Subgroups — D₂₉₁₇₂ #72292813

Order 58344.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₇₂₄	—	3	1	no	maximal, Hall
2	D₁₇₁₆	—	17	1	no	maximal, Hall
3	D₂₆₅₂	—	11	1	no	maximal, Hall
4	D₂₂₄₄	—	13	1	no	maximal, Hall
5	C₂×D₇₂₉₃	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×C₁₁×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
7	D₇₂₉₃	—	2	2	no	—
8	C₂×C₃×C₁₁×C₁₃×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×D₂₄₃₁	—	3	2	no	—
10	C₄×C₁₁×C₁₃×C₁₇	D₃	1	1	yes	characteristic, complemented
11	C₃×C₁₁×C₁₃×C₁₇	D₄	1	1	yes	characteristic, complemented, Hall
12	D₂₄₃₁	—	6	2	no	—
13	C₂×C₁₁×C₁₃×C₁₇	C₂×D₃	1	1	yes	characteristic
14	C₂×D₆₆₃	—	11	2	no	—
15	C₃×C₄×C₁₃×C₁₇	D₁₁	1	1	yes	characteristic, complemented
16	C₁₁×C₁₃×C₁₇	D₁₂	1	1	yes	characteristic, complemented, Hall
17	C₂×D₅₆₁	—	13	2	no	—
18	C₃×C₄×C₁₁×C₁₇	D₁₃	1	1	yes	characteristic, complemented
19	D₈₈₄	—	33	1	no	Hall
20	C₂×D₄₂₉	—	17	2	no	—
21	C₃×C₄×C₁₁×C₁₃	D₁₇	1	1	yes	characteristic, complemented
22	D₇₄₈	—	39	1	no	Hall
23	C₂×C₃×C₁₃×C₁₇	C₂×D₁₁	1	1	yes	characteristic
24	D₆₆₃	—	22	2	no	—
25	D₅₇₂	—	51	1	no	Hall
26	C₂×C₃×C₁₁×C₁₇	C₂×D₁₃	1	1	yes	characteristic
27	D₅₆₁	—	26	2	no	—
28	C₂×D₂₂₁	—	33	2	no	—
29	C₄×C₁₃×C₁₇	D₃₃	1	1	yes	characteristic, complemented
30	C₂×C₃×C₁₁×C₁₃	C₂×D₁₇	1	1	yes	characteristic
31	D₄₂₉	—	34	2	no	—
32	C₂×D₁₈₇	—	39	2	no	—
33	C₄×C₁₁×C₁₇	D₃₉	1	1	yes	characteristic, complemented
34	C₃×C₁₃×C₁₇	D₄₄	1	1	yes	characteristic, complemented, Hall
35	C₂×D₁₄₃	—	51	2	no	—
36	C₄×C₁₁×C₁₃	D₅₁	1	1	yes	characteristic, complemented
37	C₃×C₁₁×C₁₇	D₅₂	1	1	yes	characteristic, complemented, Hall
38	C₂×C₁₃×C₁₇	C₂×D₃₃	1	1	yes	characteristic
39	D₂₂₁	—	66	2	no	—
40	C₃×C₁₁×C₁₃	D₆₈	1	1	yes	characteristic, complemented, Hall
41	D₂₀₄	—	143	1	no	Hall
42	C₂×C₁₁×C₁₇	C₂×D₃₉	1	1	yes	characteristic
43	D₁₈₇	—	78	2	no	—
44	D₁₅₆	—	187	1	no	Hall
45	C₂×C₁₁×C₁₃	C₂×D₅₁	1	1	yes	characteristic
46	D₁₄₃	—	102	2	no	—
47	D₁₃₂	—	221	1	no	Hall
48	C₁₃×C₁₇	D₁₃₂	1	1	yes	characteristic, complemented, Hall
49	C₂×D₅₁	—	143	2	no	—
50	C₃×C₄×C₁₇	D₁₄₃	1	1	yes	characteristic, complemented
51	C₁₁×C₁₇	D₁₅₆	1	1	yes	characteristic, complemented, Hall
52	C₂×D₃₉	—	187	2	no	—
53	C₃×C₄×C₁₃	D₁₈₇	1	1	yes	characteristic, complemented
54	C₁₁×C₁₃	D₂₀₄	1	1	yes	characteristic, complemented, Hall
55	D₆₈	—	429	1	no	Hall
56	C₂×D₃₃	—	221	2	no	—
57	C₃×C₄×C₁₁	D₂₂₁	1	1	yes	characteristic, complemented
58	D₅₂	—	561	1	no	Hall
59	C₂×C₃×C₁₇	C₂×D₁₄₃	1	1	yes	characteristic
60	D₅₁	—	286	2	no	—
61	D₄₄	—	663	1	no	Hall
62	C₂×C₃×C₁₃	C₂×D₁₈₇	1	1	yes	characteristic
63	D₃₉	—	374	2	no	—
64	C₂×D₁₇	—	429	2	no	—
65	C₄×C₁₇	D₄₂₉	1	1	yes	characteristic, complemented
66	C₂×C₃×C₁₁	C₂×D₂₂₁	1	1	yes	characteristic
67	D₃₃	—	442	2	no	—
68	C₂×D₁₃	—	561	2	no	—
69	C₄×C₁₃	D₅₆₁	1	1	yes	characteristic, complemented
70	C₃×C₁₇	D₅₇₂	1	1	yes	characteristic, complemented, Hall
71	C₂×D₁₁	—	663	2	no	—
72	C₄×C₁₁	D₆₆₃	1	1	yes	characteristic, complemented
73	C₃×C₁₃	D₇₄₈	1	1	yes	characteristic, complemented, Hall
74	C₂×C₁₇	C₂×D₄₂₉	1	1	yes	characteristic
75	D₁₇	—	858	2	no	—
76	C₃×C₁₁	D₈₈₄	1	1	yes	characteristic, complemented, Hall
77	C₂×C₁₃	C₂×D₅₆₁	1	1	yes	characteristic
78	D₁₃	—	1122	2	no	—
79	D₁₂	—	2431	1	no	Hall
80	C₂×C₁₁	C₂×D₆₆₃	1	1	yes	characteristic
81	D₁₁	—	1326	2	no	—
82	C₁₇	D₁₇₁₆	1	1	yes	characteristic, complemented, Sylow
83	C₁₃	D₂₂₄₄	1	1	yes	characteristic, complemented, Sylow
84	C₂×D₃	—	2431	2	no	—
85	C₃×C₄	D₂₄₃₁	1	1	yes	characteristic, complemented
86	C₁₁	D₂₆₅₂	1	1	yes	characteristic, complemented, Sylow
87	D₄	—	7293	1	no	Sylow
88	C₂×C₃	C₂×D₂₄₃₁	1	1	yes	characteristic
89	D₃	—	4862	2	no	—
90	C₂²	—	7293	2	no	—
91	C₄	D₇₂₉₃	1	1	yes	characteristic, complemented
92	C₃	D₉₇₂₄	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	14586	2	no	—
94	C₂	C₂×D₇₂₉₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₇₂₉₃
commutator, socle, cosocle	C₂×C₃×C₁₁×C₁₃×C₁₇	C₂²
Fitting	C₃×C₄×C₁₁×C₁₃×C₁₇	C₂
hypercenter	C₄	D₇₂₉₃
hypocenter	C₃×C₁₁×C₁₃×C₁₇	D₄
LCS	G ▷ C₂×C₃×C₁₁×C₁₃×C₁₇ ▷ C₃×C₁₁×C₁₃×C₁₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
5. C₂×D₇₂₉₃	C₂	semidirect
6. C₃×C₄×C₁₁×C₁₃×C₁₇	C₂	semidirect
10. C₄×C₁₁×C₁₃×C₁₇	D₃	semidirect
11. C₃×C₁₁×C₁₃×C₁₇	D₄	semidirect
15. C₃×C₄×C₁₃×C₁₇	D₁₁	semidirect
16. C₁₁×C₁₃×C₁₇	D₁₂	semidirect
18. C₃×C₄×C₁₁×C₁₇	D₁₃	semidirect
21. C₃×C₄×C₁₁×C₁₃	D₁₇	semidirect
29. C₄×C₁₃×C₁₇	D₃₃	semidirect
33. C₄×C₁₁×C₁₇	D₃₉	semidirect
34. C₃×C₁₃×C₁₇	D₄₄	semidirect
36. C₄×C₁₁×C₁₃	D₅₁	semidirect
37. C₃×C₁₁×C₁₇	D₅₂	semidirect
40. C₃×C₁₁×C₁₃	D₆₈	semidirect
48. C₁₃×C₁₇	D₁₃₂	semidirect
50. C₃×C₄×C₁₇	D₁₄₃	semidirect
51. C₁₁×C₁₇	D₁₅₆	semidirect
53. C₃×C₄×C₁₃	D₁₈₇	semidirect
54. C₁₁×C₁₃	D₂₀₄	semidirect
57. C₃×C₄×C₁₁	D₂₂₁	semidirect
65. C₄×C₁₇	D₄₂₉	semidirect
69. C₄×C₁₃	D₅₆₁	semidirect
70. C₃×C₁₇	D₅₇₂	semidirect
72. C₄×C₁₁	D₆₆₃	semidirect
73. C₃×C₁₃	D₇₄₈	semidirect
76. C₃×C₁₁	D₈₈₄	semidirect
82. C₁₇	D₁₇₁₆	semidirect
83. C₁₃	D₂₂₄₄	semidirect
85. C₃×C₄	D₂₄₃₁	semidirect
86. C₁₁	D₂₆₅₂	semidirect
91. C₄	D₇₂₉₃	semidirect
92. C₃	D₉₇₂₄	semidirect

Maximal subgroups

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

subgroup	index
D₉₇₂₄	3
D₁₇₁₆	17
D₂₆₅₂	11
D₂₂₄₄	13
C₂×D₇₂₉₃	2
C₃×C₄×C₁₁×C₁₃×C₁₇	2

Subgroups — D29172 #72292813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉₁₇₂ #72292813