Finite Group Databasebeta

← C11×#35001 #14612194

Subgroups — C11×#35001 #14612194

Order 2816.

4298 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#534C214yesmaximal, complemented
2C22×C11×#121C212yesmaximal, complemented
3C11×#2856C214yesmaximal, complemented
4C11×#2656C214yesmaximal, complemented
5C11×#2539C218yesmaximal, complemented
6C11×#2501C214yesmaximal, complemented
7C11×#2433C214yesmaximal, complemented
8C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
9C23×D4×C11C2214yes—
10C23×D4×C11C2212yescomplemented
11C24×C4×C11C2211yescharacteristic
12C11×#534—232no—
13C2×C11×#127C2214yescomplemented
14C2×C11×#123C22116yescomplemented
15C2×C11×#121—216no—
16C2×C11×#121C2214yes—
17C2×C11×#121C2214yes—
18C2×C11×#121C2214yescomplemented
19C2×C11×#121C22116yescomplemented
20C2×C11×#121C2214yescomplemented
21C2×C11×#120C22116yescomplemented
22C22×C11×C4⋊C4C2212yescomplemented
23C22×C11×C22⋊C4C2212yes—
24C22×C11×C22⋊C4C2214yescomplemented
25C22×C42×C11C2212yescomplemented
26C11×#399C22116yescomplemented
27C11×#392C22116yescomplemented
28C11×#390C2218yescomplemented
29C11×#390C22116yescomplemented
30C11×#384C2214yescomplemented
31C4×C11×C22⋊C4C2214yescomplemented
32C4×C11×C22⋊C4C2214yescomplemented
33C2×C11×#95C2212yescomplemented
34C25×C11C2314yes—
35C25×C11C2311yescharacteristic
36C22×D4×C11—216no—
37C22×D4×C11—232no—
38C22×D4×C11—28no—
39C22×D4×C11—48no—
40C22×D4×C11C2318yes—
41C22×D4×C11C2314yes—
42C22×D4×C11C2318yes—
43C22×D4×C11C23116yes—
44C22×D4×C11C2314yes—
45C23×C4×C11—44no—
46C23×C4×C11D418yescomplemented
47C23×C4×C11C2314yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2314yes—
53C11×#127—48no—
54C11×#123—264no—
55C11×#121—216no—
56C11×#121—216no—
57C11×#121—216no—
58C11×#121—216no—
59C11×#121—264no—
60C11×#120—264no—
61C2×C11×C4⋊C4—28no—
62C2×C11×C4⋊C4C2314yes—
63C2×C11×C4⋊C4C2314yes—
64C2×C11×C4⋊C4C23116yes—
65C2×C11×C22⋊C4—216no—
66C2×C11×C22⋊C4D4116yescomplemented
67C2×C11×C22⋊C4C2318yes—
68C2×C11×C22⋊C4C2318yes—
69C2×C11×C22⋊C4C23132yes—
70C2×C11×C22⋊C4C2318yes—
71C2×C42×C11—44no—
72C2×C42×C11C2314yes—
73C2×C42×C11C2314yes—
74C11×#95C2318yes—
75#35001C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—28no—
77C24×C11—216no—
78C24×C11—42no—
79C24×C11—42no—
80C24×C11—48no—
81C24×C11—48no—
82C24×C11C2×D418yes—
83C24×C11C2×D414yes—
84C24×C11C2418yes—
85C24×C11C2412yes—
86C24×C11C2411yescharacteristic
87C2×D4×C11—232no—
88C2×D4×C11—216no—
89C2×D4×C11—216no—
90C2×D4×C11—232no—
91C2×D4×C11—28no—
92C2×D4×C11—28no—
93C2×D4×C11—232no—
94C2×D4×C11—216no—
95C2×D4×C11—48no—
96C2×D4×C11—432no—
97C2×D4×C11—416no—
98C2×D4×C11—416no—
99C2×D4×C11—464no—
100C22×C4×C11—24no—
101C22×C4×C11—28no—
102C22×C4×C11—28no—
103C22×C4×C11—216no—
104C22×C4×C11—416no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11—42no—
108C22×C4×C11—44no—
109C22×C4×C11C2×D418yes—
110C22×C4×C11C2×D414yes—
111C22×C4×C11C2×D418yes—
112C22×C4×C11C2×D414yes—
113C22×C4×C11C2×D4116yescomplemented
114C22×C4×C11C2418yes—
115C22×C4×C11C2412yes—
116C22×C4×C11C2418yes—
117C22×C4×C11C2411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C11×C4⋊C4—28no—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—232no—
122C11×C22⋊C4—216no—
123C11×C22⋊C4—216no—
124C11×C22⋊C4—264no—
125C11×C22⋊C4C2×D4132yescomplemented
126C42×C11—28no—
127C42×C11—44no—
128C2×#534C2×C1114yescomplemented
129C22×#121C2×C1112yescomplemented
130#2856C2×C1114yescomplemented
131#2656C2×C1114yescomplemented
132#2539C2×C1118yescomplemented
133#2501C2×C1114yescomplemented
134#2433C2×C1114yescomplemented
135C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
136C23×C11—22no—
137C23×C11—24no—
138C23×C11—22no—
139C23×C11—24no—
140C23×C11—28no—
141C23×C11—216no—
142C23×C11—216no—
143C23×C11—216no—
144C23×C11—44no—
145C23×C11—44no—
146C23×C11—416no—
147C23×C11—416no—
148C23×C11—416no—
149C23×C11—416no—
150C23×C11—832no—
151C23×C11#127116yescomplemented
152C23×C11C22×D418yes—
153C23×C11C22×D414yes—
154C23×C11C22×D412yes—
155C23×C11C22×D414yes—
156C23×C11C2511yescharacteristic
157D4×C11—416no—
158D4×C11—432no—
159D4×C11—432no—
160D4×C11—416no—
161D4×C11—832no—
162C2×C4×C11—28no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—28no—
166C2×C4×C11—28no—
167C2×C4×C11—216no—
168C2×C4×C11—28no—
169C2×C4×C11—216no—
170C2×C4×C11—48no—
171C2×C4×C11—44no—
172C2×C4×C11—416no—
173C2×C4×C11—416no—
174C2×C4×C11C22×D412yes—
175C2×C4×C11C22×D4116yes—
176C2×C4×C11C22×D414yes—
177C2×C4×C11C22×D412yes—
178C2×C4×C11H(5,𝔽2)14yes—
179C23×D4C22×C1114yes—
180C23×D4C22×C1112yescomplemented
181C24×C4C22×C1111yescharacteristic
182#534—232no—
183C2×#127C22×C1114yescomplemented
184C2×#123C22×C11116yescomplemented
185C2×#121—216no—
186C2×#121C22×C1114yes—
187C2×#121C22×C1114yes—
188C2×#121C22×C1114yescomplemented
189C2×#121C22×C11116yescomplemented
190C2×#121C22×C1114yescomplemented
191C2×#120C22×C11116yescomplemented
192C22×C4⋊C4C22×C1112yescomplemented
193C22×C22⋊C4C22×C1112yes—
194C22×C22⋊C4C22×C1114yescomplemented
195C22×C42C22×C1112yescomplemented
196#399C22×C11116yescomplemented
197#392C22×C11116yescomplemented
198#390C22×C1118yescomplemented
199#390C22×C11116yescomplemented
200#384C22×C1114yescomplemented
201C4×C22⋊C4C22×C1114yescomplemented
202C4×C22⋊C4C22×C1114yescomplemented
203C2×#95C22×C1112yescomplemented
204C22×C11—24no—
205C22×C11—22no—
206C22×C11—24no—
207C22×C11—22no—
208C22×C11—28no—
209C22×C11—216no—
210C22×C11—416no—
211C22×C11—48no—
212C22×C11—48no—
213C22×C11—48no—
214C22×C11—432no—
215C22×C11—832no—
216C22×C11C2×#12718yes—
217C22×C11C2×#12714yes—
218C22×C11C23×D411yescharacteristic
219C22×C11C23×D412yes—
220C22×C11C2×H(5,𝔽2)12yes—
221C22×C11#58512yes—
222C4×C11—22no—
223C4×C11—24no—
224C4×C11—216no—
225C4×C11—48no—
226C4×C11#53414yescomplemented
227C25C23×C1114yes—
228C25C23×C1111yescharacteristic
229C22×D4—216no—
230C22×D4—232no—
231C22×D4—28no—
232C22×D4—48no—
233C22×D4C23×C1118yes—
234C22×D4C23×C1114yes—
235C22×D4C23×C1118yes—
236C22×D4C23×C11116yes—
237C22×D4C23×C1114yes—
238C23×C4—44no—
239C23×C4D4×C1118yescomplemented
240C23×C4C23×C1114yes—
241C23×C4C23×C1112yes—
242C23×C4C23×C1111yescharacteristic
243C23×C4C23×C1112yes—
244C23×C4C23×C1111yescharacteristic
245C23×C4C23×C1114yes—
246#127—48no—
247#123—264no—
248#121—216no—
249#121—216no—
250#121—216no—
251#121—216no—
252#121—264no—
253#120—264no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4C23×C1114yes—
256C2×C4⋊C4C23×C1114yes—
257C2×C4⋊C4C23×C11116yes—
258C2×C22⋊C4—216no—
259C2×C22⋊C4D4×C11116yescomplemented
260C2×C22⋊C4C23×C1118yes—
261C2×C22⋊C4C23×C1118yes—
262C2×C22⋊C4C23×C11132yes—
263C2×C22⋊C4C23×C1118yes—
264C2×C42—44no—
265C2×C42C23×C1114yes—
266C2×C42C23×C1114yes—
267#95C23×C1118yes—
268C2×C11—28no—
269C2×C11—24no—
270C2×C11—88no—
271C2×C11C22×#12711yescharacteristic
272C2×C11C2×#53411yescharacteristic
273C2×C11#344911yescharacteristic
274C2×C11#349614yes—
275C24—28no—
276C24—216no—
277C24—42no—
278C24—42no—
279C24—48no—
280C24—48no—
281C24C2×D4×C1118yes—
282C24C2×D4×C1114yes—
283C24C24×C1118yes—
284C24C24×C1112yes—
285C24C24×C1111yescharacteristic
286C2×D4—232no—
287C2×D4—216no—
288C2×D4—216no—
289C2×D4—232no—
290C2×D4—28no—
291C2×D4—28no—
292C2×D4—232no—
293C2×D4—216no—
294C2×D4—48no—
295C2×D4—432no—
296C2×D4—416no—
297C2×D4—416no—
298C2×D4—464no—
299C22×C4—24no—
300C22×C4—28no—
301C22×C4—28no—
302C22×C4—216no—
303C22×C4—416no—
304C22×C4—44no—
305C22×C4—44no—
306C22×C4—42no—
307C22×C4—44no—
308C22×C4C2×D4×C1118yes—
309C22×C4C2×D4×C1114yes—
310C22×C4C2×D4×C1118yes—
311C22×C4C2×D4×C1114yes—
312C22×C4C2×D4×C11116yescomplemented
313C22×C4C24×C1118yes—
314C22×C4C24×C1112yes—
315C22×C4C24×C1118yes—
316C22×C4C24×C1111yescharacteristic
317C22×C4C24×C1111yescharacteristic
318C4⋊C4—28no—
319C4⋊C4—28no—
320C4⋊C4—232no—
321C22⋊C4—216no—
322C22⋊C4—216no—
323C22⋊C4—264no—
324C22⋊C4C2×D4×C11132yescomplemented
325C42—28no—
326C42—44no—
327C11#3500111yescharacteristic, direct product factor, Sylow
328C23—22no—
329C23—24no—
330C23—22no—
331C23—24no—
332C23—28no—
333C23—216no—
334C23—216no—
335C23—216no—
336C23—44no—
337C23—44no—
338C23—416no—
339C23—416no—
340C23—416no—
341C23—416no—
342C23—832no—
343C23C11×#127116yescomplemented
344C23C22×D4×C1118yes—
345C23C22×D4×C1114yes—
346C23C22×D4×C1112yes—
347C23C22×D4×C1114yes—
348C23C25×C1111yescharacteristic
349D4—416no—
350D4—432no—
351D4—432no—
352D4—416no—
353D4—832no—
354C2×C4—28no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—28no—
358C2×C4—28no—
359C2×C4—216no—
360C2×C4—28no—
361C2×C4—216no—
362C2×C4—44no—
363C2×C4—48no—
364C2×C4—416no—
365C2×C4—416no—
366C2×C4C22×D4×C1112yes—
367C2×C4C22×D4×C11116yes—
368C2×C4C22×D4×C1114yes—
369C2×C4C22×D4×C1112yes—
370C2×C4C11×H(5,𝔽2)14yes—
371C22—24no—
372C22—22no—
373C22—24no—
374C22—22no—
375C22—28no—
376C22—216no—
377C22—416no—
378C22—48no—
379C22—48no—
380C22—48no—
381C22—432no—
382C22—832no—
383C22C2×C11×#12718yes—
384C22C2×C11×#12714yes—
385C22C23×D4×C1111yescharacteristic
386C22C23×D4×C1112yes—
387C22C2×C11×H(5,𝔽2)12yes—
388C22C11×#58512yes—
389C4—24no—
390C4—22no—
391C4—216no—
392C4—48no—
393C4C11×#53414yescomplemented
394C2—28no—
395C2—24no—
396C2—88no—
397C2C22×C11×#12711yescharacteristic
398C2C2×C11×#53411yescharacteristic
399C2C11×#344911yescharacteristic
400C2C11×#349614yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#534C2semidirect
2. C22×C11×#121C2semidirect
3. C11×#2856C2semidirect
4. C11×#2656C2semidirect
5. C11×#2539C2semidirect
6. C11×#2501C2semidirect
7. C11×#2433C2semidirect
8. C2×C4×C11×C22⋊C4C2semidirect
10. C23×D4×C11C22semidirect
13. C2×C11×#127C22semidirect
14. C2×C11×#123C22semidirect
18. C2×C11×#121C22semidirect
19. C2×C11×#121C22semidirect
20. C2×C11×#121C22semidirect
21. C2×C11×#120C22semidirect
22. C22×C11×C4⋊C4C22semidirect
24. C22×C11×C22⋊C4C22semidirect
25. C22×C42×C11C22semidirect
26. C11×#399C22semidirect
27. C11×#392C22semidirect
28. C11×#390C22semidirect
29. C11×#390C22semidirect
30. C11×#384C22semidirect
31. C4×C11×C22⋊C4C22semidirect
32. C4×C11×C22⋊C4C22semidirect
33. C2×C11×#95C22semidirect
46. C23×C4×C11D4semidirect
66. C2×C11×C22⋊C4D4semidirect
75. #35001C11direct (N × H)
113. C22×C4×C11C2×D4semidirect
125. C11×C22⋊C4C2×D4semidirect
128. C2×#534C2×C11semidirect
129. C22×#121C2×C11semidirect
130. #2856C2×C11semidirect
131. #2656C2×C11semidirect
132. #2539C2×C11semidirect
133. #2501C2×C11semidirect
134. #2433C2×C11semidirect
135. C2×C4×C22⋊C4C2×C11semidirect
151. C23×C11#127semidirect
180. C23×D4C22×C11semidirect
183. C2×#127C22×C11semidirect
184. C2×#123C22×C11semidirect
188. C2×#121C22×C11semidirect
189. C2×#121C22×C11semidirect
190. C2×#121C22×C11semidirect
191. C2×#120C22×C11semidirect
192. C22×C4⋊C4C22×C11semidirect
194. C22×C22⋊C4C22×C11semidirect
195. C22×C42C22×C11semidirect
196. #399C22×C11semidirect
197. #392C22×C11semidirect
198. #390C22×C11semidirect
199. #390C22×C11semidirect
200. #384C22×C11semidirect
201. C4×C22⋊C4C22×C11semidirect
202. C4×C22⋊C4C22×C11semidirect
203. C2×#95C22×C11semidirect
226. C4×C11#534semidirect
239. C23×C4D4×C11semidirect
259. C2×C22⋊C4D4×C11semidirect
312. C22×C4C2×D4×C11semidirect
324. C22⋊C4C2×D4×C11semidirect
327. C11#35001direct (N × H)
343. C23C11×#127semidirect
393. C4C11×#534semidirect

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×#1212
C11×#28562
C11×#26562
C11×#25392
C11×#25012
C11×#24332
C2×C4×C11×C22⋊C42
#3500111