Finite Group Databasebeta

← #13078566

Subgroups — #13078566

Order 1408.

410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#117C211yesmaximal, characteristic
2C2×#66950C211yesmaximal, characteristic
3C11×#428C211yesmaximal, characteristic, complemented
4#10622739C211yesmaximal, characteristic
5#10622733C211yesmaximal, characteristic, complemented
6#10622617C211yesmaximal, characteristic, complemented
7#10622577C211yesmaximal, characteristic, complemented
8#10622501C212yesmaximal, complemented
9#10622497C212yesmaximal, complemented
10#10622480C212yesmaximal, complemented
11#10622475C212yesmaximal, complemented
12C22×C4×D11C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×M16C2211yescharacteristic
15C11×#117C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4—21no—
18#66979C2211yescharacteristic
19C2×C4⋊Dic11—21no—
20C2×#4318C2211yescharacteristic
21#66950—21no—
22#66950—21no—
23#66950C2212yes—
24#66950C2212yes—
25#66945C2211yescharacteristic
26#66945C2211yescharacteristic
27C4⋊C4×D11C2211yescharacteristic
28C4⋊C4×D11C2211yescharacteristic
29C22⋊C4×D11—21no—
30#66930—21no—
31#66925—21no—
32C42×D11—21no—
33C11×#107C2212yescomplemented
34C11×#106C2212yescomplemented
35(C2×D11)⋊C8C2212yes—
36(C2×D11)⋊C8C2212yes—
37#66880C2212yescomplemented
38#66880C2212yescomplemented
39#66874C2212yescomplemented
40#66874C2212yescomplemented
41#66872C2212yescomplemented
42#66871C2212yescomplemented
43C23×D11D411yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11C2311yescharacteristic
46C22×Dic11—21no—
47C22×Dic11D411yescharacteristic
48C2×C4×D11—21no—
49C2×C4×D11—21no—
50C2×C4×D11—22no—
51C2×C4×D11—22no—
52C2×C4×D11D411yescharacteristic
53C2×C4×D11D411yescharacteristic
54C2×C4×D11C2311yescharacteristic
55C2×C4×D11C2311yescharacteristic
56C2×Dic22—21no—
57C2×Dic22—22no—
58C2×Dic22—22no—
59C2×Dic22C2312yes—
60C11×M16—22no—
61C2×C8×C11C2312yes—
62C11×C4⋊C4—21no—
63C11×C4⋊C4C2312yes—
64C11×C4⋊C4C2311yescharacteristic
65C11×C4⋊C4C2311yescharacteristic
66C11×C22⋊C4—21no—
67C42×C11—21no—
68C22⋊Dic11—21no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—21no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—22no—
73C4⋊Dic11—22no—
74C4⋊Dic11—22no—
75C4⋊Dic11C2311yescharacteristic
76C4⋊Dic11C2311yescharacteristic
77Dic11⋊C4—21no—
78Dic11⋊C4—21no—
79C4×Dic11—21no—
80C4×Dic11—21no—
81C4×Dic11—21no—
82#4318—22no—
83C2×C11⋊C8C2312yes—
84#3095—111nomaximal, Sylow
85C23×C11C2×D411yescharacteristic
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—41no—
89C22×D11C2×D411yescharacteristic
90C22×D11C2×D411yescharacteristic
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—42no—
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11#4112yes—
97C2×C4×C11#4112yes—
98C2×C4×C11C2411yescharacteristic
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—42no—
104C2×Dic11C2×D411yescharacteristic
105C2×Dic11C2×D411yescharacteristic
106C4×D11—22no—
107C4×D11—22no—
108C4×D11—21no—
109C4×D11—21no—
110C4×D11—21no—
111C4×D11—21no—
112C4×D11—42no—
113C4×D11—42no—
114Dic22—22no—
115Dic22—22no—
116Dic22—42no—
117C8×C11—22no—
118C11⋊C8—22no—
119C2×C22⋊Q8—111no—
120C2×#117—111no—
121#485—112no—
122#485—112no—
123#484—112no—
124#483—112no—
125#428—111no—
126#428D1111yescharacteristic, complemented
127#419—111no—
128#419—111no—
129#407—111no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11#12312yes—
133C22×C11C22×D411yescharacteristic
134C2×D11—21no—
135C2×D11—21no—
136C2×D11—21no—
137C2×D11—21no—
138C2×D11—21no—
139C2×D11—44no—
140C2×D11#13712yes—
141C4×C11—41no—
142C4×C11—42no—
143C4×C11—41no—
144C4×C11#12312yes—
145C4×C11C2×#4111yescharacteristic
146C4×C11C2×#4111yescharacteristic
147Dic11—21no—
148Dic11—21no—
149Dic11—42no—
150Dic11—41no—
151Dic11—41no—
152C22×Q8—111no—
153C23×C4—111no—
154C2×M16—111no—
155C2×M16C2×D1111yescharacteristic
156C22⋊Q8—112no—
157C22⋊Q8—112no—
158C22⋊Q8—221no—
159C22⋊Q8—221no—
160#117—111no—
161#117—111no—
162#117—111no—
163#117—221no—
164#117—221no—
165#117C2×D1111yescharacteristic
166C2×C4⋊C4—111no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4C2×D1111yescharacteristic
170C2×C22⋊C4—221no—
171C2×C22⋊C4—221no—
172C2×C42—221no—
173#107—112no—
174#107C2×D1112yescomplemented
175#106—112no—
176#106C2×D1112yescomplemented
177#103—112no—
178#103—112no—
179#103—112no—
180#103—112no—
181C22⋊C8—112no—
182C22⋊C8—112no—
183C2×C11—22no—
184C2×C11C2×#12311yescharacteristic
185C2×C11C2×#13711yescharacteristic
186C2×C11#57511yescharacteristic
187D11—22no—
188D11—41no—
189C24—111no—
190C2×Q8—112no—
191C2×Q8—221no—
192C2×Q8—222no—
193C2×Q8—222no—
194C22×C4—21no—
195C22×C4—111no—
196C22×C4—111no—
197C22×C4—111no—
198C22×C4—111no—
199C22×C4—111no—
200C22×C4—221no—
201C22×C4—221no—
202C22×C4—222no—
203C22×C4—222no—
204C22×C4—221no—
205C22×C4C22×D1111yescharacteristic
206M16—22no—
207M16—222no—
208C2×C8—112no—
209C2×C8C22×D1112yes—
210C4⋊C4—21no—
211C4⋊C4—111no—
212C4⋊C4—111no—
213C4⋊C4—221no—
214C4⋊C4—221no—
215C4⋊C4—222no—
216C4⋊C4—222no—
217C4⋊C4C22×D1111yescharacteristic
218C4⋊C4C22×D1111yescharacteristic
219C4⋊C4C22×D1112yes—
220C22⋊C4—21no—
221C22⋊C4—221no—
222C22⋊C4—221no—
223C22⋊C4—222no—
224C22⋊C4—222no—
225C22⋊C4—221no—
226C42—21no—
227C42—221no—
228C42—221no—
229C42—221no—
230C11#309511yescharacteristic, complemented, Sylow
231C23—111no—
232C23—111no—
233C23—222no—
234C23—222no—
235C23—441no—
236C23D4×D1111yescharacteristic
237Q8—222no—
238Q8—222no—
239Q8—442no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—111no—
245C2×C4—111no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4—221no—
252C2×C4—221no—
253C2×C4—221no—
254C2×C4—221no—
255C2×C4—222no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4#433912yes—
260C2×C4D4×D1111yescharacteristic
261C2×C4#434312yes—
262C2×C4C23×D1111yescharacteristic
263C8—22no—
264C8—222no—
265C22—21no—
266C22—21no—
267C22—112no—
268C22—221no—
269C22—221no—
270C22—221no—
271C22—221no—
272C22—221no—
273C22—444no—
274C22#6694712yes—
275C22C2×D4×D1111yescharacteristic
276C4—42no—
277C4—41no—
278C4—41no—
279C4—221no—
280C4—221no—
281C4—442no—
282C4—441no—
283C4—441no—
284C4#6694712yes—
285C4C2×#433911yescharacteristic
286C4C2×#434311yescharacteristic
287C2—22no—
288C2—222no—
289C2—441no—
290C2C2×#6694711yescharacteristic
291C2#1062330411yescharacteristic
292C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
prime radicalC23×D11D4
hypercenter#428D11
hypocenterC11#3095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. C11×#428C2semidirect
5. #10622733C2semidirect
6. #10622617C2semidirect
7. #10622577C2semidirect
8. #10622501C2semidirect
9. #10622497C2semidirect
10. #10622480C2semidirect
11. #10622475C2semidirect
33. C11×#107C22semidirect
34. C11×#106C22semidirect
37. #66880C22semidirect
38. #66880C22semidirect
39. #66874C22semidirect
40. #66874C22semidirect
41. #66872C22semidirect
42. #66871C22semidirect
126. #428D11semidirect
174. #107C2×D11semidirect
176. #106C2×D11semidirect
230. C11#3095semidirect

Maximal subgroups

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

subgroupindex
D11×#1172
C2×#669502
C11×#4282
#106227392
#106227332
#106226172
#106225772
#106225012
#106224972
#106224802
#106224752
#309511