Finite Group Databasebeta

← #14763187

Subgroups — #14763187

Order 2816.

1042 conjugacy classes of subgroups; only the 267 normal subgroups are shown.

normal subgroups only

This group has 1042 conjugacy classes of subgroups — too many to draw. Only its 267 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
1C2×#10623048C211yesmaximal, characteristic
2C2×#10622331C212yesmaximal
3#13069550C218yesmaximal, complemented
4#13068687C211yesmaximal, characteristic
5#13068685C212yesmaximal
6C11×#1818C211yesmaximal, characteristic
7C2×C11×#117C2211yescharacteristic
8C2×#66979C2211yescharacteristic
9C22×C4×Dic11C2211yescharacteristic
10#10623048—28no—
11C2×#66943C412yes—
12C2×#66941C412yes—
13C2×#66931C414yes—
14C2×C4×Dic22C2214yes—
15C2×C11×C22⋊C8C2212yes—
16C2×C22⋊(C11⋊C8)C2212yes—
17C2×Dic11⋊C8C2214yes—
18C2×C8×Dic11C2214yes—
19#10622331—28no—
20C11×#336C2214yes—
21#10622188C2218yes—
22#10622162C2214yes—
23C23×C4×C11C2311yescharacteristic
24C23×Dic11C2×C412yes—
25C22×Dic22C2×C414yes—
26C22×C8×C11C2314yes—
27C11×#117—24no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C22⋊C4C2×C412yes—
30C2×C42×C11C2312yes—
31C2×C22⋊Dic11C2×C412yes—
32#66979—24no—
33C2×C4⋊Dic11C2×C414yes—
34C2×C4⋊Dic11C2×C412yes—
35C2×Dic11⋊C4C2×C414yes—
36C2×Dic11⋊C4C2×C414yes—
37C2×C4×Dic11C2×C411yescharacteristic
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11D418yes—
40C2×C4×Dic11C2312yes—
41C2×C4×Dic11C2312yes—
42C22×C11⋊C8C2314yes—
43#66943—28no—
44#66941—28no—
45#66931—216no—
46C4×Dic22—28no—
47C4×Dic22—28no—
48C11×C22⋊C8—24no—
49C22⋊(C11⋊C8)—24no—
50Dic11⋊C8—28no—
51C8×Dic11—28no—
52#21819—111nomaximal, Sylow
53C24×C11C22×C411yescharacteristic
54C22×C4×C11—24no—
55C22×C4×C11C22×C414yes—
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D414yes—
58C22×C4×C11C2411yescharacteristic
59C22×Dic11—28no—
60C22×Dic11C22⋊C418yes—
61C22×Dic11C22×C414yes—
62C22×Dic11C22×C412yes—
63C22×Dic11C22×C412yes—
64C2×Dic22—28no—
65C2×Dic22—216no—
66C2×C8×C11—24no—
67C2×C8×C11—28no—
68C11×C4⋊C4—24no—
69C11×C22⋊C4—24no—
70C42×C11—24no—
71C22⋊Dic11—24no—
72C4⋊Dic11—28no—
73C4⋊Dic11—24no—
74Dic11⋊C4—28no—
75Dic11⋊C4—28no—
76C4×Dic11—24no—
77C4×Dic11C22⋊C414yes—
78C4×Dic11C22⋊C414yes—
79C4×Dic11C2×D414yes—
80C4×Dic11C2×D414yes—
81C2×C11⋊C8—24no—
82C2×C11⋊C8—28no—
83C2×#533—111no—
84C2×#431—112no—
85#1984—118no—
86#1818—112no—
87#1818—111no—
88#1818D1111yescharacteristic
89C23×C11—22no—
90C23×C11—24no—
91C23×C11C2×C22⋊C412yes—
92C23×C11C23×C411yescharacteristic
93C2×C4×C11—22no—
94C2×C4×C11—28no—
95C2×C4×C11—24no—
96C2×C4×C11—28no—
97C2×C4×C11C2×C22⋊C412yes—
98C2×C4×C11C22×D412yes—
99C2×C4×C112−1+414yes—
100C2×Dic11—24no—
101C2×Dic11—216no—
102C2×Dic11—24no—
103C2×Dic11—28no—
104C2×Dic11C2×C22⋊C414yes—
105C2×Dic11C2×C22⋊C414yes—
106C2×Dic11#13118yes—
107Dic22—416no—
108C8×C11—44no—
109C11⋊C8—44no—
110#533—228no—
111C2×C4⋊Q8—112no—
112C2×#125—112no—
113C2×C22⋊Q8—114no—
114C2×C4×Q8—114no—
115C2×#117—111no—
116C2×#117C2×D1111yescharacteristic
117C22×C42—111no—
118#431—228no—
119C2×C4⋊C8—114no—
120C2×C22⋊C8—112no—
121C2×C22⋊C8C2×D1112yes—
122C2×C4×C8—114no—
123#336—118no—
124#336—114no—
125#336C2×D1114yes—
126C22×C11—22no—
127C22×C11—24no—
128C22×C11—44no—
129C22×C11C22×C22⋊C411yescharacteristic
130C22×C11#51912yes—
131C22×C11C2×#13114yes—
132C4×C11—22no—
133C4×C11—44no—
134C4×C11#53614yes—
135Dic11—24no—
136Dic11—44no—
137Dic11#40818yes—
138C22×Q8—114no—
139C23×C4—112no—
140C23×C4C22×D1111yescharacteristic
141C22×C8—114no—
142C22×C8C22×D1114yes—
143C4⋊Q8—228no—
144#125—228no—
145C22⋊Q8—2216no—
146C4×Q8—228no—
147C4×Q8—228no—
148#117—24no—
149#117—224no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—114no—
152C2×C4⋊C4—114no—
153C2×C4⋊C4—114no—
154C2×C4⋊C4C4×D1112yes—
155C2×C22⋊C4—112no—
156C2×C22⋊C4C4×D1112yes—
157C2×C42—111no—
158C2×C42—111no—
159C2×C42—118no—
160C2×C42—112no—
161C2×C42—112no—
162C2×C42C22×D1112yes—
163C4⋊C8—228no—
164C22⋊C8—24no—
165C22⋊C8—224no—
166C4×C8—228no—
167C2×C11—42no—
168C2×C11#231011yescharacteristic
169C2×C11C2×#40812yes—
170C2×C11#298614yes—
171C24C2×C4×D1111yescharacteristic
172C2×Q8—228no—
173C2×Q8—2216no—
174C22×C4—24no—
175C22×C4—112no—
176C22×C4—118no—
177C22×C4—112no—
178C22×C4—114no—
179C22×C4—228no—
180C22×C4C2×C4×D1114yes—
181C22×C4C2×C4×D1111yescharacteristic
182C22×C4D4×D1114yes—
183C22×C4C23×D1111yescharacteristic
184C2×C8—24no—
185C2×C8—28no—
186C2×C8—224no—
187C2×C8—228no—
188C4⋊C4—24no—
189C4⋊C4—228no—
190C4⋊C4—228no—
191C4⋊C4—228no—
192C4⋊C4—224no—
193C22⋊C4—24no—
194C22⋊C4—224no—
195C42—24no—
196C42—114no—
197C42—114no—
198C42—114no—
199C42—114no—
200C42—224no—
201C11#2181911yescharacteristic, complemented, Sylow
202C23—24no—
203C23—22no—
204C23C22⋊C4×D1112yes—
205C23C22×C4×D1111yescharacteristic
206Q8—4416no—
207C2×C4—22no—
208C2×C4—28no—
209C2×C4—24no—
210C2×C4—28no—
211C2×C4—114no—
212C2×C4—118no—
213C2×C4—114no—
214C2×C4—2216no—
215C2×C4—224no—
216C2×C4—224no—
217C2×C4—228no—
218C2×C4C22⋊C4×D1112yes—
219C2×C4C2×D4×D1112yes—
220C2×C4#6704314yes—
221C8—44no—
222C8—444no—
223C22—24no—
224C22—22no—
225C22—44no—
226C22C2×C22⋊C4×D1111yescharacteristic
227C22#1062304712yes—
228C22D11×#13114yes—
229C4—22no—
230C4—44no—
231C4—118no—
232C4—224no—
233C4—444no—
234C4#1062317914yes—
235C2—42no—
236C2#1307120111yescharacteristic
237C2D11×#40812yes—
238C2#1307771514yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1818C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1818D11
hypocenterC11#21819
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
3. #13069550C2semidirect
201. C11#21819semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106223312
#130695502
#130686872
#130686852
C11×#18182
#2181911