Subgroups — D₃×C₄²⋊C₉ #11720756

Order 864.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄²×D₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₄²⋊C₉	—	3	1	no	maximal
4	D₃×C₂²⋊C₉	—	4	1	no	maximal
5	C₂×C₃×C₄×D₃	—	3	1	no	—
6	C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
7	C₃×C₄×Dic₃	—	3	1	no	—
8	C₄²⋊C₉	—	2	1	no	—
9	C₄²⋊C₉	D₃	1	1	yes	characteristic, direct product factor
10	C₃×C₂²⋊C₉	—	4	1	no	—
11	C₂×C₃×C₄²	—	3	1	no	—
12	C₄²×D₃	C₉	1	1	yes	characteristic, complemented
13	C₂²×C₃×D₃	A₄	1	1	yes	characteristic
14	C₂×C₃²×C₄	—	3	1	no	—
15	C₂×C₃×Dic₃	—	3	1	no	—
16	C₃×C₄×D₃	—	3	2	no	—
17	C₃×C₄×D₃	—	3	2	no	—
18	C₂×C₂²⋊C₉	—	12	1	no	—
19	D₃×C₉	—	16	1	no	—
20	C₂²×C₃×C₄	—	9	1	no	—
21	C₂×C₄×D₃	—	3	1	no	—
22	C₃×C₄²	—	2	1	no	—
23	C₃×C₄²	—	9	1	no	—
24	C₃×C₄²	C₂×C₉	1	1	yes	characteristic, complemented
25	C₃×C₄²	C₃×D₃	1	1	yes	characteristic
26	C₄×Dic₃	—	3	1	no	—
27	C₂²×C₃²	C₂×A₄	1	1	yes	characteristic
28	C₂×C₃×D₃	—	3	1	no	—
29	C₂×C₃×D₃	—	3	1	no	—
30	C₃²×C₄	—	3	2	no	—
31	C₃×Dic₃	—	3	2	no	—
32	C₂²⋊C₉	—	4	1	no	—
33	C₂²⋊C₉	—	8	1	no	—
34	C₂×C₄²	—	3	1	no	Sylow
35	C₃×C₉	—	16	1	no	Sylow
36	C₂³×C₃	—	3	1	no	—
37	C₂²×D₃	C₂²⋊C₉	1	1	yes	characteristic
38	C₂×C₃×C₄	—	3	1	no	—
39	C₂×C₃×C₄	—	3	1	no	—
40	C₂×C₃×C₄	—	6	1	no	—
41	C₂×C₃×C₄	—	9	2	no	—
42	C₂×C₃×C₄	—	9	2	no	—
43	C₂×C₃×C₄	—	9	1	no	—
44	C₂×Dic₃	—	3	1	no	—
45	C₄×D₃	—	3	2	no	—
46	C₄×D₃	—	3	2	no	—
47	C₂×C₃²	—	3	1	no	—
48	C₃×D₃	—	3	1	no	—
49	C₃×D₃	C₄²⋊C₃	1	1	yes	characteristic
50	C₂×C₉	—	48	1	no	—
51	C₂²×C₄	—	9	1	no	—
52	C₄²	—	9	1	no	—
53	C₄²	D₃×C₉	1	1	yes	characteristic, complemented
54	C₂²×C₃	—	2	1	no	—
55	C₂²×C₃	—	9	1	no	—
56	C₂²×C₃	—	9	1	no	—
57	C₂²×C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
58	C₂²×C₃	D₃×A₄	1	1	yes	characteristic
59	C₂×D₃	—	3	1	no	—
60	C₂×D₃	—	3	1	no	—
61	C₃×C₄	—	3	2	no	—
62	C₃×C₄	—	3	2	no	—
63	C₃×C₄	—	6	2	no	—
64	C₃×C₄	—	9	2	no	—
65	Dic₃	—	3	2	no	—
66	C₃²	C₂×C₄²⋊C₃	1	1	yes	characteristic
67	C₉	—	16	1	no	—
68	C₉	—	32	1	no	—
69	C₂³	—	3	1	no	—
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	—	9	2	no	—
72	C₂×C₄	—	9	2	no	—
73	C₂×C₄	—	9	1	no	—
74	C₂×C₃	—	3	1	no	—
75	C₂×C₃	—	3	1	no	—
76	C₂×C₃	—	3	1	no	—
77	C₂×C₃	—	6	1	no	—
78	C₂×C₃	—	9	1	no	—
79	D₃	—	3	1	no	—
80	D₃	C₄²⋊C₉	1	1	yes	characteristic, direct product factor
81	C₂²	—	9	1	no	—
82	C₂²	—	9	1	no	—
83	C₂²	D₃×C₂²⋊C₉	1	1	yes	characteristic
84	C₄	—	3	2	no	—
85	C₄	—	9	2	no	—
86	C₃	—	2	1	no	—
87	C₃	C₂×C₄²⋊C₉	1	1	yes	characteristic, complemented
88	C₃	D₃×C₄²⋊C₃	1	1	yes	characteristic
89	C₂	—	3	1	no	—
90	C₂	—	3	1	no	—
91	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×C₄²⋊C₃
commutator, hypocenter	C₃×C₄²	C₂×C₉
Frattini	C₂²×C₃	D₃×A₄
Fitting, cosocle	C₃²×C₄²	C₂×C₃
socle	C₂²×C₃²	C₂×A₄
prime radical	C₂²×C₃×D₃	A₄
LCS	G ▷ C₃×C₄²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₄²⋊C₉	C₂	semidirect
9. C₄²⋊C₉	D₃	direct (N × H)
12. C₄²×D₃	C₉	semidirect
24. C₃×C₄²	C₂×C₉	semidirect
53. C₄²	D₃×C₉	semidirect
80. D₃	C₄²⋊C₉	direct (N × H)
87. C₃	C₂×C₄²⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²⋊C₉	2
C₃×C₄²×D₃	3
C₂×C₄²⋊C₉	3
D₃×C₂²⋊C₉	4

Subgroups — D3×C42⋊C9 #11720756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₄²⋊C₉ #11720756