Finite Group Databasebeta

← #14665833

Subgroups — #14665833

Order 2816.

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

normal subgroups only

This group has 458 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#13076653C211yesmaximal, characteristic, complemented
2#13069747C211yesmaximal, characteristic
3#13067604C212yesmaximal
4#13066617C212yesmaximal, complemented
5C11×#1317C211yesmaximal, characteristic, complemented
6C2×#66982—21no—
7C2×#66977—21no—
8#10623024C2211yescharacteristic
9C11×#381C2211yescharacteristic
10C2×#66870—21no—
11#10622566—21no—
12#10622566C2212yes—
13#10622349—22no—
14#10622272—22no—
15#10622269—22no—
16C11×#323C2212yes—
17#10622164C2211yescharacteristic
18#10622108—22no—
19C23×C4×C11D411yescharacteristic
20C22×C22⋊D11—21no—
21C22×Dic22—21no—
22C2×C11×C22⋊C4D411yescharacteristic
23C2×C11×C22⋊C4C2311yescharacteristic
24C2×C22⋊Dic11—21no—
25C2×C22⋊Dic11—22no—
26#66983—22no—
27#66982—42no—
28#66982—42no—
29C2×(C2×D11)⋊C4—41no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11D412yes—
33#66977—42no—
34#66977—42no—
35C2×Dic11⋊C4—22no—
36C2×Dic11⋊C4—41no—
37#66939—41no—
38#66935—41no—
39C11×C22⋊C8—22no—
40C11×#95—22no—
41C11⋊#95—22no—
42C11⋊#95—21no—
43C11⋊#95—22no—
44C11⋊#95D412yes—
45#66885—42no—
46#66882—42no—
47#66870—42no—
48#12095—111nomaximal, Sylow
49C24×C11C2×D411yescharacteristic
50C23×D11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11D812yes—
57C22×C4×C11C2×D412yes—
58C2×C22⋊D11—41no—
59C2×C22⋊D11—41no—
60C2×C22⋊D11—41no—
61C2×C22⋊D11—41no—
62C2×C22⋊D11—41no—
63C2×C22⋊D11—41no—
64C22×Dic11—21no—
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—41no—
68C2×D44—22no—
69C2×Dic22—42no—
70C2×Dic22—81no—
71C2×Dic22—81no—
72C2×C8×C11—42no—
73C11×C22⋊C4—41no—
74C11×C22⋊C4—41no—
75C22⋊Dic11—22no—
76C22⋊Dic11—42no—
77C22⋊Dic11—41no—
78C22⋊Dic11—42no—
79(C2×D11)⋊C4—42no—
80(C2×D11)⋊C4—44no—
81C4⋊Dic11—22no—
82C4⋊Dic11—42no—
83C4⋊Dic11—42no—
84C4⋊Dic11—81no—
85Dic11⋊C4—44no—
86Dic11⋊C4—44no—
87#2817—111no—
88#2022—111no—
89#1607—112no—
90#1344—112no—
91#1317D1111yescharacteristic, complemented
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—42no—
95C23×C11#12011yescharacteristic
96C23×C11C2×D811yescharacteristic
97C23×C11AGL(1,ℤ/8)11yescharacteristic
98C22×D11—41no—
99C22×D11—41no—
100C22×D11—41no—
101C22×D11—82no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—41no—
110C2×C4×C11—81no—
111C22⋊D11—81no—
112C22⋊D11—81no—
113C22⋊D11—81no—
114C22⋊D11—81no—
115C2×Dic11—41no—
116C2×Dic11—42no—
117C2×Dic11—44no—
118C2×Dic11—41no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—41no—
123C2×Dic11—42no—
124C2×Dic11—82no—
125D44—82no—
126Dic22—84no—
127C8×C11—82no—
128#534—111no—
129C2×#123—221no—
130C2×C22⋊Q8—221no—
131#480—222no—
132C2×#99—221no—
133#400—222no—
134#397—112no—
135#397—221no—
136#395—222no—
137#381C2×D1111yescharacteristic
138#342—111no—
139#327—222no—
140#323C2×D1112yes—
141C22×C11—22no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—42no—
147C22×C11—81no—
148C22×C11#44711yescharacteristic
149C22×C11#45311yescharacteristic
150C22×C11B(4,𝔽2)11yescharacteristic
151C2×D11—82no—
152C2×D11—81no—
153C2×D11—82no—
154C2×D11—161no—
155C4×C11—42no—
156C4×C11—42no—
157C4×C11—81no—
158Dic11—82no—
159Dic11—82no—
160Dic11—82no—
161Dic11—81no—
162C22×Q8—221no—
163C22×D4—221no—
164C23×C4D4411yescharacteristic
165#123—441no—
166#123—442no—
167#123—442no—
168C22⋊Q8—442no—
169C22⋊Q8—442no—
170#121—222no—
171#120—441no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—222no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—441no—
177C2×C22⋊C4—221no—
178C2×C22⋊C4—222no—
179C2×C22⋊C4—441no—
180C2×C22⋊C4D4411yescharacteristic
181C2×C22⋊C4C22×D1111yescharacteristic
182#107—442no—
183#102—442no—
184#99—442no—
185C22⋊C8—22no—
186#95—22no—
187#95—112no—
188#95—222no—
189#95—221no—
190#95—222no—
191C2×C11—21no—
192C2×C11—21no—
193C2×C11—41no—
194C2×C11—41no—
195C2×C11#159511yescharacteristic
196C2×C11#220112yes—
197D11—161no—
198C24—221no—
199C24C2×D4411yescharacteristic
200C2×Q8—442no—
201C2×Q8—881no—
202C2×Q8—881no—
203C2×D4—222no—
204C2×D4—441no—
205C2×D4—441no—
206C2×D4—441no—
207C2×D4—441no—
208C2×D4—441no—
209C2×D4—441no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—221no—
216C22×C4—222no—
217C22×C4—222no—
218C22×C4—441no—
219C22×C4D8812yes—
220C22×C4D4×D1112yes—
221C2×C8—42no—
222C4⋊C4—222no—
223C4⋊C4—442no—
224C4⋊C4—444no—
225C4⋊C4—442no—
226C4⋊C4—444no—
227C4⋊C4—881no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—222no—
231C22⋊C4—442no—
232C22⋊C4—444no—
233C22⋊C4—442no—
234C22⋊C4—441no—
235C22⋊C4—442no—
236C11#1209511yescharacteristic, complemented, Sylow
237C23—21no—
238C23—21no—
239C23—42no—
240C23—441no—
241C23—441no—
242C23—441no—
243C23—882no—
244C23#6693511yescharacteristic
245C23C2×D8811yescharacteristic
246C23#6696111yescharacteristic
247Q8—884no—
248D4—882no—
249D4—881no—
250D4—881no—
251D4—881no—
252D4—881no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—442no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—444no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4—441no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4—882no—
272C8—82no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—81no—
280C22—882no—
281C22—881no—
282C22—882no—
283C22—1761no—
284C22#1062234511yescharacteristic
285C22#1062235411yescharacteristic
286C22#1062236011yescharacteristic
287C4—42no—
288C4—42no—
289C4—81no—
290C4—882no—
291C4—882no—
292C4—881no—
293C4—882no—
294C2—21no—
295C2—21no—
296C2—41no—
297C2—41no—
298C2—1761no—
299C2#1306753611yescharacteristic
300C2#1307063012yes—
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1317C2
socleC22×C11B(4,𝔽2)
prime radical#10623024C22
hypercenter#1317D11
hypocenterC11#12095
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
1. #13076653C2semidirect
4. #13066617C2semidirect
5. C11×#1317C2semidirect
91. #1317D11semidirect
236. C11#12095semidirect

Maximal subgroups

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

subgroupindex
#130766532
#130697472
#130676042
#130666172
C11×#13172
#1209511