Finite Group Databasebeta

← #7647025

Subgroups — #7647025

Order 512.

6664 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C22×#542C211yesmaximal, characteristic, complemented
3#42882C212yesmaximal, complemented
4#42875C212yesmaximal, complemented
5#42795C212yesmaximal, complemented
6#42788C212yesmaximal, complemented
7#42154C214yesmaximal, complemented
8#42153C214yesmaximal, complemented
9#39467C212yesmaximal, complemented
10#39465C212yesmaximal, complemented
11#39123C212yesmaximal, complemented
12#39121C212yesmaximal, complemented
13#37843C214yesmaximal, complemented
14#37841C214yesmaximal, complemented
15#37606C212yesmaximal, complemented
16#37548C212yesmaximal, complemented
17#37193C218yesmaximal, complemented
18#35675C214yesmaximal, complemented
19#35338C212yesmaximal, complemented
20#35325C211yesmaximal, characteristic, complemented
21#35232C211yesmaximal, characteristic, complemented
22#35220C214yesmaximal, complemented
23#35145C212yesmaximal, complemented
24#34946C211yesmaximal, characteristic, complemented
25#34877C211yesmaximal, characteristic, complemented
26#34128C211yesmaximal, characteristic, complemented
27#3523—216no—
28C2×#557C2211yescharacteristic, complemented
29C2×#557C2211yescharacteristic, complemented
30C2×#557C2212yescomplemented
31C2×#556C2211yescharacteristic, complemented
32C2×#556C2212yescomplemented
33C2×#552C2212yes—
34C2×#552C2214yes—
35C2×D4×Q8C2212yes—
36C2×D4×Q8C2211yescharacteristic, complemented
37C2×#542—216no—
38C2×#542C2212yes—
39C2×#542C2212yes—
40C2×#542C2214yes—
41C2×#542C2212yes—
42C2×#542C2212yes—
43C2×#542C2214yes—
44C2×#541C2214yescomplemented
45C2×#541C2212yescomplemented
46C2×#533C2212yes—
47C2×#533C2211yescharacteristic
48C22×C4⋊Q8C2211yescharacteristic
49C2×#529C2211yescharacteristic
50C2×#529C2212yes—
51C22×#126C2212yes—
52C22×#124C2212yes—
53C22×#124C2211yescharacteristic
54C22×#123C2212yes—
55C22×C22⋊Q8C2212yes—
56C22×C22⋊Q8C2211yescharacteristic
57C22×#121C2211yescharacteristic
58C2×#519C2212yescomplemented
59C22×C4×Q8C2211yescharacteristic
60C22×C4×D4C2211yescharacteristic
61C22×#117C2211yescharacteristic
62#2861C2218yescomplemented
63#2860C2218yescomplemented
64#2855C2212yes—
65#2849C2214yes—
66#2848C2212yes—
67#2821C2214yescomplemented
68#2821C2214yescomplemented
69#2820C2214yescomplemented
70#2819C2214yescomplemented
71#2731C2218yescomplemented
72#2730C2218yescomplemented
73#2729C2218yescomplemented
74#2728C2218yescomplemented
75#2716C2218yescomplemented
76#2714C2218yes—
77#2713C2218yescomplemented
78#2711C2218yes—
79#2707C2218yescomplemented
80#2705C2218yescomplemented
81#2704C2218yescomplemented
82#2702C2218yescomplemented
83#2696C2218yescomplemented
84#2694C2218yescomplemented
85#2692C2218yescomplemented
86#2690C2218yescomplemented
87#2664C2214yescomplemented
88#2664C2218yescomplemented
89#2662C2214yescomplemented
90#2662C2218yescomplemented
91#2640C2214yescomplemented
92#2640C2214yescomplemented
93#2637C2214yescomplemented
94#2637C2214yescomplemented
95#2633C2212yescomplemented
96#2632C2214yescomplemented
97#2631C2214yescomplemented
98#2631C2212yescomplemented
99#2628C2212yescomplemented
100#2627C2214yes—
101#2626C2214yes—
102#2621C2212yescomplemented
103#2614C2214yes—
104#2613C2214yes—
105#2611C2212yescomplemented
106#2611C2214yescomplemented
107#2610C2212yescomplemented
108#2610C2218yescomplemented
109#2604C2214yescomplemented
110#2604C2218yescomplemented
111#2603C2214yescomplemented
112#2603C2214yescomplemented
113#2601C2214yescomplemented
114#2601C2218yescomplemented
115#2599C2214yescomplemented
116#2592C2214yescomplemented
117#2592C2218yescomplemented
118#2592C2214yescomplemented
119#2591C2211yescharacteristic
120#2583C2211yescharacteristic
121#2583C2212yes—
122#2580C2212yescomplemented
123#2563C2212yescomplemented
124#2562C2214yescomplemented
125#2561C2211yescharacteristic
126#2561C2212yes—
127#2561C2212yes—
128#2561C2214yes—
129#2561C2214yes—
130#2561C2212yes—
131#2561C2212yes—
132#2560C2218yescomplemented
133#2558C2218yescomplemented
134#2556C2218yescomplemented
135#2554C2218yescomplemented
136#2550C2214yescomplemented
137#2547C2212yescomplemented
138#2545C2214yescomplemented
139#2540C2214yes—
140#2539C2211yescharacteristic
141#2539C2212yes—
142#2536C2214yescomplemented
143#2535C2212yescomplemented
144#2534C2214yes—
145#2534C2214yes—
146#2503C2212yes—
147#2492C2214yescomplemented
148#2490C2214yes—
149#2486C2212yes—
150#2484C2214yes—
151#2484C2212yes—
152#2482C2214yes—
153#2482C2212yes—
154#2477C2218yescomplemented
155#2471C2218yescomplemented
156#2465C2218yescomplemented
157#2458C2218yescomplemented
158#2451C2214yescomplemented
159#2448C2214yescomplemented
160#2439C2214yescomplemented
161#2436C2214yescomplemented
162#2435C2212yes—
163#2429C2214yescomplemented
164#2426C2214yes—
165#2426C2214yescomplemented
166#2421C2214yescomplemented
167#2414C2214yes—
168#2413C2214yes—
169#2413C2212yes—
170#2411C2214yes—
171#2411C2212yes—
172#2409C2214yescomplemented
173#2408C2212yes—
174#2398C2214yescomplemented
175#2396C2212yescomplemented
176#2392C2212yescomplemented
177#2356C2212yescomplemented
178#2356C2214yescomplemented
179#2351C2212yescomplemented
180#2344C2212yes—
181#2344C2214yes—
182Q8×C22⋊C4C2212yes—
183#2324C2214yescomplemented
184#2323C2214yescomplemented
185#2322C2214yes—
186#2321C2214yes—
187#2310C2214yes—
188#2309C2214yes—
189C4×#124C2214yescomplemented
190C4×#123C2212yes—
191C4×#120C2212yes—
192#2295C2214yescomplemented
193#2295C2212yescomplemented
194#2293C2214yescomplemented
195#2283C2211yescharacteristic
196#2283C2212yes—
197#2280C2214yes—
198C42×Q8C2212yescomplemented
199C4×#117C2212yes—
200C4×#117C2211yescharacteristic
201C23×Q8C2312yes—
202C23×Q8C2312yes—
203C23×Q8C2311yescharacteristic
204C23×D4C2312yes—
205C23×D4C2311yescharacteristic
206C24×C4C2311yescharacteristic
207C24×C4C2312yes—
208#557—28no—
209#557—28no—
210#557—216no—
211#556—28no—
212#556—216no—
213#552—216no—
214#552—232no—
215D4×Q8—216no—
216D4×Q8—28no—
217#542—216no—
218#542—232no—
219#542—216no—
220#542—216no—
221#542—216no—
222#542—232no—
223#541—232no—
224#541—216no—
225#533—28no—
226#533—216no—
227C2×C4⋊Q8—28no—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237#529—28no—
238#529—216no—
239C2×#126—216no—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2312yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#125C2311yescharacteristic
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#124—28no—
259C2×#124—216no—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#124C2311yescharacteristic
265C2×#124C2314yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2314yes—
270C2×#123—216no—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2312yes—
279C2×C22⋊Q8—28no—
280C2×C22⋊Q8—216no—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×#121—28no—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#120C2314yes—
304C2×#120C2312yes—
305#519—216no—
306C2×C4×Q8D4116yescomplemented
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×D4—28no—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×#117—28no—
335C2×#117C2314yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2312yes—
345C2×#117C2314yes—
346C2×#117C2312yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2311yescharacteristic
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2311yescharacteristic
353C22×C4⋊C4C2312yes—
354C22×C22⋊C4C2311yescharacteristic
355C22×C22⋊C4C2312yes—
356C22×C22⋊C4C2312yes—
357C22×C22⋊C4C2312yes—
358C22×C22⋊C4C2312yes—
359C22×C22⋊C4C2311yescharacteristic
360C22×C22⋊C4C2312yes—
361C22×C42C2311yescharacteristic
362C22×C42C2311yescharacteristic
363C22×C42C2312yes—
364#400C2318yes—
365#400C2318yes—
366#400C2318yes—
367#400C2312yes—
368#400C2314yes—
369#399C2312yes—
370#399C2314yes—
371#399C2318yes—
372#399C2318yes—
373#399C2314yes—
374#398C2318yes—
375#398C2312yes—
376#398C2314yes—
377#398C2318yes—
378#398C2314yes—
379#398C2318yes—
380#398C2314yes—
381#398C2314yes—
382#398C2318yes—
383#397C2318yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2318yes—
390#397C2318yes—
391#397C2314yes—
392#397C2314yes—
393#396C2318yes—
394#396C2318yes—
395#396C2314yes—
396#396C2314yes—
397#396C2318yes—
398#396C2318yes—
399#396C2318yes—
400#396C2318yes—
401#395C2318yes—
402#395C2312yes—
403#395C2314yes—
404#395C2318yes—
405#395C2318yes—
406#394C2318yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2312yes—
411#394C2314yes—
412#394C2318yes—
413#394C2314yes—
414#394C2318yes—
415#393C2318yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2312yes—
421#393C2318yes—
422#393C2318yes—
423#393C2318yes—
424#393C2318yes—
425#392C2312yes—
426#392C2314yes—
427#392C2318yes—
428#392C2314yes—
429#392C2318yes—
430#391C2318yes—
431#391C2318yes—
432#391C2318yes—
433#391C2318yes—
434#391C2314yes—
435#391C2314yes—
436#391C2318yes—
437#391C2314yes—
438#390C2318yes—
439#390C2314yes—
440#390C2318yes—
441#390C2318yes—
442#390C2318yes—
443#390C2318yes—
444#390C2318yes—
445#390C2314yes—
446#390C2318yes—
447#390C2314yes—
448#390C2314yes—
449#389C2318yes—
450#389C2318yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2318yes—
456#389C2318yes—
457#389C2314yes—
458#388C2314yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2314yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2314yes—
473#388C2314yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2314yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2314yes—
488#387C2318yes—
489#387C2318yes—
490#386C2318yes—
491#386C2312yes—
492#386C2318yes—
493#386C2312yes—
494#386C2318yes—
495#386C2314yes—
496#386C2318yes—
497#386C2318yes—
498#385C2314yes—
499#385C2314yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2312yes—
504#385C2312yes—
505#385C2318yes—
506#385C2314yes—
507#383C2314yes—
508#383C2312yes—
509#382C2314yes—
510#382C2314yes—
511#382C2312yes—
512#381C2312yes—
513#381C2314yes—
514#381C2314yes—
515#381C2314yes—
516#381C2314yes—
517#381C2312yes—
518#381C2314yes—
519#380C2318yes—
520#380C2318yes—
521#380C2314yes—
522#380C2314yes—
523#380C2312yes—
524#380C2314yes—
525#379C2312yes—
526#379C2314yes—
527#379C2314yes—
528#379C2314yes—
529#379C2314yes—
530C4×C4⋊C4C2318yes—
531C4×C4⋊C4C2312yes—
532C4×C4⋊C4C2312yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C22⋊C4C2318yes—
540C4×C22⋊C4C2311yescharacteristic
541C4×C22⋊C4C2314yes—
542C4×C22⋊C4C2312yes—
543C4×C22⋊C4C2311yescharacteristic
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2318yes—
548#376C2312yes—
549#376C2314yes—
550#376C2314yes—
551#376C2312yes—
552C43C2314yes—
553C43C2312yes—
554C25C2412yes—
555C25C2411yescharacteristic
556C22×Q8—28no—
557C22×Q8—28no—
558C22×Q8—48no—
559C22×Q8—44no—
560C22×Q8—48no—
561C22×Q8C2×D418yes—
562C22×Q8C2412yes—
563C22×Q8C2411yescharacteristic
564C22×Q8C2411yescharacteristic
565C22×Q8C2411yescharacteristic
566C22×Q8C2412yes—
567C22×Q8C2414yes—
568C22×Q8C2414yes—
569C22×Q8C2414yes—
570C22×Q8C2412yes—
571C22×D4—24no—
572C22×D4—28no—
573C22×D4—44no—
574C22×D4—48no—
575C22×D4C2412yes—
576C22×D4C2412yes—
577C22×D4C2411yescharacteristic
578C22×D4C2412yes—
579C22×D4C2414yes—
580C22×D4C2414yes—
581C22×D4C2414yes—
582C22×D4C2418yes—
583C23×C4—24no—
584C23×C4—28no—
585C23×C4—44no—
586C23×C4—48no—
587C23×C4C2411yescharacteristic
588C23×C4C2412yes—
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2411yescharacteristic
592C23×C4C2412yes—
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2414yes—
597C23×C4C2412yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2412yes—
601C23×C4C2411yescharacteristic
602C4⋊Q8—28no—
603C4⋊Q8—216no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—216no—
607C4⋊Q8—24no—
608C4⋊Q8—28no—
609C4⋊Q8—24no—
610C4⋊Q8—28no—
611#126—216no—
612#126—216no—
613#126—216no—
614#126—216no—
615#126—216no—
616#126—216no—
617#126—216no—
618#126—28no—
619#126—216no—
620#125—216no—
621#125—216no—
622#125—216no—
623#125—28no—
624#125—216no—
625#125—24no—
626#125—28no—
627#125—28no—
628#125—216no—
629#124—28no—
630#124—28no—
631#124—216no—
632#124—216no—
633#124—216no—
634#124—216no—
635#124—216no—
636#124—24no—
637#124—28no—
638#124—48no—
639#123—28no—
640#123—216no—
641#123—216no—
642#123—216no—
643#123—216no—
644#123—216no—
645#123—48no—
646#123—44no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—28no—
651C22⋊Q8—216no—
652C22⋊Q8—24no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—216no—
659C22⋊Q8—216no—
660C22⋊Q8—28no—
661C22⋊Q8—216no—
662C22⋊Q8—48no—
663#121—24no—
664#121—28no—
665#121—28no—
666#121—216no—
667#121—48no—
668#120—48no—
669#120—44no—
670C4×Q8—28no—
671C4×Q8—28no—
672C4×Q8—216no—
673C4×Q8—28no—
674C4×Q8—216no—
675C4×Q8—24no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—28no—
680C4×Q8—48no—
681C4×Q8C2×D418yes—
682C4×Q8C2×D418yes—
683C4×Q8C2×D4116yes—
684C4×Q8C2×D418yes—
685C4×Q8C2×D418yes—
686C4×Q8C2×D4116yes—
687C4×D4—28no—
688C4×D4—216no—
689C4×D4—28no—
690C4×D4—28no—
691C4×D4—28no—
692C4×D4—28no—
693C4×D4—24no—
694C4×D4—28no—
695C4×D4—48no—
696#117—28no—
697#117—216no—
698#117—28no—
699#117—216no—
700#117—28no—
701#117—28no—
702#117—28no—
703#117—28no—
704#117—28no—
705#117—216no—
706#117—44no—
707#117—48no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—24no—
710C2×C4⋊C4—24no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4C2×D418yes—
714C2×C4⋊C4C2×D4116yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2418yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2418yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C22⋊C4—24no—
763C2×C22⋊C4—24no—
764C2×C22⋊C4—28no—
765C2×C22⋊C4—28no—
766C2×C22⋊C4—28no—
767C2×C22⋊C4—28no—
768C2×C22⋊C4—28no—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C42—24no—
812C2×C42C2×D418yes—
813C2×C42C2×D4116yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2418yes—
824C2×C42C2418yes—
825C2×C42C2412yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836#95C2412yes—
837#95C2414yes—
838#95C2412yes—
839#95C2418yes—
840#95C2414yes—
841#95C2414yes—
842#95C2418yes—
843#95C2414yes—
844#95C2418yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2418yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863C24—22no—
864C24—24no—
865C24—28no—
866C24—24no—
867C24—42no—
868C24—44no—
869C24—42no—
870C24—44no—
871C24C2512yes—
872C24C2514yes—
873C24C2512yes—
874C24C2511yescharacteristic
875C2×Q8—22no—
876C2×Q8—24no—
877C2×Q8—28no—
878C2×Q8—24no—
879C2×Q8—28no—
880C2×Q8—28no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—28no—
884C2×Q8—44no—
885C2×Q8—48no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×Q8—48no—
889C2×Q8—48no—
890C2×Q8—416no—
891C2×Q8—432no—
892C2×Q8—816no—
893C2×Q8C22×D414yes—
894C2×Q8C22×D414yes—
895C2×Q8C22×D418yes—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—22no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—44no—
907C2×D4—42no—
908C2×D4—416no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—48no—
912C2×D4—48no—
913C2×D4—44no—
914C2×D4—48no—
915C2×D4—48no—
916C2×D4—48no—
917C2×D4—816no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—24no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—24no—
927C22×C4—28no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—28no—
933C22×C4—24no—
934C22×C4—28no—
935C22×C4—28no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—44no—
942C22×C4—48no—
943C22×C4—48no—
944C22×C4—48no—
945C22×C4—416no—
946C22×C4—816no—
947C22×C4C22×D414yes—
948C22×C4C22×D414yes—
949C22×C4C22×D418yes—
950C22×C4C22×D414yes—
951C22×C4C22×D418yes—
952C22×C4C2514yes—
953C22×C4C2518yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2511yescharacteristic
965C22×C4C2512yes—
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2512yes—
973C22×C4C2511yescharacteristic
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—22no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—22no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—44no—
1006C4⋊C4—48no—
1007C4⋊C4—44no—
1008C4⋊C4—48no—
1009C4⋊C4—44no—
1010C4⋊C4—48no—
1011C4⋊C4—48no—
1012C4⋊C4—44no—
1013C4⋊C4—48no—
1014C4⋊C4C22×D414yes—
1015C4⋊C4C22×D418yes—
1016C4⋊C4C22×D414yes—
1017C4⋊C4C22×D418yes—
1018C4⋊C4C22×D418yes—
1019C4⋊C4C22×D418yes—
1020C4⋊C4C22×D418yes—
1021C22⋊C4—24no—
1022C22⋊C4—28no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
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—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—28no—
1043C22⋊C4—24no—
1044C22⋊C4—28no—
1045C22⋊C4—24no—
1046C22⋊C4—28no—
1047C22⋊C4—48no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—48no—
1051C22⋊C4—48no—
1052C22⋊C4—48no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—48no—
1056C22⋊C4—44no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—44no—
1061C22⋊C4—48no—
1062C22⋊C4—48no—
1063C42—24no—
1064C42—24no—
1065C42—28no—
1066C42—28no—
1067C42—28no—
1068C42—28no—
1069C42—24no—
1070C42—28no—
1071C42—42no—
1072C42—42no—
1073C42—44no—
1074C42—44no—
1075C42—48no—
1076C42—48no—
1077C42C22×D414yes—
1078C42C22×D414yes—
1079C42C22×D414yes—
1080C42C22×D414yes—
1081C42C22×D418yes—
1082C42C22×D418yes—
1083C42C22×D418yes—
1084C42C22×D418yes—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—24no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—24no—
1093C23—22no—
1094C23—22no—
1095C23—24no—
1096C23—24no—
1097C23—28no—
1098C23—24no—
1099C23—24no—
1100C23—28no—
1101C23—24no—
1102C23—44no—
1103C23—48no—
1104C23—44no—
1105C23—48no—
1106C23—48no—
1107C23—44no—
1108C23—88no—
1109C23—816no—
1110C23C23×D412yes—
1111C23#58514yes—
1112C23C2611yescharacteristic
1113Q8—28no—
1114Q8—28no—
1115Q8—48no—
1116Q8—44no—
1117Q8—48no—
1118Q8—416no—
1119Q8—48no—
1120Q8—88no—
1121Q8—88no—
1122D4—44no—
1123D4—48no—
1124D4—48no—
1125D4—48no—
1126D4—88no—
1127D4—88no—
1128D4—88no—
1129D4—168no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—28no—
1140C2×C4—216no—
1141C2×C4—28no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—28no—
1156C2×C4—28no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—28no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—28no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—28no—
1168C2×C4—28no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—44no—
1172C2×C4—48no—
1173C2×C4—48no—
1174C2×C4—416no—
1175C2×C4—44no—
1176C2×C4—44no—
1177C2×C4—48no—
1178C2×C4—44no—
1179C2×C4—48no—
1180C2×C4—48no—
1181C2×C4—88no—
1182C2×C4—88no—
1183C2×C4C23×D412yes—
1184C2×C4C23×D414yes—
1185C2×C4C23×D414yes—
1186C2×C4C23×D412yes—
1187C2×C4C23×D412yes—
1188C2×C4C23×D412yes—
1189C2×C4C23×D414yes—
1190C2×C4C23×D412yes—
1191C2×C4C23×D414yes—
1192C2×C4C23×D412yes—
1193C2×C4#58514yes—
1194C22—22no—
1195C22—22no—
1196C22—28no—
1197C22—44no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—44no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—48no—
1210C22—44no—
1211C22—48no—
1212C22—88no—
1213C22—816no—
1214C22#350014yes—
1215C22C24×D411yescharacteristic
1216C22C2×#58512yes—
1217C22C2×#58512yes—
1218C222−1+612yes—
1219C4—22no—
1220C4—22no—
1221C4—24no—
1222C4—24no—
1223C4—22no—
1224C4—22no—
1225C4—22no—
1226C4—24no—
1227C4—24no—
1228C4—44no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—44no—
1233C4—42no—
1234C4—42no—
1235C4—42no—
1236C4—44no—
1237C4—44no—
1238C4—44no—
1239C4—48no—
1240C4#344914yes—
1241C2—24no—
1242C2—82no—
1243C2—84no—
1244C2—82no—
1245C2C2×#344911yescharacteristic
1246C2C2×#350011yescharacteristic
1247C2#6284811yescharacteristic
1248C2#6294014yes—
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×#3523C2semidirect
2. C22×#542C2semidirect
3. #42882C2semidirect
4. #42875C2semidirect
5. #42795C2semidirect
6. #42788C2semidirect
7. #42154C2semidirect
8. #42153C2semidirect
9. #39467C2semidirect
10. #39465C2semidirect
11. #39123C2semidirect
12. #39121C2semidirect
13. #37843C2semidirect
14. #37841C2semidirect
15. #37606C2semidirect
16. #37548C2semidirect
17. #37193C2semidirect
18. #35675C2semidirect
19. #35338C2semidirect
20. #35325C2semidirect
21. #35232C2semidirect
22. #35220C2semidirect
23. #35145C2semidirect
24. #34946C2semidirect
25. #34877C2semidirect
26. #34128C2semidirect
28. C2×#557C22semidirect
29. C2×#557C22semidirect
30. C2×#557C22semidirect
31. C2×#556C22semidirect
32. C2×#556C22semidirect
36. C2×D4×Q8C22semidirect
44. C2×#541C22semidirect
45. C2×#541C22semidirect
58. C2×#519C22semidirect
62. #2861C22semidirect
63. #2860C22semidirect
67. #2821C22semidirect
68. #2821C22semidirect
69. #2820C22semidirect
70. #2819C22semidirect
71. #2731C22semidirect
72. #2730C22semidirect
73. #2729C22semidirect
74. #2728C22semidirect
75. #2716C22semidirect
77. #2713C22semidirect
79. #2707C22semidirect
80. #2705C22semidirect
81. #2704C22semidirect
82. #2702C22semidirect
83. #2696C22semidirect
84. #2694C22semidirect
85. #2692C22semidirect
86. #2690C22semidirect
87. #2664C22semidirect
88. #2664C22semidirect
89. #2662C22semidirect
90. #2662C22semidirect
91. #2640C22semidirect
92. #2640C22semidirect
93. #2637C22semidirect
94. #2637C22semidirect
95. #2633C22semidirect
96. #2632C22semidirect
97. #2631C22semidirect
98. #2631C22semidirect
99. #2628C22semidirect
102. #2621C22semidirect
105. #2611C22semidirect
106. #2611C22semidirect
107. #2610C22semidirect
108. #2610C22semidirect
109. #2604C22semidirect
110. #2604C22semidirect
111. #2603C22semidirect
112. #2603C22semidirect
113. #2601C22semidirect
114. #2601C22semidirect
115. #2599C22semidirect
116. #2592C22semidirect
117. #2592C22semidirect
118. #2592C22semidirect
122. #2580C22semidirect
123. #2563C22semidirect
124. #2562C22semidirect
132. #2560C22semidirect
133. #2558C22semidirect
134. #2556C22semidirect
135. #2554C22semidirect
136. #2550C22semidirect
137. #2547C22semidirect
138. #2545C22semidirect
142. #2536C22semidirect
143. #2535C22semidirect
147. #2492C22semidirect
154. #2477C22semidirect
155. #2471C22semidirect
156. #2465C22semidirect
157. #2458C22semidirect
158. #2451C22semidirect
159. #2448C22semidirect
160. #2439C22semidirect
161. #2436C22semidirect
163. #2429C22semidirect
165. #2426C22semidirect
166. #2421C22semidirect
172. #2409C22semidirect
174. #2398C22semidirect
175. #2396C22semidirect
176. #2392C22semidirect
177. #2356C22semidirect
178. #2356C22semidirect
179. #2351C22semidirect
183. #2324C22semidirect
184. #2323C22semidirect
189. C4×#124C22semidirect
192. #2295C22semidirect
193. #2295C22semidirect
194. #2293C22semidirect
198. C42×Q8C22semidirect
306. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C22×#5422
#428822
#428752
#427952
#427882
#421542
#421532
#394672
#394652
#391232
#391212
#378432
#378412
#376062
#375482
#371932
#356752
#353382
#353252
#352322
#352202
#351452
#349462
#348772
#341282