Finite Group Databasebeta

← #13079796

Subgroups — #13079796

Order 1408.

332 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623222C211yesmaximal, characteristic
2#10623219C211yesmaximal, characteristic, complemented
3C11×#499C211yesmaximal, characteristic, complemented
4#10622681C211yesmaximal, characteristic, complemented
5#10622677C211yesmaximal, characteristic, complemented
6#10622503C211yesmaximal, characteristic, complemented
7#10622501C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic
9#10622488C211yesmaximal, characteristic, complemented
10#10622483C211yesmaximal, characteristic, complemented
11#10622480C211yesmaximal, characteristic, complemented
12#10622479C211yesmaximal, characteristic
13#10622467C211yesmaximal, characteristic, complemented
14#10622310C211yesmaximal, characteristic, complemented
15#10622298C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#66951—21no—
19#66950C2211yescharacteristic
20#66949—21no—
21#66949—21no—
22#66948C2211yescharacteristic
23#66947—21no—
24#66946—21no—
25#66946C2211yescharacteristic
26#66945—21no—
27#66945C2211yescharacteristic
28#66945C2211yescharacteristic
29#66941C2211yescharacteristic
30#66941C2211yescharacteristic
31#66940—21no—
32#66940—21no—
33#66940C2211yescharacteristic
34#66928C2211yescharacteristic
35C42×D11C2211yescharacteristic
36#66923C2211yescharacteristic
37C11×#107C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#106C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C4×C8×C11C2211yescharacteristic
42#66885C2211yescharacteristic
43#66885C2211yescharacteristic
44(C2×D11)⋊C8C2211yescharacteristic
45(C2×D11)⋊C8C2211yescharacteristic
46#66880C2211yescharacteristic
47#66880C2211yescharacteristic
48Dic11⋊C8C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50#66874C2211yescharacteristic
51#66874C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×D44—21no—
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11D411yescharacteristic
63C2×C4×D11D411yescharacteristic
64C2×C4×D11C2311yescharacteristic
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C42×C11C2311yescharacteristic
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11D411yescharacteristic
98C4×Dic11D411yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3233—111nomaximal, Sylow
103C22×D11—21no—
104C22×D11C2×D411yescharacteristic
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2411yescharacteristic
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11C2×D411yescharacteristic
116C2×Dic11C2×D411yescharacteristic
117C2×Dic11C2×D411yescharacteristic
118D44—21no—
119D44—21no—
120D44—42no—
121C4×D11—21no—
122C4×D11—21no—
123C4×D11—22no—
124C4×D11—41no—
125C4×D11—42no—
126Dic22—21no—
127Dic22—21no—
128Dic22—42no—
129Dic22—42no—
130C8×C11—21no—
131C8×C11—21no—
132C11⋊C8—21no—
133C11⋊C8—21no—
134#533—111no—
135#529—111no—
136#499—111no—
137#499D1111yescharacteristic, complemented
138#488—111no—
139#488—111no—
140#485—111no—
141#485—111no—
142#482—111no—
143#482—111no—
144#477—111no—
145#476—111no—
146#475—111no—
147#474—111no—
148#431—111no—
149C22×C11C22×D411yescharacteristic
150C2×D11—21no—
151C2×D11—21no—
152C2×D11—21no—
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—41no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C112−1+411yescharacteristic
163C4×C112−1+411yescharacteristic
164Dic11—21no—
165Dic11—21no—
166Dic11—41no—
167Dic11—41no—
168Dic11—41no—
169Dic11#13512yes—
170C4⋊Q8—111no—
171C4⋊Q8—111no—
172#126—221no—
173#125—111no—
174#125C2×D1111yescharacteristic
175#125C2×D1111yescharacteristic
176#124—111no—
177#123—221no—
178C22⋊Q8—111no—
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181#121—111no—
182C4×Q8—111no—
183C4×Q8—221no—
184C4×Q8—221no—
185C4×D4—111no—
186C4×D4—221no—
187#117—111no—
188#117—111no—
189#117—221no—
190C2×C42—111no—
191#107—111no—
192#107—111no—
193#107C2×D1111yescharacteristic
194#107C2×D1111yescharacteristic
195#106—111no—
196#106—111no—
197#106C2×D1111yescharacteristic
198#106C2×D1111yescharacteristic
199C4⋊C8—111no—
200C4⋊C8—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204#103—111no—
205#102—111no—
206#102—111no—
207#102—111no—
208#102—111no—
209C22⋊C8—111no—
210C22⋊C8—111no—
211C4×C8—111no—
212C4×C8C2×D1111yescharacteristic
213C2×C11#53611yescharacteristic
214C2×C11C2×#13511yescharacteristic
215C2×C11#57511yescharacteristic
216D11—41no—
217D11—81no—
218C2×Q8—111no—
219C2×Q8—221no—
220C2×Q8—221no—
221C2×D4—111no—
222C2×D4—221no—
223C22×C4—111no—
224C22×C4—111no—
225C22×C4—111no—
226C22×C4—221no—
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4C22×D1111yescharacteristic
244C4⋊C4C22×D1111yescharacteristic
245C4⋊C4C22×D1111yescharacteristic
246C4⋊C4C22×D1111yescharacteristic
247C22⋊C4—221no—
248C22⋊C4—221no—
249C22⋊C4—221no—
250C22⋊C4—221no—
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C42—111no—
255C42—111no—
256C42—111no—
257C42—221no—
258C42—221no—
259C42—221no—
260C42C22×D1111yescharacteristic
261C11#323311yescharacteristic, complemented, Sylow
262C23—111no—
263C23—221no—
264Q8—221no—
265Q8—221no—
266Q8—442no—
267Q8—442no—
268D4—221no—
269D4—221no—
270D4—442no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—111no—
276C2×C4—111no—
277C2×C4—111no—
278C2×C4—222no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—441no—
285C2×C4—442no—
286C2×C4D4×D1111yescharacteristic
287C2×C4D4×D1111yescharacteristic
288C2×C4C23×D1111yescharacteristic
289C8—21no—
290C8—21no—
291C8—221no—
292C8—221no—
293C22—221no—
294C22—221no—
295C22—221no—
296C22—441no—
297C22—441no—
298C22—441no—
299C22C2×D4×D1111yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—112no—
307C4—221no—
308C4—221no—
309C4—441no—
310C4—441no—
311C4—441no—
312C4#6704011yescharacteristic
313C4#6704011yescharacteristic
314C2—441no—
315C2—881no—
316C2#1062325511yescharacteristic
317C2D11×#13511yescharacteristic
318C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#499C2
socleC22×C11C22×D4
prime radical#66948C22
hypercenter#499D11
hypocenterC11#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #10623219C2semidirect
3. C11×#499C2semidirect
4. #10622681C2semidirect
5. #10622677C2semidirect
6. #10622503C2semidirect
7. #10622501C2semidirect
9. #10622488C2semidirect
10. #10622483C2semidirect
11. #10622480C2semidirect
13. #10622467C2semidirect
14. #10622310C2semidirect
15. #10622298C2semidirect
137. #499D11semidirect
261. C11#3233semidirect

Maximal subgroups

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

subgroupindex
#106232222
#106232192
C11×#4992
#106226812
#106226772
#106225032
#106225012
#106224982
#106224882
#106224832
#106224802
#106224792
#106224672
#106223102
#106222982
#323311