Finite Group Databasebeta

← C11×#10237 #14587430

Subgroups — C11×#10237 #14587430

Order 2816.

560 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 154 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×#477C212yesmaximal
2C11×#2582C211yesmaximal, characteristic
3C11×#1956C211yesmaximal, characteristic
4C2×C11×Q8⋊C8C212yesmaximal
5C11×#1296C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C11C2212yes—
8C11×#477—24no—
9C11×#477—24no—
10C2×C11×#107—22no—
11C2×C11×C4⋊C8C2212yes—
12C2×C11×#103—22no—
13C2×C11×#103—22no—
14C2×C4×C8×C11C2211yescharacteristic
15C11×#398—22no—
16C11×#391—22no—
17C11×#389—22no—
18C11×#384C2211yescharacteristic
19C11×Q8⋊C8—24no—
20C22×Q8×C11—21no—
21C22×Q8×C11D412yes—
22C22×C8×C11—21no—
23C22×C8×C11—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—21no—
26C11×C4⋊Q8D412yes—
27C4×Q8×C11—22no—
28C4×Q8×C11—22no—
29C4×Q8×C11—22no—
30C4×Q8×C11—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4D412yes—
36C2×C11×C4⋊C4D412yes—
37C2×C42×C11—22no—
38C2×C42×C11C2311yescharacteristic
39C11×#107—28no—
40C11×C4⋊C8—22no—
41C11×C4⋊C8D414yes—
42C11×#103—28no—
43C11×#103—44no—
44C4×C8×C11—22no—
45C11×#95—24no—
46C11×#95—22no—
47#10237C1111yesmaximal, characteristic, direct product factor, Sylow
48C2×Q8×C11—22no—
49C2×Q8×C11—22no—
50C2×Q8×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C2×Q8×C11—41no—
57C2×Q8×C11Q1614yes—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C2×C8×C11—22no—
65C2×C8×C11—24no—
66C2×C8×C11—41no—
67C2×C8×C11—41no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C11×C4⋊C4—24no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—82no—
80C42×C11—42no—
81C42×C11—42no—
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D412yes—
84C42×C11#4111yescharacteristic
85C2×#477C2×C1112yes—
86#2582C2×C1111yescharacteristic
87#1956C2×C1111yescharacteristic
88C2×Q8⋊C8C2×C1112yes—
89#1296C2×C1111yescharacteristic
90C23×C11#12011yescharacteristic
91Q8×C11—24no—
92Q8×C11—24no—
93Q8×C11—44no—
94Q8×C11—42no—
95Q8×C11—42no—
96Q8×C11—82no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—24no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—44no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—81no—
109C2×C4×C11—81no—
110C2×C4×C11#12012yes—
111C2×C4×C11#12111yescharacteristic
112C2×C4×C11#12112yes—
113C2×C4×C11#12711yescharacteristic
114C2×C4×C11C2×Q1612yes—
115C2×C4×C11#13512yes—
116C2×C4×C11#13712yes—
117C2×C4×C11#13712yes—
118C8×C11—42no—
119C8×C11—44no—
120C2×C4⋊Q8C22×C1111yescharacteristic
121C2×C4×Q8C22×C1112yes—
122#477—24no—
123#477—24no—
124C2×#107—22no—
125C2×C4⋊C8C22×C1112yes—
126C2×#103—22no—
127C2×#103—22no—
128C2×C4×C8C22×C1111yescharacteristic
129#398—22no—
130#391—22no—
131#389—22no—
132#384C22×C1111yescharacteristic
133Q8⋊C8—24no—
134C22×C11#39211yescharacteristic
135C22×C11#45112yes—
136C22×C11#45212yes—
137C22×C11#45311yescharacteristic
138C22×C11#45411yescharacteristic
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—44no—
142C4×C11—82no—
143C4×C11—82no—
144C4×C11—82no—
145C4×C11#45112yes—
146C4×C11#45212yes—
147C4×C11#46712yes—
148C4×C11#47012yes—
149C22×Q8—21no—
150C22×Q8D4×C1112yes—
151C22×C8—21no—
152C22×C8—22no—
153C4⋊Q8—22no—
154C4⋊Q8—21no—
155C4⋊Q8D4×C1112yes—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4D4×C1112yes—
165C2×C4⋊C4D4×C1112yes—
166C2×C42—22no—
167C2×C42C23×C1111yescharacteristic
168#107—28no—
169C4⋊C8—22no—
170C4⋊C8D4×C1114yes—
171#103—28no—
172#103—44no—
173C4×C8—22no—
174#95—24no—
175#95—22no—
176C2×C11#163011yescharacteristic
177C2×C11#163311yescharacteristic
178C2×C11#163612yes—
179C2×C11#200112yes—
180C2×C11#200611yescharacteristic
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—42no—
188C2×Q8—42no—
189C2×Q8—41no—
190C2×Q8C11×Q1614yes—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—41no—
195C22×C4C2×D4×C1111yescharacteristic
196C22×C4C2×D4×C1112yes—
197C2×C8—22no—
198C2×C8—24no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—42no—
202C2×C8—42no—
203C4⋊C4—24no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—82no—
213C42—42no—
214C42—42no—
215C42C2×D4×C1111yescharacteristic
216C42C2×D4×C1112yes—
217C42C11×#4111yescharacteristic
218C11#1023711yescharacteristic, direct product factor, Sylow
219C23C11×#12011yescharacteristic
220Q8—24no—
221Q8—24no—
222Q8—44no—
223Q8—42no—
224Q8—42no—
225Q8—82no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4C11×#12012yes—
240C2×C4C11×#12111yescharacteristic
241C2×C4C11×#12112yes—
242C2×C4C11×#12711yescharacteristic
243C2×C4C2×C11×Q1612yes—
244C2×C4C11×#13512yes—
245C2×C4C11×#13712yes—
246C2×C4C11×#13712yes—
247C8—42no—
248C8—44no—
249C22C11×#39211yescharacteristic
250C22C11×#45112yes—
251C22C11×#45212yes—
252C22C11×#45311yescharacteristic
253C22C11×#45411yescharacteristic
254C4—21no—
255C4—21no—
256C4—44no—
257C4—82no—
258C4—82no—
259C4—82no—
260C4C11×#45112yes—
261C4C11×#45212yes—
262C4C11×#46712yes—
263C4C11×#47012yes—
264C2C11×#163011yescharacteristic
265C2C11×#163311yescharacteristic
266C2C11×#163612yes—
267C2C11×#200112yes—
268C2C11×#200611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
47. #10237C11direct (N × H)
218. C11#10237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4772
C11×#25822
C11×#19562
C2×C11×Q8⋊C82
C11×#12962
#1023711