Finite Group Databasebeta

← #11774054

Subgroups — #11774054

Order 1152.

430 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 60 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×#64098C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic
3#10593795C211yesmaximal, characteristic
4#10590203C212yesmaximal
5#10590202C212yesmaximal
6C2×C32×C4⋊C4C411yescharacteristic
7C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
8C2×#3750C411yescharacteristic
9C2×#3750C411yescharacteristic
10C2×#3750C411yescharacteristic
11C2×#3750C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64098—21no—
14#64098—21no—
15#64098—21no—
16#64098—21no—
17C22⋊#622C2212yes—
18C22⋊#622C2212yes—
19#63779—21no—
20#63777—21no—
21C4⋊#622—21no—
22C4×#622—21no—
23C2×#889—62no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×#622—22no—
32C2×#622—22no—
33C32×C4⋊C4—21no—
34C32×C4⋊C4—21no—
35C4⋊(C3⋊Dic3)—21no—
36C4⋊(C3⋊Dic3)—21no—
37#3750—21no—
38#3750—21no—
39#3750—21no—
40#3750—21no—
41#3750—21no—
42#3750—21no—
43#3750—21no—
44#3750—21no—
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49#1470—91nomaximal, Sylow
50C2×C3×C4⋊C4—22no—
51C2×C4⋊Dic3—62no—
52C2×Dic3⋊C4—62no—
53C2×Dic3⋊C4—62no—
54C2×Dic3⋊C4—62no—
55C2×Dic3⋊C4—62no—
56C2×C4×Dic3—62no—
57#889—64no—
58#889—64no—
59#889—64no—
60#889—64no—
61C23×C32C22×C411yescharacteristic
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—22no—
65C2×C32×C4—22no—
66C2×C32×C4—41no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79#622—42no—
80#622—42no—
81C2×#125—91no—
82#432—91no—
83#431—91no—
84#324—92no—
85#324—92no—
86C22×C3×C4—22no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C22×Dic3—62no—
92C22×Dic3—62no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95C4⋊Dic3—64no—
96C4⋊Dic3—64no—
97Dic3⋊C4—64no—
98Dic3⋊C4—64no—
99Dic3⋊C4—64no—
100Dic3⋊C4—64no—
101Dic3⋊C4—64no—
102Dic3⋊C4—64no—
103Dic3⋊C4—64no—
104Dic3⋊C4—64no—
105C4×Dic3—62no—
106C4×Dic3—62no—
107C4×Dic3—62no—
108C4×Dic3—62no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32C2×C22⋊C411yescharacteristic
112C22×C32#13112yes—
113C32×C4—21no—
114C32×C4—21no—
115C32×C4—41no—
116C32×C4—41no—
117C3⋊Dic3—21no—
118C3⋊Dic3—21no—
119C3⋊Dic3—21no—
120C3⋊Dic3—41no—
121C3⋊Dic3—41no—
122C3⋊Dic3#10112yes—
123#125—181no—
124#125—181no—
125#125—181no—
126#125—181no—
127C2×C4⋊C4—91no—
128C2×C4⋊C4—91no—
129C2×C4⋊C4—91no—
130C2×C4⋊C4—91no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4#15711yescharacteristic
133C2×C42—91no—
134C4⋊C8—181no—
135C4⋊C8—181no—
136C22⋊C8—92no—
137C22⋊C8—92no—
138#97—181no—
139C4×C8—181no—
140C23×C3—22no—
141C2×C3×C4—24no—
142C2×C3×C4—24no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—44no—
146C2×C3×C4—44no—
147C2×C3×C4—44no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—68no—
153C2×Dic3—64no—
154C2×Dic3—64no—
155C2×Dic3—124no—
156C2×Dic3—124no—
157C2×Dic3—124no—
158C2×C32—22no—
159C2×C32#40811yescharacteristic
160C2×C32#41011yescharacteristic
161C2×C32C2×#10111yescharacteristic
162C22×C4—91no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4C2×#15711yescharacteristic
167C22×C4C2×#15711yescharacteristic
168C22×C4C2×#15711yescharacteristic
169C2×C8—182no—
170C2×C8—182no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—181no—
174C4⋊C4—181no—
175C4⋊C4—181no—
176C4⋊C4—181no—
177C4⋊C4—181no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C4⋊C4—181no—
181C4⋊C4—181no—
182C4⋊C4—181no—
183C42—91no—
184C42—91no—
185C42—91no—
186C42—91no—
187C22×C3—24no—
188C22×C3—24no—
189C22×C3—24no—
190C22×C3—22no—
191C3×C4—42no—
192C3×C4—42no—
193C3×C4—44no—
194C3×C4—44no—
195Dic3—64no—
196Dic3—64no—
197Dic3—122no—
198Dic3—122no—
199Dic3—124no—
200Dic3—124no—
201C32#147011yescharacteristic, complemented, Sylow
202C23C22×#15711yescharacteristic
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—182no—
213C2×C4—182no—
214C2×C4—181no—
215C2×C4—181no—
216C2×C4—361no—
217C2×C4—361no—
218C2×C4C22⋊#15711yescharacteristic
219C2×C4C22⋊#15711yescharacteristic
220C8—362no—
221C8—362no—
222C2×C3—28no—
223C2×C3—22no—
224C2×C3—22no—
225C2×C3—22no—
226C22—21no—
227C22—21no—
228C22#6428712yes—
229C22C2×C22⋊#15711yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—41no—
234C4—92no—
235C4—181no—
236C4—181no—
237C4—181no—
238C4—361no—
239C4—361no—
240C3—22no—
241C2—22no—
242C2#1059379211yescharacteristic
243C2#1059382211yescharacteristic
244C2#1059383611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutator, prime radicalC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1470
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
201. C32#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#640982
#105938042
#105937952
#105902032
#105902022
#14709