Finite Group Databasebeta

← #14666789

Subgroups — #14666789

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#13076662C211yesmaximal, characteristic
2#13067556C212yesmaximal, complemented
3#13066618C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#2061C211yesmaximal, characteristic, complemented
6C11×#544C2211yescharacteristic
7C2×#66928—21no—
8C11×#428—21no—
9C11×#382C2211yescharacteristic
10#10622659—22no—
11#10622604—21no—
12#10622604C2212yes—
13#10622286—22no—
14#10622284—22no—
15C11×#343C2211yescharacteristic
16C11×#339—21no—
17#10622176—22no—
18#10622166C2212yes—
19C22×D44—21no—
20C22×D44—21no—
21C22×D44D412yes—
22C22×Dic22—21no—
23C2×C11×M16—21no—
24C11×C4⋊Q8—41no—
25C11×#125—41no—
26C11×C22⋊Q8—22no—
27C11×#117—21no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×#4325—42no—
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36#66928—42no—
37#66928—42no—
38C11×#107—41no—
39C11×#106—41no—
40C11×#95—22no—
41C11⋊#95—21no—
42C11⋊#95D412yes—
43C22⋊(C11⋊C8)—22no—
44#66873—42no—
45#12250—111nomaximal, Sylow
46C23×D11—22no—
47C2×Q8×C11—22no—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—22no—
53C2×D44—42no—
54C2×D44—42no—
55C2×D44—82no—
56C2×D44—81no—
57C2×D44—81no—
58C2×D44—82no—
59C2×D44—81no—
60C2×Dic22—42no—
61C2×Dic22—81no—
62C2×Dic22—81no—
63C11×M16—22no—
64C11×M16—41no—
65C2×C8×C11—41no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—41no—
73C42×C11—21no—
74C42×C11—41no—
75C42×C11SD1612yescomplemented
76#4325—84no—
77(C2×D11)⋊C4—44no—
78(C2×D11)⋊C4—42no—
79(C2×D11)⋊C4—42no—
80(C2×D11)⋊C4—82no—
81(C2×D11)⋊C4—82no—
82C2×C11⋊C8—42no—
83#2819—111no—
84#2061D1111yescharacteristic, complemented
85#1599—112no—
86#1345—112no—
87#1324—111no—
88C23×C11#12011yescharacteristic
89C22×D11—42no—
90C22×D11—42no—
91C22×D11—42no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96Q8×C11—82no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113D44—44no—
114D44—82no—
115D44—84no—
116D44—84no—
117Dic22—84no—
118C8×C11—42no—
119C11⋊C8—82no—
120#544C2×D1111yescharacteristic
121C2×#124—221no—
122#450—222no—
123#428—21no—
124#394—112no—
125#394—221no—
126#393—222no—
127#392—222no—
128#382C2×D1111yescharacteristic
129#343C2×D1111yescharacteristic
130#339—21no—
131#328—222no—
132#324—112no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11#45011yescharacteristic
136C22×C11#45611yescharacteristic
137C22×C11B(4,𝔽2)11yescharacteristic
138C2×D11—82no—
139C2×D11—82no—
140C2×D11—82no—
141C2×D11—82no—
142C2×D11—82no—
143C2×D11—82no—
144C2×D11—82no—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—42no—
148C4×C11—42no—
149C4×C11—81no—
150C4×C11—81no—
151C4×C11—81no—
152Dic11—82no—
153C22×Q8—221no—
154C22×D4—112no—
155C22×D4—221no—
156C22×D4—221no—
157C2×SD16—442no—
158C2×M16—21no—
159C4⋊Q8—41no—
160#125—41no—
161#124—442no—
162#124—442no—
163C22⋊Q8—22no—
164#117—21no—
165C2×C4⋊C4C22⋊D1111yescharacteristic
166C2×C4⋊C4C22×D1111yescharacteristic
167C2×C22⋊C4—222no—
168C2×C22⋊C4—222no—
169C2×C22⋊C4—222no—
170C2×C22⋊C4—222no—
171C2×C42C22⋊D1111yescharacteristic
172#107—41no—
173#106—41no—
174#102—442no—
175C22⋊C8—222no—
176#95—22no—
177#95—112no—
178#95—221no—
179C2×C11—21no—
180C2×C11—21no—
181C2×C11#160411yescharacteristic
182C2×C11#219911yescharacteristic
183C2×C11#220211yescharacteristic
184D11—162no—
185C24—222no—
186C2×Q8—22no—
187C2×Q8—442no—
188C2×Q8—881no—
189C2×Q8—881no—
190C2×D4—442no—
191C2×D4—442no—
192C2×D4—882no—
193C2×D4—881no—
194C2×D4—881no—
195C2×D4—882no—
196C2×D4—881no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—222no—
200C22×C4D4×D1112yes—
201C22×C4C2×C22⋊D1111yescharacteristic
202SD16—884no—
203M16—22no—
204M16—41no—
205C2×C8—41no—
206C2×C8—442no—
207C4⋊C4—22no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C22⋊C4—41no—
214C22⋊C4—444no—
215C22⋊C4—442no—
216C22⋊C4—442no—
217C22⋊C4—882no—
218C22⋊C4—882no—
219C42—21no—
220C42—41no—
221C42#432512yescomplemented
222C11#1225011yescharacteristic, complemented, Sylow
223C23—442no—
224C23—442no—
225C23—442no—
226C23—442no—
227C23—442no—
228C23—442no—
229C23—442no—
230C23#6699011yescharacteristic
231Q8—82no—
232Q8—884no—
233D4—444no—
234D4—882no—
235D4—884no—
236D4—884no—
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—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4C2×#432511yescharacteristic
252C2×C4#6700211yescharacteristic
253C8—42no—
254C8—882no—
255C22—21no—
256C22—21no—
257C22—882no—
258C22—882no—
259C22—882no—
260C22—882no—
261C22—882no—
262C22—882no—
263C22—882no—
264C22#1062264511yescharacteristic
265C22#1062265911yescharacteristic
266C22#1062270811yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—81no—
272C4—81no—
273C4—81no—
274C4—882no—
275C2—21no—
276C2—21no—
277C2—1762no—
278C2#1306758411yescharacteristic
279C2#1307061611yescharacteristic
280C2#1307063211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2061C2
socleC22×C11B(4,𝔽2)
prime radical#13076662C2
hypercenter#2061D11
hypocenterC11#12250
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2061

Complements

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

NH ≅ G/Ntype
2. #13067556C2semidirect
3. #13066618C2semidirect
4. #13066560C2semidirect
5. C11×#2061C2semidirect
75. C42×C11SD16semidirect
84. #2061D11semidirect
221. C42#4325semidirect
222. C11#12250semidirect

Maximal subgroups

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

subgroupindex
#130766622
#130675562
#130666182
#130665602
C11×#20612
#1225011