Finite Group Databasebeta

← C11×#10255 #14587448

Subgroups — C11×#10255 #14587448

Order 2816.

582 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3245C211yesmaximal, characteristic
2C11×#3037C212yesmaximal, complemented
3C11×#1984C211yesmaximal, characteristic, complemented
4C11×#1492C212yesmaximal, complemented
5C11×#1292C211yesmaximal, characteristic, complemented
6C2×C11×#137—22no—
7C11×#532C2212yes—
8C2×C4×Q8×C11C2211yescharacteristic
9C11×#474—22no—
10C11×#466—22no—
11C11×#464—24no—
12C11×#462—22no—
13C11×#460—22no—
14C11×#459—22no—
15C11×#423C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C11×#417—22no—
18C2×C4×C8×C11C2211yescharacteristic
19C11×#336—22no—
20C11×D4⋊C8—24no—
21C2×C11×#41—22no—
22C22×Q8×C11D411yescharacteristic
23C11×#137—44no—
24C11×#137—44no—
25C2×C11×Q16—24no—
26C2×C11×SD16—24no—
27C2×C11×D8—22no—
28C2×C11×M16—22no—
29C22×C8×C11—21no—
30C22×C8×C11D412yes—
31C11×C4⋊Q8D412yes—
32C11×#127D412yes—
33C11×#124—22no—
34C11×#121—22no—
35C11×#121—22no—
36C4×Q8×C11—22no—
37C4×Q8×C11—22no—
38C4×D4×C11—22no—
39C4×D4×C11—22no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C11×#107—22no—
45C11×C4⋊C8—22no—
46C11×C4⋊C8—22no—
47C11×C4⋊C8D414yes—
48C11×#103—24no—
49C11×#102—24no—
50C11×#102—24no—
51C4×C8×C11—22no—
52#10255C1111yesmaximal, characteristic, direct product factor, Sylow
53C11×#41—42no—
54C11×#41—42no—
55C11×#41—42no—
56C11×#41—42no—
57C2×Q8×C11—21no—
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—22no—
61C2×Q8×C11D812yescomplemented
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—42no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—42no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C11×Q16—48no—
73C11×SD16—48no—
74C11×D8—82no—
75C11×M16—42no—
76C11×M16—42no—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—24no—
80C2×C8×C11—42no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—42no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—42no—
89C42×C11—41no—
90C42×C11—41no—
91C42×C11C2×D412yes—
92C42×C11C2×D412yes—
93#3245C2×C1111yescharacteristic
94#3037C2×C1112yescomplemented
95#1984C2×C1111yescharacteristic, complemented
96#1492C2×C1112yescomplemented
97#1292C2×C1111yescharacteristic, complemented
98C23×C11—42no—
99C23×C11#12111yescharacteristic
100Q8×C11—24no—
101Q8×C11—42no—
102Q8×C11—42no—
103Q8×C11—42no—
104D4×C11—44no—
105D4×C11—42no—
106D4×C11—42no—
107D4×C11—42no—
108D4×C11—42no—
109D4×C11—82no—
110D4×C11—82no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—82no—
121C2×C4×C11—82no—
122C2×C4×C11#12012yes—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12112yes—
125C2×C4×C11#12711yescharacteristic
126C2×C4×C11C2×D811yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)12yes—
129C8×C11—42no—
130C8×C11—44no—
131C8×C11—42no—
132C2×#137—22no—
133#532C22×C1112yes—
134C2×C4×Q8C22×C1111yescharacteristic
135#474—22no—
136#466—22no—
137#464—24no—
138#462—22no—
139#460—22no—
140#459—22no—
141#423C22×C1112yes—
142C2×C4⋊C8C22×C1111yescharacteristic
143#417—22no—
144C2×C4×C8C22×C1111yescharacteristic
145#336—22no—
146D4⋊C8—24no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—82no—
150C22×C11—82no—
151C22×C11—82no—
152C22×C11#39211yescharacteristic
153C22×C11#46611yescharacteristic
154C22×C11#46911yescharacteristic
155C4×C11—21no—
156C4×C11—22no—
157C4×C11—42no—
158C4×C11—82no—
159C4×C11—81no—
160C4×C11#44712yes—
161C4×C11#44912yes—
162C4×C11#45511yescharacteristic
163C4×C11#45611yescharacteristic
164C2×#41—22no—
165C22×Q8D4×C1111yescharacteristic
166#137—44no—
167#137—44no—
168C2×Q16—24no—
169C2×SD16—24no—
170C2×D8—22no—
171C2×M16—22no—
172C22×C8—21no—
173C22×C8D4×C1112yes—
174C4⋊Q8D4×C1112yes—
175#127D4×C1112yes—
176#124—22no—
177#121—22no—
178#121—22no—
179C4×Q8—22no—
180C4×Q8—22no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4D4×C1111yescharacteristic
185C2×C42—21no—
186C2×C42C23×C1111yescharacteristic
187#107—22no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8D4×C1114yes—
191#103—24no—
192#102—24no—
193#102—24no—
194C4×C8—22no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11—162no—
198C2×C11#199911yescharacteristic
199C2×C11#200711yescharacteristic
200C2×C11#201711yescharacteristic
201#41—42no—
202#41—42no—
203#41—42no—
204#41—42no—
205C2×Q8—21no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8C11×D812yescomplemented
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—42no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—42no—
217C22×C4C2×D4×C1111yescharacteristic
218C22×C4C2×D4×C1111yescharacteristic
219C22×C4C11×#4111yescharacteristic
220Q16—48no—
221SD16—48no—
222D8—82no—
223M16—42no—
224M16—42no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—24no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—42no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—42no—
235C22⋊C4—42no—
236C22⋊C4—42no—
237C42—41no—
238C42—41no—
239C42C2×D4×C1112yes—
240C42C2×D4×C1112yes—
241C11#1025511yescharacteristic, direct product factor, Sylow
242C23—42no—
243C23C11×#12111yescharacteristic
244Q8—24no—
245Q8—42no—
246Q8—42no—
247Q8—42no—
248D4—44no—
249D4—42no—
250D4—42no—
251D4—42no—
252D4—42no—
253D4—82no—
254D4—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4C11×#12012yes—
267C2×C4C11×#12011yescharacteristic
268C2×C4C11×#12112yes—
269C2×C4C11×#12711yescharacteristic
270C2×C4C2×C11×D811yescharacteristic
271C2×C4C11×#13511yescharacteristic
272C2×C4C11×AGL(1,ℤ/8)12yes—
273C8—42no—
274C8—44no—
275C8—42no—
276C22—21no—
277C22—21no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22C11×#39211yescharacteristic
282C22C11×#46611yescharacteristic
283C22C11×#46911yescharacteristic
284C4—21no—
285C4—22no—
286C4—42no—
287C4—82no—
288C4—81no—
289C4C11×#44712yes—
290C4C11×#44912yes—
291C4C11×#45511yescharacteristic
292C4C11×#45611yescharacteristic
293C2—21no—
294C2—21no—
295C2—162no—
296C2C11×#199911yescharacteristic
297C2C11×#200711yescharacteristic
298C2C11×#201711yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3245C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3037C2semidirect
3. C11×#1984C2semidirect
4. C11×#1492C2semidirect
5. C11×#1292C2semidirect
52. #10255C11direct (N × H)
61. C2×Q8×C11D8semidirect
94. #3037C2×C11semidirect
95. #1984C2×C11semidirect
96. #1492C2×C11semidirect
97. #1292C2×C11semidirect
209. C2×Q8C11×D8semidirect
241. C11#10255direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32452
C11×#30372
C11×#19842
C11×#14922
C11×#12922
#1025511