Subgroups — C₃×#352 #4599

Order 192.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#123	C₂	1	1	yes	maximal, characteristic
2	C₃×#100	C₂	1	1	yes	maximal, characteristic
3	C₃×#99	C₂	1	1	yes	maximal, characteristic
4	#352	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄	C₄	1	1	yes	characteristic, complemented
7	C₃×M₁₆	—	2	1	no	—
8	C₃×C₄⋊C₄	—	2	1	no	—
9	C₃×C₂²⋊C₄	—	2	1	no	—
10	C₃×C₂²⋊C₄	—	2	1	no	—
11	C₃×C₂²⋊C₄	C₄	1	1	yes	characteristic, complemented
12	#123	C₂×C₃	1	1	yes	characteristic
13	#100	C₂×C₃	1	1	yes	characteristic
14	#99	C₂×C₃	1	1	yes	characteristic
15	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
16	C₂³×C₃	D₄	1	1	yes	characteristic
17	C₃×D₄	—	4	1	no	—
18	C₂×C₃×C₄	—	2	1	no	—
19	C₂×C₃×C₄	—	2	1	no	—
20	C₂×C₃×C₄	—	4	1	no	—
21	C₂×C₃×C₄	—	4	1	no	—
22	C₂×C₃×C₄	D₄	1	1	yes	characteristic
23	C₃×C₈	—	4	1	no	—
24	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
25	C₂²×C₄	C₃×C₄	1	1	yes	characteristic, complemented
26	M₁₆	—	2	1	no	—
27	C₄⋊C₄	—	2	1	no	—
28	C₂²⋊C₄	—	2	1	no	—
29	C₂²⋊C₄	—	2	1	no	—
30	C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic, complemented
31	C₂²×C₃	—	2	1	no	—
32	C₂²×C₃	—	2	1	no	—
33	C₂²×C₃	—	4	1	no	—
34	C₂²×C₃	—	4	1	no	—
35	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₃×C₄	—	2	1	no	—
37	C₃×C₄	—	4	1	no	—
38	C₃×C₄	—	4	1	no	—
39	C₃×C₄	—	8	1	no	—
40	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂³	C₃×D₄	1	1	yes	characteristic
42	D₄	—	4	1	no	—
43	C₂×C₄	—	2	1	no	—
44	C₂×C₄	—	2	1	no	—
45	C₂×C₄	—	4	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	C₃×D₄	1	1	yes	characteristic
48	C₈	—	4	1	no	—
49	C₂×C₃	—	2	1	no	—
50	C₂×C₃	—	4	1	no	—
51	C₂×C₃	—	4	1	no	—
52	C₂×C₃	#99	1	1	yes	characteristic
53	C₂²	—	2	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	4	1	no	—
56	C₂²	—	4	1	no	—
57	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	4	1	no	—
60	C₄	—	4	1	no	—
61	C₄	—	8	1	no	—
62	C₃	#352	1	1	yes	characteristic, direct product factor, Sylow
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	4	1	no	—
66	C₂	C₃×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#99
commutator	C₂³	C₂×C₃×C₄
Frattini, cosocle	C₂×D₄	C₂²×C₃
prime radical	C₂×C₃×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃ ◁ C₂×C₃×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
4. #352	C₃	direct (N × H)
6. C₂²×C₃×C₄	C₄	semidirect
11. C₃×C₂²⋊C₄	C₄	semidirect
25. C₂²×C₄	C₃×C₄	semidirect
30. C₂²⋊C₄	C₃×C₄	semidirect
62. C₃	#352	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×#123	2
C₃×#100	2
C₃×#99	2
#352	3

Subgroups — C3×#352 #4599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#352 #4599