Finite Group Databasebeta

← #14643086

Subgroups — #14643086

Order 2816.

322 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 79 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#13076607C211yesmaximal, characteristic
2#13070178C211yesmaximal, characteristic
3#13070178C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic
5#13066439C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#2100C211yesmaximal, characteristic
8C11×#389C2211yescharacteristic
9C11×#384C2211yescharacteristic
10#10622599—21no—
11#10622595—21no—
12#10622594—21no—
13#10622591—21no—
14#10622541C2211yescharacteristic
15#10622541C2211yescharacteristic
16#10622272—21no—
17#10622268—21no—
18C11×#340—21no—
19C11×#340—21no—
20C11×#336C2211yescharacteristic
21#10622167—21no—
22#10622167—21no—
23#10622167—21no—
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C8×C11—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—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⋊#95—21no—
53C11⋊#95—21no—
54#7832—111nomaximal, Sylow
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—41no—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C2×C8×C11—41no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C42×C11—41no—
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87C4×Dic11—81no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—41no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—41no—
93C2×C11⋊C8—41no—
94#2810—111no—
95#2100—111no—
96#2100—111no—
97#2100D1111yescharacteristic
98#1271—111no—
99#1271—111no—
100#1271—111no—
101C23×C11#12011yescharacteristic
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11#13511yescharacteristic
118C2×C4×C11#13511yescharacteristic
119C2×C4×C11#13511yescharacteristic
120C2×C4×C11#13711yescharacteristic
121C2×C4×C11#13711yescharacteristic
122C2×C4×C11#13711yescharacteristic
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
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—
135C8×C11—81no—
136C11⋊C8—81no—
137C11⋊C8—81no—
138#400—221no—
139#400—221no—
140#400—221no—
141#389—111no—
142#389—111no—
143#389C2×D1111yescharacteristic
144#387—221no—
145#387—221no—
146#387—221no—
147#384C2×D1111yescharacteristic
148#340—21no—
149#340—21no—
150#340—221no—
151#340—221no—
152#340—221no—
153#340—221no—
154#336—111no—
155#336—111no—
156#336C2×D1111yescharacteristic
157C22×C11#45211yescharacteristic
158C22×C11#45211yescharacteristic
159C22×C11#45211yescharacteristic
160C22×C11#45411yescharacteristic
161C22×C11#45411yescharacteristic
162C22×C11#45411yescharacteristic
163C22×C11#45811yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—81no—
171C4×C11—81no—
172C4×C11—161no—
173Dic11—81no—
174Dic11—81no—
175Dic11—81no—
176Dic11—81no—
177C22×C8—21no—
178C22×C8—221no—
179C22×C8—221no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4C22⋊D1111yescharacteristic
191C2×C4⋊C4C22⋊D1111yescharacteristic
192C2×C42—221no—
193C2×C42C22×D1111yescharacteristic
194#95—21no—
195#95—221no—
196#95—221no—
197#95—221no—
198#95—221no—
199#95—221no—
200#95—221no—
201#95—221no—
202#95—221no—
203#95—221no—
204C2×C11#161511yescharacteristic
205C2×C11#161511yescharacteristic
206C2×C11#161511yescharacteristic
207C2×C11#163811yescharacteristic
208C2×C11#163811yescharacteristic
209C2×C11#163811yescharacteristic
210C2×C11#165811yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—221no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4—221no—
218C22×C4D4×D1111yescharacteristic
219C22×C4D4×D1111yescharacteristic
220C22×C4C2×C22⋊D1111yescharacteristic
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—441no—
225C2×C8—441no—
226C2×C8—441no—
227C2×C8—441no—
228C2×C8—441no—
229C2×C8—441no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—441no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C42—41no—
249C42—881no—
250C11#783211yescharacteristic, complemented, Sylow
251C23#6699011yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—441no—
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#6696811yescharacteristic
280C2×C4#6696911yescharacteristic
281C2×C4#6697111yescharacteristic
282C2×C4#6697211yescharacteristic
283C2×C4#6699511yescharacteristic
284C2×C4#6700311yescharacteristic
285C8—81no—
286C8—881no—
287C8—881no—
288C22#1062266011yescharacteristic
289C22#1062266611yescharacteristic
290C22#1062267511yescharacteristic
291C22#1062278611yescharacteristic
292C22#1062280011yescharacteristic
293C22#1062281411yescharacteristic
294C22#1062281411yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—81no—
302C4—81no—
303C4—161no—
304C4—881no—
305C4—881no—
306C4—881no—
307C4—881no—
308C2#1306764411yescharacteristic
309C2#1306764511yescharacteristic
310C2#1306764611yescharacteristic
311C2#1306778511yescharacteristic
312C2#1306778611yescharacteristic
313C2#1306778711yescharacteristic
314C2#1306791711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2100C2
socle, prime radicalC23×C11#120
hypercenter#2100D11
hypocenterC11#7832
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
250. C11#7832semidirect

Maximal subgroups

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

subgroupindex
#130766072
#130701782
#130664402
#130664392
#130664382
C11×#21002
#783211