Finite Group Databasebeta

← C11×#11500 #14588693

Subgroups — C11×#11500 #14588693

Order 2816.

706 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 118 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×#381C211yesmaximal, characteristic
2C11×#1462C212yesmaximal
3C11×#1317C214yesmaximal, complemented
4C24×C4×C11C411yescharacteristic
5C22×C11×C22⋊C4C411yescharacteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C11×#407—22no—
8C11×#381—22no—
9C11×#381C412yes—
10C11×#381C2212yes—
11C2×C11×#95—22no—
12C11×#323—22no—
13C11×#323C2214yes—
14C25×C11C2×C411yescharacteristic
15C23×C4×C11—21no—
16C23×C4×C11—21no—
17C23×C4×C11—24no—
18C23×C4×C11—21no—
19C23×C4×C11—42no—
20C23×C4×C11—42no—
21C23×C4×C11C2×C412yes—
22C23×C4×C11D412yes—
23C2×C11×M16—42no—
24C2×C11×C22⋊C4—21no—
25C2×C11×C22⋊C4—42no—
26C2×C11×C22⋊C4—42no—
27C2×C11×C22⋊C4C2×C412yes—
28C2×C11×C22⋊C4C2×C411yescharacteristic
29C2×C11×C22⋊C4D412yes—
30C2×C11×C22⋊C4C2311yescharacteristic
31C11×C22⋊C8—24no—
32C11×C22⋊C8—42no—
33C11×#95—24no—
34C11×#95—24no—
35#11500C1111yesmaximal, characteristic, direct product factor, Sylow
36C24×C11—22no—
37C24×C11—22no—
38C24×C11—22no—
39C24×C11—44no—
40C24×C11C22⋊C411yescharacteristic
41C24×C11C22⋊C411yescharacteristic
42C24×C11C22×C411yescharacteristic
43C22×C4×C11—24no—
44C22×C4×C11—24no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—416no—
51C22×C4×C11—42no—
52C22×C4×C11—42no—
53C22×C4×C11—42no—
54C22×C4×C11—42no—
55C22×C4×C11—42no—
56C22×C4×C11—42no—
57C22×C4×C11—44no—
58C22×C4×C11—42no—
59C22×C4×C11—44no—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11M1614yescomplemented
62C22×C4×C11C2×D412yes—
63C11×M16—84no—
64C2×C8×C11—44no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—42no—
69C11×C22⋊C4—42no—
70C2×#381C2×C1111yescharacteristic
71#1462C2×C1112yes—
72#1317C2×C1114yescomplemented
73C23×C11—24no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—28no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—42no—
82C23×C11—42no—
83C23×C11—48no—
84C23×C11—48no—
85C23×C11—44no—
86C23×C11—44no—
87C23×C11#9912yes—
88C23×C11#10012yes—
89C23×C11C2×C22⋊C411yescharacteristic
90C23×C11C2×M1612yes—
91C2×C4×C11—24no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—48no—
95C2×C4×C11—48no—
96C2×C4×C11—44no—
97C2×C4×C11—44no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—44no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—44no—
104C2×C4×C11—42no—
105C2×C4×C11—82no—
106C2×C4×C11—84no—
107C8×C11—84no—
108C24×C4C4×C1111yescharacteristic
109C22×C22⋊C4C4×C1111yescharacteristic
110C22×C22⋊C4C22×C1111yescharacteristic
111#407—22no—
112#381—22no—
113#381C4×C1112yes—
114#381C22×C1112yes—
115C2×#95—22no—
116#323—22no—
117#323C22×C1114yes—
118C22×C11—24no—
119C22×C11—24no—
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—416no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11#35214yes—
133C22×C11#40711yescharacteristic
134C22×C11C2×#9911yescharacteristic
135C22×C11C2×#10011yescharacteristic
136C4×C11—42no—
137C4×C11—42no—
138C4×C11—44no—
139C4×C11—82no—
140C25C2×C4×C1111yescharacteristic
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—24no—
144C23×C4—21no—
145C23×C4—42no—
146C23×C4—42no—
147C23×C4C2×C4×C1112yes—
148C23×C4D4×C1112yes—
149C2×M16—42no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4—42no—
152C2×C22⋊C4—42no—
153C2×C22⋊C4C2×C4×C1112yes—
154C2×C22⋊C4C2×C4×C1111yescharacteristic
155C2×C22⋊C4D4×C1112yes—
156C2×C22⋊C4C23×C1111yescharacteristic
157C22⋊C8—24no—
158C22⋊C8—42no—
159#95—24no—
160#95—24no—
161C2×C11—21no—
162C2×C11—24no—
163C2×C11—21no—
164C2×C11—42no—
165C2×C11—42no—
166C2×C11#146211yescharacteristic
167C2×C11C2×#35212yes—
168C24—22no—
169C24—22no—
170C24—22no—
171C24—44no—
172C24C11×C22⋊C411yescharacteristic
173C24C11×C22⋊C411yescharacteristic
174C24C22×C4×C1111yescharacteristic
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—416no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—44no—
190C22×C4—42no—
191C22×C4—44no—
192C22×C4C11×C22⋊C412yes—
193C22×C4C11×M1614yescomplemented
194C22×C4C2×D4×C1112yes—
195M16—84no—
196C2×C8—44no—
197C22⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—41no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C11#1150011yescharacteristic, direct product factor, Sylow
203C23—24no—
204C23—21no—
205C23—21no—
206C23—28no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—42no—
212C23—42no—
213C23—48no—
214C23—48no—
215C23—44no—
216C23—44no—
217C23C11×#9912yes—
218C23C11×#10012yes—
219C23C2×C11×C22⋊C411yescharacteristic
220C23C2×C11×M1612yes—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—48no—
225C2×C4—48no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—84no—
237C8—84no—
238C22—24no—
239C22—24no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—416no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22C11×#35214yes—
253C22C11×#40711yescharacteristic
254C22C2×C11×#9911yescharacteristic
255C22C2×C11×#10011yescharacteristic
256C4—44no—
257C4—42no—
258C4—42no—
259C4—82no—
260C2—21no—
261C2—24no—
262C2—21no—
263C2—42no—
264C2—42no—
265C2C11×#146211yescharacteristic
266C2C2×C11×#35212yes—
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC25×C11C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1317C2semidirect
35. #11500C11direct (N × H)
61. C22×C4×C11M16semidirect
72. #1317C2×C11semidirect
193. C22×C4C11×M16semidirect
202. C11#11500direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3812
C11×#14622
C11×#13172
#1150011