Subgroups — C₃²×#214 #88829

Order 432.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃²×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×SD₁₆	—	3	1	no	maximal
5	C₃×#214	C₃	1	4	yes	maximal, direct product factor
6	C₂²×C₃³	—	2	1	no	—
7	C₃³×C₄	C₂²	1	1	yes	characteristic
8	C₃²×Dic₃	—	2	1	no	—
9	C₃²×Q₈	—	3	1	no	—
10	C₃²×D₄	—	2	4	no	—
11	C₃²×D₄	D₃	1	1	yes	characteristic
12	C₃²×D₄	C₂×C₃	1	4	yes	—
13	C₃×Dic₆	C₂×C₃	1	4	yes	complemented
14	C₃²×C₈	—	3	1	no	—
15	C₃×C₃⋊C₈	C₂×C₃	1	4	yes	complemented
16	C₂×C₃³	—	4	1	no	—
17	C₂×C₃³	D₄	1	1	yes	characteristic
18	C₃×SD₁₆	—	3	4	no	—
19	#214	C₃²	1	1	yes	characteristic, direct product factor
20	C₂²×C₃²	—	2	8	no	—
21	C₂²×C₃²	—	2	1	no	—
22	C₂²×C₃²	—	2	4	no	—
23	C₃²×C₄	—	2	4	no	—
24	C₃²×C₄	—	6	1	no	—
25	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
26	C₃²×C₄	C₂²×C₃	1	4	yes	—
27	C₃×Dic₃	—	2	4	no	—
28	C₃³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₃×Q₈	—	3	4	no	—
30	C₃×D₄	—	2	4	no	—
31	C₃×D₄	C₃×D₃	1	4	yes	—
32	C₃×D₄	C₂×C₃²	1	1	yes	characteristic
33	Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
34	C₃×C₈	—	3	4	no	—
35	C₃⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
36	C₂×C₃²	—	2	4	no	—
37	C₂×C₃²	—	4	8	no	—
38	C₂×C₃²	—	4	1	no	—
39	C₂×C₃²	—	4	4	no	—
40	C₂×C₃²	#67	1	1	yes	characteristic
41	C₂×C₃²	C₃×D₄	1	4	yes	—
42	SD₁₆	—	3	1	no	Sylow
43	C₂²×C₃	—	2	8	no	—
44	C₂²×C₃	—	2	4	no	—
45	C₂²×C₃	—	2	1	no	—
46	C₃×C₄	—	2	4	no	—
47	C₃×C₄	—	6	4	no	—
48	C₃×C₄	C₂×C₃×D₃	1	4	yes	—
49	C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
50	Dic₃	—	2	1	no	—
51	C₃²	—	2	4	no	—
52	C₃²	#214	1	1	yes	characteristic, direct product factor
53	C₃²	C₃×SD₁₆	1	4	yes	complemented
54	Q₈	—	3	1	no	—
55	D₄	C₃²×D₃	1	1	yes	characteristic
56	C₈	—	3	1	no	—
57	C₂×C₃	—	2	4	no	—
58	C₂×C₃	—	4	8	no	—
59	C₂×C₃	—	4	4	no	—
60	C₂×C₃	—	4	1	no	—
61	C₂×C₃	C₃×#67	1	4	yes	—
62	C₂×C₃	C₃²×D₄	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₄	—	6	1	no	—
65	C₄	C₂×C₃²×D₃	1	1	yes	characteristic
66	C₃	—	2	4	no	—
67	C₃	C₃×#214	1	4	yes	direct product factor
68	C₃	C₃²×SD₁₆	1	1	yes	characteristic, complemented
69	C₂	—	4	1	no	—
70	C₂	C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²	#67
commutator, cosocle	C₃×C₄	C₂²×C₃²
Frattini	C₄	C₂×C₃²×D₃
Fitting, prime radical	C₃³×D₄	C₂
socle	C₂×C₃³	D₄
hypercenter	C₃²×D₄	D₃
hypocenter	C₃	C₃²×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃² ◁ C₃²×C₄ ◁ C₃²×D₄

Complements

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

N	H ≅ G/N	type
2. C₃²×Dic₆	C₂	semidirect
3. C₃²×C₃⋊C₈	C₂	semidirect
5. C₃×#214	C₃	direct (N × H)
13. C₃×Dic₆	C₂×C₃	semidirect
15. C₃×C₃⋊C₈	C₂×C₃	semidirect
19. #214	C₃²	direct (N × H)
28. C₃³	SD₁₆	semidirect
33. Dic₆	C₂×C₃²	semidirect
35. C₃⋊C₈	C₂×C₃²	semidirect
52. C₃²	#214	direct (N × H)
53. C₃²	C₃×SD₁₆	semidirect
67. C₃	C₃×#214	direct (N × H)
68. C₃	C₃²×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₃³×D₄	2
C₃²×Dic₆	2
C₃²×C₃⋊C₈	2
C₃²×SD₁₆	3
C₃×#214	3

Subgroups — C32×#214 #88829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#214 #88829