Subgroups — C₃×#2253 #72968

Order 384.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#499	C₂	1	2	yes	maximal
2	C₃×#367	C₂	1	2	yes	maximal
3	C₃×#366	C₂	1	2	yes	maximal
4	C₃×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
5	#2253	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃×#125	—	2	2	no	—
7	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₃×#107	C₂²	1	4	yes	—
10	C₃×#106	—	2	2	no	—
11	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
12	#499	C₂×C₃	1	2	yes	—
13	#367	C₂×C₃	1	2	yes	—
14	#366	C₂×C₃	1	2	yes	—
15	C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃×C₈	D₄	1	1	yes	characteristic
17	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
18	C₃×C₄⋊C₄	—	2	4	no	—
19	C₃×C₄⋊C₄	—	4	4	no	—
20	C₃×C₄²	D₄	1	1	yes	characteristic
21	C₃×C₁₆	Q₈	1	2	yes	—
22	C₃×C₁₆	Q₈	1	2	yes	—
23	#125	—	2	2	no	—
24	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
25	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
26	#107	C₂²×C₃	1	4	yes	—
27	#106	—	2	2	no	—
28	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
29	C₂×C₃×C₄	—	4	4	no	—
30	C₂×C₃×C₄	D₈	1	2	yes	—
31	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
32	C₃×C₈	Q₁₆	1	2	yes	—
33	C₃×C₈	C₂×Q₈	1	1	yes	characteristic
34	C₃×C₈	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈	C₃×D₄	1	1	yes	characteristic
36	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
37	C₄⋊C₄	—	2	4	no	—
38	C₄⋊C₄	—	4	4	no	—
39	C₄²	C₃×D₄	1	1	yes	characteristic
40	C₁₆	C₃×Q₈	1	2	yes	—
41	C₁₆	C₃×Q₈	1	2	yes	—
42	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
43	C₃×C₄	—	2	2	no	—
44	C₃×C₄	—	8	4	no	—
45	C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
46	C₃×C₄	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₄	—	4	4	no	—
48	C₂×C₄	C₃×D₈	1	2	yes	—
49	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
50	C₈	C₃×Q₁₆	1	2	yes	—
51	C₈	C₂×C₃×Q₈	1	1	yes	characteristic
52	C₈	C₂×C₃×Q₈	1	1	yes	characteristic
53	C₂×C₃	#500	1	1	yes	characteristic
54	C₂×C₃	#508	1	2	yes	—
55	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	8	4	no	—
58	C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
59	C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
60	C₃	#2253	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	C₃×#500	1	1	yes	characteristic
62	C₂	C₃×#508	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
5. #2253	C₃	direct (N × H)
60. C₃	#2253	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×#499	2
C₃×#367	2
C₃×#366	2
C₃×C₄×C₁₆	2
#2253	3

Subgroups — C3×#2253 #72968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2253 #72968