Finite Group Databasebeta

← #14653247

Subgroups — #14653247

Order 2816.

458 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 127 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#13068788C211yesmaximal, characteristic, complemented
2#13067301C211yesmaximal, characteristic, complemented
3#13067297C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic
5#13067284C211yesmaximal, characteristic
6#13066908C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C11×#486—22no—
11C11×#486C414yes—
12C2×C11×#102—22no—
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66883—22no—
15#10622538C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622185—22no—
20#10622184—22no—
21#10622182—22no—
22#10622182—22no—
23#10622092—22no—
24C22×Q8×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×C8×C11D412yes—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8C2×C412yes—
33C11×#127—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127C2×C412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4318—21no—
41C2×#4318—21no—
42C11×#102—28no—
43C4×C8×C11C2×C412yes—
44C4×C8×C11D412yes—
45C22⋊(C11⋊C8)—21no—
46C22⋊(C11⋊C8)—21no—
47#66883—44no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D412yes—
53C4⋊(C11⋊C8)D412yes—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56#9774—111nomaximal, Sylow
57C24×C11—41no—
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C2×Q8×C11—82no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—82no—
70C2×D4×C11—82no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×C8×C11—22no—
76C2×C8×C11—22no—
77C2×C8×C11C22⋊C414yes—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C42×C11C22×C411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86#4318—42no—
87#4318—42no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8—41no—
92C2×#486D1111yescharacteristic
93#1848—111no—
94#1549—111no—
95#1548—111no—
96#1545—111no—
97#1545—111no—
98#1452—111no—
99C23×C11—42no—
100C23×C11—82no—
101C23×C11—82no—
102C23×C11—82no—
103C23×C11#12411yescharacteristic
104Q8×C11—82no—
105Q8×C11—82no—
106D4×C11—44no—
107D4×C11—82no—
108D4×C11—82no—
109D4×C11—82no—
110D4×C11—82no—
111D4×C11—81no—
112D4×C11—81no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—42no—
116C2×C4×C11—82no—
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12711yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)12yes—
124C2×C4×C11#13712yes—
125C8×C11—24no—
126C11⋊C8—42no—
127C11⋊C8—42no—
128C11⋊C8—81no—
129C11⋊C8—81no—
130C2×C4⋊Q8C2×D1111yescharacteristic
131C2×#127C2×D1111yescharacteristic
132#486—22no—
133#486Dic1114yes—
134#431—111no—
135#431—111no—
136C2×#108—222no—
137#423—111no—
138#423—111no—
139C2×#102—22no—
140C2×C4×C8C2×D1111yescharacteristic
141#333—222no—
142#332—222no—
143#331—222no—
144#331—222no—
145#322—222no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—82no—
149C22×C11—82no—
150C22×C11—82no—
151C22×C11—164no—
152C22×C11#39011yescharacteristic
153C22×C11#48912yes—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—82no—
157C4×C11#41712yes—
158C4×C11#47112yes—
159C4×C11#47212yes—
160C4×C11#49611yescharacteristic
161C4×C11#49711yescharacteristic
162C22×Q8—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C2×M16—221no—
167C2×M16—221no—
168C22×C8C22⋊D1112yes—
169C4⋊Q8—21no—
170C4⋊Q8—21no—
171C4⋊Q8—21no—
172C4⋊Q8C2×Dic1112yes—
173#127—21no—
174#127—21no—
175#127—21no—
176#127C2×Dic1112yes—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C42C22×D1111yescharacteristic
180#108—444no—
181C4⋊C8—112no—
182C4⋊C8—112no—
183C4⋊C8—221no—
184C4⋊C8—221no—
185C4⋊C8—221no—
186C4⋊C8—221no—
187#102—28no—
188C22⋊C8—221no—
189C22⋊C8—221no—
190C4×C8—221no—
191C4×C8—221no—
192C4×C8C2×Dic1112yes—
193C4×C8C22⋊D1112yes—
194C2×C11—22no—
195C2×C11—162no—
196C2×C11#195911yescharacteristic
197C2×C11#197711yescharacteristic
198C2×C11#197811yescharacteristic
199C24—41no—
200C2×Q8—22no—
201C2×Q8—41no—
202C2×Q8—82no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—42no—
210C2×D4—42no—
211C2×D4—82no—
212C2×D4—82no—
213C22×C4—41no—
214C22×C4#434111yescharacteristic
215C22×C4#434111yescharacteristic
216C22×C4C2×C22⋊D1111yescharacteristic
217M16—442no—
218M16—442no—
219C2×C8—22no—
220C2×C8—22no—
221C2×C8—222no—
222C2×C8—222no—
223C2×C8—441no—
224C2×C8—441no—
225C2×C8C22⋊Dic1114yes—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C42D4×D1111yescharacteristic
231C42D4×D1111yescharacteristic
232C42C22×Dic1111yescharacteristic
233C42C2×C22⋊D1111yescharacteristic
234C11#977411yescharacteristic, complemented, Sylow
235C23—42no—
236C23—82no—
237C23—82no—
238C23—82no—
239C23#6698911yescharacteristic
240Q8—82no—
241Q8—82no—
242D4—44no—
243D4—82no—
244D4—82no—
245D4—82no—
246D4—82no—
247D4—81no—
248D4—81no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4D4×Dic1111yescharacteristic
254C2×C4D4×Dic1111yescharacteristic
255C2×C4#6699111yescharacteristic
256C2×C4#6699111yescharacteristic
257C2×C4#6699311yescharacteristic
258C2×C4#6700212yes—
259C2×C4#6700412yes—
260C2×C4C2×C22⋊Dic1111yescharacteristic
261C8—24no—
262C8—442no—
263C8—442no—
264C8—881no—
265C8—881no—
266C22—21no—
267C22—21no—
268C22—82no—
269C22—82no—
270C22—82no—
271C22—164no—
272C22#1062266812yes—
273C22#1062283411yescharacteristic
274C4—21no—
275C4—21no—
276C4—82no—
277C4#1062267111yescharacteristic
278C4#1062267311yescharacteristic
279C4#1062277312yes—
280C4#1062279012yes—
281C4#1062284512yes—
282C2—22no—
283C2—162no—
284C2#1306943311yescharacteristic
285C2#1306952111yescharacteristic
286C2#1306952711yescharacteristic
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC22×C11#390
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenterC2×#486D11
hypocenterC11#9774
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13068788C2semidirect
2. #13067301C2semidirect
3. #13067297C2semidirect
6. #13066908C2semidirect
234. C11#9774semidirect

Maximal subgroups

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

subgroupindex
#130687882
#130673012
#130672972
#130672842
#130669082
C2×C11×#4862
#977411