Finite Group Databasebeta

← #13072266

Subgroups — #13072266

Order 1408.

1088 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D11C211yesmaximal, characteristic
2C2×#66989C211yesmaximal, characteristic, complemented
3C2×#66950C211yesmaximal, characteristic, complemented
4C2×#66928C211yesmaximal, characteristic, complemented
5C11×#390C211yesmaximal, characteristic, complemented
6#10622601C211yesmaximal, characteristic, complemented
7#10622574C214yesmaximal, complemented
8#10622568C214yesmaximal, complemented
9C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10C24×D11C2212yes—
11C22×D4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C2×D4×D11—24no—
14C2×D4×D11—24no—
15C2×D4×D11—24no—
16C22×D44C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×Dic22C2211yescharacteristic, complemented
19C2×C11×C4⋊C4C2211yescharacteristic, complemented
20C2×C11×C22⋊C4C2214yescomplemented
21C2×C42×C11C2211yescharacteristic, complemented
22C2×C22⋊Dic11C2214yescomplemented
23#66989—24no—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2214yescomplemented
27C2×(C2×D11)⋊C4C2214yescomplemented
28C2×C4⋊Dic11C2212yescomplemented
29C2×C4×Dic11C2211yescharacteristic, complemented
30#66950—24no—
31#66928—24no—
32C11⋊#95C2212yescomplemented
33C24×C11C2312yes—
34C23×D11—24no—
35C23×D11—24no—
36C23×D11—24no—
37C23×D11—28no—
38C23×D11—44no—
39C23×D11C2312yes—
40C23×D11C2311yescharacteristic
41C2×D4×C11—22no—
42C2×D4×C11—22no—
43C2×D4×C11D414yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—24no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—24no—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53D4×D11—232no—
54C2×D44—22no—
55C2×D44—22no—
56C2×D44D414yes—
57C2×C4×D11—22no—
58C2×C4×D11—22no—
59C2×C4×D11D414yes—
60C2×Dic22—22no—
61C2×Dic22—22no—
62C2×Dic22—22no—
63C11×C4⋊C4—22no—
64C11×C22⋊C4—44no—
65C42×C11—22no—
66C22⋊Dic11—28no—
67(C2×D11)⋊C4—28no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—44no—
71C4⋊Dic11—24no—
72C4×Dic11—22no—
73#2435—111nomaximal, Sylow
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—24no—
77C23×C11—24no—
78C23×C11C2×D414yes—
79C23×C11C2411yescharacteristic
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—22no—
83C22×D11—216no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—24no—
87C22×D11—24no—
88C22×D11—416no—
89C22×D11—416no—
90C22×D11—48no—
91C22×D11—48no—
92C22×D11C2×D414yes—
93C22×D11C2×D412yes—
94C22×D11#4114yes—
95D4×C11—28no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—24no—
100C2×C4×C11—22no—
101C2×C4×C11C2×D412yes—
102C2×C4×C11C2×D412yes—
103C2×C4×C11C2×D412yes—
104C22⋊D11—216no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11C2×D412yes—
114D44—28no—
115C4×D11—28no—
116Dic22—44no—
117C23×D4—111no—
118C2×#124—111no—
119C2×#124—111no—
120C2×C22⋊Q8—111no—
121#394—114no—
122#390—111no—
123#390D1111yescharacteristic, complemented
124#379—114no—
125C4×C22⋊C4—111no—
126C22×C11—24no—
127C22×C11—28no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—44no—
131C22×C11C22×D411yescharacteristic
132C22×C11C22×D411yescharacteristic
133C22×C11C22×D411yescharacteristic
134C22×C11C2×#4112yes—
135C22×C11H(5,𝔽2)12yes—
136C2×D11—22no—
137C2×D11—22no—
138C2×D11—24no—
139C2×D11—24no—
140C2×D11—24no—
141C2×D11—28no—
142C2×D11—432no—
143C2×D11—42no—
144C2×D11—42no—
145C2×D11—44no—
146C2×D11#12414yescomplemented
147C4×C11—42no—
148C4×C11—42no—
149C4×C11#12014yes—
150Dic11—22no—
151Dic11—42no—
152Dic11—42no—
153C25—112no—
154C22×Q8—111no—
155C22×D4—112no—
156C22×D4—111no—
157C22×D4—224no—
158C22×D4—224no—
159C22×D4—224no—
160C22×D4C2×D1111yescharacteristic
161C23×C4—111no—
162#124—224no—
163#124—224no—
164C22⋊Q8—224no—
165C2×C4⋊C4—112no—
166C2×C4⋊C4C2×D1111yescharacteristic, complemented
167C2×C22⋊C4—114no—
168C2×C22⋊C4—112no—
169C2×C22⋊C4—114no—
170C2×C22⋊C4—112no—
171C2×C22⋊C4—114no—
172C2×C22⋊C4C2×D1114yescomplemented
173C2×C42—111no—
174C2×C42C2×D1111yescharacteristic, complemented
175#95—112no—
176C2×C11—44no—
177C2×C11C2×#12011yescharacteristic
178C2×C11C2×#12411yescharacteristic
179C2×C11#53511yescharacteristic
180C2×C11#54612yes—
181C2×C11#54612yes—
182D11—24no—
183D11—44no—
184C24—111no—
185C24—112no—
186C24—224no—
187C24—224no—
188C24—228no—
189C24—224no—
190C24—444no—
191C24C22×D1112yes—
192C2×Q8—222no—
193C2×Q8—222no—
194C2×Q8—222no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—114no—
198C2×D4—224no—
199C2×D4—2232no—
200C2×D4—224no—
201C2×D4—224no—
202C2×D4—222no—
203C2×D4—222no—
204C2×D4D4414yes—
205C22×C4—111no—
206C22×C4—114no—
207C22×C4—112no—
208C22×C4—112no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4C22×D1112yes—
212C22×C4C22×D1112yes—
213C22×C4C22×D1111yescharacteristic
214C4⋊C4—22no—
215C4⋊C4—224no—
216C22⋊C4—44no—
217C22⋊C4—224no—
218C22⋊C4—228no—
219C22⋊C4—224no—
220C22⋊C4—228no—
221C22⋊C4—444no—
222C42—22no—
223C42—222no—
224C11#243511yescharacteristic, complemented, Sylow
225C23—22no—
226C23—22no—
227C23—24no—
228C23—24no—
229C23—112no—
230C23—114no—
231C23—114no—
232C23—2216no—
233C23—221no—
234C23—221no—
235C23—222no—
236C23—222no—
237C23—222no—
238C23—224no—
239C23—224no—
240C23—4416no—
241C23—448no—
242C23—4416no—
243C23—448no—
244C23C2×D4414yes—
245C23C23×D1111yescharacteristic
246Q8—444no—
247D4—28no—
248D4—2216no—
249D4—228no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—112no—
256C2×C4—221no—
257C2×C4—221no—
258C2×C4—228no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4C2×D4412yes—
266C2×C4D4×D1112yes—
267C2×C4D4×D1112yes—
268C22—24no—
269C22—28no—
270C22—42no—
271C22—44no—
272C22—42no—
273C22—114no—
274C22—222no—
275C22—222no—
276C22—224no—
277C22—224no—
278C22—224no—
279C22—228no—
280C22—4432no—
281C22—442no—
282C22—444no—
283C22—442no—
284C22C22×D4411yescharacteristic
285C22C2×D4×D1111yescharacteristic
286C22C2×D4×D1111yescharacteristic
287C22#6703712yes—
288C22#41×D1112yes—
289C4—42no—
290C4—42no—
291C4—222no—
292C4—442no—
293C4—442no—
294C4#6693514yes—
295C2—44no—
296C2—224no—
297C2—444no—
298C2C2×#6693511yescharacteristic
299C2#1062308512yes—
300C2#1062314312yes—
301C2D11×#12411yescharacteristic
302C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×D11C2
hypercenter#390D11
hypocenterC11#2435
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#66989C2semidirect
3. C2×#66950C2semidirect
4. C2×#66928C2semidirect
5. C11×#390C2semidirect
6. #10622601C2semidirect
7. #10622574C2semidirect
8. #10622568C2semidirect
9. C4×(C2×D11)⋊C4C2semidirect
18. C22×Dic22C22semidirect
19. C2×C11×C4⋊C4C22semidirect
20. C2×C11×C22⋊C4C22semidirect
21. C2×C42×C11C22semidirect
22. C2×C22⋊Dic11C22semidirect
26. C2×(C2×D11)⋊C4C22semidirect
27. C2×(C2×D11)⋊C4C22semidirect
28. C2×C4⋊Dic11C22semidirect
29. C2×C4×Dic11C22semidirect
32. C11⋊#95C22semidirect
123. #390D11semidirect
146. C2×D11#124semidirect
166. C2×C4⋊C4C2×D11semidirect
172. C2×C22⋊C4C2×D11semidirect
174. C2×C42C2×D11semidirect
224. C11#2435semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D112
C2×#669892
C2×#669502
C2×#669282
C11×#3902
#106226012
#106225742
#106225682
C4×(C2×D11)⋊C42
#243511