Subgroups — C₂×#10624894 #13090380

Order 1458.

1148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624894	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×#737	C₃	1	3	yes	maximal, complemented
3	C₂×C₃²×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	C₂×#6893	C₃	1	24	yes	maximal, complemented
5	C₂×#6891	C₃	1	8	yes	maximal, complemented
6	C₂×C₃×C₃²⋊C₉	C₃	1	4	yes	maximal, complemented
7	C₃×#737	C₂×C₃	1	3	yes	complemented
8	C₃²×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
9	#6893	C₂×C₃	1	24	yes	complemented
10	#6891	C₂×C₃	1	8	yes	complemented
11	C₃×C₃²⋊C₉	C₂×C₃	1	4	yes	complemented
12	C₂×C₃⁴	C₃²	1	4	yes	—
13	C₂×#737	—	3	27	no	—
14	C₂×C₃×3₋¹⁺²	C₃²	1	24	yes	complemented
15	C₂×C₃×H(3,𝔽₃)	—	3	9	no	—
16	C₂×C₃×H(3,𝔽₃)	C₃²	1	8	yes	—
17	C₂×C₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
18	C₂×C₃²×C₉	C₃²	1	12	yes	complemented
19	C₂×C₃²⋊C₉	C₃²	1	1	yes	characteristic
20	C₂×C₃²⋊C₉	C₃²	1	8	yes	—
21	C₂×C₃²⋊C₉	C₃²	1	24	yes	complemented
22	C₂×C₃²⋊C₉	C₃²	1	48	yes	complemented
23	C₃⁴	C₂×C₃²	1	4	yes	—
24	#737	—	3	27	no	—
25	C₃×3₋¹⁺²	C₂×C₃²	1	24	yes	complemented
26	C₃×H(3,𝔽₃)	—	3	9	no	—
27	C₃×H(3,𝔽₃)	C₂×C₃²	1	8	yes	—
28	C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
29	C₃²×C₉	C₂×C₃²	1	12	yes	complemented
30	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
31	C₃²⋊C₉	C₂×C₃²	1	8	yes	—
32	C₃²⋊C₉	C₂×C₃²	1	24	yes	complemented
33	C₃²⋊C₉	C₂×C₃²	1	48	yes	complemented
34	C₂×C₃³	—	3	12	no	—
35	C₂×C₃³	—	3	12	no	—
36	C₂×C₃³	—	9	8	no	—
37	C₂×C₃³	C₃³	1	8	yes	—
38	C₂×C₃³	C₃³	1	4	yes	—
39	C₂×C₃³	C₃³	1	1	yes	characteristic
40	C₂×3₋¹⁺²	—	3	72	no	—
41	C₂×H(3,𝔽₃)	—	3	24	no	—
42	C₂×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
43	C₂×C₃×C₉	—	3	36	no	—
44	C₂×C₃×C₉	C₃³	1	3	yes	—
45	C₂×C₃×C₉	C₃³	1	24	yes	—
46	C₃³	—	3	12	no	—
47	C₃³	—	3	12	no	—
48	C₃³	—	9	8	no	—
49	C₃³	C₂×C₃³	1	8	yes	—
50	C₃³	C₂×C₃³	1	4	yes	—
51	C₃³	C₂×C₃³	1	1	yes	characteristic
52	3₋¹⁺²	—	3	72	no	—
53	H(3,𝔽₃)	—	3	24	no	—
54	H(3,𝔽₃)	C₂×H(3,𝔽₃)	1	9	yes	—
55	C₃×C₉	—	3	36	no	—
56	C₃×C₉	C₂×C₃³	1	3	yes	—
57	C₃×C₉	C₂×C₃³	1	24	yes	—
58	C₂×C₃²	—	3	1	no	—
59	C₂×C₃²	—	3	4	no	—
60	C₂×C₃²	—	3	2	no	—
61	C₂×C₃²	—	3	8	no	—
62	C₂×C₃²	—	3	8	no	—
63	C₂×C₃²	—	3	8	no	—
64	C₂×C₃²	—	3	16	no	—
65	C₂×C₃²	—	9	36	no	—
66	C₂×C₃²	C₃×H(3,𝔽₃)	1	12	yes	—
67	C₂×C₃²	#737	1	3	yes	complemented
68	C₂×C₃²	C₃⁴	1	1	yes	characteristic
69	C₂×C₉	—	3	3	no	—
70	C₂×C₉	—	3	24	no	—
71	C₃²	—	3	1	no	—
72	C₃²	—	3	4	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	3	8	no	—
75	C₃²	—	3	8	no	—
76	C₃²	—	3	8	no	—
77	C₃²	—	3	16	no	—
78	C₃²	—	9	36	no	—
79	C₃²	C₂×C₃×H(3,𝔽₃)	1	12	yes	—
80	C₃²	C₂×#737	1	3	yes	complemented
81	C₃²	C₂×C₃⁴	1	1	yes	characteristic
82	C₉	—	3	3	no	—
83	C₉	—	3	24	no	—
84	C₂×C₃	—	3	3	no	—
85	C₂×C₃	—	3	12	no	—
86	C₂×C₃	—	9	8	no	—
87	C₂×C₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
88	C₂×C₃	C₃×#737	1	1	yes	characteristic
89	C₂×C₃	3₋¹⁺⁴	1	2	yes	—
90	C₃	—	3	3	no	—
91	C₃	—	3	12	no	—
92	C₃	—	9	8	no	—
93	C₃	C₂×C₃²×H(3,𝔽₃)	1	1	yes	characteristic
94	C₃	C₂×C₃×#737	1	1	yes	characteristic
95	C₃	C₂×3₋¹⁺⁴	1	2	yes	—
96	C₂	#10624894	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃²	C₃⁴
commutator, Frattini, cosocle	C₃²	C₂×C₃⁴
prime radical	C₂×C₃²×H(3,𝔽₃)	C₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. #10624894	C₂	direct (N × H)
2. C₂×C₃×#737	C₃	semidirect
4. C₂×#6893	C₃	semidirect
5. C₂×#6891	C₃	semidirect
6. C₂×C₃×C₃²⋊C₉	C₃	semidirect
7. C₃×#737	C₂×C₃	semidirect
9. #6893	C₂×C₃	semidirect
10. #6891	C₂×C₃	semidirect
11. C₃×C₃²⋊C₉	C₂×C₃	semidirect
14. C₂×C₃×3₋¹⁺²	C₃²	semidirect
18. C₂×C₃²×C₉	C₃²	semidirect
21. C₂×C₃²⋊C₉	C₃²	semidirect
22. C₂×C₃²⋊C₉	C₃²	semidirect
25. C₃×3₋¹⁺²	C₂×C₃²	semidirect
29. C₃²×C₉	C₂×C₃²	semidirect
32. C₃²⋊C₉	C₂×C₃²	semidirect
33. C₃²⋊C₉	C₂×C₃²	semidirect
67. C₂×C₃²	#737	semidirect
80. C₃²	C₂×#737	semidirect
96. C₂	#10624894	direct (N × H)

Maximal subgroups

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

subgroup	index
#10624894	2
C₂×C₃×#737	3
C₂×C₃²×H(3,𝔽₃)	3
C₂×#6893	3
C₂×#6891	3
C₂×C₃×C₃²⋊C₉	3

Subgroups — C2×#10624894 #13090380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10624894 #13090380