Finite Group Databasebeta

← #7732064

Subgroups — #7732064

Order 512.

6770 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3547C211yesmaximal, characteristic, complemented
3#47943C218yesmaximal, complemented
4#47716C218yesmaximal, complemented
5#45135C214yesmaximal, complemented
6#44906C214yesmaximal, complemented
7#39489C211yesmaximal, characteristic, complemented
8#39489C211yesmaximal, characteristic, complemented
9#38958C211yesmaximal, characteristic, complemented
10#38955C211yesmaximal, characteristic, complemented
11#38091C212yesmaximal, complemented
12#38079C212yesmaximal, complemented
13#37868C212yesmaximal, complemented
14#37863C212yesmaximal, complemented
15#37764C214yesmaximal, complemented
16#37691C214yesmaximal, complemented
17#37632C211yesmaximal, characteristic, complemented
18#37388C212yesmaximal, complemented
19#37296C212yesmaximal, complemented
20#36415C211yesmaximal, characteristic, complemented
21#36276C211yesmaximal, characteristic, complemented
22#36187C211yesmaximal, characteristic, complemented
23#36180C211yesmaximal, characteristic, complemented
24#35619C212yesmaximal, complemented
25#35530C212yesmaximal, complemented
26#35281C211yesmaximal, characteristic, complemented
27#35200C211yesmaximal, characteristic, complemented
28#34910C211yesmaximal, characteristic, complemented
29#34086C211yesmaximal, characteristic, complemented
30#3547—216no—
31C2×#562C2214yes—
32#3511—216no—
33C2×#556C2212yes—
34C2×#555C2211yescharacteristic
35C2×#555C2212yes—
36C2×#555C2211yescharacteristic
37C2×#555C2211yescharacteristic
38C2×#554C2211yescharacteristic
39C2×#554C2211yescharacteristic
40C2×#554C2211yescharacteristic
41C2×#553C2212yes—
42C2×#553C2212yes—
43C2×#553C2212yes—
44C2×#552C2212yes—
45C2×D4×Q8C2211yescharacteristic
46C2×#548C2212yes—
47C2×#548C2214yes—
48C2×#547C2211yescharacteristic
49C2×#547C2212yes—
50C2×#544C2212yes—
51C2×#542C2214yes—
52C2×#542C2214yes—
53C2×#540C2212yes—
54C2×#537C2212yes—
55C2×#537C2212yes—
56C2×#536C2212yes—
57C2×#533C2211yescharacteristic
58C2×#533C2212yes—
59C2×#532C2212yes—
60C2×#532C2211yescharacteristic
61C22×C4⋊Q8C2211yescharacteristic
62C2×#529C2211yescharacteristic
63C2×#520C2212yes—
64C2×C4×#41C2211yescharacteristic
65#2868C2211yescharacteristic
66#2868C2211yescharacteristic
67#2862C2211yescharacteristic
68#2862C2211yescharacteristic
69#2857C2212yes—
70#2857C2212yes—
71#2856C2212yes—
72#2851C2214yes—
73#2850C2212yes—
74#2821C2214yes—
75#2732C2218yes—
76#2729C2218yes—
77#2722C2218yes—
78#2720C2218yes—
79#2718C2218yes—
80#2717C2218yes—
81#2715C2218yes—
82#2710C2218yes—
83#2708C2218yes—
84#2701C2218yes—
85#2700C2218yes—
86#2692C2218yes—
87#2687C2218yes—
88#2686C2218yes—
89#2686C2218yes—
90#2682C2218yes—
91#2674C2218yes—
92#2674C2218yes—
93#2671C2218yes—
94#2671C2218yes—
95#2660C2212yes—
96#2660C2214yes—
97#2640C2212yes—
98#2638C2214yes—
99#2628C2214yes—
100#2621C2212yes—
101#2620C2212yes—
102#2620C2212yes—
103#2620C2212yes—
104#2614C2214yes—
105#2602C2214yes—
106#2601C2214yes—
107#2599C2214yes—
108#2567C2211yescharacteristic
109#2567C2211yescharacteristic
110#2567C2211yescharacteristic
111#2567C2212yes—
112#2567C2212yes—
113#2566C2211yescharacteristic
114#2565C2211yescharacteristic
115#2563C2211yescharacteristic
116#2563C2211yescharacteristic
117#2563C2211yescharacteristic
118#2557C2218yes—
119#2552C2214yes—
120#2550C2214yes—
121#2549C2218yes—
122#2547C2211yescharacteristic
123#2546C2211yescharacteristic
124#2546C2214yes—
125#2545C2211yescharacteristic
126#2544C2211yescharacteristic
127#2537C2214yes—
128#2535C2214yes—
129#2503C2212yes—
130#2503C2212yes—
131#2502C2212yes—
132#2502C2212yes—
133#2502C2212yes—
134#2502C2212yes—
135#2502C2212yes—
136#2501C2212yes—
137#2501C2212yes—
138#2501C2212yes—
139#2500C2212yes—
140#2500C2212yes—
141#2500C2211yescharacteristic
142#2499C2212yes—
143#2499C2211yescharacteristic
144#2499C2212yes—
145#2499C2212yes—
146#2499C2212yes—
147#2499C2212yes—
148#2491C2218yes—
149#2486C2214yes—
150#2485C2214yes—
151#2478C2218yes—
152#2466C2218yes—
153#2465C2218yes—
154#2462C2218yes—
155#2447C2218yes—
156#2446C2218yes—
157#2443C2218yes—
158#2443C2218yes—
159#2442C2214yes—
160#2441C2214yes—
161#2441C2214yes—
162#2440C2218yes—
163#2439C2214yes—
164#2436C2212yes—
165#2434C2212yes—
166#2434C2214yes—
167#2432C2211yescharacteristic
168#2432C2212yes—
169#2432C2212yes—
170#2431C2212yes—
171#2431C2211yescharacteristic
172#2430C2218yes—
173#2425C2218yes—
174#2423C2218yes—
175#2422C2214yes—
176#2422C2214yes—
177#2422C2218yes—
178#2420C2214yes—
179#2420C2214yes—
180#2419C2218yes—
181#2419C2218yes—
182#2413C2218yes—
183#2406C2218yes—
184#2392C2214yes—
185#2354C2214yes—
186#2352C2214yes—
187#2349C2214yes—
188D4×C4⋊C4C2214yes—
189#2337C2214yes—
190#2333C2214yes—
191#2331C2212yes—
192#2328C2212yes—
193#2327C2212yes—
194#2326C2212yes—
195#2324C2212yes—
196#2324C2212yes—
197#2317C2212yes—
198#2317C2212yes—
199#2317C2214yes—
200#2311C2212yes—
201#2310C2212yes—
202C4×C4⋊Q8C2211yescharacteristic
203C4×#127C2211yescharacteristic
204C4×#124C2211yescharacteristic
205C4×#124C2211yescharacteristic
206#2297C2212yes—
207#2297C2212yes—
208#2297C2212yes—
209C2×#391C2212yes—
210#2293C2211yescharacteristic
211#2293C2211yescharacteristic
212#2290C2212yes—
213#2290C2212yes—
214#2290C2214yes—
215#2285C2212yes—
216C2×#384C2212yes—
217#2283C2211yescharacteristic
218C42×D4C2211yescharacteristic
219C42×D4C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2311yescharacteristic
223C22×#41C2314yes—
224C22×#41C2312yes—
225C23×Q8C2312yes—
226C23×Q8C2312yes—
227#562—232no—
228#556—216no—
229#555—216no—
230#555—28no—
231#555—28no—
232#555—28no—
233#554—28no—
234#554—28no—
235#554—28no—
236#553—216no—
237#553—216no—
238#553—216no—
239#552—216no—
240D4×Q8—28no—
241#548—232no—
242#548—216no—
243#547—216no—
244#547—28no—
245#544—216no—
246#542—232no—
247#542—232no—
248#540—216no—
249#537—216no—
250#537—216no—
251#536—216no—
252#533—216no—
253#533—28no—
254#532—216no—
255#532D4116yescomplemented
256C2×C4⋊Q8—28no—
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2311yescharacteristic
273#529—28no—
274C2×#126C2312yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2311yescharacteristic
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#124C2311yescharacteristic
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#124C2311yescharacteristic
293C2×#124C2311yescharacteristic
294C2×#124C2312yes—
295C2×#123C2312yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2318yes—
303C2×#123C2318yes—
304C2×#123C2318yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2311yescharacteristic
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2311yescharacteristic
329C2×#121C2312yes—
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2318yes—
337C2×#121C2311yescharacteristic
338C2×#121C2311yescharacteristic
339C2×#121C2312yes—
340#520—216no—
341C4×#41—28no—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2314yes—
348C2×C4×Q8C2314yes—
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2311yescharacteristic
351C2×C4×D4C2314yes—
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2311yescharacteristic
369C2×#117C2312yes—
370C2×#117C2312yes—
371C2×#117C2312yes—
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2312yes—
379C2×#117C2311yescharacteristic
380C2×#117C2314yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2318yes—
390C22×C42C2312yes—
391C22×C42C2312yes—
392C22×C42C2312yes—
393C22×C42C2311yescharacteristic
394#400C2318yes—
395#400C2318yes—
396#399C2318yes—
397#399C2318yes—
398#399C2318yes—
399#398C2314yes—
400#398C2318yes—
401#398C2314yes—
402#398C2318yes—
403#398C2318yes—
404#398C2318yes—
405#398C2318yes—
406#398C2318yes—
407#398C2318yes—
408#397C2318yes—
409#397C2314yes—
410#397C2314yes—
411#397C2318yes—
412#397C2318yes—
413#397C2318yes—
414#397C2318yes—
415#397C2318yes—
416#397C2318yes—
417#396C2314yes—
418#396C2314yes—
419#396C2318yes—
420#396C2318yes—
421#396C2318yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2318yes—
426#395C2318yes—
427#395C2318yes—
428#395C2318yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2318yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2318yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2318yes—
443#393C2318yes—
444#392C2314yes—
445#392C2318yes—
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2318yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2318yes—
465#390C2311yescharacteristic
466#390C2314yes—
467#390C2311yescharacteristic
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2311yescharacteristic
472#390C2311yescharacteristic
473#390C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2314yes—
477#390C2318yes—
478#389C2314yes—
479#389C2318yes—
480#389C2318yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2318yes—
485#389C2318yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2318yes—
490#389C2318yes—
491#388C2314yes—
492#388C2314yes—
493#388C2318yes—
494#388C2314yes—
495#388C2314yes—
496#388C2318yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2318yes—
502#388C2318yes—
503#387C2314yes—
504#387C2318yes—
505#387C2318yes—
506#387C2314yes—
507#387C2314yes—
508#387C2318yes—
509#387C2314yes—
510#387C2318yes—
511#387C2318yes—
512#387C2318yes—
513#387C2318yes—
514#386C2318yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2318yes—
522#386C2314yes—
523#386C2314yes—
524#386C2318yes—
525#386C2318yes—
526#386C2318yes—
527#385C2314yes—
528#385C2318yes—
529#385C2318yes—
530#385C2318yes—
531#385C2318yes—
532#385C2314yes—
533#385C2314yes—
534#385C2318yes—
535#385C2318yes—
536#385C2314yes—
537#385C2318yes—
538#385C2318yes—
539#385C2318yes—
540#385C2318yes—
541#385C2318yes—
542#384C2311yescharacteristic
543#384C2311yescharacteristic
544#384C2312yes—
545#384C2312yes—
546#384C2312yes—
547#384C2312yes—
548#384C2312yes—
549#384C2312yes—
550#384C2312yes—
551#384C2314yes—
552#384C2314yes—
553#384C2318yes—
554#383C2312yes—
555#382C2312yes—
556#382C2312yes—
557#382C2312yes—
558#382C2311yescharacteristic
559#382C2311yescharacteristic
560#382C2314yes—
561#382C2314yes—
562#382C2312yes—
563#381C2318yes—
564#381C2312yes—
565#381C2318yes—
566#381C2318yes—
567#380C2314yes—
568#380C2314yes—
569#380C2314yes—
570#380C2318yes—
571#380C2312yes—
572#380C2314yes—
573#380C2318yes—
574#380C2318yes—
575#380C2318yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2311yescharacteristic
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2311yescharacteristic
580C4×C4⋊C4C2311yescharacteristic
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2318yes—
585C4×C22⋊C4C2312yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2318yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2311yescharacteristic
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2311yescharacteristic
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2312yes—
598#376C2312yes—
599#376C2312yes—
600C2×#95C2318yes—
601C43C2311yescharacteristic
602C43C2311yescharacteristic
603C2×#41—216no—
604C2×#41—24no—
605C2×#41—28no—
606C2×#41—44no—
607C2×#41—44no—
608C2×#41—42no—
609C2×#41—42no—
610C2×#41—44no—
611C2×#41—44no—
612C2×#41—88no—
613C2×#41C2×D4116yes—
614C22×Q8—28no—
615C22×Q8—28no—
616C22×Q8—44no—
617C22×Q8—44no—
618C22×Q8—84no—
619C22×Q8C2411yescharacteristic
620C22×Q8C2411yescharacteristic
621C22×Q8C2412yes—
622C22×Q8C2412yes—
623C22×Q8C2414yes—
624C22×Q8C2412yes—
625C22×Q8C2412yes—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×D4C2411yescharacteristic
629C22×D4C2411yescharacteristic
630C22×D4C2411yescharacteristic
631C22×D4C2411yescharacteristic
632C22×D4C2412yes—
633C22×D4C2414yes—
634C22×D4C2412yes—
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2414yes—
651C23×C4C2414yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2411yescharacteristic
660C4⋊Q8—216no—
661C4⋊Q8—28no—
662C4⋊Q8—28no—
663C4⋊Q8—28no—
664C4⋊Q8—28no—
665C4⋊Q8—24no—
666C4⋊Q8—24no—
667C4⋊Q8—24no—
668C4⋊Q8—24no—
669C4⋊Q8—42no—
670C4⋊Q8—44no—
671C4⋊Q8—84no—
672C4⋊Q8—84no—
673C4⋊Q8C2×D418yes—
674#127—42no—
675#127C2×D418yes—
676#126—216no—
677#126—216no—
678#126—216no—
679#126—28no—
680#125—28no—
681#125—28no—
682#125—216no—
683#125—28no—
684#125—24no—
685#125—28no—
686#124—216no—
687#124—216no—
688#124—216no—
689#124—216no—
690#124—216no—
691#124—216no—
692#124—24no—
693#124—44no—
694#124—42no—
695#124—42no—
696#124C2×D4116yes—
697#123—216no—
698#123—216no—
699#123—216no—
700#123—28no—
701#123—216no—
702#123—216no—
703#123—216no—
704#123—88no—
705#123—88no—
706#123—88no—
707C22⋊Q8—216no—
708C22⋊Q8—216no—
709C22⋊Q8—24no—
710C22⋊Q8—28no—
711C22⋊Q8—28no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—216no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723#121—216no—
724#121—28no—
725#121—28no—
726#121—216no—
727#121—216no—
728#121—216no—
729#121—216no—
730#121—216no—
731#121—28no—
732#121—216no—
733#121—28no—
734#121—24no—
735#121—28no—
736#121—28no—
737#121—28no—
738#121—88no—
739#121C2×D4116yes—
740#121C2×D418yes—
741#121C2×D418yes—
742C4×Q8—216no—
743C4×Q8—216no—
744C4×Q8—24no—
745C4×Q8—24no—
746C4×Q8—24no—
747C4×Q8—28no—
748C4×Q8—28no—
749C4×D4—216no—
750C4×D4—216no—
751C4×D4—216no—
752C4×D4—28no—
753C4×D4—28no—
754C4×D4—28no—
755C4×D4—28no—
756C4×D4—28no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—216no—
760C4×D4—24no—
761C4×D4—24no—
762C4×D4—24no—
763C4×D4—28no—
764C4×D4—216no—
765C4×D4—28no—
766C4×D4C2×D4116yes—
767C4×D4C2×D418yes—
768C4×D4C2×D418yes—
769#117—24no—
770#117—28no—
771#117—28no—
772#117—28no—
773#117—28no—
774#117—28no—
775#117—28no—
776#117—28no—
777#117—216no—
778#117—28no—
779#117—28no—
780#117—28no—
781#117—44no—
782#117—44no—
783C2×C4⋊C4—28no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—28no—
786C2×C4⋊C4—28no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—88no—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2418yes—
827C2×C4⋊C4C2418yes—
828C2×C4⋊C4C2418yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2418yes—
832C2×C4⋊C4C2418yes—
833C2×C4⋊C4C2418yes—
834C2×C4⋊C4C2418yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2418yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
869C2×C22⋊C4C2418yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2418yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2418yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C42—28no—
884C2×C42—44no—
885C2×C42—44no—
886C2×C42C2×D418yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911#95C2414yes—
912#95C2418yes—
913#95C2418yes—
914#95C2418yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2418yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2418yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2418yes—
935#95C2418yes—
936#95C2414yes—
937#95C2418yes—
938#95C2418yes—
939#95C2418yes—
940#95C2418yes—
941#95C2418yes—
942C24C2512yes—
943C24C2512yes—
944C24C2511yescharacteristic
945C24C2512yes—
946C24C2512yes—
947#41—432no—
948#41—416no—
949#41—816no—
950#41—832no—
951C2×Q8—22no—
952C2×Q8—22no—
953C2×Q8—24no—
954C2×Q8—28no—
955C2×Q8—24no—
956C2×Q8—28no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—22no—
960C2×Q8—22no—
961C2×Q8—24no—
962C2×Q8—22no—
963C2×Q8—22no—
964C2×Q8—24no—
965C2×Q8—48no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—44no—
972C2×Q8—44no—
973C2×Q8—816no—
974C2×Q8—816no—
975C2×Q8C22×D418yes—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—28no—
979C2×D4—28no—
980C2×D4—28no—
981C2×D4—28no—
982C2×D4—22no—
983C2×D4—22no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—28no—
987C2×D4—22no—
988C2×D4—22no—
989C2×D4—22no—
990C2×D4—22no—
991C2×D4—42no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—48no—
1002C2×D4—48no—
1003C2×D4—44no—
1004C2×D4—48no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4C22×D414yes—
1009C2×D4C22×D414yes—
1010C2×D4C22×D418yes—
1011C2×D4C22×D418yes—
1012C2×D4C22×D418yes—
1013C2×D4C22×D418yes—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—28no—
1022C22×C4—28no—
1023C22×C4—28no—
1024C22×C4—28no—
1025C22×C4—28no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—48no—
1043C22×C4—48no—
1044C22×C4—44no—
1045C22×C4—48no—
1046C22×C4—48no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4C22×D414yes—
1052C22×C4C22×D414yes—
1053C22×C4C22×D418yes—
1054C22×C4C22×D418yes—
1055C22×C4C22×D414yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C4⋊C4—22no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—22no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—44no—
1116C4⋊C4—48no—
1117C4⋊C4—48no—
1118C4⋊C4—48no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—48no—
1122C4⋊C4—48no—
1123C4⋊C4—48no—
1124C4⋊C4—48no—
1125C4⋊C4—44no—
1126C4⋊C4—48no—
1127C4⋊C4C22×D414yes—
1128C4⋊C4C22×D414yes—
1129C4⋊C4C22×D418yes—
1130C22⋊C4—24no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—48no—
1159C22⋊C4—48no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—48no—
1166C22⋊C4—48no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4C22×D418yes—
1170C22⋊C4C22×D418yes—
1171C22⋊C4C22×D418yes—
1172C22⋊C4C22×D418yes—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—28no—
1177C42—28no—
1178C42—28no—
1179C42—28no—
1180C42—24no—
1181C42—24no—
1182C42—22no—
1183C42—22no—
1184C42—24no—
1185C42—24no—
1186C42—22no—
1187C42—22no—
1188C42—44no—
1189C42—44no—
1190C42—42no—
1191C42—42no—
1192C42C22×D414yes—
1193C42C22×D414yes—
1194C42C22×D414yes—
1195C42C22×D414yes—
1196C422−1+418yes—
1197C23—22no—
1198C23—24no—
1199C23—24no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—21no—
1205C23—21no—
1206C23—22no—
1207C23—24no—
1208C23—24no—
1209C23—22no—
1210C23—22no—
1211C23—24no—
1212C23—24no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—24no—
1219C23C23×D414yes—
1220C23C23×D414yes—
1221C23C23×D412yes—
1222C23C2611yescharacteristic
1223Q8—48no—
1224Q8—416no—
1225Q8—44no—
1226Q8—48no—
1227Q8—44no—
1228Q8—84no—
1229Q8—88no—
1230Q8—84no—
1231Q8—84no—
1232D4—28no—
1233D4—28no—
1234D4—48no—
1235D4—48no—
1236D4—48no—
1237D4—48no—
1238D4—48no—
1239D4—44no—
1240D4—44no—
1241D4—88no—
1242D4—84no—
1243D4—88no—
1244D4—88no—
1245D4—88no—
1246D4—88no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—216no—
1261C2×C4—28no—
1262C2×C4—216no—
1263C2×C4—28no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—28no—
1296C2×C4—24no—
1297C2×C4—28no—
1298C2×C4—28no—
1299C2×C4—44no—
1300C2×C4—416no—
1301C2×C4—48no—
1302C2×C4—48no—
1303C2×C4—48no—
1304C2×C4—48no—
1305C2×C4—88no—
1306C2×C4—88no—
1307C2×C4—88no—
1308C2×C4—88no—
1309C2×C4—88no—
1310C2×C4—88no—
1311C2×C4—88no—
1312C2×C4C23×D412yes—
1313C2×C4C23×D414yes—
1314C2×C4C23×D412yes—
1315C2×C4C23×D412yes—
1316C2×C4C23×D414yes—
1317C2×C4C23×D412yes—
1318C2×C4C23×D412yes—
1319C2×C4C23×D412yes—
1320C2×C4C2×2−1+414yes—
1321C2×C4C2×2−1+414yes—
1322C2×C4C2×2−1+414yes—
1323C2×C4#58512yes—
1324C2×C4#58512yes—
1325C22—24no—
1326C22—22no—
1327C22—24no—
1328C22—22no—
1329C22—24no—
1330C22—24no—
1331C22—22no—
1332C22—24no—
1333C22—24no—
1334C22—44no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—44no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22C24×D411yescharacteristic
1351C22C22×2−1+412yes—
1352C22C2×#58511yescharacteristic
1353C22C2×#58511yescharacteristic
1354C22H(7,𝔽2)12yes—
1355C4—22no—
1356C4—24no—
1357C4—24no—
1358C4—22no—
1359C4—22no—
1360C4—22no—
1361C4—24no—
1362C4—24no—
1363C4—42no—
1364C4—44no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—44no—
1372C4—44no—
1373C4—42no—
1374C4—44no—
1375C4—42no—
1376C4—44no—
1377C4#348514yes—
1378C4#349914yes—
1379C2—44no—
1380C2—42no—
1381C2—44no—
1382C2—82no—
1383C2—82no—
1384C2C2×#348511yescharacteristic
1385C2C2×#349911yescharacteristic
1386C2#6285211yescharacteristic
1387C2#6292612yes—
1388C2#6292912yes—
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×#3511C2semidirect
2. C2×#3547C2semidirect
3. #47943C2semidirect
4. #47716C2semidirect
5. #45135C2semidirect
6. #44906C2semidirect
7. #39489C2semidirect
8. #39489C2semidirect
9. #38958C2semidirect
10. #38955C2semidirect
11. #38091C2semidirect
12. #38079C2semidirect
13. #37868C2semidirect
14. #37863C2semidirect
15. #37764C2semidirect
16. #37691C2semidirect
17. #37632C2semidirect
18. #37388C2semidirect
19. #37296C2semidirect
20. #36415C2semidirect
21. #36276C2semidirect
22. #36187C2semidirect
23. #36180C2semidirect
24. #35619C2semidirect
25. #35530C2semidirect
26. #35281C2semidirect
27. #35200C2semidirect
28. #34910C2semidirect
29. #34086C2semidirect
255. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#35472
#479432
#477162
#451352
#449062
#394892
#389582
#389552
#380912
#380792
#378682
#378632
#377642
#376912
#376322
#373882
#372962
#364152
#362762
#361872
#361802
#356192
#355302
#352812
#352002
#349102
#340862