Subgroups — #395×C₅₆₃ #49113015

Order 36032.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₅₆₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₅₆₃	C₂	1	3	yes	maximal
3	#95×C₅₆₃	C₂	1	3	yes	maximal
4	C₂×Q₈×C₅₆₃	—	2	6	no	—
5	C₂²×C₄×C₅₆₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₅₆₃	C₂²	1	3	yes	—
7	C₂²×C₄×C₅₆₃	C₂²	1	3	yes	—
8	C₄⋊C₄×C₅₆₃	—	2	6	no	—
9	C₂³×C₅₆₃	C₂³	1	1	yes	characteristic
10	Q₈×C₅₆₃	—	2	8	no	—
11	C₂×C₄×C₅₆₃	—	2	3	no	—
12	C₂×C₄×C₅₆₃	—	2	6	no	—
13	C₂×C₄×C₅₆₃	—	2	3	no	—
14	C₂×C₄×C₅₆₃	—	2	3	no	—
15	C₂×C₄×C₅₆₃	D₄	1	6	yes	—
16	C₂×C₄×C₅₆₃	Q₈	1	6	yes	complemented
17	C₂²×C₅₆₃	C₂×D₄	1	3	yes	—
18	C₂²×C₅₆₃	C₂×Q₈	1	3	yes	—
19	C₂²×C₅₆₃	#41	1	1	yes	characteristic
20	C₄×C₅₆₃	—	2	6	no	—
21	C₄×C₅₆₃	—	2	6	no	—
22	C₄×C₅₆₃	—	4	1	no	—
23	C₂×C₅₆₃	#120	1	1	yes	characteristic
24	C₂×C₅₆₃	C₂²⋊Q₈	1	3	yes	—
25	C₂×C₅₆₃	C₄⋊Q₈	1	3	yes	—
26	C₅₆₃	#395	1	1	yes	characteristic, direct product factor, Sylow
27	#395	C₅₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×Q₈	C₂×C₅₆₃	1	1	yes	characteristic
29	C₂×C₄⋊C₄	C₂×C₅₆₃	1	3	yes	—
30	#95	C₂×C₅₆₃	1	3	yes	—
31	C₂×Q₈	—	2	6	no	—
32	C₂²×C₄	C₂²×C₅₆₃	1	1	yes	characteristic
33	C₂²×C₄	C₂²×C₅₆₃	1	3	yes	—
34	C₂²×C₄	C₂²×C₅₆₃	1	3	yes	—
35	C₄⋊C₄	—	2	6	no	—
36	C₂³	C₂³×C₅₆₃	1	1	yes	characteristic
37	Q₈	—	2	8	no	—
38	C₂×C₄	—	2	3	no	—
39	C₂×C₄	—	2	6	no	—
40	C₂×C₄	—	2	3	no	—
41	C₂×C₄	—	2	3	no	—
42	C₂×C₄	D₄×C₅₆₃	1	6	yes	—
43	C₂×C₄	Q₈×C₅₆₃	1	6	yes	complemented
44	C₂²	C₂×D₄×C₅₆₃	1	3	yes	—
45	C₂²	C₂×Q₈×C₅₆₃	1	3	yes	—
46	C₂²	#41×C₅₆₃	1	1	yes	characteristic
47	C₄	—	2	6	no	—
48	C₄	—	2	6	no	—
49	C₄	—	4	1	no	—
50	C₂	#120×C₅₆₃	1	1	yes	characteristic
51	C₂	C₂²⋊Q₈×C₅₆₃	1	3	yes	—
52	C₂	C₄⋊Q₈×C₅₆₃	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₆₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₅₆₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₆₃ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₂×C₄×C₅₆₃	Q₈	semidirect
26. C₅₆₃	#395	direct (N × H)
27. #395	C₅₆₃	direct (N × H)
43. C₂×C₄	Q₈×C₅₆₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₅₆₃	2
C₂×C₄⋊C₄×C₅₆₃	2
#95×C₅₆₃	2
#395	563

Subgroups — #395×C563 #49113015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #395×C₅₆₃ #49113015