Finite Group Databasebeta

← #7720074

Subgroups — #7720074

Order 512.

6568 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3547C211yesmaximal, characteristic, complemented
2C2×#3552C211yesmaximal, characteristic, complemented
3#51420C218yesmaximal, complemented
4#50868C218yesmaximal, complemented
5#45316C214yesmaximal, complemented
6#45157C214yesmaximal, complemented
7#45114C214yesmaximal, complemented
8#45092C214yesmaximal, complemented
9#39173C211yesmaximal, characteristic, complemented
10#39167C211yesmaximal, characteristic, complemented
11#38958C212yesmaximal, complemented
12#38958C211yesmaximal, characteristic, complemented
13#38951C211yesmaximal, characteristic, complemented
14#38948C212yesmaximal, complemented
15#38095C212yesmaximal, complemented
16#38085C212yesmaximal, complemented
17#37422C212yesmaximal, complemented
18#37392C212yesmaximal, complemented
19#36534C211yesmaximal, characteristic, complemented
20#36446C211yesmaximal, characteristic, complemented
21#36415C211yesmaximal, characteristic, complemented
22#36303C211yesmaximal, characteristic, complemented
23#35332C212yesmaximal, complemented
24#35320C211yesmaximal, characteristic, complemented
25#35312C212yesmaximal, complemented
26#35289C211yesmaximal, characteristic, complemented
27#35201C211yesmaximal, characteristic, complemented
28#34624C211yesmaximal, characteristic, complemented
29#34151C211yesmaximal, characteristic, complemented
30#3552—216no—
31#3547—216no—
32C2×#563C2214yes—
33C2×#562C2214yes—
34C2×#557C2211yescharacteristic
35C2×#556C2211yescharacteristic
36C2×#555C2211yescharacteristic
37C2×#555C2212yes—
38C2×#554C2211yescharacteristic
39C2×#554C2212yes—
40C2×#553C2212yes—
41C2×#553C2212yes—
42C2×#552C2212yes—
43C2×D4×Q8C2212yes—
44C2×D4×Q8C2211yescharacteristic
45C2×D4×Q8C2211yescharacteristic
46C2×#548C2212yes—
47C2×#548C2212yes—
48C2×#547C2211yescharacteristic
49C2×#547C2211yescharacteristic
50C2×#544C2212yes—
51C2×#544C2212yes—
52C2×#542C2212yes—
53C2×#542C2214yes—
54C2×#541C2212yes—
55C2×#540C2212yes—
56C2×#539C2214yes—
57C2×#537C2212yes—
58C2×#536C2212yes—
59C2×#536C2212yes—
60C2×#533C2211yescharacteristic
61C2×#532C2211yescharacteristic
62C22×C4⋊Q8C2211yescharacteristic
63C2×#529C2211yescharacteristic
64C2×#529C2211yescharacteristic
65#2862C2211yescharacteristic
66#2862C2212yes—
67#2862C2211yescharacteristic
68#2862C2212yes—
69#2862C2211yescharacteristic
70#2862C2211yescharacteristic
71#2861C2212yes—
72#2861C2212yes—
73#2859C2212yes—
74#2858C2212yes—
75#2850C2212yes—
76#2850C2212yes—
77#2723C2218yes—
78#2719C2218yes—
79#2716C2218yes—
80#2713C2218yes—
81#2712C2218yes—
82#2706C2218yes—
83#2703C2218yes—
84#2703C2218yes—
85#2702C2218yes—
86#2700C2218yes—
87#2700C2218yes—
88#2700C2218yes—
89#2699C2218yes—
90#2698C2218yes—
91#2696C2218yes—
92#2696C2218yes—
93#2690C2218yes—
94#2689C2218yes—
95#2688C2218yes—
96#2687C2218yes—
97#2663C2214yes—
98#2662C2214yes—
99#2661C2214yes—
100#2660C2211yescharacteristic
101#2657C2211yescharacteristic
102#2642C2212yes—
103#2642C2212yes—
104#2642C2212yes—
105#2641C2211yescharacteristic
106#2640C2211yescharacteristic
107#2640C2212yes—
108#2640C2214yes—
109#2620C2212yes—
110#2620C2212yes—
111#2620C2211yescharacteristic
112#2620C2211yescharacteristic
113#2619C2211yescharacteristic
114#2619C2211yescharacteristic
115#2604C2214yes—
116#2568C2214yes—
117#2568C2212yes—
118#2568C2211yescharacteristic
119#2568C2214yes—
120#2567C2211yescharacteristic
121#2567C2212yes—
122#2565C2212yes—
123#2565C2212yes—
124#2563C2214yes—
125#2563C2211yescharacteristic
126#2560C2218yes—
127#2559C2218yes—
128#2559C2218yes—
129#2558C2218yes—
130#2558C2218yes—
131#2557C2218yes—
132#2547C2211yescharacteristic
133#2547C2212yes—
134#2547C2212yes—
135#2547C2211yescharacteristic
136#2547C2211yescharacteristic
137#2547C2211yescharacteristic
138#2544C2212yes—
139#2544C2212yes—
140#2542C2211yescharacteristic
141#2536C2214yes—
142#2535C2214yes—
143#2504C2214yes—
144#2503C2212yes—
145#2503C2214yes—
146#2503C2214yes—
147#2502C2212yes—
148#2500C2212yes—
149#2499C2212yes—
150#2499C2212yes—
151#2499C2212yes—
152#2492C2214yes—
153#2492C2218yes—
154#2489C2214yes—
155#2489C2218yes—
156#2489C2218yes—
157#2488C2218yes—
158#2488C2218yes—
159#2488C2218yes—
160#2477C2218yes—
161#2459C2218yes—
162#2459C2218yes—
163#2457C2218yes—
164#2450C2218yes—
165#2444C2218yes—
166#2442C2214yes—
167#2439C2214yes—
168#2439C2218yes—
169#2436C2212yes—
170#2436C2212yes—
171#2436C2212yes—
172#2436C2212yes—
173#2431C2212yes—
174#2431C2212yes—
175#2421C2214yes—
176#2420C2214yes—
177#2420C2218yes—
178#2417C2214yes—
179#2415C2214yes—
180#2415C2214yes—
181#2409C2214yes—
182#2407C2214yes—
183#2392C2214yes—
184#2388C2214yes—
185#2374C2214yes—
186#2373C2214yes—
187#2370C2212yes—
188#2367C2212yes—
189#2363C2212yes—
190#2362C2212yes—
191#2352C2214yes—
192#2352C2214yes—
193Q8×C22⋊C4C2214yes—
194#2339C2214yes—
195#2326C2212yes—
196#2326C2212yes—
197#2323C2214yes—
198#2311C2212yes—
199#2311C2214yes—
200#2310C2212yes—
201#2310C2212yes—
202#2310C2212yes—
203C4×#127C2211yescharacteristic
204C4×#127C2211yescharacteristic
205C4×#124C2212yes—
206C4×#124C2212yes—
207C4×#124C2211yescharacteristic
208C4×#124C2211yescharacteristic
209#2298C2212yes—
210#2297C2212yes—
211#2295C2211yescharacteristic
212C2×#391C2212yes—
213#2293C2212yes—
214#2293C2211yescharacteristic
215#2290C2212yes—
216C42×Q8C2211yescharacteristic
217C42×D4C2211yescharacteristic
218C4×#117C2212yes—
219C4×#117C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226C23×Q8C2312yes—
227#563—232no—
228#562—232no—
229#557—28no—
230#556—28no—
231#555—216no—
232#555—28no—
233#554—216no—
234#554—28no—
235#553—216no—
236#553—216no—
237#552—216no—
238D4×Q8—28no—
239D4×Q8—216no—
240D4×Q8—28no—
241#548—216no—
242#548—216no—
243#547—28no—
244#547—28no—
245#544—216no—
246#544—216no—
247#542—232no—
248#542—216no—
249#541—216no—
250#540—216no—
251#539—232no—
252#537—216no—
253#536—216no—
254#536—216no—
255#533—28no—
256#532—28no—
257C2×C4⋊Q8—28no—
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×#127C2311yescharacteristic
272C2×#127C2311yescharacteristic
273C2×#127C2311yescharacteristic
274#529—28no—
275#529D4116yescomplemented
276C2×#126C2314yes—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2312yes—
282C2×#125C2312yes—
283C2×#125C2311yescharacteristic
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#125C2311yescharacteristic
291C2×#124C2311yescharacteristic
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2312yes—
302C2×#124C2311yescharacteristic
303C2×#124C2311yescharacteristic
304C2×#124C2311yescharacteristic
305C2×#123C2312yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2314yes—
313C2×#123C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2311yescharacteristic
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2311yescharacteristic
338C2×#121C2311yescharacteristic
339C2×#121C2311yescharacteristic
340C2×#121C2312yes—
341C2×#121C2312yes—
342C2×#121C2314yes—
343C2×#121C2312yes—
344C2×#121C2314yes—
345C2×#121C2314yes—
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#121C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2314yes—
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C42C2312yes—
390C22×C42C2311yescharacteristic
391#400C2314yes—
392#400C2318yes—
393#400C2318yes—
394#400C2318yes—
395#400C2318yes—
396#400C2318yes—
397#400C2318yes—
398#400C2318yes—
399#400C2318yes—
400#399C2314yes—
401#398C2318yes—
402#398C2318yes—
403#398C2314yes—
404#398C2318yes—
405#397C2314yes—
406#397C2314yes—
407#397C2318yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2318yes—
412#397C2318yes—
413#397C2318yes—
414#397C2318yes—
415#397C2318yes—
416#396C2314yes—
417#396C2314yes—
418#396C2318yes—
419#396C2318yes—
420#395C2314yes—
421#395C2318yes—
422#395C2314yes—
423#394C2318yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2318yes—
429#394C2318yes—
430#394C2314yes—
431#394C2314yes—
432#394C2318yes—
433#394C2318yes—
434#393C2314yes—
435#393C2318yes—
436#393C2318yes—
437#393C2314yes—
438#393C2318yes—
439#393C2318yes—
440#393C2318yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2318yes—
446#392C2318yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2311yescharacteristic
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2318yes—
459#391C2318yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2318yes—
464#391C2318yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2318yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2318yes—
473#391C2312yes—
474#391C2311yescharacteristic
475#391C2318yes—
476#390C2314yes—
477#390C2311yescharacteristic
478#390C2311yescharacteristic
479#390C2311yescharacteristic
480#390C2311yescharacteristic
481#390C2314yes—
482#390C2318yes—
483#390C2312yes—
484#390C2318yes—
485#390C2312yes—
486#390C2311yescharacteristic
487#390C2312yes—
488#390C2314yes—
489#390C2311yescharacteristic
490#389C2314yes—
491#389C2318yes—
492#389C2318yes—
493#389C2318yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2318yes—
504#388C2318yes—
505#388C2318yes—
506#388C2318yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2318yes—
516#387C2318yes—
517#387C2318yes—
518#387C2318yes—
519#387C2318yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2318yes—
525#386C2318yes—
526#386C2318yes—
527#386C2318yes—
528#386C2318yes—
529#386C2318yes—
530#386C2318yes—
531#386C2318yes—
532#386C2318yes—
533#386C2314yes—
534#386C2318yes—
535#386C2318yes—
536#386C2318yes—
537#386C2318yes—
538#385C2318yes—
539#385C2318yes—
540#385C2314yes—
541#385C2318yes—
542#384C2311yescharacteristic
543#384C2311yescharacteristic
544#384C2312yes—
545#384C2312yes—
546#382C2312yes—
547#382C2318yes—
548#382C2311yescharacteristic
549#382C2312yes—
550#382C2311yescharacteristic
551#382C2314yes—
552#382C2314yes—
553#382C2314yes—
554#382C2314yes—
555#382C2318yes—
556#381C2318yes—
557#381C2318yes—
558#381C2318yes—
559#381C2318yes—
560#380C2314yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2318yes—
566#380C2318yes—
567#380C2318yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2311yescharacteristic
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2311yescharacteristic
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C22⋊C4C2318yes—
581C4×C22⋊C4C2314yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2318yes—
584C4×C22⋊C4C2318yes—
585C4×C22⋊C4C2312yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2312yes—
594#376C2312yes—
595#376C2312yes—
596#376C2311yescharacteristic
597#376C2311yescharacteristic
598C2×#95C2318yes—
599C43C2311yescharacteristic
600C43C2311yescharacteristic
601C43C2312yes—
602C43C2312yes—
603C2×#41—28no—
604C2×#41—28no—
605C2×#41—28no—
606C2×#41—48no—
607C2×#41—44no—
608C2×#41—44no—
609C2×#41—48no—
610C22×Q8—28no—
611C22×Q8—28no—
612C22×Q8—28no—
613C22×Q8—44no—
614C22×Q8—44no—
615C22×Q8—44no—
616C22×Q8—44no—
617C22×Q8—48no—
618C22×Q8C2412yes—
619C22×Q8C2412yes—
620C22×Q8C2411yescharacteristic
621C22×Q8C2412yes—
622C22×Q8C2411yescharacteristic
623C22×Q8C2412yes—
624C22×Q8C2414yes—
625C22×Q8C2414yes—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×D4C2411yescharacteristic
629C22×D4C2411yescharacteristic
630C22×D4C2411yescharacteristic
631C22×D4C2411yescharacteristic
632C22×D4C2412yes—
633C22×D4C2414yes—
634C22×D4C2412yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2412yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2411yescharacteristic
647C23×C4C2412yes—
648C23×C4C2411yescharacteristic
649C23×C4C2414yes—
650C23×C4C2414yes—
651C23×C4C2414yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2411yescharacteristic
657C4⋊Q8—216no—
658C4⋊Q8—28no—
659C4⋊Q8—216no—
660C4⋊Q8—28no—
661C4⋊Q8—28no—
662C4⋊Q8—24no—
663C4⋊Q8—24no—
664C4⋊Q8—28no—
665C4⋊Q8—24no—
666C4⋊Q8—24no—
667C4⋊Q8—24no—
668C4⋊Q8—28no—
669C4⋊Q8—28no—
670#127—24no—
671#127—42no—
672#127—42no—
673#126—216no—
674#126—216no—
675#126—216no—
676#126—216no—
677#126—28no—
678#126C2×D4116yes—
679#125—216no—
680#125—216no—
681#125—216no—
682#125—216no—
683#125—28no—
684#125—24no—
685#125—28no—
686#125—28no—
687#125C2×D418yes—
688#124—216no—
689#124—216no—
690#124—216no—
691#124—216no—
692#124—24no—
693#124—28no—
694#124—28no—
695#124—44no—
696#124—44no—
697#124—44no—
698#124—44no—
699#124—42no—
700#124—42no—
701#124C2×D418yes—
702#123—28no—
703#123—216no—
704#123—216no—
705#123—216no—
706#123—216no—
707#123—216no—
708#123—216no—
709#123—216no—
710#123C2×D4116yes—
711C22⋊Q8—28no—
712C22⋊Q8—28no—
713C22⋊Q8—24no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—216no—
719C22⋊Q8—28no—
720C22⋊Q8—216no—
721C22⋊Q8—28no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—216no—
726C22⋊Q8—216no—
727C22⋊Q8—216no—
728C22⋊Q8—216no—
729C22⋊Q8—216no—
730C22⋊Q8—48no—
731C22⋊Q8C2×D418yes—
732#121—28no—
733#121—216no—
734#121—216no—
735#121—216no—
736#121—28no—
737#121—24no—
738#121—24no—
739#121—24no—
740#121—28no—
741#121—28no—
742#121—28no—
743#121—216no—
744#121—216no—
745#121C2×D418yes—
746C4×Q8—28no—
747C4×Q8—24no—
748C4×Q8—28no—
749C4×Q8—28no—
750C4×Q8—28no—
751C4×Q8—28no—
752C4×Q8—44no—
753C4×Q8C2×D418yes—
754C4×D4—216no—
755C4×D4—28no—
756C4×D4—28no—
757C4×D4—216no—
758C4×D4—216no—
759C4×D4—24no—
760C4×D4—24no—
761C4×D4—28no—
762C4×D4—24no—
763C4×D4—28no—
764C4×D4—28no—
765C4×D4—44no—
766C4×D4—48no—
767C4×D4—48no—
768C4×D4C2×D418yes—
769C4×D4C2×D4116yes—
770#117—28no—
771#117—28no—
772#117—28no—
773#117—216no—
774#117—28no—
775#117—28no—
776#117—42no—
777#117—44no—
778#117—42no—
779#117—44no—
780#117C2×D4116yes—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—28no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—28no—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2418yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2418yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2418yes—
863C2×C22⋊C4C2418yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2418yes—
867C2×C22⋊C4C2418yes—
868C2×C22⋊C4C2418yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2418yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C42—44no—
879C2×C42C2×D418yes—
880C2×C42C2414yes—
881C2×C42C2411yescharacteristic
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2411yescharacteristic
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905#95C2414yes—
906#95C2418yes—
907#95C2418yes—
908#95C2418yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2418yes—
920#95C2418yes—
921#95C2418yes—
922#95C2414yes—
923#95C2414yes—
924#95C2418yes—
925#95C2418yes—
926#95C2418yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2418yes—
932#95C2418yes—
933#95C2418yes—
934#95C2418yes—
935#95C2418yes—
936#95C2418yes—
937#95C2418yes—
938C24C2512yes—
939C24C2512yes—
940C24C2512yes—
941C24C2511yescharacteristic
942C24C2512yes—
943#41—816no—
944#41—816no—
945#41—816no—
946C2×Q8—24no—
947C2×Q8—22no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—28no—
952C2×Q8—28no—
953C2×Q8—28no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—28no—
957C2×Q8—24no—
958C2×Q8—22no—
959C2×Q8—24no—
960C2×Q8—22no—
961C2×Q8—24no—
962C2×Q8—24no—
963C2×Q8—44no—
964C2×Q8—48no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—816no—
971C2×Q8—816no—
972C2×Q8—816no—
973C2×Q8C22×D414yes—
974C2×D4—24no—
975C2×D4—28no—
976C2×D4—24no—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—28no—
980C2×D4—22no—
981C2×D4—22no—
982C2×D4—22no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—22no—
987C2×D4—22no—
988C2×D4—22no—
989C2×D4—22no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—48no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—48no—
1008C2×D4C22×D414yes—
1009C2×D4C22×D418yes—
1010C22×C4—24no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—28no—
1016C22×C4—28no—
1017C22×C4—28no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—28no—
1022C22×C4—28no—
1023C22×C4—28no—
1024C22×C4—28no—
1025C22×C4—28no—
1026C22×C4—28no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—48no—
1031C22×C4—44no—
1032C22×C4—48no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—48no—
1040C22×C4C22×D414yes—
1041C22×C4C22×D414yes—
1042C22×C4C22×D418yes—
1043C22×C4C22×D414yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C4⋊C4—22no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—22no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—22no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—44no—
1102C4⋊C4—48no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—48no—
1110C4⋊C4C22×D414yes—
1111C4⋊C4C22×D414yes—
1112C4⋊C4C22×D418yes—
1113C4⋊C4C22×D418yes—
1114C4⋊C4C22×D418yes—
1115C4⋊C4C22×D418yes—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—24no—
1122C22⋊C4—28no—
1123C22⋊C4—24no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—28no—
1134C22⋊C4—24no—
1135C22⋊C4—44no—
1136C22⋊C4—48no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—42no—
1140C22⋊C4—44no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—48no—
1149C22⋊C4—48no—
1150C22⋊C4—48no—
1151C22⋊C4—48no—
1152C22⋊C4—48no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4C22×D418yes—
1156C22⋊C4C22×D418yes—
1157C22⋊C4C22×D418yes—
1158C22⋊C4C22×D418yes—
1159C22⋊C4C22×D418yes—
1160C42—28no—
1161C42—28no—
1162C42—24no—
1163C42—28no—
1164C42—28no—
1165C42—22no—
1166C42—24no—
1167C42—22no—
1168C42—24no—
1169C42—22no—
1170C42—22no—
1171C42—24no—
1172C42—24no—
1173C42—44no—
1174C42—44no—
1175C42—42no—
1176C42—42no—
1177C42—44no—
1178C42—44no—
1179C42—44no—
1180C42C22×D414yes—
1181C42C22×D414yes—
1182C42C22×D414yes—
1183C42C22×D414yes—
1184C42C22×D418yes—
1185C23—21no—
1186C23—21no—
1187C23—22no—
1188C23—22no—
1189C23—24no—
1190C23—22no—
1191C23—24no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—24no—
1199C23—22no—
1200C23—22no—
1201C23—24no—
1202C23—24no—
1203C23—22no—
1204C23—22no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23C23×D414yes—
1209C23C23×D412yes—
1210C23C2611yescharacteristic
1211Q8—28no—
1212Q8—44no—
1213Q8—48no—
1214Q8—48no—
1215Q8—48no—
1216Q8—84no—
1217Q8—88no—
1218Q8—88no—
1219Q8—88no—
1220Q8—84no—
1221D4—28no—
1222D4—48no—
1223D4—48no—
1224D4—44no—
1225D4—44no—
1226D4—44no—
1227D4—84no—
1228D4—84no—
1229D4—88no—
1230D4—84no—
1231D4—84no—
1232D4—88no—
1233D4—88no—
1234D4—88no—
1235D4—88no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—28no—
1246C2×C4—216no—
1247C2×C4—28no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—28no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—28no—
1287C2×C4—44no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—88no—
1292C2×C4—88no—
1293C2×C4—88no—
1294C2×C4—88no—
1295C2×C4—88no—
1296C2×C4—88no—
1297C2×C4—88no—
1298C2×C4C23×D412yes—
1299C2×C4C23×D414yes—
1300C2×C4C23×D414yes—
1301C2×C4C23×D414yes—
1302C2×C4C23×D412yes—
1303C2×C4C23×D412yes—
1304C2×C4C23×D412yes—
1305C2×C4C23×D412yes—
1306C2×C4C23×D412yes—
1307C2×C4#58512yes—
1308C2×C4#58512yes—
1309C2×C4#58514yes—
1310C22—22no—
1311C22—24no—
1312C22—22no—
1313C22—24no—
1314C22—22no—
1315C22—24no—
1316C22—44no—
1317C22—42no—
1318C22—42no—
1319C22—44no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—44no—
1334C22—44no—
1335C22C24×D411yescharacteristic
1336C22C2×#58511yescharacteristic
1337C22C2×#58512yes—
1338C22C2×#58511yescharacteristic
1339C222−1+612yes—
1340C4—24no—
1341C4—22no—
1342C4—22no—
1343C4—24no—
1344C4—22no—
1345C4—22no—
1346C4—24no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—44no—
1352C4—42no—
1353C4—44no—
1354C4—44no—
1355C4—42no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—42no—
1362C4#350014yes—
1363C4#350014yes—
1364C2—42no—
1365C2—44no—
1366C2—82no—
1367C2—82no—
1368C2—82no—
1369C2C2×#350011yescharacteristic
1370C2C2×#350011yescharacteristic
1371C2#6285911yescharacteristic
1372C2#6293612yes—
1373C2#6293912yes—
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×#3547C2semidirect
2. C2×#3552C2semidirect
3. #51420C2semidirect
4. #50868C2semidirect
5. #45316C2semidirect
6. #45157C2semidirect
7. #45114C2semidirect
8. #45092C2semidirect
9. #39173C2semidirect
10. #39167C2semidirect
11. #38958C2semidirect
12. #38958C2semidirect
13. #38951C2semidirect
14. #38948C2semidirect
15. #38095C2semidirect
16. #38085C2semidirect
17. #37422C2semidirect
18. #37392C2semidirect
19. #36534C2semidirect
20. #36446C2semidirect
21. #36415C2semidirect
22. #36303C2semidirect
23. #35332C2semidirect
24. #35320C2semidirect
25. #35312C2semidirect
26. #35289C2semidirect
27. #35201C2semidirect
28. #34624C2semidirect
29. #34151C2semidirect
275. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35472
C2×#35522
#514202
#508682
#453162
#451572
#451142
#450922
#391732
#391672
#389582
#389512
#389482
#380952
#380852
#374222
#373922
#365342
#364462
#364152
#363032
#353322
#353202
#353122
#352892
#352012
#346242
#341512