Subgroups — C₄×C₃⋊#157 #88990

Order 432.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊#157	C₂	1	2	yes	maximal
2	C₃×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#157	—	3	1	no	maximal
4	C₂×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₃⋊#157	C₄	1	4	yes	direct product factor
6	C₃³×C₄	C₄	1	1	yes	characteristic, complemented
7	C₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic, complemented
8	C₂×#157	—	3	2	no	—
9	C₄×C₃⋊D₃	D₃	1	1	yes	characteristic
10	C₃×C₄×D₃	—	6	2	no	—
11	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
12	C₃×C₃⋊D₃	C₂×C₄	1	2	yes	—
13	C₄×Dic₃	—	9	1	no	maximal
14	C₂×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
15	C₂×C₃×D₃	—	6	2	no	—
16	#157	—	3	4	no	—
17	C₃²×C₄	—	2	2	no	—
18	C₃²×C₄	—	4	2	no	—
19	C₃²×C₄	Dic₃	1	1	yes	characteristic, complemented
20	C₃⋊Dic₃	Dic₃	1	1	yes	characteristic, complemented
21	C₃×Dic₃	—	6	2	no	—
22	C₃³	C₄²	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃×C₄	—	9	1	no	—
24	C₂×Dic₃	—	9	2	no	—
25	C₄×D₃	—	6	2	no	—
26	C₂×C₃²	—	2	2	no	—
27	C₂×C₃²	—	4	2	no	—
28	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
29	C₃⋊D₃	C₄×D₃	1	2	yes	—
30	C₃×D₃	—	6	4	no	—
31	C₄²	—	27	1	no	Sylow
32	C₂²×C₃	—	9	1	no	—
33	C₂×D₃	—	6	2	no	—
34	C₃×C₄	—	2	2	no	—
35	C₃×C₄	—	4	2	no	—
36	C₃×C₄	—	9	1	no	—
37	C₃×C₄	#157	1	1	yes	characteristic, complemented
38	Dic₃	—	6	2	no	—
39	Dic₃	—	9	4	no	—
40	C₃²	—	2	2	no	—
41	C₃²	—	4	2	no	—
42	C₃²	C₄×Dic₃	1	1	yes	characteristic, complemented
43	C₂×C₄	—	9	1	no	—
44	C₂×C₄	—	27	2	no	—
45	C₂×C₃	—	2	2	no	—
46	C₂×C₃	—	4	2	no	—
47	C₂×C₃	—	9	2	no	—
48	C₂×C₃	C₂×#157	1	1	yes	characteristic
49	D₃	—	6	4	no	—
50	C₂²	—	9	1	no	—
51	C₄	—	9	1	no	—
52	C₄	—	27	4	no	—
53	C₄	C₃⋊#157	1	1	yes	characteristic, direct product factor
54	C₃	—	2	2	no	—
55	C₃	—	4	2	no	—
56	C₃	C₄×#157	1	1	yes	characteristic, complemented
57	C₂	—	9	2	no	—
58	C₂	C₂×C₃⋊#157	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	C₃⋊#157
commutator, hypocenter	C₃³	C₄²
Frattini	C₂	C₂×C₃⋊#157
Fitting	C₃³×C₄	C₄
socle	C₂×C₃³	C₂×C₄
prime radical, cosocle	C₂×C₃×C₃⋊D₃	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
5. C₃⋊#157	C₄	direct (N × H)
6. C₃³×C₄	C₄	semidirect
7. C₃×C₃⋊Dic₃	C₄	semidirect
19. C₃²×C₄	Dic₃	semidirect
20. C₃⋊Dic₃	Dic₃	semidirect
22. C₃³	C₄²	semidirect
37. C₃×C₄	#157	semidirect
42. C₃²	C₄×Dic₃	semidirect
53. C₄	C₃⋊#157	direct (N × H)
56. C₃	C₄×#157	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊#157	2
C₃×C₄×C₃⋊D₃	2
C₄×#157	3
C₄×Dic₃	9

Subgroups — C4×C3⋊#157 #88990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃⋊#157 #88990