Subgroups — D₇×D₁₂₀₉ #46799593

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₄₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₁₂₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₄₀₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₈₂₁	—	3	1	no	—
7	C₁₃×D₇×C₃₁	D₃	1	1	yes	characteristic, complemented
8	C₇×D₄₀₃	—	3	1	no	—
9	C₂×D₁₂₀₉	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₇×D₉₃	—	13	1	no	maximal, Hall
12	D₁₂₀₉	—	7	1	no	—
13	D₁₂₀₉	D₇	1	1	yes	characteristic, direct product factor
14	C₂×C₃×C₁₃×C₃₁	—	7	1	no	—
15	C₂×D₄₀₃	—	21	1	no	Hall
16	D₆₅₁	—	13	1	no	—
17	C₇×D₉₃	—	13	1	no	—
18	C₃×D₇×C₃₁	D₁₃	1	1	yes	characteristic, complemented
19	C₃×C₁₃×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₇×D₃₉	—	31	1	no	maximal, Hall
21	D₇×D₃₁	—	39	1	no	Hall
22	C₂×C₁₃×C₃₁	—	7	1	no	—
23	D₄₀₃	—	3	1	no	—
24	D₄₀₃	—	21	1	no	—
25	C₃×C₇×C₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	D₂₇₃	—	31	1	no	—
27	C₇×D₃₉	—	31	1	no	—
28	C₃×C₁₃×D₇	D₃₁	1	1	yes	characteristic, complemented
29	D₂₁₇	—	39	1	no	—
30	C₇×D₃₁	—	39	1	no	—
31	D₇×C₃₁	D₃₉	1	1	yes	characteristic, complemented
32	C₁₃×C₃₁	D₃×D₇	1	1	yes	characteristic, complemented, Hall
33	C₂×D₉₃	—	91	1	no	Hall
34	D₇×D₁₃	—	93	1	no	Hall
35	C₃×C₇×C₁₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
36	C₇×C₃₁	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₃₁	—	7	1	no	—
38	D₉₃	—	13	1	no	—
39	D₉₃	—	91	1	no	—
40	D₉₁	—	93	1	no	—
41	C₇×D₁₃	—	93	1	no	—
42	C₁₃×D₇	D₉₃	1	1	yes	characteristic, complemented
43	C₂×D₃₉	—	217	1	no	Hall
44	C₂×D₃₁	—	273	1	no	Hall
45	C₃×C₃₁	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
46	C₇×C₁₃	C₂×D₉₃	1	1	yes	characteristic, complemented, Hall
47	D₃×D₇	—	403	1	no	Hall
48	C₂×C₃×C₁₃	—	7	1	no	—
49	D₃₉	—	31	1	no	—
50	D₃₉	—	217	1	no	—
51	C₂×C₃₁	—	7	1	no	—
52	D₃₁	—	273	1	no	—
53	D₃₁	—	39	1	no	—
54	C₂×D₁₃	—	651	1	no	Hall
55	D₂₁	—	403	1	no	—
56	C₃×D₇	D₄₀₃	1	1	yes	characteristic, complemented
57	D₃×C₇	—	403	1	no	—
58	C₃×C₁₃	D₇×D₃₁	1	1	yes	characteristic, complemented, Hall
59	C₃₁	D₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₇	—	1209	1	no	Hall
61	C₂×C₁₃	—	7	1	no	—
62	D₁₃	—	93	1	no	—
63	D₁₃	—	651	1	no	—
64	C₃×C₇	C₂×D₄₀₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	1209	1	no	—
66	D₇	—	1209	1	no	—
67	D₇	D₁₂₀₉	1	1	yes	characteristic, direct product factor
68	C₁₃	D₇×D₉₃	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	2821	1	no	Hall
70	C₇	C₂×D₁₂₀₉	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	7	1	no	—
72	D₃	—	2821	1	no	—
73	D₃	—	403	1	no	—
74	C₂²	—	8463	1	no	Sylow
75	C₃	D₇×D₄₀₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	7	1	no	—
77	C₂	—	8463	1	no	—
78	C₂	—	1209	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃×C₃₁	C₂²
LCS	G ▷ C₃×C₇×C₁₃×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₄₆₃	C₂	semidirect
2. C₇×D₁₂₀₉	C₂	semidirect
3. C₃×C₁₃×D₇×C₃₁	C₂	semidirect
5. C₃×C₇×C₁₃×C₃₁	C₂²	semidirect
7. C₁₃×D₇×C₃₁	D₃	semidirect
10. C₇×C₁₃×C₃₁	C₂×D₃	semidirect
13. D₁₂₀₉	D₇	direct (N × H)
18. C₃×D₇×C₃₁	D₁₃	semidirect
19. C₃×C₁₃×C₃₁	C₂×D₇	semidirect
25. C₃×C₇×C₃₁	C₂×D₁₃	semidirect
28. C₃×C₁₃×D₇	D₃₁	semidirect
31. D₇×C₃₁	D₃₉	semidirect
32. C₁₃×C₃₁	D₃×D₇	semidirect
35. C₃×C₇×C₁₃	C₂×D₃₁	semidirect
36. C₇×C₃₁	C₂×D₃₉	semidirect
42. C₁₃×D₇	D₉₃	semidirect
45. C₃×C₃₁	D₇×D₁₃	semidirect
46. C₇×C₁₃	C₂×D₉₃	semidirect
56. C₃×D₇	D₄₀₃	semidirect
58. C₃×C₁₃	D₇×D₃₁	semidirect
59. C₃₁	D₇×D₃₉	semidirect
64. C₃×C₇	C₂×D₄₀₃	semidirect
67. D₇	D₁₂₀₉	direct (N × H)
68. C₁₃	D₇×D₉₃	semidirect
70. C₇	C₂×D₁₂₀₉	semidirect
75. C₃	D₇×D₄₀₃	semidirect

Maximal subgroups

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

subgroup	index
D₈₄₆₃	2
C₇×D₁₂₀₉	2
C₃×C₁₃×D₇×C₃₁	2
D₇×D₄₀₃	3
C₂×D₁₂₀₉	7
D₇×D₉₃	13
D₇×D₃₉	31

Subgroups — D7×D1209 #46799593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₁₂₀₉ #46799593