Finite Group Databasebeta

← #13075178

Subgroups — #13075178

Order 1408.

680 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#66990C211yesmaximal, characteristic
2C2×#66988C211yesmaximal, characteristic, complemented
3C11×#390C211yesmaximal, characteristic, complemented
4#10622607C212yesmaximal, complemented
5#10622574C212yesmaximal, complemented
6#10622571C212yesmaximal, complemented
7#10622568C212yesmaximal, complemented
8#10622566C212yesmaximal, complemented
9#10622553C212yesmaximal, complemented
10C24×D11C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic
12C22×C22⋊D11C2212yes—
13C23×Dic11C2211yescharacteristic, complemented
14C2×C11×C4⋊C4C2211yescharacteristic, complemented
15C2×C11×C22⋊C4C2212yes—
16C2×C11×C22⋊C4C2212yescomplemented
17C2×C42×C11C2211yescharacteristic, complemented
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2211yescharacteristic, complemented
21#66990—24no—
22#66988—24no—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2212yescomplemented
29C2×Dic11⋊C4C2212yescomplemented
30C11⋊#95C2212yescomplemented
31C11⋊#95C2212yescomplemented
32C11⋊#95C2212yescomplemented
33C24×C11C2311yescharacteristic
34C24×C11C2311yescharacteristic
35C23×D11—22no—
36C23×D11—24no—
37C23×D11—41no—
38C23×D11—41no—
39C23×D11—42no—
40C23×D11C2312yes—
41C2×D4×C11—41no—
42C2×D4×C11—41no—
43C2×D4×C11D414yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—24no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—42no—
50C22×Dic11—22no—
51C22×Dic11—41no—
52C22×Dic11—41no—
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
55C22×Dic11C2312yes—
56C11×C4⋊C4—41no—
57C11×C22⋊C4—42no—
58C11×C22⋊C4—42no—
59C42×C11—41no—
60C22⋊Dic11—24no—
61C22⋊Dic11—22no—
62C22⋊Dic11—22no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—42no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—42no—
69Dic11⋊C4—24no—
70#2697—111nomaximal, Sylow
71C23×C11—22no—
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11C2×D412yes—
80C23×C11C2×D412yes—
81C23×C11C2411yescharacteristic
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—44no—
89C22×D11—48no—
90C22×D11—48no—
91C22×D11—44no—
92C22×D11—44no—
93C22×D11#4114yes—
94D4×C11—44no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
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×C11C2×D412yes—
104C22⋊D11—48no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—44no—
115C2×#123—111no—
116C2×#120—111no—
117#397—112no—
118#396—112no—
119#394—112no—
120#390D1111yescharacteristic, complemented
121#388—112no—
122#386—112no—
123#379—112no—
124C22×C11—22no—
125C22×C11—22no—
126C22×C11—24no—
127C22×C11—24no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11C22×D411yescharacteristic
135C22×C11C2×#4112yes—
136C22×C11H(5,𝔽2)11yescharacteristic
137C22×C11H(5,𝔽2)11yescharacteristic
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—22no—
148C4×C11—42no—
149C4×C11—42no—
150Dic11—42no—
151Dic11—42no—
152Dic11—42no—
153C25—111no—
154C22×D4—112no—
155C22×D4C2×D1111yescharacteristic
156C23×C4—111no—
157#123—224no—
158#120—224no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4C2×D1111yescharacteristic, complemented
162C2×C22⋊C4—111no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—111no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4—112no—
168C2×C22⋊C4—112no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4C2×D1112yes—
171C2×C22⋊C4C2×D1112yescomplemented
172C2×C42C2×D1111yescharacteristic, complemented
173#95—112no—
174#95—112no—
175#95—112no—
176C2×C11—42no—
177C2×C11—42no—
178C2×C11#53411yescharacteristic
179C2×C11#53812yes—
180C2×C11#54612yes—
181C2×C11#55111yescharacteristic
182C2×C11#56011yescharacteristic
183D11—44no—
184C24—112no—
185C24—224no—
186C24—222no—
187C24—442no—
188C24—441no—
189C24—441no—
190C24C22×D1111yescharacteristic
191C24C22×D1111yescharacteristic
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—224no—
195C2×D4—224no—
196C2×D4—442no—
197C2×D4D4414yes—
198C22×C4—112no—
199C22×C4—112no—
200C22×C4—112no—
201C22×C4—222no—
202C22×C4—441no—
203C22×C4—441no—
204C22×C4C22×D1112yes—
205C22×C4C22×D1112yes—
206C22×C4C22×D1111yescharacteristic
207C4⋊C4—41no—
208C4⋊C4—224no—
209C4⋊C4—442no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C22⋊C4—224no—
213C22⋊C4—222no—
214C22⋊C4—222no—
215C22⋊C4—224no—
216C22⋊C4—224no—
217C22⋊C4—442no—
218C22⋊C4—442no—
219C22⋊C4—442no—
220C42—41no—
221C11#269711yescharacteristic, complemented, Sylow
222C23—22no—
223C23—22no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—22no—
229C23—22no—
230C23—114no—
231C23—222no—
232C23—222no—
233C23—222no—
234C23—222no—
235C23—222no—
236C23—222no—
237C23—448no—
238C23—444no—
239C23—444no—
240C23—448no—
241C23—444no—
242C23C2×D4412yes—
243C23C2×D4412yes—
244C23C23×D1111yescharacteristic
245D4—44no—
246D4—448no—
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—222no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—444no—
265C2×C4C2×D4412yes—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—24no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—224no—
277C22—224no—
278C22—224no—
279C22—4416no—
280C22—442no—
281C22—442no—
282C22—442no—
283C22—442no—
284C22C22×D4411yescharacteristic
285C22#6703711yescharacteristic
286C22#6703712yes—
287C22#6703711yescharacteristic
288C22#41×D1112yes—
289C4—22no—
290C4—42no—
291C4—42no—
292C4—442no—
293C4—442no—
294C4—442no—
295C2—42no—
296C2—42no—
297C2—444no—
298C2#1062302411yescharacteristic
299C2#1062308512yes—
300C2#1062314412yes—
301C2#1062321011yescharacteristic
302C2#1062325111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC2×#66990C2
hypercenter#390D11
hypocenterC11#2697
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#66988C2semidirect
3. C11×#390C2semidirect
4. #10622607C2semidirect
5. #10622574C2semidirect
6. #10622571C2semidirect
7. #10622568C2semidirect
8. #10622566C2semidirect
9. #10622553C2semidirect
13. C23×Dic11C22semidirect
14. C2×C11×C4⋊C4C22semidirect
16. C2×C11×C22⋊C4C22semidirect
17. C2×C42×C11C22semidirect
20. C2×C22⋊Dic11C22semidirect
28. C2×C4⋊Dic11C22semidirect
29. C2×Dic11⋊C4C22semidirect
30. C11⋊#95C22semidirect
31. C11⋊#95C22semidirect
32. C11⋊#95C22semidirect
120. #390D11semidirect
161. C2×C4⋊C4C2×D11semidirect
171. C2×C22⋊C4C2×D11semidirect
172. C2×C42C2×D11semidirect
221. C11#2697semidirect

Maximal subgroups

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

subgroupindex
C2×#669902
C2×#669882
C11×#3902
#106226072
#106225742
#106225712
#106225682
#106225662
#106225532
#269711