Finite Group Databasebeta

← #14666790

Subgroups — #14666790

Order 2816.

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

normal subgroups only

This group has 454 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#13069966C211yesmaximal, characteristic, complemented
2#13067555C212yesmaximal, complemented
3#13066619C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#2819C211yesmaximal, characteristic
6C2×C11×#124—21no—
7#10623031C2211yescharacteristic
8C11×#394—21no—
9C11×#394C2212yes—
10C11×#393—22no—
11C11×#392—22no—
12C11×#382C2211yescharacteristic
13#10622831—22no—
14#10622577—21no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C22×Q8×C11—21no—
20C22×D4×C11—21no—
21C22×D4×C11—21no—
22C22×D4×C11D412yes—
23C11×#124—42no—
24C11×#124—42no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11D411yescharacteristic
32C2×#4324—42no—
33#66979—21no—
34#66977—22no—
35C2×#4318—21no—
36#66943—41no—
37#66941—41no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95D412yes—
41#66896—42no—
42C22⋊(C11⋊C8)—22no—
43#66872—41no—
44#66871—41no—
45#12250—111nomaximal, Sylow
46C24×C11—22no—
47C2×Q8×C11—42no—
48C2×Q8×C11—81no—
49C2×Q8×C11—81no—
50C2×D4×C11—42no—
51C2×D4×C11—42no—
52C2×D4×C11—82no—
53C2×D4×C11—81no—
54C2×D4×C11—81no—
55C2×D4×C11—82no—
56C2×D4×C11—81no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D412yes—
62C2×Dic22—22no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C22⋊C4—44no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—82no—
69C11×C22⋊C4—82no—
70C42×C11—21no—
71C42×C11SD1612yescomplemented
72C22⋊Dic11—41no—
73#4324—84no—
74C4⋊Dic11—21no—
75C4⋊Dic11—21no—
76C4⋊Dic11—22no—
77Dic11⋊C4—42no—
78C4×Dic11—41no—
79#4318—22no—
80#4318—41no—
81C2×C11⋊C8—41no—
82C2×C11⋊C8—42no—
83#2819D1111yescharacteristic
84#2061—111no—
85#1599—112no—
86#1345—112no—
87#1324—111no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11#12011yescharacteristic
96Q8×C11—84no—
97D4×C11—44no—
98D4×C11—82no—
99D4×C11—84no—
100D4×C11—84no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11C2×SD1611yescharacteristic
114C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
115C2×Dic11—41no—
116C2×Dic11—41no—
117Dic22—82no—
118C11⋊C8—42no—
119C11⋊C8—82no—
120#544—111no—
121C2×#124—21no—
122#450—222no—
123#428—221no—
124#394—21no—
125#394C2×D1112yes—
126#393—22no—
127#392—22no—
128#382C2×D1111yescharacteristic
129#343—111no—
130#339—221no—
131#328—222no—
132#324—112no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11—82no—
136C22×C11—82no—
137C22×C11—82no—
138C22×C11—82no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11—82no—
142C22×C11#45011yescharacteristic
143C22×C11#45611yescharacteristic
144C22×C11B(4,𝔽2)11yescharacteristic
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—42no—
148C4×C11—42no—
149C4×C11—82no—
150C4×C11—81no—
151Dic11—81no—
152Dic11—81no—
153C22×Q8—21no—
154C22×D4—21no—
155C22×D4—21no—
156C22×D4C22⋊D1112yes—
157C2×SD16—442no—
158C2×M16—221no—
159C4⋊Q8—441no—
160#125—441no—
161#124—42no—
162#124—42no—
163C22⋊Q8—222no—
164#117—221no—
165C2×C4⋊C4C22⋊D1111yescharacteristic
166C2×C4⋊C4C22×D1111yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C42C22⋊D1111yescharacteristic
172#107—441no—
173#106—441no—
174#102—442no—
175C22⋊C8—222no—
176#95—21no—
177#95—22no—
178#95C22⋊D1112yes—
179C2×C11—21no—
180C2×C11—21no—
181C2×C11—162no—
182C2×C11#160411yescharacteristic
183C2×C11#219911yescharacteristic
184C2×C11#220211yescharacteristic
185C24—22no—
186C2×Q8—42no—
187C2×Q8—81no—
188C2×Q8—81no—
189C2×Q8—222no—
190C2×D4—42no—
191C2×D4—42no—
192C2×D4—82no—
193C2×D4—81no—
194C2×D4—81no—
195C2×D4—82no—
196C2×D4—81no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4C2×C22⋊D1111yescharacteristic
201C22×C4C2×C22⋊D1112yes—
202SD16—884no—
203M16—222no—
204M16—441no—
205C2×C8—441no—
206C2×C8—442no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—222no—
210C4⋊C4—221no—
211C4⋊C4—221no—
212C4⋊C4—442no—
213C22⋊C4—44no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C22⋊C4—82no—
218C22⋊C4—441no—
219C42—21no—
220C42—441no—
221C42#432412yescomplemented
222C11#1225011yescharacteristic, complemented, Sylow
223C23—42no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23#6700611yescharacteristic
231Q8—84no—
232Q8—882no—
233D4—44no—
234D4—82no—
235D4—84no—
236D4—84no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—441no—
250C2×C4—441no—
251C2×C4#6698511yescharacteristic
252C2×C4C2×#432411yescharacteristic
253C8—442no—
254C8—882no—
255C22—21no—
256C22—21no—
257C22—82no—
258C22—82no—
259C22—82no—
260C22—82no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22#1062283111yescharacteristic
265C22#1062285711yescharacteristic
266C22#1062285911yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—82no—
272C4—81no—
273C4—881no—
274C4—881no—
275C2—21no—
276C2—21no—
277C2—162no—
278C2#1306758511yescharacteristic
279C2#1307061711yescharacteristic
280C2#1307063311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2819C2
socleC22×C11B(4,𝔽2)
hypercenter#2819D11
hypocenterC11#12250
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2819

Complements

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

NH ≅ G/Ntype
1. #13069966C2semidirect
2. #13067555C2semidirect
3. #13066619C2semidirect
4. #13066560C2semidirect
71. C42×C11SD16semidirect
221. C42#4324semidirect
222. C11#12250semidirect

Maximal subgroups

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

subgroupindex
#130699662
#130675552
#130666192
#130665602
C11×#28192
#1225011