Finite Group Databasebeta

← C11×#19075 #14596268

Subgroups — C11×#19075 #14596268

Order 2816.

1116 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3548C211yesmaximal, characteristic, complemented
2C11×#3151C212yesmaximal, complemented
3C11×#3138C211yesmaximal, characteristic, complemented
4C11×#1656C218yesmaximal, complemented
5C11×#1526C211yesmaximal, characteristic, complemented
6C11×#1525C212yesmaximal, complemented
7C2×C11×AGL(1,ℤ/8)—24no—
8C11×#562C2214yescomplemented
9C11×#554—22no—
10C11×#550—22no—
11C11×#547—22no—
12C11×#540—22no—
13C11×#537—24no—
14C11×#533C2211yescharacteristic
15C11×#532C2212yes—
16C2×C11×#127C2211yescharacteristic
17C11×#496C2218yes—
18C11×#493—22no—
19C11×#492—22no—
20C11×#490C2214yes—
21C11×#486—22no—
22C11×#418—22no—
23C4×C11×M16C2212yes—
24C4×C11×M16C2211yescharacteristic
25C11×#330C2214yescomplemented
26C11×#329C2218yescomplemented
27C2×C11×#41—24no—
28C2×C11×#41D414yes—
29C22×D4×C11—21no—
30C22×D4×C11—22no—
31C11×AGL(1,ℤ/8)—416no—
32C2×C11×SD16—28no—
33C2×C11×D8—28no—
34C2×C11×M16—22no—
35C2×C11×M16—21no—
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8D412yes—
38C11×#127—22no—
39C11×#127—22no—
40C11×#127—21no—
41C11×#127D412yes—
42C11×#127C2312yes—
43C11×#125—22no—
44C11×#125C2312yes—
45C11×#124C2314yes—
46C11×#123—28no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—28no—
49C11×C22⋊Q8—22no—
50C11×#121—28no—
51C11×#121—24no—
52C11×#121—28no—
53C11×#121—22no—
54C11×#121—22no—
55C4×Q8×C11—22no—
56C4×D4×C11—24no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C11×#117D412yes—
60C2×C11×C4⋊C4—24no—
61C2×C42×C11C2311yescharacteristic
62C11×#102—28no—
63C11×#97C2312yes—
64C11×#97C2314yes—
65C4×C8×C11—22no—
66C4×C8×C11—21no—
67#19075C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—41no—
69C11×#41—48no—
70C11×#41—88no—
71C2×Q8×C11—22no—
72C2×Q8×C11C2×D414yes—
73C2×D4×C11—28no—
74C2×D4×C11—24no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—24no—
79C2×D4×C11—48no—
80C2×D4×C11—44no—
81C2×D4×C11—42no—
82C2×D4×C11—41no—
83C2×D4×C11C2×D414yes—
84C22×C4×C11—28no—
85C22×C4×C11—24no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D412yes—
88C11×SD16—416no—
89C11×D8—416no—
90C11×M16—28no—
91C11×M16—42no—
92C2×C8×C11—24no—
93C2×C8×C11—22no—
94C11×C4⋊C4—28no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4C2×D414yes—
100C11×C22⋊C4—28no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C42×C11—22no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D412yes—
107C42×C11C2411yescharacteristic
108#3548C2×C1111yescharacteristic, complemented
109#3151C2×C1112yescomplemented
110#3138C2×C1111yescharacteristic, complemented
111#1656C2×C1118yescomplemented
112#1526C2×C1111yescharacteristic, complemented
113#1525C2×C1112yescomplemented
114C23×C11—24no—
115C23×C11—42no—
116C23×C11—84no—
117C23×C11—82no—
118C23×C11#12011yescharacteristic
119Q8×C11—44no—
120Q8×C11—44no—
121D4×C11—44no—
122D4×C11—48no—
123D4×C11—44no—
124D4×C11—44no—
125D4×C11—44no—
126D4×C11—84no—
127D4×C11—88no—
128D4×C11—84no—
129D4×C11—82no—
130C2×C4×C11—24no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—48no—
135C2×C4×C11—88no—
136C2×C4×C11#12012yes—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C2×C4×C11C22×D412yes—
140C8×C11—28no—
141C8×C11—42no—
142C2×AGL(1,ℤ/8)—24no—
143#562C22×C1114yescomplemented
144#554—22no—
145#550—22no—
146#547—22no—
147#540—22no—
148#537—24no—
149#533C22×C1111yescharacteristic
150#532C22×C1112yes—
151C2×#127C22×C1111yescharacteristic
152#496C22×C1118yes—
153#493—22no—
154#492—22no—
155#490C22×C1114yes—
156#486—22no—
157#418—22no—
158C4×M16C22×C1111yescharacteristic
159C4×M16C22×C1112yes—
160#330C22×C1114yescomplemented
161#329C22×C1118yescomplemented
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—44no—
165C22×C11—44no—
166C22×C11—44no—
167C22×C11—84no—
168C22×C11—82no—
169C22×C11—164no—
170C22×C11C2×#12011yescharacteristic
171C4×C11—22no—
172C4×C11—21no—
173C4×C11—44no—
174C4×C11—44no—
175C4×C11#45314yes—
176C4×C11#45412yes—
177C2×#41—24no—
178C2×#41D4×C1114yes—
179C22×D4—22no—
180C22×D4—21no—
181AGL(1,ℤ/8)—416no—
182C2×SD16—28no—
183C2×D8—28no—
184C2×M16—22no—
185C2×M16—21no—
186C4⋊Q8D4×C1112yes—
187C4⋊Q8D4×C1112yes—
188#127—22no—
189#127—21no—
190#127—22no—
191#127D4×C1112yes—
192#127C23×C1112yes—
193#125—22no—
194#125C23×C1112yes—
195#124C23×C1114yes—
196#123—28no—
197C22⋊Q8—24no—
198C22⋊Q8—28no—
199C22⋊Q8—22no—
200#121—28no—
201#121—24no—
202#121—28no—
203#121—22no—
204#121—22no—
205C4×Q8—22no—
206C4×D4—24no—
207C4×D4—22no—
208C4×D4—22no—
209#117D4×C1112yes—
210C2×C4⋊C4—24no—
211C2×C42C23×C1111yescharacteristic
212#102—28no—
213#97C23×C1112yes—
214#97C23×C1114yes—
215C4×C8—21no—
216C4×C8—22no—
217C2×C11—41no—
218C2×C11—84no—
219C2×C11—162no—
220C2×C11C2×#45312yes—
221C2×C11C2×#45411yescharacteristic
222C24—41no—
223#41—48no—
224#41—88no—
225C2×Q8—22no—
226C2×Q8C2×D4×C1114yes—
227C2×D4—28no—
228C2×D4—24no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—24no—
233C2×D4—48no—
234C2×D4—44no—
235C2×D4—42no—
236C2×D4—41no—
237C2×D4C2×D4×C1114yes—
238C22×C4—28no—
239C22×C4—24no—
240C22×C4C2×D4×C1111yescharacteristic
241C22×C4C2×D4×C1112yes—
242SD16—416no—
243D8—416no—
244M16—28no—
245M16—42no—
246C2×C8—24no—
247C2×C8—22no—
248C4⋊C4—28no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4C2×D4×C1114yes—
254C22⋊C4—28no—
255C22⋊C4—22no—
256C22⋊C4—24no—
257C22⋊C4—24no—
258C42—22no—
259C42C2×D4×C1111yescharacteristic
260C42C2×D4×C1112yes—
261C42C24×C1111yescharacteristic
262C11#1907511yescharacteristic, direct product factor, Sylow
263C23—24no—
264C23—42no—
265C23—84no—
266C23—82no—
267C23C11×#12011yescharacteristic
268Q8—44no—
269Q8—44no—
270D4—44no—
271D4—48no—
272D4—44no—
273D4—44no—
274D4—44no—
275D4—84no—
276D4—88no—
277D4—84no—
278D4—82no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—48no—
284C2×C4—88no—
285C2×C4C11×#12012yes—
286C2×C4C11×#12011yescharacteristic
287C2×C4C22×D4×C1111yescharacteristic
288C2×C4C22×D4×C1112yes—
289C8—28no—
290C8—42no—
291C22—22no—
292C22—21no—
293C22—44no—
294C22—44no—
295C22—44no—
296C22—84no—
297C22—82no—
298C22—164no—
299C22C2×C11×#12011yescharacteristic
300C4—22no—
301C4—21no—
302C4—44no—
303C4—44no—
304C4C11×#45314yes—
305C4C11×#45412yes—
306C2—41no—
307C2—84no—
308C2—162no—
309C2C2×C11×#45312yes—
310C2C2×C11×#45411yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3548C2semidirect
2. C11×#3151C2semidirect
3. C11×#3138C2semidirect
4. C11×#1656C2semidirect
5. C11×#1526C2semidirect
6. C11×#1525C2semidirect
8. C11×#562C22semidirect
25. C11×#330C22semidirect
26. C11×#329C22semidirect
67. #19075C11direct (N × H)
108. #3548C2×C11semidirect
109. #3151C2×C11semidirect
110. #3138C2×C11semidirect
111. #1656C2×C11semidirect
112. #1526C2×C11semidirect
113. #1525C2×C11semidirect
143. #562C22×C11semidirect
160. #330C22×C11semidirect
161. #329C22×C11semidirect
262. C11#19075direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#31512
C11×#31382
C11×#16562
C11×#15262
C11×#15252
#1907511