Finite Group Databasebeta

← C11×#10230 #14587423

Subgroups — C11×#10230 #14587423

Order 2816.

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

normal subgroups only

This group has 676 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×#460C212yesmaximal
2C11×#2582C211yesmaximal, characteristic, complemented
3C11×#1957C211yesmaximal, characteristic
4C2×C11×Q8⋊C8C212yesmaximal, complemented
5C11×#1296C211yesmaximal, characteristic, complemented
6C22×C11×SD16—22no—
7C2×C11×#127C2211yescharacteristic
8C2×C4×Q8×C11C2212yes—
9C11×#460—24no—
10C11×#460—24no—
11C2×C11×C4⋊C8C2212yes—
12C2×C11×#102—22no—
13C2×C11×#102—22no—
14C2×C4×C8×C11C2211yescharacteristic
15C11×#398—22no—
16C11×#391—22no—
17C11×#389—22no—
18C11×#384C2211yescharacteristic
19C11×Q8⋊C8—24no—
20C22×Q8×C11D412yes—
21C22×D4×C11—21no—
22C22×D4×C11—22no—
23C2×C11×SD16—28no—
24C2×C11×SD16—44no—
25C2×C11×SD16—44no—
26C22×C8×C11—21no—
27C22×C8×C11—22no—
28C11×#127—22no—
29C11×#127—21no—
30C11×#127D412yes—
31C4×Q8×C11—22no—
32C4×Q8×C11—22no—
33C4×Q8×C11—22no—
34C4×Q8×C11—22no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4D412yes—
39C2×C11×C4⋊C4D412yes—
40C2×C42×C11—22no—
41C2×C42×C11C2311yescharacteristic
42C11×C4⋊C8—22no—
43C11×C4⋊C8D414yes—
44C11×#102—28no—
45C11×#102—44no—
46C4×C8×C11—22no—
47C11×#95—24no—
48C11×#95—22no—
49#10230C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11—41no—
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11SD1614yescomplemented
57C2×D4×C11—24no—
58C2×D4×C11—22no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—42no—
62C2×D4×C11—41no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—42no—
66C2×D4×C11—42no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D412yes—
72C11×SD16—416no—
73C2×C8×C11—22no—
74C2×C8×C11—24no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—42no—
78C2×C8×C11—42no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—82no—
87C42×C11—42no—
88C42×C11—42no—
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D412yes—
91C42×C11#4111yescharacteristic
92C2×#460C2×C1112yes—
93#2582C2×C1111yescharacteristic, complemented
94#1957C2×C1111yescharacteristic
95C2×Q8⋊C8C2×C1112yescomplemented
96#1296C2×C1111yescharacteristic, complemented
97C23×C11—42no—
98C23×C11—82no—
99C23×C11—82no—
100C23×C11—81no—
101C23×C11—81no—
102C23×C11#12011yescharacteristic
103Q8×C11—24no—
104Q8×C11—24no—
105Q8×C11—42no—
106Q8×C11—42no—
107D4×C11—44no—
108D4×C11—44no—
109D4×C11—44no—
110D4×C11—82no—
111D4×C11—82no—
112D4×C11—82no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—24no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—44no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11#12012yes—
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12112yes—
126C2×C4×C11#12711yescharacteristic
127C2×C4×C11C2×SD1612yes—
128C2×C4×C11#13512yes—
129C2×C4×C11AGL(1,ℤ/8)12yes—
130C2×C4×C11#13712yes—
131C8×C11—42no—
132C8×C11—44no—
133C22×SD16—22no—
134C2×#127C22×C1111yescharacteristic
135C2×C4×Q8C22×C1112yes—
136#460—24no—
137#460—24no—
138C2×C4⋊C8C22×C1112yes—
139C2×#102—22no—
140C2×#102—22no—
141C2×C4×C8C22×C1111yescharacteristic
142#398—22no—
143#391—22no—
144#389—22no—
145#384C22×C1111yescharacteristic
146Q8⋊C8—24no—
147C22×C11—84no—
148C22×C11—82no—
149C22×C11—161no—
150C22×C11—161no—
151C22×C11—162no—
152C22×C11#39211yescharacteristic
153C22×C11#44812yes—
154C22×C11#44912yes—
155C22×C11#45311yescharacteristic
156C22×C11#45411yescharacteristic
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—44no—
160C4×C11—82no—
161C4×C11—82no—
162C4×C11#45012yes—
163C4×C11#45212yes—
164C4×C11#46512yes—
165C4×C11#46812yes—
166C22×Q8D4×C1112yes—
167C22×D4—22no—
168C22×D4—21no—
169C2×SD16—28no—
170C2×SD16—44no—
171C2×SD16—44no—
172C22×C8—22no—
173C22×C8—21no—
174#127—22no—
175#127—21no—
176#127D4×C1112yes—
177C4×Q8—22no—
178C4×Q8—22no—
179C4×Q8—22no—
180C4×Q8—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4D4×C1112yes—
185C2×C4⋊C4D4×C1112yes—
186C2×C42—22no—
187C2×C42C23×C1111yescharacteristic
188C4⋊C8—22no—
189C4⋊C8D4×C1114yes—
190#102—28no—
191#102—44no—
192C4×C8—22no—
193#95—24no—
194#95—22no—
195C2×C11—162no—
196C2×C11#162011yescharacteristic
197C2×C11#162311yescharacteristic
198C2×C11#162612yes—
199C2×C11#200012yes—
200C2×C11#200611yescharacteristic
201C24—41no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8C11×SD1614yescomplemented
208C2×D4—24no—
209C2×D4—22no—
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—41no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4C2×D4×C1111yescharacteristic
222C22×C4C2×D4×C1112yes—
223SD16—416no—
224C2×C8—22no—
225C2×C8—24no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—42no—
229C2×C8—42no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—82no—
238C42—42no—
239C42—42no—
240C42C2×D4×C1111yescharacteristic
241C42C2×D4×C1112yes—
242C42C11×#4111yescharacteristic
243C11#1023011yescharacteristic, direct product factor, Sylow
244C23—42no—
245C23—82no—
246C23—82no—
247C23—81no—
248C23—81no—
249C23C11×#12011yescharacteristic
250Q8—24no—
251Q8—24no—
252Q8—42no—
253Q8—42no—
254D4—44no—
255D4—44no—
256D4—44no—
257D4—82no—
258D4—82no—
259D4—82no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—24no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4C11×#12012yes—
271C2×C4C11×#12111yescharacteristic
272C2×C4C11×#12112yes—
273C2×C4C11×#12711yescharacteristic
274C2×C4C2×C11×SD1612yes—
275C2×C4C11×#13512yes—
276C2×C4C11×AGL(1,ℤ/8)12yes—
277C2×C4C11×#13712yes—
278C8—42no—
279C8—44no—
280C22—84no—
281C22—82no—
282C22—161no—
283C22—161no—
284C22—162no—
285C22C11×#39211yescharacteristic
286C22C11×#44812yes—
287C22C11×#44912yes—
288C22C11×#45311yescharacteristic
289C22C11×#45411yescharacteristic
290C4—21no—
291C4—21no—
292C4—44no—
293C4—82no—
294C4—82no—
295C4C11×#45012yes—
296C4C11×#45212yes—
297C4C11×#46512yes—
298C4C11×#46812yes—
299C2—162no—
300C2C11×#162011yescharacteristic
301C2C11×#162311yescharacteristic
302C2C11×#162612yes—
303C2C11×#200012yes—
304C2C11×#200611yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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
2. C11×#2582C2semidirect
4. C2×C11×Q8⋊C8C2semidirect
5. C11×#1296C2semidirect
49. #10230C11direct (N × H)
56. C2×Q8×C11SD16semidirect
93. #2582C2×C11semidirect
95. C2×Q8⋊C8C2×C11semidirect
96. #1296C2×C11semidirect
207. C2×Q8C11×SD16semidirect
243. C11#10230direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C11×#25822
C11×#19572
C2×C11×Q8⋊C82
C11×#12962
#1023011