Subgroups — C₃×#492 #5366

Order 192.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×SD₁₆	C₂	1	4	yes	maximal, complemented
2	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#127	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#492	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₈	C₂²	1	2	yes	—
7	C₂×C₃×D₄	—	2	2	no	—
8	C₂×C₃×D₄	C₂²	1	2	yes	—
9	C₃×SD₁₆	—	2	8	no	—
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₃×C₄⋊C₄	—	2	2	no	—
12	C₃×C₄²	C₂²	1	1	yes	characteristic
13	C₂×SD₁₆	C₂×C₃	1	4	yes	complemented
14	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
15	#127	C₂×C₃	1	1	yes	characteristic
16	C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂³×C₃	—	2	2	no	—
18	C₃×Q₈	—	2	4	no	—
19	C₃×D₄	—	2	4	no	—
20	C₃×D₄	—	4	4	no	—
21	C₂×C₃×C₄	—	2	2	no	—
22	C₂×C₃×C₄	D₄	1	2	yes	—
23	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
24	C₃×C₈	D₄	1	4	yes	complemented
25	C₂×Q₈	C₂²×C₃	1	2	yes	—
26	C₂×D₄	—	2	2	no	—
27	C₂×D₄	C₂²×C₃	1	2	yes	—
28	SD₁₆	—	2	8	no	—
29	C₂×C₈	C₂²×C₃	1	2	yes	—
30	C₄⋊C₄	—	2	2	no	—
31	C₄²	C₂²×C₃	1	1	yes	characteristic
32	C₂²×C₃	—	4	2	no	—
33	C₂²×C₃	—	4	4	no	—
34	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
35	C₃×C₄	—	4	2	no	—
36	C₃×C₄	SD₁₆	1	4	yes	complemented
37	C₃×C₄	C₂×D₄	1	2	yes	—
38	C₂³	—	2	2	no	—
39	Q₈	—	2	4	no	—
40	D₄	—	2	4	no	—
41	D₄	—	4	4	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	C₃×D₄	1	2	yes	—
44	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
45	C₈	C₃×D₄	1	4	yes	complemented
46	C₂×C₃	—	8	2	no	—
47	C₂×C₃	#127	1	1	yes	characteristic
48	C₂×C₃	C₂×SD₁₆	1	2	yes	—
49	C₂²	—	4	2	no	—
50	C₂²	—	4	4	no	—
51	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
52	C₄	—	4	2	no	—
53	C₄	C₃×SD₁₆	1	4	yes	complemented
54	C₄	C₂×C₃×D₄	1	2	yes	—
55	C₃	#492	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	8	2	no	—
57	C₂	C₃×#127	1	1	yes	characteristic
58	C₂	C₂×C₃×SD₁₆	1	2	yes	—

	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. C₂×C₃×SD₁₆	C₂	semidirect
2. C₃×C₄⋊Q₈	C₂	semidirect
4. C₃×C₄×C₈	C₂	semidirect
5. #492	C₃	direct (N × H)
13. C₂×SD₁₆	C₂×C₃	semidirect
14. C₄⋊Q₈	C₂×C₃	semidirect
16. C₄×C₈	C₂×C₃	semidirect
24. C₃×C₈	D₄	semidirect
36. C₃×C₄	SD₁₆	semidirect
45. C₈	C₃×D₄	semidirect
53. C₄	C₃×SD₁₆	semidirect
55. C₃	#492	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×SD₁₆	2
C₃×C₄⋊Q₈	2
C₃×#127	2
C₃×C₄×C₈	2
#492	3

Subgroups — C3×#492 #5366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#492 #5366