Finite Group Databasebeta

← C11×#11504 #14588697

Subgroups — C11×#11504 #14588697

Order 2816.

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

normal subgroups only

This group has 510 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×#2310C211yesmaximal, characteristic
2C11×#1464C212yesmaximal
3C11×#1317C214yesmaximal
4C23×Q8×C11C411yescharacteristic
5C2×C11×#117C411yescharacteristic
6C2×C11×#117C2211yescharacteristic
7C11×#432—22no—
8C11×#391—22no—
9C11×#391—22no—
10C11×#381C412yes—
11C11×#381C2212yes—
12C11×#324—22no—
13C11×#323C2214yes—
14C22×Q8×C11—21no—
15C22×Q8×C11—21no—
16C22×Q8×C11—24no—
17C22×Q8×C11—41no—
18C22×Q8×C11—41no—
19C22×Q8×C11—42no—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11C2×C412yes—
22C11×#117—41no—
23C11×#117—41no—
24C11×#117—42no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4D412yes—
27C2×C11×C22⋊C4C2×C412yes—
28C2×C11×C22⋊C4C2×C411yescharacteristic
29C2×C11×C22⋊C4C2311yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11D412yes—
32C11×C4⋊C8—42no—
33C11×C22⋊C8—24no—
34C11×#97—42no—
35C11×#95—24no—
36C11×#95—24no—
37#11504C1111yesmaximal, characteristic, direct product factor, Sylow
38C24×C11C22×C411yescharacteristic
39C2×Q8×C11—24no—
40C2×Q8×C11—24no—
41C2×Q8×C11—48no—
42C2×Q8×C11—48no—
43C2×Q8×C11—42no—
44C2×Q8×C11—42no—
45C2×Q8×C11—41no—
46C2×Q8×C11—41no—
47C2×Q8×C11—42no—
48C22×C4×C11—22no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—42no—
56C22×C4×C11—42no—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11M1614yes—
61C22×C4×C11C2×D412yes—
62C2×C8×C11—44no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—42no—
68C42×C11—22no—
69C42×C11—22no—
70C42×C11—42no—
71#2310C2×C1111yescharacteristic
72#1464C2×C1112yes—
73#1317C2×C1114yes—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—42no—
77C23×C11C2×C22⋊C411yescharacteristic
78C23×C11C2×M1612yes—
79Q8×C11—44no—
80Q8×C11—44no—
81Q8×C11—48no—
82C2×C4×C11—24no—
83C2×C4×C11—24no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—24no—
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—42no—
97C2×C4×C11—44no—
98C2×C4×C11—42no—
99C2×C4×C11#9911yescharacteristic
100C2×C4×C11#9911yescharacteristic
101C2×C4×C11#10012yes—
102C8×C11—84no—
103C23×Q8C4×C1111yescharacteristic
104C2×#117C4×C1111yescharacteristic
105C2×#117C22×C1111yescharacteristic
106#432—22no—
107#391—22no—
108#391—22no—
109#381C4×C1112yes—
110#381C22×C1112yes—
111#324—22no—
112#323C22×C1114yes—
113C22×C11—22no—
114C22×C11—22no—
115C22×C11—42no—
116C22×C11—42no—
117C22×C11—42no—
118C22×C11#40711yescharacteristic
119C22×C11C2×#9911yescharacteristic
120C22×C11C2×#10011yescharacteristic
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—22no—
124C4×C11—42no—
125C4×C11—42no—
126C4×C11—44no—
127C4×C11—82no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—24no—
131C22×Q8—41no—
132C22×Q8—41no—
133C22×Q8—42no—
134C23×C4C2×C4×C1111yescharacteristic
135C23×C4C2×C4×C1112yes—
136#117—41no—
137#117—41no—
138#117—42no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4D4×C1112yes—
141C2×C22⋊C4C2×C4×C1112yes—
142C2×C22⋊C4C2×C4×C1111yescharacteristic
143C2×C22⋊C4C23×C1111yescharacteristic
144C2×C42—21no—
145C2×C42D4×C1112yes—
146C4⋊C8—42no—
147C22⋊C8—24no—
148#97—42no—
149#95—24no—
150#95—24no—
151C2×C11—21no—
152C2×C11—21no—
153C2×C11—42no—
154C2×C11#146211yescharacteristic
155C2×C11#212312yes—
156C24C22×C4×C1111yescharacteristic
157C2×Q8—24no—
158C2×Q8—24no—
159C2×Q8—48no—
160C2×Q8—48no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—42no—
166C22×C4—22no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4C11×C22⋊C411yescharacteristic
176C22×C4C11×C22⋊C411yescharacteristic
177C22×C4C11×C22⋊C412yes—
178C22×C4C11×M1614yes—
179C22×C4C2×D4×C1112yes—
180C2×C8—44no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—42no—
186C42—22no—
187C42—22no—
188C42—42no—
189C11#1150411yescharacteristic, direct product factor, Sylow
190C23—21no—
191C23—21no—
192C23—42no—
193C23C2×C11×C22⋊C411yescharacteristic
194C23C2×C11×M1612yes—
195Q8—44no—
196Q8—44no—
197Q8—48no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—44no—
214C2×C4—42no—
215C2×C4C11×#9911yescharacteristic
216C2×C4C11×#9911yescharacteristic
217C2×C4C11×#10012yes—
218C8—84no—
219C22—22no—
220C22—22no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C11×#40711yescharacteristic
225C22C2×C11×#9911yescharacteristic
226C22C2×C11×#10011yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—42no—
231C4—42no—
232C4—44no—
233C4—82no—
234C2—21no—
235C2—21no—
236C2—42no—
237C2C11×#146211yescharacteristic
238C2C11×#212312yes—
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC24×C11C22×C4
LCSG ▷ C24 ▷ 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
37. #11504C11direct (N × H)
189. C11#11504direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23102
C11×#14642
C11×#13172
#1150411