Finite Group Databasebeta

← #13074450

Subgroups — #13074450

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×#66979C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic, complemented
3C11×#380C211yesmaximal, characteristic
4#10622825C211yesmaximal, characteristic
5#10622598C211yesmaximal, characteristic, complemented
6#10622589C211yesmaximal, characteristic, complemented
7#10622586C211yesmaximal, characteristic, complemented
8#10622561C212yesmaximal
9#10622561C212yesmaximal
10#10622274C212yesmaximal, complemented
11#10622270C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C22⋊Dic11C2211yescharacteristic
18C2×C22⋊Dic11C2212yes—
19#66979—24no—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31C2×C4×Dic11C2211yescharacteristic
32#66943—24no—
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C22×C4×C11—22no—
39C22×C4×C11—22no—
40C22×C4×C11Q814yes—
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2311yescharacteristic
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53C11×C22⋊C4—42no—
54C22⋊Dic11—22no—
55C22⋊Dic11—22no—
56C22⋊Dic11—42no—
57C4⋊Dic11—24no—
58C4⋊Dic11—22no—
59C4⋊Dic11—22no—
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62C4⋊Dic11—42no—
63Dic11⋊C4—24no—
64Dic11⋊C4—42no—
65Dic11⋊C4—42no—
66Dic11⋊C4—42no—
67C4×Dic11—22no—
68C4×Dic11D414yes—
69#2629—111nomaximal, Sylow
70C23×C11—21no—
71C23×C11—21no—
72C23×C11—21no—
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11C2×Q812yes—
77C23×C11C2411yescharacteristic
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—28no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11C2×D412yes—
88C2×C4×C11C2×Q812yes—
89C2×C4×C11C2×Q812yes—
90C2×C4×C11#4112yes—
91C2×Dic11—21no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—21no—
103C2×Dic11—22no—
104C2×Dic11—21no—
105C2×Dic11—22no—
106C2×Dic11—21no—
107C2×Dic11C2×D412yes—
108C2×Dic11C2×D412yes—
109C2×#125—111no—
110C2×#117—111no—
111#398—112no—
112#398—112no—
113#396—112no—
114#396—112no—
115#389—111no—
116#389—111no—
117#384—111no—
118#380—111no—
119#380D1111yescharacteristic
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11C22×D411yescharacteristic
128C22×C11C22×Q811yescharacteristic
129C22×C11C2×#4111yescharacteristic
130C22×C11H(5,𝔽2)11yescharacteristic
131C22×C11H(5,𝔽2)11yescharacteristic
132C22×C112−1+411yescharacteristic
133C22×C112−1+411yescharacteristic
134C4×C11—22no—
135C4×C11—42no—
136C4×C11—42no—
137C4×C11C22⋊Q814yes—
138Dic11—22no—
139Dic11—22no—
140Dic11—41no—
141Dic11—41no—
142Dic11—42no—
143Dic11—42no—
144C23×C4C2×D1111yescharacteristic
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⋊C4—112no—
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C4⋊C4C2×D1111yescharacteristic
159C2×C22⋊C4—111no—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4C2×D1112yes—
163C2×C42—111no—
164C2×C42—111no—
165#95—112no—
166#95—112no—
167#95—112no—
168#95C2×D1112yes—
169C2×C11—42no—
170C2×C11C2×C22⋊Q811yescharacteristic
171C2×C11#53711yescharacteristic
172C2×C11#53711yescharacteristic
173C2×C11#54011yescharacteristic
174C2×C11#54111yescharacteristic
175C2×C11#54411yescharacteristic
176C2×C11#54411yescharacteristic
177C24C22×D1111yescharacteristic
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—111no—
181C22×C4—111no—
182C22×C4—111no—
183C22×C4—111no—
184C22×C4—112no—
185C22×C4—112no—
186C22×C4Dic2214yes—
187C22×C4C22×D1112yes—
188C22×C4C22×D1112yes—
189C22×C4C22×D1111yescharacteristic
190C22×C4C22×D1111yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—222no—
194C4⋊C4—222no—
195C4⋊C4—224no—
196C4⋊C4—224no—
197C4⋊C4—222no—
198C4⋊C4—222no—
199C4⋊C4—442no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C22⋊C4—42no—
204C22⋊C4—222no—
205C22⋊C4—222no—
206C22⋊C4—442no—
207C42—114no—
208C42—222no—
209C11#262911yescharacteristic, complemented, Sylow
210C23—21no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23—21no—
215C23—21no—
216C23C2×Dic2212yes—
217C23C23×D1111yescharacteristic
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—28no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—112no—
228C2×C4—112no—
229C2×C4—221no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—221no—
233C2×C4—221no—
234C2×C4—221no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—221no—
238C2×C4—222no—
239C2×C4—221no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—221no—
244C2×C4—221no—
245C2×C4C2×Dic2212yes—
246C2×C4C2×Dic2212yes—
247C2×C4D4×D1112yes—
248C2×C4#434112yes—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22C22×Dic2211yescharacteristic
257C22C2×D4×D1111yescharacteristic
258C22C2×#434111yescharacteristic
259C22#6703711yescharacteristic
260C22#6704011yescharacteristic
261C22#6704211yescharacteristic
262C22#6704311yescharacteristic
263C4—22no—
264C4—42no—
265C4—42no—
266C4—222no—
267C4—222no—
268C4—441no—
269C4—442no—
270C4—441no—
271C4—442no—
272C4#6693114yes—
273C2—42no—
274C2C2×#6693111yescharacteristic
275C2#1062303111yescharacteristic
276C2#1062305011yescharacteristic
277C2#1062313911yescharacteristic
278C2#1062315011yescharacteristic
279C2#1062315611yescharacteristic
280C2#1062316011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC24×C11C23
hypercenter#380D11
hypocenterC11#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#66943C2semidirect
5. #10622598C2semidirect
6. #10622589C2semidirect
7. #10622586C2semidirect
10. #10622274C2semidirect
11. #10622270C2semidirect
209. C11#2629semidirect

Maximal subgroups

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

subgroupindex
C2×#669792
C2×#669432
C11×#3802
#106228252
#106225982
#106225892
#106225862
#106225612
#106222742
#106222702
#262911