2554C22semidirect
118. #2553C22semidirect
119. #2533C22semidirect
120. #2530C22semidirect
121. #2529C22semidirect
122. #2526C22semidirect
123. #2525C22semidirect
124. #2522C22semidirect
125. #2519C22semidirect
132. #2515C22semidirect
133. #2512C22semidirect
134. #2511C22semidirect
135. #2509C22semidirect
136. #2508C22semidirect
139. #2497C22semidirect
140. #2496C22semidirect
141. #2490C22semidirect
142. #2489C22semidirect
145. #2479C22semidirect
146. #2476C22semidirect
147. #2475C22semidirect
148. #2470C22semidirect
149. #2468C22semidirect
158. #2464C22semidirect
159. #2462C22semidirect
164. #2458C22semidirect
171. #2454C22semidirect
172. #2453C22semidirect
173. #2446C22semidirect
174. #2445C22semidirect
181. #2427C22semidirect
182. #2426C22semidirect
183. #2423C22semidirect
184. #2422C22semidirect
191. #2336C22semidirect
192. #2335C22semidirect
193. #2335C22semidirect
194. #2335C22semidirect
195. #2334C22semidirect
196. #2334C22semidirect
197. #2334C22semidirect
198. #2333C22semidirect
199. #2330C22semidirect
200. #2326C22semidirect
201. #2324C22semidirect
202. #2323C22semidirect
203. #2320C22semidirect
204. #2319C22semidirect
205. #2314C22semidirect
206. #2314C22semidirect

Maximal subgroups

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

subgroupindex
#375272
#375222
#375202
#375122
#374812
#374692
#374672
#374552
#374452
#353092
#352692
#352592
#352052
#351632
#351612
#351562
#350722
#350702
#350492
#350472
#350452
#350402
#350382
#350362
C4×#5252