Finite Group Databasebeta

← #14517718

Subgroups — #14517718

Order 1944.

364 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C22×#6912C211yesmaximal, characteristic, complemented
2C2×#6912⋊C2C211yesmaximal, characteristic, complemented
3#6912⋊C4C211yesmaximal, characteristic, complemented
4C3×#611⋊C3—33nomaximal
5C3×#611⋊C3—31nomaximal
6#10619685C311yesmaximal, characteristic, complemented
7C2×#6912—21no—
8C2×#6912C2211yescharacteristic
9#6912⋊C2—21no—
10C22×C3×3−1+2D311yescharacteristic
11C22×C3×3−1+2D313yes—
12C2×C3×AGL(1,ℤ/9)—33no—
13C2×C3×AGL(1,ℤ/9)—31no—
14C3×3−1+2⋊C4—33no—
15C3×3−1+2⋊C4—31no—
16C22×#733—23no—
17C22×#733—21no—
18C22×#733C2×C311yescharacteristic, complemented
19C2×#733⋊C2C2×C311yescharacteristic, complemented
20#733⋊C4C2×C311yescharacteristic, complemented
21#6912D411yescharacteristic, complemented, Sylow
22C32×#67—91no—
23#611⋊C3—36no—
24#611⋊C3—33no—
25#611⋊C3—33no—
26C3×#611—33no—
27C3×#611—31no—
28C2×C3×3−1+2—21no—
29C2×C3×3−1+2—23no—
30C2×C3×3−1+2C2×D311yescharacteristic
31C2×C3×3−1+2C2×D313yes—
32C3×AGL(1,ℤ/9)—63no—
33C3×AGL(1,ℤ/9)—61no—
34C2×#733—26no—
35C2×#733—22no—
36C2×#733—21no—
37C2×#733—23no—
38C2×#733—21no—
39C2×#733C22×C311yescharacteristic
40#733⋊C2—21no—
41C22×C33C3⋊D311yescharacteristic
42C2×C32×D3—91no—
43C32×Dic3—91no—
44C22×3−1+2—23no—
45C22×3−1+2—36no—
46C22×3−1+2—33no—
47C22×3−1+2C3×D313yes—
48C22×C3×C9—21no—
49C22×C3×C9—33no—
50C22×C3×C9C3×D311yescharacteristic
51C2×AGL(1,ℤ/9)—36no—
52C2×AGL(1,ℤ/9)—33no—
53C2×AGL(1,ℤ/9)—33no—
54C2×C3×D9—33no—
55C2×C3×D9—31no—
563−1+2⋊C4—36no—
573−1+2⋊C4—33no—
583−1+2⋊C4—33no—
59C3×Dic9—33no—
60C3×Dic9—31no—
61C3×3−1+2#6711yescharacteristic
62C3×3−1+2#6713yes—
63#733—23no—
64#733—21no—
65#733C3×D411yescharacteristic, complemented
66C32×D4—271no—
67C3×#67—93no—
68C3×#67—91no—
69#611—33no—
70#611—31no—
71C2×C33—21no—
72C2×C33C2×C3⋊D311yescharacteristic
73C32×D3—181no—
74C2×3−1+2—26no—
75C2×3−1+2—23no—
76C2×3−1+2—23no—
77C2×3−1+2—36no—
78C2×3−1+2—33no—
79C2×3−1+2—63no—
80C2×3−1+2—66no—
81C2×3−1+2C2×C3×D313yes—
82C2×C3×C9—22no—
83C2×C3×C9—21no—
84C2×C3×C9—21no—
85C2×C3×C9—33no—
86C2×C3×C9—63no—
87C2×C3×C9C2×C3×D311yescharacteristic
88AGL(1,ℤ/9)—66no—
89AGL(1,ℤ/9)—63no—
90AGL(1,ℤ/9)—63no—
91C3×D9—63no—
92C3×D9—61no—
93C22×C32—91no—
94C22×C32—271no—
95C22×C32#27213yes—
96C22×C32C3×C3⋊D311yescharacteristic
97C2×C3×D3—93no—
98C2×C3×D3—91no—
99C32×C4—271no—
100C3×Dic3—93no—
101C3×Dic3—91no—
102C22×C9—33no—
103C22×C9—31no—
104C22×C9—61no—
105C22×C9—63no—
106C2×D9—33no—
107C2×D9—31no—
108Dic9—33no—
109Dic9—31no—
110C33#63811yescharacteristic
1113−1+2—23no—
1123−1+2—36no—
1133−1+2—33no—
1143−1+2C3×#6713yes—
115C3×C9—21no—
116C3×C9—33no—
117C3×C9C3×#6711yescharacteristic
118C3×D4—273no—
119C3×D4—271no—
120#67—91no—
121C2×C32—23no—
122C2×C32—21no—
123C2×C32—91no—
124C2×C32—181no—
125C2×C32—541no—
126C2×C32C2×#27213yes—
127C2×C32C2×C3×C3⋊D311yescharacteristic
128C3×D3—183no—
129C3×D3—181no—
130C2×C9—33no—
131C2×C9—31no—
132C2×C9—61no—
133C2×C9—63no—
134C2×C9—62no—
135C2×C9—66no—
136C2×C9—61no—
137C2×C9—63no—
138D9—63no—
139D9—61no—
140C22×C3—33no—
141C22×C3—31no—
142C22×C3—273no—
143C22×C3—271no—
144C22×C3C3×#27211yescharacteristic
145C2×D3—91no—
146C3×C4—273no—
147C3×C4—271no—
148Dic3—91no—
149C32—91no—
150C32#623513yes—
151C32C3×#63811yescharacteristic
152C9—33no—
153C9—31no—
154C9—61no—
155C9—63no—
156D4—271noSylow
157C2×C3—21no—
158C2×C3—33no—
159C2×C3—31no—
160C2×C3—63no—
161C2×C3—61no—
162C2×C3—543no—
163C2×C3—541no—
164C2×C3C2×C3×#27211yescharacteristic
165D3—181no—
166C22—271no—
167C22#6912⋊C211yescharacteristic, complemented
168C4—271no—
169C3—33no—
170C3—31no—
171C3C3×#623511yescharacteristic
172C2—21no—
173C2—541no—
174C2C2×#6912⋊C211yescharacteristic
subgroupG/H
centerC2C2×#6912⋊C2
commutator, cosocleC2×#733C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×#6912C2
socleC2×C3C2×C3×#272
hypercenterC22#6912⋊C2
hypocenter#733C3×D4
LCSG ▷ C2×#733 ▷ #733
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6912C2semidirect
2. C2×#6912⋊C2C2semidirect
3. #6912⋊C4C2semidirect
6. #10619685C3semidirect
18. C22×#733C2×C3semidirect
19. C2×#733⋊C2C2×C3semidirect
20. #733⋊C4C2×C3semidirect
21. #6912D4semidirect
65. #733C3×D4semidirect
167. C22#6912⋊C2semidirect

Maximal subgroups

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

subgroupindex
C22×#69122
C2×#6912⋊C22
#6912⋊C42
C3×#611⋊C33
#106196853