Finite Group Databasebeta

← #13072889

Subgroups — #13072889

Order 1408.

672 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C22×(C2×D11)⋊C4C211yesmaximal, characteristic
2C2×#66930C211yesmaximal, characteristic, complemented
3C11×#385C211yesmaximal, characteristic, complemented
4#10622823C211yesmaximal, characteristic, complemented
5#10622605C212yesmaximal, complemented
6#10622603C212yesmaximal, complemented
7#10622568C211yesmaximal, characteristic
8#10622568C211yesmaximal, characteristic
9#10622556C211yesmaximal, characteristic, complemented
10#10622288C212yesmaximal, complemented
11#10622282C212yesmaximal, complemented
12C24×D11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C2×C11×C4⋊C4C2212yescomplemented
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊Dic11C2211yescharacteristic
20C2×(C2×D11)⋊C4—24no—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×Dic11⋊C4C2211yescharacteristic, complemented
28C2×Dic11⋊C4C2211yescharacteristic, complemented
29C2×Dic11⋊C4C2212yescomplemented
30C2×C4×Dic11C2211yescharacteristic, complemented
31C2×C4×Dic11C2211yescharacteristic, complemented
32#66930—24no—
33C11×#95C2212yescomplemented
34C11⋊#95C2212yescomplemented
35C11⋊#95C2212yescomplemented
36C11⋊#95C2212yescomplemented
37C24×C11C2311yescharacteristic
38C23×D11—22no—
39C23×D11—24no—
40C23×D11—22no—
41C23×D11—22no—
42C23×D11—42no—
43C23×D11C2312yes—
44C22×C4×C11—22no—
45C22×C4×C11—42no—
46C22×C4×C11C2312yes—
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C22×Dic11—22no—
51C22×Dic11—22no—
52C22×Dic11D414yes—
53C22×Dic11C2312yes—
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2311yescharacteristic
58C11×C4⋊C4—42no—
59C11×C22⋊C4—22no—
60C11×C22⋊C4—22no—
61C22⋊Dic11—22no—
62C22⋊Dic11—22no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—42no—
68(C2×D11)⋊C4—42no—
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71Dic11⋊C4—42no—
72C4×Dic11—22no—
73C4×Dic11—22no—
74#2482—111nomaximal, Sylow
75C23×C11—22no—
76C23×C11—22no—
77C23×C11C2×D412yes—
78C23×C11#4112yes—
79C23×C11#4112yes—
80C23×C11C2411yescharacteristic
81C22×D11—28no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—48no—
89C22×D11—48no—
90C22×D11—44no—
91C22×D11—44no—
92C22×D11#4114yes—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—44no—
104C2×Dic11—28no—
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×Dic11C2×D412yes—
117C2×Dic11C2×D412yes—
118C2×#117—111no—
119C22×C22⋊C4—111no—
120#399—112no—
121#397—112no—
122#388—112no—
123#388—112no—
124#385—111no—
125#385D1111yescharacteristic, complemented
126#381—111no—
127#379—111no—
128#379—111no—
129C22×C11—22no—
130C22×C11—22no—
131C22×C11—24no—
132C22×C11—24no—
133C22×C11#12314yes—
134C22×C11C22×D411yescharacteristic
135C22×C11C2×#4111yescharacteristic
136C22×C11C2×#4111yescharacteristic
137C22×C11C2×#4112yes—
138C22×C11H(5,𝔽2)12yes—
139C2×D11—24no—
140C2×D11—24no—
141C2×D11—24no—
142C2×D11—416no—
143C2×D11—42no—
144C2×D11—42no—
145C2×D11—42no—
146C2×D11—42no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—42no—
150C4×C11—42no—
151Dic11—22no—
152Dic11—22no—
153Dic11—41no—
154Dic11—41no—
155Dic11—42no—
156C25—111no—
157C23×C4—111no—
158C23×C4C2×D1111yescharacteristic
159#117—224no—
160C2×C4⋊C4—111no—
161C2×C4⋊C4—111no—
162C2×C4⋊C4—112no—
163C2×C4⋊C4C2×D1112yescomplemented
164C2×C22⋊C4—111no—
165C2×C22⋊C4—111no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4—112no—
168C2×C22⋊C4—112no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—224no—
173C2×C22⋊C4C2×D1111yescharacteristic
174C2×C22⋊C4C2×D1111yescharacteristic
175C2×C42—111no—
176C2×C42—111no—
177#95—112no—
178#95—112no—
179#95—112no—
180#95C2×D1112yescomplemented
181C2×C11—24no—
182C2×C11C2×#12311yescharacteristic
183C2×C11#52511yescharacteristic
184C2×C11#53511yescharacteristic
185C2×C11#55112yes—
186C2×C11#55112yes—
187D11—44no—
188C24—112no—
189C24—224no—
190C24—222no—
191C24—222no—
192C24—222no—
193C24—442no—
194C24C22×D1111yescharacteristic
195C22×C4—22no—
196C22×C4—42no—
197C22×C4—114no—
198C22×C4—111no—
199C22×C4—111no—
200C22×C4—112no—
201C22×C4—111no—
202C22×C4—111no—
203C22×C4—222no—
204C22×C4—222no—
205C22×C4C22×D1112yes—
206C22×C4C22×D1112yes—
207C22×C4C22×D1111yescharacteristic
208C22×C4C22×D1111yescharacteristic
209C4⋊C4—42no—
210C4⋊C4—222no—
211C4⋊C4—222no—
212C4⋊C4—442no—
213C22⋊C4—22no—
214C22⋊C4—22no—
215C22⋊C4—224no—
216C22⋊C4—224no—
217C22⋊C4—224no—
218C22⋊C4—224no—
219C22⋊C4—222no—
220C22⋊C4—222no—
221C22⋊C4—442no—
222C22⋊C4—442no—
223C42—222no—
224C42—222no—
225C11#248211yescharacteristic, complemented, Sylow
226C23—22no—
227C23—22no—
228C23—114no—
229C23—228no—
230C23—222no—
231C23—222no—
232C23—222no—
233C23—222no—
234C23—222no—
235C23—222no—
236C23—448no—
237C23—448no—
238C23—444no—
239C23—444no—
240C23#433912yes—
241C23D4×D1112yes—
242C23#434312yes—
243C23C23×D1111yescharacteristic
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—44no—
255C2×C4—112no—
256C2×C4—112no—
257C2×C4—228no—
258C2×C4—221no—
259C2×C4—221no—
260C2×C4—221no—
261C2×C4—221no—
262C2×C4—221no—
263C2×C4—221no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—222no—
268C2×C4—222no—
269C22—24no—
270C22—22no—
271C22—24no—
272C22—22no—
273C22—224no—
274C22—224no—
275C22—224no—
276C22—4416no—
277C22—442no—
278C22—442no—
279C22—442no—
280C22—442no—
281C22#6694714yes—
282C22C2×#433911yescharacteristic
283C22C2×D4×D1111yescharacteristic
284C22#6703712yes—
285C22C2×#434311yescharacteristic
286C22#41×D1112yes—
287C4—42no—
288C4—42no—
289C4—41no—
290C4—41no—
291C4—222no—
292C4—222no—
293C4—441no—
294C4—442no—
295C4—441no—
296C2—24no—
297C2—444no—
298C2C2×#6694711yescharacteristic
299C2#1062308712yes—
300C2#1062312311yescharacteristic
301C2#1062316812yes—
302C2#1062318711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radicalC24×D11C22
hypercenter#385D11
hypocenterC11#2482
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#66930C2semidirect
3. C11×#385C2semidirect
4. #10622823C2semidirect
5. #10622605C2semidirect
6. #10622603C2semidirect
9. #10622556C2semidirect
10. #10622288C2semidirect
11. #10622282C2semidirect
15. C2×C11×C4⋊C4C22semidirect
27. C2×Dic11⋊C4C22semidirect
28. C2×Dic11⋊C4C22semidirect
29. C2×Dic11⋊C4C22semidirect
30. C2×C4×Dic11C22semidirect
31. C2×C4×Dic11C22semidirect
33. C11×#95C22semidirect
34. C11⋊#95C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
125. #385D11semidirect
163. C2×C4⋊C4C2×D11semidirect
180. #95C2×D11semidirect
225. C11#2482semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D11)⋊C42
C2×#669302
C11×#3852
#106228232
#106226052
#106226032
#106225682
#106225562
#106222882
#106222822
#248211