Subgroups — D₇×D₈₉₇ #38737435

Order 25116.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₂₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₈₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₂₉₉	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₉₃	—	3	1	no	—
7	C₁₃×D₇×C₂₃	D₃	1	1	yes	characteristic, complemented
8	C₇×D₂₉₉	—	3	1	no	—
9	C₂×D₈₉₇	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₇×D₆₉	—	13	1	no	maximal, Hall
12	C₂×C₃×C₁₃×C₂₃	—	7	1	no	—
13	D₈₉₇	—	7	1	no	—
14	D₈₉₇	D₇	1	1	yes	characteristic, direct product factor
15	C₂×D₂₉₉	—	21	1	no	Hall
16	D₇×D₃₉	—	23	1	no	maximal, Hall
17	D₄₈₃	—	13	1	no	—
18	C₇×D₆₉	—	13	1	no	—
19	C₃×D₇×C₂₃	D₁₃	1	1	yes	characteristic, complemented
20	C₃×C₁₃×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	D₇×D₂₃	—	39	1	no	Hall
22	C₂×C₁₃×C₂₃	—	7	1	no	—
23	D₂₉₉	—	3	1	no	—
24	D₂₉₉	—	21	1	no	—
25	D₂₇₃	—	23	1	no	—
26	C₇×D₃₉	—	23	1	no	—
27	C₃×C₁₃×D₇	D₂₃	1	1	yes	characteristic, complemented
28	C₃×C₇×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₇×D₁₃	—	69	1	no	Hall
30	D₁₆₁	—	39	1	no	—
31	C₇×D₂₃	—	39	1	no	—
32	D₇×C₂₃	D₃₉	1	1	yes	characteristic, complemented
33	C₁₃×C₂₃	D₃×D₇	1	1	yes	characteristic, complemented, Hall
34	C₂×D₆₉	—	91	1	no	Hall
35	C₃×C₇×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
36	D₉₁	—	69	1	no	—
37	C₇×D₁₃	—	69	1	no	—
38	C₁₃×D₇	D₆₉	1	1	yes	characteristic, complemented
39	C₇×C₂₃	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃₉	—	161	1	no	Hall
41	C₂×C₃×C₂₃	—	7	1	no	—
42	D₆₉	—	13	1	no	—
43	D₆₉	—	91	1	no	—
44	C₂×D₂₃	—	273	1	no	Hall
45	C₇×C₁₃	C₂×D₆₉	1	1	yes	characteristic, complemented, Hall
46	D₃×D₇	—	299	1	no	Hall
47	C₂×C₃×C₁₃	—	7	1	no	—
48	D₃₉	—	23	1	no	—
49	D₃₉	—	161	1	no	—
50	C₃×C₂₃	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	483	1	no	Hall
52	C₂×C₂₃	—	7	1	no	—
53	D₂₃	—	273	1	no	—
54	D₂₃	—	39	1	no	—
55	D₂₁	—	299	1	no	—
56	C₃×D₇	D₂₉₉	1	1	yes	characteristic, complemented
57	D₃×C₇	—	299	1	no	—
58	C₃×C₁₃	D₇×D₂₃	1	1	yes	characteristic, complemented, Hall
59	C₂×D₇	—	897	1	no	Hall
60	C₂×C₁₃	—	7	1	no	—
61	D₁₃	—	69	1	no	—
62	D₁₃	—	483	1	no	—
63	C₂₃	D₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	C₂×D₂₉₉	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	897	1	no	—
66	D₇	—	897	1	no	—
67	D₇	D₈₉₇	1	1	yes	characteristic, direct product factor
68	C₁₃	D₇×D₆₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	2093	1	no	Hall
70	C₇	C₂×D₈₉₇	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	7	1	no	—
72	D₃	—	299	1	no	—
73	D₃	—	2093	1	no	—
74	C₂²	—	6279	1	no	Sylow
75	C₃	D₇×D₂₉₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	7	1	no	—
77	C₂	—	897	1	no	—
78	C₂	—	6279	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃×C₇×C₁₃×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₂₇₉	C₂	semidirect
2. C₇×D₈₉₇	C₂	semidirect
3. C₃×C₁₃×D₇×C₂₃	C₂	semidirect
5. C₃×C₇×C₁₃×C₂₃	C₂²	semidirect
7. C₁₃×D₇×C₂₃	D₃	semidirect
10. C₇×C₁₃×C₂₃	C₂×D₃	semidirect
14. D₈₉₇	D₇	direct (N × H)
19. C₃×D₇×C₂₃	D₁₃	semidirect
20. C₃×C₁₃×C₂₃	C₂×D₇	semidirect
27. C₃×C₁₃×D₇	D₂₃	semidirect
28. C₃×C₇×C₂₃	C₂×D₁₃	semidirect
32. D₇×C₂₃	D₃₉	semidirect
33. C₁₃×C₂₃	D₃×D₇	semidirect
35. C₃×C₇×C₁₃	C₂×D₂₃	semidirect
38. C₁₃×D₇	D₆₉	semidirect
39. C₇×C₂₃	C₂×D₃₉	semidirect
45. C₇×C₁₃	C₂×D₆₉	semidirect
50. C₃×C₂₃	D₇×D₁₃	semidirect
56. C₃×D₇	D₂₉₉	semidirect
58. C₃×C₁₃	D₇×D₂₃	semidirect
63. C₂₃	D₇×D₃₉	semidirect
64. C₃×C₇	C₂×D₂₉₉	semidirect
67. D₇	D₈₉₇	direct (N × H)
68. C₁₃	D₇×D₆₉	semidirect
70. C₇	C₂×D₈₉₇	semidirect
75. C₃	D₇×D₂₉₉	semidirect

Maximal subgroups

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

subgroup	index
D₆₂₇₉	2
C₇×D₈₉₇	2
C₃×C₁₃×D₇×C₂₃	2
D₇×D₂₉₉	3
C₂×D₈₉₇	7
D₇×D₆₉	13
D₇×D₃₉	23

Subgroups — D7×D897 #38737435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₈₉₇ #38737435