Subgroups — C₃×#493 #5367

Order 192.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₈	C₂	1	4	yes	maximal, complemented
2	C₃×#127	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#493	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×D₄	—	2	4	no	—
6	C₂×C₃×D₄	C₂²	1	4	yes	—
7	C₃×D₈	—	2	8	no	—
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₂×D₈	C₂×C₃	1	4	yes	complemented
11	#127	C₂×C₃	1	2	yes	complemented
12	C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂³×C₃	—	2	4	no	—
14	C₃×D₄	—	2	8	no	—
15	C₃×D₄	—	4	8	no	—
16	C₂×C₃×C₄	D₄	1	2	yes	—
17	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
18	C₃×C₈	D₄	1	4	yes	complemented
19	C₂×D₄	—	2	4	no	—
20	C₂×D₄	C₂²×C₃	1	4	yes	—
21	D₈	—	2	8	no	—
22	C₂×C₈	C₂²×C₃	1	2	yes	—
23	C₄²	C₂²×C₃	1	1	yes	characteristic
24	C₂²×C₃	—	4	4	no	—
25	C₂²×C₃	—	4	8	no	—
26	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
27	C₃×C₄	D₈	1	4	yes	complemented
28	C₃×C₄	C₂×D₄	1	2	yes	—
29	C₂³	—	2	4	no	—
30	D₄	—	2	8	no	—
31	D₄	—	4	8	no	—
32	C₂×C₄	C₃×D₄	1	2	yes	—
33	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
34	C₈	C₃×D₄	1	4	yes	complemented
35	C₂×C₃	—	8	4	no	—
36	C₂×C₃	#127	1	1	yes	characteristic
37	C₂×C₃	C₂×D₈	1	2	yes	—
38	C₂²	—	4	4	no	—
39	C₂²	—	4	8	no	—
40	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
41	C₄	C₃×D₈	1	4	yes	complemented
42	C₄	C₂×C₃×D₄	1	2	yes	—
43	C₃	#493	1	1	yes	characteristic, direct product factor, Sylow
44	C₂	—	8	4	no	—
45	C₂	C₃×#127	1	1	yes	characteristic
46	C₂	C₂×C₃×D₈	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
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×D₈	C₂	semidirect
2. C₃×#127	C₂	semidirect
3. C₃×C₄×C₈	C₂	semidirect
4. #493	C₃	direct (N × H)
10. C₂×D₈	C₂×C₃	semidirect
11. #127	C₂×C₃	semidirect
12. C₄×C₈	C₂×C₃	semidirect
18. C₃×C₈	D₄	semidirect
27. C₃×C₄	D₈	semidirect
34. C₈	C₃×D₄	semidirect
41. C₄	C₃×D₈	semidirect
43. C₃	#493	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×#127	2
C₃×C₄×C₈	2
#493	3

Subgroups — C3×#493 #5367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#493 #5367