Finite Group Databasebeta

← #14663430

Subgroups — #14663430

Order 2816.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#13073803C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066561C212yesmaximal
4#13066559C212yesmaximal
5C11×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66923C411yescharacteristic
8C11×#432—21no—
9#10622843C411yescharacteristic
10#10622843C411yescharacteristic
11#10622597—21no—
12#10622597—21no—
13#10622590C2211yescharacteristic
14#10622589C2211yescharacteristic
15C4×C4⋊Dic11C411yescharacteristic
16#10622546—21no—
17#10622546—21no—
18#10622538—21no—
19C11×#324—21no—
20C11×#324C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C4×Q8×C11—41no—
25C4×Q8×C11—41no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41#66923—41no—
42#66923—41no—
43C11×C4⋊C8—41no—
44C11×C22⋊C8—22no—
45C11×#97—41no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55C4×C11⋊C8—41no—
56#11571—111nomaximal, Sylow
57C2×Q8×C11—22no—
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×C8×C11—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—42no—
84Dic11⋊C4—42no—
85Dic11⋊C4—42no—
86Dic11⋊C4—42no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—22no—
90C4×Dic11—22no—
91C2×C11⋊C8—42no—
92#2565—111no—
93#1467D1111yescharacteristic
94#1461—111no—
95#1325—112no—
96#1324—112no—
97C23×C11C2×C22⋊C411yescharacteristic
98Q8×C11—44no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
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—21no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11#9911yescharacteristic
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11#10112yes—
116C2×C4×C11#13112yes—
117C2×Dic11—22no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—41no—
124C2×Dic11—42no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C8×C11—82no—
129C11⋊C8—82no—
130C2×#125—111no—
131C2×C4×Q8C2×D1111yescharacteristic
132#432—21no—
133#431—221no—
134#398—221no—
135#398—221no—
136#391—111no—
137#391—111no—
138#387—221no—
139#387—221no—
140#384—111no—
141#382—111no—
142C4×C4⋊C4—111no—
143#324—21no—
144#324—112no—
145#324—221no—
146#324C2×D1112yes—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#40811yescharacteristic
150C22×C11C2×#9911yescharacteristic
151C22×C11C2×#10111yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160Dic11—42no—
161Dic11—81no—
162Dic11—81no—
163Dic11—81no—
164C22×Q8C4×D1111yescharacteristic
165#125—441no—
166#125—441no—
167C4×Q8—41no—
168C4×Q8—41no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4D4411yescharacteristic
177C2×C4⋊C4C22⋊D1111yescharacteristic
178C2×C4⋊C4C22×D1111yescharacteristic
179C2×C42—111no—
180C2×C42—111no—
181C2×C42C4×D1111yescharacteristic
182C2×C42D4411yescharacteristic
183C2×C42C22⋊D1111yescharacteristic
184C4⋊C8—41no—
185C4⋊C8—441no—
186C22⋊C8—22no—
187C22⋊C8—222no—
188#97—41no—
189C4×C8—441no—
190#95—221no—
191#95—221no—
192#95—221no—
193#95—221no—
194#95—221no—
195#95—221no—
196#95—221no—
197C2×C11—21no—
198C2×C11—21no—
199C2×C11#147211yescharacteristic
200C2×C11#212611yescharacteristic
201C2×C11#213311yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C22×C4—221no—
206C22×C4—221no—
207C22×C4—221no—
208C22×C4—221no—
209C22×C4(C2×D11)⋊C411yescharacteristic
210C22×C4(C2×D11)⋊C411yescharacteristic
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4(C2×D11)⋊C411yescharacteristic
213C22×C4C2×C4×D1111yescharacteristic
214C22×C4C2×D4411yescharacteristic
215C22×C4C2×C22⋊D1111yescharacteristic
216C2×C8—42no—
217C2×C8—442no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—442no—
224C4⋊C4—442no—
225C4⋊C4—442no—
226C4⋊C4—442no—
227C4⋊C4—441no—
228C4⋊C4—441no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—222no—
236C42—222no—
237C11#1157111yescharacteristic, complemented, Sylow
238C23C2×(C2×D11)⋊C411yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—222no—
255C2×C4—441no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—442no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4#6687011yescharacteristic
266C2×C4#6687011yescharacteristic
267C2×C4#6688812yes—
268C2×C4#6696012yes—
269C8—82no—
270C8—882no—
271C22—21no—
272C22—21no—
273C22C2×#6687011yescharacteristic
274C22#1062274211yescharacteristic
275C22C2×#6688811yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—442no—
285C4—881no—
286C4—881no—
287C4—881no—
288C2—21no—
289C2—21no—
290C2#1306698111yescharacteristic
291C2#1307027911yescharacteristic
292C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1467C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1467D11
hypocenterC11#11571
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
237. C11#11571semidirect

Maximal subgroups

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

subgroupindex
#130738032
#130669402
#130665612
#130665592
C11×#14672
#1157111