Subgroups — C₃²×Dic₃⋊C₄ #88825

Order 432.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
5. C₃×Dic₃⋊C₄	C₃	direct (N × H)
9. C₃²×Dic₃	C₄	semidirect
21. Dic₃⋊C₄	C₃²	direct (N × H)
31. C₃×Dic₃	C₃×C₄	semidirect
32. C₃³	C₄⋊C₄	semidirect
59. Dic₃	C₃²×C₄	semidirect
61. C₃²	Dic₃⋊C₄	direct (N × H)
62. C₃²	C₃×C₄⋊C₄	semidirect
80. C₃	C₃×Dic₃⋊C₄	direct (N × H)
81. C₃	C₃²×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃³×C₄	2
C₂×C₃²×Dic₃	2
C₃²×C₄⋊C₄	3
C₃×Dic₃⋊C₄	3

Subgroups — C32×Dic3⋊C4 #88825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×Dic₃⋊C₄ #88825