Finite Group Databasebeta

← #14909009

Subgroups — #14909009

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#13077527C211yesmaximal, characteristic
2#13070833C212yesmaximal, complemented
3#13070784C212yesmaximal, complemented
4#13070694C212yesmaximal, complemented
5#13070566C212yesmaximal
6#13070505C214yesmaximal, complemented
7#13070428C211yesmaximal, characteristic, complemented
8C11×#3185C211yesmaximal, characteristic, complemented
9C11×#533—21no—
10#10623279C2211yescharacteristic
11#10623276—21no—
12C11×#498C2211yescharacteristic, complemented
13C11×#494C2211yescharacteristic, complemented
14C11×#487—21no—
15C11×#470—21no—
16C11×#470C2212yes—
17C11×#441—21no—
18C11×#441C2212yescomplemented
19C4×C11×M16C2211yescharacteristic
20#10622792C2214yes—
21#10622738C2211yescharacteristic
22C2×#66869—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×M16D411yescharacteristic
37C2×C11×M16C2311yescharacteristic
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×#125—41no—
41C11×C22⋊Q8—22no—
42C11×C22⋊Q8—41no—
43C4×Q8×C11—22no—
44C4×Q8×C11—41no—
45C11×#117—41no—
46C2×C42×C11D411yescharacteristic
47C2×#4318—21no—
48#66962—22no—
49#66961—22no—
50#66960—42no—
51M16×D11—42no—
52#66957—21no—
53#66957C2312yes—
54#66954—22no—
55#66954—22no—
56C11×#106—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#33689—111nomaximal, Sylow
72C2×Q8×C11—22no—
73C2×Q8×C11—41no—
74C22×C4×C11—21no—
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—41no—
77#4339—22no—
78#4339—22no—
79#4339—41no—
80#4339—41no—
81C2×D44—21no—
82C2×C4×D11—41no—
83C2×Dic22—21no—
84C11×Q16—24no—
85C11×Q16—42no—
86C11×M16—22no—
87C11×M16—22no—
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—42no—
98C11×C22⋊C4—42no—
99C42×C11—21no—
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#3185D1111yescharacteristic, complemented
118#2956—111no—
119#2239—112no—
120#2230—112no—
121#2214—112no—
122#2191—112no—
123#2180—114no—
124#2165—111no—
125C23×C11AGL(1,ℤ/8)11yescharacteristic
126C22×D11—41no—
127Q8×C11—42no—
128Q8×C11—42no—
129Q8×C11—82no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C22⋊D11—42no—
140C22⋊D11—42no—
141C2×Dic11—41no—
142D44—22no—
143D44—41no—
144C4×D11—42no—
145C4×D11—42no—
146Dic22—22no—
147Dic22—41no—
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—21no—
156#510—114no—
157#498C2×D1111yescharacteristic, complemented
158#494C2×D1111yescharacteristic, complemented
159#487—21no—
160#470—21no—
161#470C2×D1112yes—
162#444—112no—
163#444—221no—
164#443—112no—
165#443—221no—
166#441—21no—
167#441C2×D1112yescomplemented
168#430—111no—
169C2×#104—221no—
170C4×M16C2×D1111yescharacteristic
171#365—114no—
172#364—112no—
173#362—114no—
174#360—114no—
175#349—112no—
176#347—112no—
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—82no—
186C4×C11—82no—
187C4×C11#52511yescharacteristic
188C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
189Dic11—42no—
190C2×#41—221no—
191#137—222no—
192AGL(1,ℤ/8)—222no—
193#135—112no—
194#135—221no—
195C2×Q16—21no—
196C2×Q16C22×D1112yes—
197#131—222no—
198#131—222no—
199#131—442no—
200C2×M16—221no—
201C2×M16—442no—
202C2×M16C22⋊D1111yescharacteristic
203C2×M16C22×D1111yescharacteristic
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206#125—41no—
207C22⋊Q8—22no—
208C22⋊Q8—41no—
209C4×Q8—22no—
210C4×Q8—41no—
211#117—41no—
212C2×C42C22⋊D1111yescharacteristic
213Q32—224no—
214SD32—224no—
215M32—114no—
216#108—112no—
217#108—221no—
218#106—21no—
219#106C22×D1112yes—
220#104—222no—
221#104—222no—
222#103—22no—
223#103—22no—
224#97C22⋊D1111yescharacteristic
225#97C22×D1111yescharacteristic
226C4×C8C22⋊D1111yescharacteristic
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—22no—
237C2×Q8—41no—
238C2×Q8—221no—
239C2×D4—221no—
240C2×D4—441no—
241C22×C4—21no—
242C22×C4—441no—
243C22×C4C2×C22⋊D1111yescharacteristic
244Q16—24no—
245Q16—42no—
246Q16—112no—
247Q16—221no—
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×C22⋊D1111yescharacteristic
262C2×C8C2×C22⋊D1111yescharacteristic
263C2×C8C2×C22⋊D1111yescharacteristic
264C2×C8C23×D1111yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C22⋊C4—42no—
272C42—21no—
273C42—42no—
274C42C2×C22⋊D1111yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C16—224no—
277C11#3368911yescharacteristic, complemented, Sylow
278C23—441no—
279C23#6698511yescharacteristic
280Q8—42no—
281Q8—42no—
282Q8—82no—
283Q8—222no—
284Q8—441no—
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—42no—
295C2×C4—42no—
296C2×C4—442no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4#6698511yescharacteristic
300C2×C4C22×C22⋊D1111yescharacteristic
301C8—21no—
302C8—21no—
303C8—442no—
304C8#6700212yes—
305C8#41×D1112yes—
306C22—21no—
307C22—41no—
308C22—442no—
309C22—1761no—
310C22C2×#6698511yescharacteristic
311C4—22no—
312C4—21no—
313C4—41no—
314C4—82no—
315C4—82no—
316C4—442no—
317C4C2×#6700211yescharacteristic
318C4#1062335911yescharacteristic
319C2—21no—
320C2—41no—
321C2—882no—
322C2#1307870311yescharacteristic
subgroupG/H
centerC2#13078703
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3185C2
socleC2×C11#3109
prime radical#10623279C22
hypercenter#3185D11
hypocenterC11#33689
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3185

Complements

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

NH ≅ G/Ntype
2. #13070833C2semidirect
3. #13070784C2semidirect
4. #13070694C2semidirect
6. #13070505C2semidirect
7. #13070428C2semidirect
8. C11×#3185C2semidirect
12. C11×#498C22semidirect
13. C11×#494C22semidirect
18. C11×#441C22semidirect
27. #10622203C22semidirect
30. #10622125C22semidirect
31. #10622104C22semidirect
32. #10622101C22semidirect
117. #3185D11semidirect
157. #498C2×D11semidirect
158. #494C2×D11semidirect
167. #441C2×D11semidirect
277. C11#33689semidirect

Maximal subgroups

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

subgroupindex
#130775272
#130708332
#130707842
#130706942
#130705662
#130705052
#130704282
C11×#31852
#3368911