Subgroups — C₃×#488 #5362

Order 192.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₃×#103	C₂	1	2	yes	maximal, complemented
4	C₃×#102	C₂	1	2	yes	maximal
5	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#488	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₈	C₂²	1	2	yes	—
10	C₃×C₄⋊C₄	—	2	2	no	—
11	C₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₃×C₂²⋊C₄	—	2	2	no	—
13	C₃×C₄²	C₂²	1	1	yes	characteristic
14	#125	C₂×C₃	1	1	yes	characteristic, complemented
15	#124	C₂×C₃	1	1	yes	characteristic
16	#103	C₂×C₃	1	2	yes	complemented
17	#102	C₂×C₃	1	2	yes	—
18	C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂³×C₃	—	2	1	no	—
20	C₃×Q₈	—	2	2	no	—
21	C₃×D₄	—	2	2	no	—
22	C₂×C₃×C₄	—	2	1	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	D₄	1	2	yes	—
25	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
26	C₃×C₈	—	2	2	no	—
27	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
28	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
29	C₂×C₈	C₂²×C₃	1	2	yes	—
30	C₄⋊C₄	—	2	2	no	—
31	C₄⋊C₄	C₂²×C₃	1	2	yes	—
32	C₂²⋊C₄	—	2	2	no	—
33	C₄²	C₂²×C₃	1	1	yes	characteristic
34	C₂²×C₃	—	4	1	no	—
35	C₂²×C₃	—	4	2	no	—
36	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
37	C₃×C₄	—	2	2	no	—
38	C₃×C₄	—	4	1	no	—
39	C₃×C₄	—	4	2	no	—
40	C₃×C₄	#41	1	2	yes	—
41	C₂³	—	2	1	no	—
42	Q₈	—	2	2	no	—
43	D₄	—	2	2	no	—
44	C₂×C₄	—	2	1	no	—
45	C₂×C₄	—	2	2	no	—
46	C₂×C₄	C₃×D₄	1	2	yes	—
47	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
48	C₈	—	2	2	no	—
49	C₂×C₃	—	8	1	no	—
50	C₂×C₃	#124	1	1	yes	characteristic
51	C₂×C₃	#135	1	2	yes	—
52	C₂²	—	4	1	no	—
53	C₂²	—	4	2	no	—
54	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	—	4	1	no	—
57	C₄	—	4	2	no	—
58	C₄	C₃×#41	1	2	yes	—
59	C₃	#488	1	1	yes	characteristic, direct product factor, Sylow
60	C₂	—	8	1	no	—
61	C₂	C₃×#124	1	1	yes	characteristic
62	C₂	C₃×#135	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#125	C₂	semidirect
3. C₃×#103	C₂	semidirect
5. C₃×C₄×C₈	C₂	semidirect
6. #488	C₃	direct (N × H)
14. #125	C₂×C₃	semidirect
16. #103	C₂×C₃	semidirect
18. C₄×C₈	C₂×C₃	semidirect
59. C₃	#488	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×#125	2
C₃×#124	2
C₃×#103	2
C₃×#102	2
C₃×C₄×C₈	2
#488	3

Subgroups — C3×#488 #5362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#488 #5362