Subgroups — C₃×#2262 #72977

Order 384.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#508	C₂	1	2	yes	maximal, complemented
2	C₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×SD₆₄	C₂	1	2	yes	maximal, complemented
4	C₃×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#2262	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#135	—	2	2	no	—
8	C₃×Q₃₂	C₂²	1	2	yes	—
9	C₃×SD₃₂	—	2	2	no	—
10	C₃×D₁₆	C₂²	1	2	yes	—
11	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₃×C₃₂	C₂²	1	1	yes	characteristic
13	C₃×C₃₂	C₂²	1	1	yes	characteristic
14	#508	C₂×C₃	1	2	yes	complemented
15	Q₆₄	C₂×C₃	1	1	yes	characteristic, complemented
16	SD₆₄	C₂×C₃	1	2	yes	complemented
17	D₃₂	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃₂	C₂×C₃	1	1	yes	characteristic, complemented
19	C₃×#41	—	4	2	no	—
20	C₃×Q₁₆	—	2	2	no	—
21	C₃×SD₁₆	—	4	2	no	—
22	C₃×D₈	—	2	2	no	—
23	C₂×C₃×C₈	D₄	1	1	yes	characteristic
24	C₃×C₁₆	D₄	1	1	yes	characteristic
25	C₃×C₁₆	C₂³	1	1	yes	characteristic
26	#135	—	2	2	no	—
27	Q₃₂	C₂²×C₃	1	2	yes	—
28	SD₃₂	—	2	2	no	—
29	D₁₆	C₂²×C₃	1	2	yes	—
30	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
31	C₃₂	C₂²×C₃	1	1	yes	characteristic
32	C₃₂	C₂²×C₃	1	1	yes	characteristic
33	C₃×Q₈	—	4	2	no	—
34	C₃×D₄	—	4	2	no	—
35	C₃×D₄	—	8	2	no	—
36	C₂×C₃×C₄	—	8	2	no	—
37	C₂×C₃×C₄	D₈	1	1	yes	characteristic
38	C₃×C₈	D₈	1	1	yes	characteristic
39	C₃×C₈	C₂×D₄	1	1	yes	characteristic
40	#41	—	4	2	no	—
41	Q₁₆	—	2	2	no	—
42	SD₁₆	—	4	2	no	—
43	D₈	—	2	2	no	—
44	C₂×C₈	C₃×D₄	1	1	yes	characteristic
45	C₁₆	C₃×D₄	1	1	yes	characteristic
46	C₁₆	C₂³×C₃	1	1	yes	characteristic
47	C₂²×C₃	—	8	2	no	—
48	C₂²×C₃	D₁₆	1	1	yes	characteristic
49	C₃×C₄	—	8	2	no	—
50	C₃×C₄	D₁₆	1	1	yes	characteristic
51	C₃×C₄	C₂×D₈	1	1	yes	characteristic
52	Q₈	—	4	2	no	—
53	D₄	—	4	2	no	—
54	D₄	—	8	2	no	—
55	C₂×C₄	—	8	2	no	—
56	C₂×C₄	C₃×D₈	1	1	yes	characteristic
57	C₈	C₃×D₈	1	1	yes	characteristic
58	C₈	C₂×C₃×D₄	1	1	yes	characteristic
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	16	2	no	—
61	C₂×C₃	C₂×D₁₆	1	1	yes	characteristic
62	C₂²	—	8	2	no	—
63	C₂²	C₃×D₁₆	1	1	yes	characteristic
64	C₄	—	8	2	no	—
65	C₄	C₃×D₁₆	1	1	yes	characteristic
66	C₄	C₂×C₃×D₈	1	1	yes	characteristic
67	C₃	#2262	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	2	1	no	—
69	C₂	—	16	2	no	—
70	C₂	C₂×C₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₃
socle	C₂×C₃	C₂×D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#508	C₂	semidirect
2. C₃×Q₆₄	C₂	semidirect
3. C₃×SD₆₄	C₂	semidirect
4. C₃×D₃₂	C₂	semidirect
5. C₂×C₃×C₃₂	C₂	semidirect
6. #2262	C₃	direct (N × H)
14. #508	C₂×C₃	semidirect
15. Q₆₄	C₂×C₃	semidirect
16. SD₆₄	C₂×C₃	semidirect
17. D₃₂	C₂×C₃	semidirect
18. C₂×C₃₂	C₂×C₃	semidirect
67. C₃	#2262	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×#508	2
C₃×Q₆₄	2
C₃×SD₆₄	2
C₃×D₃₂	2
C₂×C₃×C₃₂	2
#2262	3

Subgroups — C3×#2262 #72977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2262 #72977