Finite Group Databasebeta

← C11×#11520 #14588713

Subgroups — C11×#11520 #14588713

Order 2816.

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

normal subgroups only

This group has 418 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×#2317C211yesmaximal, characteristic
2C11×#1464C211yesmaximal, characteristic
3C11×#1464C211yesmaximal, characteristic
4C11×#1326C214yesmaximal
5C2×C11×#117C411yescharacteristic
6C2×C11×#117C2211yescharacteristic
7C22×C11×C4⋊C4C411yescharacteristic
8C11×#432—21no—
9C11×#432—21no—
10C11×#389—21no—
11C11×#389—21no—
12C11×#385C412yes—
13C11×#385C2212yes—
14C11×#384—21no—
15C11×#382—21no—
16C11×#324—21no—
17C11×#324—21no—
18C11×#323C2212yes—
19C11×#323C2212yes—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11C2×C412yes—
22C11×#117—24no—
23C11×#117—41no—
24C11×#117—41no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2×C412yes—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C11×C4⋊C8—41no—
41C11×C4⋊C8—41no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—22no—
44C11×#97—41no—
45C11×#97—41no—
46C11×#95—22no—
47C11×#95—22no—
48#11520C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11C22×C411yescharacteristic
50C22×C4×C11—22no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—42no—
57C22×C4×C11—82no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C2×C8×C11—42no—
65C2×C8×C11—42no—
66C11×C4⋊C4—24no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—82no—
73C11×C4⋊C4—82no—
74C11×C22⋊C4—22no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4M1614yes—
78C42×C11—24no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83#2317C2×C1111yescharacteristic
84#1464C2×C1111yescharacteristic
85#1464C2×C1111yescharacteristic
86#1326C2×C1114yes—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—41no—
90C23×C11—41no—
91C23×C11C2×C22⋊C411yescharacteristic
92C23×C11C2×M1612yes—
93C2×C4×C11—24no—
94C2×C4×C11—24no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—24no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—84no—
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11#9911yescharacteristic
116C2×C4×C11#10112yes—
117C8×C11—82no—
118C8×C11—82no—
119C2×#117C4×C1111yescharacteristic
120C2×#117C22×C1111yescharacteristic
121C22×C4⋊C4C4×C1111yescharacteristic
122#432—21no—
123#432—21no—
124#389—21no—
125#389—21no—
126#385C4×C1112yes—
127#385C22×C1112yes—
128#384—21no—
129#382—21no—
130#324—21no—
131#324—21no—
132#323C22×C1112yes—
133#323C22×C1112yes—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—22no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11#40711yescharacteristic
142C22×C11C2×#9911yescharacteristic
143C22×C11C2×#10111yescharacteristic
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—22no—
147C4×C11—44no—
148C4×C11—41no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11—41no—
152C4×C11—82no—
153C23×C4C2×C4×C1111yescharacteristic
154C23×C4C2×C4×C1112yes—
155#117—24no—
156#117—41no—
157#117—41no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4D4×C1111yescharacteristic
166C2×C4⋊C4D4×C1111yescharacteristic
167C2×C22⋊C4C2×C4×C1112yes—
168C2×C22⋊C4C2×C4×C1111yescharacteristic
169C2×C22⋊C4C23×C1111yescharacteristic
170C2×C42—21no—
171C2×C42D4×C1111yescharacteristic
172C2×C42D4×C1111yescharacteristic
173C4⋊C8—41no—
174C4⋊C8—41no—
175C22⋊C8—22no—
176C22⋊C8—22no—
177#97—41no—
178#97—41no—
179#95—22no—
180#95—22no—
181C2×C11—21no—
182C2×C11—21no—
183C2×C11—42no—
184C2×C11#146311yescharacteristic
185C2×C11#212211yescharacteristic
186C2×C11#212311yescharacteristic
187C24C22×C4×C1111yescharacteristic
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—42no—
195C22×C4—82no—
196C22×C4C11×C22⋊C411yescharacteristic
197C22×C4C11×C22⋊C411yescharacteristic
198C22×C4C11×C22⋊C411yescharacteristic
199C22×C4C11×C22⋊C411yescharacteristic
200C22×C4C2×D4×C1111yescharacteristic
201C22×C4C2×D4×C1111yescharacteristic
202C2×C8—42no—
203C2×C8—42no—
204C4⋊C4—24no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C22⋊C4—22no—
213C22⋊C4—41no—
214C22⋊C4—41no—
215C22⋊C4C11×M1614yes—
216C42—24no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C11#1152011yescharacteristic, direct product factor, Sylow
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23C2×C11×C22⋊C411yescharacteristic
227C23C2×C11×M1612yes—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—84no—
249C2×C4C11×#9911yescharacteristic
250C2×C4C11×#9911yescharacteristic
251C2×C4C11×#10112yes—
252C8—82no—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22C11×#40711yescharacteristic
262C22C2×C11×#9911yescharacteristic
263C22C2×C11×#10111yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—44no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2C11×#146311yescharacteristic
277C2C11×#212211yescharacteristic
278C2C11×#212311yescharacteristic
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
48. #11520C11direct (N × H)
221. C11#11520direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23172
C11×#14642
C11×#13262
#1152011