Finite Group Databasebeta

← #7016598

Subgroups — #7016598

Order 512.

1524 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45373C211yesmaximal, characteristic, complemented
2#42606C211yesmaximal, characteristic, complemented
3#32484C211yesmaximal, characteristic, complemented
4#32467C211yesmaximal, characteristic, complemented
5#31802C211yesmaximal, characteristic, complemented
6#31391C211yesmaximal, characteristic, complemented
7#31322C211yesmaximal, characteristic, complemented
8#31196C211yesmaximal, characteristic, complemented
9#31032C211yesmaximal, characteristic, complemented
10#31032C211yesmaximal, characteristic, complemented
11#29484C211yesmaximal, characteristic, complemented
12#28984C211yesmaximal, characteristic, complemented
13#28965C211yesmaximal, characteristic, complemented
14#28097C211yesmaximal, characteristic, complemented
15#28021C211yesmaximal, characteristic, complemented
16#27835C211yesmaximal, characteristic, complemented
17#27539C211yesmaximal, characteristic, complemented
18#27330C211yesmaximal, characteristic, complemented
19#27049C211yesmaximal, characteristic, complemented
20#26547C211yesmaximal, characteristic, complemented
21#26315C211yesmaximal, characteristic, complemented
22#26198C211yesmaximal, characteristic, complemented
23#25238C211yesmaximal, characteristic, complemented
24#25012C211yesmaximal, characteristic, complemented
25#24873C211yesmaximal, characteristic, complemented
26#24617C211yesmaximal, characteristic, complemented
27#23702C211yesmaximal, characteristic, complemented
28#23089C211yesmaximal, characteristic, complemented
29#22936C211yesmaximal, characteristic, complemented
30#22870C211yesmaximal, characteristic, complemented
31#22091C211yesmaximal, characteristic, complemented
32C2×#481C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#481C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×C4×D8C2211yescharacteristic
38C2×C8×D4C2211yescharacteristic
39C2×#433C2211yescharacteristic, complemented
40C22×#102C2211yescharacteristic
41#2824—21no—
42#2781—21no—
43#2780—21no—
44#2772—21no—
45#2750—21no—
46#2691—21no—
47#2685—21no—
48#2684—21no—
49#2676—21no—
50#2636—21no—
51#2626—21no—
52#2624C2211yescharacteristic
53#2563C2211yescharacteristic
54#2559—21no—
55#2537C2211yescharacteristic
56#2535—21no—
57#2512C2211yescharacteristic
58#2512C2211yescharacteristic, complemented
59#2508C2211yescharacteristic, complemented
60#2497C2211yescharacteristic
61#2496C2211yescharacteristic
62#2491C2211yescharacteristic
63#2487C2211yescharacteristic
64#2487C2211yescharacteristic
65#2467—21no—
66#2466—21no—
67#2452C2211yescharacteristic
68#2424—21no—
69#2420C2211yescharacteristic, complemented
70#2416C2211yescharacteristic
71#2416C2211yescharacteristic
72#2416C2211yescharacteristic
73#2414C2211yescharacteristic, complemented
74#2408C2211yescharacteristic
75#2408C2211yescharacteristic
76#2392C2211yescharacteristic
77#2361C2211yescharacteristic
78#2361C2211yescharacteristic
79#2352C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic, complemented
81#2345C2211yescharacteristic, complemented
82D4×C22⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic
84#2324C2211yescharacteristic, complemented
85#2316C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic, complemented
90#2086C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2075C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic, complemented
119#2034C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#1999C2211yescharacteristic
123#1999C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1988C2211yescharacteristic, complemented
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1970C2211yescharacteristic
131#1955C2211yescharacteristic
132#1955C2211yescharacteristic
133#1954C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1948C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1944C2211yescharacteristic, complemented
138#1944C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1941C2211yescharacteristic, complemented
141#1941C2211yescharacteristic, complemented
142#1939C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1924C2211yescharacteristic
156#1923C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic, complemented
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic
171#1869C2211yescharacteristic
172#1869C2211yescharacteristic, complemented
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1853C2211yescharacteristic, complemented
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic, complemented
183#1852C2211yescharacteristic, complemented
184#1844C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1824C2211yescharacteristic
187#1823C2211yescharacteristic, complemented
188#1807C2211yescharacteristic
189#1807C2211yescharacteristic
190#1802C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194C4×#106C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1752C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic
201#1750C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#126—21no—
212C2×#124—21no—
213C2×C22⋊Q8—21no—
214C2×#121—21no—
215C2×#121—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×#120—21no—
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4—21no—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243#482—42no—
244#481—24no—
245#481—24no—
246#481—42no—
247#447—24no—
248C4×D8—42no—
249C8×D4—42no—
250#433—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#102—42no—
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#399—21no—
312#399—21no—
313#399—21no—
314#398—21no—
315#398D411yescharacteristic
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397D411yescharacteristic
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396D411yescharacteristic
330#396D411yescharacteristic
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394D411yescharacteristic
344#394D411yescharacteristic
345#394D411yescharacteristic
346#393—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#392D411yescharacteristic
354#390—21no—
355#390—21no—
356#390—21no—
357#390—21no—
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#382—21no—
422#382—21no—
423#382C2311yescharacteristic
424#381—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
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#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×D4—22no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4C2×D411yescharacteristic
504C22×D4C2×D411yescharacteristic
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×D8—22no—
520C2×D8—22no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C22×C8—22no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#126—82no—
542#126—82no—
543#126—82no—
544#124—82no—
545C22⋊Q8—82no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121—41no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—82no—
561#121—82no—
562#121—82no—
563#121—82no—
564#120—82no—
565#120—82no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—82no—
579C4×D4—82no—
580C4×D4—82no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—41no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—21no—
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—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
634C2×C22⋊C4—21no—
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—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#106—22no—
701#106—22no—
702#106—22no—
703#106—22no—
704#106—22no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710C4⋊C8—22no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
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#4114yes—
734C22⋊C8—22no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744#97—41no—
745#97—41no—
746#97—41no—
747C4×C8—22no—
748C4×C8—41no—
749C4×C8—41no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
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#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785C24—21no—
786C24—21no—
787C24—21no—
788C24—42no—
789C24—42no—
790C24—81no—
791C24—81no—
792C24—81no—
793C24—81no—
794C24—81no—
795C24C22×D411yescharacteristic
796C24C22×D411yescharacteristic
797C24C22×D411yescharacteristic
798C2×Q8—81no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—41no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—41no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—82no—
840C2×D4—82no—
841C2×D4—82no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4C2×#4112yes—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
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—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
920D8—44no—
921D8—82no—
922C2×C8—21no—
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—82no—
945C2×C8—82no—
946C2×C8C2×#4112yes—
947C2×C8H(5,𝔽2)12yes—
948C4⋊C4—22no—
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—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—81no—
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⋊C4C2×#4112yes—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
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—81no—
1025C22⋊C4—81no—
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—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—42no—
1062C42—42no—
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—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—22no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
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—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—84no—
1108C23—84no—
1109C23—162no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23—162no—
1114C23#57712yes—
1115C23#57712yes—
1116C23C23×D411yescharacteristic
1117Q8—162no—
1118D4—22no—
1119D4—22no—
1120D4—44no—
1121D4—44no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—82no—
1133D4—84no—
1134D4—84no—
1135D4—84no—
1136D4—162no—
1137D4—162no—
1138D4—162no—
1139D4—162no—
1140D4—162no—
1141C2×C4—21no—
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—22no—
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—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—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
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—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4#57612yes—
1232C2×C4C22×#4111yescharacteristic
1233C2×C4C2×H(5,𝔽2)11yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C2×C4#58511yescharacteristic
1237C2×C4#58511yescharacteristic
1238C8—22no—
1239C8—22no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—41no—
1263C22—42no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—41no—
1269C22—41no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
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—
1289C22D4×#4111yescharacteristic
1290C22#348511yescharacteristic
1291C22#349611yescharacteristic
1292C22C2×#57611yescharacteristic
1293C22C2×#57711yescharacteristic
1294C22C2×#57711yescharacteristic
1295C22#358511yescharacteristic
1296C4—22no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—42no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4#350611yescharacteristic
1321C4#352111yescharacteristic
1322C4#356011yescharacteristic
1323C4#356611yescharacteristic
1324C2—42no—
1325C2—42no—
1326C2—81no—
1327C2—82no—
1328C2—161no—
1329C2—161no—
1330C2#4304211yescharacteristic
1331C2#6149611yescharacteristic
1332C2#6152111yescharacteristic
1333C2#6175811yescharacteristic
1334C2#6176611yescharacteristic
1335C2#6226911yescharacteristic
1336C2#6234911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45373C2semidirect
2. #42606C2semidirect
3. #32484C2semidirect
4. #32467C2semidirect
5. #31802C2semidirect
6. #31391C2semidirect
7. #31322C2semidirect
8. #31196C2semidirect
9. #31032C2semidirect
10. #31032C2semidirect
11. #29484C2semidirect
12. #28984C2semidirect
13. #28965C2semidirect
14. #28097C2semidirect
15. #28021C2semidirect
16. #27835C2semidirect
17. #27539C2semidirect
18. #27330C2semidirect
19. #27049C2semidirect
20. #26547C2semidirect
21. #26315C2semidirect
22. #26198C2semidirect
23. #25238C2semidirect
24. #25012C2semidirect
25. #24873C2semidirect
26. #24617C2semidirect
27. #23702C2semidirect
28. #23089C2semidirect
29. #22936C2semidirect
30. #22870C2semidirect
31. #22091C2semidirect
34. C2×#481C22semidirect
39. C2×#433C22semidirect
58. #2512C22semidirect
59. #2508C22semidirect
69. #2420C22semidirect
73. #2414C22semidirect
80. D4×C4⋊C4C22semidirect
81. #2345C22semidirect
84. #2324C22semidirect
85. #2316C22semidirect
86. #2100C22semidirect
87. #2099C22semidirect
89. #2088C22semidirect
90. #2086C22semidirect
91. #2086C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
99. #2075C22semidirect
102. #2071C22semidirect
103. #2067C22semidirect
109. #2065C22semidirect
110. #2058C22semidirect
118. #2034C22semidirect
119. #2034C22semidirect
121. #2023C22semidirect
126. #1993C22semidirect
127. #1988C22semidirect
133. #1954C22semidirect
134. #1949C22semidirect
135. #1948C22semidirect
136. #1944C22semidirect
137. #1944C22semidirect
138. #1944C22semidirect
139. #1941C22semidirect
140. #1941C22semidirect
141. #1941C22semidirect
142. #1939C22semidirect
149. #1934C22semidirect
152. #1926C22semidirect
156. #1923C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1919C22semidirect
160. #1919C22semidirect
161. #1918C22semidirect
165. #1893C22semidirect
172. #1869C22semidirect
176. #1862C22semidirect
177. #1854C22semidirect
178. #1853C22semidirect
179. #1853C22semidirect
182. #1852C22semidirect
183. #1852C22semidirect
184. #1844C22semidirect
185. #1825C22semidirect
187. #1823C22semidirect
193. #1776C22semidirect
194. C4×#106C22semidirect
195. #1771C22semidirect
197. #1762C22semidirect
199. #1752C22semidirect
201. #1750C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#453732
#426062
#324842
#324672
#318022
#313912
#313222
#311962
#310322
#294842
#289842
#289652
#280972
#280212
#278352
#275392
#273302
#270492
#265472
#263152
#261982
#252382
#250122
#248732
#246172
#237022
#230892
#229362
#228702
#220912