Subgroups — C₂×C₉²×A₄ #14518344

Order 1944.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉²×A₄	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₃×C₉×A₄	C₃	1	4	yes	maximal
3	C₂³×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×C₂²⋊C₉	C₃	1	8	yes	maximal, complemented
5	C₂×C₃×C₉²	—	4	1	no	maximal
6	C₃×C₉×A₄	C₂×C₃	1	4	yes	—
7	C₂²×C₉²	—	3	1	no	—
8	C₂²×C₉²	—	3	1	no	—
9	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
10	C₉×C₂²⋊C₉	C₂×C₃	1	8	yes	complemented
11	C₃×C₉²	—	4	1	no	Sylow
12	C₂×C₃²×A₄	C₃²	1	1	yes	characteristic
13	C₂³×C₃×C₉	C₃²	1	4	yes	—
14	C₂×C₃×C₂²⋊C₉	C₃²	1	8	yes	—
15	C₂×C₉×A₄	C₉	1	36	yes	direct product factor
16	C₂×C₃²×C₉	—	4	4	no	—
17	C₂×C₉²	—	3	1	no	—
18	C₂×C₉²	—	3	1	no	—
19	C₂×C₉²	—	4	8	no	—
20	C₂×C₉²	A₄	1	1	yes	characteristic, direct product factor
21	C₃²×A₄	C₂×C₃²	1	1	yes	characteristic
22	C₂²×C₃×C₉	—	3	4	no	—
23	C₂²×C₃×C₉	—	3	4	no	—
24	C₂²×C₃×C₉	C₂×C₃²	1	4	yes	—
25	C₃×C₂²⋊C₉	C₂×C₃²	1	8	yes	—
26	C₉×A₄	C₂×C₉	1	36	yes	direct product factor
27	C₃²×C₉	—	4	4	no	—
28	C₉²	—	4	8	no	—
29	C₉²	C₂×A₄	1	1	yes	characteristic, direct product factor
30	C₂³×C₃²	C₃³	1	1	yes	characteristic
31	C₂×C₃×A₄	C₃×C₉	1	12	yes	—
32	C₂³×C₉	C₃×C₉	1	12	yes	complemented
33	C₂×C₂²⋊C₉	C₃×C₉	1	24	yes	complemented
34	C₂×C₃³	—	4	1	no	—
35	C₂×C₃×C₉	—	3	4	no	—
36	C₂×C₃×C₉	—	3	4	no	—
37	C₂×C₃×C₉	—	4	8	no	—
38	C₂×C₃×C₉	—	4	36	no	—
39	C₂×C₃×C₉	C₃×A₄	1	4	yes	—
40	C₂²×C₃²	—	3	1	no	—
41	C₂²×C₃²	—	3	1	no	—
42	C₂²×C₃²	C₂×C₃³	1	1	yes	characteristic
43	C₃×A₄	C₂×C₃×C₉	1	12	yes	—
44	C₂²×C₉	—	3	12	no	—
45	C₂²×C₉	—	3	12	no	—
46	C₂²×C₉	C₂×C₃×C₉	1	12	yes	complemented
47	C₂²⋊C₉	C₂×C₃×C₉	1	24	yes	complemented
48	C₃³	—	4	1	no	—
49	C₃×C₉	—	4	8	no	—
50	C₃×C₉	—	4	36	no	—
51	C₃×C₉	C₂×C₃×A₄	1	4	yes	—
52	C₂³×C₃	C₃²×C₉	1	4	yes	—
53	C₂×A₄	C₉²	1	9	yes	direct product factor
54	C₂×C₃²	—	3	1	no	—
55	C₂×C₃²	—	3	1	no	—
56	C₂×C₃²	—	4	12	no	—
57	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
58	C₂×C₉	—	3	12	no	—
59	C₂×C₉	—	3	12	no	—
60	C₂×C₉	—	4	24	no	—
61	C₂×C₉	C₉×A₄	1	12	yes	direct product factor
62	C₂²×C₃	—	3	4	no	—
63	C₂²×C₃	—	3	4	no	—
64	C₂²×C₃	C₂×C₃²×C₉	1	4	yes	—
65	A₄	C₂×C₉²	1	9	yes	direct product factor
66	C₃²	—	4	12	no	—
67	C₃²	C₂×C₃²×A₄	1	1	yes	characteristic
68	C₉	—	4	24	no	—
69	C₉	C₂×C₉×A₄	1	12	yes	direct product factor
70	C₂³	C₃×C₉²	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	3	4	no	—
72	C₂×C₃	—	3	4	no	—
73	C₂×C₃	—	4	9	no	—
74	C₂×C₃	C₃×C₉×A₄	1	4	yes	—
75	C₂²	—	3	1	no	—
76	C₂²	—	3	1	no	—
77	C₂²	C₂×C₃×C₉²	1	1	yes	characteristic, complemented
78	C₃	—	4	9	no	—
79	C₃	C₂×C₃×C₉×A₄	1	4	yes	—
80	C₂	—	3	1	no	—
81	C₂	—	3	1	no	—
82	C₂	C₉²×A₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉²	A₄
commutator, hypocenter	C₂²	C₂×C₃×C₉²
Frattini	C₃²	C₂×C₃²×A₄
Fitting	C₂³×C₉²	C₃
socle	C₂³×C₃²	C₃³
prime radical	C₂×C₃²×A₄	C₃²
cosocle	C₂²×C₃²	C₂×C₃³
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₉²

Complements

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

N	H ≅ G/N	type
1. C₉²×A₄	C₂	direct (N × H)
3. C₂³×C₉²	C₃	semidirect
4. C₂×C₉×C₂²⋊C₉	C₃	semidirect
9. C₂²×C₉²	C₂×C₃	semidirect
10. C₉×C₂²⋊C₉	C₂×C₃	semidirect
15. C₂×C₉×A₄	C₉	direct (N × H)
20. C₂×C₉²	A₄	direct (N × H)
26. C₉×A₄	C₂×C₉	direct (N × H)
29. C₉²	C₂×A₄	direct (N × H)
32. C₂³×C₉	C₃×C₉	semidirect
33. C₂×C₂²⋊C₉	C₃×C₉	semidirect
46. C₂²×C₉	C₂×C₃×C₉	semidirect
47. C₂²⋊C₉	C₂×C₃×C₉	semidirect
53. C₂×A₄	C₉²	direct (N × H)
61. C₂×C₉	C₉×A₄	direct (N × H)
65. A₄	C₂×C₉²	direct (N × H)
69. C₉	C₂×C₉×A₄	direct (N × H)
70. C₂³	C₃×C₉²	semidirect
77. C₂²	C₂×C₃×C₉²	semidirect
82. C₂	C₉²×A₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉²×A₄	2
C₂×C₃×C₉×A₄	3
C₂³×C₉²	3
C₂×C₉×C₂²⋊C₉	3
C₂×C₃×C₉²	4

Subgroups — C2×C92×A4 #14518344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉²×A₄ #14518344