Finite Group Databasebeta

← #14671228

Subgroups — #14671228

Order 2816.

458 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 131 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#13081719C211yesmaximal, characteristic
2#13070336C212yesmaximal, complemented
3#13068662C211yesmaximal, characteristic
4#13066717C212yesmaximal, complemented
5C11×#3059C211yesmaximal, characteristic
6C22×C11×Q16C2211yescharacteristic
7C2×C11×#131C2211yescharacteristic
8C11×#536—21no—
9C11×#470C414yescomplemented
10C11×#467—22no—
11C11×#427C2211yescharacteristic
12C11×#419—21no—
13#10622853—21no—
14#10622753—24no—
15#10622719C2212yes—
16C2×#66876—22no—
17C2×#66876C2212yes—
18#10622202—24no—
19#10622195—21no—
20C2×C11×#41D411yescharacteristic
21C22×Q8×C11—21no—
22C2×C11×Q16—22no—
23C2×C11×Q16—21no—
24C2×C11×Q16—22no—
25C2×C11×Q16C2×C412yes—
26C11×#131—22no—
27C11×#131—22no—
28C2×C11×M16C2×C412yes—
29C2×C11×M16D411yescharacteristic
30C22×C8×C11D412yes—
31C22×C8×C11C2311yescharacteristic
32C11×C4⋊Q8—41no—
33C11×#124—41no—
34C11×#123—42no—
35C11×C22⋊Q8—24no—
36C11×#117—21no—
37#66979—22no—
38C11×#107—21no—
39C11×#106C2×C412yes—
40C11×#103—24no—
41#66898—42no—
42#66882—22no—
43#66881—22no—
44#66876—24no—
45#66876—22no—
46#66876—22no—
47C2×C11⋊C16—24no—
48C2×C11⋊C16D414yes—
49#13075—111nomaximal, Sylow
50C11×#41—22no—
51C11×#41—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—41no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C2×Q8×C11SD1611yescharacteristic
57C2×D4×C11D812yes—
58C2×D4×C11SD1611yescharacteristic
59C22×C4×C11—41no—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C2×D411yescharacteristic
62C11×Q16—24no—
63C11×Q16—41no—
64C11×Q16—41no—
65C11×M16—24no—
66C11×M16—22no—
67C2×C8×C11—22no—
68C2×C8×C11—22no—
69C2×C8×C11C22⋊C412yes—
70C2×C8×C11C22×C411yescharacteristic
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×D412yes—
73C2×C8×C11#4112yes—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—44no—
76C11×C22⋊C4—44no—
77C11×C22⋊C4—41no—
78C42×C11—41no—
79C22⋊Dic11—42no—
80C4⋊Dic11—42no—
81C4×Dic11—42no—
82C11⋊C16—24no—
83#3407—111no—
84#3059D1111yescharacteristic
85#2141—112no—
86#1812—111no—
87#1384—112no—
88C23×C11#10212yes—
89C23×C11C2×D811yescharacteristic
90Q8×C11—22no—
91Q8×C11—42no—
92Q8×C11—42no—
93Q8×C11—82no—
94D4×C11—24no—
95D4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—82no—
101C2×C4×C11#10212yes—
102C2×C4×C11C2×C22⋊C411yescharacteristic
103C2×C4×C11#12112yes—
104C2×C4×C11C2×SD1611yescharacteristic
105C2×C4×C11#13512yes—
106C2×Dic11—82no—
107C8×C11—22no—
108C8×C11C4×D412yes—
109C8×C11#12011yescharacteristic
110C8×C11#12311yescharacteristic
111C22×Q16C2×D1111yescharacteristic
112C2×#131C2×D1111yescharacteristic
113#536—21no—
114#504—224no—
115C2×M32—112no—
116C2×M32—222no—
117#470Dic1114yescomplemented
118#467—22no—
119#427—112no—
120#427C2×D1111yescharacteristic
121#419—21no—
122#410—221no—
123#358—224no—
124H(3,ℤ/4)—221no—
125C22×C11—22no—
126C22×C11—41no—
127C22×C11—42no—
128C22×C11C2×#10211yescharacteristic
129C22×C11#46612yes—
130C4×C11—22no—
131C4×C11—82no—
132C4×C11—82no—
133C4×C11#38611yescharacteristic
134C4×C11#41611yescharacteristic
135C4×C11#46512yes—
136Dic11—162no—
137C2×#41C22⋊D1111yescharacteristic
138C22×Q8—21no—
139C2×Q16—22no—
140C2×Q16—22no—
141C2×Q16—21no—
142C2×Q16C2×Dic1112yes—
143#131—22no—
144#131—22no—
145C2×M16C2×Dic1112yes—
146C2×M16C22⋊D1111yescharacteristic
147C22×C8C22⋊D1112yes—
148C22×C8C22×D1111yescharacteristic
149C4⋊Q8—41no—
150#124—41no—
151#123—42no—
152C22⋊Q8—24no—
153#117—21no—
154#117—222no—
155M32—224no—
156M32—222no—
157M32—222no—
158C2×C16—114no—
159C2×C16—224no—
160#107—21no—
161#107—222no—
162#106—222no—
163#106C2×Dic1112yes—
164#103—24no—
165#99—442no—
166C2×C11—22no—
167C2×C11—21no—
168C2×C11—42no—
169C2×C11#189311yescharacteristic
170#41—22no—
171#41—22no—
172C2×Q8—22no—
173C2×Q8—41no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8#432411yescharacteristic
177C2×D4#432312yes—
178C2×D4#432411yescharacteristic
179C22×C4—41no—
180C22×C4C22⋊Dic1112yes—
181C22×C4C2×C22⋊D1111yescharacteristic
182Q16—24no—
183Q16—41no—
184Q16—41no—
185M16—22no—
186M16—24no—
187C2×C8—22no—
188C2×C8—22no—
189C2×C8C22⋊Dic1112yes—
190C2×C8D4×D1112yes—
191C2×C8#434112yes—
192C2×C8C22×Dic1111yescharacteristic
193C2×C8C2×C22⋊D1111yescharacteristic
194C4⋊C4—22no—
195C4⋊C4—44no—
196C4⋊C4—442no—
197C22⋊C4—44no—
198C22⋊C4—41no—
199C22⋊C4—442no—
200C42—41no—
201C42—442no—
202C16—224no—
203C11#1307511yescharacteristic, complemented, Sylow
204C23#6689612yes—
205C23C2×#432311yescharacteristic
206Q8—22no—
207Q8—42no—
208Q8—42no—
209Q8—82no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—82no—
217C2×C4—882no—
218C2×C4#6689612yes—
219C2×C4C2×#432411yescharacteristic
220C2×C4#6699212yes—
221C2×C4#6700312yes—
222C2×C4C2×C22⋊Dic1111yescharacteristic
223C8—22no—
224C8D4×Dic1112yes—
225C8#6698811yescharacteristic
226C8#6699011yescharacteristic
227C22—22no—
228C22—41no—
229C22—42no—
230C22#1062265112yes—
231C22C2×#6689611yescharacteristic
232C4—22no—
233C4—82no—
234C4—82no—
235C4—1762no—
236C4#1062265412yes—
237C4#1062283311yescharacteristic
238C4#1062284611yescharacteristic
239C2—21no—
240C2—22no—
241C2—42no—
242C2#1306904511yescharacteristic
subgroupG/H
centerC2#13069045
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#3059C2
socleC2×C11#1893
prime radicalC2×C11×#41D4
cosocleC22×C8×C11C23
hypercenter#3059D11
hypocenterC11#13075
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3059

Complements

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

NH ≅ G/Ntype
2. #13070336C2semidirect
4. #13066717C2semidirect
9. C11×#470C4semidirect
117. #470Dic11semidirect
203. C11#13075semidirect

Maximal subgroups

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

subgroupindex
#130817192
#130703362
#130686622
#130667172
C11×#30592
#1307511