Subgroups — C₃×#3718 #88776

Order 432.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Dic₆	C₂	1	2	yes	maximal
2	C₃×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₃×#216	—	3	2	no	maximal
4	#3718	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃³×C₄	C₂²	1	1	yes	characteristic
6	C₃²×Dic₃	—	2	2	no	—
7	C₃²×Q₈	—	3	2	no	—
8	C₃×Dic₆	—	2	2	no	—
9	C₃×Dic₆	D₃	1	2	yes	—
10	C₃×Dic₆	C₂×C₃	1	2	yes	—
11	C₃⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic
12	C₃×C₃⋊C₈	—	3	2	no	—
13	C₃×C₃⋊C₈	—	6	1	no	—
14	C₂×C₃³	D₄	1	1	yes	characteristic
15	C₃×Q₁₆	—	9	1	no	—
16	#216	—	3	2	no	—
17	C₃²×C₄	—	2	1	no	—
18	C₃²×C₄	—	2	2	no	—
19	C₃²×C₄	—	4	1	no	—
20	C₃²×C₄	—	6	2	no	—
21	C₃²×C₄	C₂×D₃	1	2	yes	—
22	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
23	C₃×Dic₃	—	2	4	no	—
24	C₃×Dic₃	—	2	2	no	—
25	C₃×Dic₃	—	2	2	no	—
26	C₃³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₃×Q₈	—	3	2	no	—
28	C₃×Q₈	—	3	2	no	—
29	C₃×Q₈	—	6	2	no	—
30	Dic₆	C₃×D₃	1	2	yes	—
31	C₃×C₈	—	9	1	no	—
32	C₃⋊C₈	—	3	2	no	—
33	C₃⋊C₈	—	6	1	no	—
34	C₂×C₃²	—	2	1	no	—
35	C₂×C₃²	—	2	2	no	—
36	C₂×C₃²	—	4	1	no	—
37	C₂×C₃²	#67	1	2	yes	—
38	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
39	Q₁₆	—	9	1	no	Sylow
40	C₃×C₄	—	2	1	no	—
41	C₃×C₄	—	2	2	no	—
42	C₃×C₄	—	4	1	no	—
43	C₃×C₄	—	6	4	no	—
44	C₃×C₄	—	6	2	no	—
45	C₃×C₄	—	6	2	no	—
46	C₃×C₄	D₃²	1	1	yes	characteristic
47	C₃×C₄	C₂×C₃×D₃	1	2	yes	—
48	Dic₃	—	2	2	no	—
49	C₃²	—	2	1	no	—
50	C₃²	—	2	2	no	—
51	C₃²	—	4	1	no	—
52	C₃²	#216	1	2	yes	complemented
53	C₃²	C₃×Q₁₆	1	1	yes	characteristic, complemented
54	Q₈	—	3	2	no	—
55	C₈	—	9	1	no	—
56	C₂×C₃	—	2	2	no	—
57	C₂×C₃	—	2	1	no	—
58	C₂×C₃	—	4	1	no	—
59	C₂×C₃	#625	1	1	yes	characteristic
60	C₂×C₃	C₃×#67	1	2	yes	—
61	C₄	—	6	2	no	—
62	C₄	C₃×D₃²	1	1	yes	characteristic
63	C₃	—	2	2	no	—
64	C₃	—	2	1	no	—
65	C₃	—	4	1	no	—
66	C₃	#3718	1	1	yes	characteristic, direct product factor
67	C₃	C₃×#216	1	2	yes	complemented
68	C₂	C₃×#625	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#625
commutator, cosocle	C₃²×C₄	C₂²×C₃
Frattini	C₄	C₃×D₃²
Fitting	C₃³×C₄	C₂²
socle, prime radical	C₂×C₃³	D₄
hypercenter	C₃×C₄	D₃²
hypocenter	C₃²	C₃×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
4. #3718	C₃	direct (N × H)
26. C₃³	Q₁₆	semidirect
52. C₃²	#216	semidirect
53. C₃²	C₃×Q₁₆	semidirect
66. C₃	#3718	direct (N × H)
67. C₃	C₃×#216	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×Dic₆	2
C₃×C₃⋊(C₃⋊C₈)	2
C₃×#216	3
#3718	3

Subgroups — C3×#3718 #88776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3718 #88776