Finite Group Databasebeta

← #13078561

Subgroups — #13078561

Order 1408.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×C22⋊Q8C211yesmaximal, characteristic
2C2×#66945C211yesmaximal, characteristic
3C11×#484C211yesmaximal, characteristic, complemented
4#10622656C211yesmaximal, characteristic, complemented
5#10622583C211yesmaximal, characteristic, complemented
6#10622501C212yesmaximal, complemented
7#10622494C212yesmaximal, complemented
8#10622428C212yesmaximal, complemented
9#10622415C212yesmaximal, complemented
10#10622339C211yesmaximal, characteristic
11#10622334C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C11×C22⋊Q8C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16#66999C2211yescharacteristic
17C2×(C2×D11)⋊C4—21no—
18C2×C4⋊Dic11C2211yescharacteristic
19#66977C2211yescharacteristic
20C2×C4×Dic11—21no—
21C2×#4313C2212yes—
22#66950C2211yescharacteristic
23#66949—21no—
24#66945—21no—
25#66945—21no—
26#66945C2212yes—
27#66945C2212yes—
28C4⋊C4×D11—21no—
29C4⋊C4×D11C2211yescharacteristic
30C22⋊C4×D11—21no—
31#66931—21no—
32C11×#107C2212yescomplemented
33C11×#103C2212yescomplemented
34C11×C22⋊C8C2211yescharacteristic
35#66899C2212yescomplemented
36C22⋊(C11⋊C8)C2211yescharacteristic
37(C2×D11)⋊C8C2212yes—
38#66881C2212yescomplemented
39#66880C2212yescomplemented
40#66874C2212yescomplemented
41#66872C2212yescomplemented
42#66871C2212yescomplemented
43C23×D11D411yescharacteristic
44C2×Q8×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—21no—
48C22×Dic11D411yescharacteristic
49Q8×D11—24no—
50C2×C4×D11—24no—
51C2×C4×D11—21no—
52C2×C4×D11—21no—
53C2×C4×D11D411yescharacteristic
54C2×C4×D11D411yescharacteristic
55C2×C4×D11C2311yescharacteristic
56C2×C4×D11C2311yescharacteristic
57C2×Dic22—21no—
58C2×Dic22C2311yescharacteristic
59C2×C8×C11C2312yes—
60C11×C4⋊C4—21no—
61C11×C4⋊C4—21no—
62C11×C4⋊C4C2312yes—
63C11×C4⋊C4C2311yescharacteristic
64C11×C22⋊C4—21no—
65C22⋊Dic11—21no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—22no—
70C4⋊Dic11—21no—
71C4⋊Dic11—21no—
72C4⋊Dic11C2311yescharacteristic
73C4⋊Dic11C2312yes—
74Dic11⋊C4—21no—
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77C4×Dic11—22no—
78C4×Dic11—22no—
79C2×C11⋊C8C2312yes—
80#4313—24no—
81#3095—111nomaximal, Sylow
82C23×C11C2×D411yescharacteristic
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—41no—
86C22×D11C2×D411yescharacteristic
87C22×D11C2×D411yescharacteristic
88Q8×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—42no—
94C2×C4×C11C2×D411yescharacteristic
95C2×C4×C11C2411yescharacteristic
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—42no—
101C2×Dic11C2×D411yescharacteristic
102C2×Dic11C2×D411yescharacteristic
103C4×D11—22no—
104C4×D11—22no—
105C4×D11—22no—
106C4×D11—42no—
107C4×D11—42no—
108C4×D11#4114yes—
109Dic22—22no—
110Dic22—42no—
111C8×C11—22no—
112C11⋊C8—22no—
113C2×C22⋊Q8—111no—
114C2×#117—111no—
115#485—112no—
116#485—112no—
117#484—111no—
118#484D1111yescharacteristic, complemented
119#483—111no—
120#483—111no—
121#428—112no—
122#419—112no—
123#407—111no—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11#13712yes—
127C22×C11C22×D411yescharacteristic
128C2×D11—21no—
129C2×D11—21no—
130C2×D11—21no—
131C2×D11—21no—
132C2×D11—21no—
133C2×D11—44no—
134C2×D11#12312yes—
135C4×C11—21no—
136C4×C11—41no—
137C4×C11—42no—
138C4×C11—41no—
139C4×C11C2×#4112yes—
140Dic11—21no—
141Dic11—41no—
142Dic11—42no—
143Dic11—41no—
144Dic11#12312yes—
145C22×Q8—111no—
146C23×C4—111no—
147C2×M16—112no—
148C22⋊Q8—111no—
149C22⋊Q8—111no—
150C22⋊Q8—111no—
151C22⋊Q8—221no—
152C22⋊Q8—221no—
153C22⋊Q8C2×D1111yescharacteristic
154#117—112no—
155#117—112no—
156#117—221no—
157#117—221no—
158C2×C4⋊C4—111no—
159C2×C4⋊C4—111no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4C2×D1111yescharacteristic
162C2×C22⋊C4—221no—
163C2×C22⋊C4—221no—
164C2×C42—221no—
165#107—112no—
166#107C2×D1112yescomplemented
167#106—112no—
168#106—112no—
169#103—112no—
170#103—112no—
171#103—112no—
172#103C2×D1112yescomplemented
173C22⋊C8—111no—
174C22⋊C8—112no—
175C22⋊C8C2×D1111yescharacteristic
176C2×C11—22no—
177C2×C11C2×#12311yescharacteristic
178C2×C11C2×#13711yescharacteristic
179C2×C11#57511yescharacteristic
180D11—22no—
181D11—41no—
182C24—111no—
183C2×Q8—111no—
184C2×Q8—221no—
185C2×Q8—224no—
186C2×Q8C22×D1111yescharacteristic
187C22×C4—21no—
188C22×C4—111no—
189C22×C4—111no—
190C22×C4—111no—
191C22×C4—111no—
192C22×C4—111no—
193C22×C4—224no—
194C22×C4—221no—
195C22×C4—221no—
196C22×C4—221no—
197C22×C4C22×D1111yescharacteristic
198M16—224no—
199C2×C8—112no—
200C2×C8C22×D1112yes—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—112no—
204C4⋊C4—111no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C4⋊C4C22×D1112yes—
211C4⋊C4C22×D1111yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—222no—
214C22⋊C4—222no—
215C22⋊C4—221no—
216C22⋊C4—221no—
217C22⋊C4—221no—
218C42—222no—
219C42—222no—
220C11#309511yescharacteristic, complemented, Sylow
221C23—111no—
222C23—111no—
223C23—222no—
224C23—222no—
225C23—441no—
226C23D4×D1111yescharacteristic
227Q8—22no—
228Q8—222no—
229Q8—442no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—111no—
236C2×C4—114no—
237C2×C4—111no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—221no—
244C2×C4—221no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4D4×D1111yescharacteristic
249C2×C4C23×D1111yescharacteristic
250C8—22no—
251C8—222no—
252C22—21no—
253C22—21no—
254C22—112no—
255C22—221no—
256C22—221no—
257C22—221no—
258C22—221no—
259C22—221no—
260C22—444no—
261C22#6697112yes—
262C22C2×D4×D1111yescharacteristic
263C4—21no—
264C4—42no—
265C4—41no—
266C4—41no—
267C4—112no—
268C4—221no—
269C4—442no—
270C4—441no—
271C4—441no—
272C4#41×D1112yes—
273C2—22no—
274C2—222no—
275C2—441no—
276C2D11×#12311yescharacteristic
277C2C2×#6697111yescharacteristic
278C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#484C2
socleC22×C11C22×D4
prime radicalC23×D11D4
hypercenter#484D11
hypocenterC11#3095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. C11×#484C2semidirect
4. #10622656C2semidirect
5. #10622583C2semidirect
6. #10622501C2semidirect
7. #10622494C2semidirect
8. #10622428C2semidirect
9. #10622415C2semidirect
11. #10622334C2semidirect
32. C11×#107C22semidirect
33. C11×#103C22semidirect
35. #66899C22semidirect
38. #66881C22semidirect
39. #66880C22semidirect
40. #66874C22semidirect
41. #66872C22semidirect
42. #66871C22semidirect
118. #484D11semidirect
166. #107C2×D11semidirect
172. #103C2×D11semidirect
220. C11#3095semidirect

Maximal subgroups

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

subgroupindex
D11×C22⋊Q82
C2×#669452
C11×#4842
#106226562
#106225832
#106225012
#106224942
#106224282
#106224152
#106223392
#106223342
#309511