Finite Group Databasebeta

← #13080413

Subgroups — #13080413

Order 1408.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C11×#576C211yesmaximal, characteristic, complemented
2#10623366C212yesmaximal, complemented
3#10623300C211yesmaximal, characteristic, complemented
4#10622854C212yesmaximal, complemented
5#10622812C212yesmaximal, complemented
6#10622811C212yesmaximal, complemented
7#10622809C211yesmaximal, characteristic, complemented
8#10622773C211yesmaximal, characteristic, complemented
9#10622764C211yesmaximal, characteristic, complemented
10#10622757C211yesmaximal, characteristic, complemented
11#10622755C211yesmaximal, characteristic, complemented
12C11×H(5,𝔽2)C2212yescomplemented
13#67042C2212yescomplemented
14C11×AGL(1,ℤ/8)—22no—
15C11×AGL(1,ℤ/8)C2212yescomplemented
16C11×#135—21no—
17C11×#135C2211yescharacteristic
18C2×C11×D8—21no—
19C2×C11×D8C2211yescharacteristic, complemented
20C11×#131C2211yescharacteristic, complemented
21#67003—22no—
22#67003C2211yescharacteristic
23#67002—22no—
24#67002C2212yescomplemented
25#67002C2212yescomplemented
26#67001C2212yescomplemented
27#66993C2212yescomplemented
28#66985—22no—
29#66985C2212yescomplemented
30C2×#4323—22no—
31C2×#4323C2212yescomplemented
32#66972—21no—
33#66967—22no—
34D8×D11—21no—
35C2×D88C2211yescharacteristic, complemented
36#66954C2211yescharacteristic, complemented
37#66901C2211yescharacteristic, complemented
38#66901C2212yescomplemented
39#66897C2212yescomplemented
40#66889C2211yescharacteristic, complemented
41#66887C2212yescomplemented
42#66886C2211yescharacteristic, complemented
43#66883C2211yescharacteristic, complemented
44C8×Dic11C2211yescharacteristic, complemented
45C11×#41—22no—
46C11×#41—22no—
47C11×#41C2312yes—
48C11×#41C2311yescharacteristic
49C2×D4×C11—22no—
50C2×D4×C11—22no—
51C2×D4×C11—42no—
52C2×D4×C11C2312yes—
53C2×C22⋊D11—42no—
54#4343—22no—
55D4×D11—22no—
56D4×D11—42no—
57#4339—22no—
58#4339C2311yescharacteristic
59C2×D44—22no—
60C2×D44C2312yes—
61C11×Q16D411yescharacteristic, complemented
62C11×SD16—22no—
63C11×SD16D412yescomplemented
64C11×D8—21no—
65C11×D8—21no—
66C11×D8—22no—
67C11×D8D411yescharacteristic, complemented
68C11×M16—21no—
69C11×M16C2311yescharacteristic
70C2×C8×C11—21no—
71C2×C8×C11C2311yescharacteristic
72#4326D411yescharacteristic, complemented
73#4325—22no—
74#4325—22no—
75#4325D411yescharacteristic, complemented
76#4324—22no—
77#4324D411yescharacteristic, complemented
78#4323—22no—
79#4323—22no—
80#4323—22no—
81#4323—22no—
82#4323—22no—
83#4323D411yescharacteristic, complemented
84C4×Dic11C2311yescharacteristic
85#4318—22no—
86#4318C2312yes—
87#4318C2311yescharacteristic
88C2×C11⋊C8—22no—
89C2×C11⋊C8C2311yescharacteristic
90D88—21no—
91D88—21no—
92#4313—21no—
93C8×D11—21no—
94#3292—111nomaximal, Sylow
95C23×C11—22no—
96C23×C11—42no—
97C22×D11—22no—
98C22×D11—42no—
99Q8×C11C2×D411yescharacteristic
100Q8×C11C2×D412yes—
101D4×C11—22no—
102D4×C11—21no—
103D4×C11—22no—
104D4×C11—22no—
105D4×C11—42no—
106D4×C11—42no—
107D4×C11C2×D411yescharacteristic
108D4×C11C2×D412yes—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11C2411yescharacteristic
113C22⋊D11—21no—
114C22⋊D11—42no—
115C22⋊D11—84no—
116C2×Dic11—21no—
117D44—22no—
118D44—22no—
119D44—42no—
120D44C2×D411yescharacteristic
121C4×D11—21no—
122C4×D11—42no—
123Dic22C2×D411yescharacteristic
124C8×C11—21no—
125C8×C11C2×D411yescharacteristic
126C8×C11C2×D411yescharacteristic
127C11⋊C8—21no—
128C11⋊C8—22no—
129C11⋊C8C2×D411yescharacteristic
130C11⋊C8C2×D411yescharacteristic
131#576—112no—
132#576—111no—
133#576D1111yescharacteristic, complemented
134#493—111no—
135#472—112no—
136#472—111no—
137#472—111no—
138#453—112no—
139#453—112no—
140#443—111no—
141#443—111no—
142C22×C11—21no—
143C22×C11—22no—
144C22×C11—42no—
145C22×C11—82no—
146C22×C11—162no—
147C22×C11H(5,𝔽2)11yescharacteristic
148C2×D11—21no—
149C2×D11—42no—
150C2×D11—82no—
151C2×D11—162no—
152C4×C11—21no—
153C4×C11—22no—
154C4×C11C22×D411yescharacteristic
155C4×C11C22×D411yescharacteristic
156Dic11—22no—
157Dic11—21no—
158H(5,𝔽2)—112no—
159H(5,𝔽2)C2×D1112yescomplemented
160AGL(1,ℤ/8)—22no—
161AGL(1,ℤ/8)—112no—
162AGL(1,ℤ/8)—112no—
163AGL(1,ℤ/8)—112no—
164AGL(1,ℤ/8)—222no—
165AGL(1,ℤ/8)—222no—
166AGL(1,ℤ/8)—222no—
167AGL(1,ℤ/8)C2×D1112yescomplemented
168#135—21no—
169#135—111no—
170#135—222no—
171#135—221no—
172#135C2×D1111yescharacteristic
173C2×D8—21no—
174C2×D8—112no—
175C2×D8—111no—
176C2×D8—222no—
177C2×D8—221no—
178C2×D8C2×D1111yescharacteristic, complemented
179#131—112no—
180#131—111no—
181#131C2×D1111yescharacteristic, complemented
182#127—112no—
183#108—111no—
184#108—111no—
185#104—111no—
186#104—112no—
187#104—111no—
188#100—112no—
189#100—112no—
190C4×C8—111no—
191C2×C11—21no—
192C2×C11—42no—
193C2×C11—41no—
194C2×C11—82no—
195C2×C11D4211yescharacteristic
196D11—41no—
197D11—82no—
198#41—22no—
199#41—22no—
200#41—111no—
201#41—222no—
202#41—222no—
203#41C22×D1111yescharacteristic
204#41C22×D1112yes—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—42no—
208C2×D4—112no—
209C2×D4—222no—
210C2×D4—222no—
211C2×D4—442no—
212C2×D4—442no—
213C2×D4C22×D1112yes—
214Q16—111no—
215Q16C22⋊D1111yescharacteristic, complemented
216SD16—22no—
217SD16—111no—
218SD16—111no—
219SD16—222no—
220SD16—222no—
221SD16—222no—
222SD16C22⋊D1112yescomplemented
223D8—22no—
224D8—21no—
225D8—21no—
226D8—111no—
227D8—222no—
228D8—222no—
229D8—222no—
230D8—222no—
231D8—222no—
232D8—221no—
233D8—221no—
234D8C22⋊D1111yescharacteristic, complemented
235M16—21no—
236M16—112no—
237M16—111no—
238M16—222no—
239M16—221no—
240M16C22×D1111yescharacteristic
241C2×C8—21no—
242C2×C8—111no—
243C2×C8—222no—
244C2×C8—221no—
245C2×C8C22×D1111yescharacteristic
246C42—111no—
247C11#329211yescharacteristic, complemented, Sylow
248C23—22no—
249C23—42no—
250C23—222no—
251C23—442no—
252Q8—111no—
253Q8D4×D1111yescharacteristic
254Q8C2×C22⋊D1112yes—
255D4—21no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—111no—
262D4—221no—
263D4—222no—
264D4—222no—
265D4—442no—
266D4—442no—
267D4—884no—
268D4D4×D1111yescharacteristic
269D4C2×C22⋊D1112yes—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—442no—
276C2×C4C23×D1111yescharacteristic
277C8—21no—
278C8—111no—
279C8—111no—
280C8—222no—
281C8—221no—
282C8C2×C22⋊D1111yescharacteristic
283C8C2×C22⋊D1111yescharacteristic
284C22—21no—
285C22—22no—
286C22—42no—
287C22—82no—
288C22—162no—
289C22—221no—
290C22—442no—
291C22—882no—
292C22—1762no—
293C22#6703711yescharacteristic
294C4—21no—
295C4—22no—
296C4—222no—
297C4—221no—
298C4C2×D4×D1111yescharacteristic
299C4C22×C22⋊D1111yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—82no—
304C2—441no—
305C2—882no—
306C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#576C2
socleC2×C11D42
hypercenter#576D11
hypocenterC11#3292
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. C11×#576C2semidirect
2. #10623366C2semidirect
3. #10623300C2semidirect
4. #10622854C2semidirect
5. #10622812C2semidirect
6. #10622811C2semidirect
7. #10622809C2semidirect
8. #10622773C2semidirect
9. #10622764C2semidirect
10. #10622757C2semidirect
11. #10622755C2semidirect
12. C11×H(5,𝔽2)C22semidirect
13. #67042C22semidirect
15. C11×AGL(1,ℤ/8)C22semidirect
19. C2×C11×D8C22semidirect
20. C11×#131C22semidirect
24. #67002C22semidirect
25. #67002C22semidirect
26. #67001C22semidirect
27. #66993C22semidirect
29. #66985C22semidirect
31. C2×#4323C22semidirect
35. C2×D88C22semidirect
36. #66954C22semidirect
37. #66901C22semidirect
38. #66901C22semidirect
39. #66897C22semidirect
40. #66889C22semidirect
41. #66887C22semidirect
42. #66886C22semidirect
43. #66883C22semidirect
44. C8×Dic11C22semidirect
61. C11×Q16D4semidirect
63. C11×SD16D4semidirect
67. C11×D8D4semidirect
72. #4326D4semidirect
75. #4325D4semidirect
77. #4324D4semidirect
83. #4323D4semidirect
133. #576D11semidirect
159. H(5,𝔽2)C2×D11semidirect
167. AGL(1,ℤ/8)C2×D11semidirect
178. C2×D8C2×D11semidirect
181. #131C2×D11semidirect
215. Q16C22⋊D11semidirect
222. SD16C22⋊D11semidirect
234. D8C22⋊D11semidirect
247. C11#3292semidirect

Maximal subgroups

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

subgroupindex
C11×#5762
#106233662
#106233002
#106228542
#106228122
#106228112
#106228092
#106227732
#106227642
#106227572
#106227552
#329211