Subgroups — (C₇⋊C₉)⋊Dic₁₃₃ #45691502

Order 33516.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₉×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇⋊Dic₁₃₃	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₉×C₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₉×Dic₁₃₃	—	7	1	no	maximal
6	(C₇⋊C₉)⋊Dic₁₉	—	7	1	no	maximal
7	C₇⋊Dic₁₃₃	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
9	C₂×C₁₉×C₇⋊C₉	D₇	1	1	yes	characteristic
10	C₂×C₇×C₉×C₁₉	—	7	1	no	—
11	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
12	(C₇⋊C₉)⋊Dic₇	—	19	1	no	maximal, Hall
13	C₃×Dic₁₃₃	—	7	1	no	—
14	C₃×Dic₁₃₃	—	7	1	no	—
15	C₃×Dic₁₃₃	—	21	2	no	—
16	C₇×C₉×C₁₉	—	7	1	no	—
17	C₁₉×C₇⋊C₉	Dic₇	1	1	yes	characteristic, complemented
18	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₇⋊C₉	D₁₉	1	1	yes	characteristic
20	C₂×C₃×C₇×C₁₉	—	3	2	no	—
21	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
22	C₂×C₃×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic
23	C₉×Dic₁₉	—	49	1	no	Hall
24	C₃×C₇⋊Dic₇	—	19	1	no	—
25	Dic₁₃₃	—	7	1	no	—
26	Dic₁₃₃	—	7	1	no	—
27	Dic₁₃₃	—	21	2	no	—
28	C₇×C₇⋊C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃×C₇×C₁₉	—	3	2	no	—
30	C₃×C₇×C₁₉	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
31	C₃×C₇×C₁₉	C₃×Dic₇	1	1	yes	characteristic
32	C₂×C₉×C₁₉	—	7	1	no	—
33	C₂×C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic
34	C₂×C₇×C₁₉	—	3	2	no	—
35	C₂×C₇×C₁₉	D₇⋊C₉	1	1	yes	characteristic
36	C₂×C₇×C₁₉	C₉×D₇	1	1	yes	characteristic
37	C₉×Dic₇	—	133	1	no	—
38	Dic₇⋊C₉	—	133	1	no	—
39	C₃×Dic₁₉	—	49	1	no	—
40	C₇⋊Dic₇	—	19	1	no	Hall
41	C₉×C₁₉	—	7	1	no	Hall
42	C₃×C₇²	C₃×Dic₁₉	1	1	yes	characteristic
43	C₇×C₁₉	—	3	2	no	—
44	C₇×C₁₉	Dic₇⋊C₉	1	1	yes	characteristic, complemented
45	C₇×C₁₉	C₉×Dic₇	1	1	yes	characteristic, complemented
46	C₂×C₇×C₉	—	7	1	no	—
47	C₂×C₇⋊C₉	D₁₃₃	1	1	yes	characteristic
48	C₂×C₃×C₁₉	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic
49	C₂×C₇²	C₉×D₁₉	1	1	yes	characteristic
50	C₃×Dic₇	—	133	1	no	—
51	C₃×Dic₇	—	133	1	no	—
52	C₃×Dic₇	—	399	2	no	—
53	Dic₁₉	—	49	1	no	Hall
54	C₇×C₉	—	7	1	no	—
55	C₇⋊C₉	Dic₁₃₃	1	1	yes	characteristic, complemented
56	C₃×C₁₉	ΓL(1,𝔽₈)⋊Dic₇	1	1	yes	characteristic
57	C₇²	C₉×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃×C₇	—	3	2	no	—
59	C₂×C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic
60	C₂×C₃×C₇	C₃×D₁₃₃	1	1	yes	characteristic
61	C₂×C₁₉	(C₇⋊C₉)⋊D₇	1	1	yes	characteristic
62	C₄×C₉	—	931	1	no	Hall
63	Dic₇	—	133	1	no	—
64	Dic₇	—	133	1	no	—
65	Dic₇	—	399	2	no	—
66	C₃×C₇	—	3	2	no	—
67	C₃×C₇	ΓL(1,𝔽₈)⋊Dic₁₉	1	1	yes	characteristic
68	C₃×C₇	C₃×Dic₁₃₃	1	1	yes	characteristic
69	C₁₉	(C₇⋊C₉)⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₉	—	7	1	no	—
71	C₂×C₇	—	3	2	no	—
72	C₂×C₇	(C₇⋊C₉)⋊D₁₉	1	1	yes	characteristic
73	C₂×C₇	C₉×D₁₃₃	1	1	yes	characteristic
74	C₃×C₄	—	931	1	no	—
75	C₉	—	7	1	no	Sylow
76	C₇	—	3	2	no	—
77	C₇	(C₇⋊C₉)⋊Dic₁₉	1	1	yes	characteristic, complemented
78	C₇	C₉×Dic₁₃₃	1	1	yes	characteristic, complemented
79	C₂×C₃	ΓL(1,𝔽₈)⋊D₁₃₃	1	1	yes	characteristic
80	C₄	—	931	1	no	Sylow
81	C₃	ΓL(1,𝔽₈)⋊Dic₁₃₃	1	1	yes	characteristic
82	C₂	(C₇⋊C₉)⋊D₁₃₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₁₃₃
commutator, hypocenter	C₇²×C₁₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₉×C₇⋊C₉	C₄	semidirect
7. C₇⋊Dic₁₃₃	C₉	semidirect
17. C₁₉×C₇⋊C₉	Dic₇	semidirect
18. C₇²×C₁₉	C₄×C₉	semidirect
28. C₇×C₇⋊C₉	Dic₁₉	semidirect
44. C₇×C₁₉	Dic₇⋊C₉	semidirect
45. C₇×C₁₉	C₉×Dic₇	semidirect
55. C₇⋊C₉	Dic₁₃₃	semidirect
57. C₇²	C₉×Dic₁₉	semidirect
69. C₁₉	(C₇⋊C₉)⋊Dic₇	semidirect
77. C₇	(C₇⋊C₉)⋊Dic₁₉	semidirect
78. C₇	C₉×Dic₁₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×C₁₉×C₇⋊C₉	2
C₃×C₇⋊Dic₁₃₃	3
C₉×Dic₁₃₃	7
(C₇⋊C₉)⋊Dic₁₉	7
(C₇⋊C₉)⋊Dic₇	19

Subgroups — (C7⋊C9)⋊Dic133 #45691502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₇⋊C₉)⋊Dic₁₃₃ #45691502