Finite Group Databasebeta

← #14653254

Subgroups — #14653254

Order 2816.

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

normal subgroups only

This group has 406 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
2#13067301C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic
4#13067288C211yesmaximal, characteristic
5#13067288C211yesmaximal, characteristic
6#13066908C211yesmaximal, characteristic
7C2×C11×#487C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#487—22no—
11C11×#487C414yes—
12C2×C11×#103—22no—
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66883—22no—
15#10622538C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622185—22no—
20#10622185—22no—
21#10622185—22no—
22#10622184—22no—
23#10622092—22no—
24C22×Q8×C11—21no—
25C22×Q8×C11—21no—
26C22×C8×C11D412yes—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8C2×C412yes—
34C11×C4⋊Q8C2×C412yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4318—21no—
41C2×#4318—21no—
42C11×#103—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#9775—111nomaximal, Sylow
57C2×Q8×C11—22no—
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—42no—
62C2×Q8×C11—42no—
63C2×Q8×C11—82no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11C22⋊C414yes—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C42×C11C22×C411yescharacteristic
81C42×C11C2×D411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D411yescharacteristic
84#4318—42no—
85#4318—42no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—22no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—41no—
90C2×#487D1111yescharacteristic
91#1848—111no—
92#1549—111no—
93#1548—111no—
94#1546—111no—
95#1546—111no—
96#1452—111no—
97C23×C11#12411yescharacteristic
98Q8×C11—44no—
99Q8×C11—82no—
100Q8×C11—82no—
101Q8×C11—81no—
102Q8×C11—81no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—82no—
108C2×C4×C11—82no—
109C2×C4×C11C2×C22⋊C411yescharacteristic
110C2×C4×C11C4×D411yescharacteristic
111C2×C4×C11C4×D411yescharacteristic
112C2×C4×C11#12111yescharacteristic
113C2×C4×C11#12111yescharacteristic
114C2×C4×C11#12711yescharacteristic
115C2×C4×C11AGL(1,ℤ/8)12yes—
116C2×C4×C11#13712yes—
117C8×C11—24no—
118C11⋊C8—42no—
119C11⋊C8—42no—
120C11⋊C8—81no—
121C11⋊C8—81no—
122C2×C4⋊Q8C2×D1111yescharacteristic
123C2×C4⋊Q8C2×D1111yescharacteristic
124#487—22no—
125#487Dic1114yes—
126#431—111no—
127#431—111no—
128C2×#108—222no—
129#423—111no—
130#423—111no—
131C2×#103—22no—
132C2×C4×C8C2×D1111yescharacteristic
133#333—222no—
134#332—222no—
135#332—222no—
136#332—222no—
137#322—222no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11#39011yescharacteristic
141C22×C11#48912yes—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—82no—
145C4×C11—82no—
146C4×C11#41712yes—
147C4×C11#47112yes—
148C4×C11#47312yes—
149C4×C11#49611yescharacteristic
150C4×C11#49711yescharacteristic
151C22×Q8—21no—
152C22×Q8—21no—
153C2×M16—221no—
154C2×M16—221no—
155C22×C8C22⋊D1112yes—
156C4⋊Q8—21no—
157C4⋊Q8—21no—
158C4⋊Q8—21no—
159C4⋊Q8—21no—
160C4⋊Q8—21no—
161C4⋊Q8—21no—
162C4⋊Q8C2×Dic1112yes—
163C4⋊Q8C2×Dic1112yes—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C42C22×D1111yescharacteristic
169#108—444no—
170C4⋊C8—112no—
171C4⋊C8—112no—
172C4⋊C8—221no—
173C4⋊C8—221no—
174C4⋊C8—221no—
175C4⋊C8—221no—
176#103—28no—
177C22⋊C8—221no—
178C22⋊C8—221no—
179C4×C8—221no—
180C4×C8—221no—
181C4×C8C2×Dic1112yes—
182C4×C8C22⋊D1112yes—
183C2×C11—22no—
184C2×C11#195911yescharacteristic
185C2×C11#197711yescharacteristic
186C2×C11#197911yescharacteristic
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—42no—
192C2×Q8—42no—
193C2×Q8—82no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4#434111yescharacteristic
197C22×C4#434111yescharacteristic
198C22×C4C2×C22⋊D1111yescharacteristic
199M16—442no—
200M16—442no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—222no—
204C2×C8—222no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8C22⋊Dic1114yes—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C42D4×D1111yescharacteristic
217C42D4×D1111yescharacteristic
218C42C22×Dic1111yescharacteristic
219C42C2×C22⋊D1111yescharacteristic
220C11#977511yescharacteristic, complemented, Sylow
221C23#6698911yescharacteristic
222Q8—44no—
223Q8—82no—
224Q8—82no—
225Q8—81no—
226Q8—81no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4D4×Dic1111yescharacteristic
234C2×C4D4×Dic1111yescharacteristic
235C2×C4#6699111yescharacteristic
236C2×C4#6699111yescharacteristic
237C2×C4#6699311yescharacteristic
238C2×C4#6700212yes—
239C2×C4#6700412yes—
240C2×C4C2×C22⋊Dic1111yescharacteristic
241C8—24no—
242C8—442no—
243C8—442no—
244C8—881no—
245C8—881no—
246C22—21no—
247C22—21no—
248C22#1062266812yes—
249C22#1062283411yescharacteristic
250C4—21no—
251C4—21no—
252C4—82no—
253C4—82no—
254C4#1062267111yescharacteristic
255C4#1062267311yescharacteristic
256C4#1062279012yes—
257C4#1062280512yes—
258C4#1062284512yes—
259C2—22no—
260C2#1306943311yescharacteristic
261C2#1306952111yescharacteristic
262C2#1306953211yescharacteristic
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#487C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenterC2×#487D11
hypocenterC11#9775
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
220. C11#9775semidirect

Maximal subgroups

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

subgroupindex
#130687882
#130673012
#130672972
#130672882
#130669082
C2×C11×#4872
#977511