Subgroups — D₄₃₁₂ #72211368

Order 8624.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₁₅₆	C₂	1	2	yes	maximal, complemented
2	C₈×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅₃₉	—	2	2	no	—
4	C₄×C₁₁×C₄₉	C₂²	1	1	yes	characteristic
5	D₆₁₆	—	7	1	no	maximal
6	C₂×C₁₁×C₄₉	D₄	1	1	yes	characteristic
7	D₅₃₉	—	4	2	no	—
8	D₃₉₂	—	11	1	no	maximal, Hall
9	D₃₀₈	—	7	2	no	—
10	C₇×C₈×C₁₁	D₇	1	1	yes	characteristic
11	C₁₁×C₄₉	D₈	1	1	yes	characteristic, complemented, Hall
12	D₁₉₆	—	11	2	no	—
13	C₈×C₄₉	D₁₁	1	1	yes	characteristic, complemented
14	C₂×D₇₇	—	14	2	no	—
15	C₄×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic
16	C₂×D₄₉	—	22	2	no	—
17	C₄×C₄₉	C₂×D₁₁	1	1	yes	characteristic
18	D₈₈	—	49	1	no	Hall
19	C₂×C₇×C₁₁	D₂₈	1	1	yes	characteristic
20	D₇₇	—	28	2	no	—
21	D₅₆	—	77	1	no	—
22	C₂×C₄₉	D₄₄	1	1	yes	characteristic
23	D₄₉	—	44	2	no	—
24	D₄₄	—	49	2	no	—
25	C₈×C₁₁	D₄₉	1	1	yes	characteristic, complemented
26	C₇×C₁₁	D₅₆	1	1	yes	characteristic
27	D₂₈	—	77	2	no	—
28	C₇×C₈	D₇₇	1	1	yes	characteristic
29	C₄₉	D₈₈	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₁₁	—	98	2	no	—
31	C₄×C₁₁	C₂×D₄₉	1	1	yes	characteristic
32	C₂×D₇	—	154	2	no	—
33	C₄×C₇	C₂×D₇₇	1	1	yes	characteristic
34	C₂×C₁₁	D₁₉₆	1	1	yes	characteristic
35	D₁₁	—	196	2	no	—
36	D₈	—	539	1	no	Sylow
37	C₂×C₇	D₃₀₈	1	1	yes	characteristic
38	D₇	—	308	2	no	—
39	C₁₁	D₃₉₂	1	1	yes	characteristic, complemented, Sylow
40	D₄	—	539	2	no	—
41	C₈	D₅₃₉	1	1	yes	characteristic, complemented
42	C₇	D₆₁₆	1	1	yes	characteristic
43	C₂²	—	1078	2	no	—
44	C₄	C₂×D₅₃₉	1	1	yes	characteristic
45	C₂	—	2156	2	no	—
46	C₂	D₂₁₅₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₂₁₅₆
commutator, cosocle	C₄×C₁₁×C₄₉	C₂²
Frattini	C₄×C₇	C₂×D₇₇
Fitting	C₈×C₁₁×C₄₉	C₂
socle	C₂×C₇×C₁₁	D₂₈
hypercenter	C₈	D₅₃₉
hypocenter	C₁₁×C₄₉	D₈
LCS	G ▷ C₄×C₁₁×C₄₉ ▷ C₂×C₁₁×C₄₉ ▷ C₁₁×C₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. D₂₁₅₆	C₂	semidirect
2. C₈×C₁₁×C₄₉	C₂	semidirect
11. C₁₁×C₄₉	D₈	semidirect
13. C₈×C₄₉	D₁₁	semidirect
25. C₈×C₁₁	D₄₉	semidirect
29. C₄₉	D₈₈	semidirect
39. C₁₁	D₃₉₂	semidirect
41. C₈	D₅₃₉	semidirect

Maximal subgroups

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

subgroup	index
D₂₁₅₆	2
C₈×C₁₁×C₄₉	2
D₆₁₆	7
D₃₉₂	11

Subgroups — D4312 #72211368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃₁₂ #72211368