Finite Group Databasebeta

← #14666010

Subgroups — #14666010

Order 2816.

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

normal subgroups only

This group has 454 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#13076562C211yesmaximal, characteristic, complemented
2#13067653C212yesmaximal, complemented
3#13066642C212yesmaximal, complemented
4#13066548C211yesmaximal, characteristic, complemented
5C11×#2006C211yesmaximal, characteristic
6C2×C11×AGL(1,ℤ/8)—21no—
7C11×#537C2211yescharacteristic
8C2×C11×#104—21no—
9C11×#390C2211yescharacteristic
10#10622833—21no—
11#10622647—22no—
12#10622599C2212yes—
13#10622563—22no—
14#10622560—22no—
15#10622542—21no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×D4×C11D411yescharacteristic
21C23×Dic11—21no—
22C22×Dic22—21no—
23C11×AGL(1,ℤ/8)—42no—
24C11×AGL(1,ℤ/8)—42no—
25C2×C11×SD16—41no—
26C2×C11×D8—41no—
27C2×C11×M16—21no—
28C11×C22⋊Q8—41no—
29C11×#121—22no—
30C11×#121—41no—
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—22no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D412yes—
38C11×#104—42no—
39#66896—42no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95D412yes—
44C22⋊(C11⋊C8)—22no—
45#66872—42no—
46#12127—111nomaximal, Sylow
47C24×C11—21no—
48C11×#41—41no—
49C11×#41—41no—
50C11×#41—41no—
51C11×#41—41no—
52C2×Q8×C11—21no—
53C2×D4×C11—21no—
54C2×D4×C11—22no—
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11SD1612yes—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C22×Dic11—82no—
67C22×Dic11—81no—
68C2×Dic22—42no—
69C2×Dic22—81no—
70C2×Dic22—81no—
71C11×SD16—44no—
72C11×D8—44no—
73C11×M16—22no—
74C11×M16—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—44no—
79C11×C22⋊C4—42no—
80C42×C11—41no—
81C22⋊Dic11—82no—
82C22⋊Dic11—81no—
83C4⋊Dic11—42no—
84C4⋊Dic11—81no—
85C2×C11⋊C8—42no—
86#2804—111no—
87#2006D1111yescharacteristic
88#1616—112no—
89#1353—112no—
90#1318—111no—
91C23×C11—22no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11#12011yescharacteristic
98Q8×C11—41no—
99Q8×C11—41no—
100D4×C11—42no—
101D4×C11—41no—
102D4×C11—41no—
103D4×C11—81no—
104D4×C11—82no—
105D4×C11—81no—
106D4×C11—81no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11C2×SD1611yescharacteristic
118C2×C4×C11#13711yescharacteristic
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—84no—
126Dic22—84no—
127C8×C11—42no—
128C11⋊C8—82no—
129C2×AGL(1,ℤ/8)—21no—
130#537C2×D1111yescharacteristic
131#481—222no—
132C2×#104—21no—
133#400—112no—
134#393—222no—
135#391—221no—
136#390C2×D1111yescharacteristic
137#386—221no—
138#385—222no—
139#343C2×D1111yescharacteristic
140#327—222no—
141#324—112no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—44no—
145C22×C11—42no—
146C22×C11—82no—
147C22×C11—81no—
148C22×C11—81no—
149C22×C11—81no—
150C22×C11—81no—
151C22×C11—81no—
152C22×C11#44811yescharacteristic
153C22×C11#45311yescharacteristic
154C22×C11B(4,𝔽2)11yescharacteristic
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—42no—
158C4×C11—42no—
159C4×C11—81no—
160Dic11—82no—
161Dic11—82no—
162C2×#41—21no—
163C22×Q8—221no—
164C22×D4C22⋊D1111yescharacteristic
165C23×C4—221no—
166AGL(1,ℤ/8)—42no—
167AGL(1,ℤ/8)—42no—
168C2×SD16—41no—
169C2×D8—41no—
170C2×M16—21no—
171C22⋊Q8—41no—
172#121—22no—
173#121—41no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4C22×D1111yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—222no—
179C2×C22⋊C4—221no—
180C2×C42C22⋊D1111yescharacteristic
181#106—442no—
182#104—42no—
183#102—442no—
184C22⋊C8—222no—
185#95—112no—
186#95—222no—
187#95—222no—
188#95—222no—
189C2×C11—21no—
190C2×C11—21no—
191C2×C11—82no—
192C2×C11—161no—
193C2×C11#159611yescharacteristic
194C2×C11#219811yescharacteristic
195C2×C11#220211yescharacteristic
196C24—21no—
197#41—41no—
198#41—41no—
199#41—41no—
200#41—41no—
201C2×Q8—21no—
202C2×Q8—442no—
203C2×Q8—881no—
204C2×Q8—881no—
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4#432412yes—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—222no—
215C22×C4—222no—
216C22×C4—882no—
217C22×C4—881no—
218C22×C4D4×D1112yes—
219C22×C4C2×C22⋊D1111yescharacteristic
220SD16—44no—
221D8—44no—
222M16—22no—
223M16—41no—
224C2×C8—41no—
225C2×C8—442no—
226C4⋊C4—22no—
227C4⋊C4—41no—
228C4⋊C4—442no—
229C4⋊C4—881no—
230C22⋊C4—44no—
231C22⋊C4—42no—
232C22⋊C4—882no—
233C22⋊C4—881no—
234C42—41no—
235C11#1212711yescharacteristic, complemented, Sylow
236C23—22no—
237C23—42no—
238C23—42no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23#6699011yescharacteristic
243Q8—41no—
244Q8—41no—
245Q8—884no—
246D4—42no—
247D4—41no—
248D4—41no—
249D4—81no—
250D4—82no—
251D4—81no—
252D4—81no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4—442no—
269C2×C4—884no—
270C2×C4C2×#432411yescharacteristic
271C2×C4#6700411yescharacteristic
272C8—42no—
273C8—882no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—42no—
278C22—82no—
279C22—81no—
280C22—81no—
281C22—81no—
282C22—81no—
283C22—81no—
284C22#1062264511yescharacteristic
285C22#1062265311yescharacteristic
286C22#1062269011yescharacteristic
287C4—21no—
288C4—21no—
289C4—42no—
290C4—42no—
291C4—81no—
292C4—882no—
293C4—882no—
294C2—21no—
295C2—21no—
296C2—82no—
297C2—161no—
298C2#1306753811yescharacteristic
299C2#1307061111yescharacteristic
300C2#1307063211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2006C2
socleC22×C11B(4,𝔽2)
hypercenter#2006D11
hypocenterC11#12127
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2006

Complements

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

NH ≅ G/Ntype
1. #13076562C2semidirect
2. #13067653C2semidirect
3. #13066642C2semidirect
4. #13066548C2semidirect
235. C11#12127semidirect

Maximal subgroups

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

subgroupindex
#130765622
#130676532
#130666422
#130665482
C11×#20062
#1212711