Finite Group Databasebeta

← C11×#11499 #14588692

Subgroups — C11×#11499 #14588692

Order 2816.

1866 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 1866 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×#379C211yesmaximal, characteristic
2C11×#1462C212yesmaximal, complemented
3C11×#1316C214yesmaximal, complemented
4C26×C11C411yescharacteristic
5C22×C11×C22⋊C4—22no—
6C22×C11×C22⋊C4C411yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C11×#407—22no—
9C11×#379—22no—
10C11×#379C412yes—
11C11×#379C2212yes—
12C11×#323—22no—
13C11×#323C2214yescomplemented
14C25×C11—21no—
15C25×C11—21no—
16C25×C11—24no—
17C25×C11—48no—
18C25×C11—42no—
19C25×C11—42no—
20C25×C11C2×C411yescharacteristic
21C25×C11C2×C412yes—
22C23×C4×C11—21no—
23C23×C4×C11D412yes—
24C2×C11×M16—42no—
25C2×C11×C22⋊C4—21no—
26C2×C11×C22⋊C4—24no—
27C2×C11×C22⋊C4—24no—
28C2×C11×C22⋊C4—42no—
29C2×C11×C22⋊C4—48no—
30C2×C11×C22⋊C4—42no—
31C2×C11×C22⋊C4C2×C412yes—
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D412yes—
34C2×C11×C22⋊C4C2311yescharacteristic
35C11×C22⋊C8—24no—
36C11×C22⋊C8—42no—
37#11499C1111yesmaximal, characteristic, direct product factor, Sylow
38C24×C11—28no—
39C24×C11—24no—
40C24×C11—22no—
41C24×C11—22no—
42C24×C11—22no—
43C24×C11—22no—
44C24×C11—24no—
45C24×C11—22no—
46C24×C11—44no—
47C24×C11—42no—
48C24×C11—48no—
49C24×C11—432no—
50C24×C11—416no—
51C24×C11—42no—
52C24×C11—44no—
53C24×C11—48no—
54C24×C11—42no—
55C24×C11—42no—
56C24×C11—416no—
57C24×C11—432no—
58C24×C11—48no—
59C24×C11—42no—
60C24×C11—42no—
61C24×C11—48no—
62C24×C11C22⋊C411yescharacteristic
63C24×C11C22⋊C411yescharacteristic
64C24×C11M1614yescomplemented
65C24×C11C22×C411yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—44no—
70C22×C4×C11—44no—
71C22×C4×C11—42no—
72C22×C4×C11C22⋊C412yes—
73C22×C4×C11C2×D412yes—
74C11×M16—84no—
75C2×C8×C11—44no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—48no—
80C11×C22⋊C4—48no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83C2×#379C2×C1111yescharacteristic
84#1462C2×C1112yescomplemented
85#1316C2×C1114yescomplemented
86C23×C11—24no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—28no—
90C23×C11—216no—
91C23×C11—28no—
92C23×C11—21no—
93C23×C11—24no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—42no—
98C23×C11—48no—
99C23×C11—44no—
100C23×C11—42no—
101C23×C11—48no—
102C23×C11—416no—
103C23×C11—48no—
104C23×C11—48no—
105C23×C11—44no—
106C23×C11—48no—
107C23×C11—44no—
108C23×C11—48no—
109C23×C11—48no—
110C23×C11—416no—
111C23×C11—48no—
112C23×C11—44no—
113C23×C11—48no—
114C23×C11—416no—
115C23×C11—464no—
116C23×C11—416no—
117C23×C11—464no—
118C23×C11—416no—
119C23×C11—48no—
120C23×C11—48no—
121C23×C11—44no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11#9912yes—
125C23×C11#10012yes—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11C2×M1612yes—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—44no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—44no—
134C2×C4×C11—42no—
135C2×C4×C11—82no—
136C2×C4×C11—84no—
137C8×C11—84no—
138C26C4×C1111yescharacteristic
139C22×C22⋊C4—22no—
140C22×C22⋊C4C4×C1111yescharacteristic
141C22×C22⋊C4C22×C1111yescharacteristic
142#407—22no—
143#379—22no—
144#379C4×C1112yes—
145#379C22×C1112yes—
146#323—22no—
147#323C22×C1114yescomplemented
148C22×C11—24no—
149C22×C11—24no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—28no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11—48no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—44no—
162C22×C11—432no—
163C22×C11—416no—
164C22×C11—48no—
165C22×C11—48no—
166C22×C11—416no—
167C22×C11—432no—
168C22×C11—48no—
169C22×C11—42no—
170C22×C11—42no—
171C22×C11—44no—
172C22×C11AΣL(1,𝔽16)14yes—
173C22×C11#40711yescharacteristic
174C22×C11C2×#9911yescharacteristic
175C22×C11C2×#10011yescharacteristic
176C4×C11—42no—
177C4×C11—42no—
178C4×C11—82no—
179C25—21no—
180C25—21no—
181C25—24no—
182C25—48no—
183C25—42no—
184C25—42no—
185C25C2×C4×C1111yescharacteristic
186C25C2×C4×C1112yes—
187C23×C4—21no—
188C23×C4D4×C1112yes—
189C2×M16—42no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—42no—
194C2×C22⋊C4—48no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4C2×C4×C1112yes—
197C2×C22⋊C4C2×C4×C1111yescharacteristic
198C2×C22⋊C4D4×C1112yes—
199C2×C22⋊C4C23×C1111yescharacteristic
200C22⋊C8—24no—
201C22⋊C8—42no—
202C2×C11—21no—
203C2×C11—21no—
204C2×C11—24no—
205C2×C11—48no—
206C2×C11—42no—
207C2×C11—42no—
208C2×C11#146211yescharacteristic
209C2×C11C2×AΣL(1,𝔽16)12yes—
210C24—28no—
211C24—24no—
212C24—22no—
213C24—22no—
214C24—22no—
215C24—22no—
216C24—24no—
217C24—22no—
218C24—44no—
219C24—48no—
220C24—42no—
221C24—42no—
222C24—44no—
223C24—42no—
224C24—48no—
225C24—432no—
226C24—416no—
227C24—42no—
228C24—48no—
229C24—416no—
230C24—432no—
231C24—48no—
232C24—42no—
233C24—42no—
234C24C11×C22⋊C411yescharacteristic
235C24C11×C22⋊C411yescharacteristic
236C24C11×M1614yescomplemented
237C24C22×C4×C1111yescharacteristic
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—44no—
242C22×C4—44no—
243C22×C4—42no—
244C22×C4C11×C22⋊C412yes—
245C22×C4C2×D4×C1112yes—
246M16—84no—
247C2×C8—44no—
248C22⋊C4—41no—
249C22⋊C4—42no—
250C22⋊C4—41no—
251C22⋊C4—48no—
252C22⋊C4—48no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C11#1149911yescharacteristic, direct product factor, Sylow
256C23—24no—
257C23—21no—
258C23—21no—
259C23—28no—
260C23—216no—
261C23—28no—
262C23—21no—
263C23—24no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—42no—
268C23—48no—
269C23—44no—
270C23—42no—
271C23—48no—
272C23—416no—
273C23—48no—
274C23—48no—
275C23—48no—
276C23—44no—
277C23—48no—
278C23—44no—
279C23—48no—
280C23—416no—
281C23—48no—
282C23—44no—
283C23—48no—
284C23—416no—
285C23—416no—
286C23—464no—
287C23—464no—
288C23—48no—
289C23—416no—
290C23—48no—
291C23—44no—
292C23—42no—
293C23—42no—
294C23C11×#9912yes—
295C23C11×#10012yes—
296C23C2×C11×C22⋊C411yescharacteristic
297C23C2×C11×M1612yes—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—84no—
307C8—84no—
308C22—24no—
309C22—24no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—28no—
314C22—22no—
315C22—22no—
316C22—42no—
317C22—42no—
318C22—48no—
319C22—42no—
320C22—42no—
321C22—44no—
322C22—432no—
323C22—416no—
324C22—48no—
325C22—48no—
326C22—416no—
327C22—432no—
328C22—44no—
329C22—48no—
330C22—42no—
331C22—42no—
332C22C11×AΣL(1,𝔽16)14yes—
333C22C11×#40711yescharacteristic
334C22C2×C11×#9911yescharacteristic
335C22C2×C11×#10011yescharacteristic
336C4—42no—
337C4—42no—
338C4—82no—
339C2—21no—
340C2—21no—
341C2—24no—
342C2—48no—
343C2—42no—
344C2—42no—
345C2C11×#146211yescharacteristic
346C2C2×C11×AΣL(1,𝔽16)12yes—
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC26×C11C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1462C2semidirect
3. C11×#1316C2semidirect
13. C11×#323C22semidirect
37. #11499C11direct (N × H)
64. C24×C11M16semidirect
84. #1462C2×C11semidirect
85. #1316C2×C11semidirect
147. #323C22×C11semidirect
236. C24C11×M16semidirect
255. C11#11499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3792
C11×#14622
C11×#13162
#1149911