Finite Group Databasebeta

← #7720035

Subgroups — #7720035

Order 512.

6990 conjugacy classes of subgroups.

The subgroup lattice has 1263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3543C211yesmaximal, characteristic
2C2×#3563C211yesmaximal, characteristic, complemented
3#51979C214yesmaximal, complemented
4#51978C214yesmaximal, complemented
5#51421C218yesmaximal, complemented
6#43930C218yesmaximal, complemented
7#43890C214yesmaximal, complemented
8#43005C214yesmaximal, complemented
9#39174C212yesmaximal, complemented
10#39164C212yesmaximal, complemented
11#38093C212yesmaximal, complemented
12#38084C212yesmaximal, complemented
13#38084C212yesmaximal, complemented
14#38078C212yesmaximal, complemented
15#37424C212yesmaximal, complemented
16#37304C212yesmaximal, complemented
17#36386C212yesmaximal, complemented
18#36289C212yesmaximal, complemented
19#35332C212yesmaximal, complemented
20#35326C211yesmaximal, characteristic, complemented
21#35285C211yesmaximal, characteristic, complemented
22#35264C212yesmaximal, complemented
23#35139C211yesmaximal, characteristic, complemented
24C2×#2641C211yesmaximal, characteristic, complemented
25#34149C211yesmaximal, characteristic, complemented
26#3563—216no—
27#3543—216no—
28C2×#564C2212yescomplemented
29C2×#563C2212yescomplemented
30C2×#560C2214yes—
31C2×#559C2211yescharacteristic
32C2×#557C2212yescomplemented
33C2×#554C2212yescomplemented
34C2×#552C2212yescomplemented
35C2×#552C2214yescomplemented
36C2×#552C2212yescomplemented
37C2×#550C2211yescharacteristic
38C2×#550C2211yescharacteristic
39C2×#546C2212yes—
40C2×#546C2212yes—
41C2×D42C2212yes—
42C2×D42C2211yescharacteristic
43C2×D42C2212yes—
44C2×#544C2212yescomplemented
45C2×#544C2212yescomplemented
46C2×#541C2212yescomplemented
47C2×#541C2214yescomplemented
48C2×#540C2212yes—
49C2×#540C2212yes—
50C2×#539C2212yes—
51C2×#535C2212yes—
52C2×#535C2212yes—
53C2×#534C2214yes—
54C2×#533C2211yescharacteristic, complemented
55C22×#127C2211yescharacteristic
56C2×#529C2211yescharacteristic
57C2×#529C2211yescharacteristic
58C22×#125C2211yescharacteristic, complemented
59#2861C2212yescomplemented
60#2861C2212yescomplemented
61#2859C2212yescomplemented
62#2858C2212yescomplemented
63#2858C2212yescomplemented
64#2858C2212yescomplemented
65#2857C2212yescomplemented
66#2850C2212yes—
67#2850C2212yescomplemented
68#2850C2212yescomplemented
69#2731C2218yescomplemented
70#2711C2218yescomplemented
71#2711C2218yescomplemented
72#2711C2218yescomplemented
73#2711C2218yescomplemented
74#2711C2218yescomplemented
75#2711C2218yescomplemented
76#2709C2218yescomplemented
77#2707C2218yescomplemented
78#2694C2218yescomplemented
79#2694C2218yescomplemented
80#2691C2218yescomplemented
81#2685C2218yescomplemented
82#2685C2218yescomplemented
83#2685C2218yescomplemented
84#2685C2218yescomplemented
85#2681C2218yescomplemented
86#2681C2218yescomplemented
87#2674C2218yescomplemented
88#2672C2218yescomplemented
89#2664C2214yescomplemented
90#2660C2211yescharacteristic, complemented
91#2658C2211yescharacteristic, complemented
92#2642C2211yescharacteristic, complemented
93#2641C2212yes—
94#2641C2212yescomplemented
95#2641C2212yescomplemented
96#2641C2212yescomplemented
97#2641C2214yescomplemented
98#2641C2214yescomplemented
99#2641C2212yescomplemented
100#2641C2214yescomplemented
101#2640C2212yescomplemented
102#2640C2211yescharacteristic, complemented
103#2620C2212yescomplemented
104#2620C2212yescomplemented
105#2611C2214yescomplemented
106#2611C2214yescomplemented
107#2604C2214yescomplemented
108#2566C2212yescomplemented
109#2566C2212yescomplemented
110#2566C2212yescomplemented
111#2565C2212yescomplemented
112#2564C2214yescomplemented
113#2563C2212yescomplemented
114#2559C2218yescomplemented
115#2559C2218yescomplemented
116#2559C2218yescomplemented
117#2558C2218yescomplemented
118#2558C2218yescomplemented
119#2558C2218yescomplemented
120#2548C2212yes—
121#2548C2212yescomplemented
122#2548C2212yescomplemented
123#2548C2212yescomplemented
124#2548C2214yescomplemented
125#2545C2212yescomplemented
126#2545C2212yescomplemented
127#2542C2212yescomplemented
128#2534C2218yescomplemented
129#2504C2211yescharacteristic
130#2504C2212yescomplemented
131#2503C2211yescharacteristic, complemented
132#2502C2211yescharacteristic, complemented
133#2501C2211yescharacteristic
134#2501C2212yescomplemented
135#2500C2212yescomplemented
136#2500C2212yescomplemented
137#2498C2214yescomplemented
138#2491C2218yescomplemented
139#2490C2218yescomplemented
140#2490C2218yescomplemented
141#2476C2218yescomplemented
142#2472C2218yescomplemented
143#2472C2218yescomplemented
144#2472C2218yescomplemented
145#2472C2218yescomplemented
146#2460C2218yescomplemented
147#2460C2218yescomplemented
148#2458C2218yescomplemented
149#2437C2218yescomplemented
150#2435C2212yescomplemented
151#2435C2212yescomplemented
152#2435C2212yescomplemented
153#2435C2214yescomplemented
154#2435C2212yescomplemented
155#2432C2218yescomplemented
156#2432C2212yescomplemented
157#2432C2212yescomplemented
158#2426C2218yescomplemented
159#2418C2218yescomplemented
160#2413C2214yescomplemented
161#2411C2218yescomplemented
162#2411C2218yescomplemented
163#2405C2218yescomplemented
164#2405C2218yescomplemented
165C2×#394C2214yescomplemented
166C2×#394C2214yescomplemented
167#2373C2214yescomplemented
168#2372C2212yescomplemented
169#2371C2212yescomplemented
170#2368C2212yescomplemented
171#2364C2212yes—
172#2359C2214yescomplemented
173#2342C2218yescomplemented
174D4×C22⋊C4C2218yescomplemented
175#2327C2212yescomplemented
176#2326C2212yescomplemented
177#2326C2212yescomplemented
178#2326C2212yescomplemented
179#2322C2214yescomplemented
180#2311C2212yescomplemented
181#2309C2214yescomplemented
182#2309C2212yescomplemented
183C4×#124C2212yescomplemented
184C4×#124C2212yescomplemented
185#2298C2212yescomplemented
186#2297C2212yescomplemented
187#2295C2212yescomplemented
188C2×#390C2212yescomplemented
189C2×#390C2212yescomplemented
190C2×#390C2212yescomplemented
191#2290C2212yescomplemented
192#2290C2212yescomplemented
193C42×D4C2212yescomplemented
194C4×#117C2212yescomplemented
195C4×#117C2211yescharacteristic, complemented
196C2×#376C2211yescharacteristic, complemented
197C22×#41C2312yes—
198C22×#41C2312yes—
199C23×D4C2312yes—
200C23×D4C2312yes—
201C23×D4C2314yes—
202C23×D4C2312yes—
203C23×D4C2312yes—
204C23×D4C2312yes—
205#564—216no—
206#563—216no—
207#560—232no—
208#559—28no—
209#557—216no—
210#554—216no—
211#552—232no—
212#552—216no—
213#552—216no—
214#550—28no—
215#550—28no—
216#546—216no—
217#546—216no—
218D42—216no—
219D42—28no—
220D42—216no—
221#544—216no—
222#544—216no—
223#541—232no—
224#541—216no—
225#540—216no—
226#540—216no—
227#539—216no—
228#535—216no—
229#535—216no—
230#534—232no—
231#533—28no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×#127—28no—
239C2×#127C2312yes—
240C2×#127C2312yes—
241C2×#127C2311yescharacteristic
242C2×#127C2312yes—
243C2×#127C2311yescharacteristic
244C2×#127C2312yes—
245C2×#127C2312yes—
246#529—28no—
247#529D4116yes—
248C2×#126C2312yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2312yes—
254C2×#125—28no—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2311yescharacteristic
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#125C2311yescharacteristic
271C2×#124C2311yescharacteristic
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2318yes—
280C2×#124C2318yes—
281C2×#124C2311yescharacteristic
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2312yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2318yes—
291C2×#123C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2311yescharacteristic
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2318yes—
302C2×C22⋊Q8C2311yescharacteristic
303C2×#121C2311yescharacteristic
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2311yescharacteristic
317C2×#120C2314yes—
318C2×#120C2314yes—
319C2×#120C2314yes—
320C2×#120C2314yes—
321C2×#120C2314yes—
322C2×#120C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2314yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2311yescharacteristic
352C22×C4⋊C4C2311yescharacteristic
353C22×C22⋊C4C2314yes—
354C22×C22⋊C4C2318yes—
355C22×C22⋊C4C2318yes—
356C22×C22⋊C4C2318yes—
357C22×C42C2312yes—
358C22×C42C2312yes—
359C22×C42C2311yescharacteristic
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2318yes—
367#399C2318yes—
368#398C2318yes—
369#398C2314yes—
370#398C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2318yes—
374#397C2318yes—
375#396C2318yes—
376#396C2318yes—
377#396C2318yes—
378#396C2318yes—
379#396C2318yes—
380#396C2318yes—
381#396C2318yes—
382#395C2314yes—
383#394C2318yes—
384#394C2318yes—
385#394C2318yes—
386#394C2318yes—
387#394C2318yes—
388#394C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2318yes—
394#394C2318yes—
395#394C2318yes—
396#394C2318yes—
397#394C2318yes—
398#394C2318yes—
399#394C2318yes—
400#394C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2318yes—
405#394C2318yes—
406#394C2318yes—
407#393C2318yes—
408#393C2314yes—
409#393C2318yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2318yes—
423#390C2318yes—
424#390C2318yes—
425#390C2318yes—
426#390C2318yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2318yes—
434#390C2318yes—
435#390C2318yes—
436#390C2312yes—
437#390C2312yes—
438#390C2318yes—
439#390C2318yes—
440#390C2312yes—
441#390C2318yes—
442#390C2318yes—
443#389C2318yes—
444#389C2318yes—
445#389C2318yes—
446#389C2314yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2318yes—
454#388C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2318yes—
458#388C2318yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#387C2318yes—
468#387C2318yes—
469#387C2318yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#386C2318yes—
477#386C2318yes—
478#386C2314yes—
479#386C2318yes—
480#386C2318yes—
481#386C2318yes—
482#386C2314yes—
483#386C2314yes—
484#386C2318yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#385C2318yes—
489#385C2314yes—
490#385C2318yes—
491#385C2318yes—
492#385C2318yes—
493#385C2314yes—
494#385C2314yes—
495#385C2318yes—
496#384C2312yes—
497#384C2312yes—
498#384C2312yes—
499#382C2312yes—
500#382C2312yes—
501#382C2312yes—
502#381C2314yes—
503#380C2318yes—
504#380C2318yes—
505#380C2318yes—
506#379C2318yes—
507#379C2318yes—
508#379C2318yes—
509#379C2318yes—
510#379C2318yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2318yes—
522C4×C22⋊C4C2318yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2311yescharacteristic
529C4×C22⋊C4C2311yescharacteristic
530#376C2312yes—
531#376C2312yes—
532#376C2312yes—
533#376C2312yes—
534#376C2312yes—
535#376C2311yescharacteristic
536#376C2311yescharacteristic
537C2×#95C2312yes—
538C2×#95C2312yes—
539C43C2312yes—
540C43C2312yes—
541C25C2414yes—
542C25C2414yes—
543C2×#41—28no—
544C2×#41—28no—
545C2×#41—44no—
546C2×#41—44no—
547C2×#41—84no—
548C22×Q8C2412yes—
549C22×Q8C2411yescharacteristic
550C22×Q8C2414yes—
551C22×Q8C2412yes—
552C22×Q8C2411yescharacteristic
553C22×D4—216no—
554C22×D4—28no—
555C22×D4—28no—
556C22×D4—28no—
557C22×D4—28no—
558C22×D4—28no—
559C22×D4—44no—
560C22×D4—44no—
561C22×D4—44no—
562C22×D4—44no—
563C22×D4—48no—
564C22×D4—416no—
565C22×D4—84no—
566C22×D4—84no—
567C22×D4C2412yes—
568C22×D4C2412yes—
569C22×D4C2411yescharacteristic
570C22×D4C2412yes—
571C22×D4C2412yes—
572C22×D4C2412yes—
573C22×D4C2412yes—
574C22×D4C2414yes—
575C22×D4C2414yes—
576C22×D4C2414yes—
577C22×D4C2414yes—
578C22×D4C2412yes—
579C22×D4C2414yes—
580C22×D4C2414yes—
581C22×D4C2414yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2411yescharacteristic
586C23×C4C2412yes—
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2414yes—
592C23×C4C2414yes—
593C23×C4C2414yes—
594C23×C4C2414yes—
595C23×C4C2412yes—
596C23×C4C2414yes—
597C23×C4C2414yes—
598C23×C4C2411yescharacteristic
599C4⋊Q8—216no—
600C4⋊Q8—216no—
601C4⋊Q8—24no—
602C4⋊Q8—24no—
603C4⋊Q8—28no—
604C4⋊Q8—44no—
605#127—28no—
606#127—28no—
607#127—28no—
608#127—24no—
609#127—24no—
610#127—28no—
611#127—28no—
612#126—216no—
613#126—216no—
614#126—216no—
615#126—216no—
616#126—28no—
617#126C2×D4116yes—
618#125—216no—
619#125—216no—
620#125—216no—
621#125—216no—
622#125—216no—
623#125—216no—
624#125—216no—
625#125—216no—
626#125—28no—
627#125—28no—
628#125—28no—
629#125—28no—
630#125—24no—
631#125—28no—
632#125—28no—
633#125C2×D418yes—
634#124—28no—
635#124—24no—
636#124—28no—
637#124—44no—
638#124—44no—
639#124—44no—
640#124—44no—
641#124—44no—
642#124—88no—
643#124—88no—
644#124C2×D418yes—
645#123—216no—
646#123—216no—
647#123—28no—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—216no—
652#123—48no—
653#123—88no—
654#123C2×D4116yes—
655C22⋊Q8—24no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—216no—
664C22⋊Q8—88no—
665C22⋊Q8C2×D418yes—
666#121—24no—
667#121—28no—
668#121—28no—
669#121—216no—
670#121—216no—
671#121—216no—
672#121—28no—
673#121—28no—
674#121—216no—
675#121—216no—
676#121—216no—
677#121—216no—
678#121—216no—
679#121C2×D418yes—
680#120—216no—
681#120—216no—
682#120—216no—
683#120—216no—
684#120—216no—
685#120—216no—
686C4×Q8—216no—
687C4×Q8—24no—
688C4×Q8—28no—
689C4×Q8—28no—
690C4×Q8—28no—
691C4×Q8—28no—
692C4×Q8C2×D418yes—
693C4×D4—216no—
694C4×D4—28no—
695C4×D4—28no—
696C4×D4—28no—
697C4×D4—24no—
698C4×D4—28no—
699C4×D4—28no—
700C4×D4—48no—
701C4×D4C2×D4116yes—
702C4×D4C2×D418yes—
703#117—28no—
704#117—28no—
705#117—216no—
706#117—216no—
707#117—28no—
708#117—44no—
709#117—44no—
710#117C2×D4116yes—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—24no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4—24no—
715C2×C4⋊C4—28no—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2418yes—
751C2×C4⋊C4C2418yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C22⋊C4—216no—
759C2×C22⋊C4—416no—
760C2×C22⋊C4—88no—
761C2×C22⋊C4—88no—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2418yes—
781C2×C22⋊C4C2418yes—
782C2×C22⋊C4C2418yes—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C42—44no—
808C2×C42—44no—
809C2×C42C2×D418yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2414yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829C2×C42C2411yescharacteristic
830#95C2412yes—
831#95C2412yes—
832#95C2414yes—
833#95C2414yes—
834#95C2412yes—
835#95C2412yes—
836#95C2412yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2412yes—
841#95C2414yes—
842#95C2414yes—
843#95C2418yes—
844#95C2418yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2414yes—
849#95C2418yes—
850#95C2414yes—
851#95C2418yes—
852#95C2418yes—
853C24—28no—
854C24—216no—
855C24—28no—
856C24—48no—
857C24—44no—
858C24—44no—
859C24—44no—
860C24—48no—
861C24—48no—
862C24—44no—
863C24C2514yes—
864C24C2512yes—
865C24C2514yes—
866C24C2512yes—
867C24C2511yescharacteristic
868#41—816no—
869#41—816no—
870C2×Q8—24no—
871C2×Q8—22no—
872C2×Q8—24no—
873C2×Q8—28no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—42no—
878C2×Q8—48no—
879C2×Q8—44no—
880C2×Q8C22×D414yes—
881C2×D4—28no—
882C2×D4—24no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—24no—
888C2×D4—22no—
889C2×D4—24no—
890C2×D4—24no—
891C2×D4—24no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—24no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—42no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—48no—
909C2×D4—48no—
910C2×D4—48no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—48no—
915C2×D4—48no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—48no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—816no—
923C2×D4—816no—
924C2×D4—816no—
925C2×D4—816no—
926C2×D4—816no—
927C2×D4—832no—
928C2×D4C22×D418yes—
929C2×D4C22×D414yes—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—28no—
936C22×C4—24no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—24no—
940C22×C4—28no—
941C22×C4—28no—
942C22×C4—28no—
943C22×C4—42no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—48no—
951C22×C4—44no—
952C22×C4—48no—
953C22×C4—48no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4C22×D414yes—
957C22×C4C22×D414yes—
958C22×C4C22×D418yes—
959C22×C4C22×D414yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2514yes—
966C22×C4C2512yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2511yescharacteristic
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—24no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—48no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4—48no—
1016C4⋊C4C22×D418yes—
1017C4⋊C4C22×D418yes—
1018C4⋊C4C22×D414yes—
1019C4⋊C4C22×D414yes—
1020C4⋊C4C22×D418yes—
1021C4⋊C4C22×D418yes—
1022C22⋊C4—24no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—24no—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—48no—
1040C22⋊C4—48no—
1041C22⋊C4—48no—
1042C22⋊C4—48no—
1043C22⋊C4—48no—
1044C22⋊C4—48no—
1045C22⋊C4—48no—
1046C22⋊C4—48no—
1047C22⋊C4—48no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—44no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4C22×D418yes—
1063C22⋊C4C22×D418yes—
1064C22⋊C4C22×D418yes—
1065C22⋊C4C22×D418yes—
1066C22⋊C4C22×D418yes—
1067C42—28no—
1068C42—28no—
1069C42—24no—
1070C42—28no—
1071C42—28no—
1072C42—24no—
1073C42—24no—
1074C42—24no—
1075C42—24no—
1076C42—44no—
1077C42—44no—
1078C42—44no—
1079C42—44no—
1080C42—44no—
1081C42—44no—
1082C42C22×D414yes—
1083C42C22×D414yes—
1084C42C22×D414yes—
1085C42C22×D414yes—
1086C42C22×D418yes—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—24no—
1091C23—22no—
1092C23—24no—
1093C23—24no—
1094C23—22no—
1095C23—24no—
1096C23—24no—
1097C23—24no—
1098C23—28no—
1099C23—24no—
1100C23—24no—
1101C23—24no—
1102C23—24no—
1103C23—28no—
1104C23—28no—
1105C23—24no—
1106C23—28no—
1107C23—416no—
1108C23—88no—
1109C23—88no—
1110C23—88no—
1111C23—88no—
1112C23—88no—
1113C23—816no—
1114C23—816no—
1115C23—816no—
1116C23—168no—
1117C23C23×D414yes—
1118C23C23×D412yes—
1119C23#58514yes—
1120C23C2611yescharacteristic
1121Q8—44no—
1122Q8—48no—
1123Q8—44no—
1124Q8—84no—
1125Q8—88no—
1126D4—216no—
1127D4—44no—
1128D4—48no—
1129D4—48no—
1130D4—48no—
1131D4—44no—
1132D4—48no—
1133D4—48no—
1134D4—88no—
1135D4—88no—
1136D4—84no—
1137D4—88no—
1138D4—84no—
1139D4—88no—
1140D4—88no—
1141D4—88no—
1142D4—88no—
1143D4—88no—
1144D4—88no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—28no—
1155C2×C4—28no—
1156C2×C4—216no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—28no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—28no—
1182C2×C4—28no—
1183C2×C4—24no—
1184C2×C4—44no—
1185C2×C4—48no—
1186C2×C4—48no—
1187C2×C4—88no—
1188C2×C4—88no—
1189C2×C4—88no—
1190C2×C4—84no—
1191C2×C4—88no—
1192C2×C4—88no—
1193C2×C4—88no—
1194C2×C4C23×D412yes—
1195C2×C4C23×D412yes—
1196C2×C4C23×D414yes—
1197C2×C4C23×D414yes—
1198C2×C4C23×D414yes—
1199C2×C4C23×D412yes—
1200C2×C4C23×D412yes—
1201C2×C4C23×D412yes—
1202C2×C4C23×D412yes—
1203C2×C4#58514yes—
1204C22—22no—
1205C22—22no—
1206C22—28no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—42no—
1215C22—44no—
1216C22—42no—
1217C22—44no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—48no—
1222C22—48no—
1223C22—48no—
1224C22—48no—
1225C22—48no—
1226C22—1616no—
1227C22—1616no—
1228C22#350014yes—
1229C22C24×D411yescharacteristic
1230C22C2×#58512yes—
1231C22C2×#58512yes—
1232C22H(7,𝔽2)12yes—
1233C4—24no—
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—24no—
1238C4—22no—
1239C4—22no—
1240C4—24no—
1241C4—44no—
1242C4—42no—
1243C4—42no—
1244C4—44no—
1245C4—42no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—44no—
1250C4—44no—
1251C4—44no—
1252C4#350014yes—
1253C2—24no—
1254C2—44no—
1255C2—84no—
1256C2—84no—
1257C2—82no—
1258C2C2×#350011yescharacteristic
1259C2C2×#350011yescharacteristic
1260C2#6285211yescharacteristic
1261C2#6294114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3543C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#3563C2semidirect
3. #51979C2semidirect
4. #51978C2semidirect
5. #51421C2semidirect
6. #43930C2semidirect
7. #43890C2semidirect
8. #43005C2semidirect
9. #39174C2semidirect
10. #39164C2semidirect
11. #38093C2semidirect
12. #38084C2semidirect
13. #38084C2semidirect
14. #38078C2semidirect
15. #37424C2semidirect
16. #37304C2semidirect
17. #36386C2semidirect
18. #36289C2semidirect
19. #35332C2semidirect
20. #35326C2semidirect
21. #35285C2semidirect
22. #35264C2semidirect
23. #35139C2semidirect
24. C2×#2641C2semidirect
25. #34149C2semidirect
28. C2×#564C22semidirect
29. C2×#563C22semidirect
32. C2×#557C22semidirect
33. C2×#554C22semidirect
34. C2×#552C22semidirect
35. C2×#552C22semidirect
36. C2×#552C22semidirect
44. C2×#544C22semidirect
45. C2×#544C22semidirect
46. C2×#541C22semidirect
47. C2×#541C22semidirect
54. C2×#533C22semidirect
58. C22×#125C22semidirect
59. #2861C22semidirect
60. #2861C22semidirect
61. #2859C22semidirect
62. #2858C22semidirect
63. #2858C22semidirect
64. #2858C22semidirect
65. #2857C22semidirect
67. #2850C22semidirect
68. #2850C22semidirect
69. #2731C22semidirect
70. #2711C22semidirect
71. #2711C22semidirect
72. #2711C22semidirect
73. #2711C22semidirect
74. #2711C22semidirect
75. #2711C22semidirect
76. #2709C22semidirect
77. #2707C22semidirect
78. #2694C22semidirect
79. #2694C22semidirect
80. #2691C22semidirect
81. #2685C22semidirect
82. #2685C22semidirect
83. #2685C22semidirect
84. #2685C22semidirect
85. #2681C22semidirect
86. #2681C22semidirect
87. #2674C22semidirect
88. #2672C22semidirect
89. #2664C22semidirect
90. #2660C22semidirect
91. #2658C22semidirect
92. #2642C22semidirect
94. #2641C22semidirect
95. #2641C22semidirect
96. #2641C22semidirect
97. #2641C22semidirect
98. #2641C22semidirect
99. #2641C22semidirect
100. #2641C22semidirect
101. #2640C22semidirect
102. #2640C22semidirect
103. #2620C22semidirect
104. #2620C22semidirect
105. #2611C22semidirect
106. #2611C22semidirect
107. #2604C22semidirect
108. #2566C22semidirect
109. #2566C22semidirect
110. #2566C22semidirect
111. #2565C22semidirect
112. #2564C22semidirect
113. #2563C22semidirect
114. #2559C22semidirect
115. #2559C22semidirect
116. #2559C22semidirect
117. #2558C22semidirect
118. #2558C22semidirect
119. #2558C22semidirect
121. #2548C22semidirect
122. #2548C22semidirect
123. #2548C22semidirect
124. #2548C22semidirect
125. #2545C22semidirect
126. #2545C22semidirect
127. #2542C22semidirect
128. #2534C22semidirect
130. #2504C22semidirect
131. #2503C22semidirect
132. #2502C22semidirect
134. #2501C22semidirect
135. #2500C22semidirect
136. #2500C22semidirect
137. #2498C22semidirect
138. #2491C22semidirect
139. #2490C22semidirect
140. #2490C22semidirect
141. #2476C22semidirect
142. #2472C22semidirect
143. #2472C22semidirect
144. #2472C22semidirect
145. #2472C22semidirect
146. #2460C22semidirect
147. #2460C22semidirect
148. #2458C22semidirect
149. #2437C22semidirect
150. #2435C22semidirect
151. #2435C22semidirect
152. #2435C22semidirect
153. #2435C22semidirect
154. #2435C22semidirect
155. #2432C22semidirect
156. #2432C22semidirect
157. #2432C22semidirect
158. #2426C22semidirect
159. #2418C22semidirect
160. #2413C22semidirect
161. #2411C22semidirect
162. #2411C22semidirect
163. #2405C22semidirect
164. #2405C22semidirect
165. C2×#394C22semidirect
166. C2×#394C22semidirect
167. #2373C22semidirect
168. #2372C22semidirect
169. #2371C22semidirect
170. #2368C22semidirect
172. #2359C22semidirect
173. #2342C22semidirect
174. D4×C22⋊C4C22semidirect
175. #2327C22semidirect
176. #2326C22semidirect
177. #2326C22semidirect
178. #2326C22semidirect
179. #2322C22semidirect
180. #2311C22semidirect
181. #2309C22semidirect
182. #2309C22semidirect
183. C4×#124C22semidirect
184. C4×#124C22semidirect
185. #2298C22semidirect
186. #2297C22semidirect
187. #2295C22semidirect
188. C2×#390C22semidirect
189. C2×#390C22semidirect
190. C2×#390C22semidirect
191. #2290C22semidirect
192. #2290C22semidirect
193. C42×D4C22semidirect
194. C4×#117C22semidirect
195. C4×#117C22semidirect
196. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35432
C2×#35632
#519792
#519782
#514212
#439302
#438902
#430052
#391742
#391642
#380932
#380842
#380782
#374242
#373042
#363862
#362892
#353322
#353262
#352852
#352642
#351392
C2×#26412
#341492