Subgroups — C₂×#10624444 #13089930

Order 1458.

316 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624444	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃³×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₃²⋊C₂₇	C₃	1	3	yes	maximal, complemented
4	C₃³×C₉	C₂×C₃	1	1	yes	characteristic
5	C₃²⋊C₂₇	C₂×C₃	1	3	yes	complemented
6	C₂×C₃⁴	C₉	1	1	yes	characteristic
7	C₂×C₃²×C₉	—	3	1	no	—
8	C₂×C₃²×C₉	—	3	2	no	—
9	C₂×C₃²×C₉	—	3	9	no	—
10	C₂×C₃²×C₉	C₉	1	2	yes	—
11	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
12	C₂×C₃×C₂₇	—	3	3	no	—
13	C₃⁴	C₂×C₉	1	1	yes	characteristic
14	C₃²×C₉	—	3	1	no	—
15	C₃²×C₉	—	3	2	no	—
16	C₃²×C₉	—	3	9	no	—
17	C₃²×C₉	C₂×C₉	1	2	yes	—
18	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
19	C₃×C₂₇	—	3	3	no	—
20	C₂×C₃³	—	3	1	no	—
21	C₂×C₃³	—	3	2	no	—
22	C₂×C₃³	—	3	3	no	—
23	C₂×C₃³	—	3	6	no	—
24	C₂×C₃³	C₂₇	1	3	yes	complemented
25	C₂×C₃³	C₃×C₉	1	1	yes	characteristic
26	C₂×C₃×C₉	—	3	18	no	—
27	C₂×C₃×C₉	—	3	2	no	—
28	C₂×C₃×C₉	—	3	9	no	—
29	C₂×C₃×C₉	—	3	3	no	—
30	C₂×C₃×C₉	—	3	6	no	—
31	C₂×C₃×C₉	H(3,𝔽₃)	1	1	yes	characteristic
32	C₂×C₃×C₉	3₋¹⁺²	1	2	yes	—
33	C₂×C₂₇	—	9	3	no	—
34	C₃³	—	3	3	no	—
35	C₃³	—	3	6	no	—
36	C₃³	—	3	1	no	—
37	C₃³	—	3	2	no	—
38	C₃³	C₂×C₂₇	1	3	yes	complemented
39	C₃³	C₂×C₃×C₉	1	1	yes	characteristic
40	C₃×C₉	—	3	18	no	—
41	C₃×C₉	—	3	2	no	—
42	C₃×C₉	—	3	9	no	—
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	—	3	6	no	—
45	C₃×C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic
46	C₃×C₉	C₂×3₋¹⁺²	1	2	yes	—
47	C₂₇	—	9	3	no	—
48	C₂×C₃²	—	3	18	no	—
49	C₂×C₃²	—	3	3	no	—
50	C₂×C₃²	—	3	3	no	—
51	C₂×C₃²	—	3	1	no	—
52	C₂×C₃²	—	3	6	no	—
53	C₂×C₃²	—	3	2	no	—
54	C₂×C₃²	—	3	9	no	—
55	C₂×C₃²	C₃²⋊C₉	1	1	yes	characteristic
56	C₂×C₃²	C₃×C₂₇	1	1	yes	characteristic
57	C₂×C₃²	C₂₇⋊C₃	1	2	yes	—
58	C₂×C₉	—	3	6	no	—
59	C₂×C₉	—	3	2	no	—
60	C₂×C₉	AΣL(1,𝔽₂₇)	1	3	yes	—
61	C₃²	—	3	9	no	—
62	C₃²	—	3	18	no	—
63	C₃²	—	3	3	no	—
64	C₃²	—	3	3	no	—
65	C₃²	—	3	1	no	—
66	C₃²	—	3	6	no	—
67	C₃²	—	3	2	no	—
68	C₃²	C₂×C₃²⋊C₉	1	1	yes	characteristic
69	C₃²	C₂×C₃×C₂₇	1	1	yes	characteristic
70	C₃²	C₂×C₂₇⋊C₃	1	2	yes	—
71	C₉	—	3	6	no	—
72	C₉	—	3	2	no	—
73	C₉	C₂×AΣL(1,𝔽₂₇)	1	3	yes	—
74	C₂×C₃	—	3	9	no	—
75	C₂×C₃	—	3	1	no	—
76	C₂×C₃	—	3	2	no	—
77	C₂×C₃	C₃²⋊C₂₇	1	1	yes	characteristic
78	C₂×C₃	#6866	1	1	yes	characteristic
79	C₂×C₃	#6869	1	2	yes	—
80	C₃	—	3	9	no	—
81	C₃	—	3	1	no	—
82	C₃	—	3	2	no	—
83	C₃	C₂×C₃²⋊C₂₇	1	1	yes	characteristic
84	C₃	C₂×#6866	1	1	yes	characteristic
85	C₃	C₂×#6869	1	2	yes	—
86	C₂	#10624444	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	C₂×C₃×C₉	H(3,𝔽₃)
commutator	C₃²	C₂×C₃×C₂₇
Frattini, cosocle	C₃²×C₉	C₂×C₃²
socle	C₂×C₃²	C₃²⋊C₉
prime radical	C₂×C₃⁴	C₉
LCS	G ▷ C₃² ▷ C₃ ▷ 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. #10624444	C₂	direct (N × H)
3. C₂×C₃²⋊C₂₇	C₃	semidirect
5. C₃²⋊C₂₇	C₂×C₃	semidirect
24. C₂×C₃³	C₂₇	semidirect
38. C₃³	C₂×C₂₇	semidirect
86. C₂	#10624444	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624444	2
C₂×C₃³×C₉	3
C₂×C₃²⋊C₂₇	3

Subgroups — C2×#10624444 #13089930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624444 #13089930