Finite Group Databasebeta

← #8157208

Subgroups — #8157208

Order 512.

4106 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59424C212yesmaximal
2#59325C212yesmaximal, complemented
3#58164C214yesmaximal, complemented
4#57791C214yesmaximal, complemented
5#55990C214yesmaximal, complemented
6#54597C214yesmaximal, complemented
7#53113C212yesmaximal, complemented
8#52998C212yesmaximal, complemented
9#52603C214yesmaximal, complemented
10#45407C212yesmaximal, complemented
11#45370C212yesmaximal, complemented
12#42830C212yesmaximal, complemented
13#42700C212yesmaximal, complemented
14#42626C212yesmaximal, complemented
15#42509C212yesmaximal, complemented
16#40867C214yesmaximal, complemented
17#39542C212yesmaximal, complemented
18#39511C211yesmaximal, characteristic
19#39508C212yesmaximal, complemented
20#39495C211yesmaximal, characteristic
21#38066C212yesmaximal, complemented
22#38054C212yesmaximal
23#37460C212yesmaximal, complemented
24#36750C212yesmaximal, complemented
25#36564C211yesmaximal, characteristic, complemented
26#36552C211yesmaximal, characteristic, complemented
27#35015C211yesmaximal, characteristic, complemented
28C2×#2513C211yesmaximal, characteristic
29#34595C211yesmaximal, characteristic, complemented
30#2857C2211yescharacteristic
31#2857C2212yes—
32#2857C2211yescharacteristic
33#2855C2212yes—
34#2851C2212yes—
35#2838C2214yescomplemented
36#2838C2214yescomplemented
37#2836C2214yescomplemented
38#2836C2214yescomplemented
39#2836C2214yescomplemented
40#2835C2214yescomplemented
41#2831C2214yescomplemented
42#2831C2214yescomplemented
43#2831C2214yescomplemented
44#2831C2214yescomplemented
45#2831C2214yescomplemented
46#2817C2214yescomplemented
47#2808C2212yes—
48#2807C2214yescomplemented
49#2804C2212yes—
50#2800C2214yes—
51#2798C2214yescomplemented
52#2793C2214yescomplemented
53#2788C2214yescomplemented
54#2787C2214yescomplemented
55#2787C2214yescomplemented
56#2786C2214yes—
57#2783C2214yescomplemented
58#2780C2214yes—
59#2776C2214yescomplemented
60#2775C2214yescomplemented
61#2775C2214yescomplemented
62#2774C2214yescomplemented
63#2771C2214yescomplemented
64#2769C2214yescomplemented
65#2768C2214yescomplemented
66#2766C2214yescomplemented
67#2765C2214yescomplemented
68#2764C2214yescomplemented
69#2763C2214yescomplemented
70#2761C2214yes—
71#2759C2214yescomplemented
72#2757C2214yes—
73#2755C2214yescomplemented
74#2754C2214yescomplemented
75#2754C2214yescomplemented
76#2745C2214yescomplemented
77#2744C2214yescomplemented
78#2740C2214yes—
79#2739C2214yescomplemented
80#2737C2214yes—
81#2732C2212yes—
82#2729C2214yescomplemented
83#2727C2212yes—
84#2725C2214yescomplemented
85#2723C2214yes—
86#2722C2214yescomplemented
87#2722C2214yescomplemented
88#2720C2214yescomplemented
89#2719C2214yescomplemented
90#2716C2214yescomplemented
91#2704C2214yescomplemented
92#2704C2214yescomplemented
93#2698C2214yescomplemented
94#2698C2214yescomplemented
95#2690C2214yescomplemented
96#2689C2214yescomplemented
97#2666C2212yescomplemented
98#2666C2212yescomplemented
99#2666C2212yescomplemented
100#2666C2212yescomplemented
101#2664C2214yescomplemented
102#2664C2214yescomplemented
103#2659C2211yescharacteristic
104#2659C2211yescharacteristic
105#2654C2214yescomplemented
106#2654C2214yescomplemented
107#2652C2214yescomplemented
108#2650C2214yescomplemented
109#2647C2212yescomplemented
110#2646C2212yes—
111#2646C2212yes—
112#2645C2212yescomplemented
113#2644C2212yes—
114#2640C2212yes—
115#2637C2214yescomplemented
116#2627C2211yescharacteristic
117#2627C2211yescharacteristic
118#2627C2212yes—
119#2627C2212yes—
120#2626C2212yes—
121#2626C2212yes—
122#2625C2214yescomplemented
123#2601C2214yes—
124#2599C2214yescomplemented
125#2596C2214yescomplemented
126#2594C2214yescomplemented
127#2592C2212yes—
128#2592C2212yes—
129#2590C2214yescomplemented
130#2590C2214yescomplemented
131#2588C2214yescomplemented
132#2586C2214yescomplemented
133#2581C2212yescomplemented
134#2580C2212yes—
135#2575C2214yescomplemented
136#2568C2212yescomplemented
137#2568C2211yescharacteristic, complemented
138#2567C2211yescharacteristic, complemented
139#2566C2212yes—
140#2565C2212yescomplemented
141#2561C2214yes—
142#2560C2214yes—
143#2552C2211yescharacteristic, complemented
144#2551C2211yescharacteristic, complemented
145#2550C2212yescomplemented
146#2549C2214yes—
147#2549C2214yes—
148#2545C2212yes—
149#2538C2212yes—
150#2525C2214yescomplemented
151#2520C2214yescomplemented
152#2519C2214yescomplemented
153#2515C2214yescomplemented
154#2514C2212yescomplemented
155#2513C2212yes—
156#2513C2212yes—
157#2513C2214yes—
158#2513C2212yes—
159#2513C2212yes—
160#2513C2214yes—
161#2512C2212yes—
162#2512C2212yes—
163#2512C2212yes—
164#2512C2212yes—
165#2511C2212yescomplemented
166#2511C2212yescomplemented
167#2509C2212yescomplemented
168#2508C2212yescomplemented
169#2508C2214yescomplemented
170#2508C2212yescomplemented
171#2507C2212yescomplemented
172#2507C2212yescomplemented
173#2507C2212yescomplemented
174#2506C2212yescomplemented
175#2506C2212yescomplemented
176#2505C2214yes—
177#2505C2214yes—
178#2505C2214yes—
179#2502C2212yes—
180#2493C2214yes—
181#2493C2214yes—
182#2489C2214yescomplemented
183#2483C2214yes—
184#2480C2214yes—
185#2480C2214yes—
186#2480C2214yes—
187#2480C2214yes—
188#2478C2214yescomplemented
189#2475C2214yescomplemented
190#2473C2214yes—
191#2469C2214yescomplemented
192#2469C2214yescomplemented
193#2454C2212yes—
194#2453C2212yescomplemented
195#2453C2212yescomplemented
196#2452C2212yes—
197#2452C2212yes—
198#2451C2212yescomplemented
199#2451C2212yescomplemented
200#2448C2212yes—
201#2448C2212yes—
202#2448C2212yes—
203#2447C2212yes—
204#2447C2212yes—
205#2446C2212yescomplemented
206#2442C2212yes—
207#2442C2214yes—
208#2440C2212yes—
209#2437C2214yes—
210#2437C2214yes—
211#2437C2214yes—
212#2435C2212yes—
213#2402C2212yescomplemented
214#2402C2212yescomplemented
215#2399C2212yescomplemented
216#2399C2212yescomplemented
217C2×#397C2212yes—
218C2×#397C2212yes—
219#2369C2211yescharacteristic, complemented
220#2369C2212yescomplemented
221#2368C2214yes—
222#2367C2212yes—
223#2365C2211yescharacteristic, complemented
224#2360C2212yes—
225#2360C2212yes—
226#2355C2212yescomplemented
227#2355C2212yescomplemented
228#2354C2212yes—
229#2351C2212yescomplemented
230Q8×C4⋊C4C2211yescharacteristic, complemented
231Q8×C4⋊C4C2211yescharacteristic, complemented
232#2345C2212yes—
233#2342C2214yes—
234D4×C22⋊C4C2212yes—
235#2330C2212yescomplemented
236#2329C2212yes—
237#2326C2212yes—
238#2320C2212yescomplemented
239#2319C2212yes—
240#2315C2212yes—
241#2313C2212yes—
242#2312C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2211yescharacteristic
246C4×C22⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C2×#390C2211yescharacteristic
250C2×#390C2211yescharacteristic
251C2×#390C2211yescharacteristic
252C2×#389C2211yescharacteristic
253C2×#388C2212yes—
254C2×#388C2212yes—
255#2283C2212yes—
256C2×#382C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×D4C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#126C2314yes—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2311yescharacteristic
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×#117C2314yes—
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2312yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2314yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2312yes—
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2312yes—
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2312yes—
311#401C2314yes—
312#401C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2312yes—
430#395C2314yes—
431#395C2312yes—
432#395C2314yes—
433#395C2312yes—
434#395C2312yes—
435#395C2312yes—
436#395C2312yes—
437#395C2312yes—
438#394C2314yes—
439#394C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2314yes—
466#391C2312yes—
467#391C2311yescharacteristic
468#391C2311yescharacteristic
469#390C2314yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2311yescharacteristic
520#389C2311yescharacteristic
521#389C2314yes—
522#389C2312yes—
523#389C2314yes—
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#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#386C2314yes—
596#386C2314yes—
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#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#384C2312yes—
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2312yes—
625#384C2311yescharacteristic
626#384C2312yes—
627#383C2314yes—
628#383C2314yes—
629#383C2312yes—
630#383C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2314yes—
636#382C2314yes—
637#382C2314yes—
638#382C2314yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#381C2312yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2312yes—
648#380C2311yescharacteristic
649#380C2312yes—
650#380C2312yes—
651#380C2311yescharacteristic
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#379C2314yes—
664#379C2314yes—
665#379C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704#376C2312yes—
705#376C2312yes—
706C2×#95C2311yescharacteristic
707C2×#95C2312yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2311yescharacteristic
712C25C2412yes—
713C22×Q8C2412yes—
714C22×Q8C2411yescharacteristic
715C22×Q8C2411yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×D4—24no—
720C22×D4—42no—
721C22×D4—42no—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C23×C4C2411yescharacteristic
725C23×C4C2411yescharacteristic
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2414yes—
734C23×C4C2414yes—
735C23×C4C2411yescharacteristic
736C4⋊Q8—42no—
737C4⋊Q8—44no—
738C4⋊Q8—42no—
739C4⋊Q8—82no—
740#126—84no—
741#126—84no—
742#126—84no—
743#126—84no—
744#125—44no—
745#125—82no—
746#125—84no—
747#125—84no—
748#124—44no—
749#124—44no—
750C22⋊Q8—28no—
751C22⋊Q8—24no—
752C22⋊Q8—24no—
753C22⋊Q8—44no—
754C22⋊Q8—44no—
755C22⋊Q8—48no—
756C22⋊Q8—84no—
757C22⋊Q8—84no—
758C22⋊Q8—84no—
759C4×Q8—44no—
760C4×Q8—42no—
761C4×Q8—42no—
762C4×Q8—44no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×Q8—82no—
766C4×Q8—82no—
767C4×D4—44no—
768C4×D4—44no—
769#117—84no—
770C2×C4⋊C4—24no—
771C2×C4⋊C4—24no—
772C2×C4⋊C4—42no—
773C2×C4⋊C4—42no—
774C2×C4⋊C4—42no—
775C2×C4⋊C4—82no—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C22⋊C4—28no—
851C2×C22⋊C4—48no—
852C2×C22⋊C4—44no—
853C2×C22⋊C4—82no—
854C2×C22⋊C4—82no—
855C2×C22⋊C4—82no—
856C2×C22⋊C4—82no—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
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×C42—24no—
890C2×C42—42no—
891C2×C42—42no—
892C2×C42—82no—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995C24—24no—
996C24—24no—
997C24—24no—
998C24—42no—
999C24—42no—
1000C24—42no—
1001C24—42no—
1002C24C2514yes—
1003C24C2511yescharacteristic
1004C2×Q8—22no—
1005C2×Q8—22no—
1006C2×Q8—24no—
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—42no—
1014C2×Q8—42no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8—44no—
1018C2×Q8—42no—
1019C2×Q8—44no—
1020C2×Q8—44no—
1021C2×Q8—42no—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—24no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—88no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—22no—
1038C22×C4—24no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—44no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C42−1+414yes—
1064C22×C42−1+414yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—22no—
1104C4⋊C4—24no—
1105C4⋊C4—22no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
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—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—41no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
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—22no—
1202C42—22no—
1203C42—24no—
1204C42—24no—
1205C42—24no—
1206C42—24no—
1207C42—41no—
1208C42—41no—
1209C42—42no—
1210C42—42no—
1211C42—42no—
1212C42—42no—
1213C42—42no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C23—21no—
1223C23—21no—
1224C23—21no—
1225C23—21no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—24no—
1230C23—24no—
1231C23—24no—
1232C23—24no—
1233C23—48no—
1234C23—84no—
1235C23—84no—
1236C23—84no—
1237C23—84no—
1238C23—84no—
1239C23—84no—
1240C23C2×2−1+412yes—
1241C23C2×2−1+412yes—
1242C23#58512yes—
1243C23C2611yescharacteristic
1244Q8—44no—
1245Q8—44no—
1246Q8—48no—
1247Q8—84no—
1248Q8—162no—
1249Q8—164no—
1250D4—48no—
1251D4—84no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—28no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—44no—
1329C2×C4—44no—
1330C2×C4—82no—
1331C2×C4—84no—
1332C2×C4—82no—
1333C2×C4—82no—
1334C2×C4—82no—
1335C2×C4—84no—
1336C2×C4—84no—
1337C2×C4—88no—
1338C2×C4—164no—
1339C2×C4C2×2−1+412yes—
1340C2×C4C2×2−1+412yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4#58512yes—
1344C2×C4#58512yes—
1345C22—22no—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—168no—
1359C22#355514yes—
1360C22C22×2−1+411yescharacteristic
1361C22C22×2−1+411yescharacteristic
1362C22C2×#58511yescharacteristic
1363C22C2×#58511yescharacteristic
1364C22C2×#58511yescharacteristic
1365C22H(7,𝔽2)11yescharacteristic
1366C22H(7,𝔽2)11yescharacteristic
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—44no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—41no—
1380C4—42no—
1381C4—41no—
1382C4—42no—
1383C4—44no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—42no—
1390C4—44no—
1391C4—42no—
1392C4—42no—
1393C4#356414yes—
1394C2—24no—
1395C2—84no—
1396C2C2×#356411yescharacteristic
1397C2C2×#355511yescharacteristic
1398C2#6288111yescharacteristic
1399C2#6290211yescharacteristic
1400C2#6291011yescharacteristic
1401C2#6296211yescharacteristic
1402C2#6296511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59325C2semidirect
3. #58164C2semidirect
4. #57791C2semidirect
5. #55990C2semidirect
6. #54597C2semidirect
7. #53113C2semidirect
8. #52998C2semidirect
9. #52603C2semidirect
10. #45407C2semidirect
11. #45370C2semidirect
12. #42830C2semidirect
13. #42700C2semidirect
14. #42626C2semidirect
15. #42509C2semidirect
16. #40867C2semidirect
17. #39542C2semidirect
19. #39508C2semidirect
21. #38066C2semidirect
23. #37460C2semidirect
24. #36750C2semidirect
25. #36564C2semidirect
26. #36552C2semidirect
27. #35015C2semidirect
29. #34595C2semidirect
35. #2838C22semidirect
36. #2838C22semidirect
37. #2836C22semidirect
38. #2836C22semidirect
39. #2836C22semidirect
40. #2835C22semidirect
41. #2831C22semidirect
42. #2831C22semidirect
43. #2831C22semidirect
44. #2831C22semidirect
45. #2831C22semidirect
46. #2817C22semidirect
48. #2807C22semidirect
51. #2798C22semidirect
52. #2793C22semidirect
53. #2788C22semidirect
54. #2787C22semidirect
55. #2787C22semidirect
57. #2783C22semidirect
59. #2776C22semidirect
60. #2775C22semidirect
61. #2775C22semidirect
62. #2774C22semidirect
63. #2771C22semidirect
64. #2769C22semidirect
65. #2768C22semidirect
66. #2766C22semidirect
67. #2765C22semidirect
68. #2764C22semidirect
69. #2763C22semidirect
71. #2759C22semidirect
73. #2755C22semidirect
74. #2754C22semidirect
75. #2754C22semidirect
76. #2745C22semidirect
77. #2744C22semidirect
79. #2739C22semidirect
82. #2729C22semidirect
84. #2725C22semidirect
86. #2722C22semidirect
87. #2722C22semidirect
88. #2720C22semidirect
89. #2719C22semidirect
90. #2716C22semidirect
91. #2704C22semidirect
92. #2704C22semidirect
93. #2698C22semidirect
94. #2698C22semidirect
95. #2690C22semidirect
96. #2689C22semidirect
97. #2666C22semidirect
98. #2666C22semidirect
99. #2666C22semidirect
100. #2666C22semidirect
101. #2664C22semidirect
102. #2664C22semidirect
105. #2654C22semidirect
106. #2654C22semidirect
107. #2652C22semidirect
108. #2650C22semidirect
109. #2647C22semidirect
112. #2645C22semidirect
115. #2637C22semidirect
122. #2625C22semidirect
124. #2599C22semidirect
125. #2596C22semidirect
126. #2594C22semidirect
129. #2590C22semidirect
130. #2590C22semidirect
131. #2588C22semidirect
132. #2586C22semidirect
133. #2581C22semidirect
135. #2575C22semidirect
136. #2568C22semidirect
137. #2568C22semidirect
138. #2567C22semidirect
140. #2565C22semidirect
143. #2552C22semidirect
144. #2551C22semidirect
145. #2550C22semidirect
150. #2525C22semidirect
151. #2520C22semidirect
152. #2519C22semidirect
153. #2515C22semidirect
154. #2514C22semidirect
165. #2511C22semidirect
166. #2511C22semidirect
167. #2509C22semidirect
168. #2508C22semidirect
169. #2508C22semidirect
170. #2508C22semidirect
171. #2507C22semidirect
172. #2507C22semidirect
173. #2507C22semidirect
174. #2506C22semidirect
175. #2506C22semidirect
182. #2489C22semidirect
188. #2478C22semidirect
189. #2475C22semidirect
191. #2469C22semidirect
192. #2469C22semidirect
194. #2453C22semidirect
195. #2453C22semidirect
198. #2451C22semidirect
199. #2451C22semidirect
205. #2446C22semidirect
213. #2402C22semidirect
214. #2402C22semidirect
215. #2399C22semidirect
216. #2399C22semidirect
219. #2369C22semidirect
220. #2369C22semidirect
223. #2365C22semidirect
226. #2355C22semidirect
227. #2355C22semidirect
229. #2351C22semidirect
230. Q8×C4⋊C4C22semidirect
231. Q8×C4⋊C4C22semidirect
235. #2330C22semidirect
238. #2320C22semidirect

Maximal subgroups

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

subgroupindex
#594242
#593252
#581642
#577912
#559902
#545972
#531132
#529982
#526032
#454072
#453702
#428302
#427002
#426262
#425092
#408672
#395422
#395112
#395082
#394952
#380662
#380542
#374602
#367502
#365642
#365522
#350152
C2×#25132
#345952