Subgroups — C₃×#336 #4583

Order 192.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	#336	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₄	C₄	1	2	yes	—
5	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₈	—	2	2	no	—
7	C₂×C₃×C₈	—	2	2	no	—
8	C₂×C₃×C₈	C₄	1	4	yes	complemented
9	C₃×C₄²	—	2	2	no	—
10	C₂²×C₈	C₂×C₃	1	2	yes	—
11	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
12	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₄	—	2	2	no	—
14	C₂×C₃×C₄	—	2	2	no	—
15	C₂×C₃×C₄	C₈	1	4	yes	complemented
16	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
17	C₂×C₃×C₄	D₄	1	1	yes	characteristic
18	C₂×C₃×C₄	D₄	1	2	yes	—
19	C₂×C₃×C₄	Q₈	1	1	yes	characteristic
20	C₃×C₈	—	2	4	no	—
21	C₂²×C₄	C₃×C₄	1	2	yes	—
22	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₈	—	2	2	no	—
24	C₂×C₈	—	2	2	no	—
25	C₂×C₈	C₃×C₄	1	4	yes	complemented
26	C₄²	—	2	2	no	—
27	C₂²×C₃	C₄²	1	1	yes	characteristic
28	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₃	C₂×C₈	1	2	yes	—
31	C₂²×C₃	M₁₆	1	2	yes	—
32	C₃×C₄	—	2	4	no	—
33	C₃×C₄	C₂²⋊C₄	1	2	yes	—
34	C₃×C₄	C₄⋊C₄	1	2	yes	—
35	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
36	C₂×C₄	—	2	2	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	C₃×C₈	1	4	yes	complemented
39	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
40	C₂×C₄	C₃×D₄	1	1	yes	characteristic
41	C₂×C₄	C₃×D₄	1	2	yes	—
42	C₂×C₄	C₃×Q₈	1	1	yes	characteristic
43	C₈	—	2	4	no	—
44	C₂×C₃	#95	1	1	yes	characteristic
45	C₂×C₃	C₄×C₈	1	1	yes	characteristic
46	C₂×C₃	#97	1	1	yes	characteristic
47	C₂×C₃	C₂²⋊C₈	1	2	yes	—
48	C₂×C₃	C₄⋊C₈	1	2	yes	—
49	C₂²	C₃×C₄²	1	1	yes	characteristic
50	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
51	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
52	C₂²	C₂×C₃×C₈	1	2	yes	—
53	C₂²	C₃×M₁₆	1	2	yes	—
54	C₄	—	2	4	no	—
55	C₄	C₃×C₂²⋊C₄	1	2	yes	—
56	C₄	C₃×C₄⋊C₄	1	2	yes	—
57	C₃	#336	1	1	yes	characteristic, direct product factor, Sylow
58	C₂	C₃×#95	1	1	yes	characteristic
59	C₂	C₃×C₄×C₈	1	1	yes	characteristic
60	C₂	C₃×#97	1	1	yes	characteristic
61	C₂	C₃×C₂²⋊C₈	1	2	yes	—
62	C₂	C₃×C₄⋊C₈	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²
commutator	C₂	C₃×C₄×C₈
Frattini, cosocle	C₂²×C₄	C₂²×C₃
socle, prime radical	C₂³×C₃	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. #336	C₃	direct (N × H)
8. C₂×C₃×C₈	C₄	semidirect
15. C₂×C₃×C₄	C₈	semidirect
25. C₂×C₈	C₃×C₄	semidirect
38. C₂×C₄	C₃×C₈	semidirect
57. C₃	#336	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈	2
C₂×C₃×C₄²	2
#336	3

Subgroups — C3×#336 #4583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#336 #4583