Subgroups — Dic₃⋊#157 #88922

Order 432.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊#157	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#157	C₂	1	1	yes	maximal, characteristic
3	Dic₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#157	—	3	1	no	maximal
5	C₂×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₃⋊#157	—	2	1	no	—
7	C₃×#157	—	2	1	no	—
8	C₃⋊(C₃⋊Dic₃)	C₄	1	1	yes	characteristic, complemented
9	C₃²×Dic₃	C₄	1	1	yes	characteristic, complemented
10	C₂×#157	—	3	1	no	—
11	C₂×#157	D₃	1	1	yes	characteristic
12	C₄×C₃⋊D₃	—	3	1	no	—
13	D₃×Dic₃	—	6	2	no	—
14	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
15	C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
16	C₃×C₃⋊D₃	Q₈	1	1	yes	characteristic
17	Dic₃⋊C₄	—	9	1	no	maximal
18	C₂×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
19	C₂×C₃×D₃	—	6	2	no	—
20	#157	—	2	1	no	—
21	#157	—	6	1	no	—
22	C₃²×C₄	—	3	1	no	—
23	C₃⋊Dic₃	—	3	1	no	—
24	C₃⋊Dic₃	—	6	2	no	—
25	C₃⋊Dic₃	—	12	2	no	—
26	C₃×Dic₃	—	2	2	no	—
27	C₃³	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃×C₄	—	9	1	no	—
29	C₂×Dic₃	—	9	1	no	—
30	C₂×Dic₃	—	9	1	no	—
31	C₄×D₃	—	18	2	no	—
32	C₂×C₃²	—	2	2	no	—
33	C₂×C₃²	—	4	2	no	—
34	C₂×C₃²	C₄×D₃	1	1	yes	characteristic
35	C₃⋊D₃	Dic₆	1	1	yes	characteristic
36	C₃⋊D₃	#67	1	1	yes	characteristic
37	C₃×D₃	—	6	2	no	—
38	C₃×D₃	—	6	2	no	—
39	C₄⋊C₄	—	27	1	no	Sylow
40	C₂²×C₃	—	9	1	no	—
41	C₂×D₃	—	6	2	no	—
42	C₃×C₄	—	6	2	no	—
43	C₃×C₄	—	18	1	no	—
44	Dic₃	—	9	1	no	—
45	Dic₃	—	18	2	no	—
46	Dic₃	—	18	1	no	—
47	Dic₃	—	36	2	no	—
48	Dic₃	#157	1	1	yes	characteristic, complemented
49	C₃²	—	2	2	no	—
50	C₃²	—	4	2	no	—
51	C₃²	Dic₃⋊C₄	1	1	yes	characteristic, complemented
52	C₂×C₄	—	9	1	no	—
53	C₂×C₄	—	27	1	no	—
54	C₂×C₄	—	27	1	no	—
55	C₂×C₃	—	2	2	no	—
56	C₂×C₃	—	4	2	no	—
57	C₂×C₃	—	9	1	no	—
58	C₂×C₃	—	9	1	no	—
59	C₂×C₃	C₂×#157	1	1	yes	characteristic
60	D₃	—	6	2	no	—
61	D₃	—	6	2	no	—
62	C₂²	—	9	1	no	—
63	C₄	—	3	1	no	—
64	C₄	—	18	1	no	—
65	C₄	—	27	1	no	—
66	C₄	—	54	1	no	—
67	C₃	—	2	2	no	—
68	C₃	—	4	2	no	—
69	C₃	C₄⋊#157	1	1	yes	characteristic, complemented
70	C₂	—	9	1	no	—
71	C₂	—	9	1	no	—
72	C₂	D₃×#157	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
8. C₃⋊(C₃⋊Dic₃)	C₄	semidirect
9. C₃²×Dic₃	C₄	semidirect
27. C₃³	C₄⋊C₄	semidirect
48. Dic₃	#157	semidirect
51. C₃²	Dic₃⋊C₄	semidirect
69. 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
C₂×C₃×#157	2
Dic₃×C₃⋊D₃	2
C₄⋊#157	3
Dic₃⋊C₄	9

Subgroups — Dic3⋊#157 #88922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃⋊#157 #88922