Finite Group Databasebeta

← #13074427

Subgroups — #13074427

Order 1408.

668 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66931C211yesmaximal, characteristic, complemented
3C11×#385C211yesmaximal, characteristic, complemented
4#10622823C211yesmaximal, characteristic, complemented
5#10622607C212yesmaximal, complemented
6#10622605C212yesmaximal, complemented
7#10622568C211yesmaximal, characteristic
8#10622568C211yesmaximal, characteristic
9#10622555C211yesmaximal, characteristic, complemented
10#10622289C212yesmaximal, complemented
11#10622286C212yesmaximal, complemented
12C24×D11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C22×Dic22C2211yescharacteristic, complemented
16C2×C11×C4⋊C4C2212yescomplemented
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2211yescharacteristic
21C2×(C2×D11)⋊C4—24no—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2211yescharacteristic, complemented
29C2×Dic11⋊C4C2211yescharacteristic, complemented
30C2×Dic11⋊C4C2211yescharacteristic, complemented
31C2×Dic11⋊C4C2212yescomplemented
32C2×Dic11⋊C4C2212yescomplemented
33#66931—24no—
34C11×#95C2212yescomplemented
35C11⋊#95C2212yescomplemented
36C11⋊#95C2212yescomplemented
37C24×C11C2311yescharacteristic
38C23×D11—22no—
39C23×D11—22no—
40C23×D11—42no—
41C23×D11—42no—
42C23×D11Q814yescomplemented
43C23×D11C2312yes—
44C22×C4×C11—22no—
45C22×C4×C11—42no—
46C22×C4×C11C2312yes—
47C22×C4×C11C2312yes—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C22×Dic11—42no—
51C22×Dic11D414yes—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C2×Dic22—22no—
58C2×Dic22—42no—
59C11×C4⋊C4—42no—
60C11×C22⋊C4—22no—
61C11×C22⋊C4—22no—
62C22⋊Dic11—22no—
63C22⋊Dic11—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68(C2×D11)⋊C4—42no—
69(C2×D11)⋊C4—42no—
70C4⋊Dic11—22no—
71Dic11⋊C4—22no—
72Dic11⋊C4—22no—
73Dic11⋊C4—42no—
74Dic11⋊C4—42no—
75#2626—111nomaximal, Sylow
76C23×C11—22no—
77C23×C11—22no—
78C23×C11C2×D412yes—
79C23×C11C2×Q812yes—
80C23×C11#4112yes—
81C23×C11C2411yescharacteristic
82C22×D11—28no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—48no—
90C22×D11—44no—
91C22×D11—44no—
92C22×D11—48no—
93C22×D11C2×Q814yes—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
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—22no—
104C2×C4×C11—44no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—44no—
115C2×Dic11C2×D412yes—
116C2×Dic11C2×D412yes—
117Dic22—44no—
118C2×C22⋊Q8—111no—
119C22×C22⋊C4—111no—
120#399—112no—
121#396—112no—
122#396—112no—
123#393—112no—
124#385—111no—
125#385D1111yescharacteristic, complemented
126#380—111no—
127#379—111no—
128#379—111no—
129C22×C11—22no—
130C22×C11—22no—
131C22×C11—24no—
132C22×C11—24no—
133C22×C11C22⋊Q814yes—
134C22×C11C22×D411yescharacteristic
135C22×C11C22×Q811yescharacteristic
136C22×C11C2×#4111yescharacteristic
137C22×C11H(5,𝔽2)12yes—
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—
157C22×Q8—111no—
158C23×C4—111no—
159C23×C4C2×D1111yescharacteristic
160C22⋊Q8—224no—
161C2×C4⋊C4—111no—
162C2×C4⋊C4—111no—
163C2×C4⋊C4—111no—
164C2×C4⋊C4—112no—
165C2×C4⋊C4—112no—
166C2×C4⋊C4C2×D1112yescomplemented
167C2×C22⋊C4—111no—
168C2×C22⋊C4—111no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4—224no—
176C2×C22⋊C4C2×D1111yescharacteristic
177C2×C22⋊C4C2×D1111yescharacteristic
178#95—112no—
179#95—112no—
180#95C2×D1112yescomplemented
181C2×C11—24no—
182C2×C11C2×C22⋊Q811yescharacteristic
183C2×C11#53411yescharacteristic
184C2×C11#53511yescharacteristic
185C2×C11#53812yes—
186C2×C11#54312yes—
187D11—44no—
188C24—112no—
189C24—114no—
190C24—222no—
191C24—222no—
192C24—442no—
193C24—442no—
194C24C22×D1111yescharacteristic
195C2×Q8—222no—
196C2×Q8—442no—
197C22×C4—22no—
198C22×C4—42no—
199C22×C4—111no—
200C22×C4—111no—
201C22×C4—114no—
202C22×C4—112no—
203C22×C4—111no—
204C22×C4—111no—
205C22×C4—442no—
206C22×C4C22×D1112yes—
207C22×C4C22×D1112yes—
208C22×C4C22×D1111yescharacteristic
209C22×C4C22×D1111yescharacteristic
210C4⋊C4—42no—
211C4⋊C4—222no—
212C4⋊C4—222no—
213C4⋊C4—222no—
214C4⋊C4—442no—
215C4⋊C4—442no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—224no—
219C22⋊C4—224no—
220C22⋊C4—222no—
221C22⋊C4—222no—
222C22⋊C4—442no—
223C22⋊C4—442no—
224C22⋊C4—442no—
225C22⋊C4—442no—
226C11#262611yescharacteristic, complemented, Sylow
227C23—22no—
228C23—22no—
229C23—114no—
230C23—228no—
231C23—222no—
232C23—222no—
233C23—222no—
234C23—222no—
235C23—222no—
236C23—222no—
237C23—448no—
238C23—448no—
239C23—444no—
240C23—444no—
241C23#433912yes—
242C23D4×D1112yes—
243C23Q8×D1112yes—
244C23C23×D1111yescharacteristic
245Q8—444no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—44no—
257C2×C4—112no—
258C2×C4—112no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—221no—
263C2×C4—221no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—222no—
268C2×C4—444no—
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#6694914yes—
282C22C2×#433911yescharacteristic
283C22C2×D4×D1111yescharacteristic
284C22#6703712yes—
285C22C2×Q8×D1111yescharacteristic
286C22#6704212yes—
287C4—42no—
288C4—42no—
289C4—41no—
290C4—41no—
291C4—222no—
292C4—222no—
293C4—442no—
294C4—441no—
295C4—441no—
296C2—24no—
297C2—444no—
298C2C2×#6694911yescharacteristic
299C2#1062309112yes—
300C2#1062312311yescharacteristic
301C2#1062316512yes—
302C2#1062318411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radicalC24×D11C22
hypercenter#385D11
hypocenterC11#2626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#66931C2semidirect
3. C11×#385C2semidirect
4. #10622823C2semidirect
5. #10622607C2semidirect
6. #10622605C2semidirect
9. #10622555C2semidirect
10. #10622289C2semidirect
11. #10622286C2semidirect
15. C22×Dic22C22semidirect
16. C2×C11×C4⋊C4C22semidirect
28. C2×C4⋊Dic11C22semidirect
29. C2×Dic11⋊C4C22semidirect
30. C2×Dic11⋊C4C22semidirect
31. C2×Dic11⋊C4C22semidirect
32. C2×Dic11⋊C4C22semidirect
34. C11×#95C22semidirect
35. C11⋊#95C22semidirect
36. C11⋊#95C22semidirect
42. C23×D11Q8semidirect
125. #385D11semidirect
166. C2×C4⋊C4C2×D11semidirect
180. #95C2×D11semidirect
226. C11#2626semidirect

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×#669312
C11×#3852
#106228232
#106226072
#106226052
#106225682
#106225552
#106222892
#106222862
#262611