Subgroups — C₂×C₇⋊D₈₁₉ #37524613

Order 22932.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊D₈₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₉×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊(C₇⋊D₉₁)	—	3	1	no	maximal
4	C₇²×C₉×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃⋊(C₇⋊D₉₁)	—	3	2	no	—
6	C₂×C₃×C₇²×C₁₃	D₃	1	1	yes	characteristic
7	C₂×D₈₁₉	—	7	8	no	maximal
8	C₂×C₇⋊D₉₁	—	9	1	no	Hall
9	C₃×C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic
10	C₂×C₇⋊D₆₃	—	13	1	no	maximal, Hall
11	C₂×C₇×C₉×C₁₃	D₇	1	8	yes	complemented
12	D₈₁₉	—	7	16	no	—
13	C₂×C₇²×C₁₃	D₉	1	1	yes	characteristic, complemented
14	C₇⋊D₉₁	—	9	2	no	—
15	C₂×D₂₇₃	—	21	8	no	—
16	C₂×C₇²×C₉	D₁₃	1	1	yes	characteristic, complemented
17	C₇⋊D₆₃	—	13	2	no	—
18	C₇×C₉×C₁₃	C₂×D₇	1	8	yes	complemented
19	C₇²×C₁₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃⋊(C₇⋊D₇)	—	39	1	no	—
21	C₂×C₃×C₇×C₁₃	D₂₁	1	8	yes	—
22	D₂₇₃	—	21	16	no	—
23	C₂×D₁₁₇	—	49	1	no	Hall
24	C₇²×C₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₉₁	—	63	8	no	—
26	C₂×C₃×C₇²	D₃₉	1	1	yes	characteristic
27	C₃⋊(C₇⋊D₇)	—	39	2	no	—
28	C₃×C₇×C₁₃	C₂×D₂₁	1	8	yes	—
29	C₂×D₆₃	—	91	8	no	—
30	C₂×C₉×C₁₃	C₇⋊D₇	1	1	yes	characteristic, complemented
31	D₁₁₇	—	49	2	no	—
32	C₂×C₇⋊D₇	—	117	1	no	Hall
33	C₂×C₇×C₁₃	D₆₃	1	8	yes	complemented
34	D₉₁	—	63	16	no	—
35	C₂×D₃₉	—	147	1	no	—
36	C₃×C₇²	C₂×D₃₉	1	1	yes	characteristic
37	C₂×C₇×C₉	D₉₁	1	8	yes	complemented
38	D₆₃	—	91	16	no	—
39	C₉×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
40	C₂×C₇²	D₁₁₇	1	1	yes	characteristic, complemented
41	C₇⋊D₇	—	117	2	no	—
42	C₇×C₁₃	C₂×D₆₃	1	8	yes	complemented
43	C₂×D₂₁	—	273	8	no	—
44	C₂×C₃×C₁₃	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
45	D₃₉	—	147	2	no	—
46	C₇×C₉	C₂×D₉₁	1	8	yes	complemented
47	C₂×D₁₃	—	441	1	no	Hall
48	C₇²	C₂×D₁₁₇	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₇	D₂₇₃	1	8	yes	—
50	D₂₁	—	273	16	no	—
51	C₃×C₁₃	C₂×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
52	C₂×D₉	—	637	1	no	Hall
53	C₂×D₇	—	819	8	no	—
54	C₂×C₁₃	C₇⋊D₆₃	1	1	yes	characteristic, complemented
55	D₁₃	—	441	2	no	—
56	C₃×C₇	C₂×D₂₇₃	1	8	yes	—
57	C₂×C₉	C₇⋊D₉₁	1	1	yes	characteristic, complemented
58	D₉	—	637	2	no	—
59	C₂×C₇	D₈₁₉	1	8	yes	complemented
60	D₇	—	819	16	no	—
61	C₁₃	C₂×C₇⋊D₆₃	1	1	yes	characteristic, complemented, Sylow
62	C₂×D₃	—	1911	1	no	—
63	C₉	C₂×C₇⋊D₉₁	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₂×D₈₁₉	1	8	yes	complemented
65	C₂×C₃	C₃⋊(C₇⋊D₉₁)	1	1	yes	characteristic
66	D₃	—	1911	2	no	—
67	C₂²	—	5733	1	no	Sylow
68	C₃	C₂×C₃⋊(C₇⋊D₉₁)	1	1	yes	characteristic
69	C₂	—	5733	2	no	—
70	C₂	C₇⋊D₈₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₇⋊D₈₁₉
commutator, cosocle, hypocenter	C₇²×C₉×C₁₃	C₂²
Frattini	C₃	C₂×C₃⋊(C₇⋊D₉₁)
Fitting	C₂×C₇²×C₉×C₁₃	C₂
socle	C₂×C₃×C₇²×C₁₃	D₃
LCS	G ▷ C₇²×C₉×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₇⋊D₈₁₉	C₂	direct (N × H)
2. C₂×C₇²×C₉×C₁₃	C₂	semidirect
4. C₇²×C₉×C₁₃	C₂²	semidirect
11. C₂×C₇×C₉×C₁₃	D₇	semidirect
13. C₂×C₇²×C₁₃	D₉	semidirect
16. C₂×C₇²×C₉	D₁₃	semidirect
18. C₇×C₉×C₁₃	C₂×D₇	semidirect
19. C₇²×C₁₃	C₂×D₉	semidirect
24. C₇²×C₉	C₂×D₁₃	semidirect
30. C₂×C₉×C₁₃	C₇⋊D₇	semidirect
33. C₂×C₇×C₁₃	D₆₃	semidirect
37. C₂×C₇×C₉	D₉₁	semidirect
39. C₉×C₁₃	C₂×C₇⋊D₇	semidirect
40. C₂×C₇²	D₁₁₇	semidirect
42. C₇×C₁₃	C₂×D₆₃	semidirect
46. C₇×C₉	C₂×D₉₁	semidirect
48. C₇²	C₂×D₁₁₇	semidirect
54. C₂×C₁₃	C₇⋊D₆₃	semidirect
57. C₂×C₉	C₇⋊D₉₁	semidirect
59. C₂×C₇	D₈₁₉	semidirect
61. C₁₃	C₂×C₇⋊D₆₃	semidirect
63. C₉	C₂×C₇⋊D₉₁	semidirect
64. C₇	C₂×D₈₁₉	semidirect
70. C₂	C₇⋊D₈₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇⋊D₈₁₉	2
C₂×C₇²×C₉×C₁₃	2
C₂×C₃⋊(C₇⋊D₉₁)	3
C₂×D₈₁₉	7
C₂×C₇⋊D₆₃	13

Subgroups — C2×C7⋊D819 #37524613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊D₈₁₉ #37524613