Subgroups — C₃×C₃⋊(C₇⋊Dic₁₃₃) #45691965

Order 33516.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊Dic₁₃₃)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇⋊Dic₁₃₃	—	3	1	no	maximal
4	C₃²×C₇²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇²×C₁₉	—	2	1	no	—
6	C₂×C₃×C₇²×C₁₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₃×Dic₃₉₉	—	7	8	no	maximal
9	C₇⋊Dic₁₃₃	—	3	1	no	Hall
10	C₃×C₇²×C₁₉	—	2	1	no	—
11	C₃×C₇²×C₁₉	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₃²×C₇×C₁₉	D₇	1	8	yes	—
14	C₂×C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic
15	C₃×C₃⋊(C₇⋊Dic₇)	—	19	1	no	maximal, Hall
16	Dic₃₉₉	—	7	8	no	—
17	C₃×Dic₁₃₃	—	21	8	no	—
18	C₃²×C₇×C₁₉	Dic₇	1	8	yes	complemented
19	C₇²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃²×C₇²	D₁₉	1	1	yes	characteristic
21	C₂×C₃×C₇×C₁₉	—	2	8	no	—
22	C₂×C₃×C₇×C₁₉	C₃×D₇	1	8	yes	—
23	C₂×C₃×C₇×C₁₉	D₂₁	1	8	yes	—
24	C₃×Dic₅₇	—	49	1	no	Hall
25	C₃⋊(C₇⋊Dic₇)	—	19	1	no	—
26	C₃×C₇⋊Dic₇	—	57	1	no	—
27	Dic₁₃₃	—	21	8	no	—
28	C₃²×C₇²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃×C₇×C₁₉	—	2	8	no	—
30	C₃×C₇×C₁₉	C₃×Dic₇	1	8	yes	complemented
31	C₃×C₇×C₁₉	Dic₂₁	1	8	yes	complemented
32	C₂×C₃²×C₁₉	C₇⋊D₇	1	1	yes	characteristic
33	C₂×C₃×C₇²	—	2	1	no	—
34	C₂×C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic
35	C₂×C₃×C₇²	D₅₇	1	1	yes	characteristic
36	C₂×C₇×C₁₉	C₃×D₂₁	1	8	yes	—
37	C₃×Dic₂₁	—	133	8	no	—
38	Dic₅₇	—	49	1	no	—
39	C₃×Dic₁₉	—	147	1	no	—
40	C₇⋊Dic₇	—	57	1	no	Hall
41	C₃²×C₁₉	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
42	C₃×C₇²	—	2	1	no	—
43	C₃×C₇²	C₃×Dic₁₉	1	1	yes	characteristic, complemented
44	C₃×C₇²	Dic₅₇	1	1	yes	characteristic, complemented
45	C₇×C₁₉	C₃×Dic₂₁	1	8	yes	complemented
46	C₂×C₃²×C₇	D₁₃₃	1	8	yes	—
47	C₂×C₃×C₁₉	—	2	1	no	—
48	C₂×C₃×C₁₉	C₃×C₇⋊D₇	1	1	yes	characteristic
49	C₂×C₃×C₁₉	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
50	C₂×C₇²	C₃×D₅₇	1	1	yes	characteristic
51	Dic₂₁	—	133	8	no	—
52	C₃×Dic₇	—	399	8	no	—
53	Dic₁₉	—	147	1	no	Hall
54	C₃²×C₇	Dic₁₃₃	1	8	yes	complemented
55	C₃×C₁₉	—	2	1	no	—
56	C₃×C₁₉	C₃×C₇⋊Dic₇	1	1	yes	characteristic, complemented
57	C₃×C₁₉	C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic, complemented
58	C₇²	C₃×Dic₅₇	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃×C₇	—	2	8	no	—
60	C₂×C₃×C₇	C₃×D₁₃₃	1	8	yes	—
61	C₂×C₃×C₇	D₃₉₉	1	8	yes	—
62	C₂×C₁₉	C₃×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
63	C₃×Dic₃	—	931	1	no	Hall
64	Dic₇	—	399	8	no	—
65	C₃×C₇	—	2	8	no	—
66	C₃×C₇	C₃×Dic₁₃₃	1	8	yes	complemented
67	C₃×C₇	Dic₃₉₉	1	8	yes	complemented
68	C₁₉	C₃×C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₃²	C₇⋊D₁₃₃	1	1	yes	characteristic
70	C₂×C₇	C₃×D₃₉₉	1	8	yes	—
71	C₃×C₄	—	2793	1	no	—
72	Dic₃	—	931	1	no	—
73	C₃²	C₇⋊Dic₁₃₃	1	1	yes	characteristic, complemented, Sylow
74	C₇	C₃×Dic₃₉₉	1	8	yes	complemented
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	C₃×C₇⋊D₁₃₃	1	1	yes	characteristic
77	C₂×C₃	C₃⋊(C₇⋊D₁₃₃)	1	1	yes	characteristic
78	C₄	—	2793	1	no	Sylow
79	C₃	—	2	1	no	—
80	C₃	C₃×C₇⋊Dic₁₃₃	1	1	yes	characteristic, complemented
81	C₃	C₃⋊(C₇⋊Dic₁₃₃)	1	1	yes	characteristic, direct product factor
82	C₂	C₃×C₃⋊(C₇⋊D₁₃₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(C₇⋊D₁₃₃)
commutator, hypocenter	C₃×C₇²×C₁₉	C₃×C₄
Frattini	C₂	C₃×C₃⋊(C₇⋊D₁₃₃)
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₇⋊Dic₁₃₃)	C₃	direct (N × H)
4. C₃²×C₇²×C₁₉	C₄	semidirect
11. C₃×C₇²×C₁₉	Dic₃	semidirect
12. C₃×C₇²×C₁₉	C₃×C₄	semidirect
18. C₃²×C₇×C₁₉	Dic₇	semidirect
19. C₇²×C₁₉	C₃×Dic₃	semidirect
28. C₃²×C₇²	Dic₁₉	semidirect
30. C₃×C₇×C₁₉	C₃×Dic₇	semidirect
31. C₃×C₇×C₁₉	Dic₂₁	semidirect
41. C₃²×C₁₉	C₇⋊Dic₇	semidirect
43. C₃×C₇²	C₃×Dic₁₉	semidirect
44. C₃×C₇²	Dic₅₇	semidirect
45. C₇×C₁₉	C₃×Dic₂₁	semidirect
54. C₃²×C₇	Dic₁₃₃	semidirect
56. C₃×C₁₉	C₃×C₇⋊Dic₇	semidirect
57. C₃×C₁₉	C₃⋊(C₇⋊Dic₇)	semidirect
58. C₇²	C₃×Dic₅₇	semidirect
66. C₃×C₇	C₃×Dic₁₃₃	semidirect
67. C₃×C₇	Dic₃₉₉	semidirect
68. C₁₉	C₃×C₃⋊(C₇⋊Dic₇)	semidirect
73. C₃²	C₇⋊Dic₁₃₃	semidirect
74. C₇	C₃×Dic₃₉₉	semidirect
80. C₃	C₃×C₇⋊Dic₁₃₃	semidirect
81. C₃	C₃⋊(C₇⋊Dic₁₃₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇²×C₁₉	2
C₃⋊(C₇⋊Dic₁₃₃)	3
C₃×C₇⋊Dic₁₃₃	3
C₃×Dic₃₉₉	7
C₃×C₃⋊(C₇⋊Dic₇)	19

Subgroups — C3×C3⋊(C7⋊Dic133) #45691965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊(C₇⋊Dic₁₃₃) #45691965