Finite Group Databasebeta

← #14650757

Subgroups — #14650757

Order 2816.

360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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#13079818C211yesmaximal, characteristic
2#13077722C211yesmaximal, characteristic
3#13067242C211yesmaximal, characteristic
4#13066971C211yesmaximal, characteristic
5C11⋊#1308C211yesmaximal, characteristic
6#13066478C211yesmaximal, characteristic
7C11×#1554C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#431C2211yescharacteristic
12#10622695—21no—
13#10622693—21no—
14#10622657C412yes—
15#10622656C412yes—
16#10622637—22no—
17#10622637—22no—
18#10622635—22no—
19#10622613—22no—
20#10622539C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23C11×#333—21no—
24C11×#332—21no—
25#10622107—22no—
26#10622103—22no—
27C11×C4⋊Q8D411yescharacteristic
28C11×C4⋊Q8D411yescharacteristic
29C11×#125—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8C2×C412yes—
32C4×Q8×C11—21no—
33C4×Q8×C11D412yes—
34C11×#117—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40#66923—21no—
41#66923—21no—
42#66923—21no—
43#66923—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C22⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×#97—21no—
49C4×C8×C11—21no—
50#66899—22no—
51#66899—22no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)C2×C412yes—
54C22⋊(C11⋊C8)D412yes—
55#66872—22no—
56#66871—22no—
57C4⋊(C11⋊C8)—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61#66867—22no—
62#66867—21no—
63#66867—21no—
64#66867D412yes—
65C4×C11⋊C8—22no—
66#9336—111nomaximal, Sylow
67C2×Q8×C11—21no—
68C2×Q8×C11C22⋊C412yes—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4C22⋊C412yes—
82C11×C22⋊C4—22no—
83C42×C11—22no—
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11#4111yescharacteristic
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—22no—
99#3236—111no—
100#2987—111no—
101#1554D1111yescharacteristic
102#1534—111no—
103#1470—111no—
104#1308—111no—
105#1287—111no—
106C23×C11C4×D411yescharacteristic
107Q8×C11—42no—
108Q8×C11—81no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12311yescharacteristic
120C2×Dic11—42no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—81no—
124C8×C11—81no—
125C8×C11—81no—
126C11⋊C8—42no—
127C11⋊C8—42no—
128C11⋊C8—42no—
129#533C2×D1111yescharacteristic
130C2×#125—111no—
131#501—221no—
132#491—221no—
133#484—112no—
134#483—112no—
135#479—222no—
136#446—222no—
137#446—222no—
138#433—222no—
139#432—111no—
140#432—111no—
141#432—111no—
142#432C2×D1111yescharacteristic
143#431C2×D1111yescharacteristic
144#333—21no—
145#332—21no—
146#330—222no—
147#324—222no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11#38611yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—42no—
159C4×C11—42no—
160Dic11—81no—
161Dic11—81no—
162C4⋊Q8C22⋊D1111yescharacteristic
163C4⋊Q8C22⋊D1111yescharacteristic
164#125—21no—
165#125—221no—
166#125—221no—
167#125—221no—
168#125—221no—
169C22⋊Q8—21no—
170C22⋊Q8C4×D1112yes—
171C4×Q8—21no—
172C4×Q8D4412yes—
173#117—21no—
174C2×C4⋊C4—111no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—221no—
177C2×C4⋊C4—221no—
178C2×C42C22×D1111yescharacteristic
179#107—222no—
180#106—222no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—224no—
184C4⋊C8—221no—
185C4⋊C8—221no—
186C4⋊C8—221no—
187#103—222no—
188#103—222no—
189C22⋊C8—21no—
190C22⋊C8—21no—
191C22⋊C8—112no—
192C22⋊C8—112no—
193C22⋊C8—221no—
194#97—21no—
195#97—112no—
196#97—222no—
197#97—221no—
198#97—221no—
199C4×C8—21no—
200C4×C8—222no—
201C2×C11—41no—
202C2×C11#188111yescharacteristic
203C2×C11#190511yescharacteristic
204C2×C11#191511yescharacteristic
205C2×Q8—21no—
206C2×Q8(C2×D11)⋊C412yes—
207C22×C4—221no—
208C22×C4—221no—
209C22×C4C2×C4×D1111yescharacteristic
210C22×C4D4×D1111yescharacteristic
211C22×C4#434111yescharacteristic
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—222no—
215C2×C8—222no—
216C2×C8—222no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—221no—
223C4⋊C4—221no—
224C4⋊C4—221no—
225C4⋊C4—221no—
226C4⋊C4—441no—
227C4⋊C4—441no—
228C4⋊C4—441no—
229C4⋊C4—441no—
230C4⋊C4(C2×D11)⋊C412yes—
231C22⋊C4—22no—
232C42—22no—
233C42C2×D4411yescharacteristic
234C42D4×D1111yescharacteristic
235C42#434111yescharacteristic
236C42C2×C22⋊D1111yescharacteristic
237C11#933611yescharacteristic, complemented, Sylow
238C23(C22⋊D11)⋊C411yescharacteristic
239Q8—42no—
240Q8—81no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—442no—
247C2×C4—441no—
248C2×C4—441no—
249C2×C4—881no—
250C2×C4(C22⋊D11)⋊C411yescharacteristic
251C2×C4#6693511yescharacteristic
252C2×C4#6693911yescharacteristic
253C2×C4C2×(C2×D11)⋊C411yescharacteristic
254C2×C4#6699211yescharacteristic
255C2×C4#6699211yescharacteristic
256C8—81no—
257C8—81no—
258C8—442no—
259C8—442no—
260C8—442no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22#1062257111yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—42no—
272C4—42no—
273C4—881no—
274C4—881no—
275C2—41no—
276C2#1306897611yescharacteristic
277C2#1306910811yescharacteristic
278C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1554C2
socleC22×C11#386
prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenter#1554D11
hypocenterC11#9336
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
237. C11#9336semidirect

Maximal subgroups

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

subgroupindex
#130798182
#130777222
#130672422
#130669712
C11⋊#13082
#130664782
C11×#15542
#933611