Subgroups — C₂×#10624791 #13090277

Order 1458.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624791	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×#733	C₃	1	1	yes	maximal, characteristic
3	C₂×#6894	C₃	1	3	yes	maximal
4	C₂×C₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₂×3₋¹⁺²⋊C₉	C₃	1	6	yes	maximal
6	C₂×#6868	C₃	1	2	yes	maximal
7	C₃×#733	C₂×C₃	1	1	yes	characteristic
8	#6894	C₂×C₃	1	3	yes	—
9	C₃×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic
10	3₋¹⁺²⋊C₉	C₂×C₃	1	6	yes	—
11	#6868	C₂×C₃	1	2	yes	—
12	C₂×C₃×3₋¹⁺²	C₃²	1	3	yes	—
13	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
14	C₂×C₃²×C₉	C₃²	1	2	yes	—
15	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
16	C₂×#733	—	3	3	no	—
17	C₂×C₉⋊C₉	—	3	3	no	—
18	C₂×C₉⋊C₉	—	3	9	no	—
19	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
20	C₃×3₋¹⁺²	C₂×C₃²	1	3	yes	—
21	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
22	C₃²×C₉	C₂×C₃²	1	2	yes	—
23	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
24	#733	—	3	3	no	—
25	C₉⋊C₉	—	3	3	no	—
26	C₉⋊C₉	—	3	9	no	—
27	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
28	C₂×C₃³	C₃³	1	1	yes	characteristic
29	C₂×3₋¹⁺²	—	3	3	no	—
30	C₂×3₋¹⁺²	—	3	6	no	—
31	C₂×C₃×C₉	—	3	1	no	—
32	C₂×C₃×C₉	—	3	2	no	—
33	C₂×C₃×C₉	—	3	6	no	—
34	C₂×C₃×C₉	—	3	2	no	—
35	C₂×C₃×C₉	—	3	3	no	—
36	C₂×C₃×C₉	—	9	1	no	—
37	C₂×C₃×C₉	—	9	2	no	—
38	C₂×C₃×C₉	H(3,𝔽₃)	1	3	yes	—
39	C₂×C₃×C₉	3₋¹⁺²	1	3	yes	—
40	C₃³	C₂×C₃³	1	1	yes	characteristic
41	3₋¹⁺²	—	3	3	no	—
42	3₋¹⁺²	—	3	6	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	3	2	no	—
45	C₃×C₉	—	3	6	no	—
46	C₃×C₉	—	3	2	no	—
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	—	9	1	no	—
49	C₃×C₉	—	9	2	no	—
50	C₃×C₉	C₂×H(3,𝔽₃)	1	3	yes	—
51	C₃×C₉	C₂×3₋¹⁺²	1	3	yes	—
52	C₂×C₃²	—	3	1	no	—
53	C₂×C₃²	—	3	2	no	—
54	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
55	C₂×C₃²	C₃×3₋¹⁺²	1	1	yes	characteristic
56	C₂×C₃²	#737	1	2	yes	—
57	C₂×C₉	—	3	3	no	—
58	C₂×C₉	—	3	3	no	—
59	C₂×C₉	—	9	6	no	—
60	C₂×C₉	—	9	2	no	—
61	C₂×C₉	—	9	3	no	—
62	C₃²	—	3	1	no	—
63	C₃²	—	3	2	no	—
64	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
65	C₃²	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
66	C₃²	C₂×#737	1	2	yes	—
67	C₉	—	3	3	no	—
68	C₉	—	3	3	no	—
69	C₉	—	9	3	no	—
70	C₉	—	9	6	no	—
71	C₉	—	9	2	no	—
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	3	2	no	—
74	C₂×C₃	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
75	C₂×C₃	#6912	1	1	yes	characteristic
76	C₂×C₃	#6913	1	2	yes	—
77	C₃	—	3	1	no	—
78	C₃	—	3	2	no	—
79	C₃	C₂×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
80	C₃	C₂×#6912	1	1	yes	characteristic
81	C₃	C₂×#6913	1	2	yes	—
82	C₂	#10624791	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. #10624791	C₂	direct (N × H)
82. C₂	#10624791	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624791	2
C₂×C₃×#733	3
C₂×#6894	3
C₂×C₃×C₉⋊C₉	3
C₂×3₋¹⁺²⋊C₉	3
C₂×#6868	3

Subgroups — C2×#10624791 #13090277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624791 #13090277