Finite Group Databasebeta

← #14664626

Subgroups — #14664626

Order 2816.

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

normal subgroups only

This group has 280 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#13079356C211yesmaximal, characteristic
2#13070425C211yesmaximal, characteristic
3#13068766C211yesmaximal, characteristic
4#13066609C211yesmaximal, characteristic
5#13066605C211yesmaximal, characteristic
6#13066604C211yesmaximal, characteristic
7C11×#1342C211yesmaximal, characteristic
8#10623153—21no—
9C11×#470C2211yescharacteristic
10#10622797C411yescharacteristic, complemented
11#10622794C411yescharacteristic, complemented
12#10622750C2211yescharacteristic
13M16×Dic11C2211yescharacteristic
14#10622665—21no—
15#10622468C411yescharacteristic, complemented
16#10622466C411yescharacteristic, complemented
17#10622405—21no—
18#10622402—21no—
19C11×#349C2211yescharacteristic
20C11×#338C2211yescharacteristic
21#10622197—21no—
22#10622195C2211yescharacteristic
23#10622193—21no—
24#10622191C2211yescharacteristic
25#10622150—21no—
26#10622149—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C2×C11×M16—21no—
29C2×C11×M16C2311yescharacteristic
30C11×C22⋊Q8—21no—
31Q8×Dic11—21no—
32#66997—21no—
33C2×#4326—21no—
34#66979—21no—
35#66977—21no—
36C2×C4×Dic11D411yescharacteristic
37C2×#4318D411yescharacteristic
38C2×Dic44C2×C411yescharacteristic
39#66942—41no—
40#66941—21no—
41#66940—21no—
42#66940—41no—
43#66931—41no—
44#66930—41no—
45C11×M32—21no—
46C11×#106C2×C411yescharacteristic
47C11×#103—21no—
48#66899—21no—
49#66881C2×C411yescharacteristic
50#66880—21no—
51#66879C2×C411yescharacteristic
52#66879D411yescharacteristic
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11D411yescharacteristic
55#66876—21no—
56#66874—21no—
57#66872—21no—
58#11838—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—21no—
62C2×Dic22—21no—
63C2×Dic22—41no—
64C11×Q16—41no—
65C11×M16—41no—
66C11×M16—41no—
67C11×M16—41no—
68C2×C8×C11—41no—
69C2×C8×C11C22×C411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—41no—
74C22⋊Dic11—41no—
75C22⋊Dic11—41no—
76#4326—42no—
77C4⋊Dic11—21no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80Dic11⋊C4—41no—
81Dic11⋊C4—41no—
82Dic11⋊C4—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85C4×Dic11—21no—
86C4×Dic11—41no—
87C4×Dic11—41no—
88C4×Dic11—41no—
89C4×Dic11C22⋊C411yescharacteristic
90C4×Dic11C22⋊C411yescharacteristic
91#4318—41no—
92C2×C11⋊C8C22⋊C411yescharacteristic
93C2×C11⋊C8C22⋊C411yescharacteristic
94Dic44—41no—
95C11×C16—41no—
96C11⋊C16—41no—
97#3185—111no—
98#2165—111no—
99#1841—111no—
100#1342—111no—
101#1342D1111yescharacteristic
102#1340—111no—
103#1340—111no—
104C23×C11AGL(1,ℤ/8)11yescharacteristic
105Q8×C11—41no—
106Q8×C11—41no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—42no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118C2×Dic11—81no—
119Dic22—41no—
120Dic22—41no—
121Dic22—82no—
122C8×C11—21no—
123C8×C11—21no—
124C8×C11—81no—
125C11⋊C8—21no—
126C11⋊C8—21no—
127#533—221no—
128#498—111no—
129#494—111no—
130#487—221no—
131#470—111no—
132#470—221no—
133#470C2×D1111yescharacteristic
134#441—111no—
135#441—111no—
136#441—221no—
137C4×M16—111no—
138#364—221no—
139#349—111no—
140#349C2×D1111yescharacteristic
141#347—221no—
142#344—221no—
143#339—221no—
144#338C2×D1111yescharacteristic
145H(3,ℤ/4)—111no—
146C22×C11—21no—
147C22×C11—41no—
148C22×C11#41811yescharacteristic
149C4×C11—21no—
150C4×C11—81no—
151C4×C11—81no—
152C4×C11#41011yescharacteristic
153C4×C11#42111yescharacteristic
154Dic11—22no—
155Dic11—41no—
156Dic11—81no—
157Dic11—81no—
158Dic11—161no—
159C2×Q16—111no—
160C2×Q16—221no—
161C2×Q16C4×D1111yescharacteristic
162C2×M16—21no—
163C2×M16—111no—
164C2×M16C22×D1111yescharacteristic
165C4⋊Q8—221no—
166C4⋊Q8—221no—
167#125—441no—
168C22⋊Q8—21no—
169C22⋊Q8—221no—
170C22⋊Q8—441no—
171C4×Q8—221no—
172C4×Q8—221no—
173C4×Q8—441no—
174#117—221no—
175#117—441no—
176C2×C42—111no—
177M32—21no—
178M32—221no—
179#106—111no—
180#106—221no—
181#106C4×D1111yescharacteristic
182#103—21no—
183#103—221no—
184#103—221no—
185#103—221no—
186#97—111no—
187#97—111no—
188C4×C8—111no—
189C4×C8—111no—
190C2×C11—21no—
191C2×C11—41no—
192C2×C11#151411yescharacteristic
193C2×Q8—21no—
194C2×Q8—221no—
195C2×Q8—441no—
196C22×C4—221no—
197C22×C4D4×D1111yescharacteristic
198Q16—41no—
199Q16—441no—
200Q16—442no—
201M16—41no—
202M16—41no—
203M16—41no—
204M16—441no—
205C2×C8—41no—
206C2×C8—111no—
207C2×C8—111no—
208C2×C8C2×C4×D1111yescharacteristic
209C2×C8D4×D1111yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—41no—
212C4⋊C4—221no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C4⋊C4—441no—
220C22⋊C4—41no—
221C22⋊C4—441no—
222C22⋊C4—441no—
223C42—111no—
224C42—111no—
225C42—221no—
226C42—441no—
227C42—441no—
228C42—441no—
229C16—41no—
230C16—441no—
231C11#1183811yescharacteristic, complemented, Sylow
232C23#6696711yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—441no—
236Q8—441no—
237Q8—882no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—221no—
243C2×C4—221no—
244C2×C4—442no—
245C2×C4—441no—
246C2×C4—441no—
247C2×C4—881no—
248C2×C4C22⋊C4×D1111yescharacteristic
249C2×C4#6696411yescharacteristic
250C8—21no—
251C8—21no—
252C8—81no—
253C8—221no—
254C8—221no—
255C22—21no—
256C22—41no—
257C22#1062238311yescharacteristic
258C4—21no—
259C4—81no—
260C4—81no—
261C4—222no—
262C4—441no—
263C4—881no—
264C4—881no—
265C4—1761no—
266C4#1062235311yescharacteristic
267C4#1062243411yescharacteristic
268C2—21no—
269C2—41no—
270C2#1306716111yescharacteristic
subgroupG/H
centerC2#13067161
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1342C2
socleC2×C11#1514
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC2×C11×M16C23
hypercenter#1342D11
hypocenterC11#11838
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1342

Complements

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

NH ≅ G/Ntype
10. #10622797C4semidirect
11. #10622794C4semidirect
15. #10622468C4semidirect
16. #10622466C4semidirect
231. C11#11838semidirect

Maximal subgroups

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

subgroupindex
#130793562
#130704252
#130687662
#130666092
#130666052
#130666042
C11×#13422
#1183811