Finite Group Databasebeta

← #13071305

Subgroups — #13071305

Order 1408.

668 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66983C211yesmaximal, characteristic
2C2×#66979C211yesmaximal, characteristic, complemented
3C2×#66946C211yesmaximal, characteristic, complemented
4C11×#380C211yesmaximal, characteristic, complemented
5#10622601C211yesmaximal, characteristic, complemented
6C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#10622586C211yesmaximal, characteristic, complemented
8#10622570C212yesmaximal, complemented
9#10622569C212yesmaximal, complemented
10#10622283C212yesmaximal, complemented
11#10622281C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×D44C2211yescharacteristic
15C22×C4×D11C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊Dic11C2211yescharacteristic
21#66983C418yescomplemented
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26#66979—24no—
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2211yescharacteristic
32C2×C4×Dic11C2212yes—
33C2×C4×Dic11C2211yescharacteristic
34#66946—24no—
35C11×#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C24×C11C2311yescharacteristic
39C23×D11C2312yes—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11C2×C414yescomplemented
43C22×C4×C11C2312yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11—42no—
48C2×C22⋊D11—42no—
49C2×C22⋊D11C2×C418yescomplemented
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C2×D44—22no—
56C2×D44—22no—
57C2×D44C2×C414yes—
58C2×C4×D11—24no—
59C2×C4×D11—42no—
60C2×C4×D11—42no—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—22no—
63C11×C22⋊C4—42no—
64C22⋊Dic11—22no—
65C22⋊Dic11—22no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—42no—
68(C2×D11)⋊C4—42no—
69(C2×D11)⋊C4C2×C418yescomplemented
70C4⋊Dic11—22no—
71C4⋊Dic11—22no—
72C4⋊Dic11C2×C414yescomplemented
73Dic11⋊C4—42no—
74C4×Dic11—22no—
75C4×Dic11—42no—
76C4×Dic11D414yescomplemented
77#2324—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11C22×C412yes—
85C23×C11C2411yescharacteristic
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11—22no—
90C22×D11—22no—
91C22×D11—22no—
92C22×D11C22×C414yes—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—28no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11C22×C412yes—
103C2×C4×C11C22×C412yes—
104C2×C4×C11C2×D412yes—
105C2×C4×C11#4112yes—
106C22⋊D11—48no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11C22×C414yes—
120C2×Dic11C2×D412yes—
121C2×Dic11C2×D412yes—
122D44—28no—
123C4×D11—48no—
124C2×#121—111no—
125C2×C4×D4—111no—
126C2×#117—111no—
127#390—111no—
128#390—112no—
129#389—111no—
130#388—112no—
131#386—112no—
132#385—112no—
133#380D1111yescharacteristic, complemented
134C4×C4⋊C4—111no—
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—22no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11C23×C411yescharacteristic
143C22×C11C22×D411yescharacteristic
144C22×C11C2×#4111yescharacteristic
145C22×C11H(5,𝔽2)11yescharacteristic
146C22×C11H(5,𝔽2)11yescharacteristic
147C22×C11H(5,𝔽2)11yescharacteristic
148C22×C112−1+411yescharacteristic
149C2×D11—24no—
150C2×D11—24no—
151C2×D11—24no—
152C2×D11—42no—
153C2×D11—42no—
154C2×D11—42no—
155C2×D11—42no—
156C4×C11—22no—
157C4×C11—42no—
158C4×C11—42no—
159C4×C11C4×D414yes—
160Dic11—24no—
161Dic11—22no—
162Dic11—22no—
163Dic11—41no—
164Dic11—41no—
165C22×D4—112no—
166C22×D4—111no—
167C23×C4—112no—
168C23×C4C2×D1111yescharacteristic
169#121—118no—
170C4×D4—224no—
171#117—224no—
172C2×C4⋊C4—111no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4—111no—
175C2×C4⋊C4—112no—
176C2×C4⋊C4C2×D1111yescharacteristic
177C2×C4⋊C4C2×D1111yescharacteristic
178C2×C22⋊C4—112no—
179C2×C22⋊C4—111no—
180C2×C22⋊C4—111no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4C2×D1112yes—
185C2×C42—111no—
186C2×C42—111no—
187C2×C42—112no—
188#95—112no—
189#95—112no—
190#95C2×D1112yes—
191C2×C11—42no—
192C2×C11C2×C4×D411yescharacteristic
193C2×C11#51811yescharacteristic
194C2×C11#52011yescharacteristic
195C2×C11#53511yescharacteristic
196C2×C11#53711yescharacteristic
197C2×C11#54011yescharacteristic
198C2×C11#54211yescharacteristic
199D11—44no—
200C24—112no—
201C24C22×D1111yescharacteristic
202C2×D4—118no—
203C2×D4—114no—
204C2×D4—222no—
205C2×D4—222no—
206C2×D4—442no—
207C2×D4—442no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—112no—
211C22×C4—111no—
212C22×C4—111no—
213C22×C4—111no—
214C22×C4—111no—
215C22×C4—224no—
216C22×C4—442no—
217C22×C4—442no—
218C22×C4C4×D1114yescomplemented
219C22×C4C22×D1112yes—
220C22×C4C22×D1112yes—
221C22×C4C22×D1111yescharacteristic
222C22×C4C22×D1111yescharacteristic
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—114no—
226C4⋊C4—222no—
227C4⋊C4—222no—
228C4⋊C4—442no—
229C22⋊C4—42no—
230C22⋊C4—118no—
231C22⋊C4—224no—
232C22⋊C4—222no—
233C22⋊C4—222no—
234C22⋊C4—442no—
235C22⋊C4—442no—
236C42—114no—
237C42—222no—
238C42—442no—
239C11#232411yescharacteristic, complemented, Sylow
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—114no—
247C23—222no—
248C23—222no—
249C23—222no—
250C23—222no—
251C23—222no—
252C23—222no—
253C23C2×C4×D1112yes—
254C23C23×D1111yescharacteristic
255D4—228no—
256D4—448no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—28no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—114no—
267C2×C4—112no—
268C2×C4—112no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—448no—
282C2×C4C2×C4×D1112yes—
283C2×C4C2×C4×D1112yes—
284C2×C4D4×D1112yes—
285C2×C4#434112yes—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—224no—
294C22—224no—
295C22—224no—
296C22—442no—
297C22—442no—
298C22—442no—
299C22—442no—
300C22C22×C4×D1111yescharacteristic
301C22C2×D4×D1111yescharacteristic
302C22C2×#434111yescharacteristic
303C22#6703711yescharacteristic
304C22#6704011yescharacteristic
305C22#6704211yescharacteristic
306C22#6704211yescharacteristic
307C4—22no—
308C4—42no—
309C4—42no—
310C4—224no—
311C4—222no—
312C4—222no—
313C4—441no—
314C4—441no—
315C4(C22⋊D11)⋊C414yes—
316C2—42no—
317C2—444no—
318C2C2×(C22⋊D11)⋊C411yescharacteristic
319C2#1062303511yescharacteristic
320C2#1062305211yescharacteristic
321C2#1062313811yescharacteristic
322C2#1062315011yescharacteristic
323C2#1062316011yescharacteristic
324C2#1062317411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#380C2
socle, cosocleC23×C11C24
prime radicalC2×#66983C2
hypercenter#380D11
hypocenterC11#2324
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#66979C2semidirect
3. C2×#66946C2semidirect
4. C11×#380C2semidirect
5. #10622601C2semidirect
6. C4⋊C4×Dic11C2semidirect
7. #10622586C2semidirect
8. #10622570C2semidirect
9. #10622569C2semidirect
10. #10622283C2semidirect
11. #10622281C2semidirect
21. #66983C4semidirect
42. C22×C4×C11C2×C4semidirect
49. C2×C22⋊D11C2×C4semidirect
69. (C2×D11)⋊C4C2×C4semidirect
72. C4⋊Dic11C2×C4semidirect
76. C4×Dic11D4semidirect
133. #380D11semidirect
218. C22×C4C4×D11semidirect
239. C11#2324semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C2×#669792
C2×#669462
C11×#3802
#106226012
C4⋊C4×Dic112
#106225862
#106225702
#106225692
#106222832
#106222812
#232411