Finite Group Databasebeta

← #13071309

Subgroups — #13071309

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×C11×#117C211yesmaximal, characteristic, complemented
2C2×#66983C211yesmaximal, characteristic
3C2×C4×D44C211yesmaximal, characteristic, complemented
4#10622825C211yesmaximal, characteristic, complemented
5#10622603C212yesmaximal, complemented
6#10622602C212yesmaximal, complemented
7#10622570C212yesmaximal, complemented
8#10622569C212yesmaximal, complemented
9#10622552C211yesmaximal, characteristic, complemented
10C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
11#10622541C211yesmaximal, characteristic, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×D44C2211yescharacteristic
15C22×C4×D11C2212yes—
16C11×#117—24no—
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C42×C11C2211yescharacteristic
22C2×C42×C11C2211yescharacteristic
23C2×C22⋊Dic11C2212yes—
24#66983C418yescomplemented
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×Dic11⋊C4C2212yes—
33C2×C4×Dic11C2212yes—
34C4×D44—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×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C2×C22⋊D11—42no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11C2×C418yescomplemented
52C22×Dic11C2312yes—
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
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—22no—
64C11×C22⋊C4—22no—
65C42×C11—22no—
66C42×C11D414yescomplemented
67C22⋊Dic11—42no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—42no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4C2×C418yescomplemented
72C4⋊Dic11—22no—
73C4⋊Dic11—22no—
74C4⋊Dic11C2×C414yescomplemented
75Dic11⋊C4—42no—
76C4×Dic11—42no—
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—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—28no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11C22×C412yes—
107C2×C4×C11C22×C412yes—
108C2×C4×C11C2×D412yes—
109C2×C4×C11C2×D412yes—
110C2×C4×C11C2×D412yes—
111C2×C4×C11#4112yes—
112C22⋊D11—48no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—22no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11C22×C414yes—
122D44—28no—
123C4×D11—48no—
124C2×#121—111no—
125C2×C4×D4—111no—
126C2×#117D1111yescharacteristic, complemented
127#390—112no—
128#390—111no—
129#389—111no—
130#388—112no—
131#386—112no—
132#385—112no—
133#380—111no—
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—22no—
158C4×C11—22no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11C4×D414yes—
162Dic11—24no—
163Dic11—42no—
164Dic11—42no—
165C22×D4—112no—
166C22×D4—111no—
167C23×C4—112no—
168C23×C4C2×D1111yescharacteristic
169#121—118no—
170C4×D4—224no—
171#117—24no—
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—112no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4C2×D1111yescharacteristic
184C2×C22⋊C4C2×D1111yescharacteristic
185C2×C42—112no—
186C2×C42C2×D1111yescharacteristic
187C2×C42C2×D1111yescharacteristic
188#95—112no—
189#95—112no—
190#95—112no—
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—112no—
212C22×C4—112no—
213C22×C4—224no—
214C22×C4—442no—
215C22×C4—442no—
216C22×C4C4×D1114yescomplemented
217C22×C4C22×D1111yescharacteristic
218C22×C4C22×D1111yescharacteristic
219C22×C4C22×D1111yescharacteristic
220C22×C4C22×D1111yescharacteristic
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—22no—
230C22⋊C4—22no—
231C22⋊C4—118no—
232C22⋊C4—224no—
233C22⋊C4—442no—
234C22⋊C4—442no—
235C22⋊C4—442no—
236C42—22no—
237C42—442no—
238C42C22⋊D1114yescomplemented
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—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—28no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—114no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—222no—
275C2×C4—222no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—222no—
279C2×C4—448no—
280C2×C4C2×C4×D1112yes—
281C2×C4C2×C4×D1112yes—
282C2×C4#433912yes—
283C2×C4C2×C22⋊D1112yes—
284C2×C4C2×C22⋊D1112yes—
285C2×C4C2×C22⋊D1112yes—
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×#433911yescharacteristic
302C22#6704211yescharacteristic
303C22#6704211yescharacteristic
304C22#6704211yescharacteristic
305C22#6704311yescharacteristic
306C22C22×C22⋊D1111yescharacteristic
307C4—22no—
308C4—22no—
309C4—22no—
310C4—41no—
311C4—41no—
312C4—224no—
313C4—442no—
314C4—442no—
315C4C4×C22⋊D1114yes—
316C2—42no—
317C2—444no—
318C2#1062305211yescharacteristic
319C2#1062305411yescharacteristic
320C2#1062306511yescharacteristic
321C2#1062306611yescharacteristic
322C2C2×C4×C22⋊D1111yescharacteristic
323C2#1062336111yescharacteristic
324C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC2×C11×#117C2
socle, cosocleC23×C11C24
prime radicalC2×#66983C2
hypercenterC2×#117D11
hypocenterC11#2324
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C11×#117C2semidirect
3. C2×C4×D44C2semidirect
4. #10622825C2semidirect
5. #10622603C2semidirect
6. #10622602C2semidirect
7. #10622570C2semidirect
8. #10622569C2semidirect
9. #10622552C2semidirect
10. C4×C4⋊Dic11C2semidirect
11. #10622541C2semidirect
24. #66983C4semidirect
42. C22×C4×C11C2×C4semidirect
51. C2×C22⋊D11C2×C4semidirect
66. C42×C11D4semidirect
71. (C2×D11)⋊C4C2×C4semidirect
74. C4⋊Dic11C2×C4semidirect
126. C2×#117D11semidirect
216. C22×C4C4×D11semidirect
238. C42C22⋊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×C11×#1172
C2×#669832
C2×C4×D442
#106228252
#106226032
#106226022
#106225702
#106225692
#106225522
C4×C4⋊Dic112
#106225412
#232411