Finite Group Databasebeta

← C11×#21827 #14599020

Subgroups — C11×#21827 #14599020

Order 2816.

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 366 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×C11×#543C211yesmaximal, characteristic
2C11×#2312C212yesmaximal
3C11×#1996C218yesmaximal, complemented
4C11×#1819C214yesmaximal
5C11×#543—28no—
6C2×C11×C22⋊Q8C418yescomplemented
7C2×C11×C22⋊Q8C2214yes—
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2211yescharacteristic
10C11×#388—28no—
11C11×#380C2214yes—
12C11×#379C2214yes—
13C4×C11×C22⋊C4C2214yes—
14C11×#342C22116yes—
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⋊C4—24no—
23C2×C11×C4⋊C4C2×C4112yes—
24C2×C11×C22⋊C4—28no—
25C2×C11×C22⋊C4—24no—
26C2×C11×C22⋊C4—24no—
27C2×C11×C22⋊C4C2×C414yes—
28C2×C11×C22⋊C4C2×C414yes—
29C2×C11×C22⋊C4D418yes—
30C2×C11×C22⋊C4C2318yes—
31C2×C11×C22⋊C4C2314yes—
32C2×C42×C11—24no—
33C11×#95—24no—
34C11×#95—24no—
35#21827C1111yesmaximal, characteristic, direct product factor, 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—28no—
45C22×C4×C11—82no—
46C22×C4×C11—84no—
47C22×C4×C11C22×C418yes—
48C22×C4×C11C22×C414yes—
49C22×C4×C11C2×D414yes—
50C22×C4×C11C2×D414yes—
51C11×C4⋊C4—224no—
52C11×C4⋊C4—84no—
53C11×C22⋊C4—28no—
54C11×C22⋊C4—28no—
55C11×C22⋊C4—216no—
56C11×C22⋊C4—84no—
57C11×C22⋊C4—84no—
58C11×C22⋊C4C22⋊C4116yes—
59C42×C11—84no—
60C2×#543C2×C1111yescharacteristic
61#2312C2×C1112yes—
62#1996C2×C1118yescomplemented
63#1819C2×C1114yes—
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—48no—
82C2×C4×C11—48no—
83C2×C4×C11—48no—
84C2×C4×C11—88no—
85C2×C4×C11C2×C22⋊C418yes—
86#543—28no—
87C2×C22⋊Q8C4×C1118yescomplemented
88C2×C22⋊Q8C22×C1114yes—
89C22×C22⋊C4C22×C1112yes—
90C22×C22⋊C4C22×C1111yescharacteristic
91#388—28no—
92#380C22×C1114yes—
93#379C22×C1114yes—
94C4×C22⋊C4C22×C1114yes—
95#342C22×C11116yes—
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—
109C4×C11—88no—
110C25C23×C1111yescharacteristic
111C22×Q8C2×C4×C1114yes—
112C23×C4C2×C4×C1114yes—
113C23×C4C23×C1112yes—
114C22⋊Q8—28no—
115C22⋊Q8—28no—
116C22⋊Q8—232no—
117C2×C4⋊C4—24no—
118C2×C4⋊C4C2×C4×C11112yes—
119C2×C22⋊C4—28no—
120C2×C22⋊C4—24no—
121C2×C22⋊C4—24no—
122C2×C22⋊C4C2×C4×C1114yes—
123C2×C22⋊C4C2×C4×C1114yes—
124C2×C22⋊C4D4×C1118yes—
125C2×C22⋊C4C23×C1118yes—
126C2×C22⋊C4C23×C1114yes—
127C2×C42—24no—
128#95—24no—
129#95—24no—
130C2×C11—24no—
131C2×C11—22no—
132C2×C11—44no—
133C2×C11#231011yescharacteristic
134C2×C11#288312yes—
135C24—24no—
136C24—82no—
137C24C22×C4×C1112yes—
138C24C2×D4×C1114yes—
139C24C24×C1111yescharacteristic
140C2×Q8—28no—
141C2×Q8—84no—
142C22×C4—28no—
143C22×C4—28no—
144C22×C4—82no—
145C22×C4—84no—
146C22×C4C22×C4×C1118yes—
147C22×C4C22×C4×C1114yes—
148C22×C4C2×D4×C1114yes—
149C22×C4C2×D4×C1114yes—
150C4⋊C4—224no—
151C4⋊C4—84no—
152C22⋊C4—28no—
153C22⋊C4—28no—
154C22⋊C4—216no—
155C22⋊C4—84no—
156C22⋊C4—84no—
157C22⋊C4C11×C22⋊C4116yes—
158C42—84no—
159C11#2182711yescharacteristic, direct product factor, Sylow
160C23—24no—
161C23—28no—
162C23—44no—
163C23—42no—
164C23—44no—
165C23—44no—
166C23—88no—
167C23C2×C11×C22⋊C414yes—
168C23C23×C4×C1111yescharacteristic
169C23C22×D4×C1112yes—
170C23C11×2−1+414yes—
171Q8—88no—
172C2×C4—28no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—48no—
178C2×C4—48no—
179C2×C4—48no—
180C2×C4—88no—
181C2×C4C2×C11×C22⋊C418yes—
182C22—22no—
183C22—22no—
184C22—22no—
185C22—24no—
186C22—28no—
187C22—44no—
188C22—48no—
189C22—88no—
190C22C22×C11×C22⋊C411yescharacteristic
191C22C11×#51912yes—
192C22C11×#53614yes—
193C4—28no—
194C4—48no—
195C4—88no—
196C2—24no—
197C2—22no—
198C2—44no—
199C2C11×#231011yescharacteristic
200C2C11×#288312yes—
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1996C2semidirect
6. C2×C11×C22⋊Q8C4semidirect
35. #21827C11direct (N × H)
62. #1996C2×C11semidirect
87. C2×C22⋊Q8C4×C11semidirect
159. C11#21827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5432
C11×#23122
C11×#19962
C11×#18192
#2182711