Finite Group Databasebeta

← #14517687

Subgroups — #14517687

Order 1944.

264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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×#6903C211yesmaximal, characteristic, complemented
2C2×#92318C211yesmaximal, characteristic, complemented
3#11757622C211yesmaximal, characteristic, complemented
4#10619983—31nomaximal
5#10619677C311yesmaximal, characteristic, complemented
6#6171⋊C3—32nomaximal
7C3×#6171—31nomaximal
8C2×#6903—21no—
9C2×#6903C2211yescharacteristic
10#92318—21no—
11C22×#737D311yescharacteristic
12C2×#4207—31no—
13#66409—31no—
14C22×C27⋊C3—21no—
15C22×C27⋊C3—22no—
16C22×C27⋊C3D312yescomplemented
17C22×C3×C27—21no—
18C22×C3×C27D311yescharacteristic, complemented
19C22×C3×C27C2×C311yescharacteristic, complemented
20C2×C3⋊D27C2×C311yescharacteristic, complemented
21C2×D27⋊C3—32no—
22C2×C3×D27—31no—
23C3⋊Dic27C2×C311yescharacteristic, complemented
24(C27⋊C3)⋊C4—32no—
25C3×Dic27—31no—
26#6903D411yescharacteristic, complemented, Sylow
27#6233—31no—
28#611⋊C3—92no—
29#638⋊C3—91no—
30C3×#611—91no—
31#6171—31no—
32#6171—32no—
33C2×#737—21no—
34C2×#737C2×D311yescharacteristic
35#4207—61no—
36C2×C27⋊C3—22no—
37C2×C27⋊C3—24no—
38C2×C27⋊C3—22no—
39C2×C27⋊C3—21no—
40C2×C27⋊C3—22no—
41C2×C27⋊C3C2×D312yes—
42C2×C3×C27—22no—
43C2×C3×C27—21no—
44C2×C3×C27—21no—
45C2×C3×C27—21no—
46C2×C3×C27C2×D311yescharacteristic
47C2×C3×C27C22×C311yescharacteristic
48C3⋊D27—21no—
49D27⋊C3—62no—
50C3×D27—61no—
51C22×3−1+2—21no—
52C22×3−1+2—22no—
53C22×3−1+2D912yes—
54C22×H(3,𝔽3)D911yescharacteristic
55C22×C3×C9—21no—
56C22×C3×C9C3×D311yescharacteristic
57C22×C3×C9C3⋊D311yescharacteristic
58C2×C3⋊D9—31no—
59C2×AGL(1,ℤ/9)—92no—
60C2×(C3⋊D3)⋊C3—91no—
61C2×C3×D9—91no—
62C3⋊Dic9—31no—
633−1+2⋊C4—92no—
64(C3⋊Dic3)⋊C3—91no—
65C3×Dic9—91no—
66C22×C27—22no—
67C22×C27—21no—
68C22×C27C3×D311yescharacteristic
69C22×C27C3×D312yes—
70C2×D27—31no—
71C2×D27—32no—
72Dic27—31no—
73Dic27—32no—
74#737#6711yescharacteristic
75C27⋊C3—21no—
76C27⋊C3—22no—
77C27⋊C3#6712yescomplemented
78C3×C27—21no—
79C3×C27#6711yescharacteristic, complemented
80C3×C27C3×D411yescharacteristic, complemented
81#638—91no—
82C3×#67—271no—
83#611—92no—
84#611—91no—
85C2×3−1+2—22no—
86C2×3−1+2—24no—
87C2×3−1+2—22no—
88C2×3−1+2—21no—
89C2×3−1+2—22no—
90C2×3−1+2C2×D912yes—
91C2×H(3,𝔽3)—21no—
92C2×H(3,𝔽3)C2×D911yescharacteristic
93C2×C3×C9—22no—
94C2×C3×C9—21no—
95C2×C3×C9—21no—
96C2×C3×C9—21no—
97C2×C3×C9C2×C3×D311yescharacteristic
98C2×C3×C9C2×C3⋊D311yescharacteristic
99C3⋊D9—61no—
100AGL(1,ℤ/9)—182no—
101(C3⋊D3)⋊C3—181no—
102C3×D9—181no—
103C2×C27—24no—
104C2×C27—22no—
105C2×C27—21no—
106C2×C27—22no—
107C2×C27—22no—
108C2×C27—21no—
109C2×C27C2×C3×D311yescharacteristic
110C2×C27C2×C3×D312yes—
111D27—61no—
112D27—62no—
113C22×C32—21no—
114C22×C32C3×D911yescharacteristic
115C22×C32C3⋊D911yescharacteristic
116C2×C3⋊D3—91no—
117C2×C3×D3—271no—
118C3⋊Dic3—91no—
119C3×Dic3—271no—
120C22×C9—22no—
121C22×C9—21no—
122C22×C9C3×D912yes—
123C22×C9C3×C3⋊D311yescharacteristic
124C2×D9—92no—
125C2×D9—91no—
126Dic9—92no—
127Dic9—91no—
1283−1+2—21no—
1293−1+2—22no—
1303−1+2#61112yes—
131H(3,𝔽3)#61111yescharacteristic
132C3×C9—21no—
133C3×C9C3×#6711yescharacteristic
134C3×C9#63811yescharacteristic
135C27—22no—
136C27—21no—
137C27C3×#6711yescharacteristic
138C27C3×#6712yes—
139C3×D4—811no—
140#67—271no—
141#67—811no—
142C2×C32—22no—
143C2×C32—21no—
144C2×C32—21no—
145C2×C32—21no—
146C2×C32C2×C3×D911yescharacteristic
147C2×C32C2×C3⋊D911yescharacteristic
148C3⋊D3—181no—
149C3×D3—541no—
150C2×C9—24no—
151C2×C9—22no—
152C2×C9—22no—
153C2×C9—21no—
154C2×C9—22no—
155C2×C9—21no—
156C2×C9C2×C3×D912yes—
157C2×C9C2×C3×C3⋊D311yescharacteristic
158D9—182no—
159D9—181no—
160C22×C3—31no—
161C22×C3—31no—
162C22×C3—61no—
163C22×C3—811no—
164C22×C3C3×C3⋊D911yescharacteristic
165C2×D3—271no—
166C2×D3—811no—
167C3×C4—811no—
168Dic3—271no—
169Dic3—811no—
170C32—21no—
171C32C3×#61111yescharacteristic
172C32#623311yescharacteristic
173C9—22no—
174C9—21no—
175C9C3×#61112yes—
176C9C3×#63811yescharacteristic
177D4—811noSylow
178C2×C3—21no—
179C2×C3—31no—
180C2×C3—31no—
181C2×C3—61no—
182C2×C3—61no—
183C2×C3—62no—
184C2×C3—61no—
185C2×C3—1621no—
186C2×C3C2×C3×C3⋊D911yescharacteristic
187D3—541no—
188D3—1621no—
189C22—811no—
190C22#9231811yescharacteristic, complemented
191C4—811no—
192C3—31no—
193C3—31no—
194C3—61no—
195C3C3×#623311yescharacteristic
196C2—21no—
197C2—1621no—
198C2C2×#9231811yescharacteristic
subgroupG/H
centerC2C2×#92318
commutator, cosocleC2×C3×C27C22×C3
FrattiniC2×C9C2×C3×C3⋊D3
FittingC22×#6903C2
socleC2×C3C2×C3×C3⋊D9
hypercenterC22#92318
hypocenterC3×C27C3×D4
LCSG ▷ C2×C3×C27 ▷ C3×C27
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6903C2semidirect
2. C2×#92318C2semidirect
3. #11757622C2semidirect
5. #10619677C3semidirect
16. C22×C27⋊C3D3semidirect
18. C22×C3×C27D3semidirect
19. C22×C3×C27C2×C3semidirect
20. C2×C3⋊D27C2×C3semidirect
23. C3⋊Dic27C2×C3semidirect
26. #6903D4semidirect
77. C27⋊C3#67semidirect
79. C3×C27#67semidirect
80. C3×C27C3×D4semidirect
190. C22#92318semidirect

Maximal subgroups

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

subgroupindex
C22×#69032
C2×#923182
#117576222
#106199833
#106196773
#6171⋊C33
C3×#61713