Finite Group Databasebeta

← #14666375

Subgroups — #14666375

Order 2816.

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

normal subgroups only

This group has 360 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#13076888C211yesmaximal, characteristic, complemented
2#13069845C211yesmaximal, characteristic
3#13067655C212yesmaximal
4#13066644C212yesmaximal, complemented
5C11×#1324C211yesmaximal, characteristic, complemented
6#10623041C2211yescharacteristic
7C11×#382C2211yescharacteristic
8#10622599C2212yes—
9#10622592—21no—
10#10622579—21no—
11#10622549—21no—
12C2×#66869—21no—
13#10622348—22no—
14#10622273—22no—
15#10622269—22no—
16C11×#324C2212yes—
17#10622168C2211yescharacteristic
18#10622108—22no—
19C2×#4339—21no—
20C22×Dic22—21no—
21C2×C11×C4⋊C4D411yescharacteristic
22C2×C11×C4⋊C4C2311yescharacteristic
23C2×C42×C11D411yescharacteristic
24#66983—22no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11D412yes—
28C2×Dic11⋊C4—22no—
29C2×#4318—21no—
30#66950—41no—
31#66948—41no—
32C11×C22⋊C8—22no—
33C11×#95—22no—
34C11⋊#95—22no—
35C11⋊#95—21no—
36C11⋊#95—22no—
37C11⋊#95—22no—
38C11⋊#95D412yes—
39#66885—42no—
40#66881—42no—
41#66874—41no—
42#66873—41no—
43#66869—42no—
44#12185—111nomaximal, Sylow
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11C2×D412yes—
49C2×C22⋊D11—41no—
50C22×Dic11—22no—
51C22×Dic11—22no—
52#4339—41no—
53#4339—41no—
54#4339—41no—
55#4339—41no—
56C2×D44—21no—
57C2×D44—22no—
58C2×C4×D11—41no—
59C2×Dic22—21no—
60C2×Dic22—82no—
61C2×Dic22—81no—
62C2×C8×C11—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C42×C11—21no—
66C42×C11SD1612yes—
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—22no—
69C4⋊Dic11—42no—
70C4⋊Dic11—81no—
71C4⋊Dic11—81no—
72Dic11⋊C4—82no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—41no—
76#2844—111no—
77#2040—111no—
78#1616—112no—
79#1353—112no—
80#1324D1111yescharacteristic, complemented
81C23×C11#12011yescharacteristic
82C22×D11—41no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11C2×SD1611yescharacteristic
93C2×C4×C11#13711yescharacteristic
94C22⋊D11—81no—
95C22⋊D11—81no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—41no—
102C2×Dic11—42no—
103D44—41no—
104D44—41no—
105D44—82no—
106C4×D11—81no—
107C4×D11—81no—
108Dic22—41no—
109Dic22—41no—
110Dic22—84no—
111C8×C11—82no—
112C11⋊C8—81no—
113#537—111no—
114#481—222no—
115C2×#104—221no—
116#417—221no—
117#400—112no—
118#400—222no—
119#395—222no—
120#395—221no—
121#382—221no—
122#382C2×D1111yescharacteristic
123#343—111no—
124#327—222no—
125#324C2×D1112yes—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11#44811yescharacteristic
129C22×C11#45411yescharacteristic
130C22×C11B(4,𝔽2)11yescharacteristic
131C2×D11—81no—
132C2×D11—81no—
133C2×D11—81no—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—42no—
137C4×C11—42no—
138C4×C11—81no—
139Dic11—82no—
140Dic11—81no—
141Dic11—82no—
142C2×#41—221no—
143C22×Q8—221no—
144C2×M16—221no—
145C22⋊Q8—441no—
146#121—222no—
147#121—441no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4—222no—
152C2×C4⋊C4D4411yescharacteristic
153C2×C4⋊C4C22×D1111yescharacteristic
154C2×C42D4411yescharacteristic
155#106—442no—
156#104—442no—
157#103—441no—
158#102—441no—
159#102—442no—
160C22⋊C8—22no—
161#95—22no—
162#95—112no—
163#95—222no—
164#95—221no—
165#95—222no—
166#95—222no—
167C2×C11—21no—
168C2×C11—21no—
169C2×C11#159911yescharacteristic
170C2×C11#220111yescharacteristic
171C2×C11#220211yescharacteristic
172D11—161no—
173#41—441no—
174#41—441no—
175#41—441no—
176#41—441no—
177C2×Q8—221no—
178C2×Q8—882no—
179C2×Q8—881no—
180C2×D4—221no—
181C2×D4—222no—
182C2×D4—441no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—222no—
186C22×C4—222no—
187C22×C4—441no—
188C22×C4C2×D4411yescharacteristic
189C22×C4D4×D1112yes—
190M16—441no—
191M16—441no—
192C2×C8—42no—
193C2×C8—441no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—222no—
197C4⋊C4—442no—
198C4⋊C4—882no—
199C4⋊C4—881no—
200C4⋊C4—881no—
201C22⋊C4—442no—
202C42—21no—
203C42#431412yes—
204C11#1218511yescharacteristic, complemented, Sylow
205C23—441no—
206C23#6693511yescharacteristic
207Q8—441no—
208Q8—441no—
209Q8—884no—
210D4—441no—
211D4—441no—
212D4—882no—
213D4—881no—
214D4—881no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—441no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—881no—
232C2×C4—881no—
233C2×C4C2×#431411yescharacteristic
234C2×C4#6696211yescharacteristic
235C8—82no—
236C8—881no—
237C22—21no—
238C22—21no—
239C22—881no—
240C22—881no—
241C22—881no—
242C22#1062235111yescharacteristic
243C22#1062235411yescharacteristic
244C22#1062236611yescharacteristic
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—81no—
250C4—882no—
251C4—881no—
252C4—882no—
253C2—21no—
254C2—21no—
255C2—1761no—
256C2#1306755811yescharacteristic
257C2#1307063111yescharacteristic
258C2#1307063411yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#1324D11
hypocenterC11#12185
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
1. #13076888C2semidirect
4. #13066644C2semidirect
5. C11×#1324C2semidirect
80. #1324D11semidirect
204. C11#12185semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130698452
#130676552
#130666442
C11×#13242
#1218511