Finite Group Databasebeta

← #14516794

Subgroups — #14516794

Order 1944.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757603C211yesmaximal, characteristic
23−1+2×Dic9C211yesmaximal, characteristic
3C9×3−1+2⋊C4C211yesmaximal, characteristic
4#6189⋊C3—31nomaximal
5C3×#6189—31nomaximal
6#10619531C311yesmaximal, characteristic, complemented
7C2×C9×3−1+2C2211yescharacteristic
8C3⋊(3−1+2⋊C4)—31no—
9C3×C3⋊Dic9—31no—
10Dic3×3−1+2—31no—
11C3×3−1+2⋊C4D311yescharacteristic
12C3×C9×Dic3—31no—
13C32×Dic9D311yescharacteristic
14C9⋊Dic9C2×C311yescharacteristic
15Dic9⋊C9—21no—
16#66316—61no—
17C9×Dic9—21no—
18C9×Dic9C2×C311yescharacteristic
19C9×Dic9C2×C311yescharacteristic
20C9×3−1+2Q811yescharacteristic, complemented, Sylow
21C3×#627—91no—
223−1+2⋊Q8—91no—
23C3×Dic18—91no—
24#6189—31no—
25#6189—31no—
26C2×C3×3−1+2C2×D311yescharacteristic
27C2×C32×C9C2×D311yescharacteristic
28C2×C9⋊C9—21no—
29C2×C9⋊C9—41no—
30C2×C32⋊C9—21no—
31C2×C92—21no—
32C2×C92C22×C311yescharacteristic
33C3×C3⋊Dic3—91no—
34C32×Dic3—31no—
35C32×Dic3—31no—
36C4×3−1+2—91no—
37C3×C4×C9—91no—
38C3⋊Dic9—31no—
39C3⋊Dic9—31no—
40C3⋊Dic9—61no—
413−1+2⋊C4—21no—
423−1+2⋊C4—91no—
433−1+2⋊C4—181no—
443−1+2⋊C4D911yescharacteristic
45C9×Dic3—31no—
46C9×Dic3—31no—
47C9×Dic3—61no—
48C9×Dic3—61no—
49C3×Dic9—31no—
50C3×Dic9—91no—
51C3×Dic9—181no—
52C3×Dic9C3×D311yescharacteristic
53C3×Dic9C3×D311yescharacteristic
54C3×3−1+2Dic611yescharacteristic
55C32×C9Dic611yescharacteristic
56C9⋊C9—21no—
57C9⋊C9—41no—
58C32⋊C9—21no—
59C92—21no—
60C92C3×Q811yescharacteristic, complemented
61C3×Dic6—271no—
62C3×Dic6—271no—
63#627—91no—
64Dic18—91no—
65Dic18—91no—
66C2×C33D3211yescharacteristic
67C2×3−1+2—21no—
68C2×3−1+2—21no—
69C2×3−1+2—41no—
70C2×3−1+2C2×D911yescharacteristic
71C2×C3×C9—21no—
72C2×C3×C9—21no—
73C2×C3×C9—21no—
74C2×C3×C9—31no—
75C2×C3×C9—41no—
76C2×C3×C9—61no—
77C2×C3×C9C2×C3×D311yescharacteristic
78C2×C3×C9C2×C3×D311yescharacteristic
79C32×C4—91no—
80C32×C4—91no—
81C3⋊Dic3—91no—
82C3×Dic3—31no—
83C3×Dic3—31no—
84C3×Dic3—31no—
85C3×Dic3—61no—
86C3×Dic3—91no—
87C3×Dic3—271no—
88C3×Dic3—271no—
89C3×Dic3—541no—
90C4×C9—91no—
91C4×C9—91no—
92C4×C9—181no—
93C4×C9—181no—
94Dic9—91no—
95Dic9—91no—
96Dic9—181no—
97Dic9—181no—
98Dic9—541no—
99Dic9C3×D911yescharacteristic
100Dic9AGL(1,ℤ/9)11yescharacteristic
101C33#62711yescharacteristic
1023−1+2—21no—
1033−1+2—21no—
1043−1+2—41no—
1053−1+2Dic1811yescharacteristic, complemented
106C3×C9—21no—
107C3×C9—21no—
108C3×C9—21no—
109C3×C9—31no—
110C3×C9—41no—
111C3×C9—61no—
112C3×C9C3×Dic611yescharacteristic
113C3×C9C3×Dic611yescharacteristic
114C3×Q8—811no—
115Dic6—271no—
116Dic6—271no—
117C2×C32—21no—
118C2×C32—31no—
119C2×C32—61no—
120C2×C32D3×D911yescharacteristic
121C2×C32C3×D3211yescharacteristic
122C2×C9—21no—
123C2×C9—21no—
124C2×C9—21no—
125C2×C9—41no—
126C2×C9—61no—
127C2×C9—61no—
128C2×C9—121no—
129C2×C9C2×C3×D911yescharacteristic
130C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
131C3×C4—91no—
132C3×C4—91no—
133C3×C4—91no—
134C3×C4—181no—
135C3×C4—271no—
136C3×C4—811no—
137Dic3—31no—
138Dic3—31no—
139Dic3—271no—
140Dic3—271no—
141Dic3—541no—
142C32—21no—
143C32—31no—
144C32—61no—
145C32#618911yescharacteristic
146C32C3×#62711yescharacteristic
147C9—21no—
148C9—21no—
149C9—21no—
150C9—41no—
151C9—61no—
152C9—61no—
153C9—121no—
154C9C3×Dic1811yescharacteristic, complemented
155C93−1+2⋊Q811yescharacteristic, complemented
156Q8—811noSylow
157C2×C3—21no—
158C2×C3—31no—
159C2×C3—61no—
160C2×C3C3×D3×D911yescharacteristic
161C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
162C4—91no—
163C4—91no—
164C4—811no—
165C3—21no—
166C3—31no—
167C3—61no—
168C3C3×#618911yescharacteristic
169C3#6189⋊C311yescharacteristic
170C2D9×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC2D9×AGL(1,ℤ/9)
commutator, cosocleC2×C92C22×C3
Frattini, socleC2×C32C3×D32
FittingC2×C9×3−1+2C22
prime radicalC2×C33D32
hypocenterC92C3×Q8
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
6. #10619531C3semidirect
20. C9×3−1+2Q8semidirect
60. C92C3×Q8semidirect
105. 3−1+2Dic18semidirect
154. C9C3×Dic18semidirect
155. C93−1+2⋊Q8semidirect

Maximal subgroups

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

subgroupindex
#117576032
3−1+2×Dic92
C9×3−1+2⋊C42
#6189⋊C33
C3×#61893
#106195313