Finite Group Databasebeta

← #11771094

Subgroups — #11771094

Order 1152.

738 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C32×C4×C22⋊C4C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4#67618—34nomaximal
5C23×C32×C4C2211yescharacteristic
6C2×C32×C22⋊C4—21no—
7C2×C32×C42—21no—
8C2×#3757—21no—
9C2×C4×C3⋊Dic3—21no—
10C2×#3748C412yescomplemented
11C32×#95C412yescomplemented
12#63658C412yescomplemented
13#63657—21no—
14#63657—21no—
15C3×C4×C22⋊C4D314yes—
16C4×#217—34no—
17#5207—34no—
18C24×C32D411yescharacteristic
19C22×C32×C4—22no—
20C22×C32×C4—42no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C32×C4D411yescharacteristic
26C22×C32×C4Q811yescharacteristic
27C22×C3⋊Dic3—22no—
28C32×C22⋊C4—24no—
29C32×C42—42no—
30#3757—24no—
31C4×C3⋊Dic3—42no—
32#3748—42no—
33C2×C3⋊(C3⋊C8)—22no—
34#1297—91noSylow
35C23×C3×C4C2×D314yes—
36C2×C3×C22⋊C4—24no—
37C2×C3×C42—24no—
38C2×#217—64no—
39C2×C4×Dic3—64no—
40C2×#208—38no—
41C3×#95Dic318yescomplemented
42C3⋊#95—38no—
43#830—64no—
44#830—64no—
45C23×C32—22no—
46C23×C32—22no—
47C23×C32—41no—
48C23×C32C22⋊C411yescharacteristic
49C23×C32C22⋊C411yescharacteristic
50C23×C32C4⋊C411yescharacteristic
51C2×C32×C4—22no—
52C2×C32×C4—22no—
53C2×C32×C4—22no—
54C2×C32×C4—24no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4—41no—
58C2×C32×C4—42no—
59C2×C32×C4—42no—
60C2×C32×C4C4211yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C4⋊C411yescharacteristic
63C2×C32×C4C4⋊C411yescharacteristic
64C2×C3⋊Dic3—24no—
65C2×C3⋊Dic3—42no—
66C2×C3⋊Dic3—42no—
67C3⋊(C3⋊C8)—42no—
68#407—91no—
69C4×C22⋊C4—91no—
70C4×C22⋊C4C3⋊D311yescharacteristic
71C24×C3#6714yes—
72C22×C3×C4—28no—
73C22×C3×C4—48no—
74C22×C3×C4Dic614yes—
75C22×C3×C4C4×D314yes—
76C22×C3×C4C4×D314yes—
77C22×C3×C4D1214yes—
78C22×C3×C4C2×Dic314yes—
79C22×C3×C4#6714yes—
80C22×Dic3—68no—
81C3×C22⋊C4—216no—
82C3×C42—48no—
83#217—616no—
84C4×Dic3—128no—
85#208—128no—
86C2×C3⋊C8—68no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32—44no—
95C22×C32#9511yescharacteristic
96C22×C32#10412yes—
97C22×C32#10412yes—
98C32×C4—21no—
99C32×C4—21no—
100C32×C4—21no—
101C32×C4—44no—
102C32×C4#9912yes—
103C3⋊Dic3—44no—
104C23×C4C2×C3⋊D311yescharacteristic
105C2×M16—92no—
106C2×C22⋊C4—21no—
107C2×C22⋊C4—181no—
108C2×C42—21no—
109C2×C42—181no—
110C22⋊C8—181no—
111C22⋊C8—181no—
112#95—92no—
113#95C3⋊Dic312yescomplemented
114C23×C3—28no—
115C23×C3—28no—
116C23×C3—44no—
117C23×C3Dic3⋊C414yes—
118C23×C3(C2×D3)⋊C414yes—
119C23×C3#21714yes—
120C2×C3×C4—28no—
121C2×C3×C4—28no—
122C2×C3×C4—28no—
123C2×C3×C4—216no—
124C2×C3×C4—44no—
125C2×C3×C4—44no—
126C2×C3×C4—44no—
127C2×C3×C4—48no—
128C2×C3×C4—48no—
129C2×C3×C4C4×Dic314yes—
130C2×C3×C4Dic3⋊C414yes—
131C2×C3×C4C4⋊Dic314yes—
132C2×C3×C4(C2×D3)⋊C414yes—
133C2×Dic3—616no—
134C2×Dic3—128no—
135C2×Dic3—128no—
136C3⋊C8—128no—
137C2×C32—22no—
138C2×C32—22no—
139C2×C32—41no—
140C2×C32#33911yescharacteristic
141C2×C32#33911yescharacteristic
142C2×C32#34211yescharacteristic
143C24#63811yescharacteristic
144C22×C4—22no—
145C22×C4—42no—
146C22×C4—182no—
147C22×C4#63411yescharacteristic
148C22×C4C4×C3⋊D311yescharacteristic
149C22×C4C4×C3⋊D311yescharacteristic
150C22×C4C4⋊(C3⋊D3)11yescharacteristic
151C22×C4C2×C3⋊Dic311yescharacteristic
152C22×C4#63811yescharacteristic
153M16—362no—
154C2×C8—182no—
155C22⋊C4—24no—
156C22⋊C4—184no—
157C42—42no—
158C42—362no—
159C22×C3—24no—
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—24no—
165C22×C3—24no—
166C22×C3—416no—
167C22×C3#80518yes—
168C22×C3C3⋊#9514yes—
169C22×C3#83718yes—
170C3×C4—24no—
171C3×C4—24no—
172C3×C4—24no—
173C3×C4—416no—
174C3×C4#80618yes—
175Dic3—1216no—
176C32#129711yescharacteristic, complemented, Sylow
177C23—22no—
178C23—22no—
179C23—41no—
180C23#375011yescharacteristic
181C23#375211yescharacteristic
182C23#375711yescharacteristic
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—184no—
193C2×C4—362no—
194C2×C4—362no—
195C2×C4C4×C3⋊Dic311yescharacteristic
196C2×C4#375011yescharacteristic
197C2×C4C4⋊(C3⋊Dic3)11yescharacteristic
198C2×C4#375211yescharacteristic
199C8—362no—
200C2×C3—28no—
201C2×C3—28no—
202C2×C3—44no—
203C2×C3#452314yes—
204C2×C3#452714yes—
205C2×C3#453214yes—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—44no—
214C22#6363212yes—
215C22#6365811yescharacteristic
216C22#6366412yes—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—44no—
221C4—364no—
222C4#6363312yes—
223C3#6761814yescomplemented
224C2—22no—
225C2—22no—
226C2—41no—
227C2#1058938911yescharacteristic
228C2#1058939311yescharacteristic
229C2#1058939811yescharacteristic
subgroupG/H
centerC2×C4#3752
commutatorC2×C32×C4C42
FrattiniC23×C4C2×C3⋊D3
FittingC32×C4×C22⋊C4C2
socleC22×C32#95
prime radicalC24×C32D4
cosocleC23×C32×C4C22
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#1297
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
10. C2×#3748C4semidirect
11. C32×#95C4semidirect
12. #63658C4semidirect
41. C3×#95Dic3semidirect
113. #95C3⋊Dic3semidirect
176. C32#1297semidirect
223. C3#67618semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C22⋊C42
C4×#37572
#105929062
#676183