Subgroups — C₂×#10624588 #13090074

Order 1458.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624588	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₉×3₋¹⁺²	C₃	1	3	yes	maximal
3	C₂×#6887	C₃	1	1	yes	maximal, characteristic
4	C₂×#6861	C₃	1	3	yes	maximal
5	C₂×#6860	C₃	1	3	yes	maximal
6	C₂×#6858	C₃	1	3	yes	maximal
7	C₉×3₋¹⁺²	C₂×C₃	1	3	yes	—
8	#6887	C₂×C₃	1	1	yes	characteristic
9	#6861	C₂×C₃	1	3	yes	—
10	#6860	C₂×C₃	1	3	yes	—
11	#6858	C₂×C₃	1	3	yes	—
12	C₂×C₃×3₋¹⁺²	C₃²	1	3	yes	—
13	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
14	C₂×C₉⋊C₉	—	3	2	no	—
15	C₂×C₉⋊C₉	—	3	6	no	—
16	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
17	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
18	C₂×C₃²⋊C₉	C₃²	1	3	yes	—
19	C₂×C₉²	—	3	1	no	—
20	C₂×C₉²	—	3	3	no	—
21	C₃×3₋¹⁺²	C₂×C₃²	1	3	yes	—
22	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
23	C₉⋊C₉	—	3	2	no	—
24	C₉⋊C₉	—	3	6	no	—
25	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
26	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
27	C₃²⋊C₉	C₂×C₃²	1	3	yes	—
28	C₉²	—	3	1	no	—
29	C₉²	—	3	3	no	—
30	C₂×C₃³	C₃³	1	1	yes	characteristic
31	C₂×3₋¹⁺²	—	3	9	no	—
32	C₂×C₃×C₉	—	3	3	no	—
33	C₂×C₃×C₉	—	3	3	no	—
34	C₂×C₃×C₉	—	3	3	no	—
35	C₂×C₃×C₉	—	3	3	no	—
36	C₂×C₃×C₉	—	3	3	no	—
37	C₂×C₃×C₉	H(3,𝔽₃)	1	2	yes	—
38	C₂×C₃×C₉	H(3,𝔽₃)	1	1	yes	characteristic
39	C₃³	C₂×C₃³	1	1	yes	characteristic
40	3₋¹⁺²	—	3	9	no	—
41	C₃×C₉	—	3	3	no	—
42	C₃×C₉	—	3	3	no	—
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	—	3	3	no	—
45	C₃×C₉	—	3	3	no	—
46	C₃×C₉	C₂×H(3,𝔽₃)	1	2	yes	—
47	C₃×C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic
48	C₂×C₃²	—	3	1	no	—
49	C₂×C₃²	—	3	3	no	—
50	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
51	C₂×C₉	—	3	2	no	—
52	C₂×C₉	—	3	9	no	—
53	C₂×C₉	—	9	3	no	—
54	C₂×C₉	—	9	3	no	—
55	C₂×C₉	—	9	3	no	—
56	C₂×C₉	#733	1	3	yes	—
57	C₃²	—	3	1	no	—
58	C₃²	—	3	3	no	—
59	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
60	C₉	—	3	2	no	—
61	C₉	—	3	9	no	—
62	C₉	—	9	3	no	—
63	C₉	—	9	3	no	—
64	C₉	—	9	3	no	—
65	C₉	C₂×#733	1	3	yes	—
66	C₂×C₃	—	9	1	no	—
67	C₂×C₃	C₃×#733	1	1	yes	characteristic
68	C₂×C₃	#6908	1	3	yes	—
69	C₃	—	9	1	no	—
70	C₃	C₂×C₃×#733	1	1	yes	characteristic
71	C₃	C₂×#6908	1	3	yes	—
72	C₂	#10624588	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	C₂×C₃×C₉	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₂×C₃³
socle	C₂×C₃²	C₃×H(3,𝔽₃)
prime radical	C₂×C₃³	C₃³
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₉ ◁ C₂×C₃²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624588	C₂	direct (N × H)
72. C₂	#10624588	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624588	2
C₂×C₉×3₋¹⁺²	3
C₂×#6887	3
C₂×#6861	3
C₂×#6860	3
C₂×#6858	3

Subgroups — C2×#10624588 #13090074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624588 #13090074