Finite Group Databasebeta

← #13072131

Subgroups — #13072131

Order 1408.

652 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×#66948C211yesmaximal, characteristic
2C2×#66947C212yesmaximal, complemented
3C2×C4×D44C211yesmaximal, characteristic, complemented
4C11×#389C211yesmaximal, characteristic, complemented
5#10622602C212yesmaximal, complemented
6#10622601C211yesmaximal, characteristic, complemented
7#10622600C211yesmaximal, characteristic, complemented
8#10622589C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10#10622288C212yesmaximal, complemented
11#10622285C212yesmaximal, complemented
12C22×D44C2212yes—
13C22×D44C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2212yes—
16C2×C11×C4⋊C4C2212yes—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C42×C11C2211yescharacteristic
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31#66948—24no—
32#66947—28no—
33C4×D44—24no—
34C11×#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C11⋊#95C2211yescharacteristic
38C23×D11C2312yes—
39C23×D11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2312yes—
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C2×D44—24no—
50C2×D44—24no—
51C2×D44—22no—
52C2×D44—22no—
53C2×D44—42no—
54C2×D44D414yes—
55C2×C4×D11—24no—
56C2×C4×D11—24no—
57C2×C4×D11—22no—
58C2×C4×D11—22no—
59C2×C4×D11—22no—
60C2×C4×D11—42no—
61C11×C4⋊C4—24no—
62C11×C4⋊C4—22no—
63C11×C4⋊C4—22no—
64C42×C11—22no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70(C2×D11)⋊C4—24no—
71(C2×D11)⋊C4D414yescomplemented
72C4⋊Dic11—22no—
73Dic11⋊C4—24no—
74Dic11⋊C4—42no—
75C4×Dic11—22no—
76#2422—111nomaximal, Sylow
77C23×C11C2411yescharacteristic
78C22×D11—22no—
79C22×D11—21no—
80C22×D11—21no—
81C22×D11—22no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—21no—
88C22×D11—21no—
89C22×D11—22no—
90C22×D11C2×D412yes—
91C22×D11C2×D414yes—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11C2×D412yes—
104C2×C4×C11C2×D412yes—
105C2×C4×C11#4112yes—
106C2×C4×C11#4112yes—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—22no—
117C2×Dic11C2×D412yes—
118C2×Dic11#4112yes—
119D44—28no—
120D44—48no—
121C4×D11—48no—
122C4×D11—44no—
123C2×#123—112no—
124C2×#121—111no—
125C2×C4×D4—111no—
126#397—112no—
127#394—112no—
128#390—111no—
129#389D1111yescharacteristic, complemented
130#385—112no—
131#384—111no—
132#380—111no—
133C4×C22⋊C4—111no—
134C22×C11C22×D411yescharacteristic
135C22×C11C22×D411yescharacteristic
136C22×C11C2×#4111yescharacteristic
137C22×C11C2×#4111yescharacteristic
138C22×C11C2×#4111yescharacteristic
139C22×C11H(5,𝔽2)11yescharacteristic
140C22×C112−1+411yescharacteristic
141C2×D11—24no—
142C2×D11—22no—
143C2×D11—24no—
144C2×D11—22no—
145C2×D11—22no—
146C2×D11—24no—
147C2×D11—41no—
148C2×D11—42no—
149C2×D11—41no—
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—41no—
153C2×D11—41no—
154C2×D11—42no—
155C4×C11—22no—
156C4×C11—42no—
157C4×C11—42no—
158C4×C11—41no—
159C4×C11#12314yescomplemented
160Dic11—22no—
161Dic11—22no—
162Dic11—41no—
163Dic11—42no—
164C22×D4—111no—
165C22×D4—112no—
166C23×C4—111no—
167C23×C4—112no—
168#123—228no—
169#121—224no—
170C4×D4—224no—
171C2×C4⋊C4—111no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4C2×D1111yescharacteristic
175C2×C4⋊C4C2×D1112yes—
176C2×C4⋊C4C2×D1111yescharacteristic
177C2×C22⋊C4—111no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—111no—
183C2×C22⋊C4—112no—
184C2×C42—111no—
185C2×C42C2×D1111yescharacteristic
186#95—111no—
187#95—111no—
188#95—112no—
189#95C2×D1112yes—
190C2×C11C2×#12311yescharacteristic
191C2×C11#53211yescharacteristic
192C2×C11#54211yescharacteristic
193C2×C11D4211yescharacteristic
194C2×C11#54711yescharacteristic
195C2×C11#54711yescharacteristic
196C2×C11#55311yescharacteristic
197D11—44no—
198D11—42no—
199C24—111no—
200C24—112no—
201C2×D4—114no—
202C2×D4—224no—
203C2×D4—224no—
204C2×D4—222no—
205C2×D4—222no—
206C2×D4—442no—
207C22×C4—111no—
208C22×C4—111no—
209C22×C4—111no—
210C22×C4—112no—
211C22×C4—224no—
212C22×C4—222no—
213C22×C4—222no—
214C22×C4—224no—
215C22×C4—222no—
216C22×C4—442no—
217C22×C4C22×D1111yescharacteristic
218C22×C4C22×D1112yes—
219C22×C4C22×D1112yes—
220C22×C4C22×D1111yescharacteristic
221C22×C4C22×D1111yescharacteristic
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—24no—
225C4⋊C4—224no—
226C4⋊C4—222no—
227C4⋊C4—442no—
228C22⋊C4—114no—
229C22⋊C4—224no—
230C22⋊C4—222no—
231C22⋊C4—224no—
232C22⋊C4—224no—
233C22⋊C4—224no—
234C22⋊C4—224no—
235C42—22no—
236C42—222no—
237C11#242211yescharacteristic, complemented, Sylow
238C23—112no—
239C23—114no—
240C23—221no—
241C23—222no—
242C23—222no—
243C23—221no—
244C23—221no—
245C23—222no—
246C23—221no—
247C23—222no—
248C23—221no—
249C23—222no—
250C23—222no—
251C23—221no—
252C23C23×D1111yescharacteristic
253D4—228no—
254D4—448no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—112no—
267C2×C4—112no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—222no—
275C2×C4—222no—
276C2×C4—221no—
277C2×C4—222no—
278C2×C4—448no—
279C2×C4—444no—
280C2×C4#433912yes—
281C2×C4D4×D1112yes—
282C2×C4D4×D1112yes—
283C2×C4#434312yes—
284C22—222no—
285C22—224no—
286C22—222no—
287C22—224no—
288C22—222no—
289C22—224no—
290C22—442no—
291C22—441no—
292C22—442no—
293C22—441no—
294C22—442no—
295C22—441no—
296C22—441no—
297C22—442no—
298C22C2×#433911yescharacteristic
299C22C2×D4×D1111yescharacteristic
300C22C2×D4×D1111yescharacteristic
301C22C2×#434311yescharacteristic
302C22#6704011yescharacteristic
303C22#41×D1111yescharacteristic
304C22#6704211yescharacteristic
305C4—22no—
306C4—42no—
307C4—42no—
308C4—41no—
309C4—222no—
310C4—222no—
311C4—441no—
312C4—442no—
313C4#6694714yescomplemented
314C2—442no—
315C2—444no—
316C2C2×#6694711yescharacteristic
317C2#1062307911yescharacteristic
318C2#1062311311yescharacteristic
319C2#1062314011yescharacteristic
320C2#1062316211yescharacteristic
321C2#1062322611yescharacteristic
322C2#1062325711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC2×#66948C2
hypercenter#389D11
hypocenterC11#2422
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#66947C2semidirect
3. C2×C4×D44C2semidirect
4. C11×#389C2semidirect
5. #10622602C2semidirect
6. #10622601C2semidirect
7. #10622600C2semidirect
8. #10622589C2semidirect
9. C4×(C2×D11)⋊C4C2semidirect
10. #10622288C2semidirect
11. #10622285C2semidirect
71. (C2×D11)⋊C4D4semidirect
129. #389D11semidirect
159. C4×C11#123semidirect
237. C11#2422semidirect
313. C4#66947semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669472
C2×C4×D442
C11×#3892
#106226022
#106226012
#106226002
#106225892
C4×(C2×D11)⋊C42
#106222882
#106222852
#242211