Finite Group Databasebeta

← #7339259

Subgroups — #7339259

Order 512.

1557 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52978C211yesmaximal, characteristic, complemented
2#44874C211yesmaximal, characteristic
3#32088C211yesmaximal, characteristic, complemented
4#31982C211yesmaximal, characteristic, complemented
5#31789C211yesmaximal, characteristic, complemented
6#31500C211yesmaximal, characteristic, complemented
7#31323C211yesmaximal, characteristic, complemented
8#31306C211yesmaximal, characteristic, complemented
9#31298C211yesmaximal, characteristic, complemented
10#31298C211yesmaximal, characteristic, complemented
11#31126C211yesmaximal, characteristic, complemented
12#30947C211yesmaximal, characteristic, complemented
13#30835C211yesmaximal, characteristic, complemented
14#30775C211yesmaximal, characteristic, complemented
15#29959C211yesmaximal, characteristic, complemented
16#29702C211yesmaximal, characteristic, complemented
17#29115C211yesmaximal, characteristic, complemented
18#28958C211yesmaximal, characteristic, complemented
19#28079C211yesmaximal, characteristic, complemented
20#27773C211yesmaximal, characteristic, complemented
21#27520C211yesmaximal, characteristic, complemented
22#27262C211yesmaximal, characteristic, complemented
23#27125C211yesmaximal, characteristic, complemented
24#27039C211yesmaximal, characteristic, complemented
25#26776C211yesmaximal, characteristic, complemented
26#26479C211yesmaximal, characteristic, complemented
27#25952C211yesmaximal, characteristic, complemented
28#25891C211yesmaximal, characteristic
29#25680C211yesmaximal, characteristic, complemented
30#24033C211yesmaximal, characteristic
31#22372C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#498C2211yescharacteristic, complemented
35C2×#490C2211yescharacteristic
36C2×#489C2211yescharacteristic, complemented
37C2×#481C2211yescharacteristic
38C2×#479C2211yescharacteristic, complemented
39C2×#478C2211yescharacteristic
40C2×#478C2211yescharacteristic, complemented
41C22×#102C2211yescharacteristic
42#2839—21no—
43#2838—21no—
44#2833—21no—
45#2827—21no—
46#2787—21no—
47#2721—21no—
48#2720—21no—
49#2702—21no—
50#2697—21no—
51#2685—21no—
52#2684—21no—
53#2681—21no—
54#2629C2211yescharacteristic, complemented
55#2628C2211yescharacteristic, complemented
56#2562C2211yescharacteristic
57#2559—21no—
58#2552C2211yescharacteristic, complemented
59#2550C2211yescharacteristic, complemented
60#2544C2211yescharacteristic
61#2509C2211yescharacteristic, complemented
62#2506C2211yescharacteristic, complemented
63#2497C2211yescharacteristic, complemented
64#2496C2211yescharacteristic, complemented
65#2494C2211yescharacteristic, complemented
66#2494C2211yescharacteristic, complemented
67#2491C2211yescharacteristic
68#2487C2211yescharacteristic
69#2472—21no—
70#2452C2211yescharacteristic
71#2445C2211yescharacteristic
72#2442C2211yescharacteristic, complemented
73#2440C2211yescharacteristic, complemented
74#2435—21no—
75#2435C2211yescharacteristic
76#2435C2211yescharacteristic
77#2426C2211yescharacteristic
78#2415C2211yescharacteristic
79#2405—21no—
80#2395C2211yescharacteristic
81#2367C2211yescharacteristic
82#2363C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84#2309C2211yescharacteristic
85#2094C2211yescharacteristic, complemented
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2086C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2077C2211yescharacteristic, complemented
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic, complemented
96#2071C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2065C2211yescharacteristic, complemented
104#2065C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2058C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2042C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2036C2211yescharacteristic, complemented
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2026C2211yescharacteristic, complemented
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic, complemented
131#2023C2211yescharacteristic
132#2023C2211yescharacteristic, complemented
133#1993C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic, complemented
136#1982C2211yescharacteristic
137#1959C2211yescharacteristic
138#1958C2211yescharacteristic, complemented
139#1958C2211yescharacteristic, complemented
140#1955C2211yescharacteristic
141#1948C2211yescharacteristic, complemented
142#1943C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1940C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic, complemented
147#1936C2211yescharacteristic, complemented
148#1936C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1924C2211yescharacteristic, complemented
158#1923C2211yescharacteristic, complemented
159#1923C2211yescharacteristic, complemented
160#1923C2211yescharacteristic, complemented
161#1921C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1920C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic, complemented
169#1872C2211yescharacteristic, complemented
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic, complemented
172#1865C2211yescharacteristic, complemented
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic, complemented
176#1864C2211yescharacteristic, complemented
177#1864C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1854C2211yescharacteristic, complemented
181#1853C2211yescharacteristic, complemented
182#1850C2211yescharacteristic, complemented
183#1825C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1808C2211yescharacteristic, complemented
186#1804C2211yescharacteristic, complemented
187#1803C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1798C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201#1752C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C23×C8C2311yescharacteristic
207D42—42no—
208D42—42no—
209#542—42no—
210#542—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
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⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#120—21no—
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245#498—42no—
246#490—42no—
247#489—42no—
248#481—42no—
249#479—42no—
250#478—42no—
251#478—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#102—42no—
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×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#401—21no—
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#400—21no—
324#400—21no—
325#400D411yescharacteristic
326#399—21no—
327#399—21no—
328#399D411yescharacteristic
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398D411yescharacteristic
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397D411yescharacteristic
343#397D411yescharacteristic
344#397D411yescharacteristic
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#395—21no—
351#395—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394D411yescharacteristic
366#394D411yescharacteristic
367#393—21no—
368#393—21no—
369#393—21no—
370#391—21no—
371#391C2311yescharacteristic
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#384—21no—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444#379—21no—
445#379—21no—
446#379—21no—
447#379—21no—
448#379—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
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—41no—
505C22×D4—41no—
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×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#127—22no—
542#127—41no—
543#126—44no—
544#126—82no—
545#125—41no—
546#125—41no—
547#125—41no—
548#125—41no—
549#125—82no—
550#124—22no—
551#124—22no—
552#124—41no—
553#124—41no—
554#124—41no—
555#124—41no—
556#124—44no—
557#124—82no—
558#123—44no—
559#123—82no—
560C22⋊Q8—44no—
561C22⋊Q8—41no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—82no—
566C22⋊Q8—82no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—44no—
571#121—41no—
572#120—44no—
573#120—44no—
574C4×Q8—22no—
575C4×Q8—41no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
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—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
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—82no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#107—22no—
694#107—41no—
695#107—41no—
696#107—41no—
697#106—22no—
698#106—22no—
699#106—22no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
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—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749#97—41no—
750#97—41no—
751#97—41no—
752C4×C8—41no—
753C4×C8—41no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
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#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—42no—
801C24—42no—
802C24—81no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×D4—22no—
826C2×D4—24no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
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—41no—
844C2×D4—41no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—44no—
854C2×D4—42no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—82no—
861C2×D4—82no—
862C2×D4—82no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—82no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—816no—
871C2×D4H(5,𝔽2)12yes—
872C2×D42−1+412yes—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
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—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
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—82no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
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—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
1005C22⋊C4—24no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
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—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—42no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—22no—
1077C23—21no—
1078C23—22no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—84no—
1102C23—84no—
1103C23—84no—
1104C23—84no—
1105C23—84no—
1106C23—162no—
1107C23—162no—
1108C23—162no—
1109C23—162no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23#57712yes—
1116C23C23×D411yescharacteristic
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—162no—
1122Q8—162no—
1123D4—22no—
1124D4—22no—
1125D4—22no—
1126D4—22no—
1127D4—44no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—84no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
1140D4—84no—
1141D4—162no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
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—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
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—84no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4C2×H(5,𝔽2)11yescharacteristic
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4C2×2−1+411yescharacteristic
1232C2×C4#58511yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—42no—
1252C22—41no—
1253C22—42no—
1254C22—41no—
1255C22—42no—
1256C22—42no—
1257C22—41no—
1258C22—41no—
1259C22—42no—
1260C22—41no—
1261C22—42no—
1262C22—41no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—168no—
1279C22—168no—
1280C22#348411yescharacteristic
1281C22#348911yescharacteristic
1282C22#350011yescharacteristic
1283C22C2×#57711yescharacteristic
1284C22#358411yescharacteristic
1285C22#358511yescharacteristic
1286C22#358511yescharacteristic
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—42no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4#353511yescharacteristic
1313C4#355111yescharacteristic
1314C4#356011yescharacteristic
1315C4#356111yescharacteristic
1316C2—42no—
1317C2—81no—
1318C2—82no—
1319C2—82no—
1320C2—161no—
1321C2#4795611yescharacteristic
1322C2#6161011yescharacteristic
1323C2#6169011yescharacteristic
1324C2#6221211yescharacteristic
1325C2#6223511yescharacteristic
1326C2#6260211yescharacteristic
1327C2#6260711yescharacteristic
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. #52978C2semidirect
3. #32088C2semidirect
4. #31982C2semidirect
5. #31789C2semidirect
6. #31500C2semidirect
7. #31323C2semidirect
8. #31306C2semidirect
9. #31298C2semidirect
10. #31298C2semidirect
11. #31126C2semidirect
12. #30947C2semidirect
13. #30835C2semidirect
14. #30775C2semidirect
15. #29959C2semidirect
16. #29702C2semidirect
17. #29115C2semidirect
18. #28958C2semidirect
19. #28079C2semidirect
20. #27773C2semidirect
21. #27520C2semidirect
22. #27262C2semidirect
23. #27125C2semidirect
24. #27039C2semidirect
25. #26776C2semidirect
26. #26479C2semidirect
27. #25952C2semidirect
29. #25680C2semidirect
31. #22372C2semidirect
34. C2×#498C22semidirect
36. C2×#489C22semidirect
38. C2×#479C22semidirect
40. C2×#478C22semidirect
54. #2629C22semidirect
55. #2628C22semidirect
58. #2552C22semidirect
59. #2550C22semidirect
61. #2509C22semidirect
62. #2506C22semidirect
63. #2497C22semidirect
64. #2496C22semidirect
65. #2494C22semidirect
66. #2494C22semidirect
72. #2442C22semidirect
73. #2440C22semidirect
85. #2094C22semidirect
88. #2092C22semidirect
89. #2088C22semidirect
90. #2086C22semidirect
91. #2085C22semidirect
92. #2077C22semidirect
93. #2077C22semidirect
95. #2071C22semidirect
96. #2071C22semidirect
98. #2067C22semidirect
99. #2066C22semidirect
102. #2065C22semidirect
103. #2065C22semidirect
104. #2065C22semidirect
105. #2059C22semidirect
106. #2058C22semidirect
107. #2057C22semidirect
110. #2042C22semidirect
111. #2042C22semidirect
112. #2042C22semidirect
113. #2042C22semidirect
116. #2036C22semidirect
117. #2036C22semidirect
118. #2035C22semidirect
119. #2035C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
128. #2026C22semidirect
130. #2025C22semidirect
132. #2023C22semidirect
133. #1993C22semidirect
135. #1983C22semidirect
138. #1958C22semidirect
139. #1958C22semidirect
141. #1948C22semidirect
142. #1943C22semidirect
143. #1941C22semidirect
144. #1940C22semidirect
146. #1936C22semidirect
147. #1936C22semidirect
148. #1936C22semidirect
149. #1935C22semidirect
152. #1934C22semidirect
153. #1928C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
157. #1924C22semidirect
158. #1923C22semidirect
159. #1923C22semidirect
160. #1923C22semidirect
161. #1921C22semidirect
162. #1920C22semidirect
163. #1920C22semidirect
164. #1920C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
168. #1892C22semidirect
169. #1872C22semidirect
171. #1865C22semidirect
172. #1865C22semidirect
175. #1864C22semidirect
176. #1864C22semidirect
177. #1864C22semidirect
178. #1862C22semidirect
179. #1854C22semidirect
180. #1854C22semidirect
181. #1853C22semidirect
182. #1850C22semidirect
183. #1825C22semidirect
184. #1825C22semidirect
185. #1808C22semidirect
186. #1804C22semidirect
187. #1803C22semidirect
188. #1802C22semidirect
189. #1798C22semidirect
197. #1776C22semidirect
198. #1770C22semidirect
200. C4×#102C22semidirect
201. #1752C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#529782
#448742
#320882
#319822
#317892
#315002
#313232
#313062
#312982
#311262
#309472
#308352
#307752
#299592
#297022
#291152
#289582
#280792
#277732
#275202
#272622
#271252
#270392
#267762
#264792
#259522
#258912
#256802
#240332
#223722