Finite Group Databasebeta

← #14909014

Subgroups — #14909014

Order 2816.

520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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#13079361C211yesmaximal, characteristic, complemented
2#13077527C211yesmaximal, characteristic
3#13070836C212yesmaximal, complemented
4#13070788C212yesmaximal, complemented
5#13070698C212yesmaximal, complemented
6#13070569C212yesmaximal
7#13070509C214yesmaximal, complemented
8C11×#2165C211yesmaximal, characteristic, complemented
9#10623279C2211yescharacteristic
10#10623276—21no—
11#10623001—21no—
12C4×C11×M16C2211yescharacteristic
13#10622750—21no—
14#10622750C2212yes—
15#10622738C2211yescharacteristic
16C2×#66869—21no—
17#10622522C2214yes—
18#10622330—21no—
19#10622330C2212yes—
20#10622329—21no—
21#10622329C2212yescomplemented
22#10622313—21no—
23#10622313C2212yes—
24#10622312C2211yescharacteristic, complemented
25#10622294—21no—
26#10622293C2211yescharacteristic, complemented
27C11×#364C2212yescomplemented
28C11×#349C2212yes—
29C11×#347C2212yescomplemented
30#10622156C2214yes—
31#10622155C2214yescomplemented
32#10622151C2214yescomplemented
33C2×#4339—21no—
34C2×C11×M16D411yescharacteristic
35C2×C11×M16C2311yescharacteristic
36C2×C42×C11D411yescharacteristic
37#66979—41no—
38#66977—22no—
39#66977—41no—
40C2×#4318—21no—
41#66962—22no—
42#66961—22no—
43#66960—42no—
44M16×D11—42no—
45C2×Dic44—21no—
46C2×Dic44C2312yes—
47#66957—21no—
48#66957C2312yes—
49#66954—22no—
50#66954—22no—
51#66923—41no—
52#66922—21no—
53#66922—21no—
54C4×Dic22—22no—
55C4×Dic22—41no—
56C11×M32C2314yes—
57C11×#97D411yescharacteristic
58C11×#97C2311yescharacteristic
59C4×C8×C11D411yescharacteristic
60C4×C8×C11C2311yescharacteristic
61#66883—21no—
62#66883C2312yes—
63#66881—21no—
64#66881C2312yes—
65#66880—22no—
66#66880—22no—
67#66869—22no—
68#66869—22no—
69Dic88—24no—
70#66864—24no—
71#33689—111nomaximal, Sylow
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—41no—
75#4339—22no—
76#4339—22no—
77#4339—41no—
78#4339—41no—
79C2×D44—21no—
80C2×C4×D11—41no—
81C2×Dic22—21no—
82C2×Dic22—22no—
83C2×Dic22—41no—
84C11×M16—22no—
85C11×M16—22no—
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2411yescharacteristic
90C42×C11—21no—
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C22⋊Dic11—42no—
94C4⋊Dic11—22no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98Dic11⋊C4—42no—
99Dic11⋊C4—42no—
100C4×Dic11—42no—
101#4318—22no—
102#4318—41no—
103C2×C11⋊C8—41no—
104Dic44—21no—
105Dic44—24no—
106Dic44—42no—
107Dic44#4112yes—
108D88—21no—
109D88#4112yes—
110#4314—22no—
111#4314—22no—
112#4313—42no—
113#4313—42no—
114C8×D11—42no—
115C8×D11—42no—
116C11×C16—24no—
117#3185—111no—
118#2956—111no—
119#2239—112no—
120#2230—112no—
121#2214—112no—
122#2191—112no—
123#2180—114no—
124#2165D1111yescharacteristic, complemented
125C23×C11AGL(1,ℤ/8)11yescharacteristic
126C22×D11—41no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11C22×D411yescharacteristic
134C22⋊D11—42no—
135C22⋊D11—42no—
136C2×Dic11—41no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139D44—22no—
140D44—41no—
141C4×D11—42no—
142C4×D11—42no—
143Dic22—22no—
144Dic22—41no—
145Dic22—42no—
146Dic22—42no—
147Dic22—82no—
148C8×C11—21no—
149C8×C11—21no—
150C8×C11AGL(1,ℤ/8)12yes—
151C8×C11C2×#4112yes—
152C11⋊C8—42no—
153#575—111no—
154#568—221no—
155#533—221no—
156#510—114no—
157#498—111no—
158#494—111no—
159#487—221no—
160#470—112no—
161#470—221no—
162#444—112no—
163#444—221no—
164#443—112no—
165#443—221no—
166#441—112no—
167#441—221no—
168#430—111no—
169C2×#104—221no—
170C4×M16C2×D1111yescharacteristic
171#365—114no—
172#364C2×D1112yescomplemented
173#362—114no—
174#360—114no—
175#349C2×D1112yes—
176#347C2×D1112yescomplemented
177C22×C11—21no—
178C22×C11—41no—
179C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
180C2×D11—42no—
181C2×D11—161no—
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—41no—
185C4×C11#52511yescharacteristic
186C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
187Dic11—42no—
188Dic11—82no—
189Dic11—82no—
190C2×#41—221no—
191#137—222no—
192AGL(1,ℤ/8)—222no—
193#135—112no—
194#135—221no—
195C2×Q16—112no—
196C2×Q16—221no—
197#131—222no—
198#131—222no—
199#131—442no—
200C2×M16—221no—
201C2×M16—442no—
202C2×M16D4411yescharacteristic
203C2×M16C22×D1111yescharacteristic
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206#125—441no—
207C22⋊Q8—222no—
208C22⋊Q8—441no—
209C4×Q8—222no—
210C4×Q8—441no—
211#117—441no—
212C2×C42D4411yescharacteristic
213Q32—224no—
214SD32—224no—
215M32C22×D1114yes—
216#108—112no—
217#108—221no—
218#106—112no—
219#106—221no—
220#104—222no—
221#104—222no—
222#103—222no—
223#103—222no—
224#97D4411yescharacteristic
225#97C22×D1111yescharacteristic
226C4×C8D4411yescharacteristic
227C4×C8C22×D1111yescharacteristic
228C2×C11—21no—
229C2×C11—41no—
230C2×C11#310911yescharacteristic
231D11—82no—
232#41—222no—
233#41—222no—
234#41—441no—
235#41—441no—
236C2×Q8—221no—
237C2×Q8—222no—
238C2×Q8—441no—
239C2×D4—221no—
240C2×D4—441no—
241C22×C4—21no—
242C22×C4—441no—
243C22×C4C2×D4411yescharacteristic
244Q16—112no—
245Q16—221no—
246Q16—224no—
247Q16—442no—
248SD16—222no—
249SD16—222no—
250D8—112no—
251D8—221no—
252M16—22no—
253M16—22no—
254M16—222no—
255M16—442no—
256M16—441no—
257M16—442no—
258C2×C8—442no—
259C2×C8—441no—
260C2×C8—442no—
261C2×C8C2×D4411yescharacteristic
262C2×C8C2×D4411yescharacteristic
263C2×C8C2×D4411yescharacteristic
264C2×C8C23×D1111yescharacteristic
265C4⋊C4—222no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4—442no—
271C22⋊C4—442no—
272C42—21no—
273C42—442no—
274C42C2×D4411yescharacteristic
275C42C2×D4411yescharacteristic
276C16—24no—
277C11#3368911yescharacteristic, complemented, Sylow
278C23—441no—
279C23#6696111yescharacteristic
280Q8—222no—
281Q8—441no—
282Q8—442no—
283Q8—442no—
284Q8—882no—
285D4—222no—
286D4—441no—
287D4—442no—
288D4—442no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—442no—
295C2×C4—441no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4#6696111yescharacteristic
300C2×C4C22×D4411yescharacteristic
301C8—21no—
302C8—21no—
303C8—442no—
304C8#6696112yes—
305C8#41×D1112yes—
306C22—21no—
307C22—41no—
308C22—442no—
309C22—1761no—
310C22C2×#6696111yescharacteristic
311C4—22no—
312C4—21no—
313C4—41no—
314C4—442no—
315C4—882no—
316C4—882no—
317C4#1062305511yescharacteristic
318C4C2×#6696111yescharacteristic
319C2—21no—
320C2—41no—
321C2—882no—
322C2#1307870811yescharacteristic
subgroupG/H
centerC2#13078708
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2165C2
socleC2×C11#3109
prime radical#10623279C22
hypercenter#2165D11
hypocenterC11#33689
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
1. #13079361C2semidirect
3. #13070836C2semidirect
4. #13070788C2semidirect
5. #13070698C2semidirect
7. #13070509C2semidirect
8. C11×#2165C2semidirect
21. #10622329C22semidirect
24. #10622312C22semidirect
26. #10622293C22semidirect
27. C11×#364C22semidirect
29. C11×#347C22semidirect
31. #10622155C22semidirect
32. #10622151C22semidirect
124. #2165D11semidirect
172. #364C2×D11semidirect
176. #347C2×D11semidirect
277. C11#33689semidirect

Maximal subgroups

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

subgroupindex
#130793612
#130775272
#130708362
#130707882
#130706982
#130705692
#130705092
C11×#21652
#3368911