Subgroups — C₃×#508 #5382

Order 192.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#135	C₂	1	2	yes	maximal, complemented
2	C₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×SD₃₂	C₂	1	2	yes	maximal, complemented
4	C₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#508	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	—	2	2	no	—
8	C₃×Q₁₆	C₂²	1	2	yes	—
9	C₃×SD₁₆	—	2	2	no	—
10	C₃×D₈	C₂²	1	2	yes	—
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₁₆	C₂²	1	1	yes	characteristic
13	C₃×C₁₆	C₂²	1	1	yes	characteristic
14	#135	C₂×C₃	1	2	yes	complemented
15	Q₃₂	C₂×C₃	1	1	yes	characteristic, complemented
16	SD₃₂	C₂×C₃	1	2	yes	complemented
17	D₁₆	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
19	C₃×Q₈	—	2	2	no	—
20	C₃×D₄	—	2	2	no	—
21	C₃×D₄	—	4	2	no	—
22	C₂×C₃×C₄	—	4	2	no	—
23	C₂×C₃×C₄	D₄	1	1	yes	characteristic
24	C₃×C₈	D₄	1	1	yes	characteristic
25	C₃×C₈	C₂³	1	1	yes	characteristic
26	#41	—	2	2	no	—
27	Q₁₆	C₂²×C₃	1	2	yes	—
28	SD₁₆	—	2	2	no	—
29	D₈	C₂²×C₃	1	2	yes	—
30	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
31	C₁₆	C₂²×C₃	1	1	yes	characteristic
32	C₁₆	C₂²×C₃	1	1	yes	characteristic
33	C₂²×C₃	—	4	2	no	—
34	C₂²×C₃	D₈	1	1	yes	characteristic
35	C₃×C₄	—	4	2	no	—
36	C₃×C₄	D₈	1	1	yes	characteristic
37	C₃×C₄	C₂×D₄	1	1	yes	characteristic
38	Q₈	—	2	2	no	—
39	D₄	—	2	2	no	—
40	D₄	—	4	2	no	—
41	C₂×C₄	—	4	2	no	—
42	C₂×C₄	C₃×D₄	1	1	yes	characteristic
43	C₈	C₃×D₄	1	1	yes	characteristic
44	C₈	C₂³×C₃	1	1	yes	characteristic
45	C₂×C₃	—	2	1	no	—
46	C₂×C₃	—	8	2	no	—
47	C₂×C₃	C₂×D₈	1	1	yes	characteristic
48	C₂²	—	4	2	no	—
49	C₂²	C₃×D₈	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	C₃×D₈	1	1	yes	characteristic
52	C₄	C₂×C₃×D₄	1	1	yes	characteristic
53	C₃	#508	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	—	2	1	no	—
55	C₂	—	8	2	no	—
56	C₂	C₂×C₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₃
socle	C₂×C₃	C₂×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#135	C₂	semidirect
2. C₃×Q₃₂	C₂	semidirect
3. C₃×SD₃₂	C₂	semidirect
4. C₃×D₁₆	C₂	semidirect
5. C₂×C₃×C₁₆	C₂	semidirect
6. #508	C₃	direct (N × H)
14. #135	C₂×C₃	semidirect
15. Q₃₂	C₂×C₃	semidirect
16. SD₃₂	C₂×C₃	semidirect
17. D₁₆	C₂×C₃	semidirect
18. C₂×C₁₆	C₂×C₃	semidirect
53. C₃	#508	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×#135	2
C₃×Q₃₂	2
C₃×SD₃₂	2
C₃×D₁₆	2
C₂×C₃×C₁₆	2
#508	3

Subgroups — C3×#508 #5382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#508 #5382