Finite Group Databasebeta

← C11×#11501 #14588694

Subgroups — C11×#11501 #14588694

Order 2816.

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

normal subgroups only

This group has 662 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×#2280C211yesmaximal, characteristic
2C11×#1464C212yesmaximal, complemented
3C11×#1317C212yesmaximal, complemented
4C11×#1316C212yesmaximal
5C24×C4×C11C411yescharacteristic
6C2×C11×#117C411yescharacteristic
7C2×C11×#117C2211yescharacteristic
8C11×#432—22no—
9C11×#381C411yescharacteristic
10C11×#381C2211yescharacteristic
11C11×#380—22no—
12C11×#379C411yescharacteristic
13C11×#379C2211yescharacteristic
14C4×C11×C22⋊C4—22no—
15C11×#324—22no—
16C11×#323C2214yes—
17C25×C11C2×C411yescharacteristic
18C23×C4×C11—22no—
19C23×C4×C11—21no—
20C23×C4×C11—21no—
21C23×C4×C11—22no—
22C23×C4×C11—42no—
23C23×C4×C11—42no—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C11×#117—42no—
27C11×#117—42no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11D412yes—
38C11×C4⋊C8—42no—
39C11×C22⋊C8—24no—
40C11×#97—42no—
41C11×#95—22no—
42C11×#95—22no—
43#11501C1111yesmaximal, characteristic, direct product factor, Sylow
44C24×C11—21no—
45C24×C11—21no—
46C24×C11—41no—
47C24×C11—41no—
48C24×C11—44no—
49C24×C11M1612yes—
50C24×C11C22×C411yescharacteristic
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—24no—
56C22×C4×C11—24no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—48no—
62C22×C4×C11—48no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C412yes—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11M1612yes—
73C22×C4×C11C2×D412yes—
74C2×C8×C11—44no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—44no—
80C11×C22⋊C4—44no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C42×C11—22no—
84C42×C11—22no—
85C42×C11—42no—
86#2280C2×C1111yescharacteristic
87#1464C2×C1112yescomplemented
88#1317C2×C1112yescomplemented
89#1316C2×C1112yes—
90C23×C11—24no—
91C23×C11—22no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—42no—
95C23×C11—44no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—44no—
100C23×C11—44no—
101C23×C11—48no—
102C23×C11—44no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11C2×C22⋊C411yescharacteristic
106C23×C11C2×M1611yescharacteristic
107C23×C11C2×M1611yescharacteristic
108C2×C4×C11—24no—
109C2×C4×C11—24no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—48no—
118C2×C4×C11—48no—
119C2×C4×C11—42no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11#9912yes—
130C2×C4×C11#10012yes—
131C8×C11—84no—
132C24×C4C4×C1111yescharacteristic
133C2×#117C4×C1111yescharacteristic
134C2×#117C22×C1111yescharacteristic
135#432—22no—
136#381C4×C1111yescharacteristic
137#381C22×C1111yescharacteristic
138#380—22no—
139#379C4×C1111yescharacteristic
140#379C22×C1111yescharacteristic
141C4×C22⋊C4—22no—
142#324—22no—
143#323C22×C1114yes—
144C22×C11—22no—
145C22×C11—24no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—44no—
151C22×C11—42no—
152C22×C11—42no—
153C22×C11—44no—
154C22×C11—44no—
155C22×C11—48no—
156C22×C11—44no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11#40711yescharacteristic
160C22×C11C2×#9911yescharacteristic
161C22×C11C2×#10011yescharacteristic
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—42no—
165C4×C11—42no—
166C4×C11—42no—
167C4×C11—81no—
168C4×C11—81no—
169C25C2×C4×C1111yescharacteristic
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4—42no—
175C23×C4—42no—
176C23×C4C2×C4×C1111yescharacteristic
177C23×C4C2×C4×C1111yescharacteristic
178#117—42no—
179#117—42no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4D4×C1112yes—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4C2×C4×C1111yescharacteristic
185C2×C22⋊C4C2×C4×C1111yescharacteristic
186C2×C22⋊C4C2×C4×C1111yescharacteristic
187C2×C22⋊C4C23×C1111yescharacteristic
188C2×C42—21no—
189C2×C42D4×C1112yes—
190C4⋊C8—42no—
191C22⋊C8—24no—
192#97—42no—
193#95—22no—
194#95—22no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11—44no—
198C2×C11—41no—
199C2×C11—41no—
200C2×C11#146211yescharacteristic
201C2×C11#212012yes—
202C24—21no—
203C24—21no—
204C24—41no—
205C24—41no—
206C24—44no—
207C24C11×M1612yes—
208C24C22×C4×C1111yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—48no—
220C22×C4—48no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4C11×C22⋊C411yescharacteristic
228C22×C4C11×C22⋊C411yescharacteristic
229C22×C4C11×C22⋊C412yes—
230C22×C4C11×M1612yes—
231C22×C4C2×D4×C1112yes—
232C2×C8—44no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—44no—
238C22⋊C4—44no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C42—22no—
242C42—22no—
243C42—42no—
244C11#1150111yescharacteristic, direct product factor, Sylow
245C23—24no—
246C23—22no—
247C23—21no—
248C23—21no—
249C23—42no—
250C23—44no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—44no—
255C23—44no—
256C23—48no—
257C23—44no—
258C23—41no—
259C23—41no—
260C23C2×C11×C22⋊C411yescharacteristic
261C23C2×C11×M1611yescharacteristic
262C23C2×C11×M1611yescharacteristic
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—48no—
273C2×C4—48no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4C11×#9912yes—
285C2×C4C11×#10012yes—
286C8—84no—
287C22—22no—
288C22—24no—
289C22—21no—
290C22—21no—
291C22—41no—
292C22—41no—
293C22—44no—
294C22—42no—
295C22—42no—
296C22—44no—
297C22—44no—
298C22—48no—
299C22—42no—
300C22—44no—
301C22—42no—
302C22C11×#40711yescharacteristic
303C22C2×C11×#9911yescharacteristic
304C22C2×C11×#10011yescharacteristic
305C4—22no—
306C4—22no—
307C4—42no—
308C4—42no—
309C4—42no—
310C4—81no—
311C4—81no—
312C2—21no—
313C2—21no—
314C2—44no—
315C2—41no—
316C2—41no—
317C2C11×#146211yescharacteristic
318C2C11×#212012yes—
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 ◁ 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×#1317C2semidirect
43. #11501C11direct (N × H)
87. #1464C2×C11semidirect
88. #1317C2×C11semidirect
244. C11#11501direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#22802
C11×#14642
C11×#13172
C11×#13162
#1150111