Subgroups — C₃×#361 #4608

Order 192.

62 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	C₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#361	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	—
8	C₃×M₁₆	—	2	1	no	—
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₃×C₁₆	—	2	1	no	—
11	C₂×D₈	C₂×C₃	1	1	yes	characteristic
12	M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
13	#108	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	D₄	1	1	yes	characteristic
18	C₃×C₈	—	4	1	no	—
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	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
26	C₁₆	—	2	1	no	—
27	C₂²×C₃	—	4	2	no	—
28	C₂²×C₃	—	8	2	no	—
29	C₂²×C₃	SD₁₆	1	1	yes	characteristic
30	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
31	C₃×C₄	D₈	1	1	yes	characteristic
32	C₂³	—	4	1	no	—
33	D₄	—	2	2	no	—
34	D₄	—	4	1	no	—
35	C₂×C₄	C₃×D₄	1	1	yes	characteristic
36	C₈	—	4	1	no	—
37	C₈	C₂×C₃×C₄	1	1	yes	characteristic
38	C₈	C₃×D₄	1	1	yes	characteristic
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	—	8	2	no	—
41	C₂×C₃	#102	1	1	yes	characteristic
42	C₂²	—	4	2	no	—
43	C₂²	—	8	2	no	—
44	C₂²	C₃×SD₁₆	1	1	yes	characteristic
45	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
46	C₄	C₃×D₈	1	1	yes	characteristic
47	C₃	#361	1	1	yes	characteristic, direct product factor, Sylow
48	C₂	—	2	1	no	—
49	C₂	—	8	2	no	—
50	C₂	C₃×#102	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#102
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 ◁ C₂×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. C₃×M₃₂	C₂	semidirect
3. C₃×#108	C₂	semidirect
4. #361	C₃	direct (N × H)
12. M₃₂	C₂×C₃	semidirect
13. #108	C₂×C₃	semidirect
47. C₃	#361	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
C₃×M₃₂	2
C₃×#108	2
#361	3

Subgroups — C3×#361 #4608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#361 #4608