Finite Group Databasebeta

← #7655066

Subgroups — #7655066

Order 512.

6962 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3514C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#42875C212yesmaximal, complemented
4#42788C212yesmaximal, complemented
5#41380C214yesmaximal, complemented
6#40500C214yesmaximal, complemented
7#39960C214yesmaximal, complemented
8#38911C212yesmaximal, complemented
9#38910C212yesmaximal, complemented
10#38903C214yesmaximal, complemented
11#38902C214yesmaximal, complemented
12#38438C218yesmaximal, complemented
13#37622C211yesmaximal, characteristic, complemented
14#37551C212yesmaximal, complemented
15#36580C212yesmaximal, complemented
16#36579C212yesmaximal, complemented
17#36269C214yesmaximal, complemented
18#36033C212yesmaximal, complemented
19#35730C212yesmaximal, complemented
20#35338C212yesmaximal, complemented
21#35292C211yesmaximal, characteristic, complemented
22#35180C211yesmaximal, characteristic, complemented
23#35129C212yesmaximal, complemented
24#34964C211yesmaximal, characteristic, complemented
25#34911C212yesmaximal, complemented
26#34121C211yesmaximal, characteristic, complemented
27#3514—216no—
28#3482—216no—
29C2×#559C2211yescharacteristic
30C2×#557C2211yescharacteristic, complemented
31C2×#556C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#556C2212yescomplemented
34C2×#555C2212yes—
35C2×#552C2214yescomplemented
36C2×#552C2212yescomplemented
37C2×#551C2214yes—
38C2×D4×Q8C2211yescharacteristic
39C2×D4×Q8C2211yescharacteristic, complemented
40C2×#548C2212yes—
41C2×#548C2212yes—
42C2×#547C2211yescharacteristic
43C2×#547C2212yescomplemented
44C2×#546C2212yes—
45C2×#546C2212yes—
46C2×D42C2211yescharacteristic
47C2×#542C2212yes—
48C2×#538C2214yes—
49C2×#533C2212yescomplemented
50C2×#533C2211yescharacteristic, complemented
51C2×#532C2211yescharacteristic
52C2×#529C2212yes—
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C2×#529C2214yescomplemented
56C22×#124C2212yes—
57C2×#518C2212yes—
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2212yescomplemented
60C2×C4×#41C2211yescharacteristic, complemented
61C22×C4×Q8C2212yescomplemented
62#2861C2218yescomplemented
63#2857C2212yescomplemented
64#2856C2212yes—
65#2850C2214yes—
66#2850C2214yescomplemented
67#2850C2214yescomplemented
68#2821C2214yescomplemented
69#2821C2214yescomplemented
70#2814C2214yescomplemented
71#2696C2218yescomplemented
72#2694C2218yescomplemented
73#2692C2218yescomplemented
74#2690C2218yescomplemented
75#2689C2218yescomplemented
76#2688C2218yescomplemented
77#2687C2218yescomplemented
78#2686C2218yescomplemented
79#2685C2218yes—
80#2684C2218yescomplemented
81#2678C2218yes—
82#2668C2218yescomplemented
83#2664C2214yescomplemented
84#2663C2218yescomplemented
85#2640C2214yescomplemented
86#2640C2214yescomplemented
87#2639C2214yescomplemented
88#2638C2214yescomplemented
89#2638C2214yescomplemented
90#2632C2214yescomplemented
91#2631C2214yescomplemented
92#2628C2212yescomplemented
93#2625C2214yescomplemented
94#2625C2212yescomplemented
95#2624C2214yes—
96#2624C2212yes—
97#2624C2212yescomplemented
98#2621C2212yescomplemented
99#2615C2212yescomplemented
100#2611C2218yescomplemented
101#2610C2218yescomplemented
102#2604C2214yescomplemented
103#2603C2214yescomplemented
104#2602C2218yescomplemented
105#2601C2214yescomplemented
106#2592C2211yescharacteristic
107#2592C2212yes—
108#2592C2214yes—
109#2592C2212yescomplemented
110#2592C2212yescomplemented
111#2592C2214yescomplemented
112#2592C2212yescomplemented
113#2584C2212yescomplemented
114#2584C2211yescharacteristic, complemented
115#2582C2212yescomplemented
116#2581C2214yescomplemented
117#2580C2212yescomplemented
118#2580C2214yescomplemented
119#2568C2212yescomplemented
120#2563C2212yescomplemented
121#2562C2214yescomplemented
122#2562C2211yescharacteristic, complemented
123#2561C2218yescomplemented
124#2561C2214yescomplemented
125#2561C2214yescomplemented
126#2559C2218yescomplemented
127#2557C2218yescomplemented
128#2550C2214yescomplemented
129#2548C2212yes—
130#2547C2212yescomplemented
131#2540C2214yes—
132#2540C2211yescharacteristic
133#2540C2212yescomplemented
134#2538C2212yes—
135#2535C2212yescomplemented
136#2521C2218yescomplemented
137#2498C2212yescomplemented
138#2492C2214yescomplemented
139#2490C2214yes—
140#2482C2214yescomplemented
141#2481C2218yescomplemented
142#2480C2218yescomplemented
143#2469C2218yescomplemented
144#2468C2218yescomplemented
145#2464C2218yescomplemented
146#2458C2218yescomplemented
147#2457C2218yescomplemented
148#2448C2214yescomplemented
149#2447C2214yes—
150#2443C2218yescomplemented
151#2436C2214yescomplemented
152#2435C2214yes—
153#2430C2212yescomplemented
154#2421C2214yescomplemented
155#2420C2214yes—
156#2418C2218yescomplemented
157#2417C2212yescomplemented
158#2416C2212yes—
159#2415C2214yescomplemented
160#2415C2214yescomplemented
161#2414C2214yes—
162#2414C2214yescomplemented
163#2409C2214yescomplemented
164#2409C2214yescomplemented
165#2408C2214yes—
166#2408C2214yes—
167#2407C2214yescomplemented
168#2404C2214yescomplemented
169#2396C2212yescomplemented
170#2395C2214yescomplemented
171#2392C2212yescomplemented
172#2388C2214yescomplemented
173#2367C2214yescomplemented
174#2362C2214yescomplemented
175#2361C2214yescomplemented
176#2357C2212yes—
177#2356C2212yescomplemented
178#2355C2212yescomplemented
179#2354C2212yes—
180#2353C2214yescomplemented
181#2352C2214yescomplemented
182#2352C2214yescomplemented
183#2324C2214yescomplemented
184#2321C2218yescomplemented
185#2311C2214yescomplemented
186#2310C2214yescomplemented
187#2309C2214yes—
188C4×C22⋊Q8C2214yescomplemented
189C4×C22⋊Q8C2212yescomplemented
190C4×#121C2212yes—
191C4×#121C2214yescomplemented
192C4×#121C2214yescomplemented
193#2298C2214yescomplemented
194#2297C2212yes—
195#2293C2218yescomplemented
196#2285C2211yescharacteristic, complemented
197#2283C2212yescomplemented
198C4×#117C2212yescomplemented
199C4×#117C2212yescomplemented
200C2×C4×C4⋊C4C2211yescharacteristic, complemented
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C22×#41C2312yes—
204C22×#41C2311yescharacteristic
205C23×Q8C2312yes—
206C23×Q8C2312yes—
207C23×D4C2312yes—
208C23×D4C2312yes—
209#559—28no—
210#557—28no—
211#556—28no—
212#556—28no—
213#556—216no—
214#555—216no—
215#552—232no—
216#552—216no—
217#551—232no—
218D4×Q8—28no—
219D4×Q8—28no—
220#548—216no—
221#548—216no—
222#547—28no—
223#547—216no—
224#546—216no—
225#546—216no—
226D42—28no—
227#542—216no—
228#538—232no—
229#533—216no—
230#533—28no—
231#532—28no—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2312yes—
238C2×#127C2311yescharacteristic
239#529—216no—
240#529—232no—
241#529—216no—
242#529—28no—
243C2×#126C2314yes—
244C2×#126C2312yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2312yes—
250C2×#125C2311yescharacteristic
251C2×#125C2314yes—
252C2×#125C2312yes—
253C2×#125C2314yes—
254C2×#124—216no—
255C2×#124C2311yescharacteristic
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2312yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2311yescharacteristic
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#120C2314yes—
303C2×#120C2314yes—
304C2×#120C2318yes—
305#518—216no—
306C4×#41—216no—
307C4×#41—28no—
308C4×#41D4116yescomplemented
309C2×C4×Q8—216no—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2314yes—
340C2×C4×D4C2318yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2311yescharacteristic
345C2×#117C2314yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2314yes—
350C2×#117C2314yes—
351C2×#117C2312yes—
352C2×#117C2311yescharacteristic
353C2×#117C2312yes—
354C2×#117C2314yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2311yescharacteristic
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2314yes—
360C22×C4⋊C4C2312yes—
361C22×C22⋊C4C2314yes—
362C22×C22⋊C4C2314yes—
363C22×C22⋊C4C2314yes—
364C22×C42C2314yes—
365C22×C42C2312yes—
366C22×C42C2312yes—
367C22×C42C2312yes—
368C22×C42C2311yescharacteristic
369#400C2318yes—
370#400C2312yes—
371#400C2318yes—
372#400C2318yes—
373#400C2314yes—
374#399C2318yes—
375#399C2318yes—
376#399C2314yes—
377#399C2314yes—
378#399C2312yes—
379#398C2312yes—
380#398C2314yes—
381#398C2318yes—
382#398C2318yes—
383#398C2314yes—
384#398C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2318yes—
389#397C2314yes—
390#397C2318yes—
391#397C2314yes—
392#397C2318yes—
393#397C2318yes—
394#397C2314yes—
395#397C2318yes—
396#397C2318yes—
397#397C2318yes—
398#396C2314yes—
399#396C2314yes—
400#396C2318yes—
401#395C2312yes—
402#395C2318yes—
403#395C2314yes—
404#395C2318yes—
405#394C2312yes—
406#394C2318yes—
407#394C2314yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#394C2318yes—
412#394C2318yes—
413#394C2318yes—
414#394C2318yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2318yes—
420#393C2318yes—
421#393C2314yes—
422#393C2318yes—
423#393C2318yes—
424#392C2318yes—
425#392C2314yes—
426#392C2318yes—
427#392C2318yes—
428#392C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2318yes—
434#391C2318yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2318yes—
445#390C2318yes—
446#390C2314yes—
447#390C2314yes—
448#390C2318yes—
449#390C2314yes—
450#390C2314yes—
451#390C2318yes—
452#390C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2318yes—
462#389C2318yes—
463#388C2314yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2314yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2314yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2314yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2314yes—
498#386C2318yes—
499#386C2318yes—
500#386C2314yes—
501#386C2314yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2314yes—
507#385C2318yes—
508#384C2312yes—
509#383C2314yes—
510#382C2314yes—
511#382C2314yes—
512#382C2312yes—
513#381C2318yes—
514#381C2318yes—
515#381C2314yes—
516#380C2318yes—
517#380C2318yes—
518#380C2312yes—
519#380C2312yes—
520#380C2314yes—
521#380C2314yes—
522#380C2312yes—
523#380C2314yes—
524#380C2314yes—
525#380C2312yes—
526#380C2314yes—
527#379C2318yes—
528#379C2318yes—
529#379C2318yes—
530C4×C4⋊C4C2312yes—
531C4×C4⋊C4C2311yescharacteristic
532C4×C4⋊C4C2312yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2311yescharacteristic
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2318yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2318yes—
550#376C2314yes—
551#376C2314yes—
552C2×#95C2312yes—
553C43C2314yes—
554C25C2414yes—
555C2×#41—28no—
556C2×#41—24no—
557C2×#41—28no—
558C2×#41—48no—
559C2×#41—44no—
560C2×#41—42no—
561C2×#41—42no—
562C2×#41—48no—
563C2×#41C2×D418yes—
564C22×Q8—28no—
565C22×Q8—28no—
566C22×Q8—44no—
567C22×Q8—44no—
568C22×Q8—48no—
569C22×Q8C2412yes—
570C22×Q8C2411yescharacteristic
571C22×Q8C2412yes—
572C22×Q8C2411yescharacteristic
573C22×Q8C2414yes—
574C22×Q8C2411yescharacteristic
575C22×Q8C2412yes—
576C22×Q8C2414yes—
577C22×D4—28no—
578C22×D4—28no—
579C22×D4—44no—
580C22×D4—44no—
581C22×D4—48no—
582C22×D4C2411yescharacteristic
583C22×D4C2412yes—
584C22×D4C2411yescharacteristic
585C22×D4C2412yes—
586C22×D4C2414yes—
587C22×D4C2412yes—
588C22×D4C2411yescharacteristic
589C22×D4C2414yes—
590C22×D4C2412yes—
591C22×D4C2412yes—
592C22×D4C2414yes—
593C22×D4C2418yes—
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2414yes—
601C23×C4C2412yes—
602C23×C4C2411yescharacteristic
603C23×C4C2412yes—
604C23×C4C2411yescharacteristic
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2414yes—
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2411yescharacteristic
613C4⋊Q8—28no—
614C4⋊Q8—24no—
615C4⋊Q8—24no—
616C4⋊Q8—28no—
617C4⋊Q8—24no—
618C4⋊Q8—28no—
619#127—24no—
620#126—216no—
621#126—216no—
622#126—216no—
623#126—216no—
624#126—216no—
625#126—28no—
626#125—28no—
627#125—216no—
628#125—24no—
629#125—216no—
630#125—28no—
631#124—28no—
632#124—28no—
633#124—216no—
634#124—216no—
635#124—24no—
636#124—28no—
637#124—216no—
638#124—28no—
639#124—28no—
640#124—216no—
641#124—48no—
642#123—28no—
643#123—216no—
644#123—216no—
645#123—216no—
646#123—216no—
647#123—216no—
648#123—216no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—24no—
652C22⋊Q8—28no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—216no—
657C22⋊Q8—28no—
658C22⋊Q8—216no—
659C22⋊Q8—216no—
660C22⋊Q8—216no—
661C22⋊Q8—44no—
662C22⋊Q8—48no—
663C22⋊Q8—48no—
664#121—28no—
665#121—216no—
666#121—216no—
667#121—28no—
668#121—24no—
669#121—28no—
670#121—28no—
671#121—28no—
672#121—216no—
673#121—48no—
674#121—44no—
675#121—48no—
676#121—48no—
677#121—48no—
678#120—216no—
679#120—216no—
680#120—416no—
681C4×Q8—28no—
682C4×Q8—28no—
683C4×Q8—216no—
684C4×Q8—216no—
685C4×Q8—28no—
686C4×Q8—28no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—28no—
690C4×Q8—28no—
691C4×Q8—24no—
692C4×Q8C2×D418yes—
693C4×Q8C2×D418yes—
694C4×D4—28no—
695C4×D4—216no—
696C4×D4—28no—
697C4×D4—28no—
698C4×D4—216no—
699C4×D4—216no—
700C4×D4—28no—
701C4×D4—28no—
702C4×D4—216no—
703C4×D4—24no—
704C4×D4—24no—
705C4×D4—28no—
706C4×D4—28no—
707C4×D4—24no—
708C4×D4—28no—
709C4×D4—28no—
710C4×D4—48no—
711C4×D4—416no—
712C4×D4C2×D418yes—
713C4×D4C2×D418yes—
714C4×D4C2×D4116yes—
715C4×D4C2×D4116yes—
716#117—28no—
717#117—24no—
718#117—216no—
719#117—28no—
720#117—28no—
721#117—216no—
722#117—28no—
723#117—28no—
724#117—216no—
725#117—48no—
726#117—44no—
727#117C2×D4116yes—
728#117C2×D418yes—
729C2×C4⋊C4—28no—
730C2×C4⋊C4—216no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C22⋊C4—216no—
775C2×C22⋊C4—216no—
776C2×C22⋊C4—216no—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2418yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C42—216no—
822C2×C42—28no—
823C2×C42—44no—
824C2×C42C2×D4116yes—
825C2×C42C2×D418yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2418yes—
837C2×C42C2418yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2411yescharacteristic
845C2×C42C2412yes—
846C2×C42C2411yescharacteristic
847#95C2412yes—
848#95C2412yes—
849#95C2414yes—
850#95C2414yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2414yes—
861#95C2418yes—
862#95C2414yes—
863#95C2418yes—
864#95C2414yes—
865#95C2414yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869#95C2418yes—
870#95C2418yes—
871#95C2418yes—
872C24—28no—
873C24—44no—
874C24—44no—
875C24—48no—
876C24—48no—
877C24C2512yes—
878C24C2514yes—
879C24C2512yes—
880C24C2511yescharacteristic
881C24C2512yes—
882#41—416no—
883#41—432no—
884#41—416no—
885#41—816no—
886C2×Q8—28no—
887C2×Q8—24no—
888C2×Q8—22no—
889C2×Q8—24no—
890C2×Q8—22no—
891C2×Q8—24no—
892C2×Q8—28no—
893C2×Q8—22no—
894C2×Q8—22no—
895C2×Q8—24no—
896C2×Q8—24no—
897C2×Q8—28no—
898C2×Q8—24no—
899C2×Q8—44no—
900C2×Q8—44no—
901C2×Q8—42no—
902C2×Q8—44no—
903C2×Q8—48no—
904C2×Q8—432no—
905C2×Q8—816no—
906C2×Q8C22×D414yes—
907C2×D4—24no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—24no—
911C2×D4—28no—
912C2×D4—24no—
913C2×D4—24no—
914C2×D4—28no—
915C2×D4—216no—
916C2×D4—28no—
917C2×D4—22no—
918C2×D4—24no—
919C2×D4—22no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—28no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—28no—
928C2×D4—24no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—48no—
938C2×D4—48no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—48no—
942C2×D4—48no—
943C2×D4—432no—
944C2×D4—816no—
945C2×D4C22×D414yes—
946C2×D4C22×D418yes—
947C22×C4—22no—
948C22×C4—24no—
949C22×C4—22no—
950C22×C4—28no—
951C22×C4—28no—
952C22×C4—24no—
953C22×C4—28no—
954C22×C4—24no—
955C22×C4—28no—
956C22×C4—24no—
957C22×C4—28no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—28no—
967C22×C4—28no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—48no—
979C22×C4—44no—
980C22×C4—48no—
981C22×C4—48no—
982C22×C4C22×D418yes—
983C22×C4C22×D414yes—
984C22×C4C22×D414yes—
985C22×C4C22×D418yes—
986C22×C4C22×D418yes—
987C22×C4C22×D414yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2518yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2512yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—22no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—22no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—24no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—24no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—48no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—48no—
1045C4⋊C4—48no—
1046C4⋊C4—44no—
1047C4⋊C4C22×D414yes—
1048C4⋊C4C22×D418yes—
1049C4⋊C4C22×D414yes—
1050C4⋊C4C22×D418yes—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—28no—
1059C22⋊C4—24no—
1060C22⋊C4—28no—
1061C22⋊C4—24no—
1062C22⋊C4—24no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—24no—
1073C22⋊C4—28no—
1074C22⋊C4—48no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
1080C22⋊C4—48no—
1081C22⋊C4—48no—
1082C22⋊C4—44no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—44no—
1087C22⋊C4—48no—
1088C22⋊C4—48no—
1089C22⋊C4—44no—
1090C22⋊C4—48no—
1091C22⋊C4—48no—
1092C22⋊C4C22×D418yes—
1093C22⋊C4C22×D418yes—
1094C22⋊C4C22×D418yes—
1095C42—28no—
1096C42—24no—
1097C42—28no—
1098C42—24no—
1099C42—28no—
1100C42—24no—
1101C42—28no—
1102C42—24no—
1103C42—28no—
1104C42—42no—
1105C42—42no—
1106C42—44no—
1107C42—48no—
1108C42—48no—
1109C42C22×D418yes—
1110C42C22×D414yes—
1111C42C22×D414yes—
1112C42C22×D418yes—
1113C42C22×D414yes—
1114C42C22×D414yes—
1115C42C22×D418yes—
1116C23—22no—
1117C23—22no—
1118C23—21no—
1119C23—22no—
1120C23—24no—
1121C23—22no—
1122C23—24no—
1123C23—21no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—24no—
1132C23—22no—
1133C23—24no—
1134C23—28no—
1135C23—24no—
1136C23—22no—
1137C23—24no—
1138C23—28no—
1139C23—24no—
1140C23—416no—
1141C23—88no—
1142C23—88no—
1143C23—168no—
1144C23—168no—
1145C23C23×D414yes—
1146C23C23×D412yes—
1147C23#58514yes—
1148C23C2611yescharacteristic
1149Q8—28no—
1150Q8—416no—
1151Q8—44no—
1152Q8—48no—
1153Q8—48no—
1154Q8—44no—
1155Q8—48no—
1156Q8—88no—
1157D4—28no—
1158D4—28no—
1159D4—48no—
1160D4—48no—
1161D4—416no—
1162D4—416no—
1163D4—48no—
1164D4—44no—
1165D4—48no—
1166D4—84no—
1167D4—88no—
1168D4—88no—
1169D4—816no—
1170D4—84no—
1171D4—88no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—28no—
1182C2×C4—216no—
1183C2×C4—28no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—28no—
1198C2×C4—28no—
1199C2×C4—28no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—28no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—48no—
1218C2×C4—44no—
1219C2×C4—48no—
1220C2×C4—416no—
1221C2×C4—48no—
1222C2×C4—416no—
1223C2×C4—48no—
1224C2×C4—48no—
1225C2×C4—48no—
1226C2×C4—88no—
1227C2×C4—88no—
1228C2×C4—88no—
1229C2×C4—88no—
1230C2×C4C23×D414yes—
1231C2×C4C23×D414yes—
1232C2×C4C23×D412yes—
1233C2×C4C23×D412yes—
1234C2×C4C23×D412yes—
1235C2×C4C23×D412yes—
1236C2×C4C23×D414yes—
1237C2×C4C23×D412yes—
1238C2×C4C23×D412yes—
1239C2×C4#58512yes—
1240C2×C4#58512yes—
1241C2×C4#58514yes—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—22no—
1246C22—24no—
1247C22—22no—
1248C22—24no—
1249C22—22no—
1250C22—24no—
1251C22—42no—
1252C22—42no—
1253C22—44no—
1254C22—42no—
1255C22—42no—
1256C22—44no—
1257C22—42no—
1258C22—42no—
1259C22—44no—
1260C22—48no—
1261C22—48no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—44no—
1269C22—1616no—
1270C22C24×D411yescharacteristic
1271C22C2×#58511yescharacteristic
1272C22C2×#58512yes—
1273C22C2×#58512yes—
1274C22C2×#58511yescharacteristic
1275C4—22no—
1276C4—24no—
1277C4—24no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—24no—
1282C4—44no—
1283C4—44no—
1284C4—48no—
1285C4—42no—
1286C4—44no—
1287C4—42no—
1288C4—42no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—44no—
1294C4#344914yes—
1295C4#350014yes—
1296C2—44no—
1297C2—42no—
1298C2—44no—
1299C2—84no—
1300C2—82no—
1301C2C2×#344911yescharacteristic
1302C2C2×#350011yescharacteristic
1303C2#6281111yescharacteristic
1304C2#6302912yes—
1305C2#6303012yes—
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×#3514C2semidirect
2. C2×#3482C2semidirect
3. #42875C2semidirect
4. #42788C2semidirect
5. #41380C2semidirect
6. #40500C2semidirect
7. #39960C2semidirect
8. #38911C2semidirect
9. #38910C2semidirect
10. #38903C2semidirect
11. #38902C2semidirect
12. #38438C2semidirect
13. #37622C2semidirect
14. #37551C2semidirect
15. #36580C2semidirect
16. #36579C2semidirect
17. #36269C2semidirect
18. #36033C2semidirect
19. #35730C2semidirect
20. #35338C2semidirect
21. #35292C2semidirect
22. #35180C2semidirect
23. #35129C2semidirect
24. #34964C2semidirect
25. #34911C2semidirect
26. #34121C2semidirect
30. C2×#557C22semidirect
33. C2×#556C22semidirect
35. C2×#552C22semidirect
36. C2×#552C22semidirect
39. C2×D4×Q8C22semidirect
43. C2×#547C22semidirect
49. C2×#533C22semidirect
50. C2×#533C22semidirect
55. C2×#529C22semidirect
59. C2×C4×#41C22semidirect
60. C2×C4×#41C22semidirect
61. C22×C4×Q8C22semidirect
62. #2861C22semidirect
63. #2857C22semidirect
66. #2850C22semidirect
67. #2850C22semidirect
68. #2821C22semidirect
69. #2821C22semidirect
70. #2814C22semidirect
71. #2696C22semidirect
72. #2694C22semidirect
73. #2692C22semidirect
74. #2690C22semidirect
75. #2689C22semidirect
76. #2688C22semidirect
77. #2687C22semidirect
78. #2686C22semidirect
80. #2684C22semidirect
82. #2668C22semidirect
83. #2664C22semidirect
84. #2663C22semidirect
85. #2640C22semidirect
86. #2640C22semidirect
87. #2639C22semidirect
88. #2638C22semidirect
89. #2638C22semidirect
90. #2632C22semidirect
91. #2631C22semidirect
92. #2628C22semidirect
93. #2625C22semidirect
94. #2625C22semidirect
97. #2624C22semidirect
98. #2621C22semidirect
99. #2615C22semidirect
100. #2611C22semidirect
101. #2610C22semidirect
102. #2604C22semidirect
103. #2603C22semidirect
104. #2602C22semidirect
105. #2601C22semidirect
109. #2592C22semidirect
110. #2592C22semidirect
111. #2592C22semidirect
112. #2592C22semidirect
113. #2584C22semidirect
114. #2584C22semidirect
115. #2582C22semidirect
116. #2581C22semidirect
117. #2580C22semidirect
118. #2580C22semidirect
119. #2568C22semidirect
120. #2563C22semidirect
121. #2562C22semidirect
122. #2562C22semidirect
123. #2561C22semidirect
124. #2561C22semidirect
125. #2561C22semidirect
126. #2559C22semidirect
127. #2557C22semidirect
128. #2550C22semidirect
130. #2547C22semidirect
133. #2540C22semidirect
135. #2535C22semidirect
136. #2521C22semidirect
137. #2498C22semidirect
138. #2492C22semidirect
140. #2482C22semidirect
141. #2481C22semidirect
142. #2480C22semidirect
143. #2469C22semidirect
144. #2468C22semidirect
145. #2464C22semidirect
146. #2458C22semidirect
147. #2457C22semidirect
148. #2448C22semidirect
150. #2443C22semidirect
151. #2436C22semidirect
153. #2430C22semidirect
154. #2421C22semidirect
156. #2418C22semidirect
157. #2417C22semidirect
159. #2415C22semidirect
160. #2415C22semidirect
162. #2414C22semidirect
163. #2409C22semidirect
164. #2409C22semidirect
167. #2407C22semidirect
168. #2404C22semidirect
169. #2396C22semidirect
170. #2395C22semidirect
171. #2392C22semidirect
172. #2388C22semidirect
173. #2367C22semidirect
174. #2362C22semidirect
175. #2361C22semidirect
177. #2356C22semidirect
178. #2355C22semidirect
180. #2353C22semidirect
181. #2352C22semidirect
182. #2352C22semidirect
183. #2324C22semidirect
184. #2321C22semidirect
185. #2311C22semidirect
186. #2310C22semidirect
188. C4×C22⋊Q8C22semidirect
189. C4×C22⋊Q8C22semidirect
191. C4×#121C22semidirect
192. C4×#121C22semidirect
193. #2298C22semidirect
195. #2293C22semidirect
196. #2285C22semidirect
197. #2283C22semidirect
198. C4×#117C22semidirect
199. C4×#117C22semidirect
200. C2×C4×C4⋊C4C22semidirect
308. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35142
C2×#34822
#428752
#427882
#413802
#405002
#399602
#389112
#389102
#389032
#389022
#384382
#376222
#375512
#365802
#365792
#362692
#360332
#357302
#353382
#352922
#351802
#351292
#349642
#349112
#341212