Finite Group Databasebeta

← #14648288

Subgroups — #14648288

Order 2816.

356 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 97 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#13077717C211yesmaximal, characteristic
2#13069593C211yesmaximal, characteristic
3#13067405C211yesmaximal, characteristic
4#13067404C211yesmaximal, characteristic
5#13067280C211yesmaximal, characteristic
6#13066449C211yesmaximal, characteristic
7C11×#1276C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C43×C11C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15#10622444—21no—
16#10622443—21no—
17#10622333—22no—
18#10622292—21no—
19C8×Dic22—21no—
20#10622161—22no—
21#10622124C411yescharacteristic, complemented
22#10622124C411yescharacteristic, complemented
23#10622120C411yescharacteristic, complemented
24#10622120C411yescharacteristic, complemented
25#10622118—21no—
26#10622117—21no—
27#10622096—21no—
28#10622095—21no—
29C2×C42×C11—21no—
30C2×C42×C11—21no—
31C2×C42×C11—21no—
32C2×C42×C11C2311yescharacteristic
33#66979D412yes—
34#66977—21no—
35#66977—21no—
36C2×#4318—21no—
37#66923Q812yes—
38#66922C2×C411yescharacteristic
39#66922C2×C411yescharacteristic
40C4×Dic22—21no—
41C4×Dic22—21no—
42C11×C4⋊C8C2×C411yescharacteristic
43C11×C4⋊C8C2×C411yescharacteristic
44C11×C4⋊C8D411yescharacteristic
45C11×C4⋊C8D411yescharacteristic
46C11×C22⋊C8—21no—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C4×C8×C11—21no—
50C22⋊(C11⋊C8)—21no—
51C22⋊(C11⋊C8)—21no—
52#66879—22no—
53Dic11⋊C8—22no—
54Dic11⋊C8—22no—
55C8×Dic11—22no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)C2×C411yescharacteristic
59C4⋊(C11⋊C8)C2×C411yescharacteristic
60C4⋊(C11⋊C8)D411yescharacteristic
61C4⋊(C11⋊C8)D411yescharacteristic
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#8936—111nomaximal, Sylow
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11—22no—
78C42×C11—41no—
79C42×C11—41no—
80C42×C11—41no—
81C42×C11C22×C411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×Q811yescharacteristic
85C22⋊Dic11—22no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C4⋊C412yes—
89C4⋊Dic11C4⋊C412yes—
90Dic11⋊C4—22no—
91Dic11⋊C4—22no—
92C4×Dic11—22no—
93#4318—42no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—41no—
99#2986—111no—
100#1994—111no—
101#1574—111no—
102#1574—111no—
103#1544—111no—
104#1276—111no—
105#1276D1111yescharacteristic
106C23×C11#12311yescharacteristic
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11C2×C4⋊C411yescharacteristic
117C2×C4×C11C4×D411yescharacteristic
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11C22⋊Q811yescharacteristic
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×Dic11—22no—
123C2×Dic11—22no—
124Dic22—41no—
125Dic22—41no—
126Dic22—41no—
127Dic22—41no—
128C8×C11—41no—
129C8×C11—41no—
130C8×C11—41no—
131C8×C11—41no—
132C11⋊C8—41no—
133C11⋊C8—41no—
134C11⋊C8—41no—
135C11⋊C8—41no—
136C11⋊C8—81no—
137#533—111no—
138#446—221no—
139#446—221no—
140C8×Q8—221no—
141C8×Q8—221no—
142#433—222no—
143#431—111no—
144#431—111no—
145#431C2×D1111yescharacteristic
146#431C2×D1111yescharacteristic
147#423—111no—
148C43C2×D1111yescharacteristic
149#339—222no—
150#335—221no—
151#335—221no—
152#334—221no—
153#334—221no—
154#332—111no—
155#332—111no—
156#332—111no—
157#332—111no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38511yescharacteristic
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—44no—
166C4×C11#44311yescharacteristic
167C4×C11#44311yescharacteristic
168C4×C11#44411yescharacteristic
169C4×C11#44411yescharacteristic
170C4×C11#45411yescharacteristic
171C4×C11#45611yescharacteristic
172Dic11—42no—
173Dic11—42no—
174C2×M16—221no—
175C4⋊Q8—111no—
176C4⋊Q8—111no—
177#125—112no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C4×Q8—221no—
181C4×Q8—221no—
182#117—112no—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42—21no—
186C2×C42C22×D1111yescharacteristic
187C4⋊C8—111no—
188C4⋊C8—111no—
189C4⋊C8—111no—
190C4⋊C8—111no—
191C4⋊C8—222no—
192C4⋊C8—222no—
193C4⋊C8—221no—
194C4⋊C8—221no—
195C4⋊C8C4×D1111yescharacteristic
196C4⋊C8C4×D1111yescharacteristic
197C4⋊C8D4411yescharacteristic
198C4⋊C8D4411yescharacteristic
199C22⋊C8—21no—
200C22⋊C8—21no—
201C22⋊C8—221no—
202C22⋊C8—221no—
203#97—222no—
204C4×C8—21no—
205C4×C8—21no—
206C4×C8—222no—
207C4×C8—221no—
208C4×C8—221no—
209C2×C11—41no—
210C2×C11#185711yescharacteristic
211C2×C11#186611yescharacteristic
212C2×C11#186611yescharacteristic
213C2×Q8—221no—
214C2×Q8—221no—
215C22×C4—41no—
216C22×C4#433911yescharacteristic
217C22×C4D4×D1111yescharacteristic
218C22×C4#434111yescharacteristic
219M16—442no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—221no—
225C2×C8—221no—
226C2×C8—221no—
227C2×C8—221no—
228C2×C8—441no—
229C4⋊C4—112no—
230C4⋊C4—112no—
231C4⋊C4—221no—
232C4⋊C4—221no—
233C4⋊C4—222no—
234C4⋊C4—222no—
235C22⋊C4—222no—
236C42—22no—
237C42—22no—
238C42—22no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—222no—
243C42C2×C4×D1111yescharacteristic
244C42C2×D4411yescharacteristic
245C42D4×D1111yescharacteristic
246C42Q8×D1111yescharacteristic
247C11#893611yescharacteristic, complemented, Sylow
248C23#6693611yescharacteristic
249Q8—441no—
250Q8—441no—
251Q8—441no—
252Q8—441no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4C4×D4411yescharacteristic
265C2×C4(C22⋊D11)⋊C411yescharacteristic
266C2×C4#6693511yescharacteristic
267C2×C4C4⋊C4×D1111yescharacteristic
268C2×C4#6694911yescharacteristic
269C2×C4#6695011yescharacteristic
270C8—41no—
271C8—41no—
272C8—41no—
273C8—41no—
274C8—441no—
275C8—441no—
276C8—441no—
277C8—441no—
278C8—881no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22#1062228111yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—44no—
287C4—442no—
288C4—442no—
289C4#1062231311yescharacteristic
290C4#1062233011yescharacteristic
291C4#1062243611yescharacteristic
292C4#1062243711yescharacteristic
293C4#1062243911yescharacteristic
294C4#1062244011yescharacteristic
295C2—41no—
296C2#1306883211yescharacteristic
297C2#1306889211yescharacteristic
298C2#1306889411yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#385
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1276D11
hypocenterC11#8936
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
21. #10622124C4semidirect
22. #10622124C4semidirect
23. #10622120C4semidirect
24. #10622120C4semidirect
247. C11#8936semidirect

Maximal subgroups

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

subgroupindex
#130777172
#130695932
#130674052
#130674042
#130672802
#130664492
C11×#12762
#893611