Finite Group Databasebeta

← #13074451

Subgroups — #13074451

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66943C211yesmaximal, characteristic, complemented
2C2×#66925C211yesmaximal, characteristic
3C11×#389C211yesmaximal, characteristic, complemented
4#10622607C212yesmaximal
5#10622600C211yesmaximal, characteristic
6#10622600C211yesmaximal, characteristic
7#10622593C212yesmaximal, complemented
8#10622589C211yesmaximal, characteristic, complemented
9#10622541C211yesmaximal, characteristic, complemented
10#10622289C212yesmaximal
11#10622270C212yesmaximal, complemented
12C22×C4×D11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2212yes—
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31#66943—24no—
32#66925—24no—
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11—22no—
50C2×C4×D11Q814yes—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—42no—
54C42×C11—22no—
55(C2×D11)⋊C4—22no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—42no—
58(C2×D11)⋊C4—42no—
59C4⋊Dic11—24no—
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—24no—
65Dic11⋊C4—42no—
66Dic11⋊C4—42no—
67Dic11⋊C4—42no—
68C4×Dic11D414yes—
69#2629—111nomaximal, Sylow
70C23×C11C2411yescharacteristic
71C22×D11—21no—
72C22×D11—21no—
73C22×D11—21no—
74C22×D11—21no—
75C22×D11—21no—
76C22×D11—21no—
77C22×D11C2×Q812yes—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×Q812yes—
92C2×C4×C11#4112yes—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—21no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11C2×D412yes—
106C2×Dic11C2×D412yes—
107C2×Dic11C2×Q812yes—
108C4×D11—28no—
109C2×#125—111no—
110C2×#117—111no—
111#398—112no—
112#398—112no—
113#396—112no—
114#396—112no—
115#389—111no—
116#389D1111yescharacteristic, complemented
117#384—111no—
118#380—111no—
119#380—111no—
120C22×C11C22×D411yescharacteristic
121C22×C11C22×Q811yescharacteristic
122C22×C11C2×#4111yescharacteristic
123C22×C11H(5,𝔽2)11yescharacteristic
124C22×C11H(5,𝔽2)11yescharacteristic
125C22×C112−1+411yescharacteristic
126C22×C112−1+411yescharacteristic
127C2×D11—22no—
128C2×D11—22no—
129C2×D11—22no—
130C2×D11—41no—
131C2×D11—41no—
132C2×D11—41no—
133C2×D11—41no—
134C4×C11—42no—
135C4×C11—41no—
136C4×C11—41no—
137C4×C11—42no—
138C4×C11C22⋊Q814yes—
139Dic11—22no—
140Dic11—22no—
141Dic11—22no—
142Dic11—42no—
143Dic11—42no—
144C23×C4—111no—
145#125—224no—
146#117—224no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—111no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—111no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4C2×D1111yescharacteristic
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C4⋊C4C2×D1112yes—
159C2×C22⋊C4—111no—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4—112no—
163C2×C42—111no—
164C2×C42C2×D1111yescharacteristic
165#95—112no—
166#95—112no—
167#95—112no—
168#95C2×D1112yes—
169C2×C11C2×C22⋊Q811yescharacteristic
170C2×C11#53711yescharacteristic
171C2×C11#53711yescharacteristic
172C2×C11#54011yescharacteristic
173C2×C11#54111yescharacteristic
174C2×C11#54411yescharacteristic
175C2×C11#54411yescharacteristic
176D11—42no—
177C24—111no—
178C22×C4—111no—
179C22×C4—111no—
180C22×C4—111no—
181C22×C4—114no—
182C22×C4—112no—
183C22×C4—112no—
184C22×C4—222no—
185C22×C4—222no—
186C22×C4C22×D1111yescharacteristic
187C22×C4C22×D1112yes—
188C22×C4C22×D1112yes—
189C22×C4C22×D1111yescharacteristic
190C22×C4C22×D1111yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—222no—
195C4⋊C4—222no—
196C4⋊C4—224no—
197C4⋊C4—224no—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C22⋊C4—222no—
204C22⋊C4—222no—
205C22⋊C4—442no—
206C22⋊C4—442no—
207C42—22no—
208C42—114no—
209C11#262911yescharacteristic, complemented, Sylow
210C23—112no—
211C23—221no—
212C23—221no—
213C23—221no—
214C23—221no—
215C23—221no—
216C23—221no—
217C23C23×D1111yescharacteristic
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—112no—
231C2×C4—112no—
232C2×C4—112no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—221no—
236C2×C4—221no—
237C2×C4—221no—
238C2×C4—221no—
239C2×C4—228no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4#433912yes—
247C2×C4D4×D1112yes—
248C2×C4Q8×D1112yes—
249C22—222no—
250C22—222no—
251C22—222no—
252C22—441no—
253C22—441no—
254C22—441no—
255C22—441no—
256C22C2×#433911yescharacteristic
257C22C2×D4×D1111yescharacteristic
258C22#6703711yescharacteristic
259C22C2×Q8×D1111yescharacteristic
260C22#6704011yescharacteristic
261C22#6704211yescharacteristic
262C22#6704311yescharacteristic
263C4—42no—
264C4—41no—
265C4—42no—
266C4—41no—
267C4—222no—
268C4—222no—
269C4—222no—
270C4—442no—
271C4—442no—
272C4#6694914yes—
273C2—442no—
274C2C2×#6694911yescharacteristic
275C2#1062309311yescharacteristic
276C2#1062311411yescharacteristic
277C2#1062313911yescharacteristic
278C2#1062316011yescharacteristic
279C2#1062322011yescharacteristic
280C2#1062326011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC23×D11C23
hypercenter#389D11
hypocenterC11#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#66943C2semidirect
3. C11×#389C2semidirect
7. #10622593C2semidirect
8. #10622589C2semidirect
9. #10622541C2semidirect
11. #10622270C2semidirect
116. #389D11semidirect
209. C11#2629semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
C2×#669252
C11×#3892
#106226072
#106226002
#106225932
#106225892
#106225412
#106222892
#106222702
#262911