Finite Group Databasebeta

← #14666730

Subgroups — #14666730

Order 2816.

324 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076106C211yesmaximal, characteristic
2#13067658C211yesmaximal, characteristic
3#13067624C211yesmaximal, characteristic
4#13066642C211yesmaximal, characteristic
5#13066621C211yesmaximal, characteristic
6#13066560C211yesmaximal, characteristic
7C11×#2061C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#428—21no—
10C11×#382C2211yescharacteristic
11#10622657—21no—
12#10622656—21no—
13#10622599C2211yescharacteristic
14#10622596C2211yescharacteristic
15#10622585—21no—
16#10622546—21no—
17#10622273—21no—
18#10622270—21no—
19#10622265—21no—
20#10622264—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23#10622176—21no—
24#10622176—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×M16—21no—
28C11×C4⋊Q8—41no—
29C11×#125—41no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×#117—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C11×#107—41no—
44C11×#106—41no—
45C11×#95—21no—
46C11×#95—21no—
47#66899—41no—
48#66899—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66872—41no—
61#66871—41no—
62#12241—111nomaximal, Sylow
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C11×M16—22no—
75C11×M16—41no—
76C2×C8×C11—41no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—81no—
96C4×Dic11—42no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99#2769—111no—
100#2061D1111yescharacteristic
101#1617—111no—
102#1611—111no—
103#1353—111no—
104#1346—111no—
105#1324—111no—
106C23×C11#12011yescharacteristic
107Q8×C11—81no—
108Q8×C11—81no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×Dic11—22no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C8×C11—42no—
138C11⋊C8—81no—
139C11⋊C8—81no—
140#544C2×D1111yescharacteristic
141#484—221no—
142#483—221no—
143#428—21no—
144#400—111no—
145#400—221no—
146#398—111no—
147#398—221no—
148#389—221no—
149#387—221no—
150#387—221no—
151#383—221no—
152#382C2×D1111yescharacteristic
153#343C2×D1111yescharacteristic
154#339—21no—
155#328—221no—
156#328—221no—
157#324—111no—
158#324—111no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#45211yescharacteristic
162C22×C11#45611yescharacteristic
163C22×C11B(4,𝔽2)11yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—81no—
169C4×C11—81no—
170C4×C11—81no—
171C4×C11—81no—
172Dic11—42no—
173Dic11—81no—
174Dic11—81no—
175Dic11—81no—
176C2×M16—21no—
177C4⋊Q8—41no—
178#125—41no—
179C22⋊Q8—21no—
180C22⋊Q8—21no—
181#117—21no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4C22⋊D1111yescharacteristic
189C2×C4⋊C4C22×D1111yescharacteristic
190C2×C42—221no—
191C2×C42C22⋊D1111yescharacteristic
192#107—41no—
193#107—441no—
194#106—41no—
195#106—441no—
196#103—441no—
197#103—441no—
198C22⋊C8—221no—
199C22⋊C8—221no—
200#95—21no—
201#95—21no—
202#95—111no—
203#95—111no—
204#95—221no—
205#95—221no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11#160311yescharacteristic
214C2×C11#220111yescharacteristic
215C2×C11#220411yescharacteristic
216C2×Q8—21no—
217C2×Q8—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—221no—
221C22×C4—221no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4D4×D1111yescharacteristic
225C22×C4D4×D1111yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227M16—22no—
228M16—41no—
229C2×C8—41no—
230C2×C8—441no—
231C2×C8—441no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—441no—
241C4⋊C4—441no—
242C4⋊C4—442no—
243C4⋊C4—442no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—881no—
247C22⋊C4—41no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—442no—
252C11#1224111yescharacteristic, complemented, Sylow
253C23#6699011yescharacteristic
254Q8—81no—
255Q8—81no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—222no—
271C2×C4—441no—
272C2×C4—441no—
273C2×C4—441no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4#6699511yescharacteristic
283C2×C4#6700311yescharacteristic
284C8—42no—
285C8—881no—
286C8—881no—
287C22—21no—
288C22—21no—
289C22#1062264511yescharacteristic
290C22#1062266011yescharacteristic
291C22#1062270811yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—442no—
301C4—881no—
302C4—881no—
303C4—881no—
304C2—21no—
305C2—21no—
306C2#1306757711yescharacteristic
307C2#1307062811yescharacteristic
308C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2061C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2061D11
hypocenterC11#12241
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2061

Complements

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

NH ≅ G/Ntype
252. C11#12241semidirect

Maximal subgroups

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

subgroupindex
#130761062
#130676582
#130676242
#130666422
#130666212
#130665602
C11×#20612
#1224111