Subgroups — C₃⋊D₃×C₇⋊D₁₁₉ #44473000

Order 29988.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇⋊D₁₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×C₁₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₇⋊D₁₁₉))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇⋊D₁₁₉	—	3	4	no	maximal
5	C₃²×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊(C₇⋊D₁₁₉)	—	3	4	no	—
7	D₃×C₇²×C₁₇	—	3	4	no	—
8	C₃×C₇⋊D₁₁₉	D₃	1	4	yes	complemented
9	C₃⋊D₃×D₁₁₉	—	7	8	no	maximal
10	C₂×C₇⋊D₁₁₉	—	9	1	no	Hall
11	C₃×C₇²×C₁₇	C₂×D₃	1	4	yes	complemented
12	C₃⋊D₃₅₇	—	7	8	no	—
13	C₇×C₁₇×C₃⋊D₃	D₇	1	8	yes	complemented
14	C₃²×D₁₁₉	—	7	8	no	—
15	C₃⋊D₃×C₇⋊D₇	—	17	1	no	maximal, Hall
16	C₂×C₇²×C₁₇	—	9	1	no	—
17	C₇⋊D₁₁₉	—	9	1	no	—
18	C₇⋊D₁₁₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	D₃×D₁₁₉	—	21	32	no	—
20	C₃²×C₇×C₁₇	C₂×D₇	1	8	yes	complemented
21	C₃⋊(C₃⋊(C₇⋊D₇))	—	17	1	no	—
22	C₇²×C₃⋊D₃	D₁₇	1	1	yes	characteristic, complemented
23	C₃²×C₇⋊D₇	—	17	1	no	—
24	C₇²×C₁₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
25	D₃₅₇	—	21	32	no	—
26	D₃×C₇×C₁₇	—	3	32	no	—
27	C₃×D₁₁₉	—	7	32	no	—
28	C₃⋊D₃×D₁₇	—	49	1	no	Hall
29	D₃×C₇⋊D₇	—	51	4	no	—
30	C₂×D₁₁₉	—	63	8	no	—
31	C₃²×C₇²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₇	D₃×D₇	1	32	yes	complemented
33	C₃⋊D₅₁	—	49	1	no	—
34	C₁₇×C₃⋊D₃	C₇⋊D₇	1	1	yes	characteristic, complemented
35	C₃²×D₁₇	—	49	1	no	—
36	C₃⋊(C₇⋊D₇)	—	51	4	no	—
37	D₃×C₇²	—	3	4	no	—
38	C₃×C₇⋊D₇	—	17	4	no	—
39	D₇×C₃⋊D₃	—	119	8	no	—
40	C₂×C₇×C₁₇	—	9	8	no	—
41	D₁₁₉	—	7	8	no	—
42	D₁₁₉	—	63	8	no	—
43	D₃×D₁₇	—	147	4	no	—
44	C₂×C₇⋊D₇	—	153	1	no	Hall
45	C₃²×C₁₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
46	C₃×C₇²	D₃×D₁₇	1	4	yes	complemented
47	C₃⋊D₂₁	—	119	8	no	—
48	C₇×C₃⋊D₃	D₁₁₉	1	8	yes	complemented
49	C₃²×D₇	—	119	8	no	—
50	C₇×C₁₇	D₇×C₃⋊D₃	1	8	yes	complemented
51	D₅₁	—	147	4	no	—
52	C₃×D₁₇	—	49	4	no	—
53	D₃×C₁₇	—	3	4	no	—
54	C₂×C₇²	—	9	1	no	—
55	C₇⋊D₇	—	17	1	no	—
56	C₇⋊D₇	—	153	1	no	—
57	D₃×D₇	—	357	32	no	—
58	C₂×D₁₇	—	441	1	no	Hall
59	C₃²×C₇	C₂×D₁₁₉	1	8	yes	complemented
60	C₃×C₁₇	D₃×C₇⋊D₇	1	4	yes	complemented
61	C₇²	C₃⋊D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
62	D₂₁	—	357	32	no	—
63	C₃×D₇	—	119	32	no	—
64	D₃×C₇	—	3	32	no	—
65	C₂×C₃⋊D₃	—	833	1	no	Hall
66	C₂×C₁₇	—	9	1	no	—
67	D₁₇	—	49	1	no	—
68	D₁₇	—	441	1	no	—
69	C₂×D₇	—	1071	8	no	—
70	C₃×C₇	D₃×D₁₁₉	1	32	yes	complemented
71	C₂×C₃²	—	833	1	no	—
72	C₃⋊D₃	—	833	1	no	—
73	C₃⋊D₃	C₇⋊D₁₁₉	1	1	yes	characteristic, direct product factor
74	C₁₇	C₃⋊D₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
75	C₂×C₇	—	9	8	no	—
76	D₇	—	1071	8	no	—
77	D₇	—	119	8	no	—
78	C₂×D₃	—	2499	4	no	—
79	C₃²	C₂×C₇⋊D₁₁₉	1	1	yes	characteristic, complemented, Sylow
80	C₇	C₃⋊D₃×D₁₁₉	1	8	yes	complemented
81	C₂×C₃	—	833	4	no	—
82	D₃	—	3	4	no	—
83	D₃	—	2499	4	no	—
84	C₂²	—	7497	1	no	Sylow
85	C₃	D₃×C₇⋊D₁₁₉	1	4	yes	complemented
86	C₂	—	9	1	no	—
87	C₂	—	833	1	no	—
88	C₂	—	7497	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇²×C₁₇	C₂²
LCS	G ▷ C₃²×C₇²×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇⋊D₁₁₉	C₂	semidirect
2. C₇²×C₁₇×C₃⋊D₃	C₂	semidirect
3. C₃⋊(C₃⋊(C₇⋊D₁₁₉))	C₂	semidirect
5. C₃²×C₇²×C₁₇	C₂²	semidirect
8. C₃×C₇⋊D₁₁₉	D₃	semidirect
11. C₃×C₇²×C₁₇	C₂×D₃	semidirect
13. C₇×C₁₇×C₃⋊D₃	D₇	semidirect
18. C₇⋊D₁₁₉	C₃⋊D₃	direct (N × H)
20. C₃²×C₇×C₁₇	C₂×D₇	semidirect
22. C₇²×C₃⋊D₃	D₁₇	semidirect
24. C₇²×C₁₇	C₂×C₃⋊D₃	semidirect
31. C₃²×C₇²	C₂×D₁₇	semidirect
32. C₃×C₇×C₁₇	D₃×D₇	semidirect
34. C₁₇×C₃⋊D₃	C₇⋊D₇	semidirect
45. C₃²×C₁₇	C₂×C₇⋊D₇	semidirect
46. C₃×C₇²	D₃×D₁₇	semidirect
48. C₇×C₃⋊D₃	D₁₁₉	semidirect
50. C₇×C₁₇	D₇×C₃⋊D₃	semidirect
59. C₃²×C₇	C₂×D₁₁₉	semidirect
60. C₃×C₁₇	D₃×C₇⋊D₇	semidirect
61. C₇²	C₃⋊D₃×D₁₇	semidirect
70. C₃×C₇	D₃×D₁₁₉	semidirect
73. C₃⋊D₃	C₇⋊D₁₁₉	direct (N × H)
74. C₁₇	C₃⋊D₃×C₇⋊D₇	semidirect
79. C₃²	C₂×C₇⋊D₁₁₉	semidirect
80. C₇	C₃⋊D₃×D₁₁₉	semidirect
85. C₃	D₃×C₇⋊D₁₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇⋊D₁₁₉	2
C₇²×C₁₇×C₃⋊D₃	2
C₃⋊(C₃⋊(C₇⋊D₁₁₉))	2
D₃×C₇⋊D₁₁₉	3
C₃⋊D₃×D₁₁₉	7
C₃⋊D₃×C₇⋊D₇	17

Subgroups — C3⋊D3×C7⋊D119 #44473000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×C₇⋊D₁₁₉ #44473000