Finite Group Databasebeta

← #7079920

Subgroups — #7079920

Order 512.

1588 conjugacy classes of subgroups.

The subgroup lattice has 1349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45002C211yesmaximal, characteristic
2#42922C211yesmaximal, characteristic, complemented
3#32165C211yesmaximal, characteristic, complemented
4#31986C211yesmaximal, characteristic, complemented
5#31842C211yesmaximal, characteristic, complemented
6#31761C211yesmaximal, characteristic, complemented
7#31657C211yesmaximal, characteristic, complemented
8#31511C211yesmaximal, characteristic, complemented
9#31466C211yesmaximal, characteristic, complemented
10#31004C211yesmaximal, characteristic, complemented
11#29084C211yesmaximal, characteristic, complemented
12#29002C211yesmaximal, characteristic, complemented
13#28565C211yesmaximal, characteristic, complemented
14#27753C211yesmaximal, characteristic, complemented
15#27525C211yesmaximal, characteristic, complemented
16#27280C211yesmaximal, characteristic, complemented
17#27279C211yesmaximal, characteristic, complemented
18#26771C211yesmaximal, characteristic, complemented
19#26420C211yesmaximal, characteristic, complemented
20#26225C211yesmaximal, characteristic, complemented
21#25507C211yesmaximal, characteristic, complemented
22#25332C211yesmaximal, characteristic, complemented
23#25077C211yesmaximal, characteristic, complemented
24#24538C211yesmaximal, characteristic, complemented
25#24515C211yesmaximal, characteristic, complemented
26#24452C211yesmaximal, characteristic, complemented
27#23634C211yesmaximal, characteristic, complemented
28#23138C211yesmaximal, characteristic, complemented
29#22903C211yesmaximal, characteristic, complemented
30#22424C211yesmaximal, characteristic, complemented
31#21872C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#465C2211yescharacteristic, complemented
37C2×#460C2211yescharacteristic
38C2×#452C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#433C2211yescharacteristic, complemented
42C2×#417C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C2×#416C2211yescharacteristic
45#2836—21no—
46#2796—21no—
47#2787—21no—
48#2786—21no—
49#2747—21no—
50#2706—21no—
51#2693—21no—
52#2688—21no—
53#2668—21no—
54#2655—21no—
55#2654—21no—
56#2625C2211yescharacteristic, complemented
57#2585—21no—
58#2570C2211yescharacteristic, complemented
59#2565C2211yescharacteristic, complemented
60#2544C2211yescharacteristic
61#2535—21no—
62#2511C2211yescharacteristic, complemented
63#2507C2211yescharacteristic, complemented
64#2499C2211yescharacteristic
65#2494C2211yescharacteristic
66#2489C2211yescharacteristic
67#2454C2211yescharacteristic
68#2447C2211yescharacteristic
69#2442C2211yescharacteristic, complemented
70#2441C2211yescharacteristic
71#2433C2211yescharacteristic
72#2431C2211yescharacteristic
73#2427C2211yescharacteristic
74#2424—21no—
75#2421C2211yescharacteristic
76#2418—21no—
77#2417C2211yescharacteristic
78#2416C2211yescharacteristic
79#2412—21no—
80#2395C2211yescharacteristic
81#2366C2211yescharacteristic
82#2362C2211yescharacteristic, complemented
83#2361C2211yescharacteristic
84#2354C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2317C2211yescharacteristic, complemented
87#2311C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2076C2211yescharacteristic
94#2074C2211yescharacteristic, complemented
95#2074C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic, complemented
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2036C2211yescharacteristic
119#2033C2211yescharacteristic
120#2026C2211yescharacteristic, complemented
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic, complemented
125#2014C2211yescharacteristic
126#2001C2211yescharacteristic
127#2000C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1991C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic, complemented
133#1973C2211yescharacteristic
134#1969C2211yescharacteristic, complemented
135#1961C2211yescharacteristic
136#1959C2211yescharacteristic
137#1958C2211yescharacteristic, complemented
138#1957C2211yescharacteristic
139#1940C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic, complemented
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic, complemented
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic, complemented
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1921C2211yescharacteristic, complemented
153#1921C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic, complemented
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1893C2211yescharacteristic
163#1880C2211yescharacteristic
164#1878C2211yescharacteristic, complemented
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic, complemented
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic, complemented
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic, complemented
174#1873C2211yescharacteristic
175#1872C2211yescharacteristic, complemented
176#1870C2211yescharacteristic
177#1864C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1851C2211yescharacteristic
183#1850C2211yescharacteristic, complemented
184#1825C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic, complemented
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic, complemented
191#1788C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1770C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214#540—24no—
215#540—42no—
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×#120—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253#490—42no—
254#468—24no—
255#465—42no—
256#460—42no—
257#452—42no—
258#450—42no—
259#435—42no—
260#433—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#418—42no—
271#417—42no—
272#416—42no—
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#401—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400D411yescharacteristic
324#399—21no—
325#399—21no—
326#399D411yescharacteristic
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398D411yescharacteristic
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397D411yescharacteristic
347#397D411yescharacteristic
348#397D411yescharacteristic
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394D411yescharacteristic
358#394D411yescharacteristic
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382—21no—
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#381—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C22×C8—22no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559#127—22no—
560#127—22no—
561#127—41no—
562#127—41no—
563#125—22no—
564#125—41no—
565#125—41no—
566#125—41no—
567#124—22no—
568#124—41no—
569#124—41no—
570#124—41no—
571#123—44no—
572#123—44no—
573#123—44no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—44no—
584#121—44no—
585#121—44no—
586#121—41no—
587#121—41no—
588#121—82no—
589#121#4114yes—
590#120—44no—
591#120—82no—
592#120—82no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—82no—
606C4×D4—82no—
607#117—22no—
608#117—22no—
609#117—41no—
610#117—41no—
611#117—41no—
612#117—41no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—82no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#107—22no—
713#107—41no—
714#107—41no—
715#106—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758#97—41no—
759#97—41no—
760#97—41no—
761C4×C8—41no—
762C4×C8—41no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—21no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—44no—
821#41—44no—
822#41—82no—
823#41—82no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×D4—22no—
837C2×D4—24no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—44no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4C2×#4112yes—
887C2×D4H(5,𝔽2)12yes—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C2×#4112yes—
945C22×C4H(5,𝔽2)12yes—
946C22×C4C2511yescharacteristic
947Q16—82no—
948SD16—82no—
949SD16—82no—
950SD16—82no—
951M16—82no—
952M16—82no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—82no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4C2×#4112yes—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—24no—
1035C22⋊C4—22no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—42no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—22no—
1098C23—21no—
1099C23—21no—
1100C23—22no—
1101C23—21no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—84no—
1122C23—84no—
1123C23—84no—
1124C23—162no—
1125C23—162no—
1126C23—162no—
1127C23—162no—
1128C23#54612yes—
1129C23C23×D411yescharacteristic
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138D4—22no—
1139D4—22no—
1140D4—22no—
1141D4—22no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—82no—
1151D4—84no—
1152D4—84no—
1153D4—84no—
1154D4—84no—
1155D4—162no—
1156D4—162no—
1157D4—162no—
1158D4—162no—
1159D4—162no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—84no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4—162no—
1249C2×C4#54612yes—
1250C2×C4C22×#4111yescharacteristic
1251C2×C4C2×H(5,𝔽2)11yescharacteristic
1252C2×C4C2×H(5,𝔽2)11yescharacteristic
1253C2×C4#58511yescharacteristic
1254C2×C4#58511yescharacteristic
1255C2×C4#58511yescharacteristic
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—42no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—41no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—168no—
1300C22C2×#54611yescharacteristic
1301C22#348811yescharacteristic
1302C22#350011yescharacteristic
1303C22#358411yescharacteristic
1304C22#358511yescharacteristic
1305C22#358511yescharacteristic
1306C22#358611yescharacteristic
1307C4—22no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4#351311yescharacteristic
1333C4#352111yescharacteristic
1334C4#353411yescharacteristic
1335C4#356011yescharacteristic
1336C2—42no—
1337C2—81no—
1338C2—82no—
1339C2—82no—
1340C2—161no—
1341C2#4399811yescharacteristic
1342C2#6118011yescharacteristic
1343C2#6120111yescharacteristic
1344C2#6202711yescharacteristic
1345C2#6208411yescharacteristic
1346C2#6256411yescharacteristic
1347C2#6260011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45002C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42922C2semidirect
3. #32165C2semidirect
4. #31986C2semidirect
5. #31842C2semidirect
6. #31761C2semidirect
7. #31657C2semidirect
8. #31511C2semidirect
9. #31466C2semidirect
10. #31004C2semidirect
11. #29084C2semidirect
12. #29002C2semidirect
13. #28565C2semidirect
14. #27753C2semidirect
15. #27525C2semidirect
16. #27280C2semidirect
17. #27279C2semidirect
18. #26771C2semidirect
19. #26420C2semidirect
20. #26225C2semidirect
21. #25507C2semidirect
22. #25332C2semidirect
23. #25077C2semidirect
24. #24538C2semidirect
25. #24515C2semidirect
26. #24452C2semidirect
27. #23634C2semidirect
28. #23138C2semidirect
29. #22903C2semidirect
30. #22424C2semidirect
31. #21872C2semidirect
36. C2×#465C22semidirect
41. C2×#433C22semidirect
56. #2625C22semidirect
58. #2570C22semidirect
59. #2565C22semidirect
62. #2511C22semidirect
63. #2507C22semidirect
69. #2442C22semidirect
82. #2362C22semidirect
86. #2317C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2088C22semidirect
91. #2087C22semidirect
94. #2074C22semidirect
95. #2074C22semidirect
99. #2072C22semidirect
100. #2072C22semidirect
103. #2071C22semidirect
104. #2068C22semidirect
107. #2066C22semidirect
108. #2059C22semidirect
109. #2056C22semidirect
112. #2055C22semidirect
114. #2042C22semidirect
120. #2026C22semidirect
121. #2026C22semidirect
124. #2015C22semidirect
128. #1992C22semidirect
129. #1991C22semidirect
130. #1989C22semidirect
132. #1983C22semidirect
134. #1969C22semidirect
137. #1958C22semidirect
139. #1940C22semidirect
141. #1936C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
147. #1933C22semidirect
149. #1925C22semidirect
152. #1921C22semidirect
153. #1921C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1916C22semidirect
159. #1895C22semidirect
164. #1878C22semidirect
168. #1877C22semidirect
171. #1875C22semidirect
173. #1874C22semidirect
175. #1872C22semidirect
180. #1862C22semidirect
181. #1852C22semidirect
183. #1850C22semidirect
187. #1804C22semidirect
190. #1802C22semidirect
194. #1770C22semidirect
195. #1763C22semidirect
199. #1753C22semidirect
200. #1736C22semidirect
201. C2×#340C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#450022
#429222
#321652
#319862
#318422
#317612
#316572
#315112
#314662
#310042
#290842
#290022
#285652
#277532
#275252
#272802
#272792
#267712
#264202
#262252
#255072
#253322
#250772
#245382
#245152
#244522
#236342
#231382
#229032
#224242
#218722