Finite Group Databasebeta

← #14910567

Subgroups — #14910567

Order 2816.

668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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
1#13081753C212yesmaximal, complemented
2#13080415C212yesmaximal, complemented
3#13070733C212yesmaximal, complemented
4#13070689C212yesmaximal, complemented
5#13070572C214yesmaximal, complemented
6#13070498C211yesmaximal, characteristic, complemented
7#13070454C211yesmaximal, characteristic, complemented
8C11×#2246C211yesmaximal, characteristic, complemented
9#10623288—22no—
10#10623288C2214yescomplemented
11C2×C11×D16C2212yescomplemented
12C2×C11×D16C2212yescomplemented
13C11×#493C2212yescomplemented
14#10622773—22no—
15#10622773C2214yescomplemented
16#10622760C2214yescomplemented
17#10622690—24no—
18#10622525—22no—
19#10622524—24no—
20D11×D16—22no—
21#10622517C2211yescharacteristic
22#10622514C2212yescomplemented
23#10622313C2211yescharacteristic
24#10622313C2212yescomplemented
25C4×C11×C16C2211yescharacteristic, complemented
26#10622201C2214yescomplemented
27#10622148C2212yescomplemented
28#10622146C2212yescomplemented
29#10622144C2211yescharacteristic, complemented
30#10622101C2211yescharacteristic, complemented
31#67037—24no—
32C2×C11×D8—22no—
33C2×C11×D8C2314yes—
34C11×#127—22no—
35#66985—24no—
36#66985—24no—
37#66965—24no—
38#66965—42no—
39#66964—44no—
40#66964—44no—
41D8×D11—24no—
42D8×D11—42no—
43#66957D411yescharacteristic
44#66957C2312yes—
45#66954—22no—
46#66954C2312yes—
47C11×D16—22no—
48C11×D16—22no—
49C11×D16—42no—
50C2×C11×C16C2311yescharacteristic
51C2×C11×C16C2311yescharacteristic
52C4×C8×C11C2311yescharacteristic
53#66897—24no—
54#66891—24no—
55#66890—24no—
56#66883D411yescharacteristic
57#66883C2312yes—
58#66876C2312yes—
59#66869—22no—
60#66869D412yes—
61Dic88D411yescharacteristic, complemented
62#66864D412yescomplemented
63D176D411yescharacteristic, complemented
64#66862—22no—
65C16×D11—22no—
66#33858—111nomaximal, Sylow
67C2×D4×C11—24no—
68C2×D4×C11—82no—
69C2×C22⋊D11—84no—
70#4341—44no—
71#4341—44no—
72D4×D11—44no—
73D4×D11—44no—
74#4339—22no—
75#4339C2×D412yes—
76C11×D8—24no—
77C11×D8—24no—
78C11×D8—42no—
79C11×D8—42no—
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11C2411yescharacteristic
82C42×C11C2×D411yescharacteristic
83#4324—44no—
84#4324—44no—
85#4323—44no—
86#4323—44no—
87#4318—22no—
88#4318C2×D412yes—
89Dic44D811yescharacteristic
90Dic44C2×D412yes—
91D88D811yescharacteristic
92D88C2×D412yes—
93#4314—22no—
94#4314D812yes—
95#4313—22no—
96#4313—42no—
97C8×D11—22no—
98C8×D11—42no—
99C11×C16—21no—
100C11×C16C2×D411yescharacteristic
101C11×C16C2×D411yescharacteristic
102C11⋊C16—22no—
103#3415—112no—
104#3292—112no—
105#2246D1111yescharacteristic, complemented
106#2221—112no—
107#2213—112no—
108#2192—114no—
109#2178—111no—
110#2170—111no—
111C23×C11—44no—
112C22×D11—84no—
113D4×C11—44no—
114D4×C11—44no—
115D4×C11—164no—
116C2×C4×C11—21no—
117C2×C4×C11C22×D411yescharacteristic
118C22⋊D11—22no—
119C22⋊D11—42no—
120C22⋊D11—84no—
121C22⋊D11—84no—
122C2×Dic11—84no—
123D44—22no—
124D44C2×D812yes—
125C4×D11—22no—
126C4×D11—42no—
127Dic22—22no—
128Dic22C2×D812yes—
129C8×C11C2×D811yescharacteristic
130C8×C11C2×D811yescharacteristic
131C8×C11C22×D411yescharacteristic
132C8×C11H(5,𝔽2)11yescharacteristic
133C11⋊C8—22no—
134C11⋊C8—42no—
135#576—114no—
136#576—222no—
137#509—114no—
138#509—224no—
139#508—111no—
140#508—222no—
141C2×D16—222no—
142C2×D16C2×D1112yescomplemented
143C2×D16C2×D1112yescomplemented
144#504—112no—
145#493C2×D1112yescomplemented
146#472—114no—
147#472—222no—
148#453—224no—
149#443—111no—
150#443—112no—
151#368—111no—
152#364—111no—
153#361—114no—
154#359—112no—
155#350—112no—
156C4×C16C2×D1111yescharacteristic, complemented
157C22×C11—84no—
158C22×C11—164no—
159C22×C11#57611yescharacteristic
160C2×D11—22no—
161C2×D11—42no—
162C2×D11—324no—
163C4×C11—22no—
164C4×C11D4211yescharacteristic
165C4×C11C22×D811yescharacteristic
166Dic11—22no—
167Dic11—42no—
168H(5,𝔽2)—224no—
169AGL(1,ℤ/8)—224no—
170AGL(1,ℤ/8)—224no—
171AGL(1,ℤ/8)—444no—
172AGL(1,ℤ/8)—444no—
173#135—111no—
174#135—112no—
175#135—224no—
176#135—442no—
177C2×D8—22no—
178C2×D8—224no—
179C2×D8—442no—
180C2×D8C22×D1114yes—
181#131—112no—
182#131—222no—
183#127—22no—
184Q32—111no—
185SD32—112no—
186SD32—224no—
187D16—22no—
188D16—22no—
189D16—42no—
190D16—111no—
191D16—224no—
192M32—112no—
193M32—222no—
194C2×C16—222no—
195C2×C16C22×D1111yescharacteristic
196C2×C16C22×D1111yescharacteristic
197#108—111no—
198#108—112no—
199#104—112no—
200#104—222no—
201#100—224no—
202C4×C8C22×D1111yescharacteristic
203C2×C11—21no—
204C2×C11—164no—
205C2×C11D4×D811yescharacteristic
206D11—42no—
207D11—82no—
208#41—112no—
209#41—222no—
210#41—444no—
211#41—444no—
212C2×D4—24no—
213C2×D4—82no—
214C2×D4—444no—
215C2×D4—444no—
216C2×D4—884no—
217Q16—111no—
218Q16—112no—
219SD16—112no—
220SD16—222no—
221SD16—444no—
222SD16—444no—
223D8—24no—
224D8—24no—
225D8—42no—
226D8—42no—
227D8—111no—
228D8—112no—
229D8—444no—
230D8—444no—
231M16—112no—
232M16—222no—
233M16—222no—
234M16—442no—
235C2×C8—222no—
236C2×C8—442no—
237C2×C8D4×D1111yescharacteristic
238C2×C8C23×D1111yescharacteristic
239C42D4×D1111yescharacteristic
240C16—21no—
241C16—222no—
242C16D4×D1111yescharacteristic
243C16D4×D1111yescharacteristic
244C11#3385811yescharacteristic, complemented, Sylow
245C23—44no—
246C23—884no—
247Q8—112no—
248Q8—222no—
249D4—44no—
250D4—44no—
251D4—112no—
252D4—164no—
253D4—222no—
254D4—222no—
255D4—442no—
256D4—884no—
257D4—884no—
258C2×C4—21no—
259C2×C4—222no—
260C2×C4—442no—
261C2×C4—884no—
262C2×C4C2×D4×D1111yescharacteristic
263C8—222no—
264C8—442no—
265C8D8×D1111yescharacteristic
266C8D8×D1111yescharacteristic
267C8C2×D4×D1111yescharacteristic
268C8#6703711yescharacteristic
269C22—84no—
270C22—164no—
271C22—222no—
272C22—442no—
273C22—3524no—
274C22#1062328811yescharacteristic
275C4—22no—
276C4—222no—
277C4—442no—
278C4#1062324811yescharacteristic
279C4C2×D8×D1111yescharacteristic
280C2—21no—
281C2—164no—
282C2—442no—
283C2—882no—
284C2#1308029111yescharacteristic
subgroupG/H
centerC2#13080291
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2246C2
socleC2×C11D4×D8
hypercenter#2246D11
hypocenterC11#33858
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #13081753C2semidirect
2. #13080415C2semidirect
3. #13070733C2semidirect
4. #13070689C2semidirect
5. #13070572C2semidirect
6. #13070498C2semidirect
7. #13070454C2semidirect
8. C11×#2246C2semidirect
10. #10623288C22semidirect
11. C2×C11×D16C22semidirect
12. C2×C11×D16C22semidirect
13. C11×#493C22semidirect
15. #10622773C22semidirect
16. #10622760C22semidirect
22. #10622514C22semidirect
24. #10622313C22semidirect
25. C4×C11×C16C22semidirect
26. #10622201C22semidirect
27. #10622148C22semidirect
28. #10622146C22semidirect
29. #10622144C22semidirect
30. #10622101C22semidirect
61. Dic88D4semidirect
62. #66864D4semidirect
63. D176D4semidirect
105. #2246D11semidirect
142. C2×D16C2×D11semidirect
143. C2×D16C2×D11semidirect
145. #493C2×D11semidirect
156. C4×C16C2×D11semidirect
244. C11#33858semidirect

Maximal subgroups

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

subgroupindex
#130817532
#130804152
#130707332
#130706892
#130705722
#130704982
#130704542
C11×#22462
#3385811