Finite Group Databasebeta

← #13072048

Subgroups — #13072048

Order 1408.

604 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×#66999C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×#66945C211yesmaximal, characteristic, complemented
4C2×C4×D44C211yesmaximal, characteristic
5C11×#391C211yesmaximal, characteristic, complemented
6#10622600C211yesmaximal, characteristic, complemented
7#10622541C211yesmaximal, characteristic, complemented
8#10622288C212yesmaximal, complemented
9#10622285C212yesmaximal
10#10622282C212yesmaximal, complemented
11#10622260C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C42×C11C2211yescharacteristic
18#66999—24no—
19#66999—24no—
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×Dic11⋊C4C2212yes—
32C2×C4×Dic11C2212yes—
33#66945—24no—
34C4×D44—24no—
35C11×#95C2212yes—
36C11×#95C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C23×D11C2311yescharacteristic
40C23×D11C2311yescharacteristic
41C2×Q8×C11—22no—
42C2×Q8×C11—22no—
43C2×Q8×C11—22no—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2311yescharacteristic
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C2×D44—22no—
54C2×D44—22no—
55C2×D44—22no—
56C2×C4×D11—22no—
57C2×C4×D11—22no—
58C2×C4×D11—22no—
59C2×C4×D11—22no—
60C2×C4×D11—22no—
61C2×C4×D11D414yes—
62C11×C4⋊C4—22no—
63C42×C11—22no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—24no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—24no—
70C4⋊Dic11—22no—
71C4⋊Dic11—22no—
72C4⋊Dic11D414yescomplemented
73Dic11⋊C4—24no—
74Dic11⋊C4—24no—
75Dic11⋊C4—24no—
76C4×Dic11—24no—
77#2415—111nomaximal, Sylow
78C23×C11C2411yescharacteristic
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×D11—21no—
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—21no—
91C22×D11C2×D412yes—
92C22×D11#4112yes—
93Q8×C11—44no—
94C2×C4×C11—21no—
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×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11C2×D412yes—
106C2×C4×C11C2×D412yes—
107C2×C4×C11#4112yes—
108C2×C4×C11#4112yes—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—22no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—21no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—21no—
119C2×Dic11C2×D414yes—
120C2×Dic11C2×D412yes—
121D44—28no—
122C4×D11—28no—
123C4×D11—44no—
124C2×C22⋊Q8—111no—
125C2×C22⋊Q8—111no—
126C2×C4×D4—111no—
127C2×#117—111no—
128#397—112no—
129#394—112no—
130#391D1111yescharacteristic, complemented
131#389—111no—
132#389—112no—
133#388—112no—
134#380—111no—
135C22×C11C22×D411yescharacteristic
136C22×C11C22×D411yescharacteristic
137C22×C11C2×#4111yescharacteristic
138C22×C11C2×#4111yescharacteristic
139C22×C11C2×#4111yescharacteristic
140C22×C112−1+411yescharacteristic
141C22×C112−1+411yescharacteristic
142C2×D11—22no—
143C2×D11—22no—
144C2×D11—22no—
145C2×D11—22no—
146C2×D11—22no—
147C2×D11—22no—
148C2×D11—41no—
149C2×D11—41no—
150C2×D11—41no—
151C2×D11—41no—
152C2×D11—41no—
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—41no—
156C4×C11—22no—
157C4×C11—42no—
158C4×C11—41no—
159C4×C11—42no—
160C4×C11#12114yes—
161Dic11—22no—
162Dic11—24no—
163Dic11—41no—
164Dic11—42no—
165C22×Q8C2×D1111yescharacteristic
166C22×D4—111no—
167C23×C4—111no—
168C23×C4—111no—
169C22⋊Q8—224no—
170C22⋊Q8—224no—
171C4×D4—224no—
172#117—224no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4—111no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—112no—
177C2×C4⋊C4—112no—
178C2×C4⋊C4—112no—
179C2×C4⋊C4C2×D1111yescharacteristic
180C2×C22⋊C4—112no—
181C2×C22⋊C4—111no—
182C2×C22⋊C4—111no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4—112no—
186C2×C42—112no—
187C2×C42C2×D1111yescharacteristic
188#95—112no—
189#95—112no—
190#95C2×D1112yes—
191#95C2×D1112yes—
192C2×C11C2×#12111yescharacteristic
193C2×C11#52511yescharacteristic
194C2×C11#53611yescharacteristic
195C2×C11#54711yescharacteristic
196C2×C11#54811yescharacteristic
197C2×C11#55211yescharacteristic
198C2×C11#55611yescharacteristic
199D11—42no—
200D11—42no—
201C24—111no—
202C24—111no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×D4—222no—
207C2×D4—222no—
208C2×D4—222no—
209C22×C4—112no—
210C22×C4—111no—
211C22×C4—114no—
212C22×C4—112no—
213C22×C4—111no—
214C22×C4—222no—
215C22×C4—222no—
216C22×C4—222no—
217C22×C4—222no—
218C22×C4—222no—
219C22×C4C22×D1111yescharacteristic
220C22×C4C22×D1112yes—
221C22×C4C22×D1112yes—
222C22×C4C22×D1111yescharacteristic
223C22×C4C22×D1111yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—114no—
226C4⋊C4—222no—
227C4⋊C4—224no—
228C4⋊C4—224no—
229C4⋊C4—222no—
230C4⋊C4—224no—
231C22⋊C4—224no—
232C22⋊C4—222no—
233C22⋊C4—224no—
234C22⋊C4—222no—
235C22⋊C4—224no—
236C22⋊C4—224no—
237C42—22no—
238C42—224no—
239C11#241511yescharacteristic, complemented, Sylow
240C23—112no—
241C23—112no—
242C23—221no—
243C23—221no—
244C23—221no—
245C23—221no—
246C23—221no—
247C23—221no—
248C23—221no—
249C23—221no—
250C23—221no—
251C23—221no—
252C23—221no—
253C23—221no—
254C23C23×D1111yescharacteristic
255Q8—44no—
256D4—228no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—114no—
269C2×C4—112no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—228no—
275C2×C4—221no—
276C2×C4—222no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—444no—
282C2×C4#433912yes—
283C2×C4D4×D1112yes—
284C2×C4D4×D1112yes—
285C2×C4#434312yes—
286C22—222no—
287C22—222no—
288C22—222no—
289C22—222no—
290C22—222no—
291C22—222no—
292C22—441no—
293C22—441no—
294C22—441no—
295C22—441no—
296C22—441no—
297C22—441no—
298C22—441no—
299C22—441no—
300C22C2×#433911yescharacteristic
301C22C2×D4×D1111yescharacteristic
302C22C2×D4×D1111yescharacteristic
303C22C2×#434311yescharacteristic
304C22#6704011yescharacteristic
305C22#41×D1111yescharacteristic
306C22#6704311yescharacteristic
307C4—22no—
308C4—42no—
309C4—41no—
310C4—42no—
311C4—224no—
312C4—222no—
313C4—441no—
314C4—442no—
315C4#6693714yes—
316C2—442no—
317C2—442no—
318C2C2×#6693711yescharacteristic
319C2#1062311211yescharacteristic
320C2#1062311511yescharacteristic
321C2#1062315811yescharacteristic
322C2#1062315911yescharacteristic
323C2#1062320811yescharacteristic
324C2#1062325711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC22×D44C22
hypercenter#391D11
hypocenterC11#2415
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#66999C2semidirect
2. C2×#66999C2semidirect
3. C2×#66945C2semidirect
5. C11×#391C2semidirect
6. #10622600C2semidirect
7. #10622541C2semidirect
8. #10622288C2semidirect
10. #10622282C2semidirect
11. #10622260C2semidirect
72. C4⋊Dic11D4semidirect
130. #391D11semidirect
239. C11#2415semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×#669452
C2×C4×D442
C11×#3912
#106226002
#106225412
#106222882
#106222852
#106222822
#106222602
#241511