Finite Group Databasebeta

← #13079790

Subgroups — #13079790

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#10623219C211yesmaximal, characteristic, complemented
2#10623211C211yesmaximal, characteristic
3C11×#488C211yesmaximal, characteristic, complemented
4#10622677C211yesmaximal, characteristic, complemented
5#10622669C211yesmaximal, characteristic, complemented
6#10622428C211yesmaximal, characteristic, complemented
7#10622427C211yesmaximal, characteristic, complemented
8#10622407C211yesmaximal, characteristic, complemented
9#10622404C211yesmaximal, characteristic, complemented
10#10622397C211yesmaximal, characteristic
11#10622392C211yesmaximal, characteristic
12#10622374C211yesmaximal, characteristic, complemented
13#10622372C211yesmaximal, characteristic, complemented
14#10622298C211yesmaximal, characteristic, complemented
15#10622296C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C11×#124C2211yescharacteristic
18#66999C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20#66991C2211yescharacteristic
21D4×Dic11C2211yescharacteristic
22#66949—21no—
23#66949—21no—
24#66945C2211yescharacteristic
25#66945C2211yescharacteristic
26#66941C2211yescharacteristic
27#66941C2211yescharacteristic
28#66940—21no—
29#66940—21no—
30#66936—21no—
31(C22⋊D11)⋊C4—21no—
32#66932—21no—
33#66930—21no—
34C42×D11C2211yescharacteristic
35#66923C2211yescharacteristic
36#66923C2211yescharacteristic
37C11×#103C2211yescharacteristic
38C11×#103C2211yescharacteristic
39C11×#102C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C4×C8×C11C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44#66896C2211yescharacteristic
45#66896C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66882C2211yescharacteristic
49#66882C2211yescharacteristic
50#66881C2211yescharacteristic
51#66881C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C22×Dic11—21no—
63C2×C4×D11D411yescharacteristic
64C2×C4×D11D411yescharacteristic
65C2×C4×D11C2311yescharacteristic
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C22⋊C4—21no—
75C11×C22⋊C4—21no—
76C42×C11C2311yescharacteristic
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11C2311yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
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
103C23×C11—21no—
104C22×D11C2×D411yescharacteristic
105Q8×C11—21no—
106Q8×C11—21no—
107D4×C11—21no—
108D4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2411yescharacteristic
115C22⋊D11—42no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—42no—
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C4×D11—21no—
125C4×D11—21no—
126C4×D11—22no—
127C4×D11—41no—
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#499—111no—
138#488—111no—
139#488D1111yescharacteristic, complemented
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×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11C22×D411yescharacteristic
153C2×D11—21no—
154C2×D11—21no—
155C2×D11—21no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C112−1+411yescharacteristic
162C4×C112−1+411yescharacteristic
163Dic11—21no—
164Dic11—21no—
165Dic11—41no—
166Dic11—41no—
167Dic11—41no—
168Dic11—41no—
169Dic11#13512yes—
170C4⋊Q8—111no—
171C4⋊Q8—111no—
172#126—221no—
173#125—111no—
174#125—111no—
175#125C2×D1111yescharacteristic
176#124C2×D1111yescharacteristic
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#107—111no—
194#107—111no—
195#106—111no—
196#106—111no—
197#106—111no—
198#106—111no—
199C4⋊C8—111no—
200C4⋊C8—111no—
201#103—111no—
202#103—111no—
203#103C2×D1111yescharacteristic
204#103C2×D1111yescharacteristic
205#102—111no—
206#102—111no—
207#102C2×D1111yescharacteristic
208#102C2×D1111yescharacteristic
209C22⋊C8—111no—
210C22⋊C8—111no—
211C4×C8—111no—
212C4×C8C2×D1111yescharacteristic
213C2×C11—81no—
214C2×C11#53611yescharacteristic
215C2×C11C2×#13511yescharacteristic
216C2×C11#57511yescharacteristic
217D11—41no—
218C2×Q8—221no—
219C2×Q8—221no—
220C2×Q8C22×D1111yescharacteristic
221C2×D4—221no—
222C2×D4C22×D1111yescharacteristic
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—111no—
234C4⋊C4—111no—
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⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4C22×D1111yescharacteristic
246C4⋊C4C22×D1111yescharacteristic
247C22⋊C4—21no—
248C22⋊C4—21no—
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—21no—
263C23—111no—
264Q8—21no—
265Q8—21no—
266Q8—442no—
267Q8—442no—
268D4—21no—
269D4—21no—
270D4—442no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—111no—
275C2×C4—111no—
276C2×C4—111no—
277C2×C4—222no—
278C2×C4—221no—
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—41no—
294C22—41no—
295C22—41no—
296C22—221no—
297C22—221no—
298C22—221no—
299C22C2×D4×D1111yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—112no—
306C4—221no—
307C4—221no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4—441no—
312C4#6704311yescharacteristic
313C4#6704311yescharacteristic
314C2—81no—
315C2—441no—
316C2#1062320611yescharacteristic
317C2D11×#13511yescharacteristic
318C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#488C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#488D11
hypocenterC11#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #10623219C2semidirect
3. C11×#488C2semidirect
4. #10622677C2semidirect
5. #10622669C2semidirect
6. #10622428C2semidirect
7. #10622427C2semidirect
8. #10622407C2semidirect
9. #10622404C2semidirect
12. #10622374C2semidirect
13. #10622372C2semidirect
14. #10622298C2semidirect
15. #10622296C2semidirect
139. #488D11semidirect
261. C11#3233semidirect

Maximal subgroups

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

subgroupindex
#106232192
#106232112
C11×#4882
#106226772
#106226692
#106224282
#106224272
#106224072
#106224042
#106223972
#106223922
#106223742
#106223722
#106222982
#106222962
#323311