Subgroups — C₂×#11757765 #14518351

Order 1944.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757765	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₃×A₄)⋊C₉	C₃	1	4	yes	maximal
4	C₂×(C₂²⋊C₉)⋊C₉	C₃	1	8	yes	maximal, complemented
5	C₂×#6897	—	4	1	no	maximal
6	C₂²×C₉²	—	3	1	no	—
7	C₂²×C₉²	—	3	1	no	—
8	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
9	(C₃×A₄)⋊C₉	C₂×C₃	1	4	yes	—
10	(C₂²⋊C₉)⋊C₉	C₂×C₃	1	8	yes	complemented
11	#6897	—	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⋊C₉	—	4	8	no	—
16	C₂×C₃²⋊C₉	—	4	4	no	—
17	C₂×C₉²	—	3	1	no	—
18	C₂×C₉²	—	3	1	no	—
19	C₂×C₉²	A₄	1	1	yes	characteristic, complemented
20	C₃²×A₄	C₂×C₃²	1	1	yes	characteristic
21	C₂²×C₃×C₉	—	3	4	no	—
22	C₂²×C₃×C₉	—	3	4	no	—
23	C₂²×C₃×C₉	C₂×C₃²	1	4	yes	—
24	C₃×C₂²⋊C₉	C₂×C₃²	1	8	yes	—
25	C₉⋊C₉	—	4	8	no	—
26	C₃²⋊C₉	—	4	4	no	—
27	C₉²	C₂×A₄	1	1	yes	characteristic, complemented
28	C₂³×C₃²	C₃³	1	1	yes	characteristic
29	C₂×C₃×A₄	—	3	4	no	—
30	C₂³×C₉	—	3	4	no	—
31	C₂×C₂²⋊C₉	—	3	8	no	—
32	C₂×C₃³	—	4	1	no	—
33	C₂×C₃×C₉	—	3	4	no	—
34	C₂×C₃×C₉	—	3	4	no	—
35	C₂×C₃×C₉	—	4	8	no	—
36	C₂×C₃×C₉	C₃×A₄	1	4	yes	—
37	C₂²×C₃²	—	3	1	no	—
38	C₂²×C₃²	—	3	1	no	—
39	C₂²×C₃²	C₂×C₃³	1	1	yes	characteristic
40	C₃×A₄	—	3	4	no	—
41	C₂²×C₉	—	3	12	no	—
42	C₂²×C₉	—	3	12	no	—
43	C₂²×C₉	—	3	4	no	—
44	C₂²⋊C₉	—	3	8	no	—
45	C₃³	—	4	1	no	—
46	C₃×C₉	—	4	8	no	—
47	C₃×C₉	C₂×C₃×A₄	1	4	yes	—
48	C₂³×C₃	#737	1	4	yes	—
49	C₂×A₄	—	9	1	no	—
50	C₂×C₃²	—	3	1	no	—
51	C₂×C₃²	—	3	1	no	—
52	C₂×C₃²	—	12	4	no	—
53	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
54	C₂×C₉	—	3	12	no	—
55	C₂×C₉	—	3	12	no	—
56	C₂×C₉	—	3	4	no	—
57	C₂×C₉	—	12	8	no	—
58	C₂²×C₃	—	3	4	no	—
59	C₂²×C₃	—	3	4	no	—
60	C₂²×C₃	C₂×#737	1	4	yes	—
61	A₄	—	9	1	no	—
62	C₃²	—	12	4	no	—
63	C₃²	C₂×C₃²×A₄	1	1	yes	characteristic
64	C₉	—	3	4	no	—
65	C₉	—	12	8	no	—
66	C₂³	#6897	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃	—	3	4	no	—
68	C₂×C₃	—	3	4	no	—
69	C₂×C₃	—	36	1	no	—
70	C₂×C₃	#66436	1	4	yes	—
71	C₂²	—	3	1	no	—
72	C₂²	—	3	1	no	—
73	C₂²	C₂×#6897	1	1	yes	characteristic, complemented
74	C₃	—	36	1	no	—
75	C₃	C₂×#66436	1	4	yes	—
76	C₂	—	3	1	no	—
77	C₂	—	3	1	no	—
78	C₂	#11757765	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×#6897
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. #11757765	C₂	direct (N × H)
2. C₂³×C₉²	C₃	semidirect
4. C₂×(C₂²⋊C₉)⋊C₉	C₃	semidirect
8. C₂²×C₉²	C₂×C₃	semidirect
10. (C₂²⋊C₉)⋊C₉	C₂×C₃	semidirect
19. C₂×C₉²	A₄	semidirect
27. C₉²	C₂×A₄	semidirect
66. C₂³	#6897	semidirect
73. C₂²	C₂×#6897	semidirect
78. C₂	#11757765	direct (N × H)

Maximal subgroups

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

subgroup	index
#11757765	2
C₂³×C₉²	3
C₂×(C₃×A₄)⋊C₉	3
C₂×(C₂²⋊C₉)⋊C₉	3
C₂×#6897	4

Subgroups — C2×#11757765 #14518351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11757765 #14518351