Finite Group Databasebeta

← C11×#23925 #14601118

Subgroups — C11×#23925 #14601118

Order 2816.

2080 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 2080 conjugacy classes of subgroups — too many to draw. Only its 302 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×#535C212yesmaximal, complemented
2C2×C11×#447C214yesmaximal, complemented
3C11×#1999C214yesmaximal, complemented
4C11×#1875C214yesmaximal, complemented
5C11×#1780C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C23×D4×C11C2212yescomplemented
8C22×C11×D8C2214yes—
9C11×#535—216no—
10C2×C11×#127—22no—
11C2×C11×#124—22no—
12C2×C11×#121C2214yes—
13C2×C11×#121C2214yescomplemented
14C2×C11×#120—22no—
15C2×C11×#120—22no—
16C2×C11×#117C2212yescomplemented
17C11×#447—216no—
18C2×C11×#102C2218yescomplemented
19C2×C11×C22⋊C8C2214yescomplemented
20C2×C11×C22⋊C8C2212yescomplemented
21C11×#340C2214yescomplemented
22C25×C11—22no—
23C2×C11×#41—28no—
24C2×C11×#41—42no—
25C22×Q8×C11D411yescharacteristic
26C22×D4×C11—24no—
27C22×D4×C11—24no—
28C22×D4×C11—28no—
29C22×D4×C11—22no—
30C22×D4×C11—28no—
31C22×D4×C11—44no—
32C22×D4×C11D411yescharacteristic
33C22×D4×C11D412yes—
34C22×D4×C11C2314yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C2×C11×D8—216no—
38C2×C11×D8—44no—
39C22×C8×C11C2314yes—
40C11×#127—216no—
41C11×#124—216no—
42C11×#121—28no—
43C11×#121—28no—
44C11×#121—28no—
45C11×#121D4116yescomplemented
46C11×#120—216no—
47C11×#120—216no—
48C11×#117—28no—
49C2×C11×C4⋊C4C2314yes—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—24no—
53C2×C42×C11—22no—
54C11×#102—216no—
55C11×C22⋊C8—28no—
56C11×C22⋊C8—42no—
57#23925C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—28no—
59C24×C11—24no—
60C24×C11—44no—
61C24×C11—44no—
62C24×C11—88no—
63C24×C11C2×D411yescharacteristic
64C24×C11C2×D412yes—
65C11×#41—416no—
66C2×Q8×C11—24no—
67C2×Q8×C11—41no—
68C2×D4×C11—28no—
69C2×D4×C11—24no—
70C2×D4×C11—24no—
71C2×D4×C11—216no—
72C2×D4×C11—216no—
73C2×D4×C11—24no—
74C2×D4×C11—28no—
75C2×D4×C11—24no—
76C2×D4×C11—28no—
77C2×D4×C11—432no—
78C2×D4×C11—42no—
79C2×D4×C11—41no—
80C2×D4×C11—44no—
81C2×D4×C11—44no—
82C2×D4×C11—88no—
83C2×D4×C11—88no—
84C2×D4×C11C2×D418yes—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D418yes—
93C22×C4×C11C2411yescharacteristic
94C11×D8—416no—
95C2×C8×C11—28no—
96C2×C8×C11—24no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4C2×D418yes—
99C11×C22⋊C4—28no—
100C11×C22⋊C4—216no—
101C11×C22⋊C4—216no—
102C42×C11—28no—
103C2×#535C2×C1112yescomplemented
104C2×#447C2×C1114yescomplemented
105#1999C2×C1114yescomplemented
106#1875C2×C1114yescomplemented
107#1780C2×C1111yescharacteristic, complemented
108C23×C11—22no—
109C23×C11—22no—
110C23×C11—28no—
111C23×C11—28no—
112C23×C11—22no—
113C23×C11—21no—
114C23×C11—24no—
115C23×C11—416no—
116C23×C11—44no—
117C23×C11—44no—
118C23×C11—48no—
119C23×C11—48no—
120C23×C11—816no—
121C23×C11—816no—
122C23×C11—816no—
123C23×C11#12014yes—
124C23×C11C22×D411yescharacteristic
125Q8×C11—44no—
126D4×C11—216no—
127D4×C11—48no—
128D4×C11—416no—
129D4×C11—44no—
130D4×C11—48no—
131D4×C11—816no—
132D4×C11—816no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—216no—
136C2×C4×C11—28no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—48no—
140C2×C4×C11—44no—
141C2×C4×C11#12014yes—
142C2×C4×C11C22×D414yes—
143C2×C4×C11H(5,𝔽2)12yes—
144C8×C11—44no—
145C22×#41C22×C1111yescharacteristic
146C23×D4C22×C1112yescomplemented
147C22×D8C22×C1114yes—
148#535—216no—
149C2×#127—22no—
150C2×#124—22no—
151C2×#121C22×C1114yes—
152C2×#121C22×C1114yescomplemented
153C2×#120—22no—
154C2×#120—22no—
155C2×#117C22×C1112yescomplemented
156#447—216no—
157C2×#102C22×C1118yescomplemented
158C2×C22⋊C8C22×C1114yescomplemented
159C2×C22⋊C8C22×C1112yescomplemented
160#340C22×C1114yescomplemented
161C22×C11—24no—
162C22×C11—28no—
163C22×C11—44no—
164C22×C11—44no—
165C22×C11—41no—
166C22×C11—48no—
167C22×C11—42no—
168C22×C11—44no—
169C22×C11—48no—
170C22×C11—48no—
171C22×C11—832no—
172C22×C11—88no—
173C22×C11—88no—
174C22×C11C2×#12012yes—
175C22×C11#53411yescharacteristic
176C22×C11#57614yes—
177C4×C11—24no—
178C4×C11—41no—
179C4×C11—48no—
180C4×C11D4214yes—
181C25—22no—
182C2×#41—28no—
183C2×#41—42no—
184C22×Q8D4×C1111yescharacteristic
185C22×D4—24no—
186C22×D4—24no—
187C22×D4—28no—
188C22×D4—22no—
189C22×D4—28no—
190C22×D4—44no—
191C22×D4D4×C1111yescharacteristic
192C22×D4D4×C1112yes—
193C22×D4C23×C1114yes—
194C23×C4C23×C1111yescharacteristic
195C23×C4C23×C1112yes—
196C2×D8—216no—
197C2×D8—44no—
198C22×C8C23×C1114yes—
199#127—216no—
200#124—216no—
201#121—28no—
202#121—28no—
203#121—28no—
204#121D4×C11116yescomplemented
205#120—216no—
206#120—216no—
207#117—28no—
208C2×C4⋊C4C23×C1114yes—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—24no—
211C2×C22⋊C4—24no—
212C2×C42—22no—
213#102—216no—
214C22⋊C8—28no—
215C22⋊C8—42no—
216C2×C11—44no—
217C2×C11—81no—
218C2×C11—88no—
219C2×C11#240311yescharacteristic
220C2×C11#300814yes—
221C2×C11#319912yes—
222C24—28no—
223C24—24no—
224C24—44no—
225C24—44no—
226C24—88no—
227C24C2×D4×C1111yescharacteristic
228C24C2×D4×C1112yes—
229#41—416no—
230C2×Q8—24no—
231C2×Q8—41no—
232C2×D4—28no—
233C2×D4—24no—
234C2×D4—24no—
235C2×D4—216no—
236C2×D4—216no—
237C2×D4—24no—
238C2×D4—28no—
239C2×D4—24no—
240C2×D4—28no—
241C2×D4—432no—
242C2×D4—42no—
243C2×D4—41no—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—88no—
247C2×D4—88no—
248C2×D4C2×D4×C1118yes—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—22no—
254C22×C4C2×D4×C1111yescharacteristic
255C22×C4C2×D4×C1112yes—
256C22×C4C2×D4×C1118yes—
257C22×C4C24×C1111yescharacteristic
258D8—416no—
259C2×C8—28no—
260C2×C8—24no—
261C4⋊C4—24no—
262C4⋊C4C2×D4×C1118yes—
263C22⋊C4—28no—
264C22⋊C4—216no—
265C22⋊C4—216no—
266C42—28no—
267C11#2392511yescharacteristic, direct product factor, Sylow
268C23—22no—
269C23—22no—
270C23—28no—
271C23—28no—
272C23—22no—
273C23—21no—
274C23—24no—
275C23—416no—
276C23—44no—
277C23—44no—
278C23—48no—
279C23—48no—
280C23—816no—
281C23—816no—
282C23—816no—
283C23C11×#12014yes—
284C23C22×D4×C1111yescharacteristic
285Q8—44no—
286D4—216no—
287D4—48no—
288D4—416no—
289D4—44no—
290D4—48no—
291D4—816no—
292D4—816no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—216no—
296C2×C4—28no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—48no—
300C2×C4—44no—
301C2×C4C11×#12014yes—
302C2×C4C22×D4×C1114yes—
303C2×C4C11×H(5,𝔽2)12yes—
304C8—44no—
305C22—24no—
306C22—28no—
307C22—44no—
308C22—44no—
309C22—41no—
310C22—48no—
311C22—42no—
312C22—44no—
313C22—48no—
314C22—48no—
315C22—832no—
316C22—88no—
317C22—88no—
318C22C2×C11×#12012yes—
319C22C11×#53411yescharacteristic
320C22C11×#57614yes—
321C4—24no—
322C4—41no—
323C4—48no—
324C4D42×C1114yes—
325C2—44no—
326C2—81no—
327C2—88no—
328C2C11×#240311yescharacteristic
329C2C11×#300814yes—
330C2C11×#319912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#535C2semidirect
2. C2×C11×#447C2semidirect
3. C11×#1999C2semidirect
4. C11×#1875C2semidirect
5. C11×#1780C2semidirect
7. C23×D4×C11C22semidirect
13. C2×C11×#121C22semidirect
16. C2×C11×#117C22semidirect
18. C2×C11×#102C22semidirect
19. C2×C11×C22⋊C8C22semidirect
20. C2×C11×C22⋊C8C22semidirect
21. C11×#340C22semidirect
45. C11×#121D4semidirect
57. #23925C11direct (N × H)
103. C2×#535C2×C11semidirect
104. C2×#447C2×C11semidirect
105. #1999C2×C11semidirect
106. #1875C2×C11semidirect
107. #1780C2×C11semidirect
146. C23×D4C22×C11semidirect
152. C2×#121C22×C11semidirect
155. C2×#117C22×C11semidirect
157. C2×#102C22×C11semidirect
158. C2×C22⋊C8C22×C11semidirect
159. C2×C22⋊C8C22×C11semidirect
160. #340C22×C11semidirect
204. #121D4×C11semidirect
267. C11#23925direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4472
C11×#19992
C11×#18752
C11×#17802
#2392511