Subgroups — #44445229

Order 29632.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28414680	C₂	1	1	yes	maximal, characteristic, complemented
2	#28414602	C₂	1	2	yes	maximal, complemented
3	#28414599	C₂	1	2	yes	maximal, complemented
4	#28414598	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₄₆₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#20301790	—	2	1	no	—
7	Dic₁₈₅₂	C₂²	1	1	yes	characteristic, complemented
8	#20301779	—	2	1	no	—
9	D₃₇₀₄	C₂²	1	1	yes	characteristic, complemented
10	C₄₆₃⋊C₁₆	C₂²	1	2	yes	complemented
11	C₂×D₄×C₄₆₃	—	2	1	no	—
12	D₈×C₄₆₃	—	2	1	no	—
13	D₈×C₄₆₃	C₂²	1	2	yes	—
14	C₂×C₈×C₄₆₃	C₂²	1	1	yes	characteristic
15	Dic₉₂₆	—	2	1	no	—
16	D₁₈₅₂	—	2	1	no	—
17	C₂²⋊D₄₆₃	—	4	1	no	—
18	C₄×D₄₆₃	—	4	1	no	—
19	C₂³×C₄₆₃	—	4	1	no	—
20	D₄×C₄₆₃	—	2	2	no	—
21	D₄×C₄₆₃	—	4	1	no	—
22	C₂×C₄×C₄₆₃	D₄	1	1	yes	characteristic
23	C₈×C₄₆₃	D₄	1	1	yes	characteristic
24	C₈×C₄₆₃	C₂³	1	1	yes	characteristic
25	C₂²×C₄₆₃	—	4	2	no	—
26	C₂²×C₄₆₃	—	8	2	no	—
27	C₂²×C₄₆₃	D₈	1	1	yes	characteristic
28	C₂×D₄₆₃	—	4	1	no	—
29	C₄×C₄₆₃	D₈	1	1	yes	characteristic
30	C₄×C₄₆₃	C₂×D₄	1	1	yes	characteristic
31	Dic₄₆₃	—	4	1	no	—
32	C₂×C₄₆₃	—	2	1	no	—
33	C₂×C₄₆₃	—	8	2	no	—
34	C₂×C₄₆₃	C₂×D₈	1	1	yes	characteristic
35	D₄₆₃	—	8	1	no	—
36	C₄₆₃	#509	1	1	yes	characteristic, complemented, Sylow
37	#509	—	463	1	no	maximal, Sylow
38	#135	—	463	1	no	—
39	C₂×D₈	D₄₆₃	1	1	yes	characteristic, complemented
40	SD₃₂	—	463	2	no	—
41	D₁₆	—	463	2	no	—
42	M₃₂	—	463	1	no	—
43	#41	—	926	1	no	—
44	C₂×D₄	—	2	1	no	—
45	Q₁₆	—	463	1	no	—
46	SD₁₆	—	926	1	no	—
47	D₈	—	2	1	no	—
48	D₈	—	463	1	no	—
49	D₈	C₂×D₄₆₃	1	2	yes	—
50	C₂×C₈	C₂×D₄₆₃	1	1	yes	characteristic
51	C₁₆	—	463	2	no	—
52	C₂³	—	4	1	no	—
53	Q₈	—	926	1	no	—
54	D₄	—	2	2	no	—
55	D₄	—	4	1	no	—
56	D₄	—	1852	1	no	—
57	D₄	—	926	1	no	—
58	C₂×C₄	—	1852	1	no	—
59	C₂×C₄	C₂²⋊D₄₆₃	1	1	yes	characteristic
60	C₈	C₂²⋊D₄₆₃	1	1	yes	characteristic
61	C₈	C₂²×D₄₆₃	1	1	yes	characteristic
62	C₂²	—	4	2	no	—
63	C₂²	—	8	2	no	—
64	C₂²	—	1852	1	no	—
65	C₂²	#20301775	1	1	yes	characteristic
66	C₄	—	1852	1	no	—
67	C₄	#20301775	1	1	yes	characteristic
68	C₄	C₂×C₂²⋊D₄₆₃	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	8	2	no	—
71	C₂	—	3704	1	no	—
72	C₂	C₂×#20301775	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#20301775
commutator, cosocle	C₈×C₄₆₃	C₂³
Frattini	C₈	C₂²×D₄₆₃
Fitting	C₂×D₈×C₄₆₃	C₂
socle	C₂×C₄₆₃	C₂×D₈
hypercenter	C₂×D₈	D₄₆₃
hypocenter	C₄₆₃	#509
LCS	G ▷ C₈×C₄₆₃ ▷ C₄×C₄₆₃ ▷ C₂×C₄₆₃ ▷ C₄₆₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. #28414680	C₂	semidirect
2. #28414602	C₂	semidirect
3. #28414599	C₂	semidirect
4. #28414598	C₂	semidirect
5. C₂×D₈×C₄₆₃	C₂	semidirect
7. Dic₁₈₅₂	C₂²	semidirect
9. D₃₇₀₄	C₂²	semidirect
10. C₄₆₃⋊C₁₆	C₂²	semidirect
36. C₄₆₃	#509	semidirect
39. C₂×D₈	D₄₆₃	semidirect

Maximal subgroups

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

subgroup	index
#28414680	2
#28414602	2
#28414599	2
#28414598	2
C₂×D₈×C₄₆₃	2
#509	463