Subgroups — C₂×#10624709 #13090195

Order 1458.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624709	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×C₂₇⋊C₃	C₃	1	2	yes	maximal
3	C₂×C₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₂×#6887	C₃	1	1	yes	maximal, characteristic
5	C₂×#6875	C₃	1	9	yes	maximal, complemented
6	C₃×C₂₇⋊C₃	C₂×C₃	1	2	yes	—
7	C₃×C₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic
8	#6887	C₂×C₃	1	1	yes	characteristic
9	#6875	C₂×C₃	1	9	yes	complemented
10	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
11	C₂×C₂₇⋊C₃	—	3	2	no	—
12	C₂×C₂₇⋊C₃	—	3	2	no	—
13	C₂×C₂₇⋊C₃	C₉	1	6	yes	complemented
14	C₂×C₂₇⋊C₃	C₃²	1	6	yes	—
15	C₂×C₂₇⋊C₃	C₃²	1	3	yes	—
16	C₂×C₃×C₂₇	—	3	2	no	—
17	C₂×C₃×C₂₇	C₉	1	3	yes	complemented
18	C₂×C₉⋊C₉	—	3	1	no	—
19	C₂×C₉⋊C₉	C₃²	1	3	yes	—
20	C₂×C₃²⋊C₉	—	3	1	no	—
21	C₂×C₉²	—	3	1	no	—
22	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
23	C₂₇⋊C₃	—	3	2	no	—
24	C₂₇⋊C₃	—	3	2	no	—
25	C₂₇⋊C₃	C₂×C₉	1	6	yes	complemented
26	C₂₇⋊C₃	C₂×C₃²	1	6	yes	—
27	C₂₇⋊C₃	C₂×C₃²	1	3	yes	—
28	C₃×C₂₇	—	3	2	no	—
29	C₃×C₂₇	C₂×C₉	1	3	yes	complemented
30	C₉⋊C₉	—	3	1	no	—
31	C₉⋊C₉	C₂×C₃²	1	3	yes	—
32	C₃²⋊C₉	—	3	1	no	—
33	C₉²	—	3	1	no	—
34	C₂×C₃³	3₋¹⁺²	1	1	yes	characteristic
35	C₂×C₃×C₉	—	3	3	no	—
36	C₂×C₃×C₉	C₃×C₉	1	2	yes	—
37	C₂×C₃×C₉	C₃×C₉	1	1	yes	characteristic
38	C₂×C₃×C₉	3₋¹⁺²	1	1	yes	characteristic
39	C₂×C₃×C₉	3₋¹⁺²	1	1	yes	characteristic
40	C₂×C₃×C₉	3₋¹⁺²	1	2	yes	—
41	C₂×C₃×C₉	3₋¹⁺²	1	2	yes	—
42	C₂×C₃×C₉	3₋¹⁺²	1	2	yes	—
43	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
44	C₂×C₂₇	—	3	6	no	—
45	C₂×C₂₇	C₃×C₉	1	9	yes	—
46	C₃³	C₂×3₋¹⁺²	1	1	yes	characteristic
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	C₂×C₃×C₉	1	1	yes	characteristic
49	C₃×C₉	C₂×C₃×C₉	1	2	yes	—
50	C₃×C₉	C₂×3₋¹⁺²	1	1	yes	characteristic
51	C₃×C₉	C₂×3₋¹⁺²	1	1	yes	characteristic
52	C₃×C₉	C₂×3₋¹⁺²	1	2	yes	—
53	C₃×C₉	C₂×3₋¹⁺²	1	2	yes	—
54	C₃×C₉	C₂×3₋¹⁺²	1	2	yes	—
55	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
56	C₂₇	—	3	6	no	—
57	C₂₇	C₂×C₃×C₉	1	9	yes	—
58	C₂×C₃²	—	9	1	no	—
59	C₂×C₃²	C₉⋊C₉	1	2	yes	—
60	C₂×C₃²	C₉⋊C₉	1	1	yes	characteristic
61	C₂×C₃²	C₃×3₋¹⁺²	1	1	yes	characteristic
62	C₂×C₉	—	9	3	no	—
63	C₂×C₉	C₉⋊C₉	1	2	yes	—
64	C₂×C₉	C₉⋊C₉	1	2	yes	—
65	C₂×C₉	C₉⋊C₉	1	1	yes	characteristic
66	C₂×C₉	C₉⋊C₉	1	1	yes	characteristic
67	C₂×C₉	C₃²×C₉	1	1	yes	characteristic
68	C₂×C₉	C₃×3₋¹⁺²	1	2	yes	—
69	C₃²	—	9	1	no	—
70	C₃²	C₂×C₉⋊C₉	1	1	yes	characteristic
71	C₃²	C₂×C₉⋊C₉	1	2	yes	—
72	C₃²	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
73	C₉	—	9	3	no	—
74	C₉	C₂×C₉⋊C₉	1	1	yes	characteristic
75	C₉	C₂×C₉⋊C₉	1	2	yes	—
76	C₉	C₂×C₉⋊C₉	1	2	yes	—
77	C₉	C₂×C₉⋊C₉	1	1	yes	characteristic
78	C₉	C₂×C₃²×C₉	1	1	yes	characteristic
79	C₉	C₂×C₃×3₋¹⁺²	1	2	yes	—
80	C₂×C₃	—	3	1	no	—
81	C₂×C₃	—	3	2	no	—
82	C₂×C₃	—	3	1	no	—
83	C₂×C₃	C₃×C₉⋊C₉	1	1	yes	characteristic
84	C₃	—	3	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	2	no	—
87	C₃	C₂×C₃×C₉⋊C₉	1	1	yes	characteristic
88	C₂	#10624709	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	C₂×C₉	C₉⋊C₉
commutator	C₉	C₂×C₃²×C₉
Frattini, cosocle	C₃×C₉	C₂×C₃³
socle	C₂×C₃	C₃×C₉⋊C₉
prime radical	C₂×C₃³	3₋¹⁺²
LCS	G ▷ C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₃²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624709	C₂	direct (N × H)
5. C₂×#6875	C₃	semidirect
9. #6875	C₂×C₃	semidirect
13. C₂×C₂₇⋊C₃	C₉	semidirect
17. C₂×C₃×C₂₇	C₉	semidirect
25. C₂₇⋊C₃	C₂×C₉	semidirect
29. C₃×C₂₇	C₂×C₉	semidirect
88. C₂	#10624709	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624709	2
C₂×C₃×C₂₇⋊C₃	3
C₂×#6887	3
C₂×#6875	3

Subgroups — C2×#10624709 #13090195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624709 #13090195