Subgroups — C₂×#10624616 #13090102

Order 1458.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624616	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#6891	C₃	1	2	yes	maximal
3	C₂×C₃×C₃²⋊C₉	C₃	1	2	yes	maximal
4	C₂×#6860	C₃	1	9	yes	maximal, complemented
5	#6891	C₂×C₃	1	2	yes	—
6	C₃×C₃²⋊C₉	C₂×C₃	1	2	yes	—
7	#6860	C₂×C₃	1	9	yes	complemented
8	C₂×C₃⁴	C₃²	1	1	yes	characteristic
9	C₂×C₃×3₋¹⁺²	C₃²	1	6	yes	—
10	C₂×C₃²×C₉	—	3	2	no	—
11	C₂×C₃²⋊C₉	—	3	2	no	—
12	C₂×C₃²⋊C₉	—	3	2	no	—
13	C₂×C₃²⋊C₉	—	3	2	no	—
14	C₂×C₃²⋊C₉	—	3	4	no	—
15	C₂×C₃²⋊C₉	C₃²	1	6	yes	—
16	C₃⁴	C₂×C₃²	1	1	yes	characteristic
17	C₃×3₋¹⁺²	C₂×C₃²	1	6	yes	—
18	C₃²×C₉	—	3	2	no	—
19	C₃²⋊C₉	—	3	2	no	—
20	C₃²⋊C₉	—	3	2	no	—
21	C₃²⋊C₉	—	3	2	no	—
22	C₃²⋊C₉	—	3	4	no	—
23	C₃²⋊C₉	C₂×C₃²	1	6	yes	—
24	C₂×C₃³	—	3	6	no	—
25	C₂×C₃³	—	9	2	no	—
26	C₂×C₃³	H(3,𝔽₃)	1	1	yes	characteristic
27	C₂×C₃³	H(3,𝔽₃)	1	2	yes	—
28	C₂×C₃³	C₃³	1	1	yes	characteristic
29	C₂×3₋¹⁺²	—	9	6	no	—
30	C₂×C₃×C₉	—	3	6	no	—
31	C₂×C₃×C₉	—	3	6	no	—
32	C₂×C₃×C₉	—	9	6	no	—
33	C₃³	—	3	6	no	—
34	C₃³	—	9	2	no	—
35	C₃³	C₂×H(3,𝔽₃)	1	1	yes	characteristic
36	C₃³	C₂×H(3,𝔽₃)	1	2	yes	—
37	C₃³	C₂×C₃³	1	1	yes	characteristic
38	3₋¹⁺²	—	9	6	no	—
39	C₃×C₉	—	3	6	no	—
40	C₃×C₉	—	3	6	no	—
41	C₃×C₉	—	9	6	no	—
42	C₂×C₃²	—	3	2	no	—
43	C₂×C₃²	—	3	2	no	—
44	C₂×C₃²	—	3	2	no	—
45	C₂×C₃²	—	3	2	no	—
46	C₂×C₃²	—	3	2	no	—
47	C₂×C₃²	—	3	2	no	—
48	C₂×C₃²	—	3	2	no	—
49	C₂×C₃²	—	9	9	no	—
50	C₂×C₃²	#733	1	6	yes	—
51	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
52	C₂×C₉	—	9	6	no	—
53	C₂×C₉	—	9	6	no	—
54	C₃²	—	3	2	no	—
55	C₃²	—	3	2	no	—
56	C₃²	—	3	2	no	—
57	C₃²	—	3	2	no	—
58	C₃²	—	3	2	no	—
59	C₃²	—	3	2	no	—
60	C₃²	—	3	2	no	—
61	C₃²	—	9	9	no	—
62	C₃²	C₂×#733	1	6	yes	—
63	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
64	C₉	—	9	6	no	—
65	C₉	—	9	6	no	—
66	C₂×C₃	—	3	6	no	—
67	C₂×C₃	—	9	1	no	—
68	C₂×C₃	—	9	1	no	—
69	C₂×C₃	C₃×#733	1	2	yes	—
70	C₂×C₃	#6909	1	2	yes	—
71	C₃	—	3	6	no	—
72	C₃	—	9	1	no	—
73	C₃	—	9	1	no	—
74	C₃	C₂×C₃×#733	1	2	yes	—
75	C₃	C₂×#6909	1	2	yes	—
76	C₂	#10624616	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×C₃⁴	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃⁴ ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624616	C₂	direct (N × H)
4. C₂×#6860	C₃	semidirect
7. #6860	C₂×C₃	semidirect
76. C₂	#10624616	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624616	2
C₂×#6891	3
C₂×C₃×C₃²⋊C₉	3
C₂×#6860	3

Subgroups — C2×#10624616 #13090102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624616 #13090102