Subgroups — C₃³×GO⁺(4,𝔽₂) #14519513

Order 1944.

1508 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃³	GO⁺(4,𝔽₂)
commutator, cosocle	C₃⋊D₃	C₂²×C₃³
Frattini	C₁	G
Fitting, socle	C₃⁵	D₄
hypocenter	C₃²	C₃³×D₄
LCS	G ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₃³

Complements

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

N	H ≅ G/N	type
1. C₃³×D₃²	C₂	semidirect
2. C₃³×#157	C₂	semidirect
3. C₃²×GO⁺(4,𝔽₂)	C₃	direct (N × H)
7. C₃²×D₃²	C₂×C₃	semidirect
8. C₃²×#157	C₂×C₃	semidirect
9. C₃⁵	D₄	semidirect
10. C₃×GO⁺(4,𝔽₂)	C₃²	direct (N × H)
20. C₃×D₃²	C₂×C₃²	semidirect
21. C₃×#157	C₂×C₃²	semidirect
25. C₃⁴	C₃×D₄	semidirect
26. GO⁺(4,𝔽₂)	C₃³	direct (N × H)
39. D₃²	C₂×C₃³	semidirect
40. #157	C₂×C₃³	semidirect
46. C₃³	C₃²×D₄	semidirect
47. C₃³	GO⁺(4,𝔽₂)	direct (N × H)
65. C₃²	C₃³×D₄	semidirect
66. C₃²	C₃×GO⁺(4,𝔽₂)	direct (N × H)
78. C₃	C₃²×GO⁺(4,𝔽₂)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×D₃²	2
C₃³×#157	2
C₃²×GO⁺(4,𝔽₂)	3
C₃³×D₄	9

Subgroups — C33×GO+(4,𝔽2) #14519513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×GO⁺(4,𝔽₂) #14519513