Subgroups — C₂²⋊A₄×C₉⋊C₉ #72229230

Order 3888.

970 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂²⋊A₄	C₃	1	3	yes	maximal
2	C₃×C₉×C₂²⋊A₄	C₃	1	1	yes	maximal, characteristic
3	C₂⁴×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₉⋊(C₂²⋊(C₂²⋊C₉))	C₃	1	2	yes	maximal, complemented
5	#13048169	C₃	1	6	yes	maximal, complemented
6	A₄×C₉⋊C₉	—	4	5	no	maximal
7	C₂³×C₉⋊C₉	—	3	5	no	—
8	C₃²×C₂²⋊A₄	C₃²	1	1	yes	characteristic
9	C₂⁴×C₃×C₉	C₃²	1	3	yes	—
10	C₂⁴×C₃×C₉	C₃²	1	1	yes	characteristic
11	C₃×C₂²⋊(C₂²⋊C₉)	C₃²	1	6	yes	—
12	C₃×C₂²⋊(C₂²⋊C₉)	C₃²	1	2	yes	—
13	C₉×C₂²⋊A₄	—	3	9	no	—
14	C₉×C₂²⋊A₄	C₉	1	9	yes	complemented
15	C₃×C₉×A₄	—	4	5	no	—
16	C₃×C₉×A₄	—	4	15	no	—
17	C₂²×C₉⋊C₉	—	3	10	no	—
18	C₂²×C₉⋊C₉	A₄	1	5	yes	complemented
19	C₉⋊(C₂²⋊C₉)	—	4	10	no	—
20	(C₂²⋊C₉)⋊C₉	—	4	30	no	—
21	C₃×C₉⋊C₉	—	16	1	no	Sylow
22	C₂³×C₃×C₉	—	3	5	no	—
23	C₂³×C₃×C₉	—	3	15	no	—
24	C₂×C₉⋊C₉	—	3	5	no	—
25	C₂⁴×C₃²	C₃³	1	1	yes	characteristic
26	C₃×C₂²⋊A₄	C₃×C₉	1	3	yes	—
27	C₃×C₂²⋊A₄	3₋¹⁺²	1	9	yes	—
28	C₂⁴×C₉	—	3	3	no	—
29	C₂⁴×C₉	C₃×C₉	1	3	yes	complemented
30	C₂²⋊(C₂²⋊C₉)	—	3	6	no	—
31	C₂²⋊(C₂²⋊C₉)	C₃×C₉	1	6	yes	complemented
32	C₃²×A₄	—	4	5	no	—
33	C₂²×C₃×C₉	—	3	10	no	—
34	C₂²×C₃×C₉	—	3	30	no	—
35	C₂²×C₃×C₉	C₃×A₄	1	15	yes	—
36	C₂²×C₃×C₉	C₃×A₄	1	5	yes	—
37	C₃×C₂²⋊C₉	—	4	10	no	—
38	C₃×C₂²⋊C₉	—	4	30	no	—
39	C₉×A₄	—	4	45	no	—
40	C₉×A₄	—	12	45	no	—
41	C₃²×C₉	—	16	1	no	—
42	C₃²×C₉	—	16	3	no	—
43	C₉⋊C₉	—	16	6	no	—
44	C₉⋊C₉	—	16	2	no	—
45	C₉⋊C₉	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
46	C₂³×C₃²	—	3	5	no	—
47	C₂³×C₉	—	3	15	no	—
48	C₂³×C₉	—	9	15	no	—
49	C₂×C₃×C₉	—	3	5	no	—
50	C₂×C₃×C₉	—	3	15	no	—
51	C₂⁴×C₃	C₃²×C₉	1	1	yes	characteristic
52	C₂⁴×C₃	C₃×3₋¹⁺²	1	3	yes	—
53	C₂²⋊A₄	C₉⋊C₉	1	9	yes	direct product factor
54	C₂²×C₃²	—	3	10	no	—
55	C₂²×C₃²	C₃²×A₄	1	5	yes	—
56	C₃×A₄	—	4	15	no	—
57	C₃×A₄	—	4	45	no	—
58	C₂²×C₉	—	3	30	no	—
59	C₂²×C₉	—	3	15	no	—
60	C₂²×C₉	—	9	30	no	—
61	C₂²×C₉	C₉×A₄	1	15	yes	complemented
62	C₂²⋊C₉	—	4	30	no	—
63	C₂²⋊C₉	—	12	30	no	—
64	C₃³	—	16	1	no	—
65	C₃×C₉	—	16	2	no	—
66	C₃×C₉	—	16	9	no	—
67	C₃×C₉	—	16	6	no	—
68	C₃×C₉	—	48	9	no	—
69	C₃×C₉	C₃×C₂²⋊A₄	1	3	yes	—
70	C₃×C₉	C₃×C₂²⋊A₄	1	1	yes	characteristic
71	C₂³×C₃	—	3	5	no	—
72	C₂³×C₃	—	3	15	no	—
73	C₂×C₃²	—	3	5	no	—
74	C₂×C₉	—	3	15	no	—
75	C₂×C₉	—	9	15	no	—
76	C₂⁴	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₃	—	3	10	no	—
78	C₂²×C₃	—	3	30	no	—
79	C₂²×C₃	C₃×C₉×A₄	1	5	yes	—
80	C₂²×C₃	A₄×3₋¹⁺²	1	15	yes	—
81	A₄	—	4	45	no	—
82	C₃²	—	16	3	no	—
83	C₃²	—	16	9	no	—
84	C₃²	C₃²×C₂²⋊A₄	1	1	yes	characteristic
85	C₉	—	3	3	no	—
86	C₉	—	16	6	no	—
87	C₉	—	48	6	no	—
88	C₉	C₉×C₂²⋊A₄	1	3	yes	complemented
89	C₂³	—	3	5	no	—
90	C₂×C₃	—	3	5	no	—
91	C₂×C₃	—	3	15	no	—
92	C₂²	—	3	10	no	—
93	C₂²	A₄×C₉⋊C₉	1	5	yes	complemented
94	C₃	—	16	9	no	—
95	C₃	C₃×C₉×C₂²⋊A₄	1	1	yes	characteristic
96	C₃	3₋¹⁺²×C₂²⋊A₄	1	3	yes	—
97	C₂	—	3	5	no	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₂²⋊A₄
commutator	C₂⁴×C₃	C₃²×C₉
Fitting	C₂⁴×C₉⋊C₉	C₃
socle, cosocle	C₂⁴×C₃²	C₃³
prime radical	C₃²×C₂²⋊A₄	C₃²
hypercenter	C₉⋊C₉	C₂²⋊A₄
hypocenter	C₂⁴	C₃×C₉⋊C₉
LCS	G ▷ C₂⁴×C₃ ▷ C₂⁴
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
3. C₂⁴×C₉⋊C₉	C₃	semidirect
4. C₉⋊(C₂²⋊(C₂²⋊C₉))	C₃	semidirect
5. #13048169	C₃	semidirect
14. C₉×C₂²⋊A₄	C₉	semidirect
18. C₂²×C₉⋊C₉	A₄	semidirect
29. C₂⁴×C₉	C₃×C₉	semidirect
31. C₂²⋊(C₂²⋊C₉)	C₃×C₉	semidirect
45. C₉⋊C₉	C₂²⋊A₄	direct (N × H)
53. C₂²⋊A₄	C₉⋊C₉	direct (N × H)
61. C₂²×C₉	C₉×A₄	semidirect
76. C₂⁴	C₃×C₉⋊C₉	semidirect
88. C₉	C₉×C₂²⋊A₄	semidirect
93. C₂²	A₄×C₉⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₂²⋊A₄	3
C₂⁴×C₉⋊C₉	3
C₉⋊(C₂²⋊(C₂²⋊C₉))	3
#13048169	3
A₄×C₉⋊C₉	4

Subgroups — C22⋊A4×C9⋊C9 #72229230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊A₄×C₉⋊C₉ #72229230