Finite Group Databasebeta

← C11×#23939 #14601132

Subgroups — C11×#23939 #14601132

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#540C211yesmaximal, characteristic, complemented
2C2×C11×#447C212yesmaximal, complemented
3C11×#2309C211yesmaximal, characteristic, complemented
4C11×#2025C212yesmaximal, complemented
5C11×#2011C212yesmaximal, complemented
6C11×#1879C214yesmaximal, complemented
7C11×#1875C212yesmaximal, complemented
8C11×#1818C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C22×C11×D8C2214yes—
11C11×#540—28no—
12C2×C11×#127C2211yescharacteristic, complemented
13C2×C11×#125C2211yescharacteristic, complemented
14C2×C11×#123—22no—
15C2×C11×#121—22no—
16C2×C11×#121C2212yes—
17C2×C4×D4×C11C2212yescomplemented
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C11×#447—28no—
21C2×C11×#102C2214yes—
22C2×C11×#102C2214yescomplemented
23C2×C11×C22⋊C8C2212yes—
24C11×#390—22no—
25C11×#390C2212yes—
26C11×#390C2212yes—
27C11×#379—22no—
28C11×#340C2214yescomplemented
29C11×#336C2212yescomplemented
30C11×#336C2212yescomplemented
31C25×C11—21no—
32C22×D4×C11—22no—
33C22×D4×C11—24no—
34C22×D4×C11—21no—
35C22×D4×C11—22no—
36C22×D4×C11—24no—
37C22×D4×C11—42no—
38C22×D4×C11C2312yes—
39C22×D4×C11C2312yes—
40C23×C4×C11—22no—
41C23×C4×C11C2311yescharacteristic
42C2×C11×D8—28no—
43C2×C11×D8—28no—
44C2×C11×D8—44no—
45C22×C8×C11C2314yes—
46C11×#127—24no—
47C11×#125—24no—
48C11×#123—216no—
49C11×#121—216no—
50C11×#121—24no—
51C11×#121D418yes—
52C4×D4×C11—24no—
53C4×D4×C11—24no—
54C11×#117—24no—
55C11×#117—42no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4D412yes—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C11×#102—28no—
70C11×#102—44no—
71C11×C22⋊C8—24no—
72#23939C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—24no—
74C24×C11—22no—
75C24×C11—22no—
76C24×C11—42no—
77C24×C11—42no—
78C24×C11—84no—
79C24×C11C2×D411yescharacteristic
80C2×D4×C11—24no—
81C2×D4×C11—28no—
82C2×D4×C11—28no—
83C2×D4×C11—24no—
84C2×D4×C11—22no—
85C2×D4×C11—24no—
86C2×D4×C11—22no—
87C2×D4×C11—24no—
88C2×D4×C11—24no—
89C2×D4×C11—416no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—84no—
93C2×D4×C11—84no—
94C2×D4×C11C2×D414yes—
95C2×D4×C11#4114yes—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—28no—
100C22×C4×C11—22no—
101C22×C4×C11—84no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D414yes—
106C22×C4×C11C2411yescharacteristic
107C11×D8—416no—
108C2×C8×C11—24no—
109C2×C8×C11—24no—
110C2×C8×C11—24no—
111C11×C4⋊C4—28no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4C2×D414yes—
116C11×C22⋊C4—28no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—42no—
120C11×C22⋊C4—84no—
121C11×C22⋊C4—84no—
122C42×C11—22no—
123C42×C11—22no—
124C42×C11—42no—
125C2×#540C2×C1111yescharacteristic, complemented
126C2×#447C2×C1112yescomplemented
127#2309C2×C1111yescharacteristic, complemented
128#2025C2×C1112yescomplemented
129#2011C2×C1112yescomplemented
130#1879C2×C1114yescomplemented
131#1875C2×C1112yescomplemented
132#1818C2×C1111yescharacteristic, complemented
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—24no—
136C23×C11—24no—
137C23×C11—24no—
138C23×C11—48no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—44no—
144C23×C11—44no—
145C23×C11—44no—
146C23×C11—44no—
147C23×C11—88no—
148C23×C11—88no—
149C23×C11—88no—
150C23×C11#12012yes—
151C23×C11C22×D411yescharacteristic
152D4×C11—28no—
153D4×C11—28no—
154D4×C11—48no—
155D4×C11—44no—
156D4×C11—44no—
157D4×C11—88no—
158D4×C11—88no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—28no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—44no—
168C2×C4×C11—42no—
169C2×C4×C11—44no—
170C2×C4×C11—88no—
171C2×C4×C11#12012yes—
172C2×C4×C11C22×D412yes—
173C2×C4×C11C2×#4112yes—
174C2×C4×C11H(5,𝔽2)12yes—
175C8×C11—44no—
176C23×D4C22×C1111yescharacteristic
177C22×D8C22×C1114yes—
178#540—28no—
179C2×#127C22×C1111yescharacteristic, complemented
180C2×#125C22×C1111yescharacteristic, complemented
181C2×#123—22no—
182C2×#121—22no—
183C2×#121C22×C1112yes—
184C2×C4×D4C22×C1112yescomplemented
185C2×#117C22×C1111yescharacteristic
186C2×#117C22×C1111yescharacteristic
187#447—28no—
188C2×#102C22×C1114yes—
189C2×#102C22×C1114yescomplemented
190C2×C22⋊C8C22×C1112yes—
191#390—22no—
192#390C22×C1112yes—
193#390C22×C1112yes—
194#379—22no—
195#340C22×C1114yescomplemented
196#336C22×C1112yescomplemented
197#336C22×C1112yescomplemented
198C22×C11—22no—
199C22×C11—24no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—48no—
203C22×C11—44no—
204C22×C11—44no—
205C22×C11—44no—
206C22×C11—44no—
207C22×C11—816no—
208C22×C11—84no—
209C22×C11—84no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—84no—
213C22×C11C2×#12011yescharacteristic
214C22×C11#52511yescharacteristic
215C22×C11#53511yescharacteristic
216C22×C11#57614yes—
217C4×C11—22no—
218C4×C11—42no—
219C4×C11—42no—
220C4×C11—44no—
221C4×C11—82no—
222C4×C11#54614yes—
223C25—21no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—21no—
227C22×D4—22no—
228C22×D4—24no—
229C22×D4—42no—
230C22×D4C23×C1112yes—
231C22×D4C23×C1112yes—
232C23×C4—22no—
233C23×C4C23×C1111yescharacteristic
234C2×D8—28no—
235C2×D8—28no—
236C2×D8—44no—
237C22×C8C23×C1114yes—
238#127—24no—
239#125—24no—
240#123—216no—
241#121—216no—
242#121—24no—
243#121D4×C1118yes—
244C4×D4—24no—
245C4×D4—24no—
246#117—24no—
247#117—42no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4D4×C1112yes—
250C2×C4⋊C4C23×C1112yes—
251C2×C4⋊C4C23×C1112yes—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—24no—
256C2×C22⋊C4—24no—
257C2×C22⋊C4D4×C1112yes—
258C2×C42—21no—
259C2×C42C23×C1111yescharacteristic
260C2×C42C23×C1111yescharacteristic
261#102—28no—
262#102—44no—
263C22⋊C8—24no—
264C2×C11—42no—
265C2×C11—84no—
266C2×C11—84no—
267C2×C11#240411yescharacteristic
268C2×C11#300812yes—
269C2×C11#312212yes—
270C2×C11#322012yes—
271C24—24no—
272C24—22no—
273C24—22no—
274C24—42no—
275C24—42no—
276C24—84no—
277C24C2×D4×C1111yescharacteristic
278C2×D4—24no—
279C2×D4—28no—
280C2×D4—28no—
281C2×D4—24no—
282C2×D4—22no—
283C2×D4—24no—
284C2×D4—22no—
285C2×D4—24no—
286C2×D4—24no—
287C2×D4—416no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—84no—
291C2×D4—84no—
292C2×D4C2×D4×C1114yes—
293C2×D4C11×#4114yes—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—28no—
298C22×C4—22no—
299C22×C4—84no—
300C22×C4C2×D4×C1112yes—
301C22×C4C2×D4×C1112yes—
302C22×C4C2×D4×C1111yescharacteristic
303C22×C4C2×D4×C1114yes—
304C22×C4C24×C1111yescharacteristic
305D8—416no—
306C2×C8—24no—
307C2×C8—24no—
308C2×C8—24no—
309C4⋊C4—28no—
310C4⋊C4—24no—
311C4⋊C4—22no—
312C4⋊C4—24no—
313C4⋊C4C2×D4×C1114yes—
314C22⋊C4—28no—
315C22⋊C4—24no—
316C22⋊C4—28no—
317C22⋊C4—42no—
318C22⋊C4—84no—
319C22⋊C4—84no—
320C42—22no—
321C42—22no—
322C42—42no—
323C11#2393911yescharacteristic, direct product factor, Sylow
324C23—21no—
325C23—21no—
326C23—24no—
327C23—24no—
328C23—24no—
329C23—48no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—44no—
335C23—44no—
336C23—44no—
337C23—44no—
338C23—88no—
339C23—88no—
340C23—88no—
341C23C11×#12012yes—
342C23C22×D4×C1111yescharacteristic
343D4—28no—
344D4—28no—
345D4—48no—
346D4—44no—
347D4—44no—
348D4—88no—
349D4—88no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—28no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—88no—
362C2×C4C11×#12012yes—
363C2×C4C22×D4×C1112yes—
364C2×C4C2×C11×#4112yes—
365C2×C4C11×H(5,𝔽2)12yes—
366C8—44no—
367C22—22no—
368C22—24no—
369C22—42no—
370C22—42no—
371C22—44no—
372C22—44no—
373C22—44no—
374C22—44no—
375C22—48no—
376C22—816no—
377C22—82no—
378C22—82no—
379C22—84no—
380C22—84no—
381C22—84no—
382C22C2×C11×#12011yescharacteristic
383C22C11×#52511yescharacteristic
384C22C11×#53511yescharacteristic
385C22C11×#57614yes—
386C4—22no—
387C4—42no—
388C4—42no—
389C4—44no—
390C4—82no—
391C4C11×#54614yes—
392C2—42no—
393C2—84no—
394C2—84no—
395C2C11×#240411yescharacteristic
396C2C11×#300812yes—
397C2C11×#312212yes—
398C2C11×#322012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#540C2semidirect
2. C2×C11×#447C2semidirect
3. C11×#2309C2semidirect
4. C11×#2025C2semidirect
5. C11×#2011C2semidirect
6. C11×#1879C2semidirect
7. C11×#1875C2semidirect
8. C11×#1818C2semidirect
12. C2×C11×#127C22semidirect
13. C2×C11×#125C22semidirect
17. C2×C4×D4×C11C22semidirect
22. C2×C11×#102C22semidirect
28. C11×#340C22semidirect
29. C11×#336C22semidirect
30. C11×#336C22semidirect
72. #23939C11direct (N × H)
125. C2×#540C2×C11semidirect
126. C2×#447C2×C11semidirect
127. #2309C2×C11semidirect
128. #2025C2×C11semidirect
129. #2011C2×C11semidirect
130. #1879C2×C11semidirect
131. #1875C2×C11semidirect
132. #1818C2×C11semidirect
179. C2×#127C22×C11semidirect
180. C2×#125C22×C11semidirect
184. C2×C4×D4C22×C11semidirect
189. C2×#102C22×C11semidirect
195. #340C22×C11semidirect
196. #336C22×C11semidirect
197. #336C22×C11semidirect
323. C11#23939direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5402
C2×C11×#4472
C11×#23092
C11×#20252
C11×#20112
C11×#18792
C11×#18752
C11×#18182
#2393911