Finite Group Databasebeta

← #14763226

Subgroups — #14763226

Order 2816.

1130 conjugacy classes of subgroups; only the 315 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 315 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#13071214C212yesmaximal
2#13069602C218yesmaximal, complemented
3#13068690C214yesmaximal
4C2×C11×#543C211yesmaximal, characteristic
5C11×#543—28no—
6C2×C11×C22⋊Q8C418yescomplemented
7C2×C11×C22⋊Q8C2214yes—
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2211yescharacteristic
10#10622860C2214yes—
11#10622825C2214yes—
12C4×C22⋊Dic11C2214yes—
13#10622564—28no—
14#10622164C22116yes—
15C25×C11C2311yescharacteristic
16C22×Q8×C11C2×C414yes—
17C23×C4×C11C2×C414yes—
18C23×C4×C11C2312yes—
19C11×C22⋊Q8—28no—
20C11×C22⋊Q8—28no—
21C11×C22⋊Q8—232no—
22C2×C11×C4⋊C4C2×C4112yes—
23C2×C11×C22⋊C4—28no—
24C2×C11×C22⋊C4C2×C414yes—
25C2×C11×C22⋊C4C2×C414yes—
26C2×C11×C22⋊C4D418yes—
27C2×C11×C22⋊C4C2314yes—
28C2×C22⋊Dic11—24no—
29C2×C22⋊Dic11—24no—
30C2×C22⋊Dic11C2318yes—
31C2×C4⋊Dic11—24no—
32C2×C4×Dic11—24no—
33C11⋊#95—24no—
34C11⋊#95—24no—
35#21827—111nomaximal, Sylow
36C24×C11—24no—
37C24×C11—82no—
38C24×C11C22×C412yes—
39C24×C11C2×D414yes—
40C24×C11C2411yescharacteristic
41C2×Q8×C11—28no—
42C2×Q8×C11—84no—
43C22×C4×C11—28no—
44C22×C4×C11—82no—
45C22×C4×C11—84no—
46C22×C4×C11C22×C418yes—
47C22×C4×C11C22×C414yes—
48C22×C4×C11C2×D414yes—
49C22×C4×C11C2×D414yes—
50C22×Dic11—28no—
51C11×C4⋊C4—224no—
52C11×C22⋊C4—28no—
53C11×C22⋊C4—28no—
54C11×C22⋊C4C22⋊C4116yes—
55C22⋊Dic11—216no—
56C22⋊Dic11—84no—
57C22⋊Dic11—84no—
58C4⋊Dic11—84no—
59C4×Dic11—84no—
60C2×#543D1111yescharacteristic
61#2312—112no—
62#1996—118no—
63#1819—114no—
64C23×C11—24no—
65C23×C11—28no—
66C23×C11—44no—
67C23×C11—42no—
68C23×C11—44no—
69C23×C11—44no—
70C23×C11—88no—
71C23×C11C2×C22⋊C414yes—
72C23×C11C23×C411yescharacteristic
73C23×C11C22×D412yes—
74C23×C112−1+414yes—
75Q8×C11—88no—
76C2×C4×C11—28no—
77C2×C4×C11—44no—
78C2×C4×C11—44no—
79C2×C4×C11—44no—
80C2×C4×C11—48no—
81C2×C4×C11—88no—
82C2×C4×C11C2×C22⋊C418yes—
83C2×Dic11—48no—
84C2×Dic11—48no—
85C2×Dic11—48no—
86#543—28no—
87C2×C22⋊Q8Dic1118yescomplemented
88C2×C22⋊Q8C2×D1114yes—
89C22×C22⋊C4C2×D1112yes—
90C22×C22⋊C4C2×D1111yescharacteristic
91#388—228no—
92#380—114no—
93#379—114no—
94C4×C22⋊C4—114no—
95#342—1116no—
96C22×C11—22no—
97C22×C11—22no—
98C22×C11—22no—
99C22×C11—24no—
100C22×C11—28no—
101C22×C11—44no—
102C22×C11—48no—
103C22×C11—88no—
104C22×C11C22×C22⋊C411yescharacteristic
105C22×C11#51912yes—
106C22×C11#53614yes—
107C4×C11—28no—
108C4×C11—48no—
109Dic11—88no—
110C25C22×D1111yescharacteristic
111C22×Q8C2×Dic1114yes—
112C23×C4C2×Dic1114yes—
113C23×C4C22×D1112yes—
114C22⋊Q8—28no—
115C22⋊Q8—28no—
116C22⋊Q8—232no—
117C2×C4⋊C4—224no—
118C2×C4⋊C4C2×Dic11112yes—
119C2×C22⋊C4—28no—
120C2×C22⋊C4—118no—
121C2×C22⋊C4—224no—
122C2×C22⋊C4—224no—
123C2×C22⋊C4C2×Dic1114yes—
124C2×C22⋊C4C2×Dic1114yes—
125C2×C22⋊C4C22⋊D1118yes—
126C2×C22⋊C4C22×D1114yes—
127C2×C42—224no—
128#95—224no—
129#95—224no—
130C2×C11—24no—
131C2×C11—22no—
132C2×C11—44no—
133C2×C11#231011yescharacteristic
134C2×C11#288312yes—
135C24—24no—
136C24—82no—
137C24C22×Dic1112yes—
138C24C2×C22⋊D1114yes—
139C24C23×D1111yescharacteristic
140C2×Q8—28no—
141C2×Q8—84no—
142C22×C4—28no—
143C22×C4—82no—
144C22×C4—84no—
145C22×C4—228no—
146C22×C4C22×Dic1118yes—
147C22×C4C22×Dic1114yes—
148C22×C4C2×C22⋊D1114yes—
149C22×C4C2×C22⋊D1114yes—
150C4⋊C4—224no—
151C4⋊C4—884no—
152C22⋊C4—28no—
153C22⋊C4—28no—
154C22⋊C4—2216no—
155C22⋊C4—884no—
156C22⋊C4—884no—
157C22⋊C4C22⋊Dic11116yes—
158C42—884no—
159C11#2182711yescharacteristic, complemented, Sylow
160C23—24no—
161C23—28no—
162C23—44no—
163C23—42no—
164C23—44no—
165C23—44no—
166C23—88no—
167C23C2×C22⋊Dic1114yes—
168C23#6704014yes—
169C23C23×Dic1111yescharacteristic
170C23C22×C22⋊D1112yes—
171Q8—88no—
172C2×C4—28no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—88no—
178C2×C4—448no—
179C2×C4—448no—
180C2×C4—448no—
181C2×C4C2×C22⋊Dic1118yes—
182C22—22no—
183C22—22no—
184C22—22no—
185C22—28no—
186C22—24no—
187C22—44no—
188C22—48no—
189C22—88no—
190C22#1062334312yes—
191C22#1062334714yes—
192C22C22×C22⋊Dic1111yescharacteristic
193C4—28no—
194C4—48no—
195C4—888no—
196C2—24no—
197C2—22no—
198C2—44no—
199C2#1307120211yescharacteristic
200C2#1307707712yes—
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C11×#543C2
socleC22×C11C22×C22⋊C4
prime radicalC25×C11C23
cosocleC24×C11C24
hypercenterC2×#543D11
hypocenterC11#21827
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
2. #13069602C2semidirect
6. C2×C11×C22⋊Q8C4semidirect
87. C2×C22⋊Q8Dic11semidirect
159. C11#21827semidirect

Maximal subgroups

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

subgroupindex
#130712142
#130696022
#130686902
C2×C11×#5432
#2182711