Finite Group Databasebeta

← C11×#23941 #14601134

Subgroups — C11×#23941 #14601134

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#540C211yesmaximal, characteristic, complemented
2C2×C11×#449C212yesmaximal, complemented
3C11×#2311C211yesmaximal, characteristic, complemented
4C11×#2026C211yesmaximal, characteristic, complemented
5C11×#2025C211yesmaximal, characteristic, complemented
6C11×#2014C211yesmaximal, characteristic, complemented
7C11×#2011C211yesmaximal, characteristic, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1874C212yesmaximal, complemented
11C11×#1818C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C22×C11×D8C2212yes—
15C11×#540—28no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×#121—22no—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2212yes—
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#449—28no—
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C11×#391C2211yescharacteristic
31C11×#391C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#390C2211yescharacteristic
34C11×#386—22no—
35C11×#380—22no—
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#336C2212yes—
39C11×#336C2211yescharacteristic
40C11×#336C2211yescharacteristic
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11C2312yes—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—22no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C2×C11×SD16—24no—
56C2×C11×SD16—24no—
57C2×C11×SD16—42no—
58C2×C11×D8—24no—
59C2×C11×D8—24no—
60C2×C11×D8—42no—
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×#127—24no—
64C11×#125—24no—
65C11×#123—216no—
66C11×#121—216no—
67C11×#121—24no—
68C11×#121D418yes—
69C4×D4×C11—24no—
70C4×D4×C11—24no—
71C11×#117—24no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—42no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4D412yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×#103—24no—
87C11×#102—24no—
88C11×#102—42no—
89C11×#102—42no—
90C11×C22⋊C8—24no—
91C11×#95—22no—
92C11×#95—22no—
93#23941C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11—22no—
96C24×C11C2×D411yescharacteristic
97C11×#41—48no—
98C11×#41—48no—
99C2×Q8×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11#4112yes—
103C2×D4×C11—24no—
104C2×D4×C11—28no—
105C2×D4×C11—28no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—82no—
117C2×D4×C11—82no—
118C2×D4×C11—82no—
119C2×D4×C11—82no—
120C2×D4×C11C2×D414yes—
121C2×D4×C11#4112yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—28no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—82no—
135C22×C4×C11—82no—
136C22×C4×C11—82no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2411yescharacteristic
142C11×SD16—48no—
143C11×D8—48no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4C2×D414yes—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—82no—
161C11×C22⋊C4—82no—
162C42×C11—22no—
163C42×C11—22no—
164C2×#540C2×C1111yescharacteristic, complemented
165C2×#449C2×C1112yescomplemented
166#2311C2×C1111yescharacteristic, complemented
167#2026C2×C1111yescharacteristic, complemented
168#2025C2×C1111yescharacteristic, complemented
169#2014C2×C1111yescharacteristic, complemented
170#2011C2×C1111yescharacteristic, complemented
171#1879C2×C1112yescomplemented
172#1877C2×C1112yescomplemented
173#1874C2×C1112yescomplemented
174#1818C2×C1111yescharacteristic, complemented
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11#12012yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—24no—
194Q8×C11—42no—
195D4×C11—24no—
196D4×C11—24no—
197D4×C11—24no—
198D4×C11—48no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—88no—
203D4×C11—88no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—48no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—88no—
226C2×C4×C11—84no—
227C2×C4×C11#12012yes—
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11H(5,𝔽2)12yes—
232C8×C11—42no—
233C8×C11—42no—
234C22×#41C22×C1111yescharacteristic
235C22×SD16C22×C1112yes—
236C22×D8C22×C1112yes—
237#540—28no—
238C2×#127C22×C1111yescharacteristic
239C2×#125C22×C1111yescharacteristic
240C2×#123—22no—
241C2×#121—22no—
242C2×#121C22×C1112yes—
243C2×C4×D4C22×C1112yes—
244C2×#117C22×C1111yescharacteristic
245C22×C4⋊C4C22×C1111yescharacteristic
246#449—28no—
247C2×#103C22×C1112yes—
248C2×#102C22×C1112yes—
249C2×#102C22×C1112yes—
250C2×#102C22×C1112yes—
251C2×C22⋊C8C22×C1112yes—
252#391C22×C1111yescharacteristic
253#391C22×C1111yescharacteristic
254#390C22×C1111yescharacteristic
255#390C22×C1111yescharacteristic
256#386—22no—
257#380—22no—
258#340C22×C1112yes—
259#340C22×C1112yes—
260#336C22×C1112yes—
261#336C22×C1111yescharacteristic
262#336C22×C1111yescharacteristic
263C22×C11—22no—
264C22×C11—24no—
265C22×C11—42no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11—44no—
269C22×C11—42no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—81no—
276C22×C11—82no—
277C22×C11—81no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11C2×#12011yescharacteristic
281C22×C11#52511yescharacteristic
282C22×C11#53511yescharacteristic
283C22×C11#57612yes—
284C22×C11#57712yes—
285C4×C11—22no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—44no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11#54612yes—
293C4×C11#54612yes—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—24no—
297C2×#41—42no—
298C22×Q8C23×C1111yescharacteristic
299C22×D4—21no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4C23×C1112yes—
303C22×D4C23×C1111yescharacteristic
304C23×C4—21no—
305C23×C4—22no—
306C23×C4—21no—
307C23×C4C23×C1111yescharacteristic
308C2×SD16—24no—
309C2×SD16—24no—
310C2×SD16—42no—
311C2×D8—24no—
312C2×D8—24no—
313C2×D8—42no—
314C22×C8C23×C1112yes—
315C22×C8C23×C1112yes—
316#127—24no—
317#125—24no—
318#123—216no—
319#121—216no—
320#121—24no—
321#121D4×C1118yes—
322C4×D4—24no—
323C4×D4—24no—
324#117—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4D4×C1112yes—
329C2×C4⋊C4C23×C1111yescharacteristic
330C2×C4⋊C4C23×C1111yescharacteristic
331C2×C4⋊C4C23×C1112yes—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4D4×C1112yes—
337C2×C42C23×C1111yescharacteristic
338C2×C42C23×C1111yescharacteristic
339#103—24no—
340#102—24no—
341#102—42no—
342#102—42no—
343C22⋊C8—24no—
344#95—22no—
345#95—22no—
346C2×C11—42no—
347C2×C11—82no—
348C2×C11—84no—
349C2×C11#240411yescharacteristic
350C2×C11#301212yes—
351C2×C11#311912yes—
352C2×C11#322011yescharacteristic
353C2×C11#322111yescharacteristic
354C24—21no—
355C24—22no—
356C24C2×D4×C1111yescharacteristic
357#41—48no—
358#41—48no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8C11×#4112yes—
363C2×D4—24no—
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—82no—
377C2×D4—82no—
378C2×D4—82no—
379C2×D4—82no—
380C2×D4C2×D4×C1114yes—
381C2×D4C11×#4112yes—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—28no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—82no—
395C22×C4—82no—
396C22×C4—82no—
397C22×C4C2×D4×C1112yes—
398C22×C4C2×D4×C1112yes—
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1114yes—
401C22×C4C24×C1111yescharacteristic
402SD16—48no—
403D8—48no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C4⋊C4—28no—
411C4⋊C4—24no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—42no—
416C4⋊C4C2×D4×C1114yes—
417C22⋊C4—28no—
418C22⋊C4—24no—
419C22⋊C4—28no—
420C22⋊C4—82no—
421C22⋊C4—82no—
422C42—22no—
423C42—22no—
424C11#2394111yescharacteristic, direct product factor, Sylow
425C23—21no—
426C23—21no—
427C23—22no—
428C23—22no—
429C23—24no—
430C23—22no—
431C23—41no—
432C23—42no—
433C23—41no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23C11×#12012yes—
442C23C22×D4×C1111yescharacteristic
443Q8—24no—
444Q8—42no—
445D4—24no—
446D4—24no—
447D4—24no—
448D4—48no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—88no—
453D4—88no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—48no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—88no—
476C2×C4—84no—
477C2×C4C11×#12012yes—
478C2×C4C22×D4×C1112yes—
479C2×C4C2×C11×#4111yescharacteristic
480C2×C4C2×C11×#4111yescharacteristic
481C2×C4C11×H(5,𝔽2)12yes—
482C8—42no—
483C8—42no—
484C22—22no—
485C22—24no—
486C22—41no—
487C22—41no—
488C22—42no—
489C22—42no—
490C22—44no—
491C22—44no—
492C22—44no—
493C22—44no—
494C22—81no—
495C22—82no—
496C22—81no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—82no—
501C22C2×C11×#12011yescharacteristic
502C22C11×#52511yescharacteristic
503C22C11×#53511yescharacteristic
504C22C11×#57612yes—
505C22C11×#57712yes—
506C4—22no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—44no—
511C4—81no—
512C4—81no—
513C4C11×#54612yes—
514C4C11×#54612yes—
515C2—42no—
516C2—82no—
517C2—84no—
518C2C11×#240411yescharacteristic
519C2C11×#301212yes—
520C2C11×#311912yes—
521C2C11×#322011yescharacteristic
522C2C11×#322111yescharacteristic
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×#449C2semidirect
3. C11×#2311C2semidirect
4. C11×#2026C2semidirect
5. C11×#2025C2semidirect
6. C11×#2014C2semidirect
7. C11×#2011C2semidirect
8. C11×#1879C2semidirect
9. C11×#1877C2semidirect
10. C11×#1874C2semidirect
11. C11×#1818C2semidirect
93. #23941C11direct (N × H)
164. C2×#540C2×C11semidirect
165. C2×#449C2×C11semidirect
166. #2311C2×C11semidirect
167. #2026C2×C11semidirect
168. #2025C2×C11semidirect
169. #2014C2×C11semidirect
170. #2011C2×C11semidirect
171. #1879C2×C11semidirect
172. #1877C2×C11semidirect
173. #1874C2×C11semidirect
174. #1818C2×C11semidirect
424. C11#23941direct (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×#4492
C11×#23112
C11×#20262
C11×#20252
C11×#20142
C11×#20112
C11×#18792
C11×#18772
C11×#18742
C11×#18182
#2394111