Finite Group Databasebeta

← #14664718

Subgroups — #14664718

Order 2816.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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#13079202C211yesmaximal, characteristic
2#13070415C211yesmaximal, characteristic
3#13066627C214yesmaximal
4C11×#1834C211yesmaximal, characteristic
5#10623001—21no—
6C2×C4×C8×C11C2211yescharacteristic
7C11×#384—21no—
8#10622729—21no—
9#10622729C2212yes—
10#10622312C411yescharacteristic, complemented
11C4×Dic44—21no—
12C4×Dic44C412yescomplemented
13#10622295C411yescharacteristic, complemented
14#10622294—21no—
15C11×#340—21no—
16C11×#340C2212yes—
17C22⋊(C11⋊C16)C2212yes—
18C4⋊(C11⋊C16)—21no—
19C4×C11⋊C16—21no—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—41no—
24C2×C11×C4⋊C4—41no—
25C2×C42×C11D411yescharacteristic
26#66979—41no—
27#66977—22no—
28#66977—41no—
29C2×Dic44—21no—
30C2×Dic44C2×C412yes—
31#66923—41no—
32#66922—21no—
33#66922—21no—
34C4×Dic22—22no—
35C4×Dic22—41no—
36C4×C8×C11C2×C411yescharacteristic
37C4×C8×C11C2×C411yescharacteristic
38C4×C8×C11D411yescharacteristic
39C4×C8×C11D411yescharacteristic
40#66882—21no—
41#66882C2×C412yes—
42#66880—22no—
43#66880—22no—
44C2×C11⋊C16—22no—
45#11857—111nomaximal, Sylow
46C22×C4×C11—42no—
47C22×C4×C11D811yescharacteristic
48C22×C4×C11D811yescharacteristic
49C22×C4×C11C2×D411yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—41no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C2×C8×C11C22⋊C411yescharacteristic
55C2×C8×C11C22⋊C411yescharacteristic
56C2×C8×C11C22×C411yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—82no—
61C11×C4⋊C4—82no—
62C42×C11C22⋊C411yescharacteristic
63C42×C11C22⋊C411yescharacteristic
64C42×C11SD1611yescharacteristic
65C42×C11SD1611yescharacteristic
66C22⋊Dic11—42no—
67C4⋊Dic11—22no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71Dic11⋊C4—42no—
72Dic11⋊C4—42no—
73C4×Dic11—42no—
74Dic44—42no—
75Dic44—42no—
76C11⋊C16—42no—
77#3170—111no—
78#2162—111no—
79#1834D1111yescharacteristic
80#1348—114no—
81C23×C11C2×D811yescharacteristic
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—82no—
86C2×C4×C11—82no—
87C2×C4×C11—82no—
88C2×C4×C11#10211yescharacteristic
89C2×C4×C11#10211yescharacteristic
90C2×C4×C11#10211yescharacteristic
91C2×C4×C11#10211yescharacteristic
92C2×C4×C11SD3212yes—
93C2×C4×C11Q3212yes—
94C2×C4×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11C2×SD1611yescharacteristic
96C2×Dic11—42no—
97C2×Dic11—42no—
98Dic22—42no—
99Dic22—42no—
100Dic22—82no—
101C8×C11—21no—
102C8×C11—21no—
103C8×C11—21no—
104C8×C11—21no—
105#533—221no—
106#500—111no—
107#494—111no—
108#487—221no—
109#467—112no—
110#467—221no—
111C4×Q16—112no—
112C4×Q16—221no—
113C2×C4×C8C2×D1111yescharacteristic
114#384—21no—
115C4⋊C16—221no—
116C22⋊C16—112no—
117C4×C16—221no—
118#340—21no—
119#340C2×D1112yes—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11C2×#10211yescharacteristic
123C22×C11C2×SD3211yescharacteristic
124C22×C11C2×Q3211yescharacteristic
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—162no—
128C4×C11#35812yes—
129C4×C11#35812yes—
130C4×C11#36012yes—
131C4×C11#41011yescharacteristic
132C4×C11#42111yescharacteristic
133Dic11—82no—
134Dic11—82no—
135C2×Q16—112no—
136C2×Q16—221no—
137C22×C8C22⋊D1111yescharacteristic
138C22×C8C22×D1111yescharacteristic
139C4⋊Q8—221no—
140C4⋊Q8—221no—
141#125—441no—
142C22⋊Q8—222no—
143C22⋊Q8—441no—
144C4×Q8—222no—
145C4×Q8—441no—
146#117—441no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C42C22⋊D1111yescharacteristic
151C2×C16—222no—
152#107—112no—
153#107—221no—
154#103—222no—
155#103—222no—
156C4×C8C4×D1111yescharacteristic
157C4×C8C4×D1111yescharacteristic
158C4×C8D4411yescharacteristic
159C4×C8D4411yescharacteristic
160C2×C11—21no—
161C2×C11—21no—
162C2×C11#151711yescharacteristic
163C2×C11C2×#35811yescharacteristic
164C2×C11C2×#36011yescharacteristic
165C2×Q8—222no—
166C2×Q8—441no—
167C22×C4—42no—
168C22×C4#432311yescharacteristic
169C22×C4#432311yescharacteristic
170C22×C4C2×C22⋊D1111yescharacteristic
171Q16—442no—
172Q16—442no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8(C2×D11)⋊C411yescharacteristic
176C2×C8(C2×D11)⋊C411yescharacteristic
177C2×C8C2×C4×D1111yescharacteristic
178C2×C8C2×D4411yescharacteristic
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—82no—
182C4⋊C4—82no—
183C4⋊C4—222no—
184C4⋊C4—441no—
185C4⋊C4—441no—
186C4⋊C4—442no—
187C4⋊C4—441no—
188C4⋊C4—442no—
189C22⋊C4—442no—
190C42—442no—
191C42(C2×D11)⋊C411yescharacteristic
192C42(C2×D11)⋊C411yescharacteristic
193C42#432511yescharacteristic
194C42#432511yescharacteristic
195C16—442no—
196C11#1185711yescharacteristic, complemented, Sylow
197C23C2×#432311yescharacteristic
198Q8—442no—
199Q8—442no—
200Q8—882no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—82no—
205C2×C4—82no—
206C2×C4—82no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4#6687311yescharacteristic
210C2×C4#6687311yescharacteristic
211C2×C4#6687311yescharacteristic
212C2×C4#6687311yescharacteristic
213C2×C4#6689112yes—
214C2×C4#6689312yes—
215C2×C4C2×(C2×D11)⋊C411yescharacteristic
216C2×C4C2×#432511yescharacteristic
217C8—21no—
218C8—21no—
219C8—21no—
220C8—21no—
221C22—21no—
222C22—21no—
223C22C2×#6687311yescharacteristic
224C22C2×#6689111yescharacteristic
225C22C2×#6689311yescharacteristic
226C4—21no—
227C4—21no—
228C4—162no—
229C4—882no—
230C4—882no—
231C4#1062212612yes—
232C4#1062213012yes—
233C4#1062213012yes—
234C4#1062261811yescharacteristic
235C4#1062261911yescharacteristic
236C2—21no—
237C2—21no—
238C2#1306717511yescharacteristic
239C2C2×#1062213011yescharacteristic
240C2C2×#1062212611yescharacteristic
subgroupG/H
centerC22C2×#66873
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1834C2
socleC22×C11C2×#102
prime radicalC23×C11C2×D8
cosocleC22×C8×C11C23
hypercenter#1834D11
hypocenterC11#11857
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1834

Complements

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

NH ≅ G/Ntype
10. #10622312C4semidirect
12. C4×Dic44C4semidirect
13. #10622295C4semidirect
196. C11#11857semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130704152
#130666272
C11×#18342
#1185711