Subgroups — C₂×#10624828 #13090314

Order 1458.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624828	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×#6875	C₃	1	9	yes	maximal, complemented
4	C₂×#6869	C₃	1	3	yes	maximal
5	C₃×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic
6	#6875	C₂×C₃	1	9	yes	complemented
7	#6869	C₂×C₃	1	3	yes	—
8	C₂×C₃²×C₉	—	3	1	no	—
9	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
10	C₂×C₂₇⋊C₃	C₃²	1	9	yes	—
11	C₂×C₉⋊C₉	—	3	2	no	—
12	C₂×C₉⋊C₉	C₃²	1	3	yes	—
13	C₃²×C₉	—	3	1	no	—
14	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
15	C₂₇⋊C₃	C₂×C₃²	1	9	yes	—
16	C₉⋊C₉	—	3	2	no	—
17	C₉⋊C₉	C₂×C₃²	1	3	yes	—
18	C₂×C₃³	3₋¹⁺²	1	1	yes	characteristic
19	C₂×C₃×C₉	—	3	3	no	—
20	C₂×C₃×C₉	—	3	3	no	—
21	C₂×C₃×C₉	—	9	3	no	—
22	C₂×C₃×C₉	3₋¹⁺²	1	2	yes	—
23	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
24	C₂×C₂₇	—	3	9	no	—
25	C₃³	C₂×3₋¹⁺²	1	1	yes	characteristic
26	C₃×C₉	—	3	3	no	—
27	C₃×C₉	—	3	3	no	—
28	C₃×C₉	—	9	3	no	—
29	C₃×C₉	C₂×3₋¹⁺²	1	2	yes	—
30	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
31	C₂₇	—	3	9	no	—
32	C₂×C₃²	—	3	1	no	—
33	C₂×C₃²	—	3	3	no	—
34	C₂×C₃²	C₃×3₋¹⁺²	1	1	yes	characteristic
35	C₂×C₉	—	3	2	no	—
36	C₂×C₉	—	9	3	no	—
37	C₂×C₉	#737	1	3	yes	—
38	C₃²	—	3	3	no	—
39	C₃²	—	3	1	no	—
40	C₃²	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
41	C₉	—	3	2	no	—
42	C₉	—	9	3	no	—
43	C₉	C₂×#737	1	3	yes	—
44	C₂×C₃	—	3	1	no	—
45	C₂×C₃	—	3	3	no	—
46	C₂×C₃	#6895	1	1	yes	characteristic
47	C₃	—	3	1	no	—
48	C₃	—	3	3	no	—
49	C₃	C₂×#6895	1	1	yes	characteristic
50	C₂	#10624828	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃	#6895
commutator, Frattini, cosocle	C₃×C₉	C₂×C₃³
prime radical	C₂×C₃³	3₋¹⁺²
LCS	G ▷ C₃×C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624828	C₂	direct (N × H)
3. C₂×#6875	C₃	semidirect
6. #6875	C₂×C₃	semidirect
50. C₂	#10624828	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624828	2
C₂×C₃×C₉⋊C₉	3
C₂×#6875	3
C₂×#6869	3

Subgroups — C2×#10624828 #13090314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624828 #13090314