Finite Group Databasebeta

← #11799022

Subgroups — #11799022

Order 1152.

474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 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#10592890C211yesmaximal, characteristic
2C2×#63656C211yesmaximal, characteristic, complemented
3C2×#63627C211yesmaximal, characteristic
4#10592572C211yesmaximal, characteristic, complemented
5C32×#358C211yesmaximal, characteristic, complemented
6#10589367C211yesmaximal, characteristic, complemented
7#10589357C211yesmaximal, characteristic
8#69237—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10#64156—21no—
11C2×#3755—21no—
12C2×#3746C2211yescharacteristic
13C2×#3745C2211yescharacteristic
14#64096—21no—
15C2×C32×C16C2211yescharacteristic
16C32×#107C2211yescharacteristic
17#63656—22no—
18C8×C3⋊Dic3C2211yescharacteristic
19C2×C3⋊(C3⋊C16)C2211yescharacteristic
20#63637—21no—
21#63627—22no—
22#5191—34no—
23C2×#829—34no—
24C2×#800—34no—
25#4873—34no—
26C3×#358D314yescomplemented
27Dic3⋊C16—34no—
28#4491—34no—
29C2×C32×Q8—21no—
30C2×C4⋊(C3⋊D3)—21no—
31C2×#634—21no—
32C32×Q16—21no—
33C32×Q16—21no—
34C2×C32×C8C2311yescharacteristic
35C32×C4⋊C4—21no—
36#3755—42no—
37#3752—41no—
38#3752—41no—
39#3750—41no—
40C4×C3⋊Dic3—41no—
41C4×C3⋊Dic3D411yescharacteristic
42C2×C3⋊(C3⋊C8)D411yescharacteristic
43#3746—21no—
44#3746D412yes—
45#3745—21no—
46#3745—21no—
47C32×C16—21no—
48C3⋊(C3⋊C16)—21no—
49#2211—91noSylow
50C2×C3×Q16C2×D314yes—
51#947—64no—
52C2×#215—64no—
53C2×Dic12—34no—
54C2×D24—34no—
55#887—64no—
56C2×C3×C16C2×D314yes—
57C3×#107C2×D314yes—
58#829—68no—
59C8×Dic3—34no—
60C2×C3⋊C16—34no—
61#810—64no—
62#800—68no—
63C22×C3⋊D3—41no—
64C32×Q8—41no—
65C32×Q8—41no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3D811yescharacteristic
71C2×C3⋊Dic3D811yescharacteristic
72C4⋊(C3⋊D3)—41no—
73C4⋊(C3⋊D3)—41no—
74#634—22no—
75#634—41no—
76C32×C8C2×D411yescharacteristic
77C32×C8#4111yescharacteristic
78C3⋊(C3⋊C8)—21no—
79C2×Q32—91no—
80C2×SD32—91no—
81#495—91no—
82C4×Q16—91no—
83C4⋊C16—91no—
84#358C3⋊D311yescharacteristic, complemented
85#357—91no—
86C2×C3×Q8—24no—
87C2×D12—64no—
88C2×Dic6—64no—
89C3×Q16—24no—
90C3×Q16—24no—
91C2×C3×C8C22×D314yes—
92C3×C4⋊C4—24no—
93#215—128no—
94(C2×D3)⋊C4—124no—
95(C2×D3)⋊C4—124no—
96Dic3⋊C4—124no—
97C4×Dic3—34no—
98C4×Dic3—124no—
99C2×C3⋊C8—34no—
100Dic12—38no—
101Dic12—64no—
102D24—64no—
103D24—64no—
104C3×C16—24no—
105C3⋊C16—64no—
106C22×C32C2×D811yescharacteristic
107C2×C3⋊D3—81no—
108C2×C3⋊D3—81no—
109C2×C3⋊D3—81no—
110C32×C4—81no—
111C32×C4—81no—
112C32×C4#12111yescharacteristic
113C32×C4AGL(1,ℤ/8)11yescharacteristic
114C3⋊Dic3—21no—
115C3⋊Dic3—21no—
116C3⋊Dic3—42no—
117C2×Q16—91no—
118C2×Q16C2×C3⋊D311yescharacteristic
119C2×SD16—181no—
120C2×D8—91no—
121#124—181no—
122C4×Q8—181no—
123Q32—182no—
124SD32—182no—
125C2×C16—91no—
126C2×C16C2×C3⋊D311yescharacteristic
127#107C2×C3⋊D311yescharacteristic
128#103—181no—
129C4×C8—91no—
130C22×D3—124no—
131C3×Q8—44no—
132C3×Q8—44no—
133C2×C3×C4—44no—
134C2×C3×C4—44no—
135C2×C3×C4D3×D414yes—
136C2×Dic3—34no—
137C2×Dic3—34no—
138C2×Dic3—124no—
139D12—124no—
140D12—124no—
141Dic6—68no—
142Dic6—124no—
143C3×C8#23514yes—
144C3×C8D3×D414yes—
145C3⋊C8—64no—
146C2×C32#45911yescharacteristic
147C2×C32#50811yescharacteristic
148C2×C32#51011yescharacteristic
149C3⋊D3—161no—
150C2×Q8—21no—
151C2×Q8—181no—
152C2×D4—181no—
153Q16—21no—
154Q16—21no—
155Q16—92no—
156Q16—181no—
157SD16—362no—
158D8—181no—
159D8—181no—
160C2×C8—91no—
161C2×C8C22×C3⋊D311yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—361no—
164C22⋊C4—361no—
165C22⋊C4—361no—
166C42—91no—
167C42—361no—
168C16—21no—
169C16—181no—
170C22×C3D3×D814yes—
171C2×D3—244no—
172C2×D3—244no—
173C2×D3—244no—
174C3×C4—84no—
175C3×C4—84no—
176C3×C4#88414yes—
177C3×C4#91414yes—
178Dic3—64no—
179Dic3—64no—
180Dic3—128no—
181C32#221111yescharacteristic, complemented, Sylow
182C23—361no—
183Q8—41no—
184Q8—41no—
185Q8—182no—
186Q8—361no—
187D4—361no—
188D4—361no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—361no—
194C2×C4D4×C3⋊D311yescharacteristic
195C8—181no—
196C8#382811yescharacteristic
197C8D4×C3⋊D311yescharacteristic
198C2×C3#478614yes—
199C2×C3#491614yes—
200C2×C3#491814yes—
201D3—484no—
202C22—721no—
203C22—721no—
204C22—721no—
205C22D8×C3⋊D311yescharacteristic
206C4—81no—
207C4—81no—
208C4—181no—
209C4—181no—
210C4—362no—
211C4#6409311yescharacteristic
212C4#6412311yescharacteristic
213C3#6923714yescomplemented
214C2—1441no—
215C2#1059248511yescharacteristic
216C2#1059261511yescharacteristic
217C2#1059261711yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#358C2
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenter#358C3⋊D3
hypocenterC32#2211
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
2. C2×#63656C2semidirect
4. #10592572C2semidirect
5. C32×#358C2semidirect
6. #10589367C2semidirect
26. C3×#358D3semidirect
84. #358C3⋊D3semidirect
181. C32#2211semidirect
213. C3#69237semidirect

Maximal subgroups

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

subgroupindex
#105928902
C2×#636562
C2×#636272
#105925722
C32×#3582
#105893672
#105893572
#692373