Subgroups — D₇×C₁₁⋊(D₁₉⋊C₃) #31798260

Order 17556.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊((C₁₉⋊C₃)⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₂₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×C₁₁×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₄₆₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁×D₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₂₀₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₁₁⋊(D₁₉⋊C₃)	—	7	1	no	maximal, Hall
10	D₇×D₁₉⋊C₃	—	11	1	no	maximal, Hall
11	C₇×C₁₁×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₉⋊C₃	—	7	1	no	—
13	C₁₁⋊(D₁₉⋊C₃)	—	7	1	no	—
14	C₁₁⋊(D₁₉⋊C₃)	D₇	1	1	yes	characteristic, direct product factor
15	C₃×D₇×D₁₁	—	19	1	no	maximal, Hall
16	C₂×D₂₀₉	—	7	1	no	Hall
17	(C₁₉⋊C₃)⋊D₇	—	11	1	no	—
18	D₇×C₁₉⋊C₃	D₁₁	1	1	yes	characteristic, complemented
19	C₇×D₁₉⋊C₃	—	11	1	no	—
20	C₁₁×C₁₉⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	D₇×D₁₉	—	11	1	no	Hall
22	C₃×D₇₇	—	19	1	no	—
23	C₃×C₁₁×D₇	—	38	1	no	—
24	C₃×C₇×D₁₁	—	19	1	no	—
25	C₂×C₁₁×C₁₉	—	7	1	no	—
26	D₂₀₉	—	7	1	no	—
27	D₂₀₉	C₃×D₇	1	1	yes	characteristic, complemented
28	C₇×C₁₉⋊C₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	D₇×D₁₁	—	19	1	no	Hall
30	D₁₃₃	—	11	1	no	—
31	C₇×D₁₉	—	11	1	no	—
32	D₇×C₁₉	C₃×D₁₁	1	1	yes	characteristic, complemented
33	C₃×C₇×C₁₁	—	38	1	no	Hall
34	C₂×D₁₉⋊C₃	—	77	1	no	Hall
35	C₁₁×C₁₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
36	D₇₇	—	19	1	no	—
37	C₇×D₁₁	—	19	1	no	—
38	C₁₁×D₇	D₁₉⋊C₃	1	1	yes	characteristic, complemented
39	C₇×C₁₉	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×D₁₁	—	133	1	no	Hall
41	C₂×C₁₉⋊C₃	—	7	1	no	—
42	D₁₉⋊C₃	—	11	1	no	—
43	D₁₉⋊C₃	—	77	1	no	—
44	C₂×C₃×D₇	—	209	1	no	Hall
45	C₇×C₁₁	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
46	C₂×D₁₉	—	77	1	no	Hall
47	C₂×C₃×C₁₁	—	266	1	no	—
48	C₃×D₁₁	—	19	1	no	—
49	C₃×D₁₁	—	133	1	no	—
50	C₁₉⋊C₃	D₇×D₁₁	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₁	—	133	1	no	Hall
52	C₂×C₃×C₇	—	209	1	no	—
53	C₃×D₇	—	38	1	no	—
54	C₃×D₇	—	209	1	no	—
55	C₂×C₁₉	—	7	1	no	—
56	D₁₉	—	11	1	no	—
57	D₁₉	—	77	1	no	—
58	C₃×C₁₁	—	38	1	no	Hall
59	C₂×D₇	—	209	1	no	Hall
60	C₂×C₁₁	—	7	1	no	—
61	D₁₁	—	19	1	no	—
62	D₁₁	—	133	1	no	—
63	C₃×C₇	—	38	1	no	Hall
64	C₁₉	C₃×D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₇	—	209	1	no	—
66	D₇	—	209	1	no	—
67	D₇	C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
68	C₂²×C₃	—	1463	1	no	Hall
69	C₁₁	D₇×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
70	C₇	C₂×C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	266	1	no	—
72	C₂×C₃	—	1463	1	no	—
73	C₂×C₃	—	209	1	no	—
74	C₂²	—	1463	1	no	Sylow
75	C₃	—	38	1	no	Sylow
76	C₂	—	7	1	no	—
77	C₂	—	1463	1	no	—
78	C₂	—	209	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₁₉	C₂²×C₃
LCS	G ▷ C₇×C₁₁×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊((C₁₉⋊C₃)⋊D₇)	C₂	semidirect
2. C₁₁×D₇×C₁₉⋊C₃	C₂	semidirect
3. C₇×C₁₁⋊(D₁₉⋊C₃)	C₂	semidirect
4. D₇×D₂₀₉	C₃	semidirect
5. C₇×C₁₁×C₁₉⋊C₃	C₂²	semidirect
6. D₁₄₆₃	C₂×C₃	semidirect
7. C₁₁×D₇×C₁₉	C₂×C₃	semidirect
8. C₇×D₂₀₉	C₂×C₃	semidirect
11. C₇×C₁₁×C₁₉	C₂²×C₃	semidirect
14. C₁₁⋊(D₁₉⋊C₃)	D₇	direct (N × H)
18. D₇×C₁₉⋊C₃	D₁₁	semidirect
20. C₁₁×C₁₉⋊C₃	C₂×D₇	semidirect
27. D₂₀₉	C₃×D₇	semidirect
28. C₇×C₁₉⋊C₃	C₂×D₁₁	semidirect
32. D₇×C₁₉	C₃×D₁₁	semidirect
35. C₁₁×C₁₉	C₂×C₃×D₇	semidirect
38. C₁₁×D₇	D₁₉⋊C₃	semidirect
39. C₇×C₁₉	C₂×C₃×D₁₁	semidirect
45. C₇×C₁₁	C₂×D₁₉⋊C₃	semidirect
50. C₁₉⋊C₃	D₇×D₁₁	semidirect
64. C₁₉	C₃×D₇×D₁₁	semidirect
67. D₇	C₁₁⋊(D₁₉⋊C₃)	direct (N × H)
69. C₁₁	D₇×D₁₉⋊C₃	semidirect
70. C₇	C₂×C₁₁⋊(D₁₉⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₁₁⋊((C₁₉⋊C₃)⋊D₇)	2
C₁₁×D₇×C₁₉⋊C₃	2
C₇×C₁₁⋊(D₁₉⋊C₃)	2
D₇×D₂₀₉	3
C₂×C₁₁⋊(D₁₉⋊C₃)	7
D₇×D₁₉⋊C₃	11
C₃×D₇×D₁₁	19

Subgroups — D7×C11⋊(D19⋊C3) #31798260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₁₁⋊(D₁₉⋊C₃) #31798260