Finite Group Databasebeta

← #11771229

Subgroups — #11771229

Order 1152.

600 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 169 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×#407C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4#67685—34nomaximal
5C23×C32×C4C2211yescharacteristic
6C2×C32×M16—21no—
7C2×#3757C412yes—
8C2×C4⋊(C3⋊Dic3)—21no—
9C2×#3748C412yescomplemented
10C32×C22⋊C8—21no—
11C32×C22⋊C8C412yescomplemented
12#63658—21no—
13#63657—21no—
14#63657—21no—
15C3×#407D314yes—
16#5212—34no—
17#5207—34no—
18C24×C32C2×C411yescharacteristic
19C22×C32×C4—42no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C32×C4Q811yescharacteristic
26C22×C3⋊Dic3—22no—
27C32×M16—42no—
28C2×C32×C8—22no—
29#3757—42no—
30C4⋊(C3⋊Dic3)—42no—
31#3748—42no—
32C2×C3⋊(C3⋊C8)—22no—
33#1305—91noSylow
34C23×C3×C4C2×D314yes—
35C2×C3×M16—24no—
36C2×#217—38no—
37C2×C4⋊Dic3—64no—
38C2×#208—38no—
39C3×C22⋊C8—24no—
40C3×C22⋊C8Dic318yescomplemented
41C3⋊#95—64no—
42#830—64no—
43#830—64no—
44C23×C32—21no—
45C23×C32—21no—
46C23×C32—41no—
47C23×C32—41no—
48C23×C32C4211yescharacteristic
49C23×C32C22⋊C411yescharacteristic
50C23×C32C4⋊C411yescharacteristic
51C2×C32×C4—22no—
52C2×C32×C4—22no—
53C2×C32×C4—22no—
54C2×C32×C4—41no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C4⋊C411yescharacteristic
60C2×C32×C4C4⋊C411yescharacteristic
61C2×C3⋊Dic3—42no—
62C2×C3⋊Dic3—42no—
63C2×C3⋊Dic3—42no—
64C32×C8—42no—
65C3⋊(C3⋊C8)—42no—
66#407—91no—
67#407C3⋊D311yescharacteristic
68#380—91no—
69C24×C3C4×D314yes—
70C22×C3×C4—48no—
71C22×C3×C4Dic614yes—
72C22×C3×C4C4×D314yes—
73C22×C3×C4D1214yes—
74C22×C3×C4C2×Dic314yes—
75C22×C3×C4#6714yes—
76C22×C3×C4#6714yes—
77C22×Dic3—68no—
78C3×M16—48no—
79C2×C3×C8—28no—
80#217—128no—
81C4⋊Dic3—128no—
82#208—128no—
83C2×C3⋊C8—68no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—42no—
93C22×C32—42no—
94C22×C32#9511yescharacteristic
95C22×C32#10011yescharacteristic
96C22×C32#10111yescharacteristic
97C32×C4—21no—
98C32×C4—21no—
99C32×C4—21no—
100C32×C4#9912yes—
101C3⋊Dic3—82no—
102C23×C4C2×C3⋊D311yescharacteristic
103C2×M16—21no—
104C2×M16—92no—
105C2×C4⋊C4—181no—
106C2×C22⋊C4—92no—
107C22⋊C8—21no—
108C22⋊C8—181no—
109C22⋊C8—181no—
110C22⋊C8C3⋊Dic312yescomplemented
111#95—181no—
112C23×C3—24no—
113C23×C3—24no—
114C23×C3—44no—
115C23×C3—44no—
116C23×C3C4×Dic314yes—
117C23×C3Dic3⋊C414yes—
118C23×C3(C2×D3)⋊C414yes—
119C2×C3×C4—28no—
120C2×C3×C4—28no—
121C2×C3×C4—28no—
122C2×C3×C4—44no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×C3×C4Dic3⋊C414yes—
126C2×C3×C4C4⋊Dic314yes—
127C2×C3×C4(C2×D3)⋊C414yes—
128C2×C3×C4#21714yes—
129C2×Dic3—128no—
130C2×Dic3—128no—
131C2×Dic3—128no—
132C3×C8—48no—
133C3⋊C8—128no—
134C2×C32—21no—
135C2×C32—21no—
136C2×C32—41no—
137C2×C32—41no—
138C2×C32#34211yescharacteristic
139C2×C32#34311yescharacteristic
140C2×C32#34411yescharacteristic
141C24C4×C3⋊D311yescharacteristic
142C22×C4—42no—
143C22×C4—182no—
144C22×C4#63411yescharacteristic
145C22×C4C4×C3⋊D311yescharacteristic
146C22×C4C4⋊(C3⋊D3)11yescharacteristic
147C22×C4C2×C3⋊Dic311yescharacteristic
148C22×C4#63811yescharacteristic
149C22×C4#63811yescharacteristic
150M16—42no—
151M16—362no—
152C2×C8—22no—
153C2×C8—182no—
154C4⋊C4—362no—
155C22⋊C4—362no—
156C22×C3—24no—
157C22×C3—24no—
158C22×C3—24no—
159C22×C3—24no—
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—24no—
163C22×C3—24no—
164C22×C3—48no—
165C22×C3—48no—
166C22×C3#82314yes—
167C22×C3#82414yes—
168C22×C3C3⋊#9514yes—
169C3×C4—24no—
170C3×C4—24no—
171C3×C4—24no—
172C3×C4#80618yes—
173Dic3—248no—
174C32#130511yescharacteristic, complemented, Sylow
175C23—21no—
176C23—21no—
177C23—41no—
178C23—41no—
179C23C4×C3⋊Dic311yescharacteristic
180C23#375011yescharacteristic
181C23#375211yescharacteristic
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—362no—
189C2×C4—362no—
190C2×C4—362no—
191C2×C4#375011yescharacteristic
192C2×C4C4⋊(C3⋊Dic3)11yescharacteristic
193C2×C4#375211yescharacteristic
194C2×C4#375711yescharacteristic
195C8—42no—
196C8—362no—
197C2×C3—24no—
198C2×C3—24no—
199C2×C3—44no—
200C2×C3—44no—
201C2×C3#452714yes—
202C2×C3#455414yes—
203C2×C3#455614yes—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22#6365011yescharacteristic
215C22#6365111yescharacteristic
216C22#6365811yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—722no—
221C4#6363312yes—
222C3#6768514yescomplemented
223C2—21no—
224C2—21no—
225C2—41no—
226C2—41no—
227C2#1058939311yescharacteristic
228C2#1058942011yescharacteristic
229C2#1058942211yescharacteristic
subgroupG/H
centerC22#63658
commutatorC23×C32C42
FrattiniC23×C4C2×C3⋊D3
FittingC32×#407C2
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C32×C4C22
hypercenter#407C3⋊D3
hypocenterC32#1305
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
9. C2×#3748C4semidirect
11. C32×C22⋊C8C4semidirect
40. C3×C22⋊C8Dic3semidirect
110. C22⋊C8C3⋊Dic3semidirect
174. C32#1305semidirect
222. C3#67685semidirect

Maximal subgroups

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

subgroupindex
C32×#4072
#105929112
#105929062
#676853