Finite Group Databasebeta

← #14909013

Subgroups — #14909013

Order 2816.

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

normal subgroups only

This group has 520 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#13079361C211yesmaximal, characteristic, complemented
2#13070835C212yesmaximal, complemented
3#13070787C212yesmaximal, complemented
4#13070697C212yesmaximal, complemented
5#13070567C212yesmaximal
6#13070507C214yesmaximal, complemented
7#13070428C211yesmaximal, characteristic, complemented
8C11×#2956C211yesmaximal, characteristic
9C11×#575C2211yescharacteristic
10C11×#568—21no—
11#10623001—21no—
12C11×#444—21no—
13C11×#444C2212yes—
14C11×#443—21no—
15C11×#443C2212yes—
16C11×#430C2211yescharacteristic
17C2×C11×#104—21no—
18C4×C11×M16C2211yescharacteristic
19#10622808C2214yes—
20#10622750—21no—
21#10622750C2212yes—
22#10622329—21no—
23#10622329C2212yescomplemented
24#10622312C2211yescharacteristic, complemented
25#10622294—21no—
26#10622293C2211yescharacteristic, complemented
27#10622204C2214yes—
28#10622191C2212yes—
29#10622134C2214yescomplemented
30#10622132C2214yescomplemented
31#10622104C2212yescomplemented
32#10622101C2212yescomplemented
33C2×C11×#41—21no—
34C11×#137—22no—
35C11×AGL(1,ℤ/8)—22no—
36C11×#135—21no—
37C11×#135C2312yes—
38C11×#131—22no—
39C11×#131—22no—
40C11×#131—42no—
41C2×C11×M16—21no—
42C2×C11×M16—42no—
43C2×C11×M16D411yescharacteristic
44C2×C11×M16C2311yescharacteristic
45C2×C42×C11D411yescharacteristic
46#66979—41no—
47#66977—22no—
48#66977—41no—
49C2×Dic44—21no—
50C2×Dic44C2312yes—
51#66923—41no—
52#66922—21no—
53#66922—21no—
54C4×Dic22—22no—
55C4×Dic22—41no—
56C11×#108—21no—
57C11×#108C2312yes—
58C11×#104—22no—
59C11×#104—22no—
60C11×#97D411yescharacteristic
61C11×#97C2311yescharacteristic
62C4×C8×C11D411yescharacteristic
63C4×C8×C11C2311yescharacteristic
64#66893—24no—
65#66891—24no—
66#66881—21no—
67#66881C2312yes—
68#66880—22no—
69#66880—22no—
70#66876C2314yes—
71#33689—111nomaximal, Sylow
72C11×#41—22no—
73C11×#41—22no—
74C11×#41—41no—
75C11×#41—41no—
76C2×Q8×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C2×Dic22—22no—
83C2×Dic22—41no—
84C11×Q16—21no—
85C11×Q16#4112yes—
86C11×SD16—22no—
87C11×SD16—22no—
88C11×D8—21no—
89C11×D8#4112yes—
90C11×M16—22no—
91C11×M16—22no—
92C11×M16—22no—
93C11×M16—41no—
94C11×M16—42no—
95C11×M16—42no—
96C2×C8×C11—41no—
97C2×C8×C11—42no—
98C2×C8×C11—42no—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C42×C11—21no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—42no—
107C4⋊Dic11—22no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113C4×Dic11—42no—
114Dic44—24no—
115Dic44—42no—
116C11⋊C16—24no—
117#3185—111no—
118#2956D1111yescharacteristic
119#2239—112no—
120#2230—112no—
121#2214—112no—
122#2191—112no—
123#2180—114no—
124#2165—111no—
125C23×C11—41no—
126C23×C11AGL(1,ℤ/8)11yescharacteristic
127Q8×C11—22no—
128Q8×C11—41no—
129D4×C11—22no—
130D4×C11—41no—
131D4×C11—42no—
132D4×C11—42no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×Dic11—42no—
144C2×Dic11—42no—
145Dic22—42no—
146Dic22—42no—
147Dic22—82no—
148C8×C11—21no—
149C8×C11—21no—
150C8×C11—42no—
151C8×C11AGL(1,ℤ/8)12yes—
152C8×C11C2×#4112yes—
153#575C2×D1111yescharacteristic
154#568—21no—
155#533—221no—
156#510—114no—
157#498—111no—
158#494—111no—
159#487—221no—
160#470—112no—
161#470—221no—
162#444—21no—
163#444C2×D1112yes—
164#443—21no—
165#443C2×D1112yes—
166#441—112no—
167#441—221no—
168#430C2×D1111yescharacteristic
169C2×#104—21no—
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×C11—42no—
180C22×C11—161no—
181C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—41no—
185C4×C11—42no—
186C4×C11#52511yescharacteristic
187C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
188Dic11—82no—
189Dic11—82no—
190C2×#41—21no—
191#137—22no—
192AGL(1,ℤ/8)—22no—
193#135—21no—
194#135C22×D1112yes—
195C2×Q16—112no—
196C2×Q16—221no—
197#131—22no—
198#131—22no—
199#131—42no—
200C2×M16—21no—
201C2×M16—42no—
202C2×M16C22⋊D1111yescharacteristic
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×C42C22⋊D1111yescharacteristic
213Q32—224no—
214SD32—224no—
215M32—114no—
216#108—21no—
217#108C22×D1112yes—
218#106—112no—
219#106—221no—
220#104—22no—
221#104—22no—
222#103—222no—
223#103—222no—
224#97C22⋊D1111yescharacteristic
225#97C22×D1111yescharacteristic
226C4×C8C22⋊D1111yescharacteristic
227C4×C8C22×D1111yescharacteristic
228C2×C11—21no—
229C2×C11—41no—
230C2×C11—82no—
231C2×C11#310911yescharacteristic
232#41—22no—
233#41—22no—
234#41—41no—
235#41—41no—
236C2×Q8—21no—
237C2×Q8—222no—
238C2×Q8—441no—
239C2×D4—21no—
240C2×D4—41no—
241C22×C4—21no—
242C22×C4—41no—
243C22×C4C2×C22⋊D1111yescharacteristic
244Q16—21no—
245Q16—224no—
246Q16—442no—
247Q16#433912yes—
248SD16—22no—
249SD16—22no—
250D8—21no—
251D8#433912yes—
252M16—22no—
253M16—22no—
254M16—22no—
255M16—42no—
256M16—41no—
257M16—42no—
258C2×C8—42no—
259C2×C8—41no—
260C2×C8—42no—
261C2×C8C2×C22⋊D1111yescharacteristic
262C2×C8C2×C22⋊D1111yescharacteristic
263C2×C8C2×C22⋊D1111yescharacteristic
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×C22⋊D1111yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C16—224no—
277C11#3368911yescharacteristic, complemented, Sylow
278C23—41no—
279C23#6700211yescharacteristic
280Q8—22no—
281Q8—41no—
282Q8—442no—
283Q8—442no—
284Q8—882no—
285D4—22no—
286D4—41no—
287D4—42no—
288D4—42no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4#6700211yescharacteristic
300C2×C4C22×C22⋊D1111yescharacteristic
301C8—21no—
302C8—21no—
303C8—42no—
304C8#6698512yes—
305C8C2×#433912yes—
306C22—21no—
307C22—41no—
308C22—42no—
309C22—161no—
310C22C2×#6700211yescharacteristic
311C4—22no—
312C4—21no—
313C4—41no—
314C4—42no—
315C4—882no—
316C4—882no—
317C4#1062332211yescharacteristic
318C4C2×#6698511yescharacteristic
319C2—21no—
320C2—41no—
321C2—82no—
322C2#1307870711yescharacteristic
subgroupG/H
centerC2#13078707
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2956C2
socleC2×C11#3109
prime radicalC11×#575C22
hypercenter#2956D11
hypocenterC11#33689
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2956

Complements

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

NH ≅ G/Ntype
1. #13079361C2semidirect
2. #13070835C2semidirect
3. #13070787C2semidirect
4. #13070697C2semidirect
6. #13070507C2semidirect
7. #13070428C2semidirect
23. #10622329C22semidirect
24. #10622312C22semidirect
26. #10622293C22semidirect
29. #10622134C22semidirect
30. #10622132C22semidirect
31. #10622104C22semidirect
32. #10622101C22semidirect
277. C11#33689semidirect

Maximal subgroups

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

subgroupindex
#130793612
#130708352
#130707872
#130706972
#130705672
#130705072
#130704282
C11×#29562
#3368911