Finite Group Databasebeta

← #14653157

Subgroups — #14653157

Order 2816.

400 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 119 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#13068747C211yesmaximal, characteristic, complemented
2#13067180C212yesmaximal, complemented
3#13067176C212yesmaximal
4#13066899C211yesmaximal, characteristic, complemented
5C11×#3131C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C11×#532C2211yescharacteristic
8C11×#488—21no—
9C11×#488—21no—
10C11×#487C412yescomplemented
11C11×#486C412yescomplemented
12C11×#416—22no—
13C2×C4×C8×C11C2211yescharacteristic
14#10622549C2212yes—
15#10622538C2212yes—
16#10622189—22no—
17#10622176—24no—
18#10622175—24no—
19#10622093—21no—
20C8×C11⋊C8—21no—
21C2×C11×#41—21no—
22C22×C8×C11D412yes—
23C11×C4⋊Q8C2×C411yescharacteristic
24C11×C4⋊Q8C2×C412yes—
25C11×#127C2×C411yescharacteristic
26C11×#125—21no—
27C11×#124—21no—
28C11×C22⋊Q8—22no—
29C11×#121—22no—
30C4×Q8×C11—22no—
31C4×D4×C11—22no—
32C11×#117—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—22no—
35C11×#103—22no—
36C11×#103—22no—
37C11×#102—22no—
38C11×#102—22no—
39C4×C8×C11C2×C412yes—
40C4×C8×C11D411yescharacteristic
41C4×C8×C11D411yescharacteristic
42C11⋊#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)D414yes—
45C4⋊(C11⋊C8)—22no—
46C4×C11⋊C8—22no—
47#9757—111nomaximal, Sylow
48C11×#41—44no—
49C2×Q8×C11—21no—
50C2×Q8×C11—22no—
51C2×D4×C11—21no—
52C2×D4×C11—22no—
53C2×D4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11C2×D412yes—
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—42no—
58C2×C8×C11—24no—
59C2×C8×C11C22⋊C412yes—
60C2×C8×C11C22⋊C412yes—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—22no—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4—42no—
67C42×C11—41no—
68C42×C11C22×C411yescharacteristic
69C42×C11C2×D411yescharacteristic
70C42×C11#4112yes—
71C4⋊Dic11—44no—
72C2×C11⋊C8—24no—
73#3131D1111yescharacteristic
74#1835—111no—
75#1518—112no—
76#1517—112no—
77#1450—111no—
78C23×C11—41no—
79C23×C11#12711yescharacteristic
80Q8×C11—42no—
81Q8×C11—82no—
82D4×C11—42no—
83D4×C11—82no—
84D4×C11—82no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—41no—
88C2×C4×C11—82no—
89C2×C4×C11C2×C22⋊C411yescharacteristic
90C2×C4×C11C4×D412yes—
91C2×C4×C11#12112yes—
92C2×C4×C11#12411yescharacteristic
93C2×C4×C11#13514yes—
94C2×Dic11—84no—
95C2×Dic11—82no—
96C8×C11—22no—
97C8×C11—22no—
98C11⋊C8—44no—
99#533C2×D1111yescharacteristic
100#532C2×D1111yescharacteristic
101#488—21no—
102#488—21no—
103#487Dic1112yescomplemented
104#486Dic1112yescomplemented
105#431—112no—
106#416—22no—
107C2×C4×C8C2×D1111yescharacteristic
108#382—112no—
109#340—222no—
110#328—224no—
111#327—224no—
112#322—221no—
113C82—221no—
114C22×C11—22no—
115C22×C11—81no—
116C22×C11—82no—
117C22×C11#39011yescharacteristic
118C22×C11#49512yes—
119C4×C11—22no—
120C4×C11—22no—
121C4×C11—81no—
122C4×C11—82no—
123C4×C11#41612yes—
124C4×C11#48812yes—
125Dic11—162no—
126C2×#41—21no—
127C22×C8C22⋊D1112yes—
128C4⋊Q8C2×Dic1111yescharacteristic
129C4⋊Q8C2×Dic1112yes—
130#127C2×Dic1111yescharacteristic
131#125—21no—
132#124—21no—
133C22⋊Q8—22no—
134#121—22no—
135C4×Q8—22no—
136C4×D4—22no—
137#117—21no—
138C2×C4⋊C4—222no—
139C2×C42C22×D1111yescharacteristic
140C4⋊C8—222no—
141#103—22no—
142#103—22no—
143#102—22no—
144#102—22no—
145C22⋊C8—114no—
146C4×C8—222no—
147C4×C8C2×Dic1112yes—
148C4×C8C22⋊D1111yescharacteristic
149C4×C8C22⋊D1111yescharacteristic
150#95—222no—
151#95—222no—
152C2×C11—22no—
153C2×C11—161no—
154C2×C11#195811yescharacteristic
155C2×C11#197612yes—
156#41—44no—
157C2×Q8—22no—
158C2×Q8—21no—
159C2×D4—22no—
160C2×D4—21no—
161C2×D4—41no—
162C22×C4—41no—
163C22×C4—442no—
164C22×C4D4×D1112yes—
165C22×C4C2×C22⋊D1111yescharacteristic
166C2×C8—24no—
167C2×C8—224no—
168C2×C8C22⋊Dic1112yes—
169C2×C8C22⋊Dic1112yes—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—444no—
175C22⋊C4—41no—
176C22⋊C4—42no—
177C42—41no—
178C42#434112yes—
179C42C22×Dic1111yescharacteristic
180C42C2×C22⋊D1111yescharacteristic
181C11#975711yescharacteristic, complemented, Sylow
182C23—41no—
183C23#6699311yescharacteristic
184Q8—42no—
185Q8—82no—
186D4—42no—
187D4—82no—
188D4—82no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—82no—
193C2×C4—884no—
194C2×C4—882no—
195C2×C4D4×Dic1112yes—
196C2×C4#6698911yescharacteristic
197C2×C4#6699112yes—
198C2×C4#6700314yes—
199C2×C4C2×C22⋊Dic1111yescharacteristic
200C8—22no—
201C8—22no—
202C8—444no—
203C22—22no—
204C22—81no—
205C22—82no—
206C22#1062267212yes—
207C22#1062283411yescharacteristic
208C4—22no—
209C4—22no—
210C4—81no—
211C4—82no—
212C4—1762no—
213C4#1062266912yes—
214C4#1062284612yes—
215C2—22no—
216C2—161no—
217C2#1306942811yescharacteristic
218C2#1306951512yes—
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3131C2
socleC22×C11#390
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3131D11
hypocenterC11#9757
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #13068747C2semidirect
2. #13067180C2semidirect
4. #13066899C2semidirect
10. C11×#487C4semidirect
11. C11×#486C4semidirect
103. #487Dic11semidirect
104. #486Dic11semidirect
181. C11#9757semidirect

Maximal subgroups

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

subgroupindex
#130687472
#130671802
#130671762
#130668992
C11×#31312
#975711