Finite Group Databasebeta

← C11×#12159 #14589352

Subgroups — C11×#12159 #14589352

Order 2816.

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

normal subgroups only

This group has 390 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×#3249C211yesmaximal, characteristic, complemented
2C11×#2187C212yesmaximal
3C11×#2054C211yesmaximal, characteristic
4C11×#1348C212yesmaximal, complemented
5C11×#1322C211yesmaximal, characteristic, complemented
6C22×C11×D8C2211yescharacteristic
7C11×#533—21no—
8C2×C11×SD32—22no—
9C11×#477—22no—
10C11×#467—21no—
11C11×#467C2212yes—
12C11×#462—22no—
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#102—21no—
15C11×#390—21no—
16C11×#357—22no—
17C11×C22⋊C16C2212yes—
18C11×#340C2211yescharacteristic
19C22×D4×C11—21no—
20C2×C11×Q16—21no—
21C2×C11×Q16D412yes—
22C2×C11×D8—22no—
23C2×C11×D8—42no—
24C22×C8×C11D411yescharacteristic
25C22×C8×C11C2311yescharacteristic
26C11×C4⋊Q8—21no—
27C11×C4⋊Q8—21no—
28C11×#125—41no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8—41no—
31C4×Q8×C11—22no—
32C4×Q8×C11—41no—
33C11×#117—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C22⋊C4—41no—
36C2×C11×C22⋊C4—41no—
37C2×C42×C11D411yescharacteristic
38C11×SD32—44no—
39C2×C11×C16—22no—
40C11×#107—21no—
41C11×#107D412yes—
42C11×C4⋊C8—22no—
43C11×#103—22no—
44C11×#103—22no—
45C11×#102—42no—
46#12159C1111yesmaximal, characteristic, direct product factor, Sylow
47C24×C11—41no—
48C2×Q8×C11—22no—
49C2×Q8×C11—41no—
50C2×D4×C11—22no—
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11D811yescharacteristic
58C22×C4×C11D811yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C11×Q16—42no—
61C11×Q16—81no—
62C11×D8—24no—
63C11×D8—42no—
64C2×C8×C11—21no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C2×C8×C11C2×D412yes—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—42no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—82no—
78C11×C22⋊C4—82no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—42no—
82C11×C16—42no—
83#3249C2×C1111yescharacteristic, complemented
84#2187C2×C1112yes—
85#2054C2×C1111yescharacteristic
86#1348C2×C1112yescomplemented
87#1322C2×C1111yescharacteristic, complemented
88C23×C11—42no—
89C23×C11—81no—
90C23×C11—81no—
91C23×C11—81no—
92C23×C11—81no—
93C23×C11—81no—
94C23×C11—81no—
95C23×C11C2×D811yescharacteristic
96Q8×C11—42no—
97Q8×C11—42no—
98Q8×C11—82no—
99D4×C11—42no—
100D4×C11—42no—
101D4×C11—81no—
102D4×C11—81no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—81no—
112C2×C4×C11—81no—
113C2×C4×C11—81no—
114C2×C4×C11SD3212yescomplemented
115C2×C4×C11#12011yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C8×C11—22no—
118C8×C11—41no—
119C22×D8C22×C1111yescharacteristic
120#533—21no—
121C2×SD32—22no—
122#477—22no—
123#467—21no—
124#467C22×C1112yes—
125#462—22no—
126C2×C4⋊C8C22×C1111yescharacteristic
127C2×#102—21no—
128#390—21no—
129#357—22no—
130C22⋊C16C22×C1112yes—
131#340C22×C1111yescharacteristic
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—82no—
135C22×C11—82no—
136C22×C11—82no—
137C22×C11—161no—
138C22×C11—161no—
139C22×C11—161no—
140C22×C11—161no—
141C22×C11#44711yescharacteristic
142C22×C11C2×SD3211yescharacteristic
143C22×C11#51011yescharacteristic
144C4×C11—21no—
145C4×C11—22no—
146C4×C11—41no—
147C4×C11—82no—
148C4×C11—82no—
149C4×C11—161no—
150C4×C11#45411yescharacteristic
151C4×C11B(4,𝔽2)11yescharacteristic
152C22×D4—21no—
153C2×Q16—21no—
154C2×Q16D4×C1112yes—
155C2×D8—22no—
156C2×D8—42no—
157C22×C8D4×C1111yescharacteristic
158C22×C8C23×C1111yescharacteristic
159C4⋊Q8—21no—
160C4⋊Q8—21no—
161#125—41no—
162C22⋊Q8—22no—
163C22⋊Q8—41no—
164C4×Q8—22no—
165C4×Q8—41no—
166#117—41no—
167C2×C4⋊C4—21no—
168C2×C22⋊C4—41no—
169C2×C22⋊C4—41no—
170C2×C42D4×C1111yescharacteristic
171SD32—44no—
172C2×C16—22no—
173#107—21no—
174#107D4×C1112yes—
175C4⋊C8—22no—
176#103—22no—
177#103—22no—
178#102—42no—
179C2×C11—21no—
180C2×C11—21no—
181C2×C11—162no—
182C2×C11#159811yescharacteristic
183C2×C11#218511yescharacteristic
184C2×C11#219011yescharacteristic
185C24—41no—
186C2×Q8—22no—
187C2×Q8—41no—
188C2×D4—22no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—41no—
194C22×C4—41no—
195C22×C4C11×D811yescharacteristic
196C22×C4C11×D811yescharacteristic
197C22×C4C2×D4×C1111yescharacteristic
198Q16—42no—
199Q16—81no—
200D8—24no—
201D8—42no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8C2×D4×C1112yes—
206C4⋊C4—22no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—42no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—82no—
216C22⋊C4—82no—
217C42—21no—
218C42—21no—
219C42—42no—
220C16—42no—
221C11#1215911yescharacteristic, direct product factor, Sylow
222C23—42no—
223C23—81no—
224C23—81no—
225C23—81no—
226C23—81no—
227C23—81no—
228C23—81no—
229C23C2×C11×D811yescharacteristic
230Q8—42no—
231Q8—42no—
232Q8—82no—
233D4—42no—
234D4—42no—
235D4—81no—
236D4—81no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4C11×SD3212yescomplemented
249C2×C4C11×#12011yescharacteristic
250C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
251C8—22no—
252C8—41no—
253C22—21no—
254C22—21no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—161no—
259C22—161no—
260C22—161no—
261C22—161no—
262C22C11×#44711yescharacteristic
263C22C2×C11×SD3211yescharacteristic
264C22C11×#51011yescharacteristic
265C4—22no—
266C4—21no—
267C4—41no—
268C4—82no—
269C4—82no—
270C4—161no—
271C4C11×#45411yescharacteristic
272C4C11×B(4,𝔽2)11yescharacteristic
273C2—21no—
274C2—21no—
275C2—162no—
276C2C11×#159811yescharacteristic
277C2C11×#218511yescharacteristic
278C2C11×#219011yescharacteristic
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3249C2semidirect
4. C11×#1348C2semidirect
5. C11×#1322C2semidirect
46. #12159C11direct (N × H)
83. #3249C2×C11semidirect
86. #1348C2×C11semidirect
87. #1322C2×C11semidirect
114. C2×C4×C11SD32semidirect
221. C11#12159direct (N × H)
248. C2×C4C11×SD32semidirect

Maximal subgroups

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

subgroupindex
C11×#32492
C11×#21872
C11×#20542
C11×#13482
C11×#13222
#1215911