Finite Group Databasebeta

← #14665981

Subgroups — #14665981

Order 2816.

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

normal subgroups only

This group has 470 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#13074281C211yesmaximal, characteristic, complemented
2#13069747C211yesmaximal, characteristic
3#13067570C212yesmaximal
4#13066638C212yesmaximal, complemented
5C11×#1317C211yesmaximal, characteristic, complemented
6C2×#66982—21no—
7#10623024C2211yescharacteristic
8C11×#381C2211yescharacteristic
9C4×C22⋊Dic11—21no—
10C2×#66870—21no—
11#10622562—21no—
12#10622560C2212yes—
13#10622351—22no—
14#10622268—22no—
15#10622259—22no—
16C11×#323C2212yes—
17#10622164C2211yescharacteristic
18#10622108—22no—
19C23×C4×C11D411yescharacteristic
20C22×C22⋊D11—21no—
21C22×Dic22D412yes—
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×Dic11⋊C4—22no—
32C2×Dic11⋊C4—41no—
33C2×C4×Dic11—21no—
34C2×C4×Dic11—21no—
35C2×#4314—42no—
36#66939—41no—
37#66935—41no—
38C11×C22⋊C8—22no—
39C11×#95—22no—
40C11⋊#95—21no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95D412yes—
44#66880—42no—
45#66870—42no—
46#12121—111nomaximal, Sylow
47C24×C11C2×D411yescharacteristic
48C23×D11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—41no—
53C22×C4×C11—41no—
54C22×C4×C11SD1612yescomplemented
55C22×C4×C11C2×D412yes—
56C2×C22⋊D11—41no—
57C2×C22⋊D11—41no—
58C2×C22⋊D11—41no—
59C2×C22⋊D11—41no—
60C2×C22⋊D11—41no—
61C2×C22⋊D11—41no—
62C22×Dic11—21no—
63C22×Dic11—22no—
64C22×Dic11—22no—
65C22×Dic11—41no—
66C2×D44—22no—
67C2×Dic22—42no—
68C2×Dic22—44no—
69C2×C8×C11—42no—
70C11×C22⋊C4—41no—
71C11×C22⋊C4—41no—
72C22⋊Dic11—22no—
73C22⋊Dic11—44no—
74C22⋊Dic11—41no—
75(C2×D11)⋊C4—42no—
76(C2×D11)⋊C4—44no—
77C4⋊Dic11—22no—
78C4⋊Dic11—81no—
79Dic11⋊C4—44no—
80Dic11⋊C4—44no—
81C4×Dic11—81no—
82C4×Dic11—81no—
83#4314—84no—
84#2607—111no—
85#2022—111no—
86#1601—112no—
87#1351—112no—
88#1317D1111yescharacteristic, complemented
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—42no—
92C23×C11#12011yescharacteristic
93C23×C11C2×SD1611yescharacteristic
94C23×C11#13711yescharacteristic
95C22×D11—41no—
96C22×D11—41no—
97C22×D11—41no—
98C22×D11—82no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—81no—
108C22⋊D11—81no—
109C22⋊D11—81no—
110C22⋊D11—81no—
111C22⋊D11—81no—
112C2×Dic11—24no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—41no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—41no—
120C2×Dic11—42no—
121C2×Dic11—41no—
122C2×Dic11—82no—
123D44—82no—
124Dic22—44no—
125Dic22—82no—
126C8×C11—82no—
127#534—111no—
128C2×#123—221no—
129#448—222no—
130C2×#99—221no—
131#399—221no—
132#393—112no—
133#391—222no—
134#387—222no—
135#381C2×D1111yescharacteristic
136C4×C22⋊C4—221no—
137#342—111no—
138#327—222no—
139#323C2×D1112yes—
140C22×C11—22no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—41no—
144C22×C11—41no—
145C22×C11—42no—
146C22×C11—81no—
147C22×C11#44811yescharacteristic
148C22×C11#45311yescharacteristic
149C22×C11B(4,𝔽2)11yescharacteristic
150C2×D11—82no—
151C2×D11—81no—
152C2×D11—82no—
153C2×D11—161no—
154C4×C11—42no—
155C4×C11—42no—
156C4×C11—81no—
157Dic11—44no—
158Dic11—82no—
159Dic11—82no—
160Dic11—81no—
161C22×Q8—112no—
162C22×D4—221no—
163C23×C4D4411yescharacteristic
164C2×SD16—442no—
165#123—441no—
166#123—442no—
167#123—442no—
168#121—222no—
169#120—441no—
170C2×C4⋊C4—222no—
171C2×C4⋊C4—221no—
172C2×C4⋊C4—441no—
173C2×C22⋊C4—221no—
174C2×C22⋊C4—222no—
175C2×C22⋊C4—441no—
176C2×C22⋊C4D4411yescharacteristic
177C2×C22⋊C4C22×D1111yescharacteristic
178C2×C42—221no—
179C2×C42—221no—
180#103—442no—
181#99—442no—
182C22⋊C8—22no—
183#95—22no—
184#95—112no—
185#95—222no—
186#95—221no—
187#95—222no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—41no—
191C2×C11—41no—
192C2×C11#159611yescharacteristic
193C2×C11#219712yes—
194D11—161no—
195C24—221no—
196C24C2×D4411yescharacteristic
197C2×Q8—442no—
198C2×Q8—444no—
199C2×D4—222no—
200C2×D4—441no—
201C2×D4—441no—
202C2×D4—441no—
203C2×D4—441no—
204C2×D4—441no—
205C2×D4—441no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—222no—
212C22×C4—221no—
213C22×C4—222no—
214C22×C4—441no—
215C22×C4#431412yescomplemented
216C22×C4D4×D1112yes—
217SD16—884no—
218C2×C8—42no—
219C4⋊C4—222no—
220C4⋊C4—444no—
221C4⋊C4—444no—
222C4⋊C4—881no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—222no—
226C22⋊C4—442no—
227C22⋊C4—444no—
228C22⋊C4—444no—
229C22⋊C4—441no—
230C42—881no—
231C42—881no—
232C11#1212111yescharacteristic, complemented, Sylow
233C23—21no—
234C23—21no—
235C23—42no—
236C23—441no—
237C23—441no—
238C23—441no—
239C23—882no—
240C23#6693511yescharacteristic
241C23C2×#431411yescharacteristic
242C23#6696211yescharacteristic
243Q8—444no—
244Q8—882no—
245D4—882no—
246D4—881no—
247D4—881no—
248D4—881no—
249D4—881no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—81no—
259C2×C4—224no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—441no—
265C2×C4—442no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—442no—
269C2×C4—882no—
270C8—82no—
271C22—22no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—81no—
278C22—882no—
279C22—882no—
280C22—881no—
281C22—1761no—
282C22#1062235111yescharacteristic
283C22#1062235411yescharacteristic
284C22#1062236011yescharacteristic
285C4—42no—
286C4—42no—
287C4—81no—
288C4—444no—
289C4—882no—
290C4—882no—
291C4—881no—
292C2—21no—
293C2—21no—
294C2—41no—
295C2—41no—
296C2—1761no—
297C2#1306754111yescharacteristic
298C2#1307060712yes—
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#12121
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. #13074281C2semidirect
4. #13066638C2semidirect
5. C11×#1317C2semidirect
54. C22×C4×C11SD16semidirect
88. #1317D11semidirect
215. C22×C4#4314semidirect
232. C11#12121semidirect

Maximal subgroups

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

subgroupindex
#130742812
#130697472
#130675702
#130666382
C11×#13172
#1212111