Finite Group Databasebeta

← #7610051

Subgroups — #7610051

Order 512.

1670 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44917C211yesmaximal, characteristic, complemented
2#44874C211yesmaximal, characteristic
3#32088C211yesmaximal, characteristic, complemented
4#31738C211yesmaximal, characteristic, complemented
5#31458C211yesmaximal, characteristic, complemented
6#31294C211yesmaximal, characteristic, complemented
7#29054C211yesmaximal, characteristic, complemented
8#29032C211yesmaximal, characteristic, complemented
9#28959C211yesmaximal, characteristic, complemented
10#28080C211yesmaximal, characteristic, complemented
11#27763C211yesmaximal, characteristic, complemented
12#27591C211yesmaximal, characteristic, complemented
13#27518C211yesmaximal, characteristic, complemented
14#27397C211yesmaximal, characteristic, complemented
15#27262C211yesmaximal, characteristic, complemented
16#27262C211yesmaximal, characteristic, complemented
17#26767C211yesmaximal, characteristic, complemented
18#26692C211yesmaximal, characteristic, complemented
19#26425C211yesmaximal, characteristic, complemented
20#26216C211yesmaximal, characteristic, complemented
21#25239C211yesmaximal, characteristic, complemented
22#24495C211yesmaximal, characteristic, complemented
23#24075C211yesmaximal, characteristic, complemented
24#24044C211yesmaximal, characteristic
25#23232C211yesmaximal, characteristic, complemented
26#22935C211yesmaximal, characteristic, complemented
27#22562C211yesmaximal, characteristic, complemented
28D4×#102C211yesmaximal, characteristic
29#21567C211yesmaximal, characteristic, complemented
30#21412C211yesmaximal, characteristic, complemented
31#21089C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#485C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×C8×D4C2211yescharacteristic
38C2×#418C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C2×#405C2211yescharacteristic, complemented
42#2774—21no—
43#2770—21no—
44#2698—21no—
45#2697—21no—
46#2690—21no—
47#2685—21no—
48#2684—21no—
49#2681—21no—
50#2611—21no—
51#2606—21no—
52#2559—21no—
53#2552C2211yescharacteristic, complemented
54#2544C2211yescharacteristic
55#2509C2211yescharacteristic, complemented
56#2507C2211yescharacteristic, complemented
57#2496C2211yescharacteristic, complemented
58#2495C2211yescharacteristic, complemented
59#2491C2211yescharacteristic
60#2485C2211yescharacteristic
61#2472—21no—
62#2468—21no—
63#2452C2211yescharacteristic
64#2445C2211yescharacteristic
65#2440C2211yescharacteristic, complemented
66#2440C2211yescharacteristic, complemented
67#2435—21no—
68#2435C2211yescharacteristic
69#2435C2211yescharacteristic
70#2426C2211yescharacteristic
71#2415—21no—
72#2415C2211yescharacteristic
73#2405—21no—
74#2395C2211yescharacteristic
75#2369C2211yescharacteristic, complemented
76#2367C2211yescharacteristic
77#2363C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic
79#2346C2211yescharacteristic, complemented
80#2344C2211yescharacteristic, complemented
81D4×C22⋊C4C2211yescharacteristic
82#2316C2211yescharacteristic, complemented
83#2314C2211yescharacteristic, complemented
84#2309C2211yescharacteristic
85#2100C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2075C2211yescharacteristic, complemented
92#2075C2211yescharacteristic, complemented
93#2072C2211yescharacteristic, complemented
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic, complemented
99#2067C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2058C2211yescharacteristic, complemented
102#2057C2211yescharacteristic, complemented
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic, complemented
106#2042C2211yescharacteristic, complemented
107#2042C2211yescharacteristic, complemented
108#2042C2211yescharacteristic, complemented
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic
111#2036C2211yescharacteristic, complemented
112#2035C2211yescharacteristic, complemented
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2023C2211yescharacteristic, complemented
116#2023C2211yescharacteristic, complemented
117#1993C2211yescharacteristic, complemented
118#1990C2211yescharacteristic, complemented
119#1988C2211yescharacteristic, complemented
120#1983C2211yescharacteristic
121#1983C2211yescharacteristic, complemented
122#1982C2211yescharacteristic
123#1959C2211yescharacteristic, complemented
124#1959C2211yescharacteristic, complemented
125#1958C2211yescharacteristic, complemented
126#1957C2211yescharacteristic
127#1943C2211yescharacteristic, complemented
128#1942C2211yescharacteristic, complemented
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic, complemented
133#1936C2211yescharacteristic, complemented
134#1936C2211yescharacteristic, complemented
135#1936C2211yescharacteristic, complemented
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic, complemented
139#1934C2211yescharacteristic, complemented
140#1933C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic, complemented
145#1926C2211yescharacteristic, complemented
146#1926C2211yescharacteristic, complemented
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic, complemented
149#1923C2211yescharacteristic, complemented
150#1923C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1916C2211yescharacteristic, complemented
157#1895C2211yescharacteristic
158#1894C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1892C2211yescharacteristic, complemented
162#1892C2211yescharacteristic, complemented
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1872C2211yescharacteristic, complemented
166#1872C2211yescharacteristic, complemented
167#1870C2211yescharacteristic
168#1865C2211yescharacteristic, complemented
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic, complemented
171#1864C2211yescharacteristic, complemented
172#1863C2211yescharacteristic, complemented
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic, complemented
175#1862C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1851C2211yescharacteristic, complemented
179#1823C2211yescharacteristic, complemented
180#1818C2211yescharacteristic, complemented
181#1807C2211yescharacteristic, complemented
182#1802C2211yescharacteristic
183#1802C2211yescharacteristic, complemented
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1776C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1771C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1762C2211yescharacteristic, complemented
194#1762C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic, complemented
198#1752C2211yescharacteristic, complemented
199#1752C2211yescharacteristic, complemented
200#1752C2211yescharacteristic, complemented
201#1736C2211yescharacteristic, complemented
202#1735C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209D42—24no—
210D42—42no—
211#542—24no—
212#542—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#125—21no—
219C2×#124—21no—
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250#489—24no—
251#485—42no—
252#482—24no—
253C8×D4—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265#418—42no—
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#102—24no—
275C2×#102—24no—
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305#405—42no—
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400D411yescharacteristic
318#399D411yescharacteristic
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398D411yescharacteristic
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397D411yescharacteristic
331#397D411yescharacteristic
332#397D411yescharacteristic
333#396—21no—
334#396—21no—
335#395—21no—
336#395—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394D411yescharacteristic
350#394D411yescharacteristic
351#393—21no—
352#393—21no—
353#391—21no—
354#391—21no—
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#388—21no—
388#388—21no—
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#388—21no—
398#388—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#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#383—21no—
423#382—21no—
424#382C2311yescharacteristic
425#381—21no—
426#380—21no—
427#380—21no—
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#379—21no—
435#379—21no—
436#379—21no—
437#379—21no—
438#379—21no—
439#379—21no—
440#379—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455#376—21no—
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—44no—
514C22×D4—82no—
515C22×D4—82no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×M16—22no—
528C2×M16—41no—
529C2×M16—41no—
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—22no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548#127—22no—
549#127—41no—
550#126—44no—
551#126—82no—
552#125—82no—
553#124—22no—
554#124—22no—
555#124—41no—
556#124—41no—
557#124—41no—
558#124—41no—
559#124—44no—
560#124—82no—
561#123—44no—
562#123—82no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—44no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—82no—
569C22⋊Q8—82no—
570C22⋊Q8—82no—
571#121—22no—
572#121—22no—
573#121—44no—
574#121—41no—
575#121#4114yes—
576#120—44no—
577#120—44no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—82no—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—41no—
594#117—41no—
595#117—82no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
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—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
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—82no—
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704#107—22no—
705#107—41no—
706#107—41no—
707#107—41no—
708#106—22no—
709#106—41no—
710#106—41no—
711#106—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715#103—22no—
716#103—22no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
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#4114yes—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752#97—22no—
753#97—41no—
754#97—41no—
755#97—41no—
756C4×C8—41no—
757C4×C8—41no—
758C4×C8—41no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
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#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—21no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—42no—
804C24—42no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—42no—
823C2×Q8—42no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—24no—
831C2×D4—22no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
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—44no—
849C2×D4—44no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—44no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—82no—
861C2×D4—82no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—82no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—816no—
874C2×D4C2×#4112yes—
875C2×D4C2×#4112yes—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
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—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C2×#4112yes—
927C22×C4H(5,𝔽2)12yes—
928C22×C4C2511yescharacteristic
929M16—44no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—44no—
954C2×C8—82no—
955C2×C8C2×#4112yes—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4C2×#4112yes—
1011C4⋊C4C2×#4112yes—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—24no—
1018C22⋊C4—22no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—22no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—84no—
1110C23—84no—
1111C23—84no—
1112C23—84no—
1113C23—84no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23#54612yes—
1124C23#57612yes—
1125C23C23×D411yescharacteristic
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—162no—
1131Q8—162no—
1132D4—28no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
1149D4—84no—
1150D4—162no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
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—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—22no—
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—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
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—84no—
1233C2×C4—84no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4#54612yes—
1238C2×C4#57712yes—
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4#58511yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C8—22no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—168no—
1289C22—168no—
1290C22C2×#54611yescharacteristic
1291C22D4×#4111yescharacteristic
1292C22#350011yescharacteristic
1293C22C2×#57611yescharacteristic
1294C22C2×#57711yescharacteristic
1295C22#358511yescharacteristic
1296C22#358611yescharacteristic
1297C4—22no—
1298C4—22no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4#347511yescharacteristic
1323C4#351311yescharacteristic
1324C4#352111yescharacteristic
1325C4#353311yescharacteristic
1326C2—42no—
1327C2—42no—
1328C2—82no—
1329C2—82no—
1330C2—161no—
1331C2#5980411yescharacteristic
1332C2#6116711yescharacteristic
1333C2#6122211yescharacteristic
1334C2#6151911yescharacteristic
1335C2#6154011yescharacteristic
1336C2#6260511yescharacteristic
1337C2#6261711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
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
1. #44917C2semidirect
3. #32088C2semidirect
4. #31738C2semidirect
5. #31458C2semidirect
6. #31294C2semidirect
7. #29054C2semidirect
8. #29032C2semidirect
9. #28959C2semidirect
10. #28080C2semidirect
11. #27763C2semidirect
12. #27591C2semidirect
13. #27518C2semidirect
14. #27397C2semidirect
15. #27262C2semidirect
16. #27262C2semidirect
17. #26767C2semidirect
18. #26692C2semidirect
19. #26425C2semidirect
20. #26216C2semidirect
21. #25239C2semidirect
22. #24495C2semidirect
23. #24075C2semidirect
25. #23232C2semidirect
26. #22935C2semidirect
27. #22562C2semidirect
29. #21567C2semidirect
30. #21412C2semidirect
31. #21089C2semidirect
35. C2×#485C22semidirect
41. C2×#405C22semidirect
53. #2552C22semidirect
55. #2509C22semidirect
56. #2507C22semidirect
57. #2496C22semidirect
58. #2495C22semidirect
65. #2440C22semidirect
66. #2440C22semidirect
75. #2369C22semidirect
79. #2346C22semidirect
80. #2344C22semidirect
82. #2316C22semidirect
83. #2314C22semidirect
85. #2100C22semidirect
86. #2100C22semidirect
88. #2092C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2075C22semidirect
92. #2075C22semidirect
93. #2072C22semidirect
96. #2071C22semidirect
98. #2067C22semidirect
99. #2067C22semidirect
100. #2066C22semidirect
101. #2058C22semidirect
102. #2057C22semidirect
105. #2042C22semidirect
106. #2042C22semidirect
107. #2042C22semidirect
108. #2042C22semidirect
111. #2036C22semidirect
112. #2035C22semidirect
115. #2023C22semidirect
116. #2023C22semidirect
117. #1993C22semidirect
118. #1990C22semidirect
119. #1988C22semidirect
121. #1983C22semidirect
123. #1959C22semidirect
124. #1959C22semidirect
125. #1958C22semidirect
127. #1943C22semidirect
128. #1942C22semidirect
132. #1936C22semidirect
133. #1936C22semidirect
134. #1936C22semidirect
135. #1936C22semidirect
138. #1934C22semidirect
139. #1934C22semidirect
140. #1933C22semidirect
141. #1928C22semidirect
144. #1926C22semidirect
145. #1926C22semidirect
146. #1926C22semidirect
148. #1925C22semidirect
149. #1923C22semidirect
150. #1923C22semidirect
151. #1919C22semidirect
152. #1919C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
155. #1916C22semidirect
156. #1916C22semidirect
158. #1894C22semidirect
161. #1892C22semidirect
162. #1892C22semidirect
165. #1872C22semidirect
166. #1872C22semidirect
168. #1865C22semidirect
170. #1864C22semidirect
171. #1864C22semidirect
172. #1863C22semidirect
174. #1862C22semidirect
175. #1862C22semidirect
176. #1854C22semidirect
177. #1854C22semidirect
178. #1851C22semidirect
179. #1823C22semidirect
180. #1818C22semidirect
181. #1807C22semidirect
183. #1802C22semidirect
189. #1776C22semidirect
190. #1771C22semidirect
191. #1771C22semidirect
192. #1763C22semidirect
193. #1762C22semidirect
194. #1762C22semidirect
195. C4×#103C22semidirect
197. C4×#102C22semidirect
198. #1752C22semidirect
199. #1752C22semidirect
200. #1752C22semidirect
201. #1736C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#449172
#448742
#320882
#317382
#314582
#312942
#290542
#290322
#289592
#280802
#277632
#275912
#275182
#273972
#272622
#267672
#266922
#264252
#262162
#252392
#244952
#240752
#240442
#232322
#229352
#225622
D4×#1022
#215672
#214122
#210892