Subgroups — C₄³×C₃⋊D₃ #11800641

Order 1152.

3816 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₃⋊D₃	C₂	1	7	yes	maximal
2	C₃²×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₃⋊Dic₃	C₂	1	7	yes	maximal, complemented
4	C₄³×D₃	—	3	4	no	maximal
5	C₂²×C₄×C₃⋊D₃	C₂²	1	7	yes	—
6	C₂×C₃²×C₄²	C₂²	1	7	yes	—
7	C₂×C₄×C₃⋊Dic₃	C₂²	1	21	yes	—
8	C₄²×C₃⋊D₃	C₄	1	56	yes	direct product factor
9	C₂×C₄²×D₃	—	3	28	no	—
10	C₃×C₄³	D₃	1	4	yes	complemented
11	C₄²×Dic₃	—	3	28	no	—
12	C₂³×C₃⋊D₃	C₂³	1	1	yes	characteristic
13	C₂²×C₃²×C₄	C₂³	1	7	yes	—
14	C₂²×C₃⋊Dic₃	C₂³	1	7	yes	—
15	C₂×C₄×C₃⋊D₃	C₂×C₄	1	84	yes	—
16	C₃²×C₄²	C₂×C₄	1	28	yes	complemented
17	C₄×C₃⋊Dic₃	C₂×C₄	1	84	yes	complemented
18	C₂×C₄³	—	9	1	no	Sylow
19	C₂²×C₄×D₃	—	3	28	no	—
20	C₂×C₃×C₄²	C₂×D₃	1	28	yes	—
21	C₂×C₄×Dic₃	—	3	84	no	—
22	C₄²×D₃	—	3	224	no	—
23	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
24	C₂²×C₃⋊D₃	C₂²×C₄	1	14	yes	—
25	C₂×C₃²×C₄	C₂²×C₄	1	42	yes	—
26	C₂×C₃⋊Dic₃	C₂²×C₄	1	42	yes	—
27	C₄×C₃⋊D₃	C₄²	1	112	yes	direct product factor
28	C₂²×C₄²	—	9	7	no	—
29	C₄³	—	9	7	no	—
30	C₄³	C₃⋊D₃	1	1	yes	characteristic, direct product factor
31	C₂³×D₃	—	3	4	no	—
32	C₂²×C₃×C₄	C₂²×D₃	1	28	yes	—
33	C₂²×Dic₃	—	3	28	no	—
34	C₂×C₄×D₃	—	3	336	no	—
35	C₃×C₄²	C₄×D₃	1	112	yes	complemented
36	C₄×Dic₃	—	3	336	no	—
37	C₂²×C₃²	C₂³×C₄	1	7	yes	—
38	C₂×C₃⋊D₃	C₂×C₄²	1	28	yes	—
39	C₃²×C₄	C₂×C₄²	1	28	yes	complemented
40	C₃⋊Dic₃	C₂×C₄²	1	28	yes	complemented
41	C₂³×C₄	—	9	7	no	—
42	C₂×C₄²	—	9	21	no	—
43	C₂×C₄²	—	9	56	no	—
44	C₂×C₄²	C₂×C₃⋊D₃	1	7	yes	—
45	C₂³×C₃	C₂³×D₃	1	4	yes	—
46	C₂²×D₃	—	3	56	no	—
47	C₂×C₃×C₄	C₂×C₄×D₃	1	168	yes	—
48	C₂×Dic₃	—	3	168	no	—
49	C₄×D₃	—	3	448	no	—
50	C₂×C₃²	C₂²×C₄²	1	7	yes	—
51	C₃⋊D₃	C₄³	1	8	yes	direct product factor
52	C₂⁴	—	9	1	no	—
53	C₂²×C₄	—	9	7	no	—
54	C₂²×C₄	—	9	84	no	—
55	C₂²×C₄	C₂²×C₃⋊D₃	1	7	yes	—
56	C₄²	—	9	84	no	—
57	C₄²	C₄×C₃⋊D₃	1	28	yes	direct product factor
58	C₂²×C₃	C₂²×C₄×D₃	1	28	yes	—
59	C₂×D₃	—	3	112	no	—
60	C₃×C₄	C₄²×D₃	1	112	yes	complemented
61	Dic₃	—	3	112	no	—
62	C₃²	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
63	C₂³	—	9	14	no	—
64	C₂³	C₂³×C₃⋊D₃	1	1	yes	characteristic
65	C₂×C₄	—	9	42	no	—
66	C₂×C₄	—	9	112	no	—
67	C₂×C₄	C₂×C₄×C₃⋊D₃	1	42	yes	—
68	C₂×C₃	C₂×C₄²×D₃	1	28	yes	—
69	D₃	—	3	32	no	—
70	C₂²	—	9	28	no	—
71	C₂²	C₂²×C₄×C₃⋊D₃	1	7	yes	—
72	C₄	—	9	28	no	—
73	C₄	C₄²×C₃⋊D₃	1	28	yes	direct product factor
74	C₃	C₄³×D₃	1	4	yes	complemented
75	C₂	—	9	8	no	—
76	C₂	C₂×C₄²×C₃⋊D₃	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₄³
Frattini	C₂³	C₂³×C₃⋊D₃
Fitting	C₃²×C₄³	C₂
socle, cosocle	C₂³×C₃²	C₂⁴
prime radical	C₂³×C₃⋊D₃	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄³	C₂	semidirect
3. C₄²×C₃⋊Dic₃	C₂	semidirect
8. C₄²×C₃⋊D₃	C₄	direct (N × H)
10. C₃×C₄³	D₃	semidirect
16. C₃²×C₄²	C₂×C₄	semidirect
17. C₄×C₃⋊Dic₃	C₂×C₄	semidirect
27. C₄×C₃⋊D₃	C₄²	direct (N × H)
30. C₄³	C₃⋊D₃	direct (N × H)
35. C₃×C₄²	C₄×D₃	semidirect
39. C₃²×C₄	C₂×C₄²	semidirect
40. C₃⋊Dic₃	C₂×C₄²	semidirect
51. C₃⋊D₃	C₄³	direct (N × H)
57. C₄²	C₄×C₃⋊D₃	direct (N × H)
60. C₃×C₄	C₄²×D₃	semidirect
62. C₃²	C₂×C₄³	semidirect
73. C₄	C₄²×C₃⋊D₃	direct (N × H)
74. C₃	C₄³×D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₃⋊D₃	2
C₃²×C₄³	2
C₄²×C₃⋊Dic₃	2
C₄³×D₃	3

Subgroups — C43×C3⋊D3 #11800641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×C₃⋊D₃ #11800641