Subgroups — C₇×C₇⋊#10597480 #44472915

Order 29988.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇²×C₁₇	—	6	2	no	—
4	C₇⋊#10597480	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×#10597480	—	7	1	no	maximal
6	C₇×Dic₁₁₉	—	9	1	no	maximal, Hall
7	C₃×C₇²×C₁₇	—	2	2	no	—
8	C₇×C₁₇×C₃⋊D₃	—	2	3	no	—
9	C₇×C₁₇×C₃⋊D₃	D₇	1	1	yes	characteristic
10	C₇×C₁₇×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
11	C₇×C₇⋊#157	—	17	1	no	maximal, Hall
12	C₂×C₇²×C₁₇	—	9	1	no	—
13	C₃²×C₇×C₁₇	—	2	3	no	—
14	C₃²×C₇×C₁₇	Dic₇	1	1	yes	characteristic, complemented
15	C₃²×C₇×C₁₇	C₄×C₇	1	1	yes	characteristic, complemented
16	C₇²×C₃⋊D₃	D₁₇	1	1	yes	characteristic
17	C₇²×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
18	D₃×C₇×C₁₇	—	6	2	no	—
19	D₃×C₇×C₁₇	—	6	2	no	—
20	D₃×C₇×C₁₇	—	6	12	no	—
21	#10597480	—	7	1	no	Hall
22	Dic₁₁₉	—	9	1	no	—
23	C₇×Dic₁₇	—	63	1	no	—
24	C₃²×C₇²	Dic₁₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₇×C₁₇	—	2	12	no	—
26	C₃×C₇×C₁₇	—	2	2	no	—
27	C₃×C₇×C₁₇	—	2	2	no	—
28	C₁₇×C₃⋊D₃	C₇×D₇	1	1	yes	characteristic
29	D₃×C₇²	—	6	2	no	—
30	C₇⋊#157	—	17	1	no	—
31	C₇×#157	—	119	1	no	—
32	C₂×C₇×C₁₇	—	9	1	no	—
33	C₂×C₇×C₁₇	—	9	1	no	—
34	C₂×C₇×C₁₇	—	18	3	no	—
35	C₇×Dic₇	—	153	1	no	Hall
36	C₃²×C₁₇	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇²	—	2	2	no	—
38	C₇×C₃⋊D₃	—	2	3	no	—
39	C₇×C₃⋊D₃	C₇×D₁₇	1	1	yes	characteristic
40	C₇×C₃⋊D₃	D₁₁₉	1	1	yes	characteristic
41	C₇×C₁₇	—	2	3	no	—
42	C₇×C₁₇	C₇×#157	1	1	yes	characteristic, complemented
43	C₇×C₁₇	C₇⋊#157	1	1	yes	characteristic, complemented
44	D₃×C₁₇	—	6	2	no	—
45	C₂×C₇²	—	9	1	no	—
46	Dic₁₇	—	63	1	no	Hall
47	C₃²×C₇	—	2	3	no	—
48	C₃²×C₇	C₇×Dic₁₇	1	1	yes	characteristic, complemented
49	C₃²×C₇	Dic₁₁₉	1	1	yes	characteristic, complemented
50	C₃×C₁₇	—	2	2	no	—
51	C₇²	#10597480	1	1	yes	characteristic, complemented, Sylow
52	D₃×C₇	—	6	2	no	—
53	D₃×C₇	—	6	2	no	—
54	D₃×C₇	—	6	12	no	—
55	#157	—	119	1	no	Hall
56	C₂×C₁₇	—	9	1	no	—
57	C₄×C₇	—	1071	1	no	—
58	Dic₇	—	153	1	no	—
59	C₃×C₇	—	2	12	no	—
60	C₃×C₇	—	2	2	no	—
61	C₃×C₇	—	2	2	no	—
62	C₃⋊D₃	C₇×D₁₁₉	1	1	yes	characteristic
63	C₁₇	C₇×C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₇	—	9	1	no	—
65	C₂×C₇	—	9	1	no	—
66	C₂×C₇	—	18	3	no	—
67	C₃²	C₇×Dic₁₁₉	1	1	yes	characteristic, complemented, Sylow
68	C₇	—	2	3	no	—
69	C₇	C₇×#10597480	1	1	yes	characteristic, complemented
70	C₇	C₇⋊#10597480	1	1	yes	characteristic, direct product factor
71	D₃	—	6	2	no	—
72	C₄	—	1071	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₇⋊#10597480
commutator, hypocenter	C₃²×C₇×C₁₇	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₇	C₄
prime radical	C₇²×C₁₇×C₃⋊D₃	C₂
cosocle	C₇×C₁₇×C₃⋊D₃	C₂×C₇
LCS	G ▷ C₃²×C₇×C₁₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇²×C₁₇	C₄	semidirect
4. C₇⋊#10597480	C₇	direct (N × H)
14. C₃²×C₇×C₁₇	Dic₇	semidirect
15. C₃²×C₇×C₁₇	C₄×C₇	semidirect
17. C₇²×C₁₇	#157	semidirect
24. C₃²×C₇²	Dic₁₇	semidirect
36. C₃²×C₁₇	C₇×Dic₇	semidirect
42. C₇×C₁₇	C₇×#157	semidirect
43. C₇×C₁₇	C₇⋊#157	semidirect
48. C₃²×C₇	C₇×Dic₁₇	semidirect
49. C₃²×C₇	Dic₁₁₉	semidirect
51. C₇²	#10597480	semidirect
63. C₁₇	C₇×C₇⋊#157	semidirect
67. C₃²	C₇×Dic₁₁₉	semidirect
69. C₇	C₇×#10597480	semidirect
70. C₇	C₇⋊#10597480	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₁₇×C₃⋊D₃	2
C₇⋊#10597480	7
C₇×#10597480	7
C₇×Dic₁₁₉	9
C₇×C₇⋊#157	17

Subgroups — C7×C7⋊#10597480 #44472915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₇⋊#10597480 #44472915