Finite Group Databasebeta

← C11×#24342 #14601535

Subgroups — C11×#24342 #14601535

Order 2816.

1248 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic, complemented
3C2×C11×#440C211yesmaximal, characteristic
4C11×#2581C211yesmaximal, characteristic, complemented
5C11×#2057C212yesmaximal, complemented
6C11×#2024C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1985C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal
10C11×#1862C212yesmaximal
11C11×#1804C211yesmaximal, characteristic
12C23×Q8×C11—21no—
13C22×C11×SD16C2211yescharacteristic
14D4×Q8×C11—24no—
15D4×Q8×C11—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8—22no—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#477—24no—
25C11×#440—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#400—21no—
35C11×#395—21no—
36C11×#391C2212yes—
37C11×#389C2212yes—
38C11×#387—22no—
39C11×#382C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—28no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—48no—
49C22×Q8×C11D411yescharacteristic
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—22no—
53C23×C4×C11—21no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C2×C11×SD16Q814yescomplemented
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—24no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D414yes—
64C11×C22⋊Q8—28no—
65C11×C22⋊Q8—216no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×D4×C11—24no—
71C4×D4×C11—24no—
72C4×D4×C11—22no—
73C4×D4×C11D414yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11C2312yes—
88C2×C42×C11C2311yescharacteristic
89C11×#107—22no—
90C11×#107—24no—
91C11×C4⋊C8—22no—
92C11×#103—22no—
93C11×#103—24no—
94C11×#102—22no—
95C11×#102—24no—
96C11×#97—22no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—22no—
100C11×#95—22no—
101C11×#95—22no—
102#24342C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C2×Q8×C11—28no—
105C2×Q8×C11—22no—
106C2×Q8×C11—24no—
107C2×Q8×C11—24no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—44no—
114C2×Q8×C11—44no—
115C2×Q8×C11—432no—
116C2×Q8×C11—44no—
117C2×Q8×C11C2×Q812yescomplemented
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11C2×D412yes—
122C2×D4×C11C2×Q812yes—
123C2×D4×C11#4112yes—
124C22×C4×C11—28no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—44no—
132C22×C4×C11—44no—
133C22×C4×C11—44no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2411yescharacteristic
139C11×SD16—28no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11C2×Q812yescomplemented
149C11×C4⋊C4—28no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—44no—
161C11×C4⋊C4C2×D414yes—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—24no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—42no—
168C42×C11C2×D412yes—
169C42×C11C2×D412yes—
170C2×D4×Q8C2×C1111yescharacteristic
171C2×#477C2×C1111yescharacteristic, complemented
172C2×#440C2×C1111yescharacteristic
173#2581C2×C1111yescharacteristic, complemented
174#2057C2×C1112yescomplemented
175#2024C2×C1112yescomplemented
176#1993C2×C1111yescharacteristic, complemented
177#1985C2×C1111yescharacteristic, complemented
178#1877C2×C1112yes—
179#1862C2×C1112yes—
180#1804C2×C1111yescharacteristic
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11C22×D411yescharacteristic
187Q8×C11—28no—
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—48no—
191Q8×C11—416no—
192Q8×C11—41no—
193Q8×C11—41no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11C22⋊Q814yes—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—48no—
208C2×C4×C11—416no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11#12012yes—
220C2×C4×C11#12012yes—
221C2×C4×C11AGL(1,ℤ/8)14yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×Q811yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C8×C11—22no—
229C8×C11—41no—
230C8×C11—42no—
231C23×Q8—21no—
232C22×SD16C22×C1111yescharacteristic
233D4×Q8—24no—
234D4×Q8—24no—
235C2×C4⋊Q8C22×C1112yes—
236C2×C4⋊Q8C22×C1111yescharacteristic
237C2×C22⋊Q8—22no—
238C2×C22⋊Q8—21no—
239C2×C4×Q8C22×C1111yescharacteristic
240C2×C4×Q8C22×C1111yescharacteristic
241C2×C4×D4C22×C1112yes—
242C2×C4×D4C22×C1111yescharacteristic
243#477—24no—
244#440—24no—
245C2×#107C22×C1112yes—
246C2×#107C22×C1111yescharacteristic
247C2×C4⋊C8C22×C1111yescharacteristic
248C2×#103C22×C1112yes—
249C2×#103C22×C1111yescharacteristic
250C2×#102C22×C1112yes—
251C2×#102C22×C1111yescharacteristic
252C2×#97C22×C1111yescharacteristic
253#400—21no—
254#395—21no—
255#391C22×C1112yes—
256#389C22×C1112yes—
257#387—22no—
258#382C22×C1111yescharacteristic
259#340C22×C1112yes—
260#340C22×C1112yes—
261#340C22×C1112yes—
262#336C22×C1112yes—
263#336C22×C1112yes—
264C22×C11—24no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11C2×#12011yescharacteristic
270C22×C11#54811yescharacteristic
271C22×C11D4×Q811yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)12yes—
273C22×C11#57812yes—
274C4×C11—22no—
275C4×C11—24no—
276C4×C11—22no—
277C4×C11—42no—
278C4×C11—44no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11—81no—
283C4×C11C2×C22⋊Q811yescharacteristic
284C4×C11#53611yescharacteristic
285C4×C11#54811yescharacteristic
286C4×C11D4×Q811yescharacteristic
287C22×Q8—28no—
288C22×Q8—21no—
289C22×Q8—22no—
290C22×Q8—48no—
291C22×Q8D4×C1111yescharacteristic
292C22×Q8C23×C1111yescharacteristic
293C22×D4C23×C1111yescharacteristic
294C23×C4—22no—
295C23×C4—21no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×SD16Q8×C1114yescomplemented
299C22×C8C23×C1111yescharacteristic
300C22×C8C23×C1112yes—
301C22×C8C23×C1111yescharacteristic
302C4⋊Q8—24no—
303C4⋊Q8—24no—
304C4⋊Q8—22no—
305C4⋊Q8D4×C1114yes—
306C22⋊Q8—28no—
307C22⋊Q8—216no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—22no—
312C4×D4—24no—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4D4×C1114yes—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4D4×C1112yes—
321C2×C4⋊C4D4×C1111yescharacteristic
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1111yescharacteristic
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C42—21no—
329C2×C42C23×C1112yes—
330C2×C42C23×C1111yescharacteristic
331#107—22no—
332#107—24no—
333C4⋊C8—22no—
334#103—22no—
335#103—24no—
336#102—22no—
337#102—24no—
338#97—22no—
339#95—21no—
340#95—21no—
341#95—22no—
342#95—22no—
343#95—22no—
344C2×C11—44no—
345C2×C11#240911yescharacteristic
346C2×C11#300311yescharacteristic
347C2×C11#301111yescharacteristic
348C2×C11#336712yes—
349C2×C11#338612yes—
350C24—21no—
351C2×Q8—28no—
352C2×Q8—22no—
353C2×Q8—24no—
354C2×Q8—24no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—44no—
361C2×Q8—44no—
362C2×Q8—432no—
363C2×Q8—44no—
364C2×Q8C2×Q8×C1112yescomplemented
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C2×D4×C1112yes—
369C2×D4C2×Q8×C1112yes—
370C2×D4C11×#4112yes—
371C22×C4—28no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—44no—
379C22×C4—44no—
380C22×C4—44no—
381C22×C4C2×D4×C1112yes—
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×D4×C1112yes—
385C22×C4C24×C1111yescharacteristic
386SD16—28no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—22no—
395C2×C8C2×Q8×C1112yescomplemented
396C4⋊C4—28no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—42no—
407C4⋊C4—44no—
408C4⋊C4C2×D4×C1114yes—
409C4⋊C4C2×D4×C1112yes—
410C22⋊C4—28no—
411C22⋊C4—24no—
412C42—22no—
413C42—22no—
414C42—42no—
415C42C2×D4×C1112yes—
416C42C2×D4×C1112yes—
417C11#2434211yescharacteristic, direct product factor, Sylow
418C23—22no—
419C23—22no—
420C23—22no—
421C23—42no—
422C23—42no—
423C23C22×D4×C1111yescharacteristic
424Q8—28no—
425Q8—22no—
426Q8—22no—
427Q8—48no—
428Q8—416no—
429Q8—41no—
430Q8—41no—
431D4—22no—
432D4—22no—
433D4—22no—
434D4C11×C22⋊Q814yes—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—48no—
445C2×C4—416no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4C11×#12012yes—
457C2×C4C11×#12012yes—
458C2×C4C11×AGL(1,ℤ/8)14yes—
459C2×C4C22×D4×C1111yescharacteristic
460C2×C4C22×D4×C1111yescharacteristic
461C2×C4C22×Q8×C1111yescharacteristic
462C2×C4C2×C11×#4111yescharacteristic
463C2×C4C11×2−1+411yescharacteristic
464C2×C4C11×2−1+411yescharacteristic
465C8—22no—
466C8—41no—
467C8—42no—
468C22—24no—
469C22—42no—
470C22—42no—
471C22—44no—
472C22—44no—
473C22C2×C11×#12011yescharacteristic
474C22C11×#54811yescharacteristic
475C22D4×Q8×C1111yescharacteristic
476C22C2×C11×AGL(1,ℤ/8)12yes—
477C22C11×#57812yes—
478C4—22no—
479C4—24no—
480C4—22no—
481C4—42no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—81no—
486C4—82no—
487C4C2×C11×C22⋊Q811yescharacteristic
488C4C11×#53611yescharacteristic
489C4C11×#54811yescharacteristic
490C4D4×Q8×C1111yescharacteristic
491C2—44no—
492C2C11×#240911yescharacteristic
493C2C11×#300311yescharacteristic
494C2C11×#301111yescharacteristic
495C2C11×#336712yes—
496C2C11×#338612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#477C2semidirect
4. C11×#2581C2semidirect
5. C11×#2057C2semidirect
6. C11×#2024C2semidirect
7. C11×#1993C2semidirect
8. C11×#1985C2semidirect
56. C2×C11×SD16Q8semidirect
102. #24342C11direct (N × H)
117. C2×Q8×C11C2×Q8semidirect
148. C2×C8×C11C2×Q8semidirect
171. C2×#477C2×C11semidirect
173. #2581C2×C11semidirect
174. #2057C2×C11semidirect
175. #2024C2×C11semidirect
176. #1993C2×C11semidirect
177. #1985C2×C11semidirect
298. C2×SD16Q8×C11semidirect
364. C2×Q8C2×Q8×C11semidirect
395. C2×C8C2×Q8×C11semidirect
417. C11#24342direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4772
C2×C11×#4402
C11×#25812
C11×#20572
C11×#20242
C11×#19932
C11×#19852
C11×#18772
C11×#18622
C11×#18042
#2434211