Finite Group Databasebeta

← #7732379

Subgroups — #7732379

Order 512.

6512 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×#3559C211yesmaximal, characteristic
3#51210C214yesmaximal, complemented
4#50896C214yesmaximal, complemented
5#47762C218yesmaximal, complemented
6#44494C218yesmaximal, complemented
7#39613C212yesmaximal, complemented
8#39173C212yesmaximal, complemented
9#38085C212yesmaximal, complemented
10#38085C212yesmaximal, complemented
11#37870C212yesmaximal, complemented
12#37863C212yesmaximal, complemented
13#37747C214yesmaximal, complemented
14#37708C214yesmaximal, complemented
15#37540C211yesmaximal, characteristic, complemented
16#37420C212yesmaximal, complemented
17#37392C212yesmaximal, complemented
18#36303C212yesmaximal, complemented
19#36184C212yesmaximal, complemented
20#35678C212yesmaximal, complemented
21#35668C212yesmaximal, complemented
22#35249C211yesmaximal, characteristic, complemented
23#35180C211yesmaximal, characteristic, complemented
24C2×#2565C211yesmaximal, characteristic, complemented
25#34083C211yesmaximal, characteristic, complemented
26#3559—216no—
27C2×#563C2212yes—
28C2×#562C2212yes—
29#3523—216no—
30C2×#557C2211yescharacteristic
31C2×#557C2212yes—
32C2×#557C2211yescharacteristic
33C2×#556C2212yes—
34C2×#556C2211yescharacteristic
35C2×#554C2212yes—
36C2×#553C2212yes—
37C2×#553C2212yes—
38C2×#552C2212yes—
39C2×#552C2214yes—
40C2×D4×Q8C2211yescharacteristic
41C2×D4×Q8C2212yes—
42C2×#547C2214yes—
43C2×#547C2212yes—
44C2×#544C2212yes—
45C2×#541C2212yes—
46C2×#541C2214yes—
47C2×#540C2212yes—
48C2×#539C2212yes—
49C2×#539C2214yes—
50C2×#537C2212yes—
51C2×#533C2212yes—
52C2×#533C2211yescharacteristic
53C2×#532C2211yescharacteristic
54C2×#529C2212yes—
55C2×#529C2211yescharacteristic
56C22×#125C2211yescharacteristic
57C2×#519C2212yes—
58C22×C4×Q8C2211yescharacteristic
59#2862C2212yes—
60#2859C2212yes—
61#2854C2214yes—
62#2850C2212yes—
63#2850C2212yes—
64#2850C2212yes—
65#2850C2212yes—
66#2822C2214yes—
67#2729C2218yes—
68#2720C2218yes—
69#2719C2218yes—
70#2718C2218yes—
71#2716C2218yes—
72#2716C2218yes—
73#2713C2218yes—
74#2707C2218yes—
75#2707C2218yes—
76#2704C2218yes—
77#2698C2218yes—
78#2695C2218yes—
79#2691C2218yes—
80#2691C2218yes—
81#2690C2218yes—
82#2690C2218yes—
83#2689C2218yes—
84#2687C2218yes—
85#2687C2218yes—
86#2686C2218yes—
87#2660C2212yes—
88#2660C2212yes—
89#2642C2212yes—
90#2642C2212yes—
91#2639C2214yes—
92#2634C2214yes—
93#2632C2214yes—
94#2627C2214yes—
95#2620C2212yes—
96#2620C2212yes—
97#2592C2214yes—
98#2580C2214yes—
99#2568C2212yes—
100#2568C2212yes—
101#2567C2212yes—
102#2567C2211yescharacteristic
103#2567C2211yescharacteristic
104#2566C2212yes—
105#2566C2212yes—
106#2565C2212yes—
107#2565C2212yes—
108#2565C2214yes—
109#2565C2212yes—
110#2565C2212yes—
111#2565C2212yes—
112#2565C2212yes—
113#2565C2214yes—
114#2565C2212yes—
115#2565C2212yes—
116#2563C2212yes—
117#2562C2214yes—
118#2553C2218yes—
119#2548C2211yescharacteristic
120#2548C2212yes—
121#2548C2211yescharacteristic
122#2547C2212yes—
123#2547C2212yes—
124#2547C2212yes—
125#2519C2218yes—
126#2503C2212yes—
127#2503C2212yes—
128#2502C2212yes—
129#2502C2212yes—
130#2501C2212yes—
131#2500C2212yes—
132#2500C2212yes—
133#2499C2212yes—
134#2499C2212yes—
135#2492C2218yes—
136#2488C2218yes—
137#2488C2218yes—
138#2484C2214yes—
139#2476C2218yes—
140#2476C2218yes—
141#2473C2218yes—
142#2469C2218yes—
143#2468C2218yes—
144#2465C2218yes—
145#2458C2218yes—
146#2458C2218yes—
147#2453C2218yes—
148#2451C2218yes—
149#2450C2218yes—
150#2450C2218yes—
151#2444C2218yes—
152#2444C2218yes—
153#2442C2218yes—
154#2438C2218yes—
155#2438C2218yes—
156#2436C2212yes—
157#2436C2212yes—
158#2436C2212yes—
159#2425C2218yes—
160#2421C2218yes—
161#2413C2218yes—
162#2406C2218yes—
163#2406C2214yes—
164C2×#398C2214yes—
165#2359C2218yes—
166#2339C2218yes—
167#2337C2212yes—
168#2336C2212yes—
169#2334C2214yes—
170#2329C2212yes—
171#2326C2212yes—
172#2326C2212yes—
173#2326C2212yes—
174#2326C2212yes—
175#2325C2212yes—
176#2322C2214yes—
177#2317C2212yes—
178#2311C2214yes—
179#2310C2212yes—
180C4×#124C2212yes—
181C4×#124C2212yes—
182#2298C2212yes—
183#2296C2212yes—
184#2295C2212yes—
185C2×#391C2211yescharacteristic
186C2×#391C2211yescharacteristic
187C2×#391C2212yes—
188#2290C2212yes—
189#2290C2212yes—
190C2×#387C2214yes—
191#2285C2212yes—
192C2×#384C2211yescharacteristic
193#2283C2211yescharacteristic
194C2×#382C2211yescharacteristic
195C42×D4C2212yes—
196C2×C4×C4⋊C4C2211yescharacteristic
197C22×#41C2312yes—
198C22×#41C2314yes—
199C23×Q8C2312yes—
200C23×Q8C2311yescharacteristic
201#563—216no—
202#562—216no—
203#557—216no—
204#557—28no—
205#557—28no—
206#556—216no—
207#556—28no—
208#554—216no—
209#553—216no—
210#553—216no—
211#552—232no—
212#552—216no—
213D4×Q8—216no—
214D4×Q8—28no—
215#547—232no—
216#547—216no—
217#544—216no—
218#541—232no—
219#541—216no—
220#540—216no—
221#539—232no—
222#539—216no—
223#537—216no—
224#533—216no—
225#533—28no—
226#532—28no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2314yes—
236C2×#127C2311yescharacteristic
237#529—216no—
238#529D4116yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2312yes—
246C2×#125—28no—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2311yescharacteristic
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2318yes—
277C2×#123C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2311yescharacteristic
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2311yescharacteristic
301#519—216no—
302C2×C4×Q8—28no—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C2×#117C2314yes—
334C2×#117C2314yes—
335C2×#117C2314yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2314yes—
348C22×C42C2312yes—
349C22×C42C2311yescharacteristic
350C22×C42C2311yescharacteristic
351C22×C42C2312yes—
352C22×C42C2311yescharacteristic
353#400C2318yes—
354#400C2318yes—
355#400C2318yes—
356#400C2318yes—
357#400C2318yes—
358#400C2318yes—
359#400C2318yes—
360#400C2318yes—
361#399C2318yes—
362#398C2318yes—
363#398C2318yes—
364#398C2318yes—
365#398C2318yes—
366#398C2318yes—
367#398C2318yes—
368#398C2318yes—
369#398C2318yes—
370#398C2318yes—
371#398C2318yes—
372#398C2318yes—
373#398C2318yes—
374#397C2318yes—
375#397C2318yes—
376#397C2318yes—
377#397C2318yes—
378#397C2318yes—
379#396C2318yes—
380#396C2318yes—
381#396C2318yes—
382#396C2318yes—
383#395C2314yes—
384#395C2314yes—
385#395C2318yes—
386#395C2318yes—
387#395C2318yes—
388#394C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2314yes—
392#394C2314yes—
393#394C2318yes—
394#394C2318yes—
395#393C2318yes—
396#393C2318yes—
397#393C2318yes—
398#393C2318yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2314yes—
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2318yes—
413#391C2318yes—
414#391C2312yes—
415#391C2318yes—
416#391C2314yes—
417#391C2318yes—
418#391C2318yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2318yes—
423#390C2314yes—
424#390C2314yes—
425#390C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2318yes—
429#389C2318yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2318yes—
434#389C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#388C2314yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#387C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2318yes—
466#387C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2314yes—
470#386C2314yes—
471#386C2318yes—
472#386C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#385C2318yes—
477#385C2318yes—
478#385C2318yes—
479#385C2314yes—
480#385C2314yes—
481#385C2314yes—
482#385C2318yes—
483#385C2318yes—
484#385C2314yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#385C2318yes—
489#384C2312yes—
490#384C2312yes—
491#384C2312yes—
492#384C2314yes—
493#384C2312yes—
494#384C2312yes—
495#384C2312yes—
496#383C2312yes—
497#382C2312yes—
498#382C2312yes—
499#382C2312yes—
500#382C2312yes—
501#382C2314yes—
502#382C2312yes—
503#382C2312yes—
504#382C2312yes—
505#382C2318yes—
506#381C2318yes—
507#381C2312yes—
508#381C2318yes—
509#381C2318yes—
510#380C2318yes—
511#380C2318yes—
512#380C2312yes—
513#380C2318yes—
514#380C2318yes—
515#380C2318yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2311yescharacteristic
519C4×C4⋊C4C2311yescharacteristic
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2312yes—
524C4×C4⋊C4C2314yes—
525C4×C4⋊C4C2318yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2318yes—
529C4×C22⋊C4C2318yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2312yes—
532C4×C22⋊C4C2312yes—
533#376C2312yes—
534#376C2312yes—
535C2×#95C2312yes—
536C2×#95C2314yes—
537C2×#95C2318yes—
538C2×#95C2314yes—
539C2×#95C2314yes—
540C43C2312yes—
541C2×#41—216no—
542C2×#41—28no—
543C2×#41—48no—
544C2×#41—416no—
545C22×Q8—28no—
546C22×Q8—24no—
547C22×Q8—24no—
548C22×Q8—28no—
549C22×Q8—42no—
550C22×Q8—44no—
551C22×Q8C2411yescharacteristic
552C22×Q8C2412yes—
553C22×Q8C2412yes—
554C22×Q8C2414yes—
555C22×Q8C2411yescharacteristic
556C22×Q8C2412yes—
557C22×Q8C2414yes—
558C22×Q8C2412yes—
559C22×Q8C2411yescharacteristic
560C22×D4C2412yes—
561C22×D4C2414yes—
562C22×D4C2412yes—
563C22×D4C2414yes—
564C22×D4C2412yes—
565C22×D4C2414yes—
566C22×D4C2412yes—
567C22×D4C2411yescharacteristic
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2414yes—
572C23×C4C2411yescharacteristic
573C23×C4C2411yescharacteristic
574C23×C4C2412yes—
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2414yes—
578C23×C4C2414yes—
579C23×C4C2412yes—
580C23×C4C2414yes—
581C23×C4C2414yes—
582C23×C4C2414yes—
583C23×C4C2411yescharacteristic
584C4⋊Q8—28no—
585C4⋊Q8—28no—
586C4⋊Q8—216no—
587C4⋊Q8—216no—
588C4⋊Q8—24no—
589C4⋊Q8—24no—
590C4⋊Q8—24no—
591C4⋊Q8—28no—
592C4⋊Q8—28no—
593#127—24no—
594#126—216no—
595#126—216no—
596#126—216no—
597#126—216no—
598#126—216no—
599#126—216no—
600#126C2×D4116yes—
601#125—28no—
602#125—216no—
603#125—216no—
604#125—216no—
605#125—216no—
606#125—216no—
607#125—216no—
608#125—28no—
609#125—28no—
610#125—28no—
611#125—28no—
612#125—28no—
613#125—28no—
614#125—28no—
615#125C2×D418yes—
616#124—28no—
617#124—28no—
618#124—28no—
619#124—44no—
620#124—44no—
621#124—44no—
622#124C2×D418yes—
623#123—216no—
624#123—216no—
625#123—216no—
626#123—216no—
627#123—216no—
628#123—216no—
629#123—216no—
630#123—416no—
631#123C2×D4116yes—
632C22⋊Q8—216no—
633C22⋊Q8—28no—
634C22⋊Q8—28no—
635C22⋊Q8—28no—
636C22⋊Q8—28no—
637C22⋊Q8—216no—
638C22⋊Q8—216no—
639C22⋊Q8—216no—
640C22⋊Q8—216no—
641C22⋊Q8—216no—
642C22⋊Q8—216no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8C2×D418yes—
646#121—216no—
647#121—216no—
648#121—28no—
649#121—28no—
650#121—28no—
651#121—28no—
652#121—216no—
653#121—216no—
654#121C2×D418yes—
655C4×Q8—28no—
656C4×Q8—216no—
657C4×Q8—216no—
658C4×Q8—28no—
659C4×Q8—28no—
660C4×Q8—24no—
661C4×Q8—28no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—28no—
665C4×Q8—24no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8C2×D418yes—
671C4×D4—216no—
672C4×D4—28no—
673C4×D4—216no—
674C4×D4—216no—
675C4×D4—28no—
676C4×D4—28no—
677C4×D4—28no—
678C4×D4—28no—
679C4×D4—48no—
680C4×D4C2×D4116yes—
681C4×D4C2×D418yes—
682#117—28no—
683#117—28no—
684#117—28no—
685#117—216no—
686#117—216no—
687#117—216no—
688#117—44no—
689#117C2×D4116yes—
690C2×C4⋊C4—24no—
691C2×C4⋊C4—28no—
692C2×C4⋊C4—28no—
693C2×C4⋊C4—24no—
694C2×C4⋊C4—28no—
695C2×C4⋊C4—24no—
696C2×C4⋊C4—28no—
697C2×C4⋊C4—216no—
698C2×C4⋊C4—44no—
699C2×C4⋊C4—48no—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2418yes—
738C2×C4⋊C4C2418yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2418yes—
742C2×C4⋊C4C2418yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2418yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2418yes—
770C2×C22⋊C4C2418yes—
771C2×C22⋊C4C2418yes—
772C2×C22⋊C4C2418yes—
773C2×C22⋊C4C2418yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C42—28no—
783C2×C42—42no—
784C2×C42—44no—
785C2×C42—42no—
786C2×C42C2×D418yes—
787C2×C42C2412yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2412yes—
794C2×C42C2412yes—
795C2×C42C2412yes—
796C2×C42C2412yes—
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2412yes—
803C2×C42C2414yes—
804C2×C42C2412yes—
805C2×C42C2411yescharacteristic
806C2×C42C2412yes—
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810#95C2418yes—
811#95C2418yes—
812#95C2414yes—
813#95C2414yes—
814#95C2418yes—
815#95C2418yes—
816#95C2418yes—
817#95C2418yes—
818#95C2418yes—
819#95C2418yes—
820#95C2418yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2418yes—
829#95C2418yes—
830#95C2414yes—
831#95C2418yes—
832#95C2412yes—
833#95C2412yes—
834#95C2414yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2418yes—
840#95C2418yes—
841C24C2514yes—
842C24C2512yes—
843C24C2511yescharacteristic
844#41—816no—
845#41—832no—
846C2×Q8—22no—
847C2×Q8—24no—
848C2×Q8—28no—
849C2×Q8—24no—
850C2×Q8—22no—
851C2×Q8—24no—
852C2×Q8—28no—
853C2×Q8—24no—
854C2×Q8—28no—
855C2×Q8—24no—
856C2×Q8—24no—
857C2×Q8—22no—
858C2×Q8—22no—
859C2×Q8—24no—
860C2×Q8—22no—
861C2×Q8—42no—
862C2×Q8—44no—
863C2×Q8—42no—
864C2×Q8—44no—
865C2×Q8—48no—
866C2×Q8—44no—
867C2×Q8—416no—
868C2×Q8—432no—
869C2×Q8C22×D414yes—
870C2×Q82−1+414yes—
871C2×D4—28no—
872C2×D4—28no—
873C2×D4—216no—
874C2×D4—28no—
875C2×D4—28no—
876C2×D4—24no—
877C2×D4—24no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—42no—
882C2×D4—44no—
883C2×D4—48no—
884C2×D4—44no—
885C2×D4—48no—
886C2×D4C22×D418yes—
887C2×D4C22×D414yes—
888C22×C4—24no—
889C22×C4—22no—
890C22×C4—24no—
891C22×C4—22no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—28no—
897C22×C4—24no—
898C22×C4—28no—
899C22×C4—28no—
900C22×C4—24no—
901C22×C4—28no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—28no—
905C22×C4—28no—
906C22×C4—28no—
907C22×C4—28no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—42no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—48no—
917C22×C4—42no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—48no—
923C22×C4C22×D414yes—
924C22×C4C22×D414yes—
925C22×C4C22×D418yes—
926C22×C4C22×D414yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2514yes—
930C22×C4C2514yes—
931C22×C4C2512yes—
932C22×C4C2514yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2514yes—
936C22×C4C2514yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2512yes—
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2511yescharacteristic
947C22×C4C2512yes—
948C22×C4C2511yescharacteristic
949C4⋊C4—24no—
950C4⋊C4—28no—
951C4⋊C4—24no—
952C4⋊C4—22no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—22no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—28no—
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—28no—
964C4⋊C4—24no—
965C4⋊C4—28no—
966C4⋊C4—28no—
967C4⋊C4—24no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—28no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—28no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—48no—
987C4⋊C4—48no—
988C4⋊C4—44no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—48no—
992C4⋊C4—48no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—48no—
996C4⋊C4—48no—
997C4⋊C4C22×D418yes—
998C4⋊C4C22×D418yes—
999C4⋊C4C22×D418yes—
1000C4⋊C4C22×D414yes—
1001C4⋊C4C22×D418yes—
1002C4⋊C4C22×D414yes—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—28no—
1008C22⋊C4—28no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—216no—
1016C22⋊C4—48no—
1017C22⋊C4—44no—
1018C22⋊C4—48no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—48no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—48no—
1025C22⋊C4—48no—
1026C22⋊C4C22×D418yes—
1027C22⋊C4C22×D418yes—
1028C22⋊C4C22×D418yes—
1029C22⋊C4C22×D418yes—
1030C22⋊C4C22×D418yes—
1031C42—24no—
1032C42—24no—
1033C42—24no—
1034C42—24no—
1035C42—28no—
1036C42—28no—
1037C42—28no—
1038C42—28no—
1039C42—28no—
1040C42—24no—
1041C42—24no—
1042C42—24no—
1043C42—24no—
1044C42—42no—
1045C42—42no—
1046C42—44no—
1047C42—44no—
1048C42—44no—
1049C42C22×D414yes—
1050C42C22×D414yes—
1051C42C22×D414yes—
1052C42C22×D414yes—
1053C42C22×D418yes—
1054C23—21no—
1055C23—21no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—24no—
1060C23—24no—
1061C23—24no—
1062C23—24no—
1063C23—24no—
1064C23—28no—
1065C23—28no—
1066C23C23×D414yes—
1067C23C23×D412yes—
1068C23#58514yes—
1069C23C2611yescharacteristic
1070Q8—28no—
1071Q8—44no—
1072Q8—48no—
1073Q8—416no—
1074Q8—48no—
1075Q8—44no—
1076Q8—48no—
1077Q8—84no—
1078Q8—88no—
1079D4—216no—
1080D4—44no—
1081D4—416no—
1082D4—48no—
1083D4—84no—
1084D4—84no—
1085D4—88no—
1086D4—88no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—28no—
1100C2×C4—28no—
1101C2×C4—216no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—28no—
1125C2×C4—28no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—28no—
1130C2×C4—24no—
1131C2×C4—28no—
1132C2×C4—44no—
1133C2×C4—48no—
1134C2×C4—416no—
1135C2×C4—48no—
1136C2×C4—48no—
1137C2×C4—48no—
1138C2×C4—88no—
1139C2×C4—88no—
1140C2×C4—88no—
1141C2×C4—84no—
1142C2×C4—84no—
1143C2×C4—88no—
1144C2×C4—88no—
1145C2×C4C23×D412yes—
1146C2×C4C23×D412yes—
1147C2×C4C23×D412yes—
1148C2×C4C23×D414yes—
1149C2×C4C23×D414yes—
1150C2×C4C23×D414yes—
1151C2×C4C23×D412yes—
1152C2×C4C23×D412yes—
1153C2×C4C23×D412yes—
1154C2×C4C2×2−1+414yes—
1155C2×C4C2×2−1+412yes—
1156C2×C4#58512yes—
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—24no—
1161C22—24no—
1162C22—24no—
1163C22—24no—
1164C22—44no—
1165C22—44no—
1166C22—44no—
1167C22—44no—
1168C22—44no—
1169C22—48no—
1170C22—48no—
1171C22#350014yes—
1172C22C24×D411yescharacteristic
1173C22C22×2−1+411yescharacteristic
1174C22C2×#58511yescharacteristic
1175C22C2×#58512yes—
1176C222−1+612yes—
1177C4—22no—
1178C4—24no—
1179C4—24no—
1180C4—22no—
1181C4—22no—
1182C4—24no—
1183C4—22no—
1184C4—22no—
1185C4—24no—
1186C4—42no—
1187C4—44no—
1188C4—42no—
1189C4—42no—
1190C4—44no—
1191C4—44no—
1192C4—44no—
1193C4—44no—
1194C4—44no—
1195C4—44no—
1196C4—44no—
1197C4—44no—
1198C4#348914yes—
1199C2—24no—
1200C2—44no—
1201C2—84no—
1202C2C2×#348911yescharacteristic
1203C2C2×#350011yescharacteristic
1204C2#6285911yescharacteristic
1205C2#6290712yes—
1206C2#6294912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3559C2
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×#3523C2semidirect
3. #51210C2semidirect
4. #50896C2semidirect
5. #47762C2semidirect
6. #44494C2semidirect
7. #39613C2semidirect
8. #39173C2semidirect
9. #38085C2semidirect
10. #38085C2semidirect
11. #37870C2semidirect
12. #37863C2semidirect
13. #37747C2semidirect
14. #37708C2semidirect
15. #37540C2semidirect
16. #37420C2semidirect
17. #37392C2semidirect
18. #36303C2semidirect
19. #36184C2semidirect
20. #35678C2semidirect
21. #35668C2semidirect
22. #35249C2semidirect
23. #35180C2semidirect
24. C2×#2565C2semidirect
25. #34083C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C2×#35592
#512102
#508962
#477622
#444942
#396132
#391732
#380852
#378702
#378632
#377472
#377082
#375402
#374202
#373922
#363032
#361842
#356782
#356682
#352492
#351802
C2×#25652
#340832