Finite Group Databasebeta

← #14658777

Subgroups — #14658777

Order 2816.

334 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069448C211yesmaximal, characteristic
2#13068736C211yesmaximal, characteristic, complemented
3#13067391C211yesmaximal, characteristic, complemented
4#13067387C211yesmaximal, characteristic, complemented
5#13067016C211yesmaximal, characteristic
6#13067016C211yesmaximal, characteristic
7C11×#1274C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#376C2211yescharacteristic
12C2×#66869—22no—
13#10622537C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16#10622162—22no—
17#10622097—22no—
18#10622097—22no—
19#10622096—22no—
20#10622095—22no—
21C2×#4339—21no—
22C2×C42×C11D412yes—
23C2×C42×C11C2311yescharacteristic
24#66983—21no—
25#66983—21no—
26C2×#4318—21no—
27C22×C11⋊C8—21no—
28C22×C11⋊C8—21no—
29#66928—21no—
30#66927Q811yescharacteristic
31C4×D44—21no—
32C4×D44—21no—
33#66922Q811yescharacteristic
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C22⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11D412yes—
39C4×C8×C11D412yes—
40C11×#95—21no—
41C11×#95—21no—
42#66869—44no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49#10665—111nomaximal, Sylow
50C22×C4×C11—22no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C2×C22⋊D11—41no—
55#4339—42no—
56#4339—42no—
57C2×D44—21no—
58C2×D44—21no—
59C2×D44—21no—
60C2×C4×D11—41no—
61C2×Dic22—21no—
62C2×C8×C11—22no—
63C2×C8×C11—22no—
64C42×C11—22no—
65C42×C11—22no—
66C42×C11C2×D411yescharacteristic
67C42×C11C2×D411yescharacteristic
68C42×C11C2×Q811yescharacteristic
69C42×C11#4111yescharacteristic
70(C2×D11)⋊C4—41no—
71(C2×D11)⋊C4—41no—
72C4⋊Dic11—21no—
73C4⋊Dic11—21no—
74#4318—42no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—41no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80#1963—111no—
81#1832—111no—
82#1571—111no—
83#1570—111no—
84#1480—111no—
85#1480—111no—
86#1274D1111yescharacteristic, complemented
87C23×C11#12311yescharacteristic
88C22×D11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11C22⋊Q811yescharacteristic
95C2×C4×C11C22⋊Q811yescharacteristic
96C2×C4×C11C22⋊Q811yescharacteristic
97C2×C4×C11#12311yescharacteristic
98C2×C4×C11#12311yescharacteristic
99C2×C4×C11#12711yescharacteristic
100C2×C4×C11#13512yes—
101C2×C4×C11AGL(1,ℤ/8)12yes—
102C22⋊D11—82no—
103C2×Dic11—41no—
104D44—42no—
105D44—42no—
106D44—42no—
107C4×D11—81no—
108C4×D11—81no—
109Dic22—42no—
110C8×C11—42no—
111C8×C11—42no—
112C11⋊C8—81no—
113C11⋊C8—81no—
114C11⋊C8—81no—
115#532—111no—
116#431C2×D1111yescharacteristic
117#431C2×D1111yescharacteristic
118#423—111no—
119C2×C4⋊C8—111no—
120C2×C4⋊C8—111no—
121C2×#104—222no—
122#376C2×D1111yescharacteristic
123#336—222no—
124#335—222no—
125#334—222no—
126D4⋊C8—222no—
127D4⋊C8—222no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11#39911yescharacteristic
131C22×C11#48212yes—
132C2×D11—81no—
133C2×D11—81no—
134C2×D11—81no—
135C4×C11—21no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—82no—
140C4×C11#47812yes—
141C4×C11#49511yescharacteristic
142C4×C11#49611yescharacteristic
143Dic11—81no—
144C2×#41—221no—
145C2×M16—221no—
146C22×C8—221no—
147C22×C8—221no—
148C4⋊Q8—111no—
149#127—111no—
150#124—221no—
151#121—221no—
152#121—221no—
153C4×D4—221no—
154C4×D4—221no—
155C2×C42D4412yes—
156C2×C42C22×D1111yescharacteristic
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—221no—
160C4⋊C8—221no—
161C4⋊C8—221no—
162C4⋊C8—221no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165#104—444no—
166C22⋊C8—21no—
167C22⋊C8—21no—
168C4×C8D4412yes—
169C4×C8D4412yes—
170#95—21no—
171#95—21no—
172C2×C11—22no—
173C2×C11#209211yescharacteristic
174C2×C11#209811yescharacteristic
175C2×C11#209811yescharacteristic
176D11—161no—
177#41—442no—
178#41—442no—
179C2×Q8—221no—
180C2×D4—221no—
181C2×D4—221no—
182C2×D4—221no—
183C2×D4—441no—
184C22×C4—22no—
185C22×C4—441no—
186C22×C4C2×D4411yescharacteristic
187C22×C4#434111yescharacteristic
188C22×C4#434111yescharacteristic
189M16—442no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—441no—
193C2×C8—441no—
194C2×C8—441no—
195C2×C8—442no—
196C2×C8—442no—
197C4⋊C4—221no—
198C4⋊C4—221no—
199C22⋊C4—441no—
200C22⋊C4—441no—
201C42—22no—
202C42—22no—
203C42C2×D4411yescharacteristic
204C42C2×D4411yescharacteristic
205C42#434111yescharacteristic
206C42Q8×D1111yescharacteristic
207C11#1066511yescharacteristic, complemented, Sylow
208C23—441no—
209C23#6693911yescharacteristic
210Q8—442no—
211D4—442no—
212D4—442no—
213D4—442no—
214D4—882no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—441no—
221C2×C4—881no—
222C2×C4—881no—
223C2×C4#6692711yescharacteristic
224C2×C4#6693911yescharacteristic
225C2×C4#6693911yescharacteristic
226C2×C4#6695011yescharacteristic
227C2×C4#6695011yescharacteristic
228C2×C4#6695011yescharacteristic
229C2×C4#6695712yes—
230C2×C4#6696112yes—
231C8—42no—
232C8—42no—
233C8—881no—
234C8—881no—
235C8—881no—
236C22—21no—
237C22—21no—
238C22—881no—
239C22—881no—
240C22—881no—
241C22#1062229011yescharacteristic
242C22#1062235012yes—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—82no—
248C4—881no—
249C4#1062230911yescharacteristic
250C4#1062232511yescharacteristic
251C4#1062246012yes—
252C2—22no—
253C2—1761no—
254C2#1307013611yescharacteristic
255C2#1307017011yescharacteristic
256C2#1307017011yescharacteristic
subgroupG/H
centerC2×C4#66927
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#399
prime radical#10623008C22
hypercenter#1274D11
hypocenterC11#10665
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #13068736C2semidirect
3. #13067391C2semidirect
4. #13067387C2semidirect
7. C11×#1274C2semidirect
86. #1274D11semidirect
207. C11#10665semidirect

Maximal subgroups

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

subgroupindex
#130694482
#130687362
#130673912
#130673872
#130670162
C11×#12742
#1066511