Subgroups — #45691684

Order 33516.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₉₇	C₂	1	2	yes	maximal, complemented
2	C₉×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#26014025	—	3	1	no	maximal
4	C₇²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₃₉₉	—	3	2	no	—
6	C₃×C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic
7	D₇×D₁₇₁	—	7	2	no	maximal
8	(C₇⋊D₇)⋊D₁₉	—	9	1	no	Hall
9	C₃×C₇²×C₁₉	C₂×D₃	1	1	yes	characteristic
10	D₁₁₉₇	D₇	1	2	yes	complemented
11	C₇×D₁₇₁	—	7	2	no	—
12	C₉×D₇×C₁₉	—	7	2	no	—
13	C₉×D₇×C₁₉	—	14	3	no	—
14	C₁₉×C₇⋊D₇	D₉	1	1	yes	characteristic, complemented
15	C₇×D₁₃₃	—	9	2	no	—
16	D₆₃⋊D₇	—	19	1	no	maximal, Hall
17	D₇×D₅₇	—	21	2	no	—
18	C₇×C₉×C₁₉	—	2	3	no	—
19	C₇×C₉×C₁₉	C₂×D₇	1	2	yes	complemented
20	C₇²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
21	C₇×D₆₃	—	19	2	no	—
22	C₉×C₇⋊D₇	D₁₉	1	1	yes	characteristic, complemented
23	D₃₉₉	—	3	2	no	—
24	C₇×D₅₇	—	21	2	no	—
25	C₃×D₇×C₁₉	—	7	2	no	—
26	C₃×D₇×C₁₉	—	14	3	no	—
27	C₂×D₁₇₁	—	49	1	no	Hall
28	D₂₁⋊D₇	—	57	1	no	—
29	D₇×D₁₉	—	63	2	no	—
30	C₇²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	C₃×C₇×C₁₉	—	2	3	no	—
32	C₃×C₇×C₁₉	D₃×D₇	1	2	yes	—
33	C₂×C₉×C₁₉	—	49	1	no	—
34	D₁₇₁	—	7	2	no	—
35	C₇×D₂₁	—	57	2	no	—
36	C₃×C₇⋊D₇	D₅₇	1	1	yes	characteristic
37	D₁₃₃	—	9	2	no	—
38	C₇×D₁₉	—	63	2	no	—
39	D₇×C₁₉	—	7	2	no	—
40	D₇×C₁₉	—	14	3	no	—
41	D₇×D₉	—	133	2	no	—
42	C₂×D₅₇	—	147	1	no	—
43	D₇²	—	171	1	no	Hall
44	C₉×C₁₉	D₇²	1	1	yes	characteristic, complemented, Hall
45	C₃×C₇²	C₂×D₅₇	1	1	yes	characteristic
46	C₇×C₁₉	—	2	3	no	—
47	C₇×C₁₉	D₇×D₉	1	2	yes	complemented
48	D₆₃	—	19	2	no	—
49	C₉×D₇	—	7	2	no	—
50	C₉×D₇	—	14	3	no	—
51	C₇×D₉	—	133	2	no	—
52	C₂×C₃×C₁₉	—	49	1	no	—
53	D₅₇	—	21	2	no	—
54	C₇⋊D₇	D₁₇₁	1	1	yes	characteristic, complemented
55	C₇×D₇	—	171	2	no	—
56	D₃×D₇	—	399	2	no	—
57	C₂×D₁₉	—	441	1	no	Hall
58	C₇×C₉	—	2	3	no	—
59	C₇×C₉	D₇×D₁₉	1	2	yes	complemented
60	C₃×C₁₉	D₂₁⋊D₇	1	1	yes	characteristic
61	C₇²	C₂×D₁₇₁	1	1	yes	characteristic, complemented, Sylow
62	D₂₁	—	57	2	no	—
63	C₃×D₇	—	7	2	no	—
64	C₃×D₇	—	14	3	no	—
65	D₃×C₇	—	399	2	no	—
66	C₂×C₁₉	—	49	1	no	—
67	D₁₉	—	63	2	no	—
68	C₂×D₉	—	931	1	no	Hall
69	C₂×D₇	—	1197	2	no	—
70	C₃×C₇	—	2	3	no	—
71	C₃×C₇	D₇×D₅₇	1	2	yes	—
72	C₁₉	D₆₃⋊D₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₉	—	49	1	no	—
74	D₉	—	133	2	no	—
75	C₂×C₇	—	1197	2	no	—
76	D₇	—	7	2	no	—
77	D₇	—	14	3	no	—
78	D₇	—	171	2	no	—
79	C₂×D₃	—	2793	1	no	—
80	C₉	(C₇⋊D₇)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
81	C₇	—	2	3	no	—
82	C₇	D₇×D₁₇₁	1	2	yes	complemented
83	C₂×C₃	—	49	1	no	—
84	D₃	—	399	2	no	—
85	C₂²	—	8379	1	no	Sylow
86	C₃	#26014025	1	1	yes	characteristic
87	C₂	—	49	1	no	—
88	C₂	—	1197	2	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇²×C₉×C₁₉	C₂²
Frattini	C₃	#26014025
socle	C₃×C₇²×C₁₉	C₂×D₃
LCS	G ▷ C₇²×C₉×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₁₉₇	C₂	semidirect
2. C₉×C₁₉×C₇⋊D₇	C₂	semidirect
4. C₇²×C₉×C₁₉	C₂²	semidirect
10. D₁₁₉₇	D₇	semidirect
14. C₁₉×C₇⋊D₇	D₉	semidirect
19. C₇×C₉×C₁₉	C₂×D₇	semidirect
20. C₇²×C₁₉	C₂×D₉	semidirect
22. C₉×C₇⋊D₇	D₁₉	semidirect
30. C₇²×C₉	C₂×D₁₉	semidirect
44. C₉×C₁₉	D₇²	semidirect
47. C₇×C₁₉	D₇×D₉	semidirect
54. C₇⋊D₇	D₁₇₁	semidirect
59. C₇×C₉	D₇×D₁₉	semidirect
61. C₇²	C₂×D₁₇₁	semidirect
72. C₁₉	D₆₃⋊D₇	semidirect
80. C₉	(C₇⋊D₇)⋊D₁₉	semidirect
82. C₇	D₇×D₁₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₁₁₉₇	2
C₉×C₁₉×C₇⋊D₇	2
#26014025	3
D₇×D₁₇₁	7
D₆₃⋊D₇	19