Subgroups — C₃³×#383 #13163897

Order 1728.

1932 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₃³×#95	C₂	1	6	yes	maximal
3	C₃²×#383	C₃	1	13	yes	maximal, direct product factor
4	C₂²×C₃³×C₄	C₂²	1	4	yes	—
5	C₂²×C₃³×C₄	C₂²	1	3	yes	—
6	C₃³×C₄²	C₄	1	4	yes	complemented
7	C₂×C₃²×C₄²	C₂×C₃	1	13	yes	—
8	C₃²×#95	C₂×C₃	1	78	yes	—
9	C₂³×C₃³	C₂³	1	1	yes	characteristic
10	C₂×C₃³×C₄	—	2	6	no	—
11	C₂×C₃³×C₄	—	2	12	no	—
12	C₂×C₃³×C₄	C₂×C₄	1	6	yes	—
13	C₃×#383	C₃²	1	13	yes	direct product factor
14	C₂²×C₃²×C₄	C₂²×C₃	1	52	yes	—
15	C₂²×C₃²×C₄	C₂²×C₃	1	39	yes	—
16	C₃²×C₄²	C₃×C₄	1	52	yes	complemented
17	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₃³	#41	1	6	yes	—
19	C₃³×C₄	—	2	6	no	—
20	C₃³×C₄	—	4	4	no	—
21	C₂×C₃×C₄²	C₂×C₃²	1	13	yes	—
22	C₃×#95	C₂×C₃²	1	78	yes	—
23	C₂³×C₃²	C₂³×C₃	1	13	yes	—
24	C₂×C₃²×C₄	—	2	78	no	—
25	C₂×C₃²×C₄	—	2	156	no	—
26	C₂×C₃²×C₄	C₂×C₃×C₄	1	78	yes	—
27	#383	C₃³	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃³	#117	1	3	yes	—
29	C₂×C₃³	#126	1	4	yes	—
30	C₂²×C₃×C₄	C₂²×C₃²	1	52	yes	—
31	C₂²×C₃×C₄	C₂²×C₃²	1	39	yes	—
32	C₃×C₄²	C₃²×C₄	1	52	yes	complemented
33	C₂²×C₃²	C₂²×C₃×C₄	1	13	yes	—
34	C₂²×C₃²	C₃×#41	1	78	yes	—
35	C₃²×C₄	—	2	78	no	—
36	C₃²×C₄	—	4	52	no	—
37	C₂×C₄²	C₂×C₃³	1	1	yes	characteristic
38	#95	C₂×C₃³	1	6	yes	—
39	C₃³	#383	1	1	yes	characteristic, direct product factor, Sylow
40	C₂³×C₃	C₂³×C₃²	1	13	yes	—
41	C₂×C₃×C₄	—	2	78	no	—
42	C₂×C₃×C₄	—	2	156	no	—
43	C₂×C₃×C₄	C₂×C₃²×C₄	1	78	yes	—
44	C₂×C₃²	C₃×#117	1	39	yes	—
45	C₂×C₃²	C₃×#126	1	52	yes	—
46	C₂²×C₄	C₂²×C₃³	1	4	yes	—
47	C₂²×C₄	C₂²×C₃³	1	3	yes	—
48	C₄²	C₃³×C₄	1	4	yes	complemented
49	C₂²×C₃	C₂²×C₃²×C₄	1	13	yes	—
50	C₂²×C₃	C₃²×#41	1	78	yes	—
51	C₃×C₄	—	2	78	no	—
52	C₃×C₄	—	4	52	no	—
53	C₃²	C₃×#383	1	13	yes	direct product factor
54	C₂³	C₂³×C₃³	1	1	yes	characteristic
55	C₂×C₄	—	2	6	no	—
56	C₂×C₄	—	2	12	no	—
57	C₂×C₄	C₂×C₃³×C₄	1	6	yes	—
58	C₂×C₃	C₃²×#117	1	39	yes	—
59	C₂×C₃	C₃²×#126	1	52	yes	—
60	C₂²	C₂²×C₃³×C₄	1	1	yes	characteristic
61	C₂²	C₃³×#41	1	6	yes	—
62	C₄	—	2	6	no	—
63	C₄	—	4	4	no	—
64	C₃	C₃²×#383	1	13	yes	direct product factor
65	C₂	C₃³×#117	1	3	yes	—
66	C₂	C₃³×#126	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃³	C₂³
commutator	C₂²	C₂²×C₃³×C₄
Frattini, cosocle	C₂³	C₂³×C₃³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃³ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃²×#383	C₃	direct (N × H)
6. C₃³×C₄²	C₄	semidirect
13. C₃×#383	C₃²	direct (N × H)
16. C₃²×C₄²	C₃×C₄	semidirect
27. #383	C₃³	direct (N × H)
32. C₃×C₄²	C₃²×C₄	semidirect
39. C₃³	#383	direct (N × H)
48. C₄²	C₃³×C₄	semidirect
53. C₃²	C₃×#383	direct (N × H)
64. C₃	C₃²×#383	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×C₄²	2
C₃³×#95	2
C₃²×#383	3

Subgroups — C33×#383 #13163897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×#383 #13163897