Subgroups — C₃⋊((C₁₅₁⋊C₃)⋊Dic₇) #49184909

Order 38052.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₅₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	(C₁₅₁⋊C₃)⋊Dic₇	—	3	1	no	maximal
3	Dic₃₁₇₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₅₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₅₁⋊C₃	—	2	1	no	—
6	C₂×C₇×C₁₅₁⋊C₃	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇×C₁₅₁	C₂×C₃	1	1	yes	characteristic
8	C₃⋊((C₁₅₁⋊C₃)⋊C₄)	—	7	1	no	maximal, Hall
9	Dic₁₀₅₇	—	3	1	no	Hall
10	C₃×C₇×C₁₅₁	C₃×C₄	1	1	yes	characteristic, complemented
11	C₇×C₁₅₁⋊C₃	—	2	1	no	—
12	C₇×C₁₅₁⋊C₃	Dic₃	1	1	yes	characteristic, complemented
13	C₂×C₃×C₁₅₁⋊C₃	D₇	1	1	yes	characteristic
14	C₂×C₇×C₁₅₁	C₃×D₃	1	1	yes	characteristic
15	Dic₄₅₃	—	7	1	no	—
16	(C₁₅₁⋊C₃)⋊C₄	—	21	1	no	—
17	C₃×C₁₅₁⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
18	C₇×C₁₅₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₁₅₁	C₃×D₇	1	1	yes	characteristic
20	C₂×C₁₅₁⋊C₃	—	2	1	no	—
21	C₂×C₁₅₁⋊C₃	D₂₁	1	1	yes	characteristic
22	Dic₁₅₁	—	21	1	no	Hall
23	C₃×C₁₅₁	C₃×Dic₇	1	1	yes	characteristic, complemented
24	C₁₅₁⋊C₃	—	2	1	no	—
25	C₁₅₁⋊C₃	Dic₂₁	1	1	yes	characteristic, complemented
26	C₂×C₁₅₁	C₃×D₂₁	1	1	yes	characteristic
27	C₃×Dic₂₁	—	151	1	no	maximal, Hall
28	C₁₅₁	C₃×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²×C₇	—	151	1	no	—
30	Dic₂₁	—	151	1	no	—
31	C₃×Dic₇	—	453	1	no	—
32	C₃²×C₇	—	151	1	no	Hall
33	C₂×C₃×C₇	—	302	1	no	—
34	C₂×C₃×C₇	—	151	1	no	—
35	C₂×C₃×C₇	D₁₅₁⋊C₃	1	1	yes	characteristic
36	C₃×Dic₃	—	1057	1	no	Hall
37	Dic₇	—	453	1	no	Hall
38	C₃×C₇	—	302	1	no	—
39	C₃×C₇	—	151	1	no	—
40	C₃×C₇	(C₁₅₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
41	C₂×C₃²	—	151	1	no	—
42	C₂×C₇	C₃⋊(D₁₅₁⋊C₃)	1	1	yes	characteristic
43	C₃×C₄	—	3171	1	no	—
44	Dic₃	—	1057	1	no	—
45	C₃²	—	151	1	no	Sylow
46	C₇	C₃⋊((C₁₅₁⋊C₃)⋊C₄)	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	302	1	no	—
48	C₂×C₃	—	151	1	no	—
49	C₂×C₃	(C₁₅₁⋊C₃)⋊D₇	1	1	yes	characteristic
50	C₄	—	3171	1	no	Sylow
51	C₃	—	302	1	no	—
52	C₃	—	151	1	no	—
53	C₃	(C₁₅₁⋊C₃)⋊Dic₇	1	1	yes	characteristic, complemented
54	C₂	C₃⋊((C₁₅₁⋊C₃)⋊D₇)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊((C₁₅₁⋊C₃)⋊D₇)
commutator, hypocenter	C₃×C₇×C₁₅₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₇×C₁₅₁	C₂×C₃
prime radical	C₂×C₃×C₇×C₁₅₁⋊C₃	C₂
LCS	G ▷ C₃×C₇×C₁₅₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. Dic₃₁₇₁	C₃	semidirect
4. C₃×C₇×C₁₅₁⋊C₃	C₄	semidirect
10. C₃×C₇×C₁₅₁	C₃×C₄	semidirect
12. C₇×C₁₅₁⋊C₃	Dic₃	semidirect
17. C₃×C₁₅₁⋊C₃	Dic₇	semidirect
18. C₇×C₁₅₁	C₃×Dic₃	semidirect
23. C₃×C₁₅₁	C₃×Dic₇	semidirect
25. C₁₅₁⋊C₃	Dic₂₁	semidirect
28. C₁₅₁	C₃×Dic₂₁	semidirect
40. C₃×C₇	(C₁₅₁⋊C₃)⋊C₄	semidirect
46. C₇	C₃⋊((C₁₅₁⋊C₃)⋊C₄)	semidirect
53. C₃	(C₁₅₁⋊C₃)⋊Dic₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₅₁⋊C₃	2
(C₁₅₁⋊C₃)⋊Dic₇	3
Dic₃₁₇₁	3
C₃⋊((C₁₅₁⋊C₃)⋊C₄)	7
C₃×Dic₂₁	151

Subgroups — C3⋊((C151⋊C3)⋊Dic7) #49184909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((C₁₅₁⋊C₃)⋊Dic₇) #49184909