Finite Group Databasebeta

← #13079438

Subgroups — #13079438

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
1C2×#66999C211yesmaximal, characteristic
2D11×C22⋊Q8C211yesmaximal, characteristic
3C11×#451C211yesmaximal, characteristic, complemented
4#10622841C211yesmaximal, characteristic, complemented
5#10622802C212yesmaximal, complemented
6#10622799C212yesmaximal, complemented
7#10622656C211yesmaximal, characteristic, complemented
8#10622429C212yesmaximal, complemented
9#10622418C212yesmaximal, complemented
10#10622339C211yesmaximal, characteristic
11#10622334C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×Q8×D11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C2×C11×Q16C2212yescomplemented
16C11×C22⋊Q8C2211yescharacteristic
17#66999—21no—
18#66999—21no—
19#66999C2212yes—
20#66999C2211yescharacteristic
21#66999C2212yes—
22C2×#4326C2212yescomplemented
23C2×(C2×D11)⋊C4—21no—
24C2×C4⋊Dic11C2211yescharacteristic
25#66977C2211yescharacteristic
26C2×Dic11⋊C4—21no—
27C2×#4313C2212yes—
28#66950C2211yescharacteristic
29#66949—21no—
30C4⋊C4×D11—21no—
31C4⋊C4×D11C2211yescharacteristic
32C22⋊C4×D11—21no—
33#66931—21no—
34C11×#103C2212yescomplemented
35C11×C22⋊C8C2211yescharacteristic
36#66899C2212yescomplemented
37#66899C2212yescomplemented
38C22⋊(C11⋊C8)C2211yescharacteristic
39(C2×D11)⋊C8C2212yes—
40#66881C2212yescomplemented
41#66880C2212yescomplemented
42#66872C2212yescomplemented
43C23×D11D411yescharacteristic
44C2×Q8×C11—21no—
45C2×Q8×C11—42no—
46C2×Q8×C11C2311yescharacteristic
47C2×Q8×C11C2312yes—
48C22×C4×C11—21no—
49C22×C4×C11C2311yescharacteristic
50C22×Dic11—21no—
51C22×Dic11D411yescharacteristic
52Q8×D11—42no—
53C2×C4×D11—21no—
54C2×C4×D11—21no—
55C2×C4×D11—42no—
56C2×C4×D11D411yescharacteristic
57C2×C4×D11D411yescharacteristic
58C2×C4×D11C2311yescharacteristic
59C2×C4×D11C2311yescharacteristic
60C2×Dic22—21no—
61C2×Dic22C2311yescharacteristic
62C11×Q16—42no—
63C2×C8×C11C2312yes—
64C11×C4⋊C4—21no—
65C11×C4⋊C4C2311yescharacteristic
66C11×C22⋊C4—21no—
67C22⋊Dic11—21no—
68#4326—42no—
69(C2×D11)⋊C4—21no—
70(C2×D11)⋊C4—21no—
71(C2×D11)⋊C4—22no—
72(C2×D11)⋊C4—22no—
73C4⋊Dic11—21no—
74C4⋊Dic11—21no—
75C4⋊Dic11C2312yes—
76C4⋊Dic11C2311yescharacteristic
77Dic11⋊C4—21no—
78Dic11⋊C4—21no—
79Dic11⋊C4—22no—
80Dic11⋊C4—22no—
81Dic11⋊C4—21no—
82C2×C11⋊C8C2312yes—
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—
92Q8×C11—22no—
93Q8×C11—22no—
94Q8×C11—42no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—42no—
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2411yescharacteristic
102C2×Dic11—21no—
103C2×Dic11—22no—
104C2×Dic11—21no—
105C2×Dic11—41no—
106C2×Dic11—42no—
107C2×Dic11C2×D411yescharacteristic
108C2×Dic11C2×D411yescharacteristic
109C4×D11—22no—
110C4×D11—22no—
111C4×D11—41no—
112C4×D11—41no—
113C4×D11—42no—
114C4×D11—42no—
115Dic22—22no—
116Dic22—42no—
117C8×C11—22no—
118C11⋊C8—22no—
119C2×C22⋊Q8—111no—
120C2×C22⋊Q8—111no—
121#483—111no—
122#483—112no—
123#483—111no—
124#470—112no—
125#470—112no—
126#451—111no—
127#451—112no—
128#451D1111yescharacteristic, complemented
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—42no—
143C4×C11—41no—
144C4×C11—41no—
145C4×C11H(5,𝔽2)12yes—
146Dic11—21no—
147Dic11—21no—
148Dic11—41no—
149Dic11—41no—
150Dic11—42no—
151C22×Q8—111no—
152C22×Q8C2×D1111yescharacteristic
153C23×C4—111no—
154C2×Q16—112no—
155C2×Q16C2×D1112yescomplemented
156C2×M16—112no—
157C22⋊Q8—112no—
158C22⋊Q8—111no—
159C22⋊Q8—112no—
160C22⋊Q8—111no—
161C22⋊Q8—111no—
162C22⋊Q8—221no—
163C22⋊Q8—221no—
164C22⋊Q8—221no—
165C22⋊Q8—221no—
166C22⋊Q8C2×D1111yescharacteristic
167C2×C4⋊C4—111no—
168C2×C4⋊C4—111no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4—221no—
171C2×C22⋊C4—221no—
172C2×C22⋊C4—221no—
173#106—112no—
174#106—112no—
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—21no—
190C2×Q8—42no—
191C2×Q8—111no—
192C2×Q8—221no—
193C2×Q8—442no—
194C2×Q8C22×D1111yescharacteristic
195C2×Q8C22×D1112yes—
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—42no—
208Q16—442no—
209M16—442no—
210C2×C8—112no—
211C2×C8C22×D1112yes—
212C4⋊C4—21no—
213C4⋊C4—111no—
214C4⋊C4—112no—
215C4⋊C4—221no—
216C4⋊C4—221no—
217C4⋊C4—222no—
218C4⋊C4—222no—
219C4⋊C4—221no—
220C4⋊C4—221no—
221C4⋊C4—221no—
222C4⋊C4C22×D1111yescharacteristic
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—22no—
238Q8—22no—
239Q8—42no—
240Q8—222no—
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—222no—
252C2×C4—221no—
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#6697112yes—
274C22C2×D4×D1111yescharacteristic
275C4—21no—
276C4—41no—
277C4—42no—
278C4—41no—
279C4—221no—
280C4—221no—
281C4—442no—
282C4—441no—
283C4—441no—
284C4#6703712yes—
285C2—22no—
286C2—222no—
287C2—441no—
288C2#1062312011yescharacteristic
289C2C2×#6697111yescharacteristic
290C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
prime radicalC23×D11D4
hypercenter#451D11
hypocenterC11#3195
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. C11×#451C2semidirect
4. #10622841C2semidirect
5. #10622802C2semidirect
6. #10622799C2semidirect
7. #10622656C2semidirect
8. #10622429C2semidirect
9. #10622418C2semidirect
11. #10622334C2semidirect
15. C2×C11×Q16C22semidirect
22. C2×#4326C22semidirect
34. C11×#103C22semidirect
36. #66899C22semidirect
37. #66899C22semidirect
40. #66881C22semidirect
41. #66880C22semidirect
42. #66872C22semidirect
128. #451D11semidirect
155. C2×Q16C2×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
C2×#669992
D11×C22⋊Q82
C11×#4512
#106228412
#106228022
#106227992
#106226562
#106224292
#106224182
#106223392
#106223342
#319511