Subgroups — D₁₅₂₈₈ #72272007

Order 30576.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₆₄₄	C₂	1	2	yes	maximal, complemented
2	D₅₀₉₆	—	3	1	no	maximal, Hall
3	D₂₁₈₄	—	7	1	no	maximal
4	D₂₅₄₈	—	3	2	no	—
5	D₁₁₇₆	—	13	1	no	maximal, Hall
6	D₁₀₉₂	—	7	2	no	—
7	C₃×C₈×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₁₃×C₄₉	D₃	1	1	yes	characteristic, complemented
9	C₃×C₇×C₈×C₁₃	D₇	1	1	yes	characteristic
10	C₂×D₁₉₁₁	—	2	2	no	—
11	C₃×C₄×C₁₃×C₄₉	C₂²	1	1	yes	characteristic
12	D₁₉₁₁	—	4	2	no	—
13	C₂×C₃×C₁₃×C₄₉	D₄	1	1	yes	characteristic
14	C₂×D₆₃₇	—	6	2	no	—
15	C₄×C₁₃×C₄₉	C₂×D₃	1	1	yes	characteristic
16	C₃×C₁₃×C₄₉	D₈	1	1	yes	characteristic, complemented, Hall
17	D₇₂₈	—	21	1	no	—
18	C₂×C₁₃×C₄₉	D₁₂	1	1	yes	characteristic
19	D₆₃₇	—	12	2	no	—
20	D₅₈₈	—	13	2	no	—
21	C₃×C₈×C₄₉	D₁₃	1	1	yes	characteristic, complemented
22	C₂×D₂₇₃	—	14	2	no	—
23	C₃×C₄×C₇×C₁₃	C₂×D₇	1	1	yes	characteristic
24	D₃₉₂	—	39	1	no	Hall
25	D₃₆₄	—	21	2	no	—
26	C₇×C₈×C₁₃	D₂₁	1	1	yes	characteristic
27	C₁₃×C₄₉	D₂₄	1	1	yes	characteristic, complemented, Hall
28	D₃₁₂	—	49	1	no	Hall
29	C₂×D₁₄₇	—	26	2	no	—
30	C₃×C₄×C₄₉	C₂×D₁₃	1	1	yes	characteristic
31	C₂×C₃×C₇×C₁₃	D₂₈	1	1	yes	characteristic
32	D₂₇₃	—	28	2	no	—
33	D₁₉₆	—	39	2	no	—
34	C₈×C₄₉	D₃₉	1	1	yes	characteristic, complemented
35	C₂×D₉₁	—	42	2	no	—
36	C₄×C₇×C₁₃	C₂×D₂₁	1	1	yes	characteristic
37	D₁₆₈	—	91	1	no	—
38	D₁₅₆	—	49	2	no	—
39	C₃×C₈×C₁₃	D₄₉	1	1	yes	characteristic, complemented
40	C₂×C₃×C₄₉	D₅₂	1	1	yes	characteristic
41	D₁₄₇	—	52	2	no	—
42	C₃×C₇×C₁₃	D₅₆	1	1	yes	characteristic
43	D₁₀₄	—	147	1	no	Hall
44	C₂×D₄₉	—	78	2	no	—
45	C₄×C₄₉	C₂×D₃₉	1	1	yes	characteristic
46	C₂×C₇×C₁₃	D₈₄	1	1	yes	characteristic
47	D₉₁	—	84	2	no	—
48	D₈₄	—	91	2	no	—
49	C₃×C₇×C₈	D₉₁	1	1	yes	characteristic
50	C₂×D₃₉	—	98	2	no	—
51	C₃×C₄×C₁₃	C₂×D₄₉	1	1	yes	characteristic
52	C₃×C₄₉	D₁₀₄	1	1	yes	characteristic, complemented, Hall
53	D₅₆	—	273	1	no	—
54	D₅₂	—	147	2	no	—
55	C₈×C₁₃	D₁₄₇	1	1	yes	characteristic, complemented
56	C₂×C₄₉	D₁₅₆	1	1	yes	characteristic
57	D₄₉	—	156	2	no	—
58	C₇×C₁₃	D₁₆₈	1	1	yes	characteristic
59	C₂×D₂₁	—	182	2	no	—
60	C₃×C₄×C₇	C₂×D₉₁	1	1	yes	characteristic
61	C₂×C₃×C₁₃	D₁₉₆	1	1	yes	characteristic
62	D₃₉	—	196	2	no	—
63	D₂₈	—	273	2	no	—
64	C₇×C₈	D₂₇₃	1	1	yes	characteristic
65	C₂×D₁₃	—	294	2	no	—
66	C₄×C₁₃	C₂×D₁₄₇	1	1	yes	characteristic
67	C₄₉	D₃₁₂	1	1	yes	characteristic, complemented, Sylow
68	D₂₄	—	637	1	no	Hall
69	C₂×C₃×C₇	D₃₆₄	1	1	yes	characteristic
70	D₂₁	—	364	2	no	—
71	C₃×C₁₃	D₃₉₂	1	1	yes	characteristic, complemented, Hall
72	C₂×D₇	—	546	2	no	—
73	C₄×C₇	C₂×D₂₇₃	1	1	yes	characteristic
74	C₂×C₁₃	D₅₈₈	1	1	yes	characteristic
75	D₁₃	—	588	2	no	—
76	D₁₂	—	637	2	no	—
77	C₃×C₈	D₆₃₇	1	1	yes	characteristic, complemented
78	C₃×C₇	D₇₂₈	1	1	yes	characteristic
79	D₈	—	1911	1	no	Sylow
80	C₂×C₇	D₁₀₉₂	1	1	yes	characteristic
81	D₇	—	1092	2	no	—
82	C₁₃	D₁₁₇₆	1	1	yes	characteristic, complemented, Sylow
83	C₂×D₃	—	1274	2	no	—
84	C₃×C₄	C₂×D₆₃₇	1	1	yes	characteristic
85	D₄	—	1911	2	no	—
86	C₈	D₁₉₁₁	1	1	yes	characteristic, complemented
87	C₇	D₂₁₈₄	1	1	yes	characteristic
88	C₂×C₃	D₂₅₄₈	1	1	yes	characteristic
89	D₃	—	2548	2	no	—
90	C₂²	—	3822	2	no	—
91	C₄	C₂×D₁₉₁₁	1	1	yes	characteristic
92	C₃	D₅₀₉₆	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	7644	2	no	—
94	C₂	D₇₆₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₇₆₄₄
commutator, cosocle	C₃×C₄×C₁₃×C₄₉	C₂²
Frattini	C₄×C₇	C₂×D₂₇₃
Fitting	C₃×C₈×C₁₃×C₄₉	C₂
socle	C₂×C₃×C₇×C₁₃	D₂₈
hypercenter	C₈	D₁₉₁₁
hypocenter	C₃×C₁₃×C₄₉	D₈
LCS	G ▷ C₃×C₄×C₁₃×C₄₉ ▷ C₂×C₃×C₁₃×C₄₉ ▷ C₃×C₁₃×C₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. D₇₆₄₄	C₂	semidirect
7. C₃×C₈×C₁₃×C₄₉	C₂	semidirect
8. C₈×C₁₃×C₄₉	D₃	semidirect
16. C₃×C₁₃×C₄₉	D₈	semidirect
21. C₃×C₈×C₄₉	D₁₃	semidirect
27. C₁₃×C₄₉	D₂₄	semidirect
34. C₈×C₄₉	D₃₉	semidirect
39. C₃×C₈×C₁₃	D₄₉	semidirect
52. C₃×C₄₉	D₁₀₄	semidirect
55. C₈×C₁₃	D₁₄₇	semidirect
67. C₄₉	D₃₁₂	semidirect
71. C₃×C₁₃	D₃₉₂	semidirect
77. C₃×C₈	D₆₃₇	semidirect
82. C₁₃	D₁₁₇₆	semidirect
86. C₈	D₁₉₁₁	semidirect
92. C₃	D₅₀₉₆	semidirect

Maximal subgroups

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

subgroup	index
D₇₆₄₄	2
D₅₀₉₆	3
D₂₁₈₄	7
D₁₁₇₆	13
C₃×C₈×C₁₃×C₄₉	2

Subgroups — D15288 #72272007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅₂₈₈ #72272007