Finite Group Databasebeta

← #14666373

Subgroups — #14666373

Order 2816.

360 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069845C211yesmaximal, characteristic
2#13067652C212yesmaximal
3#13066643C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#2844C211yesmaximal, characteristic, complemented
6#10623041C2211yescharacteristic
7C11×#400—22no—
8C11×#400C2212yes—
9C11×#395—22no—
10C11×#395—21no—
11C11×#382—21no—
12C11×#382C2211yescharacteristic
13#10622581—22no—
14#10622579—21no—
15C2×#66869—21no—
16#10622168C2211yescharacteristic
17#10622166C2212yes—
18#10622089—22no—
19C22×Q8×C11—21no—
20C2×#4339—21no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4D412yes—
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C42×C11D411yescharacteristic
28#66983—22no—
29C2×#4318—21no—
30#66950—41no—
31#66948—41no—
32C11×#95—22no—
33C11×#95—21no—
34C11×#95—22no—
35C11×#95—22no—
36C11×#95—22no—
37C11×#95D412yes—
38C22⋊(C11⋊C8)—22no—
39#66874—41no—
40#66873—41no—
41#66873—42no—
42#66872—42no—
43#66869—42no—
44#12185—111nomaximal, Sylow
45C2×Q8×C11—82no—
46C2×Q8×C11—81no—
47C22×C4×C11—21no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—21no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C2×C22⋊D11—41no—
54#4339—41no—
55#4339—41no—
56#4339—41no—
57#4339—41no—
58C2×D44—21no—
59C2×D44—22no—
60C2×C4×D11—41no—
61C2×Dic22—21no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—81no—
66C11×C4⋊C4—81no—
67C11×C4⋊C4—82no—
68C42×C11—21no—
69C42×C11SD1612yes—
70(C2×D11)⋊C4—42no—
71C4⋊Dic11—22no—
72#4318—41no—
73#4318—41no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—41no—
76#2844D1111yescharacteristic, complemented
77#2040—111no—
78#1616—112no—
79#1353—112no—
80#1324—111no—
81C23×C11#12011yescharacteristic
82C22×D11—41no—
83Q8×C11—84no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—41no—
99C2×C4×C11C2×SD1611yescharacteristic
100C2×C4×C11#13711yescharacteristic
101C22⋊D11—81no—
102C22⋊D11—81no—
103C2×Dic11—41no—
104D44—41no—
105D44—41no—
106D44—82no—
107C4×D11—81no—
108C4×D11—81no—
109Dic22—41no—
110Dic22—41no—
111C11⋊C8—81no—
112C11⋊C8—82no—
113#537—111no—
114#481—222no—
115C2×#104—221no—
116#417—221no—
117#400—22no—
118#400C2×D1112yes—
119#395—22no—
120#395—21no—
121#382—21no—
122#382C2×D1111yescharacteristic
123#343—111no—
124#327—222no—
125#324—112no—
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—82no—
139C4×C11—82no—
140C4×C11—81no—
141Dic11—81no—
142C2×#41—221no—
143C22×Q8—21no—
144C2×M16—221no—
145C22⋊Q8—441no—
146#121—222no—
147#121—441no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4C22⋊D1111yescharacteristic
152C2×C4⋊C4C22⋊D1112yes—
153C2×C4⋊C4C22×D1111yescharacteristic
154C2×C42C22⋊D1111yescharacteristic
155#106—442no—
156#104—442no—
157#103—441no—
158#102—441no—
159#102—442no—
160C22⋊C8—222no—
161#95—22no—
162#95—21no—
163#95—22no—
164#95—22no—
165#95—22no—
166#95C22⋊D1112yes—
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—82no—
178C2×Q8—81no—
179C2×Q8—221no—
180C2×D4—221no—
181C2×D4—222no—
182C2×D4—441no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—21no—
187C22×C4—441no—
188C22×C4C2×C22⋊D1111yescharacteristic
189C22×C4C2×C22⋊D1112yes—
190M16—441no—
191M16—441no—
192C2×C8—442no—
193C2×C8—441no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—82no—
200C4⋊C4—222no—
201C22⋊C4—442no—
202C42—21no—
203C42#432512yes—
204C11#1218511yescharacteristic, complemented, Sylow
205C23—441no—
206C23#6700611yescharacteristic
207Q8—84no—
208Q8—441no—
209Q8—441no—
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—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—441no—
231C2×C4—881no—
232C2×C4—881no—
233C2×C4C2×#432511yescharacteristic
234C2×C4#6699511yescharacteristic
235C8—881no—
236C8—882no—
237C22—21no—
238C22—21no—
239C22—881no—
240C22—881no—
241C22—881no—
242C22#1062284011yescharacteristic
243C22#1062285711yescharacteristic
244C22#1062285811yescharacteristic
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4—881no—
253C2—21no—
254C2—21no—
255C2—1761no—
256C2#1306755611yescharacteristic
257C2#1307062911yescharacteristic
258C2#1307063311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2844C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#2844D11
hypocenterC11#12185
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2844

Complements

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

NH ≅ G/Ntype
3. #13066643C2semidirect
4. #13066560C2semidirect
5. C11×#2844C2semidirect
76. #2844D11semidirect
204. C11#12185semidirect

Maximal subgroups

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

subgroupindex
#130698452
#130676522
#130666432
#130665602
C11×#28442
#1218511