Finite Group Databasebeta

← #13079439

Subgroups — #13079439

Order 1408.

410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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×#66950C211yesmaximal, characteristic
3C11×#483C211yesmaximal, characteristic, complemented
4#10622663C211yesmaximal, characteristic, complemented
5#10622584C211yesmaximal, characteristic, complemented
6#10622481C212yesmaximal, complemented
7#10622475C212yesmaximal, complemented
8#10622429C212yesmaximal, complemented
9#10622421C212yesmaximal, complemented
10#10622352C211yesmaximal, characteristic, complemented
11#10622339C211yesmaximal, characteristic
12C2×Q8×D11C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C11×C22⋊Q8C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#66999C2211yescharacteristic
18C2×#4326C2212yescomplemented
19C2×(C2×D11)⋊C4—21no—
20C2×C4⋊Dic11—21no—
21#66977C2211yescharacteristic
22C2×Dic44C2212yescomplemented
23C2×#4313C2212yes—
24#66950—21no—
25#66950—21no—
26#66950C2212yes—
27#66950C2211yescharacteristic
28#66950C2212yes—
29#66949—21no—
30C4⋊C4×D11—21no—
31C4⋊C4×D11C2211yescharacteristic
32C22⋊C4×D11—21no—
33#66931—21no—
34C11×#106C2212yescomplemented
35C11×#103C2212yescomplemented
36C11×C22⋊C8C2211yescharacteristic
37C22⋊(C11⋊C8)C2211yescharacteristic
38(C2×D11)⋊C8C2212yes—
39#66880C2212yescomplemented
40#66874C2212yescomplemented
41#66874C2212yescomplemented
42#66872C2212yescomplemented
43C23×D11D411yescharacteristic
44C2×Q8×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—21no—
48C22×Dic11D411yescharacteristic
49Q8×D11—42no—
50C2×C4×D11—21no—
51C2×C4×D11—21no—
52C2×C4×D11—42no—
53C2×C4×D11D411yescharacteristic
54C2×C4×D11D411yescharacteristic
55C2×C4×D11C2311yescharacteristic
56C2×C4×D11C2311yescharacteristic
57C2×Dic22—21no—
58C2×Dic22—21no—
59C2×Dic22—42no—
60C2×Dic22C2311yescharacteristic
61C2×Dic22C2312yes—
62C2×C8×C11C2312yes—
63C11×C4⋊C4—21no—
64C11×C4⋊C4—21no—
65C11×C4⋊C4C2312yes—
66C11×C4⋊C4C2311yescharacteristic
67C11×C22⋊C4—21no—
68C22⋊Dic11—21no—
69#4326—42no—
70(C2×D11)⋊C4—21no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—22no—
74C4⋊Dic11—21no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4⋊Dic11C2311yescharacteristic
78Dic11⋊C4—21no—
79Dic11⋊C4—21no—
80Dic11⋊C4—21no—
81C2×C11⋊C8C2312yes—
82Dic44—42no—
83#4313—42no—
84#3195—111nomaximal, Sylow
85C23×C11C2×D411yescharacteristic
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—41no—
89C22×D11C2×D411yescharacteristic
90C22×D11C2×D411yescharacteristic
91Q8×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—42no—
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2411yescharacteristic
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—22no—
102C2×Dic11—41no—
103C2×Dic11—42no—
104C2×Dic11C2×D411yescharacteristic
105C2×Dic11C2×D411yescharacteristic
106C4×D11—22no—
107C4×D11—22no—
108C4×D11—41no—
109C4×D11—41no—
110C4×D11—42no—
111C4×D11—42no—
112Dic22—22no—
113Dic22—22no—
114Dic22—22no—
115Dic22—42no—
116Dic22—42no—
117C8×C11—22no—
118C11⋊C8—22no—
119C2×C22⋊Q8—111no—
120C2×C22⋊Q8—111no—
121#483—111no—
122#483—112no—
123#483D1111yescharacteristic, complemented
124#470—112no—
125#470—112no—
126#451—111no—
127#451—112no—
128#451—111no—
129#407—111no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11#13712yes—
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—21no—
142C4×C11—41no—
143C4×C11—42no—
144C4×C11—41no—
145C4×C11H(5,𝔽2)12yes—
146Dic11—21no—
147Dic11—21no—
148Dic11—41no—
149Dic11—42no—
150Dic11—41no—
151C22×Q8—111no—
152C22×Q8—111no—
153C23×C4—111no—
154C2×Q16—112no—
155C2×Q16—112no—
156C2×M16—112no—
157C22⋊Q8—111no—
158C22⋊Q8—111no—
159C22⋊Q8—112no—
160C22⋊Q8—111no—
161C22⋊Q8—112no—
162C22⋊Q8—221no—
163C22⋊Q8—221no—
164C22⋊Q8—221no—
165C22⋊Q8—221no—
166C22⋊Q8C2×D1111yescharacteristic
167C2×C4⋊C4—111no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4C2×D1111yescharacteristic
171C2×C22⋊C4—221no—
172C2×C22⋊C4—221no—
173#106—112no—
174#106C2×D1112yescomplemented
175#103—112no—
176#103—112no—
177#103—112no—
178#103C2×D1112yescomplemented
179C22⋊C8—111no—
180C22⋊C8—112no—
181C22⋊C8C2×D1111yescharacteristic
182C2×C11—22no—
183C2×C11#53411yescharacteristic
184C2×C11C2×#13711yescharacteristic
185C2×C11C2×#13711yescharacteristic
186D11—22no—
187D11—41no—
188C24—111no—
189C2×Q8—112no—
190C2×Q8—111no—
191C2×Q8—221no—
192C2×Q8—221no—
193C2×Q8—442no—
194C2×Q8—442no—
195C2×Q8C22×D1111yescharacteristic
196C22×C4—21no—
197C22×C4—111no—
198C22×C4—111no—
199C22×C4—111no—
200C22×C4—111no—
201C22×C4—111no—
202C22×C4—221no—
203C22×C4—221no—
204C22×C4—221no—
205C22×C4—442no—
206C22×C4C22×D1111yescharacteristic
207Q16—442no—
208Q16—442no—
209M16—442no—
210C2×C8—112no—
211C2×C8C22×D1112yes—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—111no—
215C4⋊C4—221no—
216C4⋊C4—221no—
217C4⋊C4—221no—
218C4⋊C4—222no—
219C4⋊C4—222no—
220C4⋊C4—221no—
221C4⋊C4C22×D1111yescharacteristic
222C4⋊C4C22×D1112yes—
223C22⋊C4—21no—
224C22⋊C4—221no—
225C22⋊C4—221no—
226C22⋊C4—222no—
227C22⋊C4—222no—
228C22⋊C4—221no—
229C11#319511yescharacteristic, complemented, Sylow
230C23—111no—
231C23—111no—
232C23—222no—
233C23—222no—
234C23—441no—
235C23D4×D1111yescharacteristic
236Q8—22no—
237Q8—222no—
238Q8—222no—
239Q8—222no—
240Q8—442no—
241Q8—442no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—111no—
248C2×C4—111no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—221no—
252C2×C4—222no—
253C2×C4—221no—
254C2×C4—441no—
255C2×C4—441no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—441no—
259C2×C4—442no—
260C2×C4D4×D1111yescharacteristic
261C2×C4C23×D1111yescharacteristic
262C8—22no—
263C8—222no—
264C22—21no—
265C22—21no—
266C22—112no—
267C22—221no—
268C22—221no—
269C22—221no—
270C22—221no—
271C22—221no—
272C22—444no—
273C22#6696812yes—
274C22C2×D4×D1111yescharacteristic
275C4—21no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—221no—
280C4—221no—
281C4—441no—
282C4—441no—
283C4—442no—
284C4#6704212yes—
285C2—22no—
286C2—222no—
287C2—441no—
288C2#1062318411yescharacteristic
289C2C2×#6696811yescharacteristic
290C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#483C2
socleC22×C11C22×D4
prime radicalC23×D11D4
hypercenter#483D11
hypocenterC11#3195
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. C11×#483C2semidirect
4. #10622663C2semidirect
5. #10622584C2semidirect
6. #10622481C2semidirect
7. #10622475C2semidirect
8. #10622429C2semidirect
9. #10622421C2semidirect
10. #10622352C2semidirect
18. C2×#4326C22semidirect
22. C2×Dic44C22semidirect
34. C11×#106C22semidirect
35. C11×#103C22semidirect
39. #66880C22semidirect
40. #66874C22semidirect
41. #66874C22semidirect
42. #66872C22semidirect
123. #483D11semidirect
174. #106C2×D11semidirect
178. #103C2×D11semidirect
229. C11#3195semidirect

Maximal subgroups

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

subgroupindex
D11×C22⋊Q82
C2×#669502
C11×#4832
#106226632
#106225842
#106224812
#106224752
#106224292
#106224212
#106223522
#106223392
#319511