Subgroups — C₂×C₃²×#401 #11769449

Order 1152.

1548 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃²	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×#401	C₂	direct (N × H)
3. C₂×C₃×#401	C₃	direct (N × H)
6. C₃×#401	C₂×C₃	direct (N × H)
11. C₂×#401	C₃²	direct (N × H)
18. #401	C₂×C₃²	direct (N × H)
32. C₂×C₃²	#401	direct (N × H)
40. C₃²	C₂×#401	direct (N × H)
45. C₂×C₃	C₃×#401	direct (N × H)
50. C₃	C₂×C₃×#401	direct (N × H)
51. C₂	C₃²×#401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#401	2
C₂×C₃²×#95	2
C₂×C₃×#401	3

Subgroups — C2×C32×#401 #11769449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#401 #11769449