Subgroups — C₃⋊Dic₃₁₂₉ #49176331

Order 37548.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	Dic₃₁₂₉	—	3	4	no	maximal
3	C₃²×C₇×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₄₉	D₃	1	4	yes	—
5	C₃⋊Dic₄₄₇	—	7	1	no	maximal, Hall
6	Dic₁₀₄₃	—	9	1	no	Hall
7	C₃×C₇×C₁₄₉	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₁₄₉	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₄₉	C₃⋊D₃	1	1	yes	characteristic
10	Dic₄₄₇	—	21	4	no	—
11	C₃²×C₁₄₉	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₄₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₄₉	D₂₁	1	4	yes	—
14	Dic₁₄₉	—	63	1	no	Hall
15	C₃×C₁₄₉	Dic₂₁	1	4	yes	complemented
16	C₂×C₁₄₉	C₃⋊D₂₁	1	1	yes	characteristic
17	C₃⋊Dic₂₁	—	149	1	no	maximal, Hall
18	C₁₄₉	C₃⋊Dic₂₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₇	D₁₄₉	1	1	yes	characteristic
20	Dic₂₁	—	447	4	no	—
21	C₃²×C₇	Dic₁₄₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₄₄₇	1	4	yes	—
23	C₃⋊Dic₃	—	1043	1	no	Hall
24	Dic₇	—	1341	1	no	Hall
25	C₃×C₇	Dic₄₄₇	1	4	yes	complemented
26	C₂×C₃²	D₁₀₄₃	1	1	yes	characteristic
27	C₂×C₇	C₃⋊D₄₄₇	1	1	yes	characteristic
28	Dic₃	—	3129	4	no	—
29	C₃²	Dic₁₀₄₃	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊Dic₄₄₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₃₁₂₉	1	4	yes	—
32	C₄	—	9387	1	no	Sylow
33	C₃	Dic₃₁₂₉	1	4	yes	complemented
34	C₂	C₃⋊D₃₁₂₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₃₁₂₉
commutator, hypocenter	C₃²×C₇×C₁₄₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃²×C₇×C₁₄₉	C₂
LCS	G ▷ C₃²×C₇×C₁₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇×C₁₄₉	C₄	semidirect
7. C₃×C₇×C₁₄₉	Dic₃	semidirect
11. C₃²×C₁₄₉	Dic₇	semidirect
12. C₇×C₁₄₉	C₃⋊Dic₃	semidirect
15. C₃×C₁₄₉	Dic₂₁	semidirect
18. C₁₄₉	C₃⋊Dic₂₁	semidirect
21. C₃²×C₇	Dic₁₄₉	semidirect
25. C₃×C₇	Dic₄₄₇	semidirect
29. C₃²	Dic₁₀₄₃	semidirect
30. C₇	C₃⋊Dic₄₄₇	semidirect
33. C₃	Dic₃₁₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇×C₁₄₉	2
Dic₃₁₂₉	3
C₃⋊Dic₄₄₇	7
C₃⋊Dic₂₁	149

Subgroups — C3⋊Dic3129 #49176331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊Dic₃₁₂₉ #49176331