Subgroups — #157⋊(C₃⋊(C₃⋊D₃)) #14519525

Order 1944.

1508 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758167	C₂	1	2	yes	maximal, complemented
2	C₃³×#157	C₂	1	1	yes	maximal, characteristic, complemented
3	#157⋊(C₃⋊D₃)	—	3	13	no	maximal
4	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
5	C₃³×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₃⋊#1113	—	3	26	no	—
7	D₃×C₃⋊(C₃⋊D₃)	—	6	2	no	—
8	C₃²×#157	D₃	1	13	yes	complemented
9	C₃⁵	D₄	1	1	yes	characteristic, complemented, Sylow
10	#157⋊D₃	—	9	13	no	—
11	C₄⋊(C₃⋊(C₃⋊D₃))	—	9	1	no	maximal
12	C₃⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
13	C₃×C₃⋊(C₃⋊D₃)	—	6	2	no	—
14	C₃×C₃⋊(C₃⋊D₃)	—	6	26	no	—
15	C₃×C₃⋊(C₃⋊D₃)	—	12	26	no	—
16	C₃²×C₃⋊D₃	C₂×D₃	1	13	yes	—
17	C₃³×D₃	—	6	2	no	—
18	C₂×C₃⋊(C₃⋊D₃)	—	9	2	no	—
19	#1113	—	9	26	no	—
20	D₃×C₃⋊D₃	—	18	26	no	—
21	C₃×#157	C₃⋊D₃	1	13	yes	complemented
22	C₃³×C₄	—	9	1	no	—
23	C₃⁴	—	2	2	no	—
24	C₃⁴	—	4	26	no	—
25	C₃⁴	D₁₂	1	13	yes	complemented
26	GO⁺(4,𝔽₂)	—	27	1	no	—
27	C₄⋊(C₃⋊D₃)	—	27	13	no	—
28	C₂×C₃³	—	9	1	no	—
29	C₃⋊(C₃⋊D₃)	—	6	2	no	—
30	C₃⋊(C₃⋊D₃)	—	6	26	no	—
31	C₃⋊(C₃⋊D₃)	—	12	26	no	—
32	C₃×C₃⋊D₃	—	18	26	no	—
33	C₃×C₃⋊D₃	—	18	26	no	—
34	C₃×C₃⋊D₃	—	36	104	no	—
35	C₃×C₃⋊D₃	C₂×C₃⋊D₃	1	13	yes	—
36	C₃²×D₃	—	6	26	no	—
37	C₂×C₃⋊D₃	—	27	26	no	—
38	D₃²	—	27	2	no	—
39	D₃²	—	54	26	no	—
40	#157	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
41	C₃²×C₄	—	9	13	no	—
42	C₃³	—	2	26	no	—
43	C₃³	—	4	104	no	—
44	C₃³	—	4	26	no	—
45	C₃³	—	8	78	no	—
46	C₃³	C₄⋊(C₃⋊D₃)	1	13	yes	complemented
47	C₃³	GO⁺(4,𝔽₂)	1	1	yes	characteristic, complemented
48	D₁₂	—	81	13	no	—
49	C₂×C₃²	—	9	13	no	—
50	C₃⋊D₃	—	18	26	no	—
51	C₃⋊D₃	—	18	26	no	—
52	C₃⋊D₃	—	36	104	no	—
53	C₃⋊D₃	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
54	C₃×D₃	—	6	26	no	—
55	C₃×D₃	—	54	26	no	—
56	C₃×D₃	—	54	2	no	—
57	C₃×D₃	—	108	26	no	—
58	C₂×D₃	—	81	26	no	—
59	C₂×D₃	—	162	2	no	—
60	C₃×C₄	—	9	13	no	—
61	C₃²	—	2	26	no	—
62	C₃²	—	4	26	no	—
63	C₃²	—	4	104	no	—
64	C₃²	—	8	78	no	—
65	C₃²	C₄⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic, complemented
66	C₃²	#157⋊D₃	1	13	yes	complemented
67	D₄	—	243	1	no	Sylow
68	C₂×C₃	—	9	13	no	—
69	C₂×C₃	—	162	2	no	—
70	D₃	—	6	2	no	—
71	D₃	—	54	2	no	—
72	D₃	—	54	26	no	—
73	D₃	—	108	26	no	—
74	C₂²	—	243	2	no	—
75	C₄	—	9	1	no	—
76	C₃	—	2	2	no	—
77	C₃	—	4	26	no	—
78	C₃	#157⋊(C₃⋊D₃)	1	13	yes	complemented
79	C₂	—	9	1	no	—
80	C₂	—	162	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₃³×C₃⋊D₃	C₂²
Fitting, socle, hypocenter	C₃⁵	D₄
LCS	G ▷ C₃³×C₃⋊D₃ ▷ C₃⁵
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #11758167	C₂	semidirect
2. C₃³×#157	C₂	semidirect
8. C₃²×#157	D₃	semidirect
9. C₃⁵	D₄	semidirect
21. C₃×#157	C₃⋊D₃	semidirect
25. C₃⁴	D₁₂	semidirect
40. #157	C₃⋊(C₃⋊D₃)	semidirect
46. C₃³	C₄⋊(C₃⋊D₃)	semidirect
47. C₃³	GO⁺(4,𝔽₂)	semidirect
65. C₃²	C₄⋊(C₃⋊(C₃⋊D₃))	semidirect
66. C₃²	#157⋊D₃	semidirect
78. C₃	#157⋊(C₃⋊D₃)	semidirect

Maximal subgroups

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

subgroup	index
#11758167	2
C₃³×#157	2
#157⋊(C₃⋊D₃)	3
C₄⋊(C₃⋊(C₃⋊D₃))	9

Subgroups — #157⋊(C3⋊(C3⋊D3)) #14519525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #157⋊(C₃⋊(C₃⋊D₃)) #14519525