Subgroups — #407×C₄₆₃ #44444332

Order 29632.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₄₆₃	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×C₄₆₃	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₈×C₄₆₃	C₂	1	4	yes	maximal, complemented
4	C₂⁴×C₄₆₃	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₄₆₃	—	2	4	no	—
6	C₂²×C₄×C₄₆₃	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₄₆₃	C₄	1	2	yes	—
8	C₂²×C₄×C₄₆₃	C₂²	1	2	yes	—
9	C₂²×C₄×C₄₆₃	C₂²	1	1	yes	characteristic
10	M₁₆×C₄₆₃	—	2	4	no	—
11	C₂×C₈×C₄₆₃	C₂²	1	4	yes	complemented
12	C₂³×C₄₆₃	—	2	2	no	—
13	C₂³×C₄₆₃	—	2	4	no	—
14	C₂³×C₄₆₃	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄₆₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₄₆₃	—	2	2	no	—
17	C₂×C₄×C₄₆₃	—	2	4	no	—
18	C₂×C₄×C₄₆₃	—	2	4	no	—
19	C₂×C₄×C₄₆₃	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₄₆₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₆₃	D₄	1	4	yes	—
22	C₂×C₄×C₄₆₃	C₂³	1	1	yes	characteristic
23	C₈×C₄₆₃	—	2	4	no	—
24	C₂²×C₄₆₃	—	2	8	no	—
25	C₂²×C₄₆₃	—	2	2	no	—
26	C₂²×C₄₆₃	—	2	2	no	—
27	C₂²×C₄₆₃	—	2	2	no	—
28	C₂²×C₄₆₃	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₄₆₃	M₁₆	1	4	yes	complemented
30	C₂²×C₄₆₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₆₃	—	2	2	no	—
32	C₄×C₄₆₃	C₂²⋊C₄	1	2	yes	—
33	C₄×C₄₆₃	C₂×D₄	1	2	yes	—
34	C₂×C₄₆₃	—	2	2	no	—
35	C₂×C₄₆₃	—	2	4	no	—
36	C₂×C₄₆₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄₆₃	C₂×M₁₆	1	2	yes	—
38	C₄₆₃	#407	1	1	yes	characteristic, direct product factor, Sylow
39	#407	C₄₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂³×C₄	C₂×C₄₆₃	1	1	yes	characteristic
41	C₂×M₁₆	C₂×C₄₆₃	1	2	yes	complemented
42	C₂²⋊C₈	C₂×C₄₆₃	1	4	yes	complemented
43	C₂⁴	C₄×C₄₆₃	1	1	yes	characteristic
44	C₂²×C₄	—	2	4	no	—
45	C₂²×C₄	C₄×C₄₆₃	1	1	yes	characteristic
46	C₂²×C₄	C₄×C₄₆₃	1	2	yes	—
47	C₂²×C₄	C₂²×C₄₆₃	1	2	yes	—
48	C₂²×C₄	C₂²×C₄₆₃	1	1	yes	characteristic
49	M₁₆	—	2	4	no	—
50	C₂×C₈	C₂²×C₄₆₃	1	4	yes	complemented
51	C₂³	—	2	2	no	—
52	C₂³	—	2	4	no	—
53	C₂³	C₂×C₄×C₄₆₃	1	1	yes	characteristic
54	C₂³	C₂×C₄×C₄₆₃	1	2	yes	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	4	no	—
58	C₂×C₄	C₂×C₄×C₄₆₃	1	2	yes	—
59	C₂×C₄	C₂×C₄×C₄₆₃	1	1	yes	characteristic
60	C₂×C₄	D₄×C₄₆₃	1	4	yes	—
61	C₂×C₄	C₂³×C₄₆₃	1	1	yes	characteristic
62	C₈	—	2	4	no	—
63	C₂²	—	2	8	no	—
64	C₂²	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	—	2	2	no	—
67	C₂²	C₂²⋊C₄×C₄₆₃	1	2	yes	—
68	C₂²	M₁₆×C₄₆₃	1	4	yes	complemented
69	C₂²	C₂²×C₄×C₄₆₃	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	C₂²⋊C₄×C₄₆₃	1	2	yes	—
72	C₄	C₂×D₄×C₄₆₃	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	—	2	4	no	—
75	C₂	C₂×C₂²⋊C₄×C₄₆₃	1	1	yes	characteristic
76	C₂	C₂×M₁₆×C₄₆₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₆₃	C₂³
commutator	C₂²	C₂²×C₄×C₄₆₃
Frattini, cosocle	C₂×C₄	C₂³×C₄₆₃
socle	C₂²×C₄₆₃	C₂²×C₄
prime radical	C₂⁴×C₄₆₃	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₆₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×C₄₆₃	C₂	semidirect
3. C₂²⋊C₈×C₄₆₃	C₂	semidirect
11. C₂×C₈×C₄₆₃	C₂²	semidirect
29. C₂²×C₄₆₃	M₁₆	semidirect
38. C₄₆₃	#407	direct (N × H)
39. #407	C₄₆₃	direct (N × H)
41. C₂×M₁₆	C₂×C₄₆₃	semidirect
42. C₂²⋊C₈	C₂×C₄₆₃	semidirect
50. C₂×C₈	C₂²×C₄₆₃	semidirect
68. C₂²	M₁₆×C₄₆₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₄₆₃	2
C₂×M₁₆×C₄₆₃	2
C₂²⋊C₈×C₄₆₃	2
#407	463

Subgroups — #407×C463 #44444332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #407×C₄₆₃ #44444332