Finite Group Databasebeta

← #14666185

Subgroups — #14666185

Order 2816.

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

normal subgroups only

This group has 424 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#13069840C211yesmaximal, characteristic
2#13067618C212yesmaximal
3#13066622C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2582C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11—21no—
7#10623041C2211yescharacteristic
8C11×#398—21no—
9C11×#398C2212yes—
10C11×#391—22no—
11C11×#389—22no—
12C11×#384C2211yescharacteristic
13#10622580—22no—
14#10622579—21no—
15C2×#66869—21no—
16#10622168C2211yescharacteristic
17#10622166C2212yes—
18#10622089—22no—
19C22×Q8×C11—21no—
20C2×#4339—21no—
21C4×Q8×C11—42no—
22C4×Q8×C11—42no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11—22no—
31C2×C42×C11D411yescharacteristic
32#66983—22no—
33C2×#4318—21no—
34#66950—41no—
35#66948—41no—
36C11×#95—22no—
37C11×#95—21no—
38C11×#95—22no—
39C11×#95D412yes—
40C22⋊(C11⋊C8)—22no—
41#66874—41no—
42#66873—41no—
43#66873—42no—
44#66871—42no—
45#66869—42no—
46#12153—111nomaximal, Sylow
47C2×Q8×C11—24no—
48C2×Q8×C11—42no—
49C2×Q8×C11—42no—
50C22×C4×C11—21no—
51C22×C4×C11—22no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D412yes—
56C2×C22⋊D11—41no—
57#4339—41no—
58#4339—41no—
59#4339—41no—
60#4339—41no—
61C2×D44—21no—
62C2×D44—22no—
63C2×C4×D11—41no—
64C2×Dic22—21no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—44no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—81no—
73C42×C11—21no—
74C42×C11—44no—
75C42×C11D812yes—
76(C2×D11)⋊C4—42no—
77C4⋊Dic11—22no—
78#4318—41no—
79#4318—41no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—41no—
82#2582D1111yescharacteristic, complemented
83#2039—111no—
84#1610—112no—
85#1346—112no—
86#1325—111no—
87C23×C11#12011yescharacteristic
88C22×D11—41no—
89Q8×C11—48no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—24no—
96C2×C4×C11—22no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
107C22⋊D11—81no—
108C22⋊D11—81no—
109C2×Dic11—41no—
110D44—41no—
111D44—41no—
112D44—82no—
113C4×D11—81no—
114C4×D11—81no—
115Dic22—41no—
116Dic22—41no—
117C11⋊C8—81no—
118C11⋊C8—82no—
119#537—111no—
120C2×C4×Q8—21no—
121#480—222no—
122C2×#104—221no—
123#417—221no—
124#398—21no—
125#398C2×D1112yes—
126#391—22no—
127#389—22no—
128#384C2×D1111yescharacteristic
129#343—111no—
130#327—222no—
131#324—112no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11#44711yescharacteristic
135C22×C11#45411yescharacteristic
136C22×C11B(4,𝔽2)11yescharacteristic
137C2×D11—81no—
138C2×D11—81no—
139C2×D11—81no—
140C4×C11—24no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—44no—
144C4×C11—42no—
145C4×C11—82no—
146C4×C11—81no—
147Dic11—81no—
148C2×#41—221no—
149C22×Q8—21no—
150C2×M16—221no—
151C22⋊Q8—441no—
152#121—222no—
153#121—441no—
154C4×Q8—42no—
155C4×Q8—42no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4C22⋊D1111yescharacteristic
161C2×C4⋊C4C22⋊D1112yes—
162C2×C4⋊C4C22×D1111yescharacteristic
163C2×C42—22no—
164C2×C42C22⋊D1111yescharacteristic
165#107—442no—
166#104—442no—
167#103—441no—
168#102—441no—
169#102—442no—
170C22⋊C8—222no—
171#95—22no—
172#95—21no—
173#95—22no—
174#95C22⋊D1112yes—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11#159811yescharacteristic
178C2×C11#219811yescharacteristic
179C2×C11#220511yescharacteristic
180D11—161no—
181#41—441no—
182#41—441no—
183#41—441no—
184#41—441no—
185C2×Q8—24no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—221no—
189C2×D4—221no—
190C2×D4—222no—
191C2×D4—441no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—441no—
197C22×C4C2×C22⋊D1111yescharacteristic
198C22×C4C2×C22⋊D1112yes—
199M16—441no—
200M16—441no—
201C2×C8—442no—
202C2×C8—441no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—81no—
211C4⋊C4—222no—
212C22⋊C4—442no—
213C42—21no—
214C42—44no—
215C42#432312yes—
216C11#1215311yescharacteristic, complemented, Sylow
217C23—441no—
218C23#6700611yescharacteristic
219Q8—48no—
220Q8—441no—
221Q8—441no—
222D4—441no—
223D4—441no—
224D4—882no—
225D4—881no—
226D4—881no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—441no—
243C2×C4—881no—
244C2×C4—881no—
245C2×C4C2×#432311yescharacteristic
246C2×C4#6698511yescharacteristic
247C8—881no—
248C8—882no—
249C22—21no—
250C22—21no—
251C22—881no—
252C22—881no—
253C22—881no—
254C22#1062283011yescharacteristic
255C22#1062285711yescharacteristic
256C22#1062285811yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—42no—
262C4—81no—
263C4—82no—
264C4—881no—
265C2—21no—
266C2—21no—
267C2—1761no—
268C2#1306755111yescharacteristic
269C2#1307061211yescharacteristic
270C2#1307064611yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2582C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#2582D11
hypocenterC11#12153
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2582

Complements

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

NH ≅ G/Ntype
3. #13066622C2semidirect
4. #13066562C2semidirect
5. C11×#2582C2semidirect
82. #2582D11semidirect
216. C11#12153semidirect

Maximal subgroups

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

subgroupindex
#130698402
#130676182
#130666222
#130665622
C11×#25822
#1215311