Subgroups — D₁₇₇⋊D₅₁ #49115685

Order 36108.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₁₇₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃₀₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₁⋊D₅₉	—	3	1	no	maximal
5	D₅₁×D₅₉	—	3	1	no	maximal
6	C₃²×C₁₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃₀₀₉	D₃	1	1	yes	characteristic, complemented
8	C₅₉×D₅₁	—	3	1	no	—
9	C₅₉×D₅₁	—	3	1	no	—
10	C₅₉×D₅₁	—	6	1	no	—
11	C₁₇×D₁₇₇	D₃	1	1	yes	characteristic, complemented
12	C₃×D₁₀₀₃	—	3	1	no	—
13	C₃×C₁₇×D₅₉	—	3	1	no	—
14	D₁₇×D₅₉	—	9	1	no	Hall
15	C₃×C₁₇×C₅₉	—	2	1	no	—
16	C₃×C₁₇×C₅₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₇×C₅₉	C₂×D₃	1	1	yes	characteristic, complemented
18	(C₃⋊D₃)⋊D₅₉	—	17	1	no	maximal, Hall
19	D₁₀₀₃	—	3	1	no	—
20	C₁₇×D₅₉	—	3	1	no	—
21	D₁₇×C₅₉	—	9	1	no	—
22	C₃⋊D₃×C₅₉	—	17	1	no	—
23	C₃×D₁₇₇	—	17	1	no	—
24	C₃×D₁₇₇	D₁₇	1	1	yes	characteristic, complemented
25	C₁₇×C₅₉	D₃²	1	1	yes	characteristic, complemented, Hall
26	D₃×D₅₉	—	51	1	no	—
27	D₃×D₅₉	—	51	1	no	—
28	D₃×D₅₁	—	59	1	no	maximal, Hall
29	C₃²×C₅₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	D₁₇₇	—	17	1	no	—
31	D₁₇₇	D₅₁	1	1	yes	characteristic, complemented
32	C₃×D₅₉	—	3	1	no	—
33	C₃×D₅₉	—	51	1	no	—
34	D₃×C₅₉	—	51	1	no	—
35	D₃×C₅₉	—	51	1	no	—
36	D₃×C₅₉	—	102	1	no	—
37	C₃⋊D₅₁	D₅₉	1	1	yes	characteristic, complemented
38	C₃×D₅₁	—	59	1	no	—
39	C₃×D₃×C₁₇	—	59	1	no	—
40	C₂×D₅₉	—	153	1	no	Hall
41	C₂×D₅₁	—	177	1	no	—
42	D₃×D₁₇	—	177	1	no	—
43	C₃×C₅₉	—	2	1	no	—
44	C₃×C₅₉	D₃×D₁₇	1	1	yes	characteristic, complemented
45	C₃×C₅₉	C₂×D₅₁	1	1	yes	characteristic, complemented
46	C₃²×C₁₇	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
47	C₂×C₅₉	—	153	1	no	—
48	D₅₉	—	3	1	no	—
49	D₅₉	—	51	1	no	—
50	C₂×C₃×C₁₇	—	177	1	no	—
51	D₅₁	—	3	1	no	—
52	D₅₁	—	3	1	no	—
53	D₅₁	—	6	1	no	—
54	D₅₁	—	59	1	no	—
55	C₃×D₁₇	—	177	1	no	—
56	D₃×C₁₇	—	59	1	no	—
57	C₂×D₁₇	—	531	1	no	Hall
58	C₅₉	D₃×D₅₁	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₁₇	—	2	1	no	—
60	C₃×C₁₇	D₃×D₅₉	1	1	yes	characteristic, complemented
61	C₃×C₁₇	D₃×D₅₉	1	1	yes	characteristic, complemented
62	D₃²	—	1003	1	no	Hall
63	C₂×C₁₇	—	177	1	no	—
64	D₁₇	—	9	1	no	—
65	D₁₇	—	177	1	no	—
66	C₃⋊D₃	—	17	1	no	—
67	C₃×D₃	—	59	1	no	—
68	C₃×D₃	—	1003	1	no	—
69	C₁₇	(C₃⋊D₃)⋊D₅₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₃	—	3009	1	no	—
71	C₂×D₃	—	3009	1	no	—
72	C₃²	D₁₇×D₅₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	177	1	no	—
74	C₂×C₃	—	3009	1	no	—
75	D₃	—	51	1	no	—
76	D₃	—	51	1	no	—
77	D₃	—	59	1	no	—
78	D₃	—	102	1	no	—
79	D₃	—	1003	1	no	—
80	C₂²	—	9027	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₅₁×D₅₉	1	1	yes	characteristic, complemented
83	C₃	D₅₁⋊D₅₉	1	1	yes	characteristic, complemented
84	C₂	—	153	1	no	—
85	C₂	—	177	1	no	—
86	C₂	—	3009	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₇×C₅₉	C₂²
LCS	G ▷ C₃²×C₁₇×C₅₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×D₁₇₇	C₂	semidirect
2. C₃×D₃₀₀₉	C₂	semidirect
3. C₅₉×C₃⋊D₅₁	C₂	semidirect
6. C₃²×C₁₇×C₅₉	C₂²	semidirect
7. D₃₀₀₉	D₃	semidirect
11. C₁₇×D₁₇₇	D₃	semidirect
16. C₃×C₁₇×C₅₉	C₂×D₃	semidirect
17. C₃×C₁₇×C₅₉	C₂×D₃	semidirect
24. C₃×D₁₇₇	D₁₇	semidirect
25. C₁₇×C₅₉	D₃²	semidirect
29. C₃²×C₅₉	C₂×D₁₇	semidirect
31. D₁₇₇	D₅₁	semidirect
37. C₃⋊D₅₁	D₅₉	semidirect
44. C₃×C₅₉	D₃×D₁₇	semidirect
45. C₃×C₅₉	C₂×D₅₁	semidirect
46. C₃²×C₁₇	C₂×D₅₉	semidirect
58. C₅₉	D₃×D₅₁	semidirect
60. C₃×C₁₇	D₃×D₅₉	semidirect
61. C₃×C₁₇	D₃×D₅₉	semidirect
69. C₁₇	(C₃⋊D₃)⋊D₅₉	semidirect
72. C₃²	D₁₇×D₅₉	semidirect
82. C₃	D₅₁×D₅₉	semidirect
83. C₃	D₅₁⋊D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₇×D₁₇₇	2
C₃×D₃₀₀₉	2
C₅₉×C₃⋊D₅₁	2
D₅₁⋊D₅₉	3
D₅₁×D₅₉	3
(C₃⋊D₃)⋊D₅₉	17
D₃×D₅₁	59

Subgroups — D177⋊D51 #49115685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇₇⋊D₅₁ #49115685