Finite Group Databasebeta

← #13072126

Subgroups — #13072126

Order 1408.

652 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic
2C2×#66988C212yesmaximal, complemented
3C2×D4×Dic11C211yesmaximal, characteristic, complemented
4#10622835C212yesmaximal, complemented
5#10622834C211yesmaximal, characteristic, complemented
6#10622825C211yesmaximal, characteristic, complemented
7C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
8#10622589C211yesmaximal, characteristic, complemented
9#10622586C211yesmaximal, characteristic, complemented
10#10622565C212yesmaximal, complemented
11#10622559C212yesmaximal, complemented
12C22×D4×C11C2212yes—
13C22×D4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C23×Dic11C2212yes—
16C11×#121—24no—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25#66988—28no—
26D4×Dic11—24no—
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2212yes—
32C2×C4×Dic11C2211yescharacteristic
33C2×C4×Dic11C2211yescharacteristic
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2212yes—
38C24×C11C2311yescharacteristic
39C24×C11C2312yes—
40C2×D4×C11—24no—
41C2×D4×C11—24no—
42C2×D4×C11—22no—
43C2×D4×C11—22no—
44C2×D4×C11—42no—
45C2×D4×C11D414yes—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11C2311yescharacteristic
50C22×C4×C11C2312yes—
51C22×C4×C11C2311yescharacteristic
52C22×Dic11—24no—
53C22×Dic11—24no—
54C22×Dic11—42no—
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2312yes—
57C22×Dic11C2312yes—
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C11×C4⋊C4—22no—
62C11×C22⋊C4—24no—
63C22⋊Dic11—24no—
64C22⋊Dic11—24no—
65C22⋊Dic11—22no—
66C22⋊Dic11—24no—
67C22⋊Dic11—24no—
68C22⋊Dic11D414yescomplemented
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71Dic11⋊C4—24no—
72Dic11⋊C4—24no—
73Dic11⋊C4—42no—
74C4×Dic11—22no—
75C4×Dic11—22no—
76#2422—111nomaximal, Sylow
77C23×C11—22no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—22no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—21no—
87C23×C11—21no—
88C23×C11—22no—
89C23×C11C2×D412yes—
90C23×C11C2×D414yes—
91C23×C11C2411yescharacteristic
92D4×C11—28no—
93D4×C11—48no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—44no—
101C2×C4×C11C2×D412yes—
102C2×C4×C11#4112yes—
103C2×C4×C11#4112yes—
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11—22no—
118C2×Dic11—21no—
119C2×Dic11—48no—
120C2×Dic11C2×D412yes—
121C2×Dic11C2×D412yes—
122C2×Dic11#4112yes—
123C2×#123—112no—
124C2×#121D1111yescharacteristic
125C2×C4×D4—111no—
126#397—112no—
127#394—112no—
128#390—111no—
129#389—111no—
130#385—112no—
131#384—111no—
132#380—111no—
133C4×C22⋊C4—111no—
134C22×C11—24no—
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—24no—
138C22×C11—24no—
139C22×C11—22no—
140C22×C11—41no—
141C22×C11—42no—
142C22×C11—41no—
143C22×C11—42no—
144C22×C11—41no—
145C22×C11—42no—
146C22×C11—41no—
147C22×C11—42no—
148C22×C11C22×D411yescharacteristic
149C22×C11C22×D411yescharacteristic
150C22×C11C2×#4111yescharacteristic
151C22×C11C2×#4111yescharacteristic
152C22×C11C2×#4111yescharacteristic
153C22×C11H(5,𝔽2)11yescharacteristic
154C22×C112−1+411yescharacteristic
155C4×C11—41no—
156C4×C11—42no—
157C4×C11#12314yescomplemented
158Dic11—22no—
159Dic11—22no—
160Dic11—22no—
161Dic11—42no—
162Dic11—42no—
163Dic11—41no—
164C22×D4C2×D1112yes—
165C22×D4C2×D1111yescharacteristic
166C23×C4—112no—
167C23×C4C2×D1111yescharacteristic
168#123—228no—
169#121—24no—
170C4×D4—224no—
171C2×C4⋊C4—111no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4—111no—
175C2×C4⋊C4—112no—
176C2×C4⋊C4C2×D1111yescharacteristic
177C2×C22⋊C4—111no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—111no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4C2×D1112yes—
184C2×C42—111no—
185C2×C42—111no—
186#95—111no—
187#95—111no—
188#95—112no—
189#95—112no—
190C2×C11—44no—
191C2×C11—42no—
192C2×C11C2×#12311yescharacteristic
193C2×C11#53211yescharacteristic
194C2×C11#54211yescharacteristic
195C2×C11D4211yescharacteristic
196C2×C11#54711yescharacteristic
197C2×C11#54711yescharacteristic
198C2×C11#55311yescharacteristic
199C24C22×D1111yescharacteristic
200C24C22×D1112yes—
201C2×D4—24no—
202C2×D4—24no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—42no—
206C2×D4C22⋊D1114yes—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—111no—
211C22×C4—111no—
212C22×C4—111no—
213C22×C4—111no—
214C22×C4—112no—
215C22×C4—112no—
216C22×C4—224no—
217C22×C4—224no—
218C22×C4—442no—
219C22×C4C22×D1111yescharacteristic
220C22×C4C22×D1112yes—
221C22×C4C22×D1111yescharacteristic
222C4⋊C4—22no—
223C4⋊C4—224no—
224C4⋊C4—224no—
225C4⋊C4—222no—
226C4⋊C4—222no—
227C4⋊C4—442no—
228C22⋊C4—24no—
229C22⋊C4—114no—
230C22⋊C4—224no—
231C22⋊C4—222no—
232C22⋊C4—224no—
233C22⋊C4—224no—
234C22⋊C4—224no—
235C42—222no—
236C42—222no—
237C11#242211yescharacteristic, complemented, Sylow
238C23—22no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—21no—
245C23—22no—
246C23—21no—
247C23—22no—
248C23—21no—
249C23—21no—
250C23D4×D1112yes—
251C23C2×C22⋊D1114yes—
252C23C23×D1111yescharacteristic
253D4—28no—
254D4—48no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—44no—
262C2×C4—112no—
263C2×C4—112no—
264C2×C4—112no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—221no—
276C2×C4—222no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—222no—
280C2×C4—448no—
281C2×C4#434112yes—
282C2×C4#434112yes—
283C2×C4C2×C22⋊D1112yes—
284C22—24no—
285C22—24no—
286C22—22no—
287C22—24no—
288C22—22no—
289C22—22no—
290C22—41no—
291C22—41no—
292C22—42no—
293C22—41no—
294C22—42no—
295C22—42no—
296C22—41no—
297C22—42no—
298C22C2×D4×D1111yescharacteristic
299C22C2×#434111yescharacteristic
300C22C2×#434111yescharacteristic
301C22#6703711yescharacteristic
302C22#41×D1111yescharacteristic
303C22#6704311yescharacteristic
304C22C22×C22⋊D1111yescharacteristic
305C4—41no—
306C4—42no—
307C4—222no—
308C4—222no—
309C4—222no—
310C4—442no—
311C4—441no—
312C4—442no—
313C4#6698814yescomplemented
314C2—44no—
315C2—42no—
316C2#1062312711yescharacteristic
317C2#1062313411yescharacteristic
318C2#1062314211yescharacteristic
319C2#1062314511yescharacteristic
320C2C2×#6698811yescharacteristic
321C2D4×C22⋊D1111yescharacteristic
322C2#1062335511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2422
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66988C2semidirect
3. C2×D4×Dic11C2semidirect
4. #10622835C2semidirect
5. #10622834C2semidirect
6. #10622825C2semidirect
7. C4×C22⋊Dic11C2semidirect
8. #10622589C2semidirect
9. #10622586C2semidirect
10. #10622565C2semidirect
11. #10622559C2semidirect
68. C22⋊Dic11D4semidirect
157. C4×C11#123semidirect
237. C11#2422semidirect
313. C4#66988semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669882
C2×D4×Dic112
#106228352
#106228342
#106228252
C4×C22⋊Dic112
#106225892
#106225862
#106225652
#106225592
#242211