Finite Group Databasebeta

← #7699154

Subgroups — #7699154

Order 512.

7170 conjugacy classes of subgroups.

The subgroup lattice has 1474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic, complemented
2C2×#3517C211yesmaximal, characteristic, complemented
3#59657C213yesmaximal, complemented
4#59139C213yesmaximal, complemented
5#59057C213yesmaximal, complemented
6#52157C213yesmaximal, complemented
7#45271C213yesmaximal, complemented
8#45159C213yesmaximal, complemented
9#45042C213yesmaximal, complemented
10#45034C213yesmaximal, complemented
11#45034C213yesmaximal, complemented
12#44878C213yesmaximal, complemented
13#39725C213yesmaximal, complemented
14#39426C213yesmaximal, complemented
15#39169C213yesmaximal, complemented
16#39118C213yesmaximal, complemented
17#37756C213yesmaximal, complemented
18#37706C213yesmaximal, complemented
19#36583C211yesmaximal, characteristic, complemented
20#36455C211yesmaximal, characteristic, complemented
21#36431C211yesmaximal, characteristic, complemented
22#36049C211yesmaximal, characteristic, complemented
23#36049C211yesmaximal, characteristic, complemented
24#36040C211yesmaximal, characteristic, complemented
25#36029C211yesmaximal, characteristic, complemented
26#36029C211yesmaximal, characteristic, complemented
27#35816C211yesmaximal, characteristic, complemented
28#34336C211yesmaximal, characteristic, complemented
29#34313C211yesmaximal, characteristic, complemented
30#34295C211yesmaximal, characteristic, complemented
31#34295C211yesmaximal, characteristic, complemented
32#3517—216no—
33#3504—216no—
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#554C2213yes—
39C2×#554C2213yes—
40C2×#554C2213yes—
41C2×#554C2213yes—
42C2×#553C2213yes—
43C2×#553C2213yes—
44C2×#550C2213yes—
45C2×#550C2211yescharacteristic
46C2×#550C2211yescharacteristic
47C2×#550C2211yescharacteristic
48C2×#550C2211yescharacteristic
49C2×#550C2211yescharacteristic
50C2×#550C2211yescharacteristic
51C2×#547C2213yes—
52C2×#544C2213yes—
53C2×#544C2213yes—
54C2×#540C2213yes—
55C2×#540C2213yes—
56C2×#533C2213yes—
57C2×#532C2213yes—
58C2×#529C2213yes—
59C22×#125C2213yes—
60C2×#520C2211yescharacteristic
61C2×#520C2211yescharacteristic
62C2×#520C2211yescharacteristic
63C2×#520C2211yescharacteristic
64C2×C4×#41C2211yescharacteristic
65C2×C4×#41C2211yescharacteristic
66#2858C2213yes—
67#2856C2213yes—
68#2851C2213yes—
69#2731C2213yes—
70#2730C2216yes—
71#2730C2213yes—
72#2729C2213yes—
73#2728C2216yes—
74#2728C2213yes—
75#2725C2213yes—
76#2723C2213yes—
77#2719C2211yescharacteristic
78#2716C2213yes—
79#2711C2216yes—
80#2711C2216yes—
81#2711C2213yes—
82#2707C2213yes—
83#2707C2216yes—
84#2702C2213yes—
85#2696C2216yes—
86#2696C2216yes—
87#2696C2213yes—
88#2690C2213yes—
89#2681C2216yes—
90#2681C2213yes—
91#2676C2213yes—
92#2676C2216yes—
93#2676C2216yes—
94#2676C2216yes—
95#2676C2216yes—
96#2676C2216yes—
97#2674C2213yes—
98#2641C2213yes—
99#2641C2213yes—
100#2629C2213yes—
101#2628C2213yes—
102#2619C2213yes—
103#2619C2213yes—
104#2580C2213yes—
105#2580C2213yes—
106#2566C2213yes—
107#2566C2213yes—
108#2563C2213yes—
109#2562C2213yes—
110#2562C2213yes—
111#2560C2216yes—
112#2558C2216yes—
113#2548C2213yes—
114#2548C2213yes—
115#2548C2213yes—
116#2547C2213yes—
117#2541C2213yes—
118#2541C2213yes—
119#2541C2213yes—
120#2540C2216yes—
121#2540C2216yes—
122#2538C2213yes—
123#2537C2213yes—
124#2535C2213yes—
125#2535C2213yes—
126#2491C2216yes—
127#2491C2213yes—
128#2491C2213yes—
129#2491C2213yes—
130#2491C2213yes—
131#2490C2213yes—
132#2490C2213yes—
133#2490C2213yes—
134#2490C2213yes—
135#2490C2213yes—
136#2490C2213yes—
137#2490C2213yes—
138#2490C2213yes—
139#2481C2216yes—
140#2463C2216yes—
141#2461C2216yes—
142#2461C2216yes—
143#2460C2216yes—
144#2454C2213yes—
145#2454C2213yes—
146#2454C2213yes—
147#2454C2213yes—
148#2452C2213yes—
149#2452C2213yes—
150#2443C2216yes—
151#2443C2216yes—
152#2443C2216yes—
153#2442C2213yes—
154#2442C2213yes—
155#2442C2213yes—
156#2441C2213yes—
157#2440C2213yes—
158#2439C2213yes—
159#2432C2216yes—
160#2428C2213yes—
161#2428C2213yes—
162#2428C2213yes—
163#2428C2213yes—
164#2428C2213yes—
165#2428C2213yes—
166#2427C2216yes—
167#2416C2216yes—
168#2416C2216yes—
169#2416C2213yes—
170#2416C2213yes—
171#2416C2213yes—
172#2416C2213yes—
173#2416C2216yes—
174#2414C2213yes—
175#2414C2213yes—
176#2407C2216yes—
177#2407C2216yes—
178#2407C2216yes—
179#2398C2213yes—
180#2398C2213yes—
181#2396C2213yes—
182#2396C2213yes—
183#2392C2213yes—
184#2392C2213yes—
185#2370C2213yes—
186#2370C2213yes—
187#2369C2213yes—
188#2366C2213yes—
189#2366C2213yes—
190#2366C2213yes—
191#2363C2213yes—
192#2363C2213yes—
193#2361C2213yes—
194#2361C2216yes—
195#2361C2213yes—
196#2361C2213yes—
197#2361C2213yes—
198#2355C2213yes—
199#2352C2213yes—
200#2352C2213yes—
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207D4×C4⋊C4C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2331C2213yes—
219#2330C2213yes—
220#2328C2213yes—
221#2328C2213yes—
222#2324C2213yes—
223#2324C2213yes—
224#2324C2213yes—
225#2324C2213yes—
226C4×#127C2213yes—
227C4×#125C2213yes—
228C4×#124C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232C4×#121C2213yes—
233#2295C2213yes—
234#2293C2213yes—
235#2290C2213yes—
236#2290C2213yes—
237#2276C2211yescharacteristic
238#2276C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2316yes—
245#557—28no—
246#557—28no—
247#557—28no—
248#557D4116yescomplemented
249#554—224no—
250#554—224no—
251#554—224no—
252#554—224no—
253#553—224no—
254#553—224no—
255#550—28no—
256#550—28no—
257#550—28no—
258#550—224no—
259#550—28no—
260#550—28no—
261#550—28no—
262#547—224no—
263#544—224no—
264#544—224no—
265#540—224no—
266#540—224no—
267#533—224no—
268#532—224no—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2313yes—
274C2×C4⋊Q8C2313yes—
275C2×#127C2313yes—
276C2×#127C2313yes—
277C2×#127C2313yes—
278C2×#127C2313yes—
279C2×#127C2313yes—
280C2×#127C2313yes—
281#529—224no—
282C2×#126C2313yes—
283C2×#126C2313yes—
284C2×#125—224no—
285C2×#125C2313yes—
286C2×#125C2313yes—
287C2×#125C2313yes—
288C2×#125C2316yes—
289C2×#125C2313yes—
290C2×#125C2313yes—
291C2×#125C2311yescharacteristic
292C2×#125C2311yescharacteristic
293C2×#125C2313yes—
294C2×#125C2313yes—
295C2×#125C2313yes—
296C2×#125C2313yes—
297C2×#124C2313yes—
298C2×#124C2313yes—
299C2×#124C2316yes—
300C2×#124C2316yes—
301C2×#124C2316yes—
302C2×#123C2313yes—
303C2×#123C2313yes—
304C2×#123C2316yes—
305C2×#123C2316yes—
306C2×C22⋊Q8C2316yes—
307C2×C22⋊Q8C2313yes—
308C2×C22⋊Q8C2316yes—
309C2×C22⋊Q8C2313yes—
310C2×C22⋊Q8C2313yes—
311C2×C22⋊Q8C2313yes—
312C2×C22⋊Q8C2313yes—
313C2×C22⋊Q8C2316yes—
314C2×C22⋊Q8C2316yes—
315C2×C22⋊Q8C2313yes—
316C2×C22⋊Q8C2316yes—
317C2×#121C2313yes—
318C2×#121C2313yes—
319C2×#121C2313yes—
320C2×#121C2313yes—
321C2×#121C2313yes—
322C2×#121C2313yes—
323C2×#121C2313yes—
324C2×#121C2313yes—
325C2×#121C2313yes—
326C2×#121C2316yes—
327C2×#121C2316yes—
328C2×#121C2313yes—
329C2×#121C2313yes—
330C2×#121C2313yes—
331C2×#121C2313yes—
332C2×#121C2316yes—
333C2×#121C2316yes—
334C2×#121C2313yes—
335C2×#121C2316yes—
336C2×#121C2316yes—
337C2×#121C2316yes—
338C2×#121C2316yes—
339C2×#121C2316yes—
340#520—28no—
341#520—28no—
342#520—28no—
343#520—28no—
344C4×#41—28no—
345C4×#41—28no—
346C2×C4×Q8C2313yes—
347C2×C4×Q8C2313yes—
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2313yes—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2313yes—
369C2×C4×D4C2313yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2313yes—
374C2×C4×D4C2313yes—
375C2×C4×D4C2313yes—
376C2×C4×D4C2316yes—
377C2×C4×D4C2313yes—
378C2×C4×D4C2313yes—
379C2×C4×D4C2313yes—
380C2×C4×D4C2316yes—
381C2×C4×D4C2316yes—
382C2×C4×D4C2316yes—
383C2×C4×D4C2316yes—
384C2×#117C2313yes—
385C2×#117C2313yes—
386C2×#117C2313yes—
387C2×#117C2313yes—
388C2×#117C2313yes—
389C2×#117C2313yes—
390C22×C4⋊C4C2313yes—
391C22×C4⋊C4C2313yes—
392C22×C4⋊C4C2313yes—
393C22×C4⋊C4C2313yes—
394C22×C4⋊C4C2316yes—
395C22×C4⋊C4C2316yes—
396C22×C42C2313yes—
397C22×C42C2313yes—
398#400C2313yes—
399#400C2313yes—
400#400C2316yes—
401#400C2311yescharacteristic
402#400C2313yes—
403#400C2311yescharacteristic
404#400C2311yescharacteristic
405#399C2313yes—
406#399C2316yes—
407#399C2316yes—
408#399C2313yes—
409#398C2316yes—
410#398C2313yes—
411#398C2311yescharacteristic
412#398C2311yescharacteristic
413#398C2311yescharacteristic
414#398C2313yes—
415#398C2313yes—
416#397C2313yes—
417#397C2313yes—
418#397C2313yes—
419#397C2313yes—
420#397C2313yes—
421#397C2313yes—
422#397C2316yes—
423#397C2316yes—
424#396C2313yes—
425#396C2316yes—
426#396C2316yes—
427#396C2316yes—
428#396C2316yes—
429#396C2313yes—
430#396C2313yes—
431#396C2313yes—
432#396C2313yes—
433#396C2313yes—
434#396C2313yes—
435#396C2313yes—
436#395C2313yes—
437#395C2313yes—
438#394C2316yes—
439#394C2316yes—
440#394C2316yes—
441#394C2313yes—
442#394C2313yes—
443#394C2316yes—
444#394C2316yes—
445#394C2313yes—
446#394C2313yes—
447#394C2316yes—
448#394C2316yes—
449#394C2316yes—
450#394C2316yes—
451#394C2313yes—
452#394C2313yes—
453#394C2313yes—
454#394C2313yes—
455#394C2313yes—
456#394C2313yes—
457#394C2316yes—
458#394C2316yes—
459#394C2316yes—
460#393C2316yes—
461#393C2313yes—
462#393C2316yes—
463#393C2313yes—
464#393C2313yes—
465#393C2313yes—
466#393C2313yes—
467#393C2313yes—
468#392C2316yes—
469#392C2316yes—
470#392C2316yes—
471#392C2316yes—
472#392C2313yes—
473#392C2313yes—
474#392C2316yes—
475#392C2316yes—
476#391C2313yes—
477#391C2313yes—
478#391C2316yes—
479#391C2313yes—
480#391C2313yes—
481#390C2316yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2313yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2316yes—
495#390C2316yes—
496#390C2313yes—
497#390C2313yes—
498#390C2313yes—
499#390C2313yes—
500#390C2313yes—
501#390C2313yes—
502#390C2313yes—
503#390C2313yes—
504#390C2313yes—
505#390C2313yes—
506#390C2316yes—
507#390C2316yes—
508#390C2316yes—
509#390C2316yes—
510#390C2313yes—
511#390C2316yes—
512#390C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2313yes—
518#389C2313yes—
519#389C2313yes—
520#389C2313yes—
521#389C2313yes—
522#389C2313yes—
523#389C2316yes—
524#389C2313yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#389C2313yes—
529#389C2313yes—
530#389C2311yescharacteristic
531#389C2311yescharacteristic
532#388C2316yes—
533#388C2316yes—
534#388C2316yes—
535#388C2316yes—
536#388C2316yes—
537#388C2313yes—
538#388C2313yes—
539#388C2316yes—
540#388C2313yes—
541#388C2313yes—
542#388C2313yes—
543#388C2313yes—
544#388C2313yes—
545#388C2313yes—
546#388C2313yes—
547#388C2313yes—
548#388C2313yes—
549#388C2313yes—
550#388C2313yes—
551#388C2313yes—
552#387C2316yes—
553#387C2313yes—
554#387C2316yes—
555#387C2316yes—
556#387C2316yes—
557#387C2313yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2311yescharacteristic
563#387C2311yescharacteristic
564#387C2311yescharacteristic
565#387C2311yescharacteristic
566#386C2316yes—
567#386C2316yes—
568#386C2316yes—
569#386C2316yes—
570#386C2316yes—
571#386C2313yes—
572#386C2313yes—
573#386C2316yes—
574#386C2316yes—
575#386C2316yes—
576#386C2316yes—
577#386C2313yes—
578#386C2316yes—
579#386C2313yes—
580#386C2313yes—
581#386C2316yes—
582#386C2316yes—
583#386C2313yes—
584#385C2313yes—
585#385C2316yes—
586#385C2316yes—
587#385C2316yes—
588#385C2313yes—
589#385C2313yes—
590#385C2316yes—
591#385C2316yes—
592#385C2313yes—
593#385C2316yes—
594#385C2316yes—
595#385C2316yes—
596#385C2313yes—
597#385C2313yes—
598#384C2313yes—
599#384C2313yes—
600#382C2313yes—
601#382C2313yes—
602#382C2313yes—
603#382C2313yes—
604#382C2311yescharacteristic
605#380C2313yes—
606#380C2313yes—
607#380C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2316yes—
613#380C2316yes—
614#380C2313yes—
615#380C2313yes—
616#380C2313yes—
617#380C2316yes—
618#380C2313yes—
619#380C2313yes—
620C4×C4⋊C4C2316yes—
621C4×C4⋊C4C2313yes—
622C4×C4⋊C4C2313yes—
623C4×C4⋊C4C2316yes—
624C4×C4⋊C4C2313yes—
625C4×C4⋊C4C2313yes—
626C4×C4⋊C4C2313yes—
627C4×C4⋊C4C2313yes—
628C4×C4⋊C4C2313yes—
629C4×C4⋊C4C2313yes—
630C4×C4⋊C4C2313yes—
631C4×C4⋊C4C2313yes—
632C4×C4⋊C4C2313yes—
633C4×C4⋊C4C2313yes—
634C4×C4⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2313yes—
637C4×C22⋊C4C2316yes—
638C4×C22⋊C4C2313yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2313yes—
647C4×C22⋊C4C2313yes—
648C4×C22⋊C4C2316yes—
649#376C2313yes—
650#376C2313yes—
651C43C2313yes—
652C2×#41—24no—
653C2×#41—24no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—224no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41—24no—
661C2×#41—24no—
662C2×#41—24no—
663C2×#41—24no—
664C2×#41—86no—
665C2×#41—86no—
666C2×#41#4118yescomplemented
667C22×Q8C2413yes—
668C22×Q8C2413yes—
669C22×Q8C2413yes—
670C22×Q8C2413yes—
671C22×Q8C2411yescharacteristic
672C22×D4C2413yes—
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2416yes—
678C22×D4C2413yes—
679C22×D4C2416yes—
680C22×D4C2416yes—
681C22×D4C2413yes—
682C22×D4C2416yes—
683C22×D4C2413yes—
684C22×D4C2413yes—
685C22×D4C2413yes—
686C22×D4C2416yes—
687C22×D4C2416yes—
688C23×C4C2413yes—
689C23×C4C2413yes—
690C23×C4C2413yes—
691C23×C4C2413yes—
692C23×C4C2416yes—
693C23×C4C2416yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2416yes—
697C23×C4C2416yes—
698C23×C4C2413yes—
699C23×C4C2413yes—
700C4⋊Q8—212no—
701C4⋊Q8—212no—
702C4⋊Q8—212no—
703C4⋊Q8—212no—
704C4⋊Q8—212no—
705C4⋊Q8C2×D4124yes—
706#127—212no—
707#127—212no—
708#127—212no—
709#127—212no—
710#127—212no—
711#127—212no—
712#126—212no—
713#126—212no—
714#125—212no—
715#125—224no—
716#125—212no—
717#125—212no—
718#125—24no—
719#125—24no—
720#125—212no—
721#125—212no—
722#125—212no—
723#125—212no—
724#125C2×D4124yes—
725#125C2×D4124yes—
726#124—212no—
727#124—46no—
728#124—86no—
729#124—86no—
730#124—86no—
731#123—212no—
732#123—212no—
733#123—224no—
734#123—224no—
735C22⋊Q8—212no—
736C22⋊Q8—212no—
737C22⋊Q8—224no—
738C22⋊Q8—212no—
739C22⋊Q8—212no—
740C22⋊Q8—212no—
741C22⋊Q8—224no—
742C22⋊Q8—224no—
743C22⋊Q8—224no—
744C22⋊Q8—46no—
745C22⋊Q8—86no—
746#121—212no—
747#121—212no—
748#121—212no—
749#121—212no—
750#121—212no—
751#121—212no—
752#121—212no—
753#121—224no—
754#121—212no—
755#121—212no—
756#121—212no—
757#121—212no—
758#121—224no—
759#121—224no—
760#121—212no—
761#121—212no—
762#121—412no—
763#121—46no—
764#121—86no—
765#121—86no—
766#121—86no—
767#121—86no—
768#121—86no—
769C4×Q8—24no—
770C4×Q8—24no—
771C4×Q8—24no—
772C4×Q8—24no—
773C4×Q8—24no—
774C4×Q8—24no—
775C4×Q8—24no—
776C4×Q8—24no—
777C4×Q8—212no—
778C4×Q8—212no—
779C4×Q8—212no—
780C4×Q8C2×D418yes—
781C4×Q8C2×D418yes—
782C4×Q8C2×D418yes—
783C4×Q8C2×D4124yes—
784C4×D4—212no—
785C4×D4—212no—
786C4×D4—212no—
787C4×D4—212no—
788C4×D4—212no—
789C4×D4—212no—
790C4×D4—212no—
791C4×D4—212no—
792C4×D4—212no—
793C4×D4—224no—
794C4×D4—212no—
795C4×D4—212no—
796C4×D4—212no—
797C4×D4—212no—
798C4×D4—212no—
799C4×D4—212no—
800C4×D4—212no—
801C4×D4—212no—
802C4×D4—212no—
803C4×D4—86no—
804C4×D4—86no—
805C4×D4—86no—
806C4×D4—86no—
807#117—212no—
808#117—212no—
809#117—212no—
810#117—212no—
811#117—212no—
812#117—212no—
813C2×C4⋊C4—212no—
814C2×C4⋊C4—212no—
815C2×C4⋊C4—212no—
816C2×C4⋊C4—212no—
817C2×C4⋊C4—224no—
818C2×C4⋊C4—224no—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2416yes—
830C2×C4⋊C4C2416yes—
831C2×C4⋊C4C2416yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2416yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2416yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2416yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2416yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2416yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2416yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2416yes—
904C2×C22⋊C4C2416yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2416yes—
911C2×C22⋊C4C2416yes—
912C2×C22⋊C4C2416yes—
913C2×C22⋊C4C2416yes—
914C2×C22⋊C4C2416yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2416yes—
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2413yes—
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2416yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2413yes—
925C2×C22⋊C4C2413yes—
926C2×C42—212no—
927C2×C42—212no—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2413yes—
935C2×C42C2413yes—
936C2×C42C2413yes—
937C2×C42C2413yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2413yes—
942C2×C42C2413yes—
943C2×C42C2416yes—
944C2×C42C2416yes—
945C2×C42C2413yes—
946C2×C42C2413yes—
947C2×C42C2413yes—
948C2×C42C2413yes—
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2411yescharacteristic
960#95C2411yescharacteristic
961#95C2411yescharacteristic
962#95C2411yescharacteristic
963#95C2411yescharacteristic
964#95C2411yescharacteristic
965#95C2411yescharacteristic
966#95C2411yescharacteristic
967#95C2411yescharacteristic
968#95C2411yescharacteristic
969#95C2413yes—
970#95C2413yes—
971#95C2416yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2416yes—
979#95C2411yescharacteristic
980#95C2413yes—
981#95C2411yescharacteristic
982#95C2416yes—
983#95C2413yes—
984#95C2411yescharacteristic
985#95C2411yescharacteristic
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2416yes—
992#95C2416yes—
993#95C2413yes—
994C24C2513yes—
995C24C2513yes—
996C24C2513yes—
997C24C2513yes—
998#41—232no—
999#41—416no—
1000#41—416no—
1001#41—416no—
1002#41—848no—
1003C2×Q8—26no—
1004C2×Q8—26no—
1005C2×Q8—26no—
1006C2×Q8—43no—
1007C2×Q8—43no—
1008C2×Q8—43no—
1009C2×Q8—43no—
1010C2×Q8—43no—
1011C2×Q8—43no—
1012C2×Q8—43no—
1013C2×Q8—43no—
1014C2×Q8C22×D4112yes—
1015C2×Q8C22×D414yes—
1016C2×Q8C2×#4114yes—
1017C2×Q82−1+414yes—
1018C2×D4—26no—
1019C2×D4—26no—
1020C2×D4—26no—
1021C2×D4—212no—
1022C2×D4—212no—
1023C2×D4—212no—
1024C2×D4—26no—
1025C2×D4—26no—
1026C2×D4—26no—
1027C2×D4—26no—
1028C2×D4—26no—
1029C2×D4—212no—
1030C2×D4—26no—
1031C2×D4—26no—
1032C2×D4—212no—
1033C2×D4—212no—
1034C2×D4—26no—
1035C2×D4—26no—
1036C2×D4—26no—
1037C2×D4—26no—
1038C2×D4—26no—
1039C2×D4—26no—
1040C2×D4—26no—
1041C2×D4—26no—
1042C2×D4—43no—
1043C2×D4—43no—
1044C2×D4—43no—
1045C2×D4—46no—
1046C2×D4—46no—
1047C2×D4—46no—
1048C2×D4—43no—
1049C2×D4—46no—
1050C2×D4—46no—
1051C2×D4—43no—
1052C2×D4—43no—
1053C2×D4—46no—
1054C2×D4—46no—
1055C2×D4—43no—
1056C2×D4—43no—
1057C2×D4—43no—
1058C2×D4—46no—
1059C2×D4—46no—
1060C2×D4—46no—
1061C2×D4—46no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—46no—
1065C2×D4C2×#41112yes—
1066C22×C4—26no—
1067C22×C4—26no—
1068C22×C4—26no—
1069C22×C4—26no—
1070C22×C4—26no—
1071C22×C4—26no—
1072C22×C4—26no—
1073C22×C4—26no—
1074C22×C4—26no—
1075C22×C4—26no—
1076C22×C4—26no—
1077C22×C4—26no—
1078C22×C4—26no—
1079C22×C4—26no—
1080C22×C4—26no—
1081C22×C4—212no—
1082C22×C4—212no—
1083C22×C4—212no—
1084C22×C4—212no—
1085C22×C4—43no—
1086C22×C4—43no—
1087C22×C4—43no—
1088C22×C4—43no—
1089C22×C4—46no—
1090C22×C4—46no—
1091C22×C4—46no—
1092C22×C4—46no—
1093C22×C4—46no—
1094C22×C4—46no—
1095C22×C4—43no—
1096C22×C4—46no—
1097C22×C4—43no—
1098C22×C4—43no—
1099C22×C4—43no—
1100C22×C4—46no—
1101C22×C4C2×#41112yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2513yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2513yes—
1110C22×C4C2513yes—
1111C22×C4C2513yes—
1112C22×C4C2513yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2513yes—
1116C22×C4C2513yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2513yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2513yes—
1123C22×C4C2513yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2513yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2513yes—
1129C4⋊C4—26no—
1130C4⋊C4—26no—
1131C4⋊C4—26no—
1132C4⋊C4—26no—
1133C4⋊C4—26no—
1134C4⋊C4—26no—
1135C4⋊C4—26no—
1136C4⋊C4—26no—
1137C4⋊C4—26no—
1138C4⋊C4—26no—
1139C4⋊C4—212no—
1140C4⋊C4—212no—
1141C4⋊C4—212no—
1142C4⋊C4—22no—
1143C4⋊C4—22no—
1144C4⋊C4—22no—
1145C4⋊C4—22no—
1146C4⋊C4—26no—
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—22no—
1150C4⋊C4—22no—
1151C4⋊C4—22no—
1152C4⋊C4—22no—
1153C4⋊C4—26no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—22no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—26no—
1160C4⋊C4—26no—
1161C4⋊C4—26no—
1162C4⋊C4—26no—
1163C4⋊C4—22no—
1164C4⋊C4—26no—
1165C4⋊C4—22no—
1166C4⋊C4—43no—
1167C4⋊C4—43no—
1168C4⋊C4—43no—
1169C4⋊C4—46no—
1170C4⋊C4—43no—
1171C4⋊C4—43no—
1172C4⋊C4—43no—
1173C4⋊C4—43no—
1174C4⋊C4—46no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4C22×D4112yes—
1178C4⋊C4C22×D4112yes—
1179C4⋊C4C22×D4112yes—
1180C4⋊C4C22×D4112yes—
1181C4⋊C4C22×D4124yes—
1182C4⋊C4C22×D414yes—
1183C4⋊C4C22×D4112yes—
1184C22⋊C4—26no—
1185C22⋊C4—26no—
1186C22⋊C4—26no—
1187C22⋊C4—26no—
1188C22⋊C4—26no—
1189C22⋊C4—212no—
1190C22⋊C4—26no—
1191C22⋊C4—26no—
1192C22⋊C4—26no—
1193C22⋊C4—26no—
1194C22⋊C4—212no—
1195C22⋊C4—26no—
1196C22⋊C4—26no—
1197C22⋊C4—26no—
1198C22⋊C4—26no—
1199C22⋊C4—26no—
1200C22⋊C4—26no—
1201C22⋊C4—26no—
1202C22⋊C4—26no—
1203C22⋊C4—26no—
1204C22⋊C4—26no—
1205C22⋊C4—26no—
1206C22⋊C4—26no—
1207C22⋊C4—26no—
1208C22⋊C4—43no—
1209C22⋊C4—43no—
1210C22⋊C4—43no—
1211C22⋊C4—46no—
1212C22⋊C4—43no—
1213C22⋊C4—46no—
1214C22⋊C4—46no—
1215C22⋊C4—46no—
1216C22⋊C4—43no—
1217C22⋊C4—43no—
1218C22⋊C4—43no—
1219C22⋊C4—43no—
1220C22⋊C4—43no—
1221C22⋊C4—43no—
1222C22⋊C4—46no—
1223C22⋊C4—46no—
1224C22⋊C4—46no—
1225C22⋊C4—46no—
1226C22⋊C4—46no—
1227C22⋊C4—43no—
1228C22⋊C4—43no—
1229C22⋊C4—43no—
1230C22⋊C4—43no—
1231C22⋊C4—46no—
1232C22⋊C4—43no—
1233C22⋊C4—43no—
1234C22⋊C4—43no—
1235C22⋊C4—43no—
1236C42—22no—
1237C42—22no—
1238C42—26no—
1239C42—26no—
1240C42—26no—
1241C42—26no—
1242C42—26no—
1243C42—26no—
1244C42—26no—
1245C42—26no—
1246C42—26no—
1247C42—26no—
1248C42—22no—
1249C42—43no—
1250C42—43no—
1251C42—46no—
1252C42—46no—
1253C42—43no—
1254C42C22×D4112yes—
1255C42C22×D4112yes—
1256C42C22×D4112yes—
1257C23—23no—
1258C23—23no—
1259C23—23no—
1260C23—23no—
1261C23—23no—
1262C23—23no—
1263C23—23no—
1264C23—23no—
1265C23—23no—
1266C23—23no—
1267C23—23no—
1268C23—23no—
1269C23—23no—
1270C23—23no—
1271C23—23no—
1272C23—23no—
1273C23—23no—
1274C23—23no—
1275C23—23no—
1276C23—23no—
1277C23—23no—
1278C23—23no—
1279C23—23no—
1280C23—23no—
1281C23—23no—
1282C23—23no—
1283C23—23no—
1284C23C22×#4116yes—
1285C23C2611yescharacteristic
1286Q8—412no—
1287Q8—86no—
1288Q8—86no—
1289Q8—86no—
1290Q8#548116yes—
1291D4—224no—
1292D4—412no—
1293D4—412no—
1294D4—412no—
1295D4—412no—
1296D4—412no—
1297D4—86no—
1298D4—812no—
1299D4—86no—
1300D4—812no—
1301D4—812no—
1302D4—812no—
1303D4—86no—
1304D4—812no—
1305D4—812no—
1306D4—86no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—23no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—23no—
1316C2×C4—23no—
1317C2×C4—23no—
1318C2×C4—23no—
1319C2×C4—21no—
1320C2×C4—23no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—224no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—23no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—23no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—23no—
1350C2×C4—23no—
1351C2×C4—23no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—23no—
1356C2×C4—23no—
1357C2×C4—21no—
1358C2×C4—23no—
1359C2×C4—23no—
1360C2×C4—23no—
1361C2×C4—23no—
1362C2×C4—21no—
1363C2×C4—23no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—23no—
1377C2×C4—23no—
1378C2×C4—412no—
1379C2×C4—412no—
1380C2×C4—412no—
1381C2×C4—412no—
1382C2×C4—86no—
1383C2×C4—86no—
1384C2×C4—812no—
1385C2×C4—812no—
1386C2×C4—86no—
1387C2×C4—812no—
1388C2×C4—812no—
1389C2×C4C23×D412yes—
1390C2×C4C23×D412yes—
1391C2×C4C23×D416yes—
1392C2×C4C23×D416yes—
1393C2×C4C23×D412yes—
1394C2×C4C23×D416yes—
1395C2×C4C23×D416yes—
1396C2×C4C22×#4112yes—
1397C2×C4C22×#4116yes—
1398C2×C4C2×2−1+416yes—
1399C2×C4#58512yes—
1400C22—26no—
1401C22—26no—
1402C22—26no—
1403C22—43no—
1404C22—43no—
1405C22—43no—
1406C22—43no—
1407C22—43no—
1408C22—43no—
1409C22—43no—
1410C22—43no—
1411C22—43no—
1412C22—43no—
1413C22—43no—
1414C22—43no—
1415C22—43no—
1416C22—43no—
1417C22—43no—
1418C22—43no—
1419C22—43no—
1420C22—43no—
1421C22—43no—
1422C22—43no—
1423C22—43no—
1424C22—43no—
1425C22—43no—
1426C22—43no—
1427C22—43no—
1428C22C24×D411yescharacteristic
1429C22C23×#4111yescharacteristic
1430C22C22×2−1+411yescharacteristic
1431C22C2×#58511yescharacteristic
1432C22H(7,𝔽2)11yescharacteristic
1433C22H(7,𝔽2)11yescharacteristic
1434C22H(7,𝔽2)11yescharacteristic
1435C4—22no—
1436C4—26no—
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—26no—
1441C4—26no—
1442C4—22no—
1443C4—41no—
1444C4—43no—
1445C4—43no—
1446C4—41no—
1447C4—43no—
1448C4—41no—
1449C4—43no—
1450C4—43no—
1451C4—41no—
1452C4—43no—
1453C4—41no—
1454C4—43no—
1455C4—43no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
1459C4—41no—
1460C4—41no—
1461C4C2×#548112yes—
1462C2—46no—
1463C2—83no—
1464C2—83no—
1465C2—83no—
1466C2C22×#54811yescharacteristic
1467C2#6285211yescharacteristic
1468C2#6285811yescharacteristic
1469C2#6295211yescharacteristic
1470C2#6300311yescharacteristic
1471C2#6300811yescharacteristic
1472C2#6307011yescharacteristic
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. C2×#3504C2semidirect
2. C2×#3517C2semidirect
3. #59657C2semidirect
4. #59139C2semidirect
5. #59057C2semidirect
6. #52157C2semidirect
7. #45271C2semidirect
8. #45159C2semidirect
9. #45042C2semidirect
10. #45034C2semidirect
11. #45034C2semidirect
12. #44878C2semidirect
13. #39725C2semidirect
14. #39426C2semidirect
15. #39169C2semidirect
16. #39118C2semidirect
17. #37756C2semidirect
18. #37706C2semidirect
19. #36583C2semidirect
20. #36455C2semidirect
21. #36431C2semidirect
22. #36049C2semidirect
23. #36049C2semidirect
24. #36040C2semidirect
25. #36029C2semidirect
26. #36029C2semidirect
27. #35816C2semidirect
28. #34336C2semidirect
29. #34313C2semidirect
30. #34295C2semidirect
31. #34295C2semidirect
248. #557D4semidirect
666. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#35172
#596572
#591392
#590572
#521572
#452712
#451592
#450422
#450342
#448782
#397252
#394262
#391692
#391182
#377562
#377062
#365832
#364552
#364312
#360492
#360402
#360292
#358162
#343362
#343132
#342952