Finite Group Databasebeta

← #13078455

Subgroups — #13078455

Order 1408.

362 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#10623220C211yesmaximal, characteristic
2#10623103C211yesmaximal, characteristic
3C11×#479C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622634C211yesmaximal, characteristic, complemented
6#10622494C211yesmaximal, characteristic
7#10622488C211yesmaximal, characteristic, complemented
8#10622473C211yesmaximal, characteristic
9#10622470C211yesmaximal, characteristic, complemented
10#10622464C211yesmaximal, characteristic, complemented
11#10622452C211yesmaximal, characteristic
12#10622415C211yesmaximal, characteristic
13D11×#103C211yesmaximal, characteristic
14#10622412C211yesmaximal, characteristic, complemented
15#10622404C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C11×#125C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20C2×#4313C2211yescharacteristic
21C2×C8×D11C2211yescharacteristic
22#66950—21no—
23#66949—21no—
24#66945—21no—
25#66945C2211yescharacteristic
26#66945C2211yescharacteristic
27C4⋊C4×D11C2211yescharacteristic
28#66943C2211yescharacteristic
29#66942—21no—
30#66941—21no—
31#66941C2211yescharacteristic
32#66940—21no—
33#66940C2211yescharacteristic
34#66925—21no—
35#66925C2211yescharacteristic
36#66922C2211yescharacteristic
37C4×Dic22—21no—
38C4×Dic22C2211yescharacteristic
39C11×#107C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×C4⋊C8C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66881C2211yescharacteristic
47#66881C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60Q8×D11—22no—
61Q8×D11Q814yescomplemented
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×C4×D11C2311yescharacteristic
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4D411yescharacteristic
82(C2×D11)⋊C4D411yescharacteristic
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4D411yescharacteristic
95Dic11⋊C4D411yescharacteristic
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105C8×D11—22no—
106#3082—111nomaximal, Sylow
107C22×D11C2×D411yescharacteristic
108Q8×C11—21no—
109Q8×C11C2×Q812yes—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C4×D11—24no—
125C4×D11—81no—
126C4×D11C2×Q812yes—
127C4×D11#4112yes—
128Dic22—21no—
129Dic22—24no—
130Dic22—81no—
131Dic22—81no—
132Dic22C2×Q812yes—
133C8×C11—21no—
134C8×C11—21no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137#544—111no—
138#519—111no—
139#479—111no—
140#479—111no—
141#479—111no—
142#479D1111yescharacteristic, complemented
143#477—111no—
144#477—111no—
145#475—111no—
146#475—111no—
147#428—111no—
148#427—111no—
149#424—111no—
150#419—111no—
151C2×#103—111no—
152C22×C11C22×D411yescharacteristic
153C2×D11—21no—
154C2×D11—21no—
155C2×D11C22⋊Q812yes—
156C4×C11—22no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11C22×Q811yescharacteristic
163C4×C11C2×#4111yescharacteristic
164Dic11—22no—
165Dic11—21no—
166Dic11—21no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170Dic11C22⋊Q812yes—
171C22×Q8—111no—
172C2×M16—111no—
173C22×C8—111no—
174C4⋊Q8—111no—
175C4⋊Q8—111no—
176C4⋊Q8—221no—
177#125—111no—
178#125—221no—
179#125C2×D1111yescharacteristic
180C22⋊Q8—221no—
181C22⋊Q8—221no—
182C4×Q8—111no—
183C4×Q8—111no—
184C4×Q8—111no—
185C4×Q8—221no—
186C4×Q8—221no—
187C4×Q8C2×D1111yescharacteristic
188#117—111no—
189#117—111no—
190#117—111no—
191#117—221no—
192#117—221no—
193C2×C4⋊C4—111no—
194#107—111no—
195#107—111no—
196#107—111no—
197#107C2×D1111yescharacteristic
198#106—111no—
199#106—111no—
200#106—111no—
201#106C2×D1111yescharacteristic
202C4⋊C8—111no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8C2×D1111yescharacteristic
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103C2×D1111yescharacteristic
213#103C2×D1111yescharacteristic
214C2×C11C2×C22⋊Q811yescharacteristic
215C2×C11#57711yescharacteristic
216C2×C11#57811yescharacteristic
217D11—22no—
218C2×Q8—114no—
219C2×Q8—111no—
220C2×Q8—221no—
221C2×Q8—221no—
222C2×Q8—222no—
223C2×Q8—221no—
224C2×Q8C22×D1111yescharacteristic
225C22×C4—111no—
226C22×C4—221no—
227C22×C4—221no—
228M16—222no—
229C2×C8—111no—
230C2×C8—111no—
231C2×C8—222no—
232C2×C8C22×D1111yescharacteristic
233C2×C8C22×D1111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—111no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4C22×D1111yescharacteristic
251C4⋊C4C22×D1111yescharacteristic
252C4⋊C4C22×D1111yescharacteristic
253C22⋊C4—111no—
254C22⋊C4—111no—
255C22⋊C4—221no—
256C22⋊C4—221no—
257C42—21no—
258C42—111no—
259C42—221no—
260C42—221no—
261C42—221no—
262C42—221no—
263C42—221no—
264C42C22×D1111yescharacteristic
265C11#308211yescharacteristic, complemented, Sylow
266C23—111no—
267Q8—21no—
268Q8—112no—
269Q8—224no—
270Q8—221no—
271Q8—881no—
272Q8—881no—
273Q8Q8×D1112yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—111no—
279C2×C4—112no—
280C2×C4—112no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—224no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—881no—
289C2×C4D4×D1111yescharacteristic
290C2×C4D4×D1111yescharacteristic
291C2×C4C23×D1111yescharacteristic
292C8—21no—
293C8—21no—
294C8—221no—
295C8—221no—
296C22—112no—
297C22—221no—
298C22—221no—
299C22C2×D4×D1111yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—112no—
307C4—221no—
308C4—221no—
309C4—222no—
310C4—441no—
311C4—441no—
312C4—441no—
313C4C2×Q8×D1111yescharacteristic
314C4#41×D1111yescharacteristic
315C2—222no—
316C2D11×C22⋊Q811yescharacteristic
317C2#1062330111yescharacteristic
318C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#479D11
hypocenterC11#3082
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. C11×#479C2semidirect
4. #10622676C2semidirect
5. #10622634C2semidirect
7. #10622488C2semidirect
9. #10622470C2semidirect
10. #10622464C2semidirect
14. #10622412C2semidirect
15. #10622404C2semidirect
61. Q8×D11Q8semidirect
142. #479D11semidirect
265. C11#3082semidirect

Maximal subgroups

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

subgroupindex
#106232202
#106231032
C11×#4792
#106226762
#106226342
#106224942
#106224882
#106224732
#106224702
#106224642
#106224522
#106224152
D11×#1032
#106224122
#106224042
#308211