Finite Group Databasebeta

← #14658788

Subgroups — #14658788

Order 2816.

354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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#13069449C211yesmaximal, characteristic
2#13068769C211yesmaximal, characteristic, complemented
3#13067391C211yesmaximal, characteristic, complemented
4#13067390C211yesmaximal, characteristic, complemented
5#13067015C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1480C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×#66901—22no—
12C2×Dic11⋊C8—22no—
13#10622545C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C11×D4⋊C8—22no—
18D4⋊(C11⋊C8)—22no—
19#10622117—22no—
20#10622096—22no—
21C2×C11×#41—21no—
22C22×C8×C11—21no—
23C11×C4⋊Q8Q811yescharacteristic
24C11×#127Q811yescharacteristic
25C11×#124—21no—
26C11×#121—21no—
27C11×#121—21no—
28C4×D4×C11—21no—
29C4×D4×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×C4×Dic11D412yes—
32C2×#4318—21no—
33C22×C11⋊C8—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11D412yes—
39#66901—44no—
40C11⋊#95—21no—
41C11⋊#95—21no—
42C22⋊(C11⋊C8)—21no—
43Dic11⋊C8—44no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4×C11⋊C8D412yes—
50#10667—111nomaximal, Sylow
51C11×#41—42no—
52C11×#41—42no—
53C2×Q8×C11—21no—
54C2×D4×C11—21no—
55C2×D4×C11—21no—
56C2×D4×C11—21no—
57C2×D4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C22×Dic11—22no—
63C2×C8×C11—22no—
64C2×C8×C11—41no—
65C2×C8×C11—42no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C22⋊C4—41no—
69C11×C22⋊C4—41no—
70C42×C11C2×D411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11C2×Q811yescharacteristic
73C42×C11#4111yescharacteristic
74C4×Dic11—22no—
75C4×Dic11D814yes—
76#4318—42no—
77C2×C11⋊C8—22no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—41no—
80C2×C11⋊C8—42no—
81#1963—111no—
82#1843—111no—
83#1571—111no—
84#1571—111no—
85#1480—111no—
86#1480D1111yescharacteristic
87#1274—111no—
88C23×C11—41no—
89C23×C11#12311yescharacteristic
90Q8×C11—42no—
91D4×C11—42no—
92D4×C11—42no—
93D4×C11—42no—
94D4×C11—82no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—81no—
99C2×C4×C11—81no—
100C2×C4×C11C22⋊Q811yescharacteristic
101C2×C4×C11C22⋊Q811yescharacteristic
102C2×C4×C11C22⋊Q811yescharacteristic
103C2×C4×C11#12311yescharacteristic
104C2×C4×C11#12311yescharacteristic
105C2×C4×C11#12711yescharacteristic
106C2×C4×C11C2×D812yes—
107C2×C4×C11#13712yes—
108C2×Dic11—24no—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C8×C11—42no—
112C8×C11—81no—
113C11⋊C8—42no—
114C11⋊C8—81no—
115C11⋊C8—81no—
116#532C2×D1111yescharacteristic
117#431—111no—
118#431C2×D1111yescharacteristic
119#423—111no—
120C2×C4⋊C8—111no—
121C2×C4⋊C8—222no—
122C2×C4⋊C8C2×D1111yescharacteristic
123C2×#104—222no—
124#376—111no—
125#335—222no—
126#335—222no—
127D4⋊C8—22no—
128D4⋊C8—222no—
129C22×C11—21no—
130C22×C11—21no—
131C22×C11—81no—
132C22×C11—81no—
133C22×C11—81no—
134C22×C11#39911yescharacteristic
135C22×C11#48012yes—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—21no—
140C4×C11—81no—
141C4×C11#47412yes—
142C4×C11#49311yescharacteristic
143C4×C11#49711yescharacteristic
144Dic11—44no—
145C2×#41—21no—
146C2×M16—221no—
147C22×C8—21no—
148C22×C8—221no—
149C4⋊Q8Dic2211yescharacteristic
150#127Dic2211yescharacteristic
151#124—21no—
152#121—21no—
153#121—21no—
154C4×D4—21no—
155C4×D4—21no—
156C2×C42—112no—
157C2×C42C22×D1111yescharacteristic
158C4⋊C8—21no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—221no—
162C4⋊C8—221no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165C4⋊C8—221no—
166C4⋊C8—444no—
167#104—444no—
168C22⋊C8—21no—
169C22⋊C8—221no—
170C4×C8—112no—
171C4×C8C22⋊D1112yes—
172#95—221no—
173#95—221no—
174C2×C11—22no—
175C2×C11—161no—
176C2×C11#209311yescharacteristic
177C2×C11#209811yescharacteristic
178C2×C11#209811yescharacteristic
179#41—42no—
180#41—42no—
181C2×Q8—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—41no—
186C22×C4—41no—
187C22×C4—222no—
188C22×C4#433911yescharacteristic
189C22×C4D4×D1111yescharacteristic
190C22×C4#434111yescharacteristic
191M16—442no—
192C2×C8—22no—
193C2×C8—42no—
194C2×C8—41no—
195C2×C8—222no—
196C2×C8—442no—
197C2×C8—441no—
198C2×C8—441no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C22⋊C4—41no—
202C22⋊C4—41no—
203C42—114no—
204C42—222no—
205C42C2×Dic2211yescharacteristic
206C42D4×D1111yescharacteristic
207C42#434111yescharacteristic
208C42C2×C22⋊D1111yescharacteristic
209C11#1066711yescharacteristic, complemented, Sylow
210C23—41no—
211C23#6693611yescharacteristic
212Q8—42no—
213D4—42no—
214D4—42no—
215D4—42no—
216D4—82no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—224no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4#6693111yescharacteristic
226C2×C4#6693111yescharacteristic
227C2×C4#6693611yescharacteristic
228C2×C4D8×D1112yes—
229C2×C4#6696812yes—
230C2×C4#6697711yescharacteristic
231C2×C4#6698811yescharacteristic
232C2×C4#6699311yescharacteristic
233C8—42no—
234C8—81no—
235C8—442no—
236C8—881no—
237C8—881no—
238C22—21no—
239C22—21no—
240C22—81no—
241C22—81no—
242C22—81no—
243C22#1062238712yes—
244C22#1062256211yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—81no—
250C4—444no—
251C4#1062237212yes—
252C4#1062276411yescharacteristic
253C4#1062278011yescharacteristic
254C2—22no—
255C2—161no—
256C2#1307014211yescharacteristic
257C2#1307016911yescharacteristic
258C2#1307017111yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1480C2
socleC22×C11#399
prime radicalC11×#532C22
hypercenter#1480D11
hypocenterC11#10667
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #13068769C2semidirect
3. #13067391C2semidirect
4. #13067390C2semidirect
6. #13066444C2semidirect
209. C11#10667semidirect

Maximal subgroups

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

subgroupindex
#130694492
#130687692
#130673912
#130673902
#130670152
#130664442
C11×#14802
#1066711