Subgroups — D₉×C₂²⋊A₄ #11724061

Order 864.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂²⋊A₄	—	3	1	no	maximal
3	C₂⁴×D₉	C₃	1	1	yes	maximal, characteristic, complemented
4	A₄×D₉	—	4	5	no	maximal
5	C₃×C₂²⋊A₄	D₃	1	1	yes	characteristic
6	C₂⁴×C₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂³×D₉	—	3	5	no	—
8	C₂³×D₉	—	3	5	no	—
9	C₂²⋊(C₂²⋊C₉)	—	2	1	no	—
10	C₉×A₄	—	4	5	no	—
11	C₂⁴×D₃	—	3	1	no	—
12	C₂×C₂²⋊A₄	—	9	1	no	—
13	D₃×A₄	—	12	5	no	—
14	C₂³×C₉	—	3	5	no	—
15	C₂²×D₉	—	3	30	no	—
16	C₂²×D₉	—	3	10	no	—
17	C₂²×D₉	—	3	5	no	—
18	C₂²×D₉	A₄	1	5	yes	complemented
19	C₃×D₉	—	16	1	no	—
20	C₂⁴×C₃	C₃×D₃	1	1	yes	characteristic
21	C₂³×D₃	—	9	5	no	—
22	C₂³×D₃	—	9	5	no	—
23	C₂²⋊A₄	—	2	1	no	—
24	C₂²⋊A₄	D₉	1	1	yes	characteristic, direct product factor
25	C₃×A₄	—	4	5	no	—
26	C₂²×C₉	—	3	10	no	—
27	C₂²×C₉	C₂×A₄	1	5	yes	complemented
28	C₂×D₉	—	3	30	no	—
29	C₂×D₉	—	3	5	no	—
30	C₂×D₉	—	3	5	no	—
31	C₂²⋊C₉	—	8	5	no	—
32	C₂⁵	—	9	1	no	Sylow
33	C₃×C₉	—	16	1	no	Sylow
34	C₂³×C₃	—	3	5	no	—
35	C₂²×D₃	—	3	5	no	—
36	C₂²×D₃	—	9	10	no	—
37	C₂²×D₃	—	9	30	no	—
38	C₂²×D₃	—	9	5	no	—
39	C₂×A₄	—	36	5	no	—
40	C₃×D₃	—	48	1	no	—
41	C₂×C₉	—	3	5	no	—
42	D₉	—	3	5	no	—
43	D₉	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
44	C₂⁴	—	27	5	no	—
45	C₂⁴	—	27	5	no	—
46	C₂⁴	C₃×D₉	1	1	yes	characteristic, complemented
47	C₂²×C₃	—	3	10	no	—
48	C₂²×C₃	D₃×A₄	1	5	yes	—
49	C₂×D₃	—	9	5	no	—
50	C₂×D₃	—	9	30	no	—
51	C₂×D₃	—	9	5	no	—
52	A₄	—	4	5	no	—
53	A₄	—	8	5	no	—
54	C₃²	—	16	1	no	—
55	C₉	—	32	1	no	—
56	C₉	C₂×C₂²⋊A₄	1	1	yes	characteristic, complemented
57	C₂³	—	3	5	no	—
58	C₂³	—	9	5	no	—
59	C₂³	—	27	10	no	—
60	C₂³	—	27	30	no	—
61	C₂³	—	27	5	no	—
62	C₂×C₃	—	3	5	no	—
63	C₂×C₃	—	144	1	no	—
64	D₃	—	3	1	no	—
65	D₃	—	9	5	no	—
66	C₂²	—	3	10	no	—
67	C₂²	—	27	5	no	—
68	C₂²	—	27	5	no	—
69	C₂²	—	27	30	no	—
70	C₂²	A₄×D₉	1	5	yes	complemented
71	C₃	—	16	1	no	—
72	C₃	—	32	1	no	—
73	C₃	D₃×C₂²⋊A₄	1	1	yes	characteristic
74	C₂	—	3	5	no	—
75	C₂	—	9	1	no	—
76	C₂	—	27	5	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂⁴×C₉	C₂×C₃
Frattini	C₃	D₃×C₂²⋊A₄
socle	C₂⁴×C₃	C₃×D₃
LCS	G ▷ C₂⁴×C₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₉×C₂²⋊A₄	C₂	semidirect
3. C₂⁴×D₉	C₃	semidirect
6. C₂⁴×C₉	C₂×C₃	semidirect
18. C₂²×D₉	A₄	semidirect
24. C₂²⋊A₄	D₉	direct (N × H)
27. C₂²×C₉	C₂×A₄	semidirect
43. D₉	C₂²⋊A₄	direct (N × H)
46. C₂⁴	C₃×D₉	semidirect
56. C₉	C₂×C₂²⋊A₄	semidirect
70. C₂²	A₄×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₂²⋊A₄	2
D₃×C₂²⋊A₄	3
C₂⁴×D₉	3
A₄×D₉	4

Subgroups — D9×C22⋊A4 #11724061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₂²⋊A₄ #11724061