Subgroups — C₃×#1357 #67917

Order 384.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₃×#364	C₂	1	2	yes	maximal, complemented
3	#1357	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×D₈	—	2	2	no	—
5	C₃×#127	C₄	1	2	yes	—
6	C₃×M₃₂	—	2	2	no	—
7	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
8	#493	C₂×C₃	1	1	yes	characteristic
9	#364	C₂×C₃	1	2	yes	complemented
10	C₂×C₃×D₄	—	2	2	no	—
11	C₂×C₃×D₄	—	4	2	no	—
12	C₃×D₈	—	4	2	no	—
13	C₃×D₈	—	4	2	no	—
14	C₂×C₃×C₈	D₄	1	2	yes	—
15	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
16	C₃×C₁₆	—	4	2	no	—
17	C₂×D₈	—	2	2	no	—
18	#127	C₃×C₄	1	2	yes	—
19	M₃₂	—	2	2	no	—
20	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
21	C₂³×C₃	—	4	2	no	—
22	C₃×D₄	—	4	4	no	—
23	C₃×D₄	—	8	4	no	—
24	C₂×C₃×C₄	—	2	1	no	—
25	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
26	C₃×C₈	D₈	1	2	yes	—
27	C₃×C₈	SD₁₆	1	2	yes	—
28	C₂×D₄	—	2	2	no	—
29	C₂×D₄	—	4	2	no	—
30	D₈	—	4	2	no	—
31	D₈	—	4	2	no	—
32	C₂×C₈	C₃×D₄	1	2	yes	—
33	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
34	C₁₆	—	4	2	no	—
35	C₂²×C₃	—	8	4	no	—
36	C₂²×C₃	—	8	2	no	—
37	C₂²×C₃	#100	1	1	yes	characteristic
38	C₃×C₄	—	2	2	no	—
39	C₃×C₄	#102	1	2	yes	—
40	C₂³	—	4	2	no	—
41	D₄	—	4	4	no	—
42	D₄	—	8	4	no	—
43	C₂×C₄	—	2	1	no	—
44	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
45	C₈	C₃×D₈	1	2	yes	—
46	C₈	C₃×SD₁₆	1	2	yes	—
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	—	16	2	no	—
49	C₂×C₃	#331	1	1	yes	characteristic
50	C₂²	—	8	4	no	—
51	C₂²	—	8	2	no	—
52	C₂²	C₃×#100	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	C₃×#102	1	2	yes	—
55	C₃	#1357	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	2	1	no	—
57	C₂	—	16	2	no	—
58	C₂	C₃×#331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#331
commutator	C₄²	C₂×C₃×C₄
Frattini, cosocle	C₄×C₈	C₂²×C₃
prime radical	C₃×#493	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#364	C₂	semidirect
3. #1357	C₃	direct (N × H)
9. #364	C₂×C₃	semidirect
55. C₃	#1357	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×#493	2
C₃×#364	2
#1357	3

Subgroups — C3×#1357 #67917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1357 #67917