Finite Group Databasebeta

← C11×#24339 #14601532

Subgroups — C11×#24339 #14601532

Order 2816.

1112 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#554C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic, complemented
3C2×C11×#442C211yesmaximal, characteristic
4C11×#2580C211yesmaximal, characteristic, complemented
5C11×#2059C212yesmaximal, complemented
6C11×#2025C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1985C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal
10C11×#1862C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C11×#554—24no—
14C11×#554—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4—21no—
24C11×#474—24no—
25C11×#442—24no—
26C2×C11×#107C2212yes—
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#399—21no—
35C11×#393—21no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#385—22no—
39C11×#382C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C2×C11×D8—22no—
53C2×C11×D8—22no—
54C2×C11×D8Q814yescomplemented
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D414yes—
60C11×#125—24no—
61C11×#125—24no—
62C11×C22⋊Q8—28no—
63C11×C22⋊Q8—216no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11D414yes—
72C2×C11×C4⋊C4—28no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C11×#107—24no—
91C11×#106—22no—
92C11×C4⋊C8—22no—
93C11×#102—22no—
94C11×#102—24no—
95C11×#102—22no—
96C11×#102—24no—
97C11×#97—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—22no—
101#24339C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—24no—
106C2×Q8×C11—42no—
107C2×Q8×C11—82no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11C2×D412yes—
117C2×D4×C11C2×Q812yes—
118C2×D4×C11C2×Q812yes—
119C2×D4×C11#4112yes—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—28no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—44no—
127C22×C4×C11—42no—
128C22×C4×C11—82no—
129C22×C4×C11—82no—
130C22×C4×C11—82no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C11×D8—28no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11C2×Q812yes—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—82no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D414yes—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—82no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169C2×#554C2×C1111yescharacteristic, complemented
170C2×#474C2×C1111yescharacteristic, complemented
171C2×#442C2×C1111yescharacteristic
172#2580C2×C1111yescharacteristic, complemented
173#2059C2×C1112yescomplemented
174#2025C2×C1112yescomplemented
175#1993C2×C1111yescharacteristic, complemented
176#1985C2×C1111yescharacteristic, complemented
177#1879C2×C1112yes—
178#1862C2×C1112yescomplemented
179#1804C2×C1111yescharacteristic, complemented
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—44no—
192Q8×C11—84no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11C22⋊Q814yes—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—48no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—84no—
221C2×C4×C11—88no—
222C2×C4×C11#12012yes—
223C2×C4×C11#12012yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×Q811yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C2×C4×C112−1+411yescharacteristic
230C8×C11—22no—
231C8×C11—41no—
232C8×C11—42no—
233C22×D8C22×C1111yescharacteristic
234#554—24no—
235#554—24no—
236C2×C4⋊Q8C22×C1111yescharacteristic
237C2×#125C22×C1112yes—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—22no—
240C2×C4×Q8C22×C1111yescharacteristic
241C2×C4×D4C22×C1111yescharacteristic
242C2×C4×D4C22×C1112yes—
243C2×C4×D4C22×C1111yescharacteristic
244C22×C4⋊C4—21no—
245#474—24no—
246#442—24no—
247C2×#107C22×C1112yes—
248C2×#106C22×C1111yescharacteristic
249C2×C4⋊C8C22×C1111yescharacteristic
250C2×#102C22×C1112yes—
251C2×#102C22×C1111yescharacteristic
252C2×#102C22×C1112yes—
253C2×#102C22×C1111yescharacteristic
254C2×#97C22×C1111yescharacteristic
255#399—21no—
256#393—21no—
257#390C22×C1112yes—
258#389C22×C1112yes—
259#385—22no—
260#382C22×C1111yescharacteristic
261#340C22×C1112yes—
262#340C22×C1112yes—
263#340C22×C1112yes—
264#336C22×C1112yes—
265#336C22×C1112yes—
266C22×C11—24no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—44no—
272C22×C11—42no—
273C22×C11—82no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11C2×#12011yescharacteristic
277C22×C11#54811yescharacteristic
278C22×C11D4×Q811yescharacteristic
279C22×C11#57512yes—
280C22×C11#57612yes—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—44no—
287C4×C11—82no—
288C4×C11—81no—
289C4×C11C2×C22⋊Q811yescharacteristic
290C4×C11#53611yescharacteristic
291C4×C11#54811yescharacteristic
292C4×C11D4×Q811yescharacteristic
293C22×Q8—21no—
294C22×Q8D4×C1111yescharacteristic
295C22×D4C23×C1111yescharacteristic
296C22×D4C23×C1111yescharacteristic
297C23×C4—21no—
298C23×C4—22no—
299C23×C4—21no—
300C2×D8—22no—
301C2×D8—22no—
302C2×D8Q8×C1114yescomplemented
303C22×C8C23×C1111yescharacteristic
304C22×C8C23×C1112yes—
305C22×C8C23×C1111yescharacteristic
306C4⋊Q8—22no—
307C4⋊Q8D4×C1114yes—
308#125—24no—
309#125—24no—
310C22⋊Q8—28no—
311C22⋊Q8—216no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4D4×C1114yes—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4D4×C1111yescharacteristic
326C2×C4⋊C4D4×C1112yes—
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C4⋊C4C23×C1112yes—
329C2×C4⋊C4C23×C1111yescharacteristic
330C2×C4⋊C4C23×C1112yes—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C42C23×C1112yes—
337C2×C42C23×C1111yescharacteristic
338#107—24no—
339#106—22no—
340C4⋊C8—22no—
341#102—22no—
342#102—24no—
343#102—22no—
344#102—24no—
345#97—22no—
346#95—21no—
347#95—21no—
348#95—22no—
349C2×C11—44no—
350C2×C11—82no—
351C2×C11#240911yescharacteristic
352C2×C11#300511yescharacteristic
353C2×C11#300811yescharacteristic
354C2×C11#337012yes—
355C2×C11#338912yes—
356C24—21no—
357C24—21no—
358C2×Q8—22no—
359C2×Q8—24no—
360C2×Q8—42no—
361C2×Q8—82no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4C2×D4×C1112yes—
371C2×D4C2×Q8×C1112yes—
372C2×D4C2×Q8×C1112yes—
373C2×D4C11×#4112yes—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—28no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—44no—
381C22×C4—42no—
382C22×C4—82no—
383C22×C4—82no—
384C22×C4—82no—
385C22×C4C2×D4×C1112yes—
386C22×C4C2×D4×C1112yes—
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C24×C1111yescharacteristic
390D8—28no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—22no—
399C2×C8C2×Q8×C1112yes—
400C4⋊C4—28no—
401C4⋊C4—28no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—82no—
412C4⋊C4C2×D4×C1112yes—
413C4⋊C4C2×D4×C1114yes—
414C22⋊C4—28no—
415C22⋊C4—24no—
416C22⋊C4—44no—
417C22⋊C4—42no—
418C22⋊C4—82no—
419C42—22no—
420C42—22no—
421C42C2×D4×C1112yes—
422C42C2×D4×C1112yes—
423C11#2433911yescharacteristic, direct product factor, Sylow
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23C22×D4×C1111yescharacteristic
435Q8—44no—
436Q8—84no—
437D4—22no—
438D4—22no—
439D4—22no—
440D4—22no—
441D4—22no—
442D4—41no—
443D4—41no—
444D4C11×C22⋊Q814yes—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—48no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—84no—
465C2×C4—88no—
466C2×C4C11×#12012yes—
467C2×C4C11×#12012yes—
468C2×C4C22×D4×C1111yescharacteristic
469C2×C4C22×D4×C1111yescharacteristic
470C2×C4C22×Q8×C1111yescharacteristic
471C2×C4C2×C11×#4111yescharacteristic
472C2×C4C11×2−1+411yescharacteristic
473C2×C4C11×2−1+411yescharacteristic
474C8—22no—
475C8—41no—
476C8—42no—
477C22—24no—
478C22—42no—
479C22—42no—
480C22—44no—
481C22—44no—
482C22—42no—
483C22—44no—
484C22—81no—
485C22—81no—
486C22—82no—
487C22C2×C11×#12011yescharacteristic
488C22C11×#54811yescharacteristic
489C22D4×Q8×C1111yescharacteristic
490C22C11×#57512yes—
491C22C11×#57612yes—
492C4—22no—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—44no—
498C4—81no—
499C4—82no—
500C4C2×C11×C22⋊Q811yescharacteristic
501C4C11×#53611yescharacteristic
502C4C11×#54811yescharacteristic
503C4D4×Q8×C1111yescharacteristic
504C2—44no—
505C2—82no—
506C2C11×#240911yescharacteristic
507C2C11×#300511yescharacteristic
508C2C11×#300811yescharacteristic
509C2C11×#337012yes—
510C2C11×#338912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
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
1. C2×C11×#554C2semidirect
2. C2×C11×#474C2semidirect
4. C11×#2580C2semidirect
5. C11×#2059C2semidirect
6. C11×#2025C2semidirect
7. C11×#1993C2semidirect
8. C11×#1985C2semidirect
10. C11×#1862C2semidirect
11. C11×#1804C2semidirect
54. C2×C11×D8Q8semidirect
101. #24339C11direct (N × H)
169. C2×#554C2×C11semidirect
170. C2×#474C2×C11semidirect
172. #2580C2×C11semidirect
173. #2059C2×C11semidirect
174. #2025C2×C11semidirect
175. #1993C2×C11semidirect
176. #1985C2×C11semidirect
178. #1862C2×C11semidirect
179. #1804C2×C11semidirect
302. C2×D8Q8×C11semidirect
423. C11#24339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C11×#4742
C2×C11×#4422
C11×#25802
C11×#20592
C11×#20252
C11×#19932
C11×#19852
C11×#18792
C11×#18622
C11×#18042
#2433911