Subgroups — C₂²×#1094 #88902

Order 432.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1094	C₂	1	3	yes	maximal, direct product factor
2	C₂⁴×C₃²	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₉	C₃	1	3	yes	maximal, complemented
4	C₂²×3₋¹⁺²	—	4	1	no	maximal
5	#1094	C₂²	1	1	yes	characteristic, direct product factor
6	C₂³×C₃²	—	3	3	no	—
7	C₂³×C₃²	—	3	1	no	—
8	C₂³×C₃²	C₂×C₃	1	3	yes	—
9	C₂×C₂²⋊C₉	C₂×C₃	1	9	yes	complemented
10	C₂×3₋¹⁺²	—	4	3	no	—
11	C₂⁴×C₃	—	3	1	no	—
12	C₂⁴×C₃	C₃²	1	1	yes	characteristic
13	C₂²×C₃²	—	3	3	no	—
14	C₂²×C₃²	—	3	2	no	—
15	C₂²×C₃²	—	3	3	no	—
16	C₂²×C₃²	—	3	3	no	—
17	C₂²×C₃²	A₄	1	1	yes	characteristic
18	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
19	C₂²×C₉	—	4	3	no	—
20	C₂²⋊C₉	C₂²×C₃	1	3	yes	complemented
21	3₋¹⁺²	—	4	1	no	Sylow
22	C₂³×C₃	—	3	3	no	—
23	C₂³×C₃	—	3	9	no	—
24	C₂³×C₃	—	3	3	no	—
25	C₂³×C₃	—	3	1	no	—
26	C₂³×C₃	—	3	3	no	—
27	C₂³×C₃	C₂×C₃²	1	3	yes	—
28	C₂×C₃²	—	3	3	no	—
29	C₂×C₃²	—	3	1	no	—
30	C₂×C₃²	C₂×A₄	1	3	yes	—
31	C₂×C₉	—	4	9	no	—
32	C₂⁴	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	—	3	3	no	—
34	C₂²×C₃	—	3	9	no	—
35	C₂²×C₃	—	3	6	no	—
36	C₂²×C₃	—	3	2	no	—
37	C₂²×C₃	—	3	9	no	—
38	C₂²×C₃	—	3	9	no	—
39	C₂²×C₃	—	3	3	no	—
40	C₂²×C₃	—	3	3	no	—
41	C₂²×C₃	—	3	1	no	—
42	C₂²×C₃	—	3	1	no	—
43	C₂²×C₃	C₃×A₄	1	1	yes	characteristic
44	C₂²×C₃	C₂²×C₃²	1	1	yes	characteristic
45	C₃²	C₂²×A₄	1	1	yes	characteristic
46	C₉	—	4	3	no	—
47	C₂³	—	3	3	no	—
48	C₂³	—	3	1	no	—
49	C₂³	C₂×3₋¹⁺²	1	3	yes	complemented
50	C₂×C₃	—	3	3	no	—
51	C₂×C₃	—	3	9	no	—
52	C₂×C₃	—	3	1	no	—
53	C₂×C₃	—	3	3	no	—
54	C₂×C₃	—	3	3	no	—
55	C₂×C₃	C₂×C₃×A₄	1	3	yes	—
56	C₂²	—	3	3	no	—
57	C₂²	—	3	2	no	—
58	C₂²	—	3	3	no	—
59	C₂²	—	3	3	no	—
60	C₂²	#1094	1	1	yes	characteristic, direct product factor
61	C₂²	C₂²×3₋¹⁺²	1	1	yes	characteristic, complemented
62	C₃	—	3	1	no	—
63	C₃	C₂²×C₃×A₄	1	1	yes	characteristic
64	C₂	—	3	1	no	—
65	C₂	—	3	3	no	—
66	C₂	C₂×#1094	1	3	yes	direct product factor

	subgroup	G/H
center	C₂²×C₃	C₃×A₄
commutator, cosocle	C₂²×C₃	C₂²×C₃²
Frattini	C₃	C₂²×C₃×A₄
Fitting, prime radical	C₂⁴×C₃²	C₃
socle	C₂⁴×C₃	C₃²
hypercenter	C₂²×C₃²	A₄
hypocenter	C₂²	C₂²×3₋¹⁺²
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×#1094	C₂	direct (N × H)
3. C₂²×C₂²⋊C₉	C₃	semidirect
5. #1094	C₂²	direct (N × H)
9. C₂×C₂²⋊C₉	C₂×C₃	semidirect
20. C₂²⋊C₉	C₂²×C₃	semidirect
32. C₂⁴	3₋¹⁺²	semidirect
49. C₂³	C₂×3₋¹⁺²	semidirect
60. C₂²	#1094	direct (N × H)
61. C₂²	C₂²×3₋¹⁺²	semidirect
66. C₂	C₂×#1094	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#1094	2
C₂⁴×C₃²	3
C₂²×C₂²⋊C₉	3
C₂²×3₋¹⁺²	4

Subgroups — C22×#1094 #88902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#1094 #88902