Subgroups — C₇×D₂₁⋊D₃₁ #32912268

Order 18228.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₂₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₇×D₃₁	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₂₁₇	D₃	1	1	yes	characteristic, complemented
7	C₇×D₇×C₃₁	—	3	1	no	—
8	C₇²×D₃₁	—	3	1	no	—
9	D₂₁⋊D₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor
10	D₃×C₇×D₃₁	—	7	1	no	maximal
11	C₇²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃₁×D₂₁	C₂×C₇	1	1	yes	characteristic, complemented
13	C₇×D₉₃	—	2	3	no	—
14	C₇×D₉₃	D₇	1	1	yes	characteristic, complemented
15	C₇×D₉₃	C₂×C₇	1	1	yes	characteristic, complemented
16	D₃×C₇×C₃₁	—	7	1	no	—
17	C₃×D₂₁₇	C₂×C₇	1	1	yes	characteristic, complemented
18	C₃×C₇×D₃₁	—	7	1	no	—
19	C₂×C₇×D₃₁	—	21	1	no	—
20	D₇×D₃₁	—	3	1	no	—
21	C₃×C₇×C₃₁	—	2	3	no	—
22	C₃×C₇×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented
23	C₃×C₇×C₃₁	C₂²×C₇	1	1	yes	characteristic, complemented
24	D₃×C₇×D₇	—	31	1	no	maximal, Hall
25	C₂×C₇×C₃₁	—	21	1	no	—
26	D₂₁₇	D₃×C₇	1	1	yes	characteristic, complemented
27	C₇×D₃₁	—	3	1	no	—
28	C₇×D₃₁	—	3	1	no	—
29	C₇×D₃₁	—	6	3	no	—
30	C₇×D₃₁	—	7	1	no	—
31	D₇×C₃₁	—	3	1	no	—
32	D₃×D₃₁	—	7	1	no	Hall
33	C₇×D₂₁	D₃₁	1	1	yes	characteristic, complemented
34	D₃×C₇²	—	31	1	no	—
35	C₃×C₇×D₇	—	31	1	no	—
36	C₇×C₃₁	—	2	3	no	—
37	C₇×C₃₁	D₃×D₇	1	1	yes	characteristic, complemented
38	C₇×C₃₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented
39	C₂×C₇×D₇	—	93	1	no	Hall
40	D₉₃	C₇×D₇	1	1	yes	characteristic, complemented
41	C₃×D₃₁	—	7	1	no	—
42	D₃×C₃₁	—	7	1	no	—
43	C₃×C₇²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃₁	—	21	1	no	Hall
45	C₂×C₇²	—	93	1	no	—
46	C₇×D₇	—	3	1	no	—
47	C₇×D₇	—	31	1	no	—
48	C₃×C₃₁	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
49	C₂×D₃×C₇	—	217	1	no	—
50	D₃×D₇	—	31	1	no	—
51	C₂×C₃₁	—	21	1	no	—
52	D₃₁	—	3	1	no	—
53	D₃₁	—	7	1	no	—
54	C₇²	D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₇	—	217	1	no	—
56	D₂₁	C₇×D₃₁	1	1	yes	characteristic, complemented
57	C₃×D₇	—	31	1	no	—
58	D₃×C₇	—	7	1	no	—
59	D₃×C₇	—	31	1	no	—
60	D₃×C₇	—	31	1	no	—
61	D₃×C₇	—	62	3	no	—
62	C₃₁	D₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₇	—	651	1	no	—
64	C₂×D₇	—	93	1	no	—
65	C₃×C₇	—	2	3	no	—
66	C₃×C₇	D₇×D₃₁	1	1	yes	characteristic, complemented
67	C₃×C₇	C₂×C₇×D₃₁	1	1	yes	characteristic, complemented
68	C₂×C₇	—	21	1	no	—
69	C₂×C₇	—	93	1	no	—
70	C₂×C₇	—	93	1	no	—
71	C₂×C₇	—	186	3	no	—
72	C₂×C₇	—	217	1	no	—
73	D₇	—	3	1	no	—
74	D₇	—	31	1	no	—
75	C₂×D₃	—	217	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₃×C₇×D₃₁	1	1	yes	characteristic, complemented
78	C₇	D₂₁⋊D₃₁	1	1	yes	characteristic, direct product factor
79	C₂×C₃	—	217	1	no	—
80	D₃	—	7	1	no	—
81	D₃	—	31	1	no	—
82	C₂²	—	651	1	no	Sylow
83	C₃	C₇×D₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	21	1	no	—
85	C₂	—	93	1	no	—
86	C₂	—	217	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₂₁⋊D₃₁
commutator, cosocle, hypocenter	C₃×C₇×C₃₁	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₃₁	C₂²
LCS	G ▷ C₃×C₇×C₃₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₁×D₂₁	C₂	semidirect
2. C₇²×D₉₃	C₂	semidirect
3. C₃×C₇×D₂₁₇	C₂	semidirect
5. C₃×C₇²×C₃₁	C₂²	semidirect
6. C₇×D₂₁₇	D₃	semidirect
9. D₂₁⋊D₃₁	C₇	direct (N × H)
11. C₇²×C₃₁	C₂×D₃	semidirect
12. C₃₁×D₂₁	C₂×C₇	semidirect
14. C₇×D₉₃	D₇	semidirect
15. C₇×D₉₃	C₂×C₇	semidirect
17. C₃×D₂₁₇	C₂×C₇	semidirect
22. C₃×C₇×C₃₁	C₂×D₇	semidirect
23. C₃×C₇×C₃₁	C₂²×C₇	semidirect
26. D₂₁₇	D₃×C₇	semidirect
33. C₇×D₂₁	D₃₁	semidirect
37. C₇×C₃₁	D₃×D₇	semidirect
38. C₇×C₃₁	C₂×D₃×C₇	semidirect
40. D₉₃	C₇×D₇	semidirect
43. C₃×C₇²	C₂×D₃₁	semidirect
48. C₃×C₃₁	C₂×C₇×D₇	semidirect
54. C₇²	D₃×D₃₁	semidirect
56. D₂₁	C₇×D₃₁	semidirect
62. C₃₁	D₃×C₇×D₇	semidirect
66. C₃×C₇	D₇×D₃₁	semidirect
67. C₃×C₇	C₂×C₇×D₃₁	semidirect
77. C₇	D₃×C₇×D₃₁	semidirect
78. C₇	D₂₁⋊D₃₁	direct (N × H)
83. C₃	C₇×D₇×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₃₁×D₂₁	2
C₇²×D₉₃	2
C₃×C₇×D₂₁₇	2
C₇×D₇×D₃₁	3
D₂₁⋊D₃₁	7
D₃×C₇×D₃₁	7
D₃×C₇×D₇	31

Subgroups — C7×D21⋊D31 #32912268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₂₁⋊D₃₁ #32912268