Finite Group Databasebeta

← #13073082

Subgroups — #13073082

Order 1408.

708 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 161 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×#66947C212yesmaximal, complemented
2C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C2×#66937C211yesmaximal, characteristic
4C2×#66936C212yesmaximal, complemented
5C11×#399C211yesmaximal, characteristic, complemented
6#10622605C211yesmaximal, characteristic, complemented
7#10622589C212yesmaximal, complemented
8#10622570C212yesmaximal, complemented
9#10622562C211yesmaximal, characteristic, complemented
10#10622290C211yesmaximal, characteristic, complemented
11#10622279C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×D44C2211yescharacteristic
15C22×C4×D11C2212yes—
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2212yes—
19C2×C11×C22⋊C4C2212yes—
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic11C2212yes—
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2212yes—
27C2×C4⋊Dic11C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2212yes—
32C2×C4×Dic11C2212yes—
33#66947—28no—
34C4⋊C4×D11—24no—
35#66937—24no—
36#66936—28no—
37C11×#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C24×C11C2311yescharacteristic
40C23×D11C2311yescharacteristic
41C23×D11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C2×C22⋊D11—22no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—22no—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C2×D44—22no—
55C2×D44—24no—
56C2×C4×D11—24no—
57C2×C4×D11—24no—
58C2×C4×D11—24no—
59C2×C4×D11—24no—
60C2×C4×D11D414yes—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—24no—
63C11×C22⋊C4—24no—
64C11×C22⋊C4—22no—
65C22⋊Dic11—24no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4D418yescomplemented
70C4⋊Dic11—24no—
71C4⋊Dic11—22no—
72Dic11⋊C4—24no—
73Dic11⋊C4—22no—
74Dic11⋊C4—24no—
75Dic11⋊C4—24no—
76C4×Dic11—24no—
77#2501—111nomaximal, Sylow
78C23×C11—22no—
79C23×C11—21no—
80C23×C11—22no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11C2411yescharacteristic
84C22×D11—22no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11—22no—
88C22×D11—21no—
89C22×D11—22no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11C2×D414yes—
93C22×D11C2×D412yes—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11C2×D414yes—
103C2×C4×C11C2×D412yes—
104C22⋊D11—44no—
105C22⋊D11—44no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—22no—
113C2×Dic11C2×D414yes—
114C2×Dic11C2×D412yes—
115C2×Dic11#4114yes—
116D44—44no—
117C4×D11—28no—
118C4×D11—48no—
119C2×#123—112no—
120C2×#123—112no—
121C2×#121—111no—
122C22×C4⋊C4—111no—
123#399—111no—
124#399—111no—
125#399—111no—
126#399D1111yescharacteristic, complemented
127#390—112no—
128#384—112no—
129C4×C22⋊C4—111no—
130C22×C11—41no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11—42no—
134C22×C11—42no—
135C22×C11C22×D411yescharacteristic
136C22×C11C22×D412yes—
137C22×C11C2×#4112yes—
138C22×C112−1+411yescharacteristic
139C22×C112−1+411yescharacteristic
140C2×D11—22no—
141C2×D11—22no—
142C2×D11—24no—
143C2×D11—24no—
144C2×D11—41no—
145C2×D11—41no—
146C2×D11—41no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11#12714yes—
150C4×C11—22no—
151C4×C11—24no—
152C4×C11—42no—
153C4×C11—41no—
154Dic11—24no—
155Dic11—42no—
156Dic11—41no—
157Dic11#12314yescomplemented
158C22×D4—111no—
159C22×D4—111no—
160C22×D4—111no—
161C23×C4—111no—
162C23×C4—112no—
163#123—228no—
164#123—228no—
165#121—224no—
166C2×C4⋊C4—112no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—111no—
169C2×C4⋊C4—112no—
170C2×C4⋊C4—112no—
171C2×C4⋊C4—112no—
172C2×C4⋊C4—224no—
173C2×C4⋊C4C2×D1111yescharacteristic
174C2×C4⋊C4C2×D1112yes—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4—111no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4C2×D1111yescharacteristic
181C2×C22⋊C4C2×D1112yes—
182C2×C42—112no—
183#95—111no—
184#95C2×D1111yescharacteristic
185C2×C11—81no—
186C2×C11C2×#12311yescharacteristic
187C2×C11C2×#12711yescharacteristic
188C2×C11#53611yescharacteristic
189C2×C11#54712yes—
190C2×C11#54712yes—
191D11—24no—
192D11—81no—
193C24—111no—
194C24—111no—
195C24C22×D1111yescharacteristic
196C2×D4—222no—
197C2×D4—224no—
198C2×D4—222no—
199C2×D4—224no—
200C2×D4—222no—
201C2×D4—224no—
202C22×C4—111no—
203C22×C4—112no—
204C22×C4—114no—
205C22×C4—112no—
206C22×C4—111no—
207C22×C4—224no—
208C22×C4—224no—
209C22×C4—224no—
210C22×C4—224no—
211C22×C4C22×D1112yes—
212C22×C4C22×D1111yescharacteristic
213C22×C4C22×D1111yescharacteristic
214C22×C4C22×D1112yes—
215C4⋊C4—22no—
216C4⋊C4—24no—
217C4⋊C4—224no—
218C4⋊C4—222no—
219C4⋊C4—224no—
220C4⋊C4—224no—
221C4⋊C4—222no—
222C4⋊C4—224no—
223C22⋊C4—22no—
224C22⋊C4—24no—
225C22⋊C4—118no—
226C22⋊C4—224no—
227C22⋊C4—224no—
228C22⋊C4—222no—
229C22⋊C4—224no—
230C42—224no—
231C11#250111yescharacteristic, complemented, Sylow
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—21no—
237C23—114no—
238C23—112no—
239C23—221no—
240C23—222no—
241C23—221no—
242C23—222no—
243C23—221no—
244C23—221no—
245C23—222no—
246C23—221no—
247C23C23×D1111yescharacteristic
248D4—444no—
249D4—444no—
250D4—444no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—112no—
260C2×C4—114no—
261C2×C4—114no—
262C2×C4—228no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—221no—
268C2×C4—222no—
269C2×C4—222no—
270C2×C4—448no—
271C2×C4D4×D1114yes—
272C2×C4D4×D1112yes—
273C22—41no—
274C22—41no—
275C22—42no—
276C22—41no—
277C22—42no—
278C22—114no—
279C22—222no—
280C22—224no—
281C22—222no—
282C22—224no—
283C22—441no—
284C22—441no—
285C22—442no—
286C22—441no—
287C22—442no—
288C22C2×D4×D1111yescharacteristic
289C22C2×D4×D1112yes—
290C22#6704011yescharacteristic
291C22#41×D1112yes—
292C22#6704311yescharacteristic
293C4—22no—
294C4—24no—
295C4—42no—
296C4—41no—
297C4—114no—
298C4—224no—
299C4—442no—
300C4—441no—
301C2—81no—
302C2—224no—
303C2—881no—
304C2#1062315911yescharacteristic
305C2#1062316212yes—
306C2D11×#12311yescharacteristic
307C2#1062318612yes—
308C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radicalC2×#66937C2
hypercenter#399D11
hypocenterC11#2501
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66947C2semidirect
2. C2×C4⋊C4×D11C2semidirect
4. C2×#66936C2semidirect
5. C11×#399C2semidirect
6. #10622605C2semidirect
7. #10622589C2semidirect
8. #10622570C2semidirect
9. #10622562C2semidirect
10. #10622290C2semidirect
11. #10622279C2semidirect
69. (C2×D11)⋊C4D4semidirect
126. #399D11semidirect
157. Dic11#123semidirect
231. C11#2501semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C2×C4⋊C4×D112
C2×#669372
C2×#669362
C11×#3992
#106226052
#106225892
#106225702
#106225622
#106222902
#106222792
#250111