Finite Group Databasebeta

← #13073032

Subgroups — #13073032

Order 1408.

468 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66929C212yesmaximal
2C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
3#10622600C211yesmaximal, characteristic
4#10622600C211yesmaximal, characteristic
5#10622589C211yesmaximal, characteristic, complemented
6#10622586C211yesmaximal, characteristic, complemented
7C4×(C2×D11)⋊C4C211yesmaximal, characteristic
8#10622546C212yesmaximal, complemented
9#10622541C211yesmaximal, characteristic, complemented
10#10622288C212yesmaximal
11#10622271C212yesmaximal, complemented
12C22×C4×D11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28#66929—28no—
29C11×#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C23×D11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2311yescharacteristic
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C2×C4×D11—22no—
48C2×C4×D11—22no—
49C2×C4×D11—22no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—22no—
52C42×C11—24no—
53C42×C11—22no—
54(C2×D11)⋊C4—22no—
55(C2×D11)⋊C4—24no—
56(C2×D11)⋊C4—24no—
57(C2×D11)⋊C4D414yes—
58C4⋊Dic11—22no—
59C4⋊Dic11—22no—
60Dic11⋊C4—24no—
61Dic11⋊C4—24no—
62Dic11⋊C4—24no—
63Dic11⋊C4—24no—
64C4×Dic11—22no—
65#2496—111nomaximal, Sylow
66C23×C11C2411yescharacteristic
67C22×D11—21no—
68C22×D11—21no—
69C22×D11—21no—
70C22×D11—21no—
71C22×D11—21no—
72C22×D11—21no—
73C22×D11C2×D412yes—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11C2×D412yes—
86C2×C4×C11#4112yes—
87C2×C4×C11#4112yes—
88C2×C4×C11#4112yes—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—22no—
102C2×Dic11C2×D412yes—
103C2×Dic11#4112yes—
104C4×D11—44no—
105C2×#126—112no—
106#400—112no—
107#397—112no—
108#389—111no—
109#389—111no—
110#387—112no—
111#384—111no—
112#380—111no—
113#380—111no—
114C4×C4⋊C4D1111yescharacteristic, complemented
115C4×C22⋊C4—111no—
116C22×C11C22×D411yescharacteristic
117C22×C11C2×#4111yescharacteristic
118C22×C11C2×#4111yescharacteristic
119C22×C11C2×#4111yescharacteristic
120C22×C11C2×#4111yescharacteristic
121C22×C112−1+411yescharacteristic
122C22×C112−1+411yescharacteristic
123C2×D11—22no—
124C2×D11—22no—
125C2×D11—22no—
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—41no—
129C2×D11—41no—
130C4×C11—22no—
131C4×C11—42no—
132C4×C11—42no—
133C4×C11—41no—
134C4×C11#12614yescomplemented
135Dic11—22no—
136Dic11—22no—
137Dic11—41no—
138Dic11—42no—
139Dic11—42no—
140C23×C4—111no—
141#126—228no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4C2×D1111yescharacteristic
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C22⋊C4—111no—
151C2×C22⋊C4—112no—
152C2×C22⋊C4—112no—
153C2×C22⋊C4—111no—
154C2×C42—111no—
155C2×C42C2×D1112yes—
156C2×C42C2×D1111yescharacteristic
157#95—111no—
158#95—111no—
159#95—112no—
160#95—112no—
161#95—112no—
162#95—112no—
163#95C2×D1112yes—
164C2×C11C2×#12611yescharacteristic
165C2×C11#53211yescharacteristic
166C2×C11#54111yescharacteristic
167C2×C11#54711yescharacteristic
168C2×C11#54711yescharacteristic
169C2×C11#55211yescharacteristic
170C2×C11#55611yescharacteristic
171D11—42no—
172C24—111no—
173C22×C4—111no—
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—112no—
177C22×C4—112no—
178C22×C4—222no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4C22×D1111yescharacteristic
182C22×C4C22×D1112yes—
183C22×C4C22×D1112yes—
184C22×C4C22×D1111yescharacteristic
185C22×C4C22×D1111yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—224no—
189C4⋊C4—224no—
190C4⋊C4—224no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—224no—
194C22⋊C4—114no—
195C22⋊C4—222no—
196C22⋊C4—224no—
197C22⋊C4—224no—
198C42—22no—
199C42—24no—
200C42—222no—
201C11#249611yescharacteristic, complemented, Sylow
202C23—112no—
203C23—221no—
204C23—221no—
205C23—221no—
206C23—221no—
207C23—221no—
208C23—221no—
209C23C23×D1111yescharacteristic
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—112no—
222C2×C4—112no—
223C2×C4—221no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—221no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—221no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—444no—
237C2×C4#433912yes—
238C2×C4#433912yes—
239C2×C4#433912yes—
240C2×C4D4×D1112yes—
241C22—222no—
242C22—222no—
243C22—222no—
244C22—441no—
245C22—441no—
246C22—441no—
247C22—441no—
248C22C2×#433911yescharacteristic
249C22C2×#433911yescharacteristic
250C22C2×#433911yescharacteristic
251C22C2×D4×D1111yescharacteristic
252C22#6704011yescharacteristic
253C22#41×D1111yescharacteristic
254C22#6704311yescharacteristic
255C4—22no—
256C4—41no—
257C4—42no—
258C4—42no—
259C4—222no—
260C4—222no—
261C4—441no—
262C4—442no—
263C4—442no—
264C4#6692914yescomplemented
265C2—442no—
266C2C2×#6692911yescharacteristic
267C2#1062303811yescharacteristic
268C2#1062306411yescharacteristic
269C2#1062307911yescharacteristic
270C2#1062308211yescharacteristic
271C2#1062311211yescharacteristic
272C2#1062311411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C4⋊C4C2
prime radicalC23×D11C23
hypercenterC4×C4⋊C4D11
hypocenterC11#2496
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C11×C4⋊C4C2semidirect
5. #10622589C2semidirect
6. #10622586C2semidirect
8. #10622546C2semidirect
9. #10622541C2semidirect
11. #10622271C2semidirect
114. C4×C4⋊C4D11semidirect
134. C4×C11#126semidirect
201. C11#2496semidirect
264. C4#66929semidirect

Maximal subgroups

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

subgroupindex
C2×#669292
C4×C11×C4⋊C42
#106226002
#106225892
#106225862
C4×(C2×D11)⋊C42
#106225462
#106225412
#106222882
#106222712
#249611