Finite Group Databasebeta

← #14909047

Subgroups — #14909047

Order 2816.

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

normal subgroups only

This group has 512 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#13077520C211yesmaximal, characteristic
2#13070833C212yesmaximal, complemented
3#13070789C212yesmaximal, complemented
4#13070694C212yesmaximal, complemented
5#13070566C212yesmaximal
6#13070505C214yesmaximal, complemented
7#13070432C211yesmaximal, characteristic, complemented
8C11×#3177C211yesmaximal, characteristic, complemented
9C11×#541—21no—
10#10623279C2211yescharacteristic
11C2×#66954—21no—
12C11×#499C2211yescharacteristic, complemented
13C11×#494C2211yescharacteristic, complemented
14C11×#491—21no—
15C11×#470C2212yes—
16C11×#467—21no—
17C11×#441C2212yescomplemented
18C4×C11×Q16—21no—
19C11×#405C2211yescharacteristic
20#10622792C2214yes—
21#10622738C2211yescharacteristic
22#10622618—21no—
23#10622330—21no—
24#10622330C2212yes—
25#10622313—21no—
26#10622313C2212yes—
27#10622203C2214yescomplemented
28#10622191C2212yes—
29#10622126C2214yes—
30#10622125C2214yescomplemented
31#10622104C2212yescomplemented
32#10622101C2212yescomplemented
33C2×#4339—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16C2312yes—
36C2×C11×M16C2311yescharacteristic
37C22×C8×C11D411yescharacteristic
38C11×C4⋊Q8—21no—
39C11×#126—42no—
40C11×#125—21no—
41C11×#125—42no—
42C11×C22⋊Q8—22no—
43C4×Q8×C11—22no—
44C11×#117D411yescharacteristic
45C2×#4318—21no—
46#66962—22no—
47#66961—22no—
48#66957—21no—
49#66957C2312yes—
50#66954—22no—
51#66954—22no—
52#66954—41no—
53#66954—41no—
54C2×#4313—41no—
55C2×C8×D11—41no—
56C11×#107—21no—
57C11×#106C2312yes—
58C11×#103—22no—
59C11×#103—22no—
60C11×#97D411yescharacteristic
61C11×#97C2311yescharacteristic
62C4×C8×C11D411yescharacteristic
63C4×C8×C11C2311yescharacteristic
64#66893—24no—
65#66892—24no—
66#66883—21no—
67#66883C2312yes—
68#66876C2314yes—
69#66869—22no—
70#66869—22no—
71#33693—111nomaximal, Sylow
72C2×Q8×C11—22no—
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—
82C11×Q16—24no—
83C11×Q16—41no—
84C11×Q16—41no—
85C11×M16—22no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—21no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—42no—
98C11×C22⋊C4—21no—
99C11×C22⋊C4—42no—
100C42×C11—42no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103#4318—22no—
104#4318—41no—
105C2×C11⋊C8—41no—
106Dic44—21no—
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#3177D1111yescharacteristic, complemented
118#2955—111no—
119#2239—112no—
120#2231—112no—
121#2214—112no—
122#2191—112no—
123#2180—114no—
124#2166—111no—
125C23×C11AGL(1,ℤ/8)11yescharacteristic
126C22×D11—41no—
127Q8×C11—42no—
128Q8×C11—42no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11C22×D411yescharacteristic
137C22⋊D11—42no—
138C22⋊D11—42no—
139C2×Dic11—41no—
140D44—22no—
141D44—41no—
142C4×D11—42no—
143C4×D11—42no—
144Dic22—22no—
145Dic22—41no—
146C8×C11—21no—
147C8×C11—21no—
148C8×C11AGL(1,ℤ/8)11yescharacteristic
149C8×C11AGL(1,ℤ/8)11yescharacteristic
150C8×C11C2×#4112yes—
151C11⋊C8—42no—
152#575—111no—
153C2×#131—221no—
154#541—21no—
155#510—114no—
156#499C2×D1111yescharacteristic, complemented
157#494C2×D1111yescharacteristic, complemented
158#491—21no—
159#470C2×D1112yes—
160#467—21no—
161#444—112no—
162#444—221no—
163#443—112no—
164#443—221no—
165#441C2×D1112yescomplemented
166C4×Q16—21no—
167#430—111no—
168#421—221no—
169#405C2×D1111yescharacteristic
170#365—114no—
171#364—112no—
172#362—114no—
173#360—114no—
174#349—112no—
175#347—112no—
176C22×C11—21no—
177C22×C11—41no—
178C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
179C2×D11—42no—
180C2×D11—82no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—82no—
185C4×C11—82no—
186C4×C11#52511yescharacteristic
187C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
188Dic11—42no—
189C2×#41—221no—
190#137—222no—
191AGL(1,ℤ/8)—222no—
192#135—112no—
193#135—221no—
194C2×Q16—21no—
195C2×Q16C22×D1112yes—
196#131—222no—
197#131—222no—
198#131—441no—
199#131—441no—
200C2×M16—221no—
201C2×M16—441no—
202C2×M16C22×D1111yescharacteristic
203C22×C8—441no—
204C22×C8C22⋊D1111yescharacteristic
205C4⋊Q8—21no—
206#126—42no—
207#125—21no—
208#125—42no—
209C22⋊Q8—22no—
210C4×Q8—22no—
211#117C22⋊D1111yescharacteristic
212Q32—224no—
213SD32—224no—
214M32—114no—
215#108—112no—
216#108—221no—
217#107—21no—
218#106C22×D1112yes—
219#104—222no—
220#104—222no—
221#103—22no—
222#103—22no—
223#97C22⋊D1111yescharacteristic
224#97C22×D1111yescharacteristic
225C4×C8C22⋊D1111yescharacteristic
226C4×C8C22×D1111yescharacteristic
227C2×C11—21no—
228C2×C11—41no—
229C2×C11#310911yescharacteristic
230D11—82no—
231#41—222no—
232#41—222no—
233#41—441no—
234#41—441no—
235C2×Q8—22no—
236C2×Q8—221no—
237C2×D4—221no—
238C2×D4—441no—
239C22×C4—441no—
240C22×C4C2×C22⋊D1111yescharacteristic
241Q16—24no—
242Q16—41no—
243Q16—41no—
244Q16—112no—
245Q16—221no—
246SD16—222no—
247SD16—222no—
248D8—112no—
249D8—221no—
250M16—22no—
251M16—222no—
252M16—442no—
253M16—441no—
254M16—442no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—442no—
258C2×C8—441no—
259C2×C8—442no—
260C2×C8C2×C22⋊D1111yescharacteristic
261C2×C8C2×C22⋊D1111yescharacteristic
262C2×C8C2×C22⋊D1111yescharacteristic
263C2×C8C23×D1111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C22⋊C4—21no—
271C22⋊C4—42no—
272C42—42no—
273C42C2×C22⋊D1111yescharacteristic
274C42C2×C22⋊D1111yescharacteristic
275C16—224no—
276C11#3369311yescharacteristic, complemented, Sylow
277C23—441no—
278C23#6698511yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—222no—
282Q8—441no—
283D4—222no—
284D4—441no—
285D4—442no—
286D4—442no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—442no—
294C2×C4—441no—
295C2×C4—442no—
296C2×C4#6698511yescharacteristic
297C2×C4C22×C22⋊D1111yescharacteristic
298C8—21no—
299C8—21no—
300C8—442no—
301C8#6700211yescharacteristic
302C8#6700211yescharacteristic
303C8#41×D1112yes—
304C22—21no—
305C22—41no—
306C22—442no—
307C22—882no—
308C22C2×#6698511yescharacteristic
309C4—21no—
310C4—41no—
311C4—41no—
312C4—82no—
313C4—82no—
314C4—442no—
315C4C2×#6700211yescharacteristic
316C4#1062335911yescharacteristic
317C2—21no—
318C2—41no—
319C2—882no—
320C2#1307870311yescharacteristic
subgroupG/H
centerC2#13078703
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3177C2
socleC2×C11#3109
prime radical#10623279C22
hypercenter#3177D11
hypocenterC11#33693
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #3177

Complements

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

NH ≅ G/Ntype
2. #13070833C2semidirect
3. #13070789C2semidirect
4. #13070694C2semidirect
6. #13070505C2semidirect
7. #13070432C2semidirect
8. C11×#3177C2semidirect
12. C11×#499C22semidirect
13. C11×#494C22semidirect
17. C11×#441C22semidirect
27. #10622203C22semidirect
30. #10622125C22semidirect
31. #10622104C22semidirect
32. #10622101C22semidirect
117. #3177D11semidirect
156. #499C2×D11semidirect
157. #494C2×D11semidirect
165. #441C2×D11semidirect
276. C11#33693semidirect

Maximal subgroups

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

subgroupindex
#130775202
#130708332
#130707892
#130706942
#130705662
#130705052
#130704322
C11×#31772
#3369311