Subgroups — (C₃⋊D₃)⋊(C₇⋊D₁₃₃) #45692725

Order 33516.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊(C₇⋊D₁₃₃)	C₂	1	2	yes	maximal, complemented
2	C₇²×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₇⋊D₁₃₃	—	3	2	no	maximal
4	C₃²×C₇²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃⋊(C₇⋊D₁₃₃)	D₃	1	2	yes	complemented
6	D₃×C₇²×C₁₉	—	3	2	no	—
7	D₃×C₇²×C₁₉	—	6	1	no	—
8	C₃×C₇⋊D₁₃₃	—	3	2	no	—
9	(C₃⋊D₃)⋊D₁₃₃	—	7	8	no	maximal
10	C₂×C₇⋊D₁₃₃	—	9	1	no	Hall
11	C₃×C₇²×C₁₉	—	2	1	no	—
12	C₃×C₇²×C₁₉	C₂×D₃	1	2	yes	complemented
13	C₇×C₃⋊D₃×C₁₉	D₇	1	8	yes	complemented
14	C₃×D₃₉₉	—	7	16	no	—
15	C₂×C₇²×C₁₉	—	9	1	no	—
16	C₇⋊D₁₃₃	—	3	2	no	—
17	(C₃⋊D₃)⋊(C₇⋊D₇)	—	19	1	no	maximal, Hall
18	D₃×D₁₃₃	—	21	16	no	—
19	C₃²×C₇×C₁₉	C₂×D₇	1	8	yes	complemented
20	C₇²×C₁₉	D₃²	1	1	yes	characteristic, complemented, Hall
21	C₇²×C₃⋊D₃	D₁₉	1	1	yes	characteristic, complemented
22	C₃×C₃⋊(C₇⋊D₇)	—	19	2	no	—
23	D₃₉₉	—	7	16	no	—
24	D₃×C₇×C₁₉	—	3	16	no	—
25	D₃×C₇×C₁₉	—	6	8	no	—
26	C₃×D₁₃₃	—	21	16	no	—
27	(C₃⋊D₃)⋊D₁₉	—	49	1	no	Hall
28	D₃×C₇⋊D₇	—	57	2	no	—
29	C₂×D₁₃₃	—	63	8	no	—
30	C₃²×C₇²	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	C₃×C₇×C₁₉	—	2	8	no	—
32	C₃×C₇×C₁₉	D₃×D₇	1	16	yes	complemented
33	C₃⋊D₃×C₁₉	C₇⋊D₇	1	1	yes	characteristic, complemented
34	C₃×D₅₇	—	49	2	no	—
35	C₃⋊(C₇⋊D₇)	—	19	2	no	—
36	D₃×C₇²	—	3	2	no	—
37	D₃×C₇²	—	6	1	no	—
38	C₃×C₇⋊D₇	—	57	2	no	—
39	C₂×C₇×C₁₉	—	9	8	no	—
40	D₁₃₃	—	21	16	no	—
41	(C₃⋊D₃)⋊D₇	—	133	8	no	—
42	D₃×D₁₉	—	147	2	no	—
43	C₂×C₇⋊D₇	—	171	1	no	Hall
44	C₃²×C₁₉	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
45	C₃×C₇²	—	2	1	no	—
46	C₃×C₇²	D₃×D₁₉	1	2	yes	complemented
47	C₇×C₁₉	(C₃⋊D₃)⋊D₇	1	8	yes	complemented
48	C₇×C₃⋊D₃	D₁₃₃	1	8	yes	complemented
49	C₃×D₂₁	—	133	16	no	—
50	D₅₇	—	49	2	no	—
51	C₃×D₁₉	—	147	2	no	—
52	D₃×C₁₉	—	3	2	no	—
53	D₃×C₁₉	—	6	1	no	—
54	C₂×C₇²	—	9	1	no	—
55	C₇⋊D₇	—	57	2	no	—
56	D₃×D₇	—	399	16	no	—
57	C₂×D₁₉	—	441	1	no	Hall
58	C₃²×C₇	C₂×D₁₃₃	1	8	yes	complemented
59	C₃×C₁₉	—	2	1	no	—
60	C₃×C₁₉	D₃×C₇⋊D₇	1	2	yes	complemented
61	C₇²	(C₃⋊D₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
62	D₂₁	—	133	16	no	—
63	C₃×D₇	—	399	16	no	—
64	D₃×C₇	—	3	16	no	—
65	D₃×C₇	—	6	8	no	—
66	C₂×C₁₉	—	9	1	no	—
67	D₁₉	—	147	2	no	—
68	D₃²	—	931	1	no	Hall
69	C₂×D₇	—	1197	8	no	—
70	C₃×C₇	—	2	8	no	—
71	C₃×C₇	D₃×D₁₃₃	1	16	yes	complemented
72	C₁₉	(C₃⋊D₃)⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
73	C₃⋊D₃	C₇⋊D₁₃₃	1	1	yes	characteristic, complemented
74	C₃×D₃	—	931	2	no	—
75	C₂×C₇	—	9	8	no	—
76	D₇	—	399	16	no	—
77	C₂×D₃	—	2793	2	no	—
78	C₃²	C₂×C₇⋊D₁₃₃	1	1	yes	characteristic, complemented, Sylow
79	C₇	(C₃⋊D₃)⋊D₁₃₃	1	8	yes	complemented
80	C₂×C₃	—	2793	2	no	—
81	D₃	—	3	2	no	—
82	D₃	—	6	1	no	—
83	D₃	—	931	2	no	—
84	C₂²	—	8379	1	no	Sylow
85	C₃	—	2	1	no	—
86	C₃	D₃×C₇⋊D₁₃₃	1	2	yes	complemented
87	C₂	—	9	1	no	—
88	C₂	—	2793	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇²×C₁₉	C₂²
LCS	G ▷ C₃²×C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₃⋊(C₇⋊D₁₃₃)	C₂	semidirect
2. C₇²×C₃⋊D₃×C₁₉	C₂	semidirect
4. C₃²×C₇²×C₁₉	C₂²	semidirect
5. C₃⋊(C₇⋊D₁₃₃)	D₃	semidirect
12. C₃×C₇²×C₁₉	C₂×D₃	semidirect
13. C₇×C₃⋊D₃×C₁₉	D₇	semidirect
19. C₃²×C₇×C₁₉	C₂×D₇	semidirect
20. C₇²×C₁₉	D₃²	semidirect
21. C₇²×C₃⋊D₃	D₁₉	semidirect
30. C₃²×C₇²	C₂×D₁₉	semidirect
32. C₃×C₇×C₁₉	D₃×D₇	semidirect
33. C₃⋊D₃×C₁₉	C₇⋊D₇	semidirect
44. C₃²×C₁₉	C₂×C₇⋊D₇	semidirect
46. C₃×C₇²	D₃×D₁₉	semidirect
47. C₇×C₁₉	(C₃⋊D₃)⋊D₇	semidirect
48. C₇×C₃⋊D₃	D₁₃₃	semidirect
58. C₃²×C₇	C₂×D₁₃₃	semidirect
60. C₃×C₁₉	D₃×C₇⋊D₇	semidirect
61. C₇²	(C₃⋊D₃)⋊D₁₉	semidirect
71. C₃×C₇	D₃×D₁₃₃	semidirect
72. C₁₉	(C₃⋊D₃)⋊(C₇⋊D₇)	semidirect
73. C₃⋊D₃	C₇⋊D₁₃₃	semidirect
78. C₃²	C₂×C₇⋊D₁₃₃	semidirect
79. C₇	(C₃⋊D₃)⋊D₁₃₃	semidirect
86. C₃	D₃×C₇⋊D₁₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃⋊(C₇⋊D₁₃₃)	2
C₇²×C₃⋊D₃×C₁₉	2
D₃×C₇⋊D₁₃₃	3
(C₃⋊D₃)⋊D₁₃₃	7
(C₃⋊D₃)⋊(C₇⋊D₇)	19

Subgroups — (C3⋊D3)⋊(C7⋊D133) #45692725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊(C₇⋊D₁₃₃) #45692725