Finite Group Databasebeta

← #13079556

Subgroups — #13079556

Order 1408.

488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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×#127C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic, complemented
3C11×#460C211yesmaximal, characteristic, complemented
4#10622788C212yesmaximal, complemented
5#10622782C212yesmaximal, complemented
6#10622688C211yesmaximal, characteristic, complemented
7#10622640C211yesmaximal, characteristic, complemented
8#10622461C211yesmaximal, characteristic, complemented
9#10622446C211yesmaximal, characteristic, complemented
10#10622389C212yesmaximal, complemented
11#10622373C212yesmaximal, complemented
12C2×D4×D11—21no—
13C2×D4×D11—21no—
14C2×D4×D11C2212yes—
15C2×C11×SD16C2212yescomplemented
16C11×#127C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic, complemented
18#66999C2211yescharacteristic
19#66997C2211yescharacteristic, complemented
20C2×#4325C2212yescomplemented
21#66993—21no—
22#66993—21no—
23#66993C2212yes—
24C2×#4324C2212yescomplemented
25C2×#4314C2212yescomplemented
26#66950C2211yescharacteristic
27#66949—21no—
28#66942—21no—
29#66941C2211yescharacteristic, complemented
30#66927C2211yescharacteristic
31#66925—21no—
32C42×D11C2211yescharacteristic
33C4×Dic22—21no—
34C4×Dic22C2211yescharacteristic, complemented
35C11×C4⋊C8C2211yescharacteristic, complemented
36C11×#102C2212yescomplemented
37#66896C2212yescomplemented
38#66885C2212yescomplemented
39(C2×D11)⋊C8C2212yes—
40C8×Dic11C2212yescomplemented
41#66873C2212yescomplemented
42C4⋊(C11⋊C8)C2211yescharacteristic, complemented
43C23×D11—22no—
44C2×Q8×C11C2311yescharacteristic
45C2×D4×C11—21no—
46C2×D4×C11—21no—
47C2×D4×C11C2312yes—
48C2×C22⋊D11—22no—
49C2×C22⋊D11—22no—
50C2×C22⋊D11—22no—
51D4×D11—42no—
52D4×D11—42no—
53D4×D11—44no—
54D4×D11—44no—
55C2×D44—21no—
56C2×D44—21no—
57C2×D44C2312yes—
58C2×C4×D11D411yescharacteristic
59C2×C4×D11D411yescharacteristic
60C2×C4×D11C2311yescharacteristic
61C2×Dic22—21no—
62C2×Dic22C2311yescharacteristic
63C11×SD16—42no—
64C2×C8×C11C2312yes—
65C11×C4⋊C4—21no—
66C11×C4⋊C4C2311yescharacteristic
67C42×C11—21no—
68C42×C11C2311yescharacteristic
69#4325—42no—
70#4324—42no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—21no—
73C4⋊Dic11—21no—
74C4⋊Dic11C2311yescharacteristic
75Dic11⋊C4—21no—
76Dic11⋊C4—21no—
77Dic11⋊C4—21no—
78Dic11⋊C4—21no—
79Dic11⋊C4—21no—
80C4×Dic11—21no—
81C4×Dic11D411yescharacteristic
82C4×Dic11D411yescharacteristic
83C4×Dic11C2311yescharacteristic
84C2×C11⋊C8C2312yes—
85#4314—42no—
86#3208—111nomaximal, Sylow
87C23×C11—22no—
88C22×D11—22no—
89C22×D11—44no—
90C22×D11—44no—
91C22×D11—44no—
92C22×D11C2×D411yescharacteristic
93Q8×C11—21no—
94Q8×C11—21no—
95D4×C11—22no—
96D4×C11—22no—
97D4×C11—42no—
98D4×C11—42no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11C2411yescharacteristic
104C22⋊D11—44no—
105C22⋊D11—44no—
106C22⋊D11—44no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11C2×D411yescharacteristic
110C2×Dic11C2×D411yescharacteristic
111C2×Dic11C2×D411yescharacteristic
112D44—22no—
113D44—22no—
114D44—42no—
115D44—42no—
116C4×D11—21no—
117C4×D11—21no—
118C4×D11—22no—
119C4×D11SD1614yescomplemented
120Dic22—21no—
121Dic22—21no—
122Dic22—42no—
123C8×C11—22no—
124C11⋊C8—22no—
125#533—111no—
126C2×#127—111no—
127#492—112no—
128#486—112no—
129#460—111no—
130#460—111no—
131#460—111no—
132#460D1111yescharacteristic, complemented
133#450—112no—
134#450—112no—
135#431—111no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11C22×D411yescharacteristic
140C2×D11—21no—
141C2×D11—21no—
142C2×D11—42no—
143C2×D11—42no—
144C2×D11—42no—
145C2×D11—88no—
146C2×D11C2×SD1612yes—
147C4×C11—21no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11C2×SD1612yes—
151C4×C11H(5,𝔽2)11yescharacteristic
152C4×C11H(5,𝔽2)11yescharacteristic
153Dic11—21no—
154Dic11—41no—
155Dic11—41no—
156Dic11C2×SD1612yes—
157Dic11AGL(1,ℤ/8)12yes—
158C22×D4—112no—
159C22×D4—221no—
160C22×D4—221no—
161C2×SD16—112no—
162C2×SD16—112no—
163C2×SD16—112no—
164C2×SD16C2×D1112yescomplemented
165C4⋊Q8—111no—
166C4⋊Q8—111no—
167#127—112no—
168#127—111no—
169#127—221no—
170#127—221no—
171#127C2×D1111yescharacteristic
172#125—221no—
173C22⋊Q8—111no—
174C22⋊Q8—111no—
175C22⋊Q8—221no—
176C4×Q8—111no—
177C4×Q8—221no—
178C4×Q8C2×D1111yescharacteristic, complemented
179#117—221no—
180C2×C42—111no—
181C4⋊C8—111no—
182C4⋊C8C2×D1111yescharacteristic, complemented
183#102—112no—
184#102—112no—
185#102—112no—
186#102C2×D1112yescomplemented
187C22⋊C8—112no—
188C4×C8—112no—
189C2×C11—82no—
190C2×C11#53511yescharacteristic
191C2×C11C22×SD1611yescharacteristic
192C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
193D11—22no—
194D11—82no—
195C24—222no—
196C2×Q8—111no—
197C2×Q8—221no—
198C2×Q8C22×D1111yescharacteristic
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—112no—
202C2×D4—222no—
203C2×D4—222no—
204C2×D4—222no—
205C2×D4—221no—
206C2×D4—221no—
207C2×D4—444no—
208C2×D4—442no—
209C2×D4—442no—
210C2×D4—444no—
211C2×D4C22×D1112yes—
212C22×C4—111no—
213C22×C4—111no—
214C22×C4—111no—
215SD16—42no—
216SD16—442no—
217SD16—442no—
218SD16—442no—
219C2×C8—112no—
220C2×C8C22×D1112yes—
221C4⋊C4—21no—
222C4⋊C4—111no—
223C4⋊C4—221no—
224C4⋊C4—221no—
225C4⋊C4—221no—
226C4⋊C4—221no—
227C4⋊C4—221no—
228C4⋊C4—221no—
229C4⋊C4C22×D1111yescharacteristic
230C22⋊C4—221no—
231C22⋊C4—221no—
232C42—21no—
233C42—111no—
234C42—111no—
235C42—111no—
236C42—221no—
237C42C22×D1111yescharacteristic
238C11#320811yescharacteristic, complemented, Sylow
239C23—22no—
240C23—111no—
241C23—222no—
242C23—444no—
243C23—444no—
244C23—444no—
245Q8—21no—
246Q8—21no—
247Q8—221no—
248Q8—221no—
249Q8—442no—
250D4—22no—
251D4—22no—
252D4—42no—
253D4—42no—
254D4—222no—
255D4—222no—
256D4—442no—
257D4—444no—
258D4—444no—
259D4—444no—
260D4—442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—111no—
264C2×C4—111no—
265C2×C4—114no—
266C2×C4—111no—
267C2×C4—222no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4D4×D1111yescharacteristic
273C2×C4D4×D1111yescharacteristic
274C2×C4C23×D1111yescharacteristic
275C8—22no—
276C8—222no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—112no—
281C22—221no—
282C22—221no—
283C22—442no—
284C22—442no—
285C22—442no—
286C22—888no—
287C22C2×D4×D1111yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—112no—
292C4—112no—
293C4—221no—
294C4—441no—
295C4—441no—
296C4SD16×D1112yes—
297C4#6703711yescharacteristic
298C4#6704211yescharacteristic
299C2—82no—
300C2—222no—
301C2—882no—
302C2#1062313811yescharacteristic
303C2C2×SD16×D1111yescharacteristic
304C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#460C2
socleC22×C11C22×D4
prime radicalD11×#127C2
hypercenter#460D11
hypocenterC11#3208
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #10623109C2semidirect
3. C11×#460C2semidirect
4. #10622788C2semidirect
5. #10622782C2semidirect
6. #10622688C2semidirect
7. #10622640C2semidirect
8. #10622461C2semidirect
9. #10622446C2semidirect
10. #10622389C2semidirect
11. #10622373C2semidirect
15. C2×C11×SD16C22semidirect
17. C4×Q8×C11C22semidirect
19. #66997C22semidirect
20. C2×#4325C22semidirect
24. C2×#4324C22semidirect
25. C2×#4314C22semidirect
29. #66941C22semidirect
34. C4×Dic22C22semidirect
35. C11×C4⋊C8C22semidirect
36. C11×#102C22semidirect
37. #66896C22semidirect
38. #66885C22semidirect
40. C8×Dic11C22semidirect
41. #66873C22semidirect
42. C4⋊(C11⋊C8)C22semidirect
119. C4×D11SD16semidirect
132. #460D11semidirect
164. C2×SD16C2×D11semidirect
178. C4×Q8C2×D11semidirect
182. C4⋊C8C2×D11semidirect
186. #102C2×D11semidirect
238. C11#3208semidirect

Maximal subgroups

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

subgroupindex
D11×#1272
#106231092
C11×#4602
#106227882
#106227822
#106226882
#106226402
#106224612
#106224462
#106223892
#106223732
#320811