Finite Group Databasebeta

← #14653156

Subgroups — #14653156

Order 2816.

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

normal subgroups only

This group has 400 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#13078939C211yesmaximal, characteristic
2#13068747C211yesmaximal, characteristic, complemented
3#13067181C212yesmaximal, complemented
4#13067177C212yesmaximal
5C11×#1450C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7#10623001C2211yescharacteristic
8C11×#431C2212yes—
9C2×C4×C8×C11C2211yescharacteristic
10#10622726—22no—
11#10622549C2212yes—
12#10622310—21no—
13#10622310—21no—
14#10622307C412yescomplemented
15#10622294C412yescomplemented
16C11×#322—21no—
17C82×C11—21no—
18#10622189—22no—
19#10622108—24no—
20#10622105—24no—
21C2×#4339—21no—
22C22×C8×C11D412yes—
23C2×C42×C11C2311yescharacteristic
24#66983—22no—
25#66979—21no—
26C2×C4⋊Dic11—22no—
27#66977—22no—
28#66928—21no—
29#66927C2×C411yescharacteristic
30C4×D44—22no—
31#66923—21no—
32#66922C2×C412yes—
33#66922C2×C411yescharacteristic
34C4×Dic22—22no—
35C11×C4⋊C8—22no—
36C11×C22⋊C8D414yes—
37C4×C8×C11—22no—
38C4×C8×C11C2×C412yes—
39C4×C8×C11D411yescharacteristic
40C4×C8×C11D411yescharacteristic
41C11⋊#95—22no—
42C11⋊#95—22no—
43#66885—22no—
44#66885—22no—
45#66880—22no—
46#66880—22no—
47#9757—111nomaximal, Sylow
48C22×C4×C11C2×D412yes—
49C22×C4×C11C2×D411yescharacteristic
50C2×C22⋊D11—41no—
51C22×Dic11—42no—
52#4339—44no—
53C2×D44—21no—
54C2×D44—22no—
55C2×C4×D11—41no—
56C2×Dic22—21no—
57C2×Dic22—22no—
58C2×C8×C11—24no—
59C2×C8×C11—24no—
60C2×C8×C11C22⋊C412yes—
61C2×C8×C11C22⋊C412yes—
62C42×C11C22×C411yescharacteristic
63C42×C11C2×D411yescharacteristic
64C42×C11#4112yes—
65C22⋊Dic11—41no—
66(C2×D11)⋊C4—42no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—22no—
70C4⋊Dic11—44no—
71Dic11⋊C4—42no—
72C4×Dic11—41no—
73#3131—111no—
74#1835—111no—
75#1518—112no—
76#1517—112no—
77#1450D1111yescharacteristic, complemented
78C23×C11#12711yescharacteristic
79C22×D11—41no—
80C2×C4×C11—42no—
81C2×C4×C11C2×C22⋊C411yescharacteristic
82C2×C4×C11C4×D412yes—
83C2×C4×C11#12112yes—
84C2×C4×C11#12411yescharacteristic
85C2×C4×C11#13514yes—
86C22⋊D11—82no—
87C2×Dic11—42no—
88C2×Dic11—41no—
89C2×Dic11—84no—
90C2×Dic11—82no—
91D44—42no—
92D44—82no—
93C4×D11—82no—
94Dic22—42no—
95Dic22—82no—
96C8×C11—22no—
97C8×C11—22no—
98C8×C11—44no—
99#533—111no—
100#532—111no—
101#488—221no—
102#488—221no—
103#487—112no—
104#486—112no—
105#431C2×D1112yes—
106#416—222no—
107C2×C4×C8C2×D1111yescharacteristic
108#382—112no—
109#340—222no—
110#328—224no—
111#327—224no—
112#322—21no—
113C82—21no—
114C22×C11—22no—
115C22×C11#39011yescharacteristic
116C22×C11#49512yes—
117C2×D11—81no—
118C2×D11—82no—
119C4×C11—22no—
120C4×C11—22no—
121C4×C11#41612yes—
122C4×C11#48812yes—
123Dic11—81no—
124Dic11—82no—
125Dic11—162no—
126C2×#41—221no—
127C22×C8D4412yes—
128C4⋊Q8—111no—
129C4⋊Q8—112no—
130#127—111no—
131#125—221no—
132#124—221no—
133C22⋊Q8—222no—
134#121—222no—
135C4×Q8—222no—
136C4×D4—222no—
137#117—221no—
138C2×C4⋊C4—222no—
139C2×C42C22×D1111yescharacteristic
140C4⋊C8—22no—
141#103—222no—
142#103—222no—
143#102—222no—
144#102—222no—
145C22⋊C8D4414yes—
146C4×C8—22no—
147C4×C8C4×D1112yes—
148C4×C8C22⋊D1111yescharacteristic
149C4×C8C22⋊D1111yescharacteristic
150#95—222no—
151#95—222no—
152C2×C11—22no—
153C2×C11#195811yescharacteristic
154C2×C11#197612yes—
155D11—161no—
156#41—444no—
157C2×Q8—222no—
158C2×Q8—221no—
159C2×D4—222no—
160C2×D4—221no—
161C2×D4—441no—
162C22×C4—441no—
163C22×C4—442no—
164C22×C4C2×D4412yes—
165C22×C4C2×D4411yescharacteristic
166C2×C8—24no—
167C2×C8—24no—
168C2×C8(C2×D11)⋊C412yes—
169C2×C8(C2×D11)⋊C412yes—
170C4⋊C4—222no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4—442no—
174C4⋊C4—444no—
175C22⋊C4—441no—
176C22⋊C4—442no—
177C42—441no—
178C42C2×C4×D1111yescharacteristic
179C42#433912yes—
180C42C2×C22⋊D1111yescharacteristic
181C11#975711yescharacteristic, complemented, Sylow
182C23—441no—
183C23#6692711yescharacteristic
184Q8—442no—
185Q8—882no—
186D4—442no—
187D4—882no—
188D4—882no—
189C2×C4—42no—
190C2×C4—442no—
191C2×C4—441no—
192C2×C4—882no—
193C2×C4—884no—
194C2×C4—882no—
195C2×C4C4×D4412yes—
196C2×C4#6692811yescharacteristic
197C2×C4#6695714yes—
198C2×C4C2×(C2×D11)⋊C411yescharacteristic
199C2×C4#6698312yes—
200C8—22no—
201C8—22no—
202C8—44no—
203C22—22no—
204C22—881no—
205C22—882no—
206C22#1062230912yes—
207C22#1062255211yescharacteristic
208C4—22no—
209C4—22no—
210C4—881no—
211C4—882no—
212C4—1762no—
213C4#1062231012yes—
214C4#1062272612yes—
215C2—22no—
216C2—1761no—
217C2#1306942711yescharacteristic
218C2#1306951412yes—
subgroupG/H
centerC22#10622552
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1450C2
socleC22×C11#390
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1450D11
hypocenterC11#9757
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1450

Complements

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

NH ≅ G/Ntype
2. #13068747C2semidirect
3. #13067181C2semidirect
5. C11×#1450C2semidirect
14. #10622307C4semidirect
15. #10622294C4semidirect
77. #1450D11semidirect
181. C11#9757semidirect

Maximal subgroups

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

subgroupindex
#130789392
#130687472
#130671812
#130671772
C11×#14502
#975711