Subgroups — Dic₃×C₂²⋊C₉ #88624

Order 432.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₃	C₃	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊C₉	—	3	1	no	maximal
4	C₃×C₂²⋊C₉	C₄	1	1	yes	characteristic, complemented
5	C₉×Dic₃	—	4	1	no	maximal
6	C₂³×C₃²	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×Dic₃	—	3	1	no	—
8	C₂×C₃×Dic₃	—	3	1	no	—
9	C₂×C₂²⋊C₉	—	2	1	no	—
10	C₂×C₂²⋊C₉	D₃	1	1	yes	characteristic
11	C₂×C₃×C₉	—	4	1	no	—
12	C₂²×C₃×C₄	—	3	1	no	—
13	C₂²×Dic₃	C₉	1	1	yes	characteristic, complemented
14	C₂²×C₃²	—	3	1	no	—
15	C₂²×C₃²	—	3	1	no	—
16	C₂²×C₃²	C₃×C₄	1	1	yes	characteristic
17	C₃×Dic₃	—	3	1	no	—
18	C₃×Dic₃	A₄	1	1	yes	characteristic
19	C₂²⋊C₉	—	2	1	no	—
20	C₂²⋊C₉	Dic₃	1	1	yes	characteristic, direct product factor
21	C₄×C₉	—	12	1	no	—
22	C₃×C₉	—	4	1	no	Sylow
23	C₂³×C₃	—	2	1	no	—
24	C₂³×C₃	C₂×C₉	1	1	yes	characteristic
25	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
26	C₂×C₃×C₄	—	9	1	no	—
27	C₂×C₃×C₄	—	9	1	no	—
28	C₂×Dic₃	—	3	1	no	—
29	C₂×Dic₃	—	3	1	no	—
30	C₂×C₃²	—	3	1	no	—
31	C₂×C₃²	—	3	1	no	—
32	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
33	C₂×C₉	—	4	1	no	—
34	C₂×C₉	—	8	1	no	—
35	C₂²×C₄	—	3	1	no	Sylow
36	C₂²×C₃	—	2	1	no	—
37	C₂²×C₃	—	3	1	no	—
38	C₂²×C₃	—	3	1	no	—
39	C₂²×C₃	—	3	1	no	—
40	C₂²×C₃	—	3	1	no	—
41	C₂²×C₃	—	6	1	no	—
42	C₂²×C₃	—	6	1	no	—
43	C₂²×C₃	C₄×C₉	1	1	yes	characteristic, complemented
44	C₂²×C₃	C₃×Dic₃	1	1	yes	characteristic
45	C₃×C₄	—	3	1	no	—
46	C₃×C₄	—	9	1	no	—
47	Dic₃	—	3	1	no	—
48	Dic₃	C₂²⋊C₉	1	1	yes	characteristic, direct product factor
49	C₃²	C₄×A₄	1	1	yes	characteristic
50	C₉	—	4	1	no	—
51	C₉	—	8	1	no	—
52	C₂³	D₃×C₉	1	1	yes	characteristic
53	C₂×C₄	—	9	1	no	—
54	C₂×C₄	—	9	1	no	—
55	C₂×C₃	—	2	1	no	—
56	C₂×C₃	—	3	1	no	—
57	C₂×C₃	—	3	1	no	—
58	C₂×C₃	—	3	1	no	—
59	C₂×C₃	—	3	1	no	—
60	C₂×C₃	—	6	1	no	—
61	C₂×C₃	—	6	1	no	—
62	C₂×C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
63	C₂×C₃	D₃×A₄	1	1	yes	characteristic
64	C₂²	—	3	1	no	—
65	C₂²	—	3	1	no	—
66	C₂²	C₉×Dic₃	1	1	yes	characteristic, complemented
67	C₄	—	3	1	no	—
68	C₄	—	9	1	no	—
69	C₃	—	2	1	no	—
70	C₃	C₄×C₂²⋊C₉	1	1	yes	characteristic, complemented
71	C₃	Dic₃×A₄	1	1	yes	characteristic
72	C₂	—	3	1	no	—
73	C₂	—	3	1	no	—
74	C₂	D₃×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×A₄
commutator, hypocenter	C₂²×C₃	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂³×C₃²	C₂×C₃
LCS	G ▷ C₂²×C₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
4. C₃×C₂²⋊C₉	C₄	semidirect
13. C₂²×Dic₃	C₉	semidirect
20. C₂²⋊C₉	Dic₃	direct (N × H)
43. C₂²×C₃	C₄×C₉	semidirect
48. Dic₃	C₂²⋊C₉	direct (N × H)
66. C₂²	C₉×Dic₃	semidirect
70. C₃	C₄×C₂²⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂²⋊C₉	2
C₂²×C₃×Dic₃	3
C₄×C₂²⋊C₉	3
C₉×Dic₃	4

Subgroups — Dic3×C22⋊C9 #88624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₂²⋊C₉ #88624