Finite Group Databasebeta

← #14665830

Subgroups — #14665830

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#13067602C212yesmaximal
3#13066615C212yesmaximal, complemented
4#13066546C211yesmaximal, characteristic, complemented
5C11×#2022C211yesmaximal, characteristic
6C11×#534C2211yescharacteristic
7C2×C11×#123—21no—
8C2×#66977—21no—
9C2×C11×#99—21no—
10C11×#381C2211yescharacteristic
11#10622646—22no—
12#10622566—21no—
13#10622566C2212yes—
14#10622272—22no—
15#10622269—22no—
16C11×#342C2211yescharacteristic
17#10622175—22no—
18#10622163C2212yes—
19C22×D4×C11—21no—
20C23×C4×C11D411yescharacteristic
21C22×Dic22—21no—
22C11×#123—42no—
23C11×#123—41no—
24C11×#123—42no—
25C11×#121—22no—
26C11×#120—41no—
27C2×C11×C4⋊C4—41no—
28C2×C11×C22⋊C4—21no—
29C2×C11×C22⋊C4—41no—
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D412yes—
36#66977—42no—
37#66977—42no—
38C2×Dic11⋊C4—22no—
39C11×#99—42no—
40C11×#95—22no—
41#66896—42no—
42C11⋊#95—22no—
43C11⋊#95—21no—
44C11⋊#95—22no—
45C11⋊#95D412yes—
46C22⋊(C11⋊C8)—22no—
47#66871—42no—
48#12095—111nomaximal, Sylow
49C24×C11—21no—
50C24×C11C2×D411yescharacteristic
51C2×D4×C11—22no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11D812yes—
66C22×C4×C11C2×D412yes—
67C22×Dic11—22no—
68C22×Dic11—22no—
69C2×Dic22—42no—
70C2×Dic22—81no—
71C2×Dic22—81no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—44no—
74C11×C22⋊C4—22no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—44no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C22⋊Dic11—42no—
81C22⋊Dic11—42no—
82C4⋊Dic11—42no—
83C4⋊Dic11—42no—
84C4⋊Dic11—81no—
85Dic11⋊C4—44no—
86C2×C11⋊C8—42no—
87#2817—111no—
88#2022D1111yescharacteristic
89#1607—112no—
90#1344—112no—
91#1317—111no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—42no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—82no—
99C23×C11#12011yescharacteristic
100C23×C11C2×D811yescharacteristic
101C23×C11AGL(1,ℤ/8)11yescharacteristic
102D4×C11—82no—
103D4×C11—81no—
104D4×C11—81no—
105D4×C11—81no—
106D4×C11—81no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—81no—
120C2×C4×C11—82no—
121C2×Dic11—44no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126Dic22—84no—
127C11⋊C8—82no—
128#534C2×D1111yescharacteristic
129C2×#123—21no—
130C2×C22⋊Q8—221no—
131#480—222no—
132C2×#99—21no—
133#400—222no—
134#397—112no—
135#397—221no—
136#395—222no—
137#381C2×D1111yescharacteristic
138#342C2×D1111yescharacteristic
139#327—222no—
140#323—112no—
141C22×C11—22no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—42no—
147C22×C11—81no—
148C22×C11—82no—
149C22×C11—81no—
150C22×C11—82no—
151C22×C11—161no—
152C22×C11#44711yescharacteristic
153C22×C11#45311yescharacteristic
154C22×C11B(4,𝔽2)11yescharacteristic
155C4×C11—42no—
156C4×C11—42no—
157C4×C11—81no—
158C4×C11—82no—
159C4×C11—81no—
160Dic11—82no—
161Dic11—82no—
162C22×Q8—221no—
163C22×D4—21no—
164C23×C4C22⋊D1111yescharacteristic
165#123—42no—
166#123—41no—
167#123—42no—
168C22⋊Q8—442no—
169C22⋊Q8—442no—
170#121—22no—
171#120—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—221no—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—41no—
179C2×C22⋊C4—222no—
180C2×C22⋊C4C22⋊D1111yescharacteristic
181C2×C22⋊C4C22×D1111yescharacteristic
182#107—442no—
183#102—442no—
184#99—42no—
185C22⋊C8—222no—
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—161no—
196C2×C11#159511yescharacteristic
197C2×C11#220112yes—
198C24—21no—
199C24C2×C22⋊D1111yescharacteristic
200C2×Q8—442no—
201C2×Q8—881no—
202C2×Q8—881no—
203C2×D4—22no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—222no—
218C22×C4—222no—
219C22×C4#432312yes—
220C22×C4D4×D1112yes—
221C2×C8—442no—
222C4⋊C4—22no—
223C4⋊C4—44no—
224C4⋊C4—442no—
225C4⋊C4—444no—
226C4⋊C4—442no—
227C4⋊C4—881no—
228C22⋊C4—22no—
229C22⋊C4—41no—
230C22⋊C4—42no—
231C22⋊C4—44no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—442no—
235C22⋊C4—442no—
236C11#1209511yescharacteristic, complemented, Sylow
237C23—21no—
238C23—21no—
239C23—42no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—82no—
244C23C2×#432311yescharacteristic
245C23#6699011yescharacteristic
246C23#6700211yescharacteristic
247Q8—884no—
248D4—82no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—81no—
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—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—82no—
267C2×C4—444no—
268C2×C4—442no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4—442no—
272C8—882no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—81no—
280C22—82no—
281C22—81no—
282C22—82no—
283C22—161no—
284C22#1062264511yescharacteristic
285C22#1062264911yescharacteristic
286C22#1062269011yescharacteristic
287C4—42no—
288C4—42no—
289C4—81no—
290C4—82no—
291C4—81no—
292C4—882no—
293C4—882no—
294C2—21no—
295C2—21no—
296C2—41no—
297C2—41no—
298C2—161no—
299C2#1306753311yescharacteristic
300C2#1307062712yes—
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2022C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#534C22
hypercenter#2022D11
hypocenterC11#12095
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #13076653C2semidirect
3. #13066615C2semidirect
4. #13066546C2semidirect
236. C11#12095semidirect

Maximal subgroups

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

subgroupindex
#130766532
#130676022
#130666152
#130665462
C11×#20222
#1209511