Subgroups — C₃×#1658 #72373

Order 384.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#490	C₂	1	3	yes	maximal
3	C₃×#330	C₂	1	3	yes	maximal, complemented
4	#1658	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#127	C₂²	1	1	yes	characteristic
6	C₃×#125	—	2	6	no	—
7	C₃×#125	C₂²	1	3	yes	—
8	C₃×#102	—	2	6	no	—
9	C₃×#97	C₂²	1	3	yes	—
10	#564	C₂×C₃	1	1	yes	characteristic, complemented
11	#490	C₂×C₃	1	3	yes	—
12	#330	C₂×C₃	1	3	yes	complemented
13	C₂×C₃×D₄	—	2	3	no	—
14	C₂×C₃×C₈	—	2	3	no	—
15	C₃×C₄⋊C₄	—	2	6	no	—
16	C₃×C₄⋊C₄	—	2	6	no	—
17	C₃×C₄⋊C₄	D₄	1	6	yes	—
18	C₃×C₄²	—	2	2	no	—
19	C₃×C₄²	C₂³	1	1	yes	characteristic
20	#127	C₂²×C₃	1	1	yes	characteristic
21	#125	—	2	6	no	—
22	#125	C₂²×C₃	1	3	yes	—
23	#102	—	2	6	no	—
24	#97	C₂²×C₃	1	3	yes	—
25	C₂³×C₃	—	4	1	no	—
26	C₃×D₄	—	4	6	no	—
27	C₂×C₃×C₄	—	2	6	no	—
28	C₂×C₃×C₄	C₂×D₄	1	3	yes	—
29	C₃×C₈	—	4	3	no	—
30	C₂×D₄	—	2	3	no	—
31	C₂×C₈	—	2	3	no	—
32	C₄⋊C₄	—	2	6	no	—
33	C₄⋊C₄	—	2	6	no	—
34	C₄⋊C₄	C₃×D₄	1	6	yes	—
35	C₄²	—	2	2	no	—
36	C₄²	C₂³×C₃	1	1	yes	characteristic
37	C₂²×C₃	—	8	3	no	—
38	C₂²×C₃	#120	1	1	yes	characteristic
39	C₃×C₄	—	2	3	no	—
40	C₃×C₄	—	4	6	no	—
41	C₂³	—	4	1	no	—
42	D₄	—	4	6	no	—
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	C₂×C₃×D₄	1	3	yes	—
45	C₈	—	4	3	no	—
46	C₂×C₃	—	16	1	no	—
47	C₂×C₃	#454	1	3	yes	—
48	C₂²	—	8	3	no	—
49	C₂²	C₃×#120	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	4	6	no	—
52	C₃	#1658	1	1	yes	characteristic, direct product factor, Sylow
53	C₂	—	16	1	no	—
54	C₂	C₃×#454	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃
prime radical	C₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#564	C₂	semidirect
3. C₃×#330	C₂	semidirect
4. #1658	C₃	direct (N × H)
10. #564	C₂×C₃	semidirect
12. #330	C₂×C₃	semidirect
52. C₃	#1658	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#564	2
C₃×#490	2
C₃×#330	2
#1658	3

Subgroups — C3×#1658 #72373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1658 #72373