Finite Group Databasebeta

← #13072981

Subgroups — #13072981

Order 1408.

632 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic
2C2×#66989C212yesmaximal, complemented
3C2×#66941C211yesmaximal, characteristic, complemented
4#10622835C212yesmaximal, complemented
5#10622834C211yesmaximal, characteristic, complemented
6#10622834C211yesmaximal, characteristic, complemented
7#10622825C211yesmaximal, characteristic, complemented
8C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#10622560C212yesmaximal, complemented
11#10622558C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C23×C4×C11C2211yescharacteristic
15C22×Dic22C2212yes—
16C11×#121—24no—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2212yes—
25C2×C22⋊Dic11C2211yescharacteristic
26#66989—28no—
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31C2×C4×Dic11C2212yes—
32C2×C4×Dic11C2211yescharacteristic
33#66941—24no—
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2212yes—
38C24×C11C2312yes—
39C24×C11C2311yescharacteristic
40C2×D4×C11—24no—
41C2×D4×C11—24no—
42C2×D4×C11—22no—
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11—42no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11C2311yescharacteristic
50C22×C4×C11C2312yes—
51C22×C4×C11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2311yescharacteristic
58C2×Dic22—24no—
59C2×Dic22—24no—
60C2×Dic22—42no—
61C11×C4⋊C4D414yes—
62C11×C22⋊C4—24no—
63C22⋊Dic11—24no—
64C22⋊Dic11—24no—
65C22⋊Dic11—22no—
66C22⋊Dic11—24no—
67C22⋊Dic11—24no—
68C22⋊Dic11—42no—
69C22⋊Dic11D414yescomplemented
70C4⋊Dic11—22no—
71C4⋊Dic11—22no—
72Dic11⋊C4—24no—
73C4×Dic11—24no—
74C4×Dic11—22no—
75C4×Dic11—22no—
76#2491—111nomaximal, Sylow
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11C2×D412yes—
91C23×C11C2411yescharacteristic
92D4×C11—48no—
93D4×C11—44no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—44no—
100C2×C4×C11C2×D414yes—
101C2×C4×C11C2×D412yes—
102C2×C4×C11#4112yes—
103C2×C4×C11#4112yes—
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—22no—
119C2×Dic11C2×D412yes—
120C2×Dic11C2×D412yes—
121C2×Dic11#4112yes—
122Dic22—48no—
123C2×C4⋊Q8—111no—
124C2×#124—112no—
125C2×#121D1111yescharacteristic
126#394—112no—
127#393—112no—
128#390—111no—
129#390—111no—
130#388—112no—
131#380—111no—
132C4×C4⋊C4—111no—
133C4×C22⋊C4—111no—
134C22×C11—22no—
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—42no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11C22×D411yescharacteristic
149C22×C11C22×D411yescharacteristic
150C22×C11C2×#4111yescharacteristic
151C22×C11C2×#4111yescharacteristic
152C22×C11C2×#4111yescharacteristic
153C22×C11H(5,𝔽2)11yescharacteristic
154C22×C112−1+411yescharacteristic
155C4×C11—24no—
156C4×C11—41no—
157C4×C11#12414yescomplemented
158Dic11—22no—
159Dic11—22no—
160Dic11—22no—
161Dic11—42no—
162Dic11—42no—
163Dic11—41no—
164C22×Q8—112no—
165C22×D4C2×D1111yescharacteristic
166C22×D4C2×D1112yes—
167C23×C4C2×D1111yescharacteristic
168C4⋊Q8—224no—
169#124—228no—
170#121—24no—
171C2×C4⋊C4—111no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4C2×D1111yescharacteristic
175C2×C22⋊C4—111no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4—112no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—111no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4C2×D1112yes—
183C2×C42—112no—
184C2×C42—111no—
185C2×C42—111no—
186#95—111no—
187#95—111no—
188#95—112no—
189#95—112no—
190C2×C11—42no—
191C2×C11—82no—
192C2×C11C2×#12411yescharacteristic
193C2×C11#53211yescharacteristic
194C2×C11#54211yescharacteristic
195C2×C11D4211yescharacteristic
196C2×C11#54711yescharacteristic
197C2×C11#54811yescharacteristic
198C2×C11#55511yescharacteristic
199C24C22×D1112yes—
200C24C22×D1111yescharacteristic
201C2×Q8—224no—
202C2×Q8—224no—
203C2×Q8—442no—
204C2×D4—24no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—24no—
208C2×D4—22no—
209C2×D4—42no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—111no—
214C22×C4—111no—
215C22×C4—111no—
216C22×C4—111no—
217C22×C4—112no—
218C22×C4—112no—
219C22×C4C22×D1111yescharacteristic
220C22×C4C22×D1112yes—
221C22×C4C22×D1111yescharacteristic
222C4⋊C4—222no—
223C4⋊C4—224no—
224C4⋊C4—222no—
225C4⋊C4C22⋊D1114yes—
226C22⋊C4—24no—
227C22⋊C4—114no—
228C22⋊C4—224no—
229C22⋊C4—224no—
230C22⋊C4—222no—
231C22⋊C4—224no—
232C22⋊C4—224no—
233C22⋊C4—442no—
234C42—224no—
235C42—222no—
236C42—222no—
237C11#249111yescharacteristic, complemented, Sylow
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23D4×D1112yes—
252C23C23×D1111yescharacteristic
253Q8—448no—
254D4—48no—
255D4—44no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—44no—
262C2×C4—112no—
263C2×C4—112no—
264C2×C4—112no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—221no—
274C2×C4—222no—
275C2×C4—221no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—221no—
279C2×C4—222no—
280C2×C4#434112yes—
281C2×C4#434112yes—
282C2×C4C2×C22⋊D1114yes—
283C2×C4C2×C22⋊D1112yes—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—42no—
298C22C2×D4×D1111yescharacteristic
299C22C2×#434111yescharacteristic
300C22C2×#434111yescharacteristic
301C22#6703711yescharacteristic
302C22#41×D1111yescharacteristic
303C22#6704311yescharacteristic
304C22C22×C22⋊D1111yescharacteristic
305C4—24no—
306C4—41no—
307C4—222no—
308C4—222no—
309C4—222no—
310C4—442no—
311C4—442no—
312C4—441no—
313C4#6698914yescomplemented
314C2—42no—
315C2—82no—
316C2#1062312711yescharacteristic
317C2#1062313411yescharacteristic
318C2#1062314211yescharacteristic
319C2#1062314711yescharacteristic
320C2C2×#6698911yescharacteristic
321C2D4×C22⋊D1111yescharacteristic
322C2#1062336211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2491
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66989C2semidirect
3. C2×#66941C2semidirect
4. #10622835C2semidirect
5. #10622834C2semidirect
6. #10622834C2semidirect
7. #10622825C2semidirect
8. C4×C22⋊Dic11C2semidirect
9. C4⋊C4×Dic11C2semidirect
10. #10622560C2semidirect
11. #10622558C2semidirect
69. C22⋊Dic11D4semidirect
157. C4×C11#124semidirect
237. C11#2491semidirect
313. C4#66989semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669892
C2×#669412
#106228352
#106228342
#106228252
C4×C22⋊Dic112
C4⋊C4×Dic112
#106225602
#106225582
#249111