Subgroups — C₂×#10624453 #13089939

Order 1458.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624453	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	C₂×C₃²⋊C₂₇	C₃	1	2	yes	maximal, complemented
5	C₃×C₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
7	C₃²⋊C₂₇	C₂×C₃	1	2	yes	complemented
8	C₂×C₃×H(3,𝔽₃)	C₉	1	1	yes	characteristic
9	C₂×C₃²×C₉	—	3	1	no	—
10	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
11	C₂×C₂₇⋊C₃	—	3	3	no	—
12	C₂×C₃×C₂₇	—	3	1	no	—
13	C₂×C₃×C₂₇	—	3	2	no	—
14	C₂×C₃²⋊C₉	—	3	2	no	—
15	C₂×C₃²⋊C₉	C₉	1	2	yes	—
16	C₃×H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic
17	C₃²×C₉	—	3	1	no	—
18	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
19	C₂₇⋊C₃	—	3	3	no	—
20	C₃×C₂₇	—	3	1	no	—
21	C₃×C₂₇	—	3	2	no	—
22	C₃²⋊C₉	—	3	2	no	—
23	C₃²⋊C₉	C₂×C₉	1	2	yes	—
24	C₂×C₃³	—	3	1	no	—
25	C₂×C₃³	C₃×C₉	1	1	yes	characteristic
26	C₂×H(3,𝔽₃)	—	3	3	no	—
27	C₂×C₃×C₉	—	3	1	no	—
28	C₂×C₃×C₉	—	3	1	no	—
29	C₂×C₃×C₉	—	3	1	no	—
30	C₂×C₃×C₉	—	3	2	no	—
31	C₂×C₃×C₉	—	9	1	no	—
32	C₂×C₃×C₉	—	9	1	no	—
33	C₂×C₃×C₉	—	9	1	no	—
34	C₂×C₃×C₉	H(3,𝔽₃)	1	1	yes	characteristic
35	C₂×C₃×C₉	3₋¹⁺²	1	2	yes	—
36	C₂×C₂₇	—	3	3	no	—
37	C₂×C₂₇	—	9	2	no	—
38	C₃³	—	3	1	no	—
39	C₃³	C₂×C₃×C₉	1	1	yes	characteristic
40	H(3,𝔽₃)	—	3	3	no	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	3	1	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	3	2	no	—
45	C₃×C₉	—	9	1	no	—
46	C₃×C₉	—	9	1	no	—
47	C₃×C₉	—	9	1	no	—
48	C₃×C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃×C₉	C₂×3₋¹⁺²	1	2	yes	—
50	C₂₇	—	3	3	no	—
51	C₂₇	—	9	2	no	—
52	C₂×C₃²	—	3	1	no	—
53	C₂×C₃²	—	3	3	no	—
54	C₂×C₃²	—	3	1	no	—
55	C₂×C₃²	—	3	1	no	—
56	C₂×C₃²	—	3	1	no	—
57	C₂×C₃²	—	9	1	no	—
58	C₂×C₃²	—	9	1	no	—
59	C₂×C₃²	—	9	1	no	—
60	C₂×C₃²	C₃²⋊C₉	1	1	yes	characteristic
61	C₂×C₉	—	3	2	no	—
62	C₂×C₉	—	9	2	no	—
63	C₂×C₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
64	C₂×C₉	#731	1	1	yes	characteristic
65	C₂×C₉	#732	1	1	yes	characteristic
66	C₃²	—	3	1	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	3	1	no	—
69	C₃²	—	3	1	no	—
70	C₃²	—	3	1	no	—
71	C₃²	—	9	1	no	—
72	C₃²	—	9	1	no	—
73	C₃²	—	9	1	no	—
74	C₃²	C₂×C₃²⋊C₉	1	1	yes	characteristic
75	C₉	—	3	2	no	—
76	C₉	—	9	2	no	—
77	C₉	C₂×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
78	C₉	C₂×#731	1	1	yes	characteristic
79	C₉	C₂×#732	1	1	yes	characteristic
80	C₂×C₃	—	9	1	no	—
81	C₂×C₃	—	9	3	no	—
82	C₂×C₃	#6869	1	1	yes	characteristic
83	C₂×C₃	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
84	C₂×C₃	#6872	1	1	yes	characteristic
85	C₂×C₃	#6873	1	1	yes	characteristic
86	C₃	—	9	1	no	—
87	C₃	—	9	3	no	—
88	C₃	C₂×#6869	1	1	yes	characteristic
89	C₃	C₂×H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
90	C₃	C₂×#6872	1	1	yes	characteristic
91	C₃	C₂×#6873	1	1	yes	characteristic
92	C₂	#10624453	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	C₂×C₃×C₉	H(3,𝔽₃)
commutator	C₃³	C₂×C₃×C₉
Frattini, cosocle	C₃²×C₉	C₂×C₃²
socle	C₂×C₃²	C₃²⋊C₉
prime radical	C₂×C₃×H(3,𝔽₃)	C₉
LCS	G ▷ C₃³ ▷ C₃² ▷ 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. #10624453	C₂	direct (N × H)
2. C₂×C₃×C₂₇⋊C₃	C₃	semidirect
4. C₂×C₃²⋊C₂₇	C₃	semidirect
5. C₃×C₂₇⋊C₃	C₂×C₃	semidirect
7. C₃²⋊C₂₇	C₂×C₃	semidirect
92. C₂	#10624453	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624453	2
C₂×C₃×C₂₇⋊C₃	3
C₂×C₉×H(3,𝔽₃)	3
C₂×C₃²⋊C₂₇	3

Subgroups — C2×#10624453 #13089939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624453 #13089939