Finite Group Databasebeta

← C11×#21213 #14598406

Subgroups — C11×#21213 #14598406

Order 2816.

1858 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#534C211yesmaximal, characteristic
2C22×C11×#99C214yesmaximal, complemented
3C11×#2315C211yesmaximal, characteristic, complemented
4C11×#2273C211yesmaximal, characteristic, complemented
5C11×#1964C218yesmaximal, complemented
6C23×D4×C11C2212yes—
7C11×#534—24no—
8C11×#534—24no—
9C2×C11×#123C414yescomplemented
10C2×C11×#121C2214yes—
11C2×C11×#120C414yescomplemented
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2211yescharacteristic
15C2×C11×#99—216no—
16C2×C11×#99C22116yescomplemented
17C11×#385—24no—
18C11×#380C2214yescomplemented
19C4×C11×C22⋊C4—24no—
20C4×C11×C22⋊C4C2214yescomplemented
21C25×C11C2×C412yes—
22C25×C11C2311yescharacteristic
23C22×D4×C11—24no—
24C22×D4×C11—24no—
25C22×D4×C11—28no—
26C22×D4×C11—28no—
27C22×D4×C11C2×C414yes—
28C22×D4×C11C2×C414yescomplemented
29C22×D4×C11C2314yes—
30C23×C4×C11—22no—
31C23×C4×C11—22no—
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2312yes—
34C11×#123—216no—
35C11×#121—28no—
36C11×#121—28no—
37C11×#120—216no—
38C2×C11×C4⋊C4—24no—
39C2×C11×C4⋊C4C2×C414yescomplemented
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—28no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4C2×C414yes—
45C2×C11×C22⋊C4C2×C418yescomplemented
46C2×C11×C22⋊C4D414yes—
47C2×C11×C22⋊C4D414yes—
48C2×C11×C22⋊C4D418yescomplemented
49C2×C11×C22⋊C4C2314yes—
50C2×C11×C22⋊C4C2314yes—
51C2×C42×C11—24no—
52C11×#99—232no—
53C11×#95—24no—
54C11×#95—24no—
55#21213C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11—24no—
57C24×C11—28no—
58C24×C11—82no—
59C24×C11—84no—
60C24×C11C22×C414yes—
61C24×C11C22×C412yes—
62C24×C11C2×D412yes—
63C24×C11C2×D412yes—
64C24×C11C2×D414yes—
65C24×C11#4114yes—
66C24×C11C2411yescharacteristic
67C2×D4×C11—28no—
68C2×D4×C11—216no—
69C2×D4×C11—28no—
70C2×D4×C11—24no—
71C2×D4×C11—24no—
72C2×D4×C11—28no—
73C2×D4×C11—28no—
74C2×D4×C11—48no—
75C2×D4×C11—48no—
76C2×D4×C11—48no—
77C2×D4×C11—48no—
78C2×D4×C11—84no—
79C22×C4×C11—24no—
80C22×C4×C11—28no—
81C22×C4×C11—24no—
82C22×C4×C11—28no—
83C22×C4×C11—24no—
84C22×C4×C11—44no—
85C22×C4×C11—82no—
86C22×C4×C11—84no—
87C22×C4×C11—84no—
88C22×C4×C11C22×C414yes—
89C22×C4×C11C22×C414yes—
90C22×C4×C11C2×D414yes—
91C22×C4×C11C2×D414yes—
92C11×C4⋊C4—28no—
93C11×C4⋊C4—84no—
94C11×C22⋊C4—28no—
95C11×C22⋊C4—24no—
96C11×C22⋊C4—216no—
97C11×C22⋊C4—28no—
98C11×C22⋊C4—44no—
99C11×C22⋊C4C22⋊C4116yes—
100C11×C22⋊C4C2×D418yes—
101C42×C11—84no—
102C2×#534C2×C1111yescharacteristic
103C22×#99C2×C1114yescomplemented
104#2315C2×C1111yescharacteristic, complemented
105#2273C2×C1111yescharacteristic, complemented
106#1964C2×C1118yescomplemented
107C23×C11—24no—
108C23×C11—28no—
109C23×C11—44no—
110C23×C11—44no—
111C23×C11—42no—
112C23×C11—44no—
113C23×C11—48no—
114C23×C11—48no—
115C23×C11—88no—
116C23×C11—84no—
117C23×C11—84no—
118C23×C11—816no—
119C23×C11C2×C22⋊C414yes—
120C23×C11C4×D418yes—
121C23×C11#12114yes—
122C23×C11#12114yes—
123C23×C11#12414yes—
124C23×C11#12714yes—
125C23×C11C23×C411yescharacteristic
126C23×C11C22×D411yescharacteristic
127C23×C11C22×D411yescharacteristic
128C23×C11C22×D412yes—
129C23×C11C2×#4112yes—
130D4×C11—48no—
131D4×C11—44no—
132D4×C11—44no—
133D4×C11—416no—
134D4×C11—88no—
135C2×C4×C11—24no—
136C2×C4×C11—28no—
137C2×C4×C11—28no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11—44no—
141C2×C4×C11—48no—
142C2×C4×C11—48no—
143C2×C4×C11—48no—
144C2×C4×C11—44no—
145C2×C4×C11—88no—
146C2×C4×C11—88no—
147C2×C4×C11C2×C22⋊C418yes—
148C23×D4C22×C1112yes—
149#534—24no—
150#534—24no—
151C2×#123C4×C1114yescomplemented
152C2×#121C22×C1114yes—
153C2×#120C4×C1114yescomplemented
154C22×C22⋊C4C22×C1112yes—
155C22×C22⋊C4C22×C1112yes—
156C22×C22⋊C4C22×C1111yescharacteristic
157C2×#99—216no—
158C2×#99C22×C11116yescomplemented
159#385—24no—
160#380C22×C1114yescomplemented
161C4×C22⋊C4—24no—
162C4×C22⋊C4C22×C1114yescomplemented
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—28no—
167C22×C11—44no—
168C22×C11—44no—
169C22×C11—48no—
170C22×C11—44no—
171C22×C11—44no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—48no—
175C22×C11—44no—
176C22×C11—88no—
177C22×C11—816no—
178C22×C11#39018yes—
179C22×C11C22×C22⋊C411yescharacteristic
180C22×C11C2×C4×D412yes—
181C22×C11C2×#12112yes—
182C22×C11C2×#12411yescharacteristic
183C22×C11C2×#12711yescharacteristic
184C4×C11—28no—
185C4×C11—48no—
186C4×C11—44no—
187C4×C11—84no—
188C25C2×C4×C1112yes—
189C25C23×C1111yescharacteristic
190C22×D4—24no—
191C22×D4—24no—
192C22×D4—28no—
193C22×D4—28no—
194C22×D4C2×C4×C1114yes—
195C22×D4C2×C4×C1114yescomplemented
196C22×D4C23×C1114yes—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4C2×C4×C1112yes—
200C23×C4C23×C1112yes—
201#123—216no—
202#121—28no—
203#121—28no—
204#120—216no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4C2×C4×C1114yescomplemented
207C2×C22⋊C4—22no—
208C2×C22⋊C4—24no—
209C2×C22⋊C4—28no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4C2×C4×C1114yes—
212C2×C22⋊C4C2×C4×C1118yescomplemented
213C2×C22⋊C4D4×C1114yes—
214C2×C22⋊C4D4×C1114yes—
215C2×C22⋊C4D4×C1118yescomplemented
216C2×C22⋊C4C23×C1114yes—
217C2×C22⋊C4C23×C1114yes—
218C2×C42—24no—
219#99—232no—
220#95—24no—
221#95—24no—
222C2×C11—22no—
223C2×C11—21no—
224C2×C11—22no—
225C2×C11—28no—
226C2×C11—21no—
227C2×C11—84no—
228C2×C11C2×#39011yescharacteristic
229C2×C11#288312yes—
230C24—24no—
231C24—28no—
232C24—82no—
233C24—84no—
234C24C22×C4×C1114yes—
235C24C22×C4×C1112yes—
236C24C2×D4×C1112yes—
237C24C2×D4×C1112yes—
238C24C2×D4×C1114yes—
239C24C11×#4114yes—
240C24C24×C1111yescharacteristic
241C2×D4—28no—
242C2×D4—216no—
243C2×D4—28no—
244C2×D4—24no—
245C2×D4—24no—
246C2×D4—28no—
247C2×D4—28no—
248C2×D4—48no—
249C2×D4—48no—
250C2×D4—48no—
251C2×D4—48no—
252C2×D4—84no—
253C22×C4—24no—
254C22×C4—28no—
255C22×C4—24no—
256C22×C4—28no—
257C22×C4—24no—
258C22×C4—44no—
259C22×C4—82no—
260C22×C4—84no—
261C22×C4—84no—
262C22×C4C22×C4×C1114yes—
263C22×C4C22×C4×C1114yes—
264C22×C4C2×D4×C1114yes—
265C22×C4C2×D4×C1114yes—
266C4⋊C4—28no—
267C4⋊C4—84no—
268C22⋊C4—28no—
269C22⋊C4—24no—
270C22⋊C4—216no—
271C22⋊C4—28no—
272C22⋊C4—44no—
273C22⋊C4C11×C22⋊C4116yes—
274C22⋊C4C2×D4×C1118yes—
275C42—84no—
276C11#2121311yescharacteristic, direct product factor, Sylow
277C23—24no—
278C23—28no—
279C23—44no—
280C23—44no—
281C23—42no—
282C23—44no—
283C23—48no—
284C23—48no—
285C23—88no—
286C23—84no—
287C23—84no—
288C23—816no—
289C23C2×C11×C22⋊C414yes—
290C23C4×D4×C1118yes—
291C23C11×#12114yes—
292C23C11×#12114yes—
293C23C11×#12414yes—
294C23C11×#12714yes—
295C23C23×C4×C1111yescharacteristic
296C23C22×D4×C1111yescharacteristic
297C23C22×D4×C1111yescharacteristic
298C23C22×D4×C1112yes—
299C23C2×C11×#4112yes—
300D4—48no—
301D4—44no—
302D4—416no—
303D4—44no—
304D4—88no—
305C2×C4—24no—
306C2×C4—28no—
307C2×C4—28no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—48no—
312C2×C4—48no—
313C2×C4—48no—
314C2×C4—44no—
315C2×C4—88no—
316C2×C4—88no—
317C2×C4C2×C11×C22⋊C418yes—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—28no—
322C22—44no—
323C22—44no—
324C22—48no—
325C22—44no—
326C22—44no—
327C22—42no—
328C22—42no—
329C22—44no—
330C22—48no—
331C22—88no—
332C22—816no—
333C22C11×#39018yes—
334C22C22×C11×C22⋊C411yescharacteristic
335C22C2×C4×D4×C1112yes—
336C22C2×C11×#12112yes—
337C22C2×C11×#12411yescharacteristic
338C22C2×C11×#12711yescharacteristic
339C4—28no—
340C4—48no—
341C4—44no—
342C4—84no—
343C2—22no—
344C2—21no—
345C2—22no—
346C2—28no—
347C2—21no—
348C2—84no—
349C2C2×C11×#39011yescharacteristic
350C2C11×#288312yes—
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#534C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#99C2semidirect
3. C11×#2315C2semidirect
4. C11×#2273C2semidirect
5. C11×#1964C2semidirect
9. C2×C11×#123C4semidirect
11. C2×C11×#120C4semidirect
16. C2×C11×#99C22semidirect
18. C11×#380C22semidirect
20. C4×C11×C22⋊C4C22semidirect
28. C22×D4×C11C2×C4semidirect
39. C2×C11×C4⋊C4C2×C4semidirect
45. C2×C11×C22⋊C4C2×C4semidirect
48. C2×C11×C22⋊C4D4semidirect
55. #21213C11direct (N × H)
103. C22×#99C2×C11semidirect
104. #2315C2×C11semidirect
105. #2273C2×C11semidirect
106. #1964C2×C11semidirect
151. C2×#123C4×C11semidirect
153. C2×#120C4×C11semidirect
158. C2×#99C22×C11semidirect
160. #380C22×C11semidirect
162. C4×C22⋊C4C22×C11semidirect
195. C22×D4C2×C4×C11semidirect
206. C2×C4⋊C4C2×C4×C11semidirect
212. C2×C22⋊C4C2×C4×C11semidirect
215. C2×C22⋊C4D4×C11semidirect
276. C11#21213direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5342
C22×C11×#992
C11×#23152
C11×#22732
C11×#19642
#2121311