Subgroups — D₃×C₇×D₂₁₃ #31822098

Order 17892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₂₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₂₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₂₁₃	—	3	1	no	maximal
5	D₃×C₇×D₇₁	—	3	1	no	maximal
6	C₃²×C₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₇×D₂₁₃	—	3	1	no	—
8	C₇×D₂₁₃	—	3	1	no	—
9	C₇×D₂₁₃	—	6	1	no	—
10	C₇×D₂₁₃	D₃	1	1	yes	characteristic, direct product factor
11	D₃×C₇×C₇₁	D₃	1	1	yes	characteristic, complemented
12	C₃×C₇×D₇₁	—	3	1	no	—
13	C₂×C₃×C₇×C₇₁	—	3	1	no	—
14	D₃×D₂₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₇×D₇₁	—	9	1	no	Hall
16	C₃×C₇×C₇₁	—	2	1	no	—
17	C₃×C₇×C₇₁	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₇×C₇₁	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊D₂₁₃	C₂×C₇	1	1	yes	characteristic, complemented
20	C₃×D₂₁₃	C₂×C₇	1	1	yes	characteristic, complemented
21	C₃×D₃×C₇₁	C₂×C₇	1	1	yes	characteristic, complemented
22	C₂×C₇×C₇₁	—	3	1	no	—
23	C₇×D₇₁	—	3	1	no	—
24	C₇×D₇₁	—	9	1	no	—
25	C₂×D₂₁₃	—	3	1	no	—
26	D₃×D₇₁	—	3	1	no	—
27	C₃²×C₇₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₇₁	D₃²	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇₁	—	3	1	no	—
30	D₂₁₃	—	3	1	no	—
31	D₂₁₃	—	3	1	no	—
32	D₂₁₃	—	6	1	no	—
33	D₂₁₃	D₃×C₇	1	1	yes	characteristic, direct product factor
34	C₃×D₇₁	—	3	1	no	—
35	D₃×C₇₁	D₃×C₇	1	1	yes	characteristic, complemented
36	C₂×D₇₁	—	9	1	no	Hall
37	D₃²×C₇	—	71	1	no	maximal, Hall
38	C₃×C₇₁	—	2	1	no	—
39	C₃×C₇₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented
40	C₃×C₇₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented
41	C₂×C₇₁	—	3	1	no	—
42	D₇₁	—	3	1	no	—
43	D₇₁	—	9	1	no	—
44	C₇×C₃⋊D₃	—	71	1	no	—
45	C₃×D₃×C₇	—	71	1	no	—
46	C₃×D₃×C₇	D₇₁	1	1	yes	characteristic, complemented
47	C₂×D₃×C₇	—	213	1	no	—
48	C₂×D₃×C₇	—	213	1	no	—
49	C₇₁	D₃²×C₇	1	1	yes	characteristic, complemented, Sylow
50	C₃²×C₇	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₇	—	3	1	no	—
52	C₂×C₃×C₇	—	213	1	no	—
53	D₃×C₇	—	71	1	no	—
54	D₃×C₇	—	426	1	no	—
55	D₃×C₇	—	213	1	no	—
56	D₃×C₇	—	213	1	no	—
57	D₃×C₇	D₂₁₃	1	1	yes	characteristic, direct product factor
58	D₃²	—	71	1	no	Hall
59	C₂²×C₇	—	639	1	no	Hall
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	D₃×D₇₁	1	1	yes	characteristic, complemented
62	C₃×C₇	C₂×D₂₁₃	1	1	yes	characteristic, complemented
63	C₃⋊D₃	—	71	1	no	—
64	C₃×D₃	—	71	1	no	—
65	C₃×D₃	C₇×D₇₁	1	1	yes	characteristic, complemented
66	C₂×C₇	—	3	1	no	—
67	C₂×C₇	—	639	1	no	—
68	C₂×C₇	—	213	1	no	—
69	C₂×D₃	—	213	1	no	—
70	C₂×D₃	—	213	1	no	—
71	C₃²	C₂×C₇×D₇₁	1	1	yes	characteristic, complemented, Sylow
72	C₇	D₃×D₂₁₃	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	213	1	no	—
75	D₃	—	71	1	no	—
76	D₃	—	426	1	no	—
77	D₃	—	213	1	no	—
78	D₃	—	213	1	no	—
79	D₃	C₇×D₂₁₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	639	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₇×D₇₁	1	1	yes	characteristic, complemented
83	C₃	C₂×C₇×D₂₁₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	639	1	no	—
86	C₂	—	213	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₃×D₂₁₃
commutator, cosocle, hypocenter	C₃²×C₇₁	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₇₁	C₂²
LCS	G ▷ C₃²×C₇₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃⋊D₂₁₃	C₂	semidirect
2. C₃×C₇×D₂₁₃	C₂	semidirect
3. C₃×D₃×C₇×C₇₁	C₂	semidirect
6. C₃²×C₇×C₇₁	C₂²	semidirect
10. C₇×D₂₁₃	D₃	direct (N × H)
11. D₃×C₇×C₇₁	D₃	semidirect
14. D₃×D₂₁₃	C₇	direct (N × H)
17. C₃×C₇×C₇₁	C₂×D₃	semidirect
18. C₃×C₇×C₇₁	C₂×D₃	semidirect
19. C₃⋊D₂₁₃	C₂×C₇	semidirect
20. C₃×D₂₁₃	C₂×C₇	semidirect
21. C₃×D₃×C₇₁	C₂×C₇	semidirect
27. C₃²×C₇₁	C₂²×C₇	semidirect
28. C₇×C₇₁	D₃²	semidirect
33. D₂₁₃	D₃×C₇	direct (N × H)
35. D₃×C₇₁	D₃×C₇	semidirect
39. C₃×C₇₁	C₂×D₃×C₇	semidirect
40. C₃×C₇₁	C₂×D₃×C₇	semidirect
46. C₃×D₃×C₇	D₇₁	semidirect
49. C₇₁	D₃²×C₇	semidirect
50. C₃²×C₇	C₂×D₇₁	semidirect
57. D₃×C₇	D₂₁₃	direct (N × H)
61. C₃×C₇	D₃×D₇₁	semidirect
62. C₃×C₇	C₂×D₂₁₃	semidirect
65. C₃×D₃	C₇×D₇₁	semidirect
71. C₃²	C₂×C₇×D₇₁	semidirect
72. C₇	D₃×D₂₁₃	direct (N × H)
79. D₃	C₇×D₂₁₃	direct (N × H)
82. C₃	D₃×C₇×D₇₁	semidirect
83. C₃	C₂×C₇×D₂₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₃⋊D₂₁₃	2
C₃×C₇×D₂₁₃	2
C₃×D₃×C₇×C₇₁	2
C₂×C₇×D₂₁₃	3
D₃×C₇×D₇₁	3
D₃×D₂₁₃	7
D₃²×C₇	71

Subgroups — D3×C7×D213 #31822098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×D₂₁₃ #31822098