Subgroups — C₂×#11757420 #14516592

Order 1944.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757420	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×#66359	C₃	1	3	yes	maximal
4	C₂×#6882	—	4	1	no	maximal
5	C₂²×C₉⋊C₉	—	3	1	no	—
6	C₂²×C₉⋊C₉	—	3	1	no	—
7	C₂²×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic
8	#66359	C₂×C₃	1	3	yes	—
9	#6882	—	4	1	no	Sylow
10	C₂³×C₃×C₉	—	3	1	no	—
11	C₂³×C₃×C₉	C₃²	1	1	yes	characteristic
12	C₂×#1094	—	3	3	no	—
13	C₂×#733	—	4	3	no	—
14	C₂×C₉⋊C₉	—	3	1	no	—
15	C₂×C₉⋊C₉	—	3	1	no	—
16	C₂×C₉⋊C₉	A₄	1	1	yes	characteristic
17	C₂²×C₃×C₉	—	3	3	no	—
18	C₂²×C₃×C₉	—	3	3	no	—
19	C₂²×C₃×C₉	—	3	1	no	—
20	C₂²×C₃×C₉	—	3	1	no	—
21	C₂²×C₃×C₉	—	3	1	no	—
22	C₂²×C₃×C₉	C₂×C₃²	1	1	yes	characteristic
23	#1094	—	3	3	no	—
24	#733	—	4	3	no	—
25	C₉⋊C₉	C₂×A₄	1	1	yes	characteristic
26	C₂³×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
27	C₂³×C₉	—	3	1	no	—
28	C₂³×C₉	—	9	1	no	—
29	C₂×C₂²⋊C₉	—	9	3	no	—
30	C₂×3₋¹⁺²	—	12	3	no	—
31	C₂×C₃×C₉	—	3	1	no	—
32	C₂×C₃×C₉	—	3	1	no	—
33	C₂×C₃×C₉	—	3	3	no	—
34	C₂×C₃×C₉	—	3	3	no	—
35	C₂×C₃×C₉	—	3	1	no	—
36	C₂×C₃×C₉	C₃×A₄	1	1	yes	characteristic
37	C₂²×C₃²	—	3	1	no	—
38	C₂²×C₃²	—	3	1	no	—
39	C₂²×C₃²	C₂×H(3,𝔽₃)	1	1	yes	characteristic
40	C₂²×C₉	—	3	3	no	—
41	C₂²×C₉	—	3	3	no	—
42	C₂²×C₉	—	3	1	no	—
43	C₂²×C₉	—	9	3	no	—
44	C₂²×C₉	—	9	3	no	—
45	C₂²×C₉	—	9	1	no	—
46	C₂²⋊C₉	—	9	3	no	—
47	3₋¹⁺²	—	12	3	no	—
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	C₂×C₃×A₄	1	1	yes	characteristic
50	C₂³×C₃	—	3	1	no	—
51	C₂³×C₃	#732	1	1	yes	characteristic
52	C₂×C₃²	—	3	1	no	—
53	C₂×C₃²	—	3	1	no	—
54	C₂×C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
55	C₂×C₉	—	3	3	no	—
56	C₂×C₉	—	3	3	no	—
57	C₂×C₉	—	3	1	no	—
58	C₂×C₉	—	9	3	no	—
59	C₂×C₉	—	9	3	no	—
60	C₂×C₉	—	9	1	no	—
61	C₂×C₉	—	36	3	no	—
62	C₂²×C₃	—	3	1	no	—
63	C₂²×C₃	—	3	3	no	—
64	C₂²×C₃	—	3	3	no	—
65	C₂²×C₃	—	3	1	no	—
66	C₂²×C₃	—	3	1	no	—
67	C₂²×C₃	C₂×#732	1	1	yes	characteristic
68	C₃²	C₂×C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
69	C₉	—	3	1	no	—
70	C₉	—	9	1	no	—
71	C₉	—	36	3	no	—
72	C₂³	#6882	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	3	no	—
74	C₂×C₃	—	3	3	no	—
75	C₂×C₃	—	3	1	no	—
76	C₂×C₃	—	3	1	no	—
77	C₂×C₃	—	3	1	no	—
78	C₂×C₃	#66358	1	1	yes	characteristic
79	C₂²	—	3	1	no	—
80	C₂²	—	3	1	no	—
81	C₂²	C₂×#6882	1	1	yes	characteristic, complemented
82	C₃	—	3	1	no	—
83	C₃	C₂×#66358	1	1	yes	characteristic
84	C₂	—	3	1	no	—
85	C₂	—	3	1	no	—
86	C₂	#11757420	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center	C₂×C₃	#66358
commutator, cosocle	C₂²×C₃×C₉	C₂×C₃²
Frattini	C₃×C₉	C₂×C₃×A₄
Fitting	C₂³×C₉⋊C₉	C₃
socle	C₂³×C₃	#732
prime radical	C₂³×C₃²	H(3,𝔽₃)
hypercenter	C₂×C₉⋊C₉	A₄
hypocenter	C₂²	C₂×#6882
LCS	G ▷ C₂²×C₃×C₉ ▷ C₂²×C₃² ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃² ◁ C₂×C₃×C₉ ◁ C₂×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
1. #11757420	C₂	direct (N × H)
72. C₂³	#6882	semidirect
81. C₂²	C₂×#6882	semidirect
86. C₂	#11757420	direct (N × H)

Maximal subgroups

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

subgroup	index
#11757420	2
C₂³×C₉⋊C₉	3
C₂×#66359	3
C₂×#6882	4

Subgroups — C2×#11757420 #14516592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11757420 #14516592