Subgroups — D₉₀₄₈ #72213870

Order 18096.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₅₂₄	C₂	1	2	yes	maximal, complemented
2	D₃₀₁₆	—	3	1	no	maximal, Hall
3	D₁₅₀₈	—	3	2	no	—
4	C₃×C₈×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₁₃×C₂₉	D₃	1	1	yes	characteristic, complemented
6	C₂×D₁₁₃₁	—	2	2	no	—
7	C₃×C₄×C₁₃×C₂₉	C₂²	1	1	yes	characteristic
8	D₁₁₃₁	—	4	2	no	—
9	C₂×C₃×C₁₃×C₂₉	D₄	1	1	yes	characteristic
10	C₂×D₃₇₇	—	6	2	no	—
11	C₄×C₁₃×C₂₉	C₂×D₃	1	1	yes	characteristic
12	D₆₉₆	—	13	1	no	maximal, Hall
13	C₃×C₁₃×C₂₉	D₈	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₂₉	D₁₂	1	1	yes	characteristic
15	D₃₇₇	—	12	2	no	—
16	D₃₄₈	—	13	2	no	—
17	C₃×C₈×C₂₉	D₁₃	1	1	yes	characteristic, complemented
18	D₃₁₂	—	29	1	no	maximal, Hall
19	D₂₃₂	—	39	1	no	Hall
20	C₁₃×C₂₉	D₂₄	1	1	yes	characteristic, complemented, Hall
21	C₂×D₈₇	—	26	2	no	—
22	C₃×C₄×C₂₉	C₂×D₁₃	1	1	yes	characteristic
23	D₁₅₆	—	29	2	no	—
24	C₃×C₈×C₁₃	D₂₉	1	1	yes	characteristic, complemented
25	D₁₁₆	—	39	2	no	—
26	C₈×C₂₉	D₃₉	1	1	yes	characteristic, complemented
27	D₁₀₄	—	87	1	no	Hall
28	C₂×C₃×C₂₉	D₅₂	1	1	yes	characteristic
29	D₈₇	—	52	2	no	—
30	C₂×D₃₉	—	58	2	no	—
31	C₃×C₄×C₁₃	C₂×D₂₉	1	1	yes	characteristic
32	C₂×D₂₉	—	78	2	no	—
33	C₄×C₂₉	C₂×D₃₉	1	1	yes	characteristic
34	D₅₂	—	87	2	no	—
35	C₈×C₁₃	D₈₇	1	1	yes	characteristic, complemented
36	C₃×C₂₉	D₁₀₄	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₁₃	D₁₁₆	1	1	yes	characteristic
38	D₃₉	—	116	2	no	—
39	C₂×C₂₉	D₁₅₆	1	1	yes	characteristic
40	D₂₉	—	156	2	no	—
41	C₂×D₁₃	—	174	2	no	—
42	C₄×C₁₃	C₂×D₈₇	1	1	yes	characteristic
43	D₂₄	—	377	1	no	Hall
44	C₃×C₁₃	D₂₃₂	1	1	yes	characteristic, complemented, Hall
45	C₂₉	D₃₁₂	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₃	D₃₄₈	1	1	yes	characteristic
47	D₁₃	—	348	2	no	—
48	D₁₂	—	377	2	no	—
49	C₃×C₈	D₃₇₇	1	1	yes	characteristic, complemented
50	D₈	—	1131	1	no	Sylow
51	C₁₃	D₆₉₆	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₃	—	754	2	no	—
53	C₃×C₄	C₂×D₃₇₇	1	1	yes	characteristic
54	D₄	—	1131	2	no	—
55	C₈	D₁₁₃₁	1	1	yes	characteristic, complemented
56	C₂×C₃	D₁₅₀₈	1	1	yes	characteristic
57	D₃	—	1508	2	no	—
58	C₂²	—	2262	2	no	—
59	C₄	C₂×D₁₁₃₁	1	1	yes	characteristic
60	C₃	D₃₀₁₆	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	4524	2	no	—
62	C₂	D₄₅₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄₅₂₄
commutator, cosocle	C₃×C₄×C₁₃×C₂₉	C₂²
Frattini	C₄	C₂×D₁₁₃₁
Fitting	C₃×C₈×C₁₃×C₂₉	C₂
socle	C₂×C₃×C₁₃×C₂₉	D₄
hypercenter	C₈	D₁₁₃₁
hypocenter	C₃×C₁₃×C₂₉	D₈
LCS	G ▷ C₃×C₄×C₁₃×C₂₉ ▷ C₂×C₃×C₁₃×C₂₉ ▷ C₃×C₁₃×C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. D₄₅₂₄	C₂	semidirect
4. C₃×C₈×C₁₃×C₂₉	C₂	semidirect
5. C₈×C₁₃×C₂₉	D₃	semidirect
13. C₃×C₁₃×C₂₉	D₈	semidirect
17. C₃×C₈×C₂₉	D₁₃	semidirect
20. C₁₃×C₂₉	D₂₄	semidirect
24. C₃×C₈×C₁₃	D₂₉	semidirect
26. C₈×C₂₉	D₃₉	semidirect
35. C₈×C₁₃	D₈₇	semidirect
36. C₃×C₂₉	D₁₀₄	semidirect
44. C₃×C₁₃	D₂₃₂	semidirect
45. C₂₉	D₃₁₂	semidirect
49. C₃×C₈	D₃₇₇	semidirect
51. C₁₃	D₆₉₆	semidirect
55. C₈	D₁₁₃₁	semidirect
60. C₃	D₃₀₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₄₅₂₄	2
D₃₀₁₆	3
C₃×C₈×C₁₃×C₂₉	2
D₆₉₆	13
D₃₁₂	29

Subgroups — D9048 #72213870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉₀₄₈ #72213870