Subgroups — #352×C₄₆₃ #44444277

Order 29632.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#123×C₄₆₃	C₂	1	1	yes	maximal, characteristic
2	#100×C₄₆₃	C₂	1	1	yes	maximal, characteristic
3	#99×C₄₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂×D₄×C₄₆₃	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₄₆₃	C₄	1	1	yes	characteristic, complemented
6	M₁₆×C₄₆₃	—	2	1	no	—
7	C₄⋊C₄×C₄₆₃	—	2	1	no	—
8	C₂²⋊C₄×C₄₆₃	—	2	1	no	—
9	C₂²⋊C₄×C₄₆₃	—	2	1	no	—
10	C₂²⋊C₄×C₄₆₃	C₄	1	1	yes	characteristic, complemented
11	C₂³×C₄₆₃	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄₆₃	D₄	1	1	yes	characteristic
13	D₄×C₄₆₃	—	4	1	no	—
14	C₂×C₄×C₄₆₃	—	2	1	no	—
15	C₂×C₄×C₄₆₃	—	2	1	no	—
16	C₂×C₄×C₄₆₃	—	4	1	no	—
17	C₂×C₄×C₄₆₃	—	4	1	no	—
18	C₂×C₄×C₄₆₃	D₄	1	1	yes	characteristic
19	C₈×C₄₆₃	—	4	1	no	—
20	C₂²×C₄₆₃	—	2	1	no	—
21	C₂²×C₄₆₃	—	2	1	no	—
22	C₂²×C₄₆₃	—	4	1	no	—
23	C₂²×C₄₆₃	—	4	1	no	—
24	C₂²×C₄₆₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₄₆₃	—	2	1	no	—
26	C₄×C₄₆₃	—	4	1	no	—
27	C₄×C₄₆₃	—	4	1	no	—
28	C₄×C₄₆₃	—	8	1	no	—
29	C₂×C₄₆₃	—	2	1	no	—
30	C₂×C₄₆₃	—	4	1	no	—
31	C₂×C₄₆₃	—	4	1	no	—
32	C₂×C₄₆₃	#99	1	1	yes	characteristic
33	C₄₆₃	#352	1	1	yes	characteristic, direct product factor, Sylow
34	#352	C₄₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	#123	C₂×C₄₆₃	1	1	yes	characteristic
36	#100	C₂×C₄₆₃	1	1	yes	characteristic
37	#99	C₂×C₄₆₃	1	1	yes	characteristic
38	C₂×D₄	C₂²×C₄₆₃	1	1	yes	characteristic
39	C₂²×C₄	C₄×C₄₆₃	1	1	yes	characteristic, complemented
40	M₁₆	—	2	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₂²⋊C₄	—	2	1	no	—
43	C₂²⋊C₄	—	2	1	no	—
44	C₂²⋊C₄	C₄×C₄₆₃	1	1	yes	characteristic, complemented
45	C₂³	C₂×C₄×C₄₆₃	1	1	yes	characteristic
46	C₂³	D₄×C₄₆₃	1	1	yes	characteristic
47	D₄	—	4	1	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	D₄×C₄₆₃	1	1	yes	characteristic
53	C₈	—	4	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	4	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂²⋊C₄×C₄₆₃	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	—	4	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	4	1	no	—
66	C₂	#99×C₄₆₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₆₃	#99
commutator	C₂³	C₂×C₄×C₄₆₃
Frattini, cosocle	C₂×D₄	C₂²×C₄₆₃
prime radical	C₂×D₄×C₄₆₃	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₆₃ ◁ C₂²×C₄₆₃ ◁ C₂×D₄×C₄₆₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂²×C₄×C₄₆₃	C₄	semidirect
10. C₂²⋊C₄×C₄₆₃	C₄	semidirect
33. C₄₆₃	#352	direct (N × H)
34. #352	C₄₆₃	direct (N × H)
39. C₂²×C₄	C₄×C₄₆₃	semidirect
44. C₂²⋊C₄	C₄×C₄₆₃	semidirect

Maximal subgroups

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

subgroup	index
#123×C₄₆₃	2
#100×C₄₆₃	2
#99×C₄₆₃	2
#352	463

Subgroups — #352×C463 #44444277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #352×C₄₆₃ #44444277