Subgroups — C₃×#357 #4604

Order 192.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#357	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×D₄	—	2	1	no	—
6	C₃×D₈	—	2	1	no	—
7	C₃×D₈	C₄	1	2	yes	complemented
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₃×C₄⋊C₄	—	2	1	no	—
10	C₃×C₁₆	—	2	1	no	—
11	C₂×D₈	C₂×C₃	1	1	yes	characteristic
12	C₂×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
13	#107	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂³×C₃	—	4	1	no	—
15	C₃×D₄	—	2	2	no	—
16	C₃×D₄	—	4	1	no	—
17	C₂×C₃×C₄	—	4	1	no	—
18	C₂×C₃×C₄	D₄	1	1	yes	characteristic
19	C₃×C₈	C₂×C₄	1	1	yes	characteristic
20	C₃×C₈	D₄	1	1	yes	characteristic
21	C₂×D₄	—	2	1	no	—
22	D₈	—	2	1	no	—
23	D₈	C₃×C₄	1	2	yes	complemented
24	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
25	C₄⋊C₄	—	2	1	no	—
26	C₁₆	—	2	1	no	—
27	C₂²×C₃	—	4	2	no	—
28	C₂²×C₃	—	8	1	no	—
29	C₂²×C₃	—	8	1	no	—
30	C₂²×C₃	D₈	1	1	yes	characteristic
31	C₃×C₄	—	8	1	no	—
32	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
33	C₃×C₄	SD₁₆	1	1	yes	characteristic
34	C₂³	—	4	1	no	—
35	D₄	—	2	2	no	—
36	D₄	—	4	1	no	—
37	C₂×C₄	—	4	1	no	—
38	C₂×C₄	C₃×D₄	1	1	yes	characteristic
39	C₈	C₂×C₃×C₄	1	1	yes	characteristic
40	C₈	C₃×D₄	1	1	yes	characteristic
41	C₂×C₃	—	8	2	no	—
42	C₂×C₃	#102	1	1	yes	characteristic
43	C₂×C₃	D₁₆	1	1	yes	characteristic
44	C₂×C₃	SD₃₂	1	1	yes	characteristic
45	C₂²	—	4	2	no	—
46	C₂²	—	8	1	no	—
47	C₂²	—	8	1	no	—
48	C₂²	C₃×D₈	1	1	yes	characteristic
49	C₄	—	8	1	no	—
50	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
51	C₄	C₃×SD₁₆	1	1	yes	characteristic
52	C₃	#357	1	1	yes	characteristic, direct product factor, Sylow
53	C₂	—	8	2	no	—
54	C₂	C₃×#102	1	1	yes	characteristic
55	C₂	C₃×D₁₆	1	1	yes	characteristic
56	C₂	C₃×SD₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₈
commutator	C₈	C₂×C₃×C₄
Frattini, cosocle	C₂×C₈	C₂²×C₃
prime radical	C₂×C₃×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₁₆	C₂	semidirect
3. C₃×#107	C₂	semidirect
4. #357	C₃	direct (N × H)
7. C₃×D₈	C₄	semidirect
12. C₂×C₁₆	C₂×C₃	semidirect
13. #107	C₂×C₃	semidirect
23. D₈	C₃×C₄	semidirect
52. C₃	#357	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×C₃×D₈	2
C₂×C₃×C₁₆	2
C₃×#107	2
#357	3

Subgroups — C3×#357 #4604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#357 #4604