Finite Group Databasebeta

← #14517716

Subgroups — #14517716

Order 1944.

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

normal subgroups only

This group has 442 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×#6911C211yesmaximal, characteristic, complemented
2C2×#92333C211yesmaximal, characteristic, complemented
3#11757637C211yesmaximal, characteristic, complemented
4C3×#611⋊C3—31nomaximal
5C3×#638⋊C3—33nomaximal
6#10619683C311yesmaximal, characteristic, complemented
7C2×#6911—21no—
8C2×#6911C2211yescharacteristic
9#92333—21no—
10C22×C3×3−1+2D311yescharacteristic, complemented
11C22×C3×H(3,𝔽3)D313yescomplemented
12C2×C3×AGL(1,ℤ/9)—31no—
13C2×C3×(C3⋊D3)⋊C3—33no—
14C3×3−1+2⋊C4—31no—
15C3×(C3⋊Dic3)⋊C3—33no—
16C22×#732—23no—
17C22×#732—21no—
18C22×#732C2×C311yescharacteristic, complemented
19C2×#4185C2×C311yescharacteristic, complemented
20#66332C2×C311yescharacteristic, complemented
21#6911D411yescharacteristic, complemented, Sylow
22C3×#638—33no—
23C32×#67—91no—
24#611⋊C3—33no—
25#638⋊C3—36no—
26#638⋊C3—33no—
27C3×#611—31no—
28C2×C3×3−1+2—21no—
29C2×C3×3−1+2C2×D311yescharacteristic
30C2×C3×H(3,𝔽3)—23no—
31C2×C3×H(3,𝔽3)C2×D313yes—
32C3×AGL(1,ℤ/9)—61no—
33C3×(C3⋊D3)⋊C3—63no—
34C2×#732—26no—
35C2×#732—22no—
36C2×#732—21no—
37C2×#732—23no—
38C2×#732—21no—
39C2×#732C22×C311yescharacteristic
40#4185—21no—
41C22×C33—33no—
42C22×C33C3⋊D311yescharacteristic
43C2×C3×C3⋊D3—33no—
44C2×C32×D3—91no—
45C3×C3⋊Dic3—33no—
46C32×Dic3—91no—
47C22×3−1+2—33no—
48C22×H(3,𝔽3)—23no—
49C22×H(3,𝔽3)—36no—
50C22×H(3,𝔽3)C3×D313yescomplemented
51C22×C3×C9—21no—
52C22×C3×C9C3×D311yescharacteristic, complemented
53C2×AGL(1,ℤ/9)—33no—
54C2×(C3⋊D3)⋊C3—36no—
55C2×(C3⋊D3)⋊C3—33no—
56C2×C3×D9—31no—
573−1+2⋊C4—33no—
58(C3⋊Dic3)⋊C3—36no—
59(C3⋊Dic3)⋊C3—33no—
60C3×Dic9—31no—
61C3×3−1+2#6711yescharacteristic, complemented
62C3×H(3,𝔽3)#6713yescomplemented
63#732—23no—
64#732—21no—
65#732C3×D411yescharacteristic, complemented
66C32×D4—271no—
67#638—33no—
68C3×#67—93no—
69C3×#67—91no—
70C3×#67—273no—
71#611—31no—
72C2×C33—21no—
73C2×C33—33no—
74C2×C33—63no—
75C2×C33C2×C3⋊D311yescharacteristic
76C3×C3⋊D3—63no—
77C32×D3—181no—
78C2×3−1+2—33no—
79C2×3−1+2—63no—
80C2×H(3,𝔽3)—26no—
81C2×H(3,𝔽3)—23no—
82C2×H(3,𝔽3)—23no—
83C2×H(3,𝔽3)—36no—
84C2×H(3,𝔽3)—66no—
85C2×H(3,𝔽3)C2×C3×D313yes—
86C2×C3×C9—22no—
87C2×C3×C9—21no—
88C2×C3×C9—21no—
89C2×C3×C9C2×C3×D311yescharacteristic
90AGL(1,ℤ/9)—63no—
91(C3⋊D3)⋊C3—66no—
92(C3⋊D3)⋊C3—63no—
93C3×D9—61no—
94C22×C32—33no—
95C22×C32—63no—
96C22×C32—91no—
97C22×C32—93no—
98C22×C32—183no—
99C22×C32—271no—
100C22×C32#27213yes—
101C22×C32C3×C3⋊D311yescharacteristic
102C2×C3⋊D3—33no—
103C2×C3×D3—93no—
104C2×C3×D3—91no—
105C2×C3×D3—273no—
106C32×C4—271no—
107C3⋊Dic3—33no—
108C3×Dic3—93no—
109C3×Dic3—91no—
110C3×Dic3—273no—
111C22×C9—31no—
112C22×C9—61no—
113C2×D9—31no—
114Dic9—31no—
115C33—33no—
116C33#63811yescharacteristic
1173−1+2—33no—
118H(3,𝔽3)—23no—
119H(3,𝔽3)—36no—
120H(3,𝔽3)C3×#6713yescomplemented
121C3×C9—21no—
122C3×C9C3×#6711yescharacteristic, complemented
123C3×D4—273no—
124C3×D4—271no—
125#67—91no—
126#67—273no—
127C2×C32—23no—
128C2×C32—21no—
129C2×C32—33no—
130C2×C32—63no—
131C2×C32—66no—
132C2×C32—63no—
133C2×C32—91no—
134C2×C32—93no—
135C2×C32—183no—
136C2×C32—181no—
137C2×C32—183no—
138C2×C32—186no—
139C2×C32—541no—
140C2×C32C2×#27213yes—
141C2×C32C2×C3×C3⋊D311yescharacteristic
142C3⋊D3—63no—
143C3×D3—183no—
144C3×D3—181no—
145C3×D3—543no—
146C2×C9—31no—
147C2×C9—61no—
148C2×C9—62no—
149C2×C9—61no—
150D9—61no—
151C22×C3—33no—
152C22×C3—31no—
153C22×C3—93no—
154C22×C3—183no—
155C22×C3—273no—
156C22×C3—271no—
157C22×C3C3×#27211yescharacteristic
158C2×D3—91no—
159C2×D3—273no—
160C3×C4—273no—
161C3×C4—271no—
162Dic3—91no—
163Dic3—273no—
164C32—33no—
165C32—63no—
166C32—91no—
167C32—93no—
168C32—183no—
169C32#623513yes—
170C32C3×#63811yescharacteristic
171C9—31no—
172C9—61no—
173D4—271noSylow
174C2×C3—21no—
175C2×C3—33no—
176C2×C3—31no—
177C2×C3—61no—
178C2×C3—63no—
179C2×C3—93no—
180C2×C3—183no—
181C2×C3—186no—
182C2×C3—183no—
183C2×C3—543no—
184C2×C3—541no—
185C2×C3C2×C3×#27211yescharacteristic
186D3—181no—
187D3—543no—
188C22—271no—
189C22#9233311yescharacteristic, complemented
190C4—271no—
191C3—33no—
192C3—31no—
193C3—93no—
194C3—183no—
195C3C3×#623511yescharacteristic
196C2—21no—
197C2—541no—
198C2C2×#9233311yescharacteristic
subgroupG/H
centerC2C2×#92333
commutator, cosocleC2×#732C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×#6911C2
socleC2×C3C2×C3×#272
hypercenterC22#92333
hypocenter#732C3×D4
LCSG ▷ C2×#732 ▷ #732
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6911C2semidirect
2. C2×#92333C2semidirect
3. #11757637C2semidirect
6. #10619683C3semidirect
10. C22×C3×3−1+2D3semidirect
11. C22×C3×H(3,𝔽3)D3semidirect
18. C22×#732C2×C3semidirect
19. C2×#4185C2×C3semidirect
20. #66332C2×C3semidirect
21. #6911D4semidirect
50. C22×H(3,𝔽3)C3×D3semidirect
52. C22×C3×C9C3×D3semidirect
61. C3×3−1+2#67semidirect
62. C3×H(3,𝔽3)#67semidirect
65. #732C3×D4semidirect
120. H(3,𝔽3)C3×#67semidirect
122. C3×C9C3×#67semidirect
189. C22#92333semidirect

Maximal subgroups

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

subgroupindex
C22×#69112
C2×#923332
#117576372
C3×#611⋊C33
C3×#638⋊C33
#106196833