Finite Group Databasebeta

← C11×#11512 #14588705

Subgroups — C11×#11512 #14588705

Order 2816.

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

normal subgroups only

This group has 578 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×#384C211yesmaximal, characteristic
2C11×#1463C212yesmaximal
3C11×#1325C214yesmaximal, complemented
4C22×C11×C4⋊C4—22no—
5C22×C11×C4⋊C4C411yescharacteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C22×C42×C11C411yescharacteristic
8C11×#407—22no—
9C11×#384—22no—
10C11×#384C412yes—
11C11×#384C2212yes—
12C11×#324—22no—
13C11×#324C2214yes—
14C23×C4×C11—21no—
15C23×C4×C11—21no—
16C23×C4×C11C2×C411yescharacteristic
17C23×C4×C11D412yes—
18C2×C11×M16—42no—
19C2×C11×C4⋊C4—24no—
20C2×C11×C4⋊C4—21no—
21C2×C11×C4⋊C4—24no—
22C2×C11×C4⋊C4—41no—
23C2×C11×C4⋊C4—41no—
24C2×C11×C4⋊C4—41no—
25C2×C11×C4⋊C4—41no—
26C2×C11×C4⋊C4—48no—
27C2×C11×C4⋊C4C2×C412yes—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4D412yes—
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11—21no—
32C2×C42×C11—24no—
33C2×C42×C11C2×C412yes—
34C11×C22⋊C8—24no—
35C11×C22⋊C8—42no—
36#11512C1111yesmaximal, characteristic, direct product factor, Sylow
37C24×C11C22⋊C411yescharacteristic
38C22×C4×C11—24no—
39C22×C4×C11—24no—
40C22×C4×C11—24no—
41C22×C4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—44no—
50C22×C4×C11—44no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C412yes—
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D412yes—
57C11×M16—84no—
58C2×C8×C11—44no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—48no—
63C11×C4⋊C4—48no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C42×C11—24no—
67C42×C11—22no—
68C42×C11M1614yescomplemented
69C2×#384C2×C1111yescharacteristic
70#1463C2×C1112yes—
71#1325C2×C1114yescomplemented
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11#9911yescharacteristic
77C23×C11#9911yescharacteristic
78C23×C11C2×C22⋊C411yescharacteristic
79C2×C4×C11—24no—
80C2×C4×C11—216no—
81C2×C4×C11—24no—
82C2×C4×C11—24no—
83C2×C4×C11—24no—
84C2×C4×C11—21no—
85C2×C4×C11—24no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—44no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—44no—
95C2×C4×C11—42no—
96C2×C4×C11—82no—
97C2×C4×C11—82no—
98C2×C4×C11—82no—
99C2×C4×C11#10112yes—
100C2×C4×C11C2×M1612yes—
101C8×C11—84no—
102C22×C4⋊C4—22no—
103C22×C4⋊C4C4×C1111yescharacteristic
104C22×C4⋊C4C22×C1111yescharacteristic
105C22×C42C4×C1111yescharacteristic
106#407—22no—
107#384—22no—
108#384C4×C1112yes—
109#384C22×C1112yes—
110#324—22no—
111#324C22×C1114yes—
112C22×C11—24no—
113C22×C11—24no—
114C22×C11—21no—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—21no—
120C22×C11#35312yes—
121C22×C11#35612yes—
122C22×C11#40711yescharacteristic
123C22×C11C2×#9911yescharacteristic
124C22×C11C2×#10111yescharacteristic
125C4×C11—28no—
126C4×C11—22no—
127C4×C11—22no—
128C4×C11—42no—
129C4×C11—42no—
130C4×C11—82no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4C2×C4×C1111yescharacteristic
134C23×C4D4×C1112yes—
135C2×M16—42no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—24no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—48no—
144C2×C4⋊C4C2×C4×C1112yes—
145C2×C4⋊C4C2×C4×C1111yescharacteristic
146C2×C4⋊C4D4×C1112yes—
147C2×C4⋊C4C23×C1111yescharacteristic
148C2×C42—21no—
149C2×C42—24no—
150C2×C42C2×C4×C1112yes—
151C22⋊C8—24no—
152C22⋊C8—42no—
153C2×C11—21no—
154C2×C11—22no—
155C2×C11—22no—
156C2×C11—21no—
157C2×C11#146311yescharacteristic
158C2×C11C2×#35311yescharacteristic
159C2×C11C2×#35611yescharacteristic
160C24C11×C22⋊C411yescharacteristic
161C22×C4—24no—
162C22×C4—24no—
163C22×C4—24no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—44no—
173C22×C4—44no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4C11×C22⋊C411yescharacteristic
177C22×C4C11×C22⋊C412yes—
178C22×C4C22×C4×C1111yescharacteristic
179C22×C4C2×D4×C1112yes—
180M16—84no—
181C2×C8—44no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—48no—
187C4⋊C4—48no—
188C4⋊C4—42no—
189C42—24no—
190C42—22no—
191C42C11×M1614yescomplemented
192C11#1151211yescharacteristic, direct product factor, Sylow
193C23—22no—
194C23—22no—
195C23—21no—
196C23—21no—
197C23C11×#9911yescharacteristic
198C23C11×#9911yescharacteristic
199C23C2×C11×C22⋊C411yescharacteristic
200C2×C4—24no—
201C2×C4—216no—
202C2×C4—24no—
203C2×C4—24no—
204C2×C4—24no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—44no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4—82no—
219C2×C4—82no—
220C2×C4C11×#10112yes—
221C2×C4C2×C11×M1612yes—
222C8—84no—
223C22—24no—
224C22—24no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22C11×#35312yes—
232C22C11×#35612yes—
233C22C11×#40711yescharacteristic
234C22C2×C11×#9911yescharacteristic
235C22C2×C11×#10111yescharacteristic
236C4—28no—
237C4—22no—
238C4—22no—
239C4—42no—
240C4—42no—
241C4—82no—
242C2—21no—
243C2—22no—
244C2—22no—
245C2—21no—
246C2C11×#146311yescharacteristic
247C2C2×C11×#35311yescharacteristic
248C2C2×C11×#35611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC24×C11C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1325C2semidirect
36. #11512C11direct (N × H)
68. C42×C11M16semidirect
71. #1325C2×C11semidirect
191. C42C11×M16semidirect
192. C11#11512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3842
C11×#14632
C11×#13252
#1151211