Subgroups — C₂×#11757761 #14518347

Order 1944.

372 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757761	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₃×C₉⋊A₄	C₃	1	4	yes	maximal
3	C₂³×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉⋊(C₂²⋊C₉)	C₃	1	8	yes	maximal, complemented
5	C₂×#6900	—	4	1	no	maximal
6	C₃×C₉⋊A₄	C₂×C₃	1	4	yes	—
7	C₂²×C₉²	—	3	1	no	—
8	C₂²×C₉²	—	3	1	no	—
9	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
10	C₉⋊(C₂²⋊C₉)	C₂×C₃	1	8	yes	complemented
11	#6900	—	4	1	no	Sylow
12	C₂×C₃²×A₄	C₃²	1	1	yes	characteristic
13	C₂³×C₃×C₉	C₃²	1	4	yes	—
14	C₂×C₃×C₂²⋊C₉	C₃²	1	8	yes	—
15	C₂×C₉⋊A₄	—	3	12	no	—
16	C₂×C₃×3₋¹⁺²	—	4	4	no	—
17	C₂×C₉⋊C₉	—	4	8	no	—
18	C₂×C₉²	—	3	1	no	—
19	C₂×C₉²	—	3	1	no	—
20	C₂×C₉²	A₄	1	1	yes	characteristic, complemented
21	C₃²×A₄	C₂×C₃²	1	1	yes	characteristic
22	C₂²×C₃×C₉	—	3	4	no	—
23	C₂²×C₃×C₉	—	3	4	no	—
24	C₂²×C₃×C₉	C₂×C₃²	1	4	yes	—
25	C₃×C₂²⋊C₉	C₂×C₃²	1	8	yes	—
26	C₉⋊A₄	—	3	12	no	—
27	C₃×3₋¹⁺²	—	4	4	no	—
28	C₉⋊C₉	—	4	8	no	—
29	C₉²	C₂×A₄	1	1	yes	characteristic, complemented
30	C₂³×C₃²	C₃³	1	1	yes	characteristic
31	C₂×C₃×A₄	—	3	4	no	—
32	C₂³×C₉	3₋¹⁺²	1	12	yes	complemented
33	C₂×C₂²⋊C₉	—	3	8	no	—
34	C₂×C₃³	—	4	1	no	—
35	C₂×3₋¹⁺²	—	12	12	no	—
36	C₂×C₃×C₉	—	3	4	no	—
37	C₂×C₃×C₉	—	3	4	no	—
38	C₂×C₃×C₉	—	4	8	no	—
39	C₂×C₃×C₉	C₃×A₄	1	4	yes	—
40	C₂²×C₃²	—	3	1	no	—
41	C₂²×C₃²	—	3	1	no	—
42	C₂²×C₃²	C₂×C₃³	1	1	yes	characteristic
43	C₃×A₄	—	3	4	no	—
44	C₂²×C₉	—	3	12	no	—
45	C₂²×C₉	—	3	12	no	—
46	C₂²×C₉	C₂×3₋¹⁺²	1	12	yes	complemented
47	C₂²⋊C₉	—	3	8	no	—
48	C₃³	—	4	1	no	—
49	3₋¹⁺²	—	12	12	no	—
50	C₃×C₉	—	4	8	no	—
51	C₃×C₉	C₂×C₃×A₄	1	4	yes	—
52	C₂³×C₃	C₃×3₋¹⁺²	1	4	yes	—
53	C₂×A₄	—	9	1	no	—
54	C₂×C₃²	—	3	1	no	—
55	C₂×C₃²	—	3	1	no	—
56	C₂×C₃²	—	12	4	no	—
57	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
58	C₂×C₉	—	3	12	no	—
59	C₂×C₉	—	3	12	no	—
60	C₂×C₉	—	12	8	no	—
61	C₂×C₉	C₉⋊A₄	1	12	yes	complemented
62	C₂²×C₃	—	3	4	no	—
63	C₂²×C₃	—	3	4	no	—
64	C₂²×C₃	C₂×C₃×3₋¹⁺²	1	4	yes	—
65	A₄	—	9	1	no	—
66	C₃²	—	12	4	no	—
67	C₃²	C₂×C₃²×A₄	1	1	yes	characteristic
68	C₉	—	12	8	no	—
69	C₉	C₂×C₉⋊A₄	1	12	yes	complemented
70	C₂³	#6900	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	3	4	no	—
72	C₂×C₃	—	3	4	no	—
73	C₂×C₃	—	36	1	no	—
74	C₂×C₃	C₃×C₉⋊A₄	1	4	yes	—
75	C₂²	—	3	1	no	—
76	C₂²	—	3	1	no	—
77	C₂²	C₂×#6900	1	1	yes	characteristic, complemented
78	C₃	—	36	1	no	—
79	C₃	C₂×C₃×C₉⋊A₄	1	4	yes	—
80	C₂	—	3	1	no	—
81	C₂	—	3	1	no	—
82	C₂	#11757761	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center	C₂×C₃²	C₃²×A₄
commutator, cosocle	C₂²×C₃²	C₂×C₃³
Frattini	C₃²	C₂×C₃²×A₄
Fitting	C₂³×C₉²	C₃
socle	C₂³×C₃²	C₃³
prime radical	C₂×C₃²×A₄	C₃²
hypercenter	C₂×C₉²	A₄
hypocenter	C₂²	C₂×#6900
LCS	G ▷ C₂²×C₃² ▷ C₂²
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₉²

Complements

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

N	H ≅ G/N	type
1. #11757761	C₂	direct (N × H)
3. C₂³×C₉²	C₃	semidirect
4. C₂×C₉⋊(C₂²⋊C₉)	C₃	semidirect
9. C₂²×C₉²	C₂×C₃	semidirect
10. C₉⋊(C₂²⋊C₉)	C₂×C₃	semidirect
20. C₂×C₉²	A₄	semidirect
29. C₉²	C₂×A₄	semidirect
32. C₂³×C₉	3₋¹⁺²	semidirect
46. C₂²×C₉	C₂×3₋¹⁺²	semidirect
61. C₂×C₉	C₉⋊A₄	semidirect
69. C₉	C₂×C₉⋊A₄	semidirect
70. C₂³	#6900	semidirect
77. C₂²	C₂×#6900	semidirect
82. C₂	#11757761	direct (N × H)

Maximal subgroups

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

subgroup	index
#11757761	2
C₂×C₃×C₉⋊A₄	3
C₂³×C₉²	3
C₂×C₉⋊(C₂²⋊C₉)	3
C₂×#6900	4

Subgroups — C2×#11757761 #14518347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11757761 #14518347