Subgroups — C₃⋊D₃×#401 #11808868

Order 1152.

1548 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#401	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃×#95	C₂	1	7	yes	maximal
3	#10592361	C₂	1	7	yes	maximal, complemented
4	D₃×#401	—	3	4	no	maximal
5	C₂²×C₄×C₃⋊D₃	C₂²	1	7	yes	—
6	C₃²×#95	C₂²	1	7	yes	—
7	#63658	C₂²	1	21	yes	—
8	C₃×#401	D₃	1	4	yes	complemented
9	D₃×#95	—	3	28	no	—
10	C₃⋊#401	—	3	28	no	—
11	C₂³×C₃⋊D₃	C₂³	1	1	yes	characteristic
12	C₂²×C₃²×C₄	C₂³	1	7	yes	—
13	C₂²×C₃⋊Dic₃	C₂³	1	7	yes	—
14	C₂×C₄×C₃⋊D₃	—	2	42	no	—
15	C₂×#401	—	9	1	no	Sylow
16	C₂²×C₄×D₃	—	3	28	no	—
17	C₃×#95	C₂×D₃	1	28	yes	—
18	C₃⋊#95	—	3	84	no	—
19	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
20	C₂²×C₃⋊D₃	#41	1	14	yes	—
21	C₂×C₃²×C₄	—	2	21	no	—
22	C₂×C₃⋊Dic₃	—	2	21	no	—
23	C₄×C₃⋊D₃	—	4	28	no	—
24	#401	—	9	7	no	—
25	#401	C₃⋊D₃	1	1	yes	characteristic, direct product factor
26	C₂×#95	—	9	7	no	—
27	C₂³×D₃	—	3	4	no	—
28	C₂²×C₃×C₄	C₂²×D₃	1	28	yes	—
29	C₂²×Dic₃	—	3	28	no	—
30	C₂×C₄×D₃	—	6	168	no	—
31	C₂²×C₃²	C₂×#41	1	7	yes	—
32	C₂×C₃⋊D₃	#126	1	28	yes	—
33	C₃²×C₄	—	4	7	no	—
34	C₃⋊Dic₃	—	4	7	no	—
35	C₂³×C₄	—	9	7	no	—
36	#95	—	9	21	no	—
37	#95	C₂×C₃⋊D₃	1	7	yes	—
38	C₂³×C₃	C₂³×D₃	1	4	yes	—
39	C₂²×D₃	—	3	56	no	—
40	C₂×C₃×C₄	—	2	84	no	—
41	C₂×Dic₃	—	6	84	no	—
42	C₄×D₃	—	12	112	no	—
43	C₂×C₃²	C₂×#126	1	7	yes	—
44	C₃⋊D₃	#401	1	8	yes	direct product factor
45	C₂⁴	—	9	1	no	—
46	C₂²×C₄	—	9	7	no	—
47	C₂²×C₄	—	18	42	no	—
48	C₂²×C₄	C₂²×C₃⋊D₃	1	7	yes	—
49	C₂²×C₃	D₃×#41	1	28	yes	—
50	C₂×D₃	—	3	112	no	—
51	C₃×C₄	—	4	28	no	—
52	Dic₃	—	12	28	no	—
53	C₃²	C₂×#401	1	1	yes	characteristic, complemented, Sylow
54	C₂³	—	9	14	no	—
55	C₂³	C₂³×C₃⋊D₃	1	1	yes	characteristic
56	C₂×C₄	—	2	21	no	—
57	C₂×C₄	—	18	21	no	—
58	C₂×C₄	—	36	28	no	—
59	C₂×C₃	D₃×#126	1	28	yes	—
60	D₃	—	3	32	no	—
61	C₂²	—	9	28	no	—
62	C₂²	#41×C₃⋊D₃	1	7	yes	—
63	C₄	—	4	7	no	—
64	C₄	—	36	7	no	—
65	C₃	D₃×#401	1	4	yes	complemented
66	C₂	—	9	8	no	—
67	C₂	C₃⋊D₃×#126	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×C₃⋊D₃
commutator, socle, cosocle	C₂³×C₃²	C₂⁴
Fitting	C₃²×#401	C₂
prime radical	C₂³×C₃⋊D₃	C₂³
hypercenter	#401	C₃⋊D₃
hypocenter	C₃²	C₂×#401
LCS	G ▷ C₂³×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ #401

Complements

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

N	H ≅ G/N	type
1. C₃²×#401	C₂	semidirect
3. #10592361	C₂	semidirect
8. C₃×#401	D₃	semidirect
25. #401	C₃⋊D₃	direct (N × H)
44. C₃⋊D₃	#401	direct (N × H)
53. C₃²	C₂×#401	semidirect
65. C₃	D₃×#401	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#401	2
C₃⋊D₃×#95	2
#10592361	2
D₃×#401	3

Subgroups — C3⋊D3×#401 #11808868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#401 #11808868