Finite Group Databasebeta

← C11×#12103 #14589296

Subgroups — C11×#12103 #14589296

Order 2816.

476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3189C211yesmaximal, characteristic, complemented
2C11×#2187C212yesmaximal, complemented
3C11×#1999C211yesmaximal, characteristic
4C11×#1348C212yesmaximal, complemented
5C11×#1314C211yesmaximal, characteristic, complemented
6C22×C11×D8C2211yescharacteristic
7C2×C11×C22⋊Q8—21no—
8C2×C11×#121—21no—
9C2×C11×SD32—22no—
10C11×#484—22no—
11C11×#467—21no—
12C11×#467C2212yes—
13C11×#451—22no—
14C2×C11×#102—21no—
15C2×C11×C22⋊C8C2211yescharacteristic
16C11×#357—22no—
17C11×C22⋊C16C2212yes—
18C11×#340C2211yescharacteristic
19C22×Q8×C11—21no—
20C22×D4×C11—21no—
21C22×D4×C11—41no—
22C23×C4×C11D411yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16D412yescomplemented
25C2×C11×D8—22no—
26C2×C11×D8—42no—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8—22no—
31C11×C22⋊Q8—41no—
32C11×C22⋊Q8—41no—
33C11×#121—42no—
34C11×#121—42no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—41no—
38C2×C11×C22⋊C4—41no—
39C2×C11×C22⋊C4—41no—
40C11×SD32—44no—
41C2×C11×C16—22no—
42C11×#107—21no—
43C11×#107D412yescomplemented
44C11×#103—22no—
45C11×#103—22no—
46C11×#102—42no—
47C11×C22⋊C8—22no—
48#12103C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11—41no—
50C24×C11D811yescharacteristic
51C2×Q8×C11—22no—
52C2×Q8×C11—41no—
53C2×Q8×C11—81no—
54C2×Q8×C11—81no—
55C2×D4×C11—22no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D4×C11—44no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—82no—
63C2×D4×C11—82no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11D811yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C11×Q16—42no—
74C11×Q16—81no—
75C11×D8—24no—
76C11×D8—42no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11C2×D412yes—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—42no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—44no—
89C11×C22⋊C4—42no—
90C11×C16—42no—
91#3189C2×C1111yescharacteristic, complemented
92#2187C2×C1112yescomplemented
93#1999C2×C1111yescharacteristic
94#1348C2×C1112yescomplemented
95#1314C2×C1111yescharacteristic, complemented
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11—42no—
101C23×C11—81no—
102C23×C11—81no—
103C23×C11—81no—
104C23×C11—81no—
105C23×C11—81no—
106C23×C11—81no—
107C23×C11SD3212yescomplemented
108C23×C11C2×D811yescharacteristic
109Q8×C11—42no—
110Q8×C11—42no—
111Q8×C11—82no—
112D4×C11—42no—
113D4×C11—42no—
114D4×C11—81no—
115D4×C11—88no—
116D4×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—82no—
129C2×C4×C11—82no—
130C2×C4×C11—81no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C8×C11—22no—
134C8×C11—41no—
135C22×D8C22×C1111yescharacteristic
136C2×C22⋊Q8—21no—
137C2×#121—21no—
138C2×SD32—22no—
139#484—22no—
140#467—21no—
141#467C22×C1112yes—
142#451—22no—
143C2×#102—21no—
144C2×C22⋊C8C22×C1111yescharacteristic
145#357—22no—
146C22⋊C16C22×C1112yes—
147#340C22×C1111yescharacteristic
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—22no—
151C22×C11—42no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—81no—
155C22×C11—82no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11—161no—
159C22×C11—161no—
160C22×C11—161no—
161C22×C11—161no—
162C22×C11#44711yescharacteristic
163C22×C11C2×SD3211yescharacteristic
164C22×C11#51011yescharacteristic
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—82no—
168C4×C11—82no—
169C4×C11—82no—
170C4×C11#45311yescharacteristic
171C4×C11B(4,𝔽2)11yescharacteristic
172C22×Q8—21no—
173C22×D4—21no—
174C22×D4—41no—
175C23×C4D4×C1111yescharacteristic
176C2×Q16—21no—
177C2×Q16D4×C1112yescomplemented
178C2×D8—22no—
179C2×D8—42no—
180C22×C8D4×C1111yescharacteristic
181C22×C8C23×C1111yescharacteristic
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—41no—
185C22⋊Q8—41no—
186#121—42no—
187#121—42no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—41no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—41no—
193SD32—44no—
194C2×C16—22no—
195#107—21no—
196#107D4×C1112yescomplemented
197#103—22no—
198#103—22no—
199#102—42no—
200C22⋊C8—22no—
201C2×C11—21no—
202C2×C11—21no—
203C2×C11—42no—
204C2×C11—162no—
205C2×C11#159511yescharacteristic
206C2×C11#218511yescharacteristic
207C2×C11#219011yescharacteristic
208C24—41no—
209C24C11×D811yescharacteristic
210C2×Q8—22no—
211C2×Q8—41no—
212C2×Q8—81no—
213C2×Q8—81no—
214C2×D4—22no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—44no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—82no—
222C2×D4—82no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4C11×D811yescharacteristic
231C22×C4C2×D4×C1111yescharacteristic
232Q16—42no—
233Q16—81no—
234D8—24no—
235D8—42no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8C2×D4×C1112yes—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—44no—
248C22⋊C4—42no—
249C16—42no—
250C11#1210311yescharacteristic, direct product factor, Sylow
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—42no—
256C23—81no—
257C23—81no—
258C23—81no—
259C23—81no—
260C23—81no—
261C23—81no—
262C23C11×SD3212yescomplemented
263C23C2×C11×D811yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—82no—
267D4—42no—
268D4—42no—
269D4—81no—
270D4—88no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—81no—
286C2×C4C11×#12011yescharacteristic
287C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
288C8—22no—
289C8—41no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22—161no—
301C22—161no—
302C22—161no—
303C22—161no—
304C22C11×#44711yescharacteristic
305C22C2×C11×SD3211yescharacteristic
306C22C11×#51011yescharacteristic
307C4—21no—
308C4—41no—
309C4—82no—
310C4—82no—
311C4—82no—
312C4C11×#45311yescharacteristic
313C4C11×B(4,𝔽2)11yescharacteristic
314C2—21no—
315C2—21no—
316C2—42no—
317C2—162no—
318C2C11×#159511yescharacteristic
319C2C11×#218511yescharacteristic
320C2C11×#219011yescharacteristic
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC11×#1999C2
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3189C2semidirect
2. C11×#2187C2semidirect
4. C11×#1348C2semidirect
5. C11×#1314C2semidirect
24. C2×C11×Q16D4semidirect
43. C11×#107D4semidirect
48. #12103C11direct (N × H)
91. #3189C2×C11semidirect
92. #2187C2×C11semidirect
94. #1348C2×C11semidirect
95. #1314C2×C11semidirect
107. C23×C11SD32semidirect
177. C2×Q16D4×C11semidirect
196. #107D4×C11semidirect
250. C11#12103direct (N × H)
262. C23C11×SD32semidirect

Maximal subgroups

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

subgroupindex
C11×#31892
C11×#21872
C11×#19992
C11×#13482
C11×#13142
#1210311