Finite Group Databasebeta

← #14518782

Subgroups — #14518782

Order 1944.

1399 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 1399 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C2×C3⋊(C3⋊#272)C211yesmaximal, characteristic
2C3×C3⋊#1084C211yesmaximal, characteristic, complemented
3C3×Dic3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
4C3×#6289—34nomaximal
5C4×C3⋊#272—31nomaximal
6#10619890—39nomaximal
7C2×C32×H(3,𝔽3)C2211yescharacteristic
8C3⋊(C3⋊#272)C412yescomplemented
9C2×C3×C3⋊(C3⋊D3)—34no—
10C32×C3⋊Dic3—34no—
11C33×Dic3D314yescomplemented
12C2×C3⋊#272—31no—
13C2×C3⋊#272—39no—
14C2×C3⋊#272—69no—
15C2×C3⋊#272—64no—
16C3×C4×H(3,𝔽3)—31no—
17C3⋊#1084D311yescharacteristic, complemented
18C3×#1084—39no—
19Dic3×H(3,𝔽3)D319yescomplemented
20C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
21C3×C4×C3⋊D3—94no—
22#6289—34no—
23C3×#624—91no—
24C3×#624—912no—
25C4×#272—99no—
26C2×C34C2×D314yes—
27C3×C3⋊(C3⋊D3)—38no—
28C2×C3×H(3,𝔽3)—24no—
29C2×C3×H(3,𝔽3)—29no—
30C2×C3×H(3,𝔽3)C2×D319yes—
31C2×C3×H(3,𝔽3)C2×D311yescharacteristic
32C3⋊#272—32no—
33C3⋊#272—318no—
34C3⋊#272—618no—
35C3⋊#272—68no—
36C2×C3⋊(C3⋊D3)—34no—
37C2×C3×C3⋊D3—94no—
38C2×C3×C3⋊D3—912no—
39C2×C3×C3⋊D3—91no—
40C2×C3×C3⋊D3—1812no—
41C2×C3×C3⋊D3—184no—
42C33×C4—34no—
43C3×C3⋊Dic3—34no—
44C3×C3⋊Dic3—34no—
45C3×C3⋊Dic3—64no—
46C32×Dic3—34no—
47C32×Dic3—64no—
48C32×Dic3—912no—
49C32×Dic3—91no—
50C32×Dic3C3⋊D311yescharacteristic
51C32×Dic3C3⋊D3112yescomplemented
52C2×#272—99no—
53C2×#272—1836no—
54C4×H(3,𝔽3)—39no—
55#1084—39no—
56C34C4×D314yescomplemented
57C3×H(3,𝔽3)—24no—
58C3×H(3,𝔽3)—29no—
59C3×H(3,𝔽3)C4×D319yescomplemented
60C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
61C4×C3⋊D3—94no—
62C3×C4×D3—2712no—
63C3×C4×D3—271no—
64C3×C4×D3—271no—
65#624—912no—
66#624—91no—
67C2×C33—212no—
68C2×C33—24no—
69C2×C33—34no—
70C2×C33—64no—
71C2×C33—64no—
72C2×C33—124no—
73C2×C33D3214yes—
74C2×C33C2×C3⋊D311yescharacteristic
75C2×C33C2×C3⋊D3112yes—
76C3⋊(C3⋊D3)—38no—
77C3×C3⋊D3—98no—
78C3×C3⋊D3—92no—
79C3×C3⋊D3—924no—
80C3×C3⋊D3—188no—
81C3×C3⋊D3—1824no—
82C2×H(3,𝔽3)—236no—
83C2×H(3,𝔽3)D3219yes—
84#272—918no—
85#272—1872no—
86C2×C3⋊D3—94no—
87C2×C3⋊D3—912no—
88C2×C3⋊D3—91no—
89C2×C3⋊D3—1812no—
90C2×C3⋊D3—184no—
91C2×C3×D3—2712no—
92C2×C3×D3—271no—
93C2×C3×D3—271no—
94C2×C3×D3—5412no—
95C2×C3×D3—541no—
96C32×C4—31no—
97C32×C4—312no—
98C32×C4—94no—
99C32×C4—184no—
100C32×C4—271no—
101C3⋊Dic3—34no—
102C3×Dic3—21no—
103C3×Dic3—312no—
104C3×Dic3—912no—
105C3×Dic3—91no—
106C3×Dic3—912no—
107C3×Dic3—91no—
108C3×Dic3—181no—
109C3×Dic3—1812no—
110C3×Dic3#27211yescharacteristic, complemented
111C3×Dic3C3⋊(C3⋊D3)11yescharacteristic
112C33—24no—
113C33—212no—
114C33—34no—
115C33—64no—
116C33—64no—
117C33—124no—
118C33#62414yescomplemented
119C33C4×C3⋊D311yescharacteristic
120C33C4×C3⋊D3112yescomplemented
121H(3,𝔽3)—236no—
122H(3,𝔽3)#62419yescomplemented
123C2×C3×C4—811no—
124C4×D3—271no—
125C4×D3—2712no—
126C4×D3—271no—
127C2×C32—21no—
128C2×C32—21no—
129C2×C32—21no—
130C2×C32—212no—
131C2×C32—34no—
132C2×C32—312no—
133C2×C32—41no—
134C2×C32—64no—
135C2×C32—612no—
136C2×C32—612no—
137C2×C32—64no—
138C2×C32—124no—
139C2×C32—1212no—
140C2×C32C2×#27211yescharacteristic
141C2×C32D3×C3⋊D311yescharacteristic
142C2×C32D3×C3⋊D3112yes—
143C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
144C3⋊D3—98no—
145C3⋊D3—924no—
146C3⋊D3—92no—
147C3⋊D3—1824no—
148C3⋊D3—188no—
149C3×D3—272no—
150C3×D3—2724no—
151C3×D3—272no—
152C3×D3—5424no—
153C3×D3—542no—
154C22×C3—811no—
155C2×D3—2712no—
156C2×D3—271no—
157C2×D3—271no—
158C2×D3—541no—
159C2×D3—5412no—
160C3×C4—31no—
161C3×C4—31no—
162C3×C4—61no—
163C3×C4—912no—
164C3×C4—271no—
165C3×C4—271no—
166C3×C4—541no—
167Dic3—912no—
168Dic3—91no—
169Dic3C3⋊#27211yescharacteristic, complemented
170C32—21no—
171C32—21no—
172C32—21no—
173C32—212no—
174C32—34no—
175C32—312no—
176C32—41no—
177C32—64no—
178C32—612no—
179C32—612no—
180C32—64no—
181C32—124no—
182C32—1212no—
183C32C4×#27211yescharacteristic, complemented
184C32#628911yescharacteristic
185C32#6289112yescomplemented
186C32C4×C3⋊(C3⋊D3)11yescharacteristic
187C2×C4—811noSylow
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—312no—
192C2×C3—41no—
193C2×C3—612no—
194C2×C3—812no—
195C2×C3D3×#27211yescharacteristic
196C2×C3C2×C3⋊#27211yescharacteristic
197C2×C3D3×C3⋊(C3⋊D3)11yescharacteristic
198D3—2724no—
199D3—272no—
200D3—272no—
201D3—542no—
202D3—5424no—
203C22—811no—
204C4—31no—
205C4—271no—
206C3—21no—
207C3—21no—
208C3—21no—
209C3—312no—
210C3—41no—
211C3—612no—
212C3#1061989011yescharacteristic, complemented
213C3C4×C3⋊#27211yescharacteristic, complemented
214C3#1062014411yescharacteristic
215C2—812no—
216C2D3×C3⋊#27211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C3D3×C3⋊(C3⋊D3)
commutator, hypocenterC32×H(3,𝔽3)C2×C4
Fitting, cosocleC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3⋊D3
prime radicalC2×C3⋊(C3⋊#272)C2
LCSG ▷ C32×H(3,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊#1084C2semidirect
3. C3×Dic3×H(3,𝔽3)C2semidirect
8. C3⋊(C3⋊#272)C4semidirect
11. C33×Dic3D3semidirect
17. C3⋊#1084D3semidirect
19. Dic3×H(3,𝔽3)D3semidirect
20. C32×H(3,𝔽3)C2×C4semidirect
51. C32×Dic3C3⋊D3semidirect
56. C34C4×D3semidirect
59. C3×H(3,𝔽3)C4×D3semidirect
60. C3×H(3,𝔽3)C4×D3semidirect
110. C3×Dic3#272semidirect
118. C33#624semidirect
120. C33C4×C3⋊D3semidirect
122. H(3,𝔽3)#624semidirect
169. Dic3C3⋊#272semidirect
183. C32C4×#272semidirect
185. C32#6289semidirect
212. C3#10619890semidirect
213. C3C4×C3⋊#272semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊#272)2
C3×C3⋊#10842
C3×Dic3×H(3,𝔽3)2
C3×#62893
C4×C3⋊#2723
#106198903