Finite Group Databasebeta

← #14666732

Subgroups — #14666732

Order 2816.

324 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069966C211yesmaximal, characteristic
2#13067657C211yesmaximal, characteristic
3#13067623C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic
5#13066622C211yesmaximal, characteristic
6#13066560C211yesmaximal, characteristic
7C11×#2769C211yesmaximal, characteristic
8#10623031C2211yescharacteristic
9C11×#400—21no—
10C11×#400C2211yescharacteristic
11C11×#398—21no—
12C11×#398C2211yescharacteristic
13C11×#389—21no—
14C11×#387—21no—
15C11×#387—21no—
16C11×#383—21no—
17C11×#382C2211yescharacteristic
18#10622584—21no—
19#10622583—21no—
20#10622577—21no—
21#10622168C2211yescharacteristic
22#10622166C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622161—21no—
25#10622090—21no—
26#10622090—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11D411yescharacteristic
37#66979—21no—
38#66977—21no—
39#66977—21no—
40C2×#4318—21no—
41#66943—41no—
42#66941—41no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95D411yescharacteristic
53C11×#95D411yescharacteristic
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56#66874—41no—
57#66874—41no—
58#66872—41no—
59#66872—41no—
60#66871—41no—
61#66871—41no—
62#12241—111nomaximal, Sylow
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×Dic22—21no—
73C2×Dic22—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—81no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—42no—
86C22⋊Dic11—41no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C4×Dic11—41no—
94#4318—22no—
95#4318—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99#2769D1111yescharacteristic
100#2061—111no—
101#1617—111no—
102#1611—111no—
103#1353—111no—
104#1346—111no—
105#1324—111no—
106C23×C11#12011yescharacteristic
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—41no—
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—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—41no—
134C2×Dic11—41no—
135Dic22—81no—
136Dic22—81no—
137C11⋊C8—42no—
138C11⋊C8—81no—
139C11⋊C8—81no—
140#544—111no—
141#484—221no—
142#483—221no—
143#428—221no—
144#400—21no—
145#400C2×D1111yescharacteristic
146#398—21no—
147#398C2×D1111yescharacteristic
148#389—21no—
149#387—21no—
150#387—21no—
151#383—21no—
152#382C2×D1111yescharacteristic
153#343—111no—
154#339—221no—
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—42no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—81no—
170C4×C11—81no—
171C4×C11—81no—
172C4×C11—81no—
173C4×C11—81no—
174Dic11—81no—
175Dic11—81no—
176C2×M16—221no—
177C4⋊Q8—441no—
178#125—441no—
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181#117—221no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C22⋊D1111yescharacteristic
187C2×C4⋊C4C22⋊D1111yescharacteristic
188C2×C4⋊C4C22⋊D1111yescharacteristic
189C2×C4⋊C4C22×D1111yescharacteristic
190C2×C42—21no—
191C2×C42C22⋊D1111yescharacteristic
192#107—441no—
193#107—441no—
194#106—441no—
195#106—441no—
196#103—441no—
197#103—441no—
198C22⋊C8—221no—
199C22⋊C8—221no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95C22⋊D1111yescharacteristic
210#95C22⋊D1111yescharacteristic
211C2×C11—21no—
212C2×C11—21no—
213C2×C11#160311yescharacteristic
214C2×C11#220111yescharacteristic
215C2×C11#220411yescharacteristic
216C2×Q8—221no—
217C2×Q8—221no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4C2×C22⋊D1111yescharacteristic
225C22×C4C2×C22⋊D1111yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227M16—222no—
228M16—441no—
229C2×C8—441no—
230C2×C8—441no—
231C2×C8—441no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—81no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C22⋊C4—441no—
248C42—21no—
249C42—21no—
250C42—42no—
251C42—441no—
252C11#1224111yescharacteristic, complemented, Sylow
253C23#6700611yescharacteristic
254Q8—881no—
255Q8—881no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
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—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4#6700311yescharacteristic
283C2×C4#6700411yescharacteristic
284C8—442no—
285C8—881no—
286C8—881no—
287C22—21no—
288C22—21no—
289C22#1062285211yescharacteristic
290C22#1062285711yescharacteristic
291C22#1062285911yescharacteristic
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—881no—
303C4—881no—
304C2—21no—
305C2—21no—
306C2#1306757911yescharacteristic
307C2#1307062911yescharacteristic
308C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2769C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2769D11
hypocenterC11#12241
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2769

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
#130699662
#130676572
#130676232
#130666432
#130666222
#130665602
C11×#27692
#1224111