Finite Group Databasebeta

← C11×#11509 #14588702

Subgroups — C11×#11509 #14588702

Order 2816.

670 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C11×#2309C211yesmaximal, characteristic
2C11×#1464C212yesmaximal, complemented
3C11×#1318C214yesmaximal, complemented
4C23×D4×C11C411yescharacteristic
5C2×C11×#117C411yescharacteristic
6C2×C11×#117C2211yescharacteristic
7C11×#432—22no—
8C11×#390—22no—
9C11×#390C412yes—
10C11×#390C2212yes—
11C11×#379—22no—
12C11×#324C2214yescomplemented
13C11×#323—22no—
14C25×C11—21no—
15C22×D4×C11—24no—
16C22×D4×C11—21no—
17C22×D4×C11—42no—
18C22×D4×C11—42no—
19C22×D4×C11C2×C412yes—
20C23×C4×C11C2×C411yescharacteristic
21C11×#117—42no—
22C11×#117—42no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4C2×C411yescharacteristic
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C11×C22⋊C4—21no—
27C2×C11×C22⋊C4—24no—
28C2×C11×C22⋊C4—24no—
29C2×C11×C22⋊C4D412yes—
30C2×C42×C11C2×C412yes—
31C2×C42×C11D412yes—
32C11×C4⋊C8—42no—
33C11×C22⋊C8—24no—
34C11×#97—42no—
35#11509C1111yesmaximal, characteristic, direct product factor, Sylow
36C24×C11—24no—
37C24×C11—22no—
38C24×C11—42no—
39C24×C11—42no—
40C24×C11—82no—
41C24×C11—82no—
42C24×C11C22⋊C411yescharacteristic
43C2×D4×C11—24no—
44C2×D4×C11—22no—
45C2×D4×C11—416no—
46C2×D4×C11—42no—
47C2×D4×C11—42no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C2×D4×C11M1614yes—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11C22⋊C412yes—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D412yes—
59C2×C8×C11—44no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—42no—
63C11×C22⋊C4—42no—
64C11×C22⋊C4—42no—
65C11×C22⋊C4—84no—
66C11×C22⋊C4—84no—
67C42×C11—22no—
68C42×C11—22no—
69C42×C11—42no—
70#2309C2×C1111yescharacteristic
71#1464C2×C1112yescomplemented
72#1318C2×C1114yescomplemented
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—24no—
76C23×C11—41no—
77C23×C11—41no—
78C23×C11—44no—
79C23×C11—44no—
80C23×C11—48no—
81C23×C11—42no—
82C23×C11—42no—
83C23×C11—88no—
84C23×C11—88no—
85C23×C11—84no—
86C23×C11—84no—
87C23×C11#10012yes—
88C23×C11C2×C22⋊C411yescharacteristic
89D4×C11—44no—
90D4×C11—48no—
91D4×C11—44no—
92C2×C4×C11—28no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11#9912yes—
105C2×C4×C11C2×M1612yes—
106C8×C11—84no—
107C23×D4C4×C1111yescharacteristic
108C2×#117C4×C1111yescharacteristic
109C2×#117C22×C1111yescharacteristic
110#432—22no—
111#390—22no—
112#390C4×C1112yes—
113#390C22×C1112yes—
114#379—22no—
115#324C22×C1114yescomplemented
116#323—22no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—22no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—48no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—44no—
126C22×C11—84no—
127C22×C11—816no—
128C22×C11—82no—
129C22×C11—82no—
130C22×C11#40711yescharacteristic
131C22×C11C2×#9911yescharacteristic
132C22×C11C2×#10011yescharacteristic
133C4×C11—22no—
134C4×C11—22no—
135C4×C11—42no—
136C4×C11—42no—
137C4×C11—82no—
138C25—21no—
139C22×D4—24no—
140C22×D4—21no—
141C22×D4—42no—
142C22×D4—42no—
143C22×D4C2×C4×C1112yes—
144C23×C4C2×C4×C1111yescharacteristic
145#117—42no—
146#117—42no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4C2×C4×C1111yescharacteristic
149C2×C4⋊C4C23×C1111yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—24no—
152C2×C22⋊C4—24no—
153C2×C22⋊C4D4×C1112yes—
154C2×C42C2×C4×C1112yes—
155C2×C42D4×C1112yes—
156C4⋊C8—42no—
157C22⋊C8—24no—
158#97—42no—
159C2×C11—21no—
160C2×C11—21no—
161C2×C11—42no—
162C2×C11—84no—
163C2×C11#146211yescharacteristic
164C2×C11#212811yescharacteristic
165C2×C11#213411yescharacteristic
166C24—24no—
167C24—22no—
168C24—42no—
169C24—42no—
170C24—82no—
171C24—82no—
172C24C11×C22⋊C411yescharacteristic
173C2×D4—24no—
174C2×D4—22no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—416no—
178C2×D4—42no—
179C2×D4—42no—
180C2×D4C11×M1614yes—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4C11×C22⋊C411yescharacteristic
186C22×C4C11×C22⋊C412yes—
187C22×C4C22×C4×C1111yescharacteristic
188C22×C4C2×D4×C1112yes—
189C2×C8—44no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C22⋊C4—42no—
194C22⋊C4—42no—
195C22⋊C4—84no—
196C22⋊C4—84no—
197C42—22no—
198C42—22no—
199C42—42no—
200C11#1150911yescharacteristic, direct product factor, Sylow
201C23—21no—
202C23—21no—
203C23—24no—
204C23—41no—
205C23—41no—
206C23—44no—
207C23—44no—
208C23—48no—
209C23—42no—
210C23—42no—
211C23—88no—
212C23—88no—
213C23—84no—
214C23—84no—
215C23C11×#10012yes—
216C23C2×C11×C22⋊C411yescharacteristic
217D4—44no—
218D4—48no—
219D4—44no—
220C2×C4—28no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4C11×#9912yes—
233C2×C4C2×C11×M1612yes—
234C8—84no—
235C22—21no—
236C22—21no—
237C22—22no—
238C22—42no—
239C22—42no—
240C22—48no—
241C22—41no—
242C22—41no—
243C22—44no—
244C22—84no—
245C22—816no—
246C22—82no—
247C22—82no—
248C22C11×#40711yescharacteristic
249C22C2×C11×#9911yescharacteristic
250C22C2×C11×#10011yescharacteristic
251C4—22no—
252C4—22no—
253C4—42no—
254C4—42no—
255C4—82no—
256C2—21no—
257C2—21no—
258C2—42no—
259C2—84no—
260C2C11×#146211yescharacteristic
261C2C11×#212811yescharacteristic
262C2C11×#213411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC23×D4×C11C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1464C2semidirect
3. C11×#1318C2semidirect
12. C11×#324C22semidirect
35. #11509C11direct (N × H)
71. #1464C2×C11semidirect
72. #1318C2×C11semidirect
115. #324C22×C11semidirect
200. C11#11509direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23092
C11×#14642
C11×#13182
#1150911