Subgroups — C₃×#486 #5360

Order 192.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₃×#102	C₂	1	4	yes	maximal, complemented
4	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#486	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₈	—	2	1	no	—
7	C₂×C₃×D₄	—	2	1	no	—
8	C₂×C₃×D₄	—	2	1	no	—
9	C₂×C₃×D₄	C₂²	1	2	yes	—
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₄²	C₂²	1	1	yes	characteristic
14	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
15	#127	C₂×C₃	1	1	yes	characteristic
16	#102	C₂×C₃	1	4	yes	complemented
17	C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂³×C₃	—	2	2	no	—
19	C₃×Q₈	—	4	2	no	—
20	C₃×D₄	—	2	4	no	—
21	C₃×D₄	—	4	2	no	—
22	C₃×D₄	—	4	2	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	D₄	1	1	yes	characteristic
25	C₂×C₃×C₄	D₄	1	1	yes	characteristic
26	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
27	C₃×C₈	—	2	2	no	—
28	C₂×Q₈	—	2	1	no	—
29	C₂×D₄	—	2	1	no	—
30	C₂×D₄	—	2	1	no	—
31	C₂×D₄	C₂²×C₃	1	2	yes	—
32	C₂×C₈	C₂²×C₃	1	2	yes	—
33	C₄⋊C₄	—	2	1	no	—
34	C₄⋊C₄	C₂²×C₃	1	2	yes	—
35	C₄²	C₂²×C₃	1	1	yes	characteristic
36	C₂²×C₃	—	4	2	no	—
37	C₂²×C₃	—	4	2	no	—
38	C₂²×C₃	—	4	2	no	—
39	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
40	C₃×C₄	—	4	2	no	—
41	C₃×C₄	D₈	1	2	yes	—
42	C₃×C₄	SD₁₆	1	2	yes	—
43	C₃×C₄	#41	1	2	yes	—
44	C₂³	—	2	2	no	—
45	Q₈	—	4	2	no	—
46	D₄	—	2	4	no	—
47	D₄	—	4	2	no	—
48	D₄	—	4	2	no	—
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	C₃×D₄	1	1	yes	characteristic
51	C₂×C₄	C₃×D₄	1	1	yes	characteristic
52	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
53	C₈	—	2	2	no	—
54	C₂×C₃	—	8	2	no	—
55	C₂×C₃	#124	1	1	yes	characteristic
56	C₂×C₃	C₂×D₈	1	1	yes	characteristic
57	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
58	C₂²	—	4	2	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
62	C₄	—	4	2	no	—
63	C₄	C₃×D₈	1	2	yes	—
64	C₄	C₃×SD₁₆	1	2	yes	—
65	C₄	C₃×#41	1	2	yes	—
66	C₃	#486	1	1	yes	characteristic, direct product factor, Sylow
67	C₂	—	8	2	no	—
68	C₂	C₃×#124	1	1	yes	characteristic
69	C₂	C₂×C₃×D₈	1	1	yes	characteristic
70	C₂	C₂×C₃×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₃×#127	C₂
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×C₄⋊Q₈	C₂	semidirect
3. C₃×#102	C₂	semidirect
4. C₃×C₄×C₈	C₂	semidirect
5. #486	C₃	direct (N × H)
14. C₄⋊Q₈	C₂×C₃	semidirect
16. #102	C₂×C₃	semidirect
17. C₄×C₈	C₂×C₃	semidirect
66. C₃	#486	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×C₄⋊Q₈	2
C₃×#127	2
C₃×#102	2
C₃×C₄×C₈	2
#486	3

Subgroups — C3×#486 #5360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#486 #5360