Finite Group Databasebeta

← #13079792

Subgroups — #13079792

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#10623131C211yesmaximal, characteristic
2#10623048C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic
4#10622648C211yesmaximal, characteristic
5#10622609C211yesmaximal, characteristic, complemented
6#10622491C211yesmaximal, characteristic, complemented
7#10622488C211yesmaximal, characteristic, complemented
8#10622471C211yesmaximal, characteristic, complemented
9#10622467C211yesmaximal, characteristic, complemented
10#10622381C211yesmaximal, characteristic, complemented
11#10622381C211yesmaximal, characteristic, complemented
12#10622374C211yesmaximal, characteristic, complemented
13#10622372C211yesmaximal, characteristic, complemented
14#10622336C211yesmaximal, characteristic, complemented
15#10622331C211yesmaximal, characteristic, complemented
16C11×#121C2211yescharacteristic
17C11×#117C2211yescharacteristic
18#66989C2211yescharacteristic
19#66988—21no—
20D4×Dic11—21no—
21D4×Dic11C2211yescharacteristic
22#66979C2211yescharacteristic
23#66977C2211yescharacteristic
24C2×C4×Dic11C2211yescharacteristic
25#66943C2211yescharacteristic
26#66943C2211yescharacteristic
27#66943C2211yescharacteristic
28#66941C2211yescharacteristic
29#66941C2211yescharacteristic
30#66940C2211yescharacteristic
31#66932—21no—
32#66931—21no—
33#66931—21no—
34#66930—21no—
35C4×Dic22—21no—
36C4×Dic22—21no—
37C11×#107C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×#102C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42#66896C2211yescharacteristic
43#66896C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66882C2211yescharacteristic
46#66881C2211yescharacteristic
47#66880C2211yescharacteristic
48#66880C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×Dic11—21no—
63C22×Dic11D411yescharacteristic
64C22×Dic11D411yescharacteristic
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4C2311yescharacteristic
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C22⋊C4—21no—
74C11×C22⋊C4—21no—
75C42×C11—21no—
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
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×Dic11D411yescharacteristic
97C4×Dic11D411yescharacteristic
98C4×Dic11C2311yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3233—111nomaximal, Sylow
103C23×C11—21no—
104C23×C11C2×D411yescharacteristic
105D4×C11—21no—
106D4×C11—21no—
107D4×C11—42no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2411yescharacteristic
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—41no—
121C2×Dic11—42no—
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
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#499—111no—
138#488—111no—
139#488—111no—
140#485—111no—
141#485—111no—
142#482—111no—
143#482D1111yescharacteristic
144#477—111no—
145#476—111no—
146#475—111no—
147#474—111no—
148#431—111no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11C22×D411yescharacteristic
156C4×C11—21no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C112−1+411yescharacteristic
161C4×C112−1+411yescharacteristic
162Dic11—21no—
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#125—111no—
176#124—111no—
177#123—221no—
178C22⋊Q8—111no—
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181#121C2×D1111yescharacteristic
182C4×Q8—111no—
183C4×Q8—221no—
184C4×Q8—221no—
185C4×D4—111no—
186C4×D4—221no—
187#117—111no—
188#117—221no—
189#117C2×D1111yescharacteristic
190C2×C42—111no—
191#107—111no—
192#107—111no—
193#107—111no—
194#107C2×D1111yescharacteristic
195#106—111no—
196#106—111no—
197#106—111no—
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#102C2×D1111yescharacteristic
208#102C2×D1111yescharacteristic
209C22⋊C8—111no—
210C22⋊C8C2×D1111yescharacteristic
211C4×C8—111no—
212C4×C8—111no—
213C2×C11—41no—
214C2×C11—81no—
215C2×C11#53611yescharacteristic
216C2×C11C2×#13511yescharacteristic
217C2×C11#57511yescharacteristic
218C2×Q8—111no—
219C2×Q8—221no—
220C2×Q8—221no—
221C2×D4—21no—
222C2×D4C22×D1111yescharacteristic
223C22×C4—111no—
224C22×C4—111no—
225C22×C4—221no—
226C22×C4C22×D1111yescharacteristic
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—111no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—221no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4C22×D1111yescharacteristic
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—21no—
255C42—111no—
256C42—111no—
257C42—111no—
258C42—111no—
259C42—221no—
260C42—221no—
261C11#323311yescharacteristic, complemented, Sylow
262C23—21no—
263C23D4×D1111yescharacteristic
264Q8—221no—
265Q8—221no—
266Q8—442no—
267Q8—442no—
268D4—21no—
269D4—21no—
270D4—42no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—111no—
277C2×C4—111no—
278C2×C4—111no—
279C2×C4—111no—
280C2×C4—222no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—442no—
286C2×C4—441no—
287C2×C4D4×D1111yescharacteristic
288C2×C4C23×D1111yescharacteristic
289C8—21no—
290C8—21no—
291C8—221no—
292C8—221no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22C2×D4×D1111yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—112no—
305C4—221no—
306C4—221no—
307C4—221no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4—441no—
312C4#6704311yescharacteristic
313C4#6704311yescharacteristic
314C2—41no—
315C2—81no—
316C2#1062317911yescharacteristic
317C2D11×#13511yescharacteristic
318C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#482D11
hypocenterC11#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #10623048C2semidirect
5. #10622609C2semidirect
6. #10622491C2semidirect
7. #10622488C2semidirect
8. #10622471C2semidirect
9. #10622467C2semidirect
10. #10622381C2semidirect
11. #10622381C2semidirect
12. #10622374C2semidirect
13. #10622372C2semidirect
14. #10622336C2semidirect
15. #10622331C2semidirect
261. C11#3233semidirect

Maximal subgroups

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

subgroupindex
#106231312
#106230482
C11×#4822
#106226482
#106226092
#106224912
#106224882
#106224712
#106224672
#106223812
#106223742
#106223722
#106223362
#106223312
#323311