Finite Group Databasebeta

← #7645606

Subgroups — #7645606

Order 512.

4468 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42318C214yesmaximal, complemented
2#42208C214yesmaximal, complemented
3#42031C214yesmaximal, complemented
4#41964C214yesmaximal, complemented
5#39766C212yesmaximal, complemented
6#39765C212yesmaximal, complemented
7#38981C212yesmaximal, complemented
8#38980C212yesmaximal, complemented
9#38057C212yesmaximal, complemented
10#38056C212yesmaximal
11#38055C212yesmaximal, complemented
12#38054C212yesmaximal, complemented
13#37581C212yesmaximal, complemented
14#37572C212yesmaximal, complemented
15#37031C212yesmaximal, complemented
16#37026C212yesmaximal, complemented
17#36837C212yesmaximal, complemented
18#36832C212yesmaximal, complemented
19#35379C214yesmaximal, complemented
20#35219C212yesmaximal, complemented
21#35188C212yesmaximal, complemented
22#35131C211yesmaximal, characteristic
23#35111C211yesmaximal, characteristic, complemented
24#35027C214yesmaximal, complemented
25#34966C211yesmaximal, characteristic, complemented
26C2×#2592C211yesmaximal, characteristic, complemented
27#34240C211yesmaximal, characteristic, complemented
28#34153C211yesmaximal, characteristic, complemented
29#34059C211yesmaximal, characteristic, complemented
30C2×#529C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2866C2214yescomplemented
34#2865C2214yescomplemented
35#2861C2212yes—
36#2858C2212yes—
37#2855C2212yes—
38#2854C2212yes—
39#2853C2214yescomplemented
40#2852C2214yescomplemented
41#2838C2214yescomplemented
42#2837C2214yescomplemented
43#2832C2214yescomplemented
44#2831C2214yescomplemented
45#2808C2214yescomplemented
46#2808C2214yescomplemented
47#2804C2214yescomplemented
48#2796C2214yescomplemented
49#2796C2214yescomplemented
50#2788C2214yescomplemented
51#2787C2214yescomplemented
52#2783C2214yescomplemented
53#2777C2214yescomplemented
54#2775C2214yescomplemented
55#2764C2214yescomplemented
56#2763C2214yescomplemented
57#2762C2214yescomplemented
58#2762C2214yescomplemented
59#2761C2214yes—
60#2759C2214yescomplemented
61#2759C2214yescomplemented
62#2758C2214yescomplemented
63#2757C2214yes—
64#2756C2214yes—
65#2755C2214yescomplemented
66#2754C2214yescomplemented
67#2753C2214yes—
68#2751C2214yescomplemented
69#2751C2214yescomplemented
70#2749C2214yes—
71#2745C2214yescomplemented
72#2737C2214yes—
73#2724C2214yescomplemented
74#2723C2214yes—
75#2706C2214yes—
76#2689C2214yescomplemented
77#2665C2214yescomplemented
78#2663C2214yescomplemented
79#2662C2212yes—
80#2662C2212yes—
81#2654C2214yescomplemented
82#2654C2214yescomplemented
83#2653C2214yescomplemented
84#2653C2214yescomplemented
85#2653C2214yescomplemented
86#2652C2214yescomplemented
87#2650C2214yescomplemented
88#2650C2214yescomplemented
89#2649C2214yescomplemented
90#2649C2214yescomplemented
91#2645C2212yescomplemented
92#2645C2212yescomplemented
93#2644C2212yes—
94#2644C2212yes—
95#2642C2212yescomplemented
96#2641C2212yes—
97#2640C2212yes—
98#2640C2212yescomplemented
99#2623C2212yes—
100#2614C2212yes—
101#2610C2212yes—
102#2610C2212yes—
103#2606C2212yescomplemented
104#2605C2212yescomplemented
105#2604C2214yescomplemented
106#2599C2212yescomplemented
107#2599C2212yescomplemented
108#2597C2214yescomplemented
109#2597C2214yescomplemented
110#2596C2214yescomplemented
111#2595C2214yescomplemented
112#2595C2214yescomplemented
113#2594C2214yescomplemented
114#2592C2214yes—
115#2592C2212yes—
116#2592C2212yes—
117#2592C2212yes—
118#2592C2212yes—
119#2592C2212yes—
120#2592C2212yes—
121#2592C2211yescharacteristic, complemented
122#2592C2211yescharacteristic, complemented
123#2584C2211yescharacteristic, complemented
124#2584C2211yescharacteristic, complemented
125#2581C2212yescomplemented
126#2580C2212yescomplemented
127#2578C2214yescomplemented
128#2577C2214yescomplemented
129#2576C2214yescomplemented
130#2575C2214yescomplemented
131#2574C2214yescomplemented
132#2573C2214yescomplemented
133#2573C2214yescomplemented
134#2573C2214yescomplemented
135#2572C2214yescomplemented
136#2570C2212yescomplemented
137#2569C2214yes—
138#2564C2214yes—
139#2561C2214yes—
140#2553C2214yescomplemented
141#2550C2212yescomplemented
142#2545C2212yes—
143#2544C2212yes—
144#2534C2214yes—
145#2530C2214yescomplemented
146#2527C2214yescomplemented
147#2525C2214yescomplemented
148#2516C2214yescomplemented
149#2516C2214yescomplemented
150#2514C2212yescomplemented
151#2513C2212yes—
152#2512C2212yes—
153#2511C2212yescomplemented
154#2510C2214yes—
155#2505C2214yes—
156#2494C2214yescomplemented
157#2493C2214yes—
158#2493C2214yes—
159#2488C2214yes—
160#2483C2214yes—
161#2480C2214yes—
162#2477C2214yescomplemented
163#2470C2214yescomplemented
164#2469C2214yescomplemented
165#2458C2214yescomplemented
166#2458C2214yescomplemented
167#2454C2212yes—
168#2453C2212yescomplemented
169#2452C2212yes—
170#2451C2212yescomplemented
171#2448C2212yes—
172#2448C2212yescomplemented
173#2447C2212yes—
174#2447C2212yescomplemented
175#2446C2212yescomplemented
176#2446C2212yescomplemented
177#2445C2212yes—
178#2445C2212yes—
179#2442C2212yes—
180#2440C2212yes—
181#2438C2214yes—
182#2437C2214yes—
183#2436C2211yescharacteristic
184#2435C2211yescharacteristic
185#2434C2211yescharacteristic
186#2433C2211yescharacteristic
187#2421C2214yescomplemented
188#2419C2214yes—
189#2418C2214yes—
190#2412C2214yes—
191#2412C2214yes—
192#2411C2214yes—
193#2402C2212yescomplemented
194#2399C2212yescomplemented
195C2×#397C2212yes—
196C2×#393C2212yes—
197#2373C2214yescomplemented
198#2372C2214yes—
199#2370C2212yescomplemented
200#2367C2212yes—
201#2367C2212yes—
202#2367C2212yescomplemented
203#2361C2212yes—
204#2360C2212yes—
205#2359C2214yes—
206#2342C2214yes—
207Q8×C22⋊C4C2212yes—
208D4×C22⋊C4C2212yes—
209#2337C2212yes—
210#2337C2212yes—
211#2328C2212yes—
212#2327C2212yescomplemented
213#2326C2212yes—
214#2326C2212yescomplemented
215#2322C2214yes—
216#2321C2214yes—
217#2320C2212yescomplemented
218#2320C2211yescharacteristic, complemented
219#2320C2211yescharacteristic, complemented
220#2320C2211yescharacteristic, complemented
221#2320C2212yescomplemented
222#2320C2211yescharacteristic, complemented
223#2320C2212yescomplemented
224#2320C2212yescomplemented
225#2319C2212yes—
226#2319C2212yes—
227#2316C2212yes—
228#2313C2212yes—
229#2313C2212yes—
230#2312C2212yes—
231#2310C2212yes—
232C4×C4⋊Q8C2212yescomplemented
233C4×#125C2212yescomplemented
234C4×#124C2212yes—
235C4×#124C2212yes—
236C4×C22⋊Q8C2214yes—
237#2298C2212yescomplemented
238#2296C2212yescomplemented
239#2295C2212yescomplemented
240#2295C2212yescomplemented
241#2295C2212yescomplemented
242#2295C2212yescomplemented
243#2295C2211yescharacteristic, complemented
244C2×#391C2212yes—
245#2293C2211yescharacteristic, complemented
246C2×#390C2212yes—
247#2290C2212yes—
248C2×#388C2214yes—
249#2283C2212yes—
250#2283C2212yes—
251#2283C2211yescharacteristic
252#2273C2212yes—
253C42×Q8C2211yescharacteristic, complemented
254C42×D4C2212yes—
255C42×D4C2211yescharacteristic, complemented
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×D4C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×#127C2312yes—
265#529—28no—
266C2×#126C2312yes—
267C2×#126C2314yes—
268C2×#125C2311yescharacteristic
269C2×#125C2312yes—
270C2×#124—28no—
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2311yescharacteristic
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#123C2312yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×#121C2311yescharacteristic
286C2×#120C2314yes—
287C2×C4×Q8—28no—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2312yes—
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2314yes—
316C22×C22⋊C4C2314yes—
317C22×C42C2312yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2312yes—
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#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#397C2312yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2312yes—
393#395C2312yes—
394#395C2314yes—
395#395C2312yes—
396#395C2312yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2312yes—
407#394C2312yes—
408#394C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2312yes—
420#393C2312yes—
421#393C2312yes—
422#393C2312yes—
423#392C2312yes—
424#392C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2312yes—
450#391C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2314yes—
463#390C2312yes—
464#390C2312yes—
465#390C2314yes—
466#390C2314yes—
467#390C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
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#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
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#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#384C2312yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#383C2312yes—
620#383C2312yes—
621#383C2312yes—
622#383C2312yes—
623#383C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2314yes—
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2314yes—
632#381C2312yes—
633#381C2314yes—
634#381C2312yes—
635#381C2312yes—
636#381C2312yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2312yes—
641#381C2314yes—
642#380C2312yes—
643#380C2314yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2314yes—
652#379C2314yes—
653#379C2314yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2311yescharacteristic
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2311yescharacteristic
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2311yescharacteristic
699#376C2312yes—
700#376C2312yes—
701#376C2311yescharacteristic
702#376C2311yescharacteristic
703#376C2312yes—
704#376C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708C2×#95C2314yes—
709C2×#95C2312yes—
710C2×#95C2314yes—
711C43C2312yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C43C2311yescharacteristic
715C25C2412yes—
716C22×Q8—24no—
717C22×Q8—24no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×D4—24no—
728C22×D4—44no—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2411yescharacteristic
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748#127—44no—
749#126—28no—
750#126—84no—
751#125—24no—
752#125—44no—
753#124—28no—
754#124—28no—
755#124—28no—
756#124—28no—
757#124—24no—
758#124—44no—
759#124—44no—
760#123—28no—
761#123—48no—
762#123—84no—
763#123—84no—
764C22⋊Q8—24no—
765C22⋊Q8—48no—
766C22⋊Q8—84no—
767#121—24no—
768#120—48no—
769C4×Q8—24no—
770C4×Q8—24no—
771C4×Q8—28no—
772C4×Q8—24no—
773C4×Q8—24no—
774C4×Q8—28no—
775C4×Q8—24no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—84no—
780C4×D4—28no—
781C4×D4—24no—
782C4×D4—44no—
783C4×D4—44no—
784C4×D4—44no—
785C4×D4—48no—
786#117—28no—
787#117—44no—
788#117—44no—
789#117—82no—
790C2×C4⋊C4—28no—
791C2×C4⋊C4—24no—
792C2×C4⋊C4—44no—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C22⋊C4—28no—
844C2×C22⋊C4—28no—
845C2×C22⋊C4—48no—
846C2×C22⋊C4—48no—
847C2×C22⋊C4—84no—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C42—28no—
892C2×C42—82no—
893C2×C42—82no—
894C2×C42#4118yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006C24—24no—
1007C24—28no—
1008C24—42no—
1009C24—44no—
1010C24—42no—
1011C24C2514yes—
1012C24C2512yes—
1013C24C2511yescharacteristic
1014C2×Q8—22no—
1015C2×Q8—22no—
1016C2×Q8—24no—
1017C2×Q8—22no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—42no—
1026C2×Q8—42no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—416no—
1032C2×Q8—88no—
1033C2×D4—24no—
1034C2×D4—28no—
1035C2×D4—22no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—88no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—24no—
1058C22×C4—41no—
1059C22×C4—42no—
1060C22×C4—41no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4114yes—
1078C22×C4C2×#4114yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—28no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
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—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—24no—
1202C42—24no—
1203C42—24no—
1204C42—24no—
1205C42—24no—
1206C42—24no—
1207C42—42no—
1208C42—41no—
1209C42—42no—
1210C42—44no—
1211C42—44no—
1212C42—42no—
1213C42—42no—
1214C42—41no—
1215C42—41no—
1216C42—42no—
1217C42—42no—
1218C42—42no—
1219C42—42no—
1220C42—41no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42—42no—
1226C42—42no—
1227C42C2×#4114yes—
1228C42C2×#4114yes—
1229C42C2×#4114yes—
1230C42C2×#4114yes—
1231C23—22no—
1232C23—21no—
1233C23—21no—
1234C23—22no—
1235C23—24no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23—24no—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—48no—
1247C23—84no—
1248C23—84no—
1249C23—88no—
1250C23—88no—
1251C23C22×#4112yes—
1252C23#58514yes—
1253C23C2611yescharacteristic
1254Q8—44no—
1255Q8—44no—
1256Q8—48no—
1257Q8—44no—
1258Q8—48no—
1259Q8—84no—
1260Q8—88no—
1261D4—48no—
1262D4—44no—
1263D4—48no—
1264D4—84no—
1265D4—164no—
1266D4—164no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—28no—
1275C2×C4—28no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—44no—
1335C2×C4—48no—
1336C2×C4—48no—
1337C2×C4—84no—
1338C2×C4—88no—
1339C2×C4—84no—
1340C2×C4—88no—
1341C2×C4—164no—
1342C2×C4—164no—
1343C2×C4C22×#4112yes—
1344C2×C4C22×#4112yes—
1345C2×C4C22×#4112yes—
1346C2×C4C22×#4112yes—
1347C2×C4C22×#4112yes—
1348C2×C4C22×#4112yes—
1349C2×C4#58514yes—
1350C22—22no—
1351C22—22no—
1352C22—24no—
1353C22—24no—
1354C22—44no—
1355C22—42no—
1356C22—42no—
1357C22—44no—
1358C22—42no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—168no—
1367C22#345514yes—
1368C22C23×#4111yescharacteristic
1369C22C2×#58512yes—
1370C22C2×#58512yes—
1371C22H(7,𝔽2)11yescharacteristic
1372C222−1+611yescharacteristic
1373C4—22no—
1374C4—22no—
1375C4—22no—
1376C4—22no—
1377C4—22no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—44no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4#351014yes—
1399C2—24no—
1400C2—82no—
1401C2—84no—
1402C2C2×#345511yescharacteristic
1403C2C2×#351011yescharacteristic
1404C2#6285611yescharacteristic
1405C2#6296412yes—
1406C2#6296512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2433C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42318C2semidirect
2. #42208C2semidirect
3. #42031C2semidirect
4. #41964C2semidirect
5. #39766C2semidirect
6. #39765C2semidirect
7. #38981C2semidirect
8. #38980C2semidirect
9. #38057C2semidirect
11. #38055C2semidirect
12. #38054C2semidirect
13. #37581C2semidirect
14. #37572C2semidirect
15. #37031C2semidirect
16. #37026C2semidirect
17. #36837C2semidirect
18. #36832C2semidirect
19. #35379C2semidirect
20. #35219C2semidirect
21. #35188C2semidirect
23. #35111C2semidirect
24. #35027C2semidirect
25. #34966C2semidirect
26. C2×#2592C2semidirect
27. #34240C2semidirect
28. #34153C2semidirect
29. #34059C2semidirect
33. #2866C22semidirect
34. #2865C22semidirect
39. #2853C22semidirect
40. #2852C22semidirect
41. #2838C22semidirect
42. #2837C22semidirect
43. #2832C22semidirect
44. #2831C22semidirect
45. #2808C22semidirect
46. #2808C22semidirect
47. #2804C22semidirect
48. #2796C22semidirect
49. #2796C22semidirect
50. #2788C22semidirect
51. #2787C22semidirect
52. #2783C22semidirect
53. #2777C22semidirect
54. #2775C22semidirect
55. #2764C22semidirect
56. #2763C22semidirect
57. #2762C22semidirect
58. #2762C22semidirect
60. #2759C22semidirect
61. #2759C22semidirect
62. #2758C22semidirect
65. #2755C22semidirect
66. #2754C22semidirect
68. #2751C22semidirect
69. #2751C22semidirect
71. #2745C22semidirect
73. #2724C22semidirect
76. #2689C22semidirect
77. #2665C22semidirect
78. #2663C22semidirect
81. #2654C22semidirect
82. #2654C22semidirect
83. #2653C22semidirect
84. #2653C22semidirect
85. #2653C22semidirect
86. #2652C22semidirect
87. #2650C22semidirect
88. #2650C22semidirect
89. #2649C22semidirect
90. #2649C22semidirect
91. #2645C22semidirect
92. #2645C22semidirect
95. #2642C22semidirect
98. #2640C22semidirect
103. #2606C22semidirect
104. #2605C22semidirect
105. #2604C22semidirect
106. #2599C22semidirect
107. #2599C22semidirect
108. #2597C22semidirect
109. #2597C22semidirect
110. #2596C22semidirect
111. #2595C22semidirect
112. #2595C22semidirect
113. #2594C22semidirect
121. #2592C22semidirect
122. #2592C22semidirect
123. #2584C22semidirect
124. #2584C22semidirect
125. #2581C22semidirect
126. #2580C22semidirect
127. #2578C22semidirect
128. #2577C22semidirect
129. #2576C22semidirect
130. #2575C22semidirect
131. #2574C22semidirect
132. #2573C22semidirect
133. #2573C22semidirect
134. #2573C22semidirect
135. #2572C22semidirect
136. #2570C22semidirect
140. #2553C22semidirect
141. #2550C22semidirect
145. #2530C22semidirect
146. #2527C22semidirect
147. #2525C22semidirect
148. #2516C22semidirect
149. #2516C22semidirect
150. #2514C22semidirect
153. #2511C22semidirect
156. #2494C22semidirect
162. #2477C22semidirect
163. #2470C22semidirect
164. #2469C22semidirect
165. #2458C22semidirect
166. #2458C22semidirect
168. #2453C22semidirect
170. #2451C22semidirect
172. #2448C22semidirect
174. #2447C22semidirect
175. #2446C22semidirect
176. #2446C22semidirect
187. #2421C22semidirect
193. #2402C22semidirect
194. #2399C22semidirect
197. #2373C22semidirect
199. #2370C22semidirect
202. #2367C22semidirect
212. #2327C22semidirect
214. #2326C22semidirect
217. #2320C22semidirect
218. #2320C22semidirect
219. #2320C22semidirect
220. #2320C22semidirect
221. #2320C22semidirect
222. #2320C22semidirect
223. #2320C22semidirect
224. #2320C22semidirect
232. C4×C4⋊Q8C22semidirect
233. C4×#125C22semidirect
237. #2298C22semidirect
238. #2296C22semidirect
239. #2295C22semidirect
240. #2295C22semidirect
241. #2295C22semidirect
242. #2295C22semidirect
243. #2295C22semidirect
245. #2293C22semidirect
253. C42×Q8C22semidirect
255. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#423182
#422082
#420312
#419642
#397662
#397652
#389812
#389802
#380572
#380562
#380552
#380542
#375812
#375722
#370312
#370262
#368372
#368322
#353792
#352192
#351882
#351312
#351112
#350272
#349662
C2×#25922
#342402
#341532
#340592