Finite Group Databasebeta

← #13072922

Subgroups — #13072922

Order 1408.

624 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66947C212yesmaximal
2C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C2×C4×D44C211yesmaximal, characteristic
4C11×#389C211yesmaximal, characteristic, complemented
5#10622600C211yesmaximal, characteristic, complemented
6#10622600C211yesmaximal, characteristic, complemented
7#10622600C211yesmaximal, characteristic, complemented
8#10622597C212yesmaximal, complemented
9#10622541C211yesmaximal, characteristic, complemented
10#10622288C212yesmaximal, complemented
11#10622277C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×C4×D11C2212yes—
15C22×C4×D11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C42×C11C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30#66947—28no—
31C4⋊C4×D11—24no—
32C4×D44—24no—
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2212yes—
38C23×D11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C2×D44—22no—
50C2×D44—22no—
51C2×D44D414yes—
52C2×C4×D11—24no—
53C2×C4×D11—24no—
54C2×C4×D11—24no—
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11—22no—
58C2×C4×D11—22no—
59C2×C4×D11—22no—
60C2×C4×D11D414yes—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—24no—
63C11×C4⋊C4—22no—
64C42×C11—22no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—24no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70C4⋊Dic11—22no—
71C4⋊Dic11—22no—
72C4⋊Dic11—22no—
73Dic11⋊C4—24no—
74Dic11⋊C4—24no—
75#2486—111nomaximal, Sylow
76C23×C11C2411yescharacteristic
77C22×D11—21no—
78C22×D11—21no—
79C22×D11—21no—
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11C2×D412yes—
88C22×D11C2×D412yes—
89C22×D11C2×D412yes—
90C22×D11#4112yes—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11C2×D412yes—
103C2×C4×C11C2×D412yes—
104C2×C4×C11#4112yes—
105C2×C4×C11#4112yes—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—22no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11C2×D412yes—
118D44—28no—
119C4×D11—28no—
120C4×D11—48no—
121C4×D11—44no—
122C2×#123—112no—
123C2×C4×D4—111no—
124C22×C4⋊C4—111no—
125#398—112no—
126#397—112no—
127#389—111no—
128#389D1111yescharacteristic, complemented
129#381—112no—
130#380—111no—
131#380—111no—
132#380—111no—
133C22×C11C22×D411yescharacteristic
134C22×C11C22×D411yescharacteristic
135C22×C11C2×#4111yescharacteristic
136C22×C11C2×#4111yescharacteristic
137C22×C11C2×#4111yescharacteristic
138C22×C112−1+411yescharacteristic
139C22×C112−1+411yescharacteristic
140C2×D11—22no—
141C2×D11—22no—
142C2×D11—22no—
143C2×D11—22no—
144C2×D11—22no—
145C2×D11—22no—
146C2×D11—22no—
147C2×D11—22no—
148C2×D11—22no—
149C2×D11—41no—
150C2×D11—41no—
151C2×D11—41no—
152C2×D11—41no—
153C2×D11#12114yes—
154C4×C11—22no—
155C4×C11—42no—
156C4×C11—41no—
157C4×C11—42no—
158C4×C11#12314yescomplemented
159Dic11—22no—
160Dic11—42no—
161Dic11—41no—
162Dic11—42no—
163C22×D4—111no—
164C23×C4—111no—
165C23×C4—112no—
166C23×C4—111no—
167#123—228no—
168C4×D4—224no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—112no—
171C2×C4⋊C4—111no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4—224no—
175C2×C4⋊C4C2×D1111yescharacteristic
176C2×C4⋊C4C2×D1112yes—
177C2×C4⋊C4C2×D1111yescharacteristic
178C2×C22⋊C4—111no—
179C2×C22⋊C4—111no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C42C2×D1111yescharacteristic
184#95—112no—
185#95—112no—
186#95—112no—
187#95—112no—
188#95C2×D1112yes—
189C2×C11C2×#12111yescharacteristic
190C2×C11C2×#12311yescharacteristic
191C2×C11#53611yescharacteristic
192C2×C11#54711yescharacteristic
193C2×C11#54711yescharacteristic
194C2×C11#55211yescharacteristic
195C2×C11#55211yescharacteristic
196D11—24no—
197D11—42no—
198C24—111no—
199C24—111no—
200C2×D4—114no—
201C2×D4—222no—
202C2×D4—222no—
203C22×C4—111no—
204C22×C4—114no—
205C22×C4—111no—
206C22×C4—112no—
207C22×C4—112no—
208C22×C4—224no—
209C22×C4—224no—
210C22×C4—224no—
211C22×C4—222no—
212C22×C4—222no—
213C22×C4—222no—
214C22×C4—222no—
215C22×C4—222no—
216C22×C4C22×D1111yescharacteristic
217C22×C4C22×D1112yes—
218C22×C4C22×D1112yes—
219C22×C4C22×D1111yescharacteristic
220C22×C4C22×D1111yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—24no—
224C4⋊C4—224no—
225C4⋊C4—222no—
226C4⋊C4—222no—
227C4⋊C4—224no—
228C4⋊C4—222no—
229C22⋊C4—222no—
230C22⋊C4—222no—
231C22⋊C4—224no—
232C22⋊C4—224no—
233C22⋊C4—224no—
234C42—22no—
235C11#248611yescharacteristic, complemented, Sylow
236C23—112no—
237C23—112no—
238C23—112no—
239C23—112no—
240C23—221no—
241C23—221no—
242C23—221no—
243C23—221no—
244C23—221no—
245C23—221no—
246C23—221no—
247C23—221no—
248C23—221no—
249C23—221no—
250C23C23×D1111yescharacteristic
251D4—228no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—112no—
264C2×C4—221no—
265C2×C4—221no—
266C2×C4—228no—
267C2×C4—221no—
268C2×C4—222no—
269C2×C4—221no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—221no—
274C2×C4—222no—
275C2×C4—222no—
276C2×C4—448no—
277C2×C4—444no—
278C2×C4#433912yes—
279C2×C4D4×D1112yes—
280C2×C4D4×D1112yes—
281C2×C4#434312yes—
282C22—114no—
283C22—222no—
284C22—222no—
285C22—222no—
286C22—222no—
287C22—222no—
288C22—222no—
289C22—222no—
290C22—222no—
291C22—222no—
292C22—441no—
293C22—441no—
294C22—441no—
295C22—441no—
296C22C2×#433911yescharacteristic
297C22C2×D4×D1111yescharacteristic
298C22C2×D4×D1111yescharacteristic
299C22C2×#434311yescharacteristic
300C22#6704011yescharacteristic
301C22#41×D1111yescharacteristic
302C22#6704311yescharacteristic
303C4—22no—
304C4—42no—
305C4—42no—
306C4—41no—
307C4—222no—
308C4—442no—
309C4—441no—
310C4—442no—
311C4#6694714yescomplemented
312C2—224no—
313C2—442no—
314C2C2×#6694711yescharacteristic
315C2#1062308211yescharacteristic
316C2#1062311211yescharacteristic
317C2D11×#12111yescharacteristic
318C2#1062315911yescharacteristic
319C2#1062322511yescharacteristic
320C2#1062325711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC22×D44C22
hypercenter#389D11
hypocenterC11#2486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D11C2semidirect
4. C11×#389C2semidirect
5. #10622600C2semidirect
6. #10622600C2semidirect
7. #10622600C2semidirect
8. #10622597C2semidirect
9. #10622541C2semidirect
10. #10622288C2semidirect
11. #10622277C2semidirect
128. #389D11semidirect
158. C4×C11#123semidirect
235. C11#2486semidirect
311. C4#66947semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C2×C4⋊C4×D112
C2×C4×D442
C11×#3892
#106226002
#106225972
#106225412
#106222882
#106222772
#248611