Finite Group Databasebeta

← C11×#24783 #14601976

Subgroups — C11×#24783 #14601976

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#470C211yesmaximal, characteristic, complemented
2C2×C11×#467C211yesmaximal, characteristic, complemented
3C2×C11×#435C211yesmaximal, characteristic
4C22×C11×#106C211yesmaximal, characteristic, complemented
5C11×#2417C212yesmaximal
6C11×#2066C212yesmaximal, complemented
7C11×#2035C212yesmaximal, complemented
8C11×#1971C211yesmaximal, characteristic, complemented
9C11×#1944C211yesmaximal, characteristic, complemented
10C11×#1872C212yesmaximal, complemented
11C11×#1809C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C11×C22⋊Q8C2212yes—
17C2×C4×D4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C11×#470—24no—
20C11×#467—24no—
21C11×#435—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106—24no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2212yes—
26C2×C11×#106C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#398—22no—
35C11×#396—22no—
36C11×#391C2212yes—
37C11×#389C2212yes—
38C11×#386—22no—
39C11×#380—22no—
40C11×#380C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C22×Q8×C11C2312yes—
44C22×D4×C11D411yescharacteristic
45C23×C4×C11—22no—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C2×C11×Q16—22no—
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C22×C8×C11—22no—
55C22×C8×C11—22no—
56C22×C8×C11D414yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—42no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—42no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C11×#107—22no—
84C11×#106—22no—
85C11×#106—24no—
86C11×#106D414yescomplemented
87C11×C4⋊C8—22no—
88C11×#103—24no—
89C11×#103—24no—
90C11×#103—42no—
91C11×C22⋊C8—22no—
92C11×C22⋊C8—22no—
93C11×#97—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—22no—
98#24783C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11C2×D411yescharacteristic
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—24no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—44no—
124C22×C4×C11—44no—
125C22×C4×C11—82no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11#4112yes—
132C22×C4×C11C2411yescharacteristic
133C11×Q16—44no—
134C11×M16—44no—
135C2×C8×C11—28no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D412yes—
146C2×C8×C11C2×D412yes—
147C2×C8×C11#4112yes—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—44no—
155C11×C4⋊C4—44no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—82no—
158C11×C4⋊C4C2×D414yes—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—82no—
164C42×C11—21no—
165C42×C11—21no—
166C2×#470C2×C1111yescharacteristic, complemented
167C2×#467C2×C1111yescharacteristic, complemented
168C2×#435C2×C1111yescharacteristic
169C22×#106C2×C1111yescharacteristic, complemented
170#2417C2×C1112yes—
171#2066C2×C1112yescomplemented
172#2035C2×C1112yescomplemented
173#1971C2×C1111yescharacteristic, complemented
174#1944C2×C1111yescharacteristic, complemented
175#1872C2×C1112yescomplemented
176#1809C2×C1111yescharacteristic, complemented
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—22no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11#12112yes—
186C23×C11#13714yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—42no—
191Q8×C11—42no—
192D4×C11—44no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—24no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—88no—
223C2×C4×C11#12112yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C112−1+411yescharacteristic
230C8×C11—22no—
231C8×C11—41no—
232C8×C11—41no—
233C8×C11#12114yes—
234C22×Q16C22×C1111yescharacteristic
235C22×M16C22×C1111yescharacteristic
236C23×C8C22×C1111yescharacteristic
237C2×C22⋊Q8C22×C1112yes—
238C2×C22⋊Q8C22×C1112yes—
239C2×C4×D4C22×C1111yescharacteristic
240C22×C4⋊C4C22×C1112yes—
241#470—24no—
242#467—24no—
243#435—24no—
244C2×#107C22×C1111yescharacteristic
245C2×#106—24no—
246C2×#106C22×C1111yescharacteristic
247C2×#106C22×C1112yes—
248C2×#106C22×C1111yescharacteristic
249C2×C4⋊C8C22×C1111yescharacteristic
250C2×#103C22×C1112yes—
251C2×#103C22×C1112yes—
252C2×#103C22×C1112yes—
253C2×C22⋊C8C22×C1111yescharacteristic
254C2×C22⋊C8C22×C1111yescharacteristic
255C2×#97C22×C1111yescharacteristic
256#398—22no—
257#396—22no—
258#391C22×C1112yes—
259#389C22×C1112yes—
260#386—22no—
261#380—22no—
262#380C22×C1112yes—
263#340C22×C1112yes—
264#340C22×C1112yes—
265C22×C11—24no—
266C22×C11—22no—
267C22×C11—24no—
268C22×C11—22no—
269C22×C11—42no—
270C22×C11—41no—
271C22×C11—42no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11#47014yescomplemented
275C22×C11C2×#12111yescharacteristic
276C22×C11D4211yescharacteristic
277C22×C11#54711yescharacteristic
278C22×C11C2×#13712yes—
279C22×C11#57712yes—
280C4×C11—22no—
281C4×C11—41no—
282C4×C11—44no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11—82no—
286C4×C11—82no—
287C4×C11—82no—
288C4×C11C2×#12111yescharacteristic
289C4×C11#53711yescharacteristic
290C4×C11#54811yescharacteristic
291C4×C11#55311yescharacteristic
292C22×Q8C23×C1112yes—
293C22×D4D4×C1111yescharacteristic
294C23×C4—22no—
295C23×C4C23×C1111yescharacteristic
296C23×C4C23×C1111yescharacteristic
297C2×Q16—22no—
298C2×Q16—22no—
299C2×Q16—22no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8D4×C1114yes—
306C22×C8C23×C1111yescharacteristic
307C22×C8C23×C1111yescharacteristic
308C22×C8C23×C1111yescharacteristic
309C22×C8C23×C1111yescharacteristic
310C22⋊Q8—24no—
311C22⋊Q8—24no—
312C22⋊Q8—24no—
313C22⋊Q8—42no—
314C4×D4—22no—
315C4×D4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4D4×C1111yescharacteristic
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1112yes—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4D4×C1111yescharacteristic
330C2×C22⋊C4D4×C1111yescharacteristic
331C2×C42C23×C1111yescharacteristic
332#107—22no—
333#106—22no—
334#106—24no—
335#106D4×C1114yescomplemented
336C4⋊C8—22no—
337#103—24no—
338#103—24no—
339#103—42no—
340C22⋊C8—22no—
341C22⋊C8—22no—
342#97—22no—
343#95—22no—
344#95—22no—
345#95—22no—
346#95—22no—
347C2×C11—24no—
348C2×C11—81no—
349C2×C11#241611yescharacteristic
350C2×C11C2×#47011yescharacteristic
351C2×C11#306011yescharacteristic
352C2×C11#326612yes—
353C2×C11#334412yes—
354C24C2×D4×C1111yescharacteristic
355C24C2×D4×C1111yescharacteristic
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×D4—22no—
363C2×D4—24no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—44no—
379C22×C4—44no—
380C22×C4—82no—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1112yes—
386C22×C4C11×#4112yes—
387C22×C4C24×C1111yescharacteristic
388Q16—44no—
389M16—44no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—28no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×D4×C1112yes—
400C2×C8C2×D4×C1112yes—
401C2×C8C2×D4×C1112yes—
402C2×C8C11×#4112yes—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—44no—
410C4⋊C4—44no—
411C4⋊C4—44no—
412C4⋊C4—82no—
413C4⋊C4C2×D4×C1114yes—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C22⋊C4—82no—
419C42—21no—
420C42—21no—
421C11#2478311yescharacteristic, direct product factor, Sylow
422C23—21no—
423C23—21no—
424C23—22no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—22no—
429C23—22no—
430C23C11×#12112yes—
431C23C11×#13714yes—
432C23C22×D4×C1111yescharacteristic
433Q8—42no—
434Q8—42no—
435Q8—42no—
436Q8—42no—
437D4—44no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—88no—
468C2×C4C11×#12112yes—
469C2×C4C22×D4×C1111yescharacteristic
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C2×C11×#4111yescharacteristic
472C2×C4C2×C11×#4111yescharacteristic
473C2×C4C11×H(5,𝔽2)11yescharacteristic
474C2×C4C11×2−1+411yescharacteristic
475C8—22no—
476C8—41no—
477C8—41no—
478C8C11×#12114yes—
479C22—22no—
480C22—24no—
481C22—22no—
482C22—24no—
483C22—41no—
484C22—42no—
485C22—41no—
486C22—41no—
487C22—42no—
488C22C11×#47014yescomplemented
489C22C2×C11×#12111yescharacteristic
490C22D42×C1111yescharacteristic
491C22C11×#54711yescharacteristic
492C22C2×C11×#13712yes—
493C22C11×#57712yes—
494C4—22no—
495C4—41no—
496C4—44no—
497C4—41no—
498C4—41no—
499C4—82no—
500C4—82no—
501C4—82no—
502C4C2×C11×#12111yescharacteristic
503C4C11×#53711yescharacteristic
504C4C11×#54811yescharacteristic
505C4C11×#55311yescharacteristic
506C2—24no—
507C2—81no—
508C2C11×#241611yescharacteristic
509C2C2×C11×#47011yescharacteristic
510C2C11×#306011yescharacteristic
511C2C11×#326612yes—
512C2C11×#334412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#470C2semidirect
2. C2×C11×#467C2semidirect
4. C22×C11×#106C2semidirect
6. C11×#2066C2semidirect
7. C11×#2035C2semidirect
8. C11×#1971C2semidirect
9. C11×#1944C2semidirect
10. C11×#1872C2semidirect
11. C11×#1809C2semidirect
86. C11×#106D4semidirect
98. #24783C11direct (N × H)
166. C2×#470C2×C11semidirect
167. C2×#467C2×C11semidirect
169. C22×#106C2×C11semidirect
171. #2066C2×C11semidirect
172. #2035C2×C11semidirect
173. #1971C2×C11semidirect
174. #1944C2×C11semidirect
175. #1872C2×C11semidirect
176. #1809C2×C11semidirect
274. C22×C11#470semidirect
335. #106D4×C11semidirect
421. C11#24783direct (N × H)
488. C22C11×#470semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4702
C2×C11×#4672
C2×C11×#4352
C22×C11×#1062
C11×#24172
C11×#20662
C11×#20352
C11×#19712
C11×#19442
C11×#18722
C11×#18092
#2478311