Finite Group Databasebeta

← #13073085

Subgroups — #13073085

Order 1408.

708 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic
3C2×#66988C211yesmaximal, characteristic, complemented
4C2×#66982C211yesmaximal, characteristic, complemented
5C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
6C2×#66939C211yesmaximal, characteristic, complemented
7#10622605C212yesmaximal, complemented
8#10622589C212yesmaximal, complemented
9#10622570C212yesmaximal, complemented
10#10622562C212yesmaximal, complemented
11C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×C22⋊D11C2211yescharacteristic
16C23×Dic11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C11×#123—24no—
19C2×C11×C4⋊C4C2212yes—
20C2×C11×C22⋊C4C2212yes—
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25#66992—24no—
26#66988—24no—
27#66982—24no—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×C4⋊Dic11C2212yes—
32C2×Dic11⋊C4—24no—
33C2×Dic11⋊C4C2212yes—
34C2×Dic11⋊C4C2212yes—
35C2×Dic11⋊C4C2212yes—
36C2×Dic11⋊C4C2212yes—
37C2×Dic11⋊C4C2211yescharacteristic
38C2×C4×Dic11C2212yes—
39#66939—24no—
40C11⋊#95C2212yes—
41C24×C11C2311yescharacteristic
42C24×C11C2311yescharacteristic
43C23×D11C2311yescharacteristic
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11C2312yes—
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2312yes—
53C2×C22⋊D11—22no—
54C2×C22⋊D11—24no—
55C2×C22⋊D11—22no—
56C2×C22⋊D11—22no—
57C2×C22⋊D11—22no—
58C22×Dic11—24no—
59C22×Dic11—22no—
60C22×Dic11—22no—
61C22×Dic11—22no—
62C22×Dic11D414yes—
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2312yes—
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2312yes—
67C22×Dic11C2311yescharacteristic
68C11×C4⋊C4—24no—
69C11×C22⋊C4—24no—
70C11×C22⋊C4D414yescomplemented
71C22⋊Dic11—24no—
72C22⋊Dic11—22no—
73C22⋊Dic11D414yescomplemented
74(C2×D11)⋊C4—24no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—24no—
77C4⋊Dic11—24no—
78Dic11⋊C4—24no—
79Dic11⋊C4—24no—
80Dic11⋊C4—24no—
81Dic11⋊C4—24no—
82Dic11⋊C4—22no—
83C4×Dic11—24no—
84#2501—111nomaximal, Sylow
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11C2×D412yes—
93C23×C11C2×D412yes—
94C23×C11C2×D412yes—
95C23×C11C2411yescharacteristic
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—21no—
99C22×D11—22no—
100C22×D11—22no—
101D4×C11—44no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—44no—
111C2×C4×C11C2×D414yes—
112C22⋊D11—44no—
113C22⋊D11—44no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—28no—
118C2×Dic11—22no—
119C2×Dic11—21no—
120C2×Dic11—22no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—22no—
124C2×Dic11—44no—
125C2×Dic11C2×D414yes—
126C2×Dic11C2×D412yes—
127C2×Dic11C2×D412yes—
128C2×Dic11#4114yes—
129C2×#123—111no—
130C2×#123—111no—
131C2×#123—111no—
132C2×#123D1111yescharacteristic, complemented
133C2×#121—111no—
134C22×C4⋊C4—111no—
135#399—112no—
136#399—112no—
137#390—112no—
138#384—112no—
139C4×C22⋊C4—111no—
140C22×C11—22no—
141C22×C11—22no—
142C22×C11—24no—
143C22×C11—24no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—42no—
148C22×C11—42no—
149C22×C11#12714yes—
150C22×C11C22×D411yescharacteristic
151C22×C11C22×D411yescharacteristic
152C22×C11C22×D411yescharacteristic
153C22×C11C2×#4112yes—
154C22×C112−1+412yes—
155C2×D11—41no—
156C2×D11—41no—
157C2×D11—41no—
158C2×D11—42no—
159C2×D11—42no—
160C4×C11—24no—
161C4×C11—42no—
162C4×C11—41no—
163Dic11—22no—
164Dic11—24no—
165Dic11—42no—
166Dic11—41no—
167Dic11#12314yescomplemented
168C22×D4—111no—
169C22×D4—111no—
170C22×D4C2×D1111yescharacteristic
171C23×C4—111no—
172C23×C4—111no—
173C23×C4C2×D1111yescharacteristic
174#123—24no—
175#123—224no—
176#123—224no—
177#123—224no—
178#121—224no—
179C2×C4⋊C4—112no—
180C2×C4⋊C4—112no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4—112no—
183C2×C4⋊C4—112no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—224no—
186C2×C4⋊C4C2×D1112yes—
187C2×C22⋊C4—111no—
188C2×C22⋊C4—111no—
189C2×C22⋊C4—112no—
190C2×C22⋊C4—111no—
191C2×C22⋊C4—112no—
192C2×C22⋊C4—112no—
193C2×C22⋊C4C2×D1112yes—
194C2×C22⋊C4C2×D1111yescharacteristic
195C2×C42—112no—
196#95—112no—
197C2×C11—24no—
198C2×C11—81no—
199C2×C11C2×#12311yescharacteristic
200C2×C11C2×#12711yescharacteristic
201C2×C11#53611yescharacteristic
202C2×C11#54712yes—
203C2×C11#54712yes—
204D11—81no—
205C24—111no—
206C24C22×D1111yescharacteristic
207C24C22×D1111yescharacteristic
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—222no—
212C2×D4—224no—
213C2×D4—222no—
214C2×D4—222no—
215C2×D4—222no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—111no—
220C22×C4—114no—
221C22×C4—111no—
222C22×C4—112no—
223C22×C4—112no—
224C22×C4—111no—
225C22×C4—224no—
226C22×C4—222no—
227C22×C4—222no—
228C22×C4—222no—
229C22×C4C22×D1112yes—
230C22×C4C22×D1111yescharacteristic
231C22×C4C22×D1112yes—
232C4⋊C4—24no—
233C4⋊C4—224no—
234C4⋊C4—224no—
235C4⋊C4—222no—
236C4⋊C4—224no—
237C4⋊C4—224no—
238C4⋊C4—224no—
239C22⋊C4—24no—
240C22⋊C4—114no—
241C22⋊C4—222no—
242C22⋊C4—224no—
243C22⋊C4—222no—
244C22⋊C4—224no—
245C22⋊C4—224no—
246C22⋊C4C22⋊D1114yescomplemented
247C42—224no—
248C11#250111yescharacteristic, complemented, Sylow
249C23—22no—
250C23—22no—
251C23—21no—
252C23—21no—
253C23—22no—
254C23—22no—
255C23—21no—
256C23—221no—
257C23—221no—
258C23—222no—
259C23—222no—
260C23—221no—
261C23D4×D1112yes—
262C23D4×D1112yes—
263C23C2×C22⋊D1112yes—
264C23C23×D1111yescharacteristic
265D4—44no—
266D4—444no—
267D4—444no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—44no—
277C2×C4—112no—
278C2×C4—114no—
279C2×C4—114no—
280C2×C4—112no—
281C2×C4—228no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—222no—
286C2×C4—221no—
287C2×C4—222no—
288C2×C4—221no—
289C2×C4—222no—
290C2×C4—221no—
291C2×C4—444no—
292C2×C4C2×C22⋊D1114yes—
293C22—24no—
294C22—22no—
295C22—22no—
296C22—24no—
297C22—41no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—42no—
302C22—441no—
303C22—442no—
304C22—441no—
305C22—441no—
306C22—442no—
307C22#6699314yes—
308C22C2×D4×D1111yescharacteristic
309C22C2×D4×D1111yescharacteristic
310C22#41×D1112yes—
311C22#6704312yes—
312C22C22×C22⋊D1111yescharacteristic
313C4—24no—
314C4—42no—
315C4—41no—
316C4—114no—
317C4—222no—
318C4—224no—
319C4—442no—
320C4—441no—
321C2—24no—
322C2—81no—
323C2—881no—
324C2#1062317911yescharacteristic
325C2D11×#12311yescharacteristic
326C2#1062318612yes—
327C2C2×#6699311yescharacteristic
328C2#1062335512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#123C2
prime radicalC2×#66992C2
hypercenterC2×#123D11
hypocenterC11#2501
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C11×#123C2semidirect
3. C2×#66988C2semidirect
4. C2×#66982C2semidirect
5. C22×Dic11⋊C4C2semidirect
6. C2×#66939C2semidirect
7. #10622605C2semidirect
8. #10622589C2semidirect
9. #10622570C2semidirect
10. #10622562C2semidirect
11. C22⋊C4×Dic11C2semidirect
70. C11×C22⋊C4D4semidirect
73. C22⋊Dic11D4semidirect
132. C2×#123D11semidirect
167. Dic11#123semidirect
246. C22⋊C4C22⋊D11semidirect
248. C11#2501semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×#669922
C2×#669882
C2×#669822
C22×Dic11⋊C42
C2×#669392
#106226052
#106225892
#106225702
#106225622
C22⋊C4×Dic112
#250111