Finite Group Databasebeta

← #13079884

Subgroups — #13079884

Order 1408.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#544C211yesmaximal, characteristic
2#10623049C211yesmaximal, characteristic
3#10622707C211yesmaximal, characteristic, complemented
4#10622706C211yesmaximal, characteristic, complemented
5#10622704C211yesmaximal, characteristic, complemented
6#10622693C211yesmaximal, characteristic, complemented
7#10622682C211yesmaximal, characteristic, complemented
8#10622677C211yesmaximal, characteristic, complemented
9#10622676C211yesmaximal, characteristic, complemented
10#10622676C211yesmaximal, characteristic, complemented
11#10622613C211yesmaximal, characteristic
12#10622609C211yesmaximal, characteristic
13#10622609C211yesmaximal, characteristic
14#10622584C211yesmaximal, characteristic
15#10622583C211yesmaximal, characteristic
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic
19C11×#125—21no—
20C11×#125C2211yescharacteristic
21C11×#125C2211yescharacteristic
22C11×C22⋊Q8—21no—
23C11×C22⋊Q8—21no—
24C11×#117C2211yescharacteristic
25C11×#117C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic
29#66942—21no—
30#66942—21no—
31#66932—21no—
32#66932—21no—
33#66923C2211yescharacteristic
34#66922C2211yescharacteristic
35C4×Dic22C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C22⋊(C11⋊C8)C2211yescharacteristic
38C22⋊(C11⋊C8)C2211yescharacteristic
39#66874C2211yescharacteristic
40#66874C2211yescharacteristic
41#66874C2211yescharacteristic
42#66874C2211yescharacteristic
43#66874C2211yescharacteristic
44#66874C2211yescharacteristic
45#66874C2211yescharacteristic
46#66874C2211yescharacteristic
47#66872C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66871C2211yescharacteristic
52#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56C4⋊(C11⋊C8)C2211yescharacteristic
57#66867C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C2×Dic22C2311yescharacteristic
64C2×Dic22C2311yescharacteristic
65C11×C4⋊C4—21no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4D411yescharacteristic
73C11×C4⋊C4D411yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C11×C22⋊C4D411yescharacteristic
80C11×C22⋊C4D411yescharacteristic
81C42×C11—21no—
82C42×C11C2311yescharacteristic
83C42×C11C2311yescharacteristic
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C2×C11⋊C8C2311yescharacteristic
99C2×C11⋊C8C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3242—111nomaximal, Sylow
103C23×C11C2×D411yescharacteristic
104Q8×C11—81no—
105Q8×C11—81no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—81no—
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123Dic22—21no—
124Dic22—21no—
125Dic22—21no—
126Dic22—21no—
127C11⋊C8—21no—
128C11⋊C8—21no—
129C11⋊C8—21no—
130C11⋊C8—21no—
131#544D1111yescharacteristic
132#541—111no—
133#501—111no—
134#499—111no—
135#491—111no—
136#487—111no—
137#485—111no—
138#485—111no—
139#484—111no—
140#483—111no—
141#479—111no—
142#479—111no—
143#477—111no—
144#475—111no—
145#433—111no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11C22×D411yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C112−1+411yescharacteristic
160C4×C112−1+411yescharacteristic
161Dic11—41no—
162Dic11—41no—
163Dic11—41no—
164Dic11—41no—
165C4⋊Q8—21no—
166C4⋊Q8—111no—
167C4⋊Q8C2×D1111yescharacteristic
168C4⋊Q8C2×D1111yescharacteristic
169#126—221no—
170#126—221no—
171#125—21no—
172#125—111no—
173#125—221no—
174#125—221no—
175#125C2×D1111yescharacteristic
176#125C2×D1111yescharacteristic
177C22⋊Q8—21no—
178C22⋊Q8—21no—
179C22⋊Q8—111no—
180C22⋊Q8—111no—
181C4×Q8—111no—
182C4×Q8—111no—
183#117C2×D1111yescharacteristic
184#117C2×D1111yescharacteristic
185C2×C4⋊C4C2×D1111yescharacteristic
186#107—111no—
187#107—111no—
188#107—111no—
189#107—111no—
190#106—111no—
191#106—111no—
192#106—111no—
193#106—111no—
194C4⋊C8—111no—
195C4⋊C8—111no—
196#103—111no—
197#103—111no—
198#103—111no—
199#103—111no—
200#103—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204C22⋊C8—111no—
205C22⋊C8—111no—
206#97—111no—
207C4×C8—111no—
208C2×C11—41no—
209C2×C11#53611yescharacteristic
210C2×C11#57711yescharacteristic
211C2×C11#57811yescharacteristic
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—111no—
215C2×Q8—111no—
216C22×C4—21no—
217C22×C4C22×D1111yescharacteristic
218C2×C8—111no—
219C2×C8—111no—
220C2×C8—111no—
221C2×C8—111no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—111no—
230C4⋊C4—111no—
231C4⋊C4—221no—
232C4⋊C4—221no—
233C4⋊C4—221no—
234C4⋊C4—221no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4C22⋊D1111yescharacteristic
240C4⋊C4C22⋊D1111yescharacteristic
241C4⋊C4C22×D1111yescharacteristic
242C4⋊C4C22×D1111yescharacteristic
243C4⋊C4C22×D1111yescharacteristic
244C4⋊C4C22×D1111yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—221no—
247C22⋊C4—221no—
248C22⋊C4C22⋊D1111yescharacteristic
249C22⋊C4C22⋊D1111yescharacteristic
250C42—21no—
251C42—221no—
252C42—221no—
253C42C22×D1111yescharacteristic
254C42C22×D1111yescharacteristic
255C11#324211yescharacteristic, complemented, Sylow
256C23C2×C22⋊D1111yescharacteristic
257Q8—81no—
258Q8—81no—
259Q8—221no—
260Q8—221no—
261Q8—221no—
262Q8—221no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—81no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4C2×C22⋊D1111yescharacteristic
275C2×C4C2×C22⋊D1111yescharacteristic
276C2×C4C2×C22⋊D1111yescharacteristic
277C2×C4C2×C22⋊D1111yescharacteristic
278C2×C4C2×C22⋊D1111yescharacteristic
279C2×C4C23×D1111yescharacteristic
280C8—221no—
281C8—221no—
282C8—221no—
283C8—221no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×C22⋊D1111yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—441no—
298C4—441no—
299C4—441no—
300C4—441no—
301C4#6704011yescharacteristic
302C4#6704011yescharacteristic
303C2—41no—
304C2#1062334711yescharacteristic
305C2#1062336711yescharacteristic
306C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#544C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#544D11
hypocenterC11#3242
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #10622707C2semidirect
4. #10622706C2semidirect
5. #10622704C2semidirect
6. #10622693C2semidirect
7. #10622682C2semidirect
8. #10622677C2semidirect
9. #10622676C2semidirect
10. #10622676C2semidirect
255. C11#3242semidirect

Maximal subgroups

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

subgroupindex
C11×#5442
#106230492
#106227072
#106227062
#106227042
#106226932
#106226822
#106226772
#106226762
#106226132
#106226092
#106225842
#106225832
#324211