Subgroups — C₂×#10624845 #13090331

Order 1458.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624845	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×#6908	C₃	1	3	yes	maximal, complemented
3	C₂×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#6883	C₃	1	3	yes	maximal, complemented
5	C₂×#6882	C₃	1	3	yes	maximal, complemented
6	C₂×#6881	C₃	1	3	yes	maximal, complemented
7	#6908	C₂×C₃	1	3	yes	complemented
8	#6887	C₂×C₃	1	1	yes	characteristic, complemented
9	#6883	C₂×C₃	1	3	yes	complemented
10	#6882	C₂×C₃	1	3	yes	complemented
11	#6881	C₂×C₃	1	3	yes	complemented
12	C₂×#737	—	3	3	no	—
13	C₂×C₃²×C₉	C₃²	1	1	yes	characteristic
14	C₂×#733	C₃²	1	3	yes	—
15	C₂×#733	C₃²	1	3	yes	—
16	C₂×#732	C₃²	1	3	yes	—
17	C₂×#731	—	3	3	no	—
18	C₂×AΣL(1,𝔽₂₇)	—	3	3	no	—
19	C₂×C₉⋊C₉	—	3	1	no	—
20	C₂×C₉⋊C₉	C₃²	1	3	yes	—
21	C₂×C₃²⋊C₉	—	3	1	no	—
22	C₂×C₉²	—	3	1	no	—
23	#737	—	3	3	no	—
24	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
25	#733	C₂×C₃²	1	3	yes	—
26	#733	C₂×C₃²	1	3	yes	—
27	#732	C₂×C₃²	1	3	yes	—
28	#731	—	3	3	no	—
29	AΣL(1,𝔽₂₇)	—	3	3	no	—
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	H(3,𝔽₃)	1	1	yes	characteristic
35	C₂×3₋¹⁺²	—	3	3	no	—
36	C₂×3₋¹⁺²	—	3	3	no	—
37	C₂×3₋¹⁺²	—	9	6	no	—
38	C₂×H(3,𝔽₃)	—	3	3	no	—
39	C₂×C₃×C₉	—	3	2	no	—
40	C₂×C₃×C₉	—	3	1	no	—
41	C₂×C₃×C₉	—	3	3	no	—
42	C₂×C₃×C₉	—	9	3	no	—
43	C₂×C₃×C₉	H(3,𝔽₃)	1	1	yes	characteristic
44	C₂×C₃×C₉	H(3,𝔽₃)	1	1	yes	characteristic
45	C₂×C₃×C₉	C₃³	1	1	yes	characteristic
46	C₃³	C₂×H(3,𝔽₃)	1	1	yes	characteristic
47	3₋¹⁺²	—	3	3	no	—
48	3₋¹⁺²	—	3	3	no	—
49	3₋¹⁺²	—	9	6	no	—
50	H(3,𝔽₃)	—	3	3	no	—
51	C₃×C₉	—	3	2	no	—
52	C₃×C₉	—	3	1	no	—
53	C₃×C₉	—	3	3	no	—
54	C₃×C₉	—	9	3	no	—
55	C₃×C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic
56	C₃×C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic
57	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
58	C₂×C₃²	—	3	1	no	—
59	C₂×C₃²	—	9	1	no	—
60	C₂×C₃²	—	9	3	no	—
61	C₂×C₃²	C₃×H(3,𝔽₃)	1	1	yes	characteristic
62	C₂×C₉	—	3	1	no	—
63	C₂×C₉	—	3	1	no	—
64	C₂×C₉	—	9	3	no	—
65	C₂×C₉	—	9	3	no	—
66	C₂×C₉	—	9	3	no	—
67	C₂×C₉	#732	1	2	yes	—
68	C₂×C₉	#732	1	1	yes	characteristic
69	C₃²	—	3	1	no	—
70	C₃²	—	9	1	no	—
71	C₃²	—	9	3	no	—
72	C₃²	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
73	C₉	—	3	1	no	—
74	C₉	—	3	1	no	—
75	C₉	—	9	3	no	—
76	C₉	—	9	3	no	—
77	C₉	—	9	3	no	—
78	C₉	C₂×#732	1	2	yes	—
79	C₉	C₂×#732	1	1	yes	characteristic
80	C₂×C₃	—	3	1	no	—
81	C₂×C₃	—	9	1	no	—
82	C₂×C₃	—	27	3	no	—
83	C₂×C₃	C₃×#732	1	1	yes	characteristic
84	C₃	—	3	1	no	—
85	C₃	—	9	1	no	—
86	C₃	—	27	3	no	—
87	C₃	C₂×C₃×#732	1	1	yes	characteristic
88	C₂	#10624845	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	C₂×C₉	#732
commutator, Frattini, cosocle	C₃×C₉	C₂×C₃³
socle	C₂×C₃	C₃×#732
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₃×C₉ ◁ C₂×C₃²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624845	C₂	direct (N × H)
2. C₂×#6908	C₃	semidirect
3. C₂×#6887	C₃	semidirect
4. C₂×#6883	C₃	semidirect
5. C₂×#6882	C₃	semidirect
6. C₂×#6881	C₃	semidirect
7. #6908	C₂×C₃	semidirect
8. #6887	C₂×C₃	semidirect
9. #6883	C₂×C₃	semidirect
10. #6882	C₂×C₃	semidirect
11. #6881	C₂×C₃	semidirect
88. C₂	#10624845	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624845	2
C₂×#6908	3
C₂×#6887	3
C₂×#6883	3
C₂×#6882	3
C₂×#6881	3

Subgroups — C2×#10624845 #13090331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624845 #13090331