Finite Group Databasebeta

← C11×#24727 #14601920

Subgroups — C11×#24727 #14601920

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C212yesmaximal
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic
4C11×#2547C211yesmaximal, characteristic, complemented
5D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#2068C212yesmaximal, complemented
7C11×#2042C212yesmaximal, complemented
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1877C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C22×C11×D8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4—21no—
20C11×#463—28no—
21C11×#461—24no—
22C4×C11×D8—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C4×C8×C11C2211yescharacteristic
33C11×#397—22no—
34C11×#391C2212yes—
35C11×#389C2212yes—
36C11×#385—22no—
37C11×#384C2211yescharacteristic
38C11×#380—21no—
39C11×#380—21no—
40C11×#380—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2312yes—
45C22×D4×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C2×C11×SD16—24no—
51C2×C11×SD16—24no—
52C2×C11×SD16—24no—
53C2×C11×D8—22no—
54C2×C11×D8—22no—
55C2×C11×D8D414yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×#124—24no—
62C11×#124—42no—
63C4×D4×C11—24no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—42no—
68C4×D4×C11D414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87C11×#107—22no—
88C11×C4⋊C8—24no—
89C11×C4⋊C8—22no—
90C11×#103—24no—
91C11×#103—24no—
92C11×#103—42no—
93C11×#102—22no—
94C11×#102—24no—
95C11×#102—22no—
96C4×C8×C11—22no—
97C11×#95—22no—
98C11×#95—22no—
99C11×#95—22no—
100C11×#95D412yes—
101#24727C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
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×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11C2×D412yes—
119C2×D4×C11C2×D412yes—
120C2×D4×C11C2×D412yes—
121C2×D4×C11#4112yes—
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—44no—
128C22×C4×C11—44no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—82no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C11×SD16—48no—
141C11×D8—28no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11C2×D412yes—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—81no—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—44no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—42no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D412yes—
172C42×C11#4112yes—
173C2×#463C2×C1112yes—
174C2×#461C2×C1111yescharacteristic, complemented
175C2×C4×D8C2×C1111yescharacteristic
176#2547C2×C1111yescharacteristic, complemented
177D4×C4⋊C4C2×C1111yescharacteristic, complemented
178#2068C2×C1112yescomplemented
179#2042C2×C1112yescomplemented
180#1956C2×C1111yescharacteristic, complemented
181#1939C2×C1111yescharacteristic, complemented
182#1877C2×C1112yescomplemented
183#1802C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C22×D411yescharacteristic
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—42no—
202Q8×C11—42no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—22no—
207D4×C11—22no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11#12114yes—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—48no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—88no—
233C2×C4×C11—84no—
234C2×C4×C11#12112yes—
235C2×C4×C11#12112yes—
236C2×C4×C11#13512yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C8×C11—22no—
245C8×C11—42no—
246C8×C11—41no—
247C22×SD16C22×C1112yes—
248C22×D8C22×C1111yescharacteristic
249C2×C4⋊Q8C22×C1111yescharacteristic
250C2×#124C22×C1112yes—
251C2×C4×D4C22×C1111yescharacteristic
252C2×C4×D4C22×C1112yes—
253C2×C4×D4C22×C1111yescharacteristic
254C22×C4⋊C4—21no—
255#463—28no—
256#461—24no—
257C4×D8—24no—
258C2×#107C22×C1111yescharacteristic
259C2×C4⋊C8C22×C1111yescharacteristic
260C2×C4⋊C8C22×C1112yes—
261C2×#103C22×C1112yes—
262C2×#103C22×C1112yes—
263C2×#103C22×C1112yes—
264C2×#102C22×C1112yes—
265C2×#102C22×C1111yescharacteristic
266C2×#102C22×C1111yescharacteristic
267C2×C4×C8C22×C1111yescharacteristic
268#397—22no—
269#391C22×C1112yes—
270#389C22×C1112yes—
271#385—22no—
272#384C22×C1111yescharacteristic
273#380—21no—
274#380—21no—
275#380—21no—
276C4×C4⋊C4C22×C1111yescharacteristic
277#340C22×C1112yes—
278#336C22×C1112yes—
279C22×C11—24no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11C2×#12111yescharacteristic
294C22×C11D4211yescharacteristic
295C22×C11#54811yescharacteristic
296C22×C11C2×#13511yescharacteristic
297C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C11#57711yescharacteristic
299C22×C11#57811yescharacteristic
300C4×C11—22no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—82no—
305C4×C11—82no—
306C4×C11—81no—
307C4×C11#46314yescomplemented
308C4×C11C2×#12111yescharacteristic
309C4×C11#53711yescharacteristic
310C4×C11#54711yescharacteristic
311C4×C11#55311yescharacteristic
312C22×Q8C23×C1112yes—
313C22×D4C23×C1111yescharacteristic
314C22×D4C23×C1111yescharacteristic
315C23×C4—21no—
316C23×C4—21no—
317C23×C4—22no—
318C2×SD16—24no—
319C2×SD16—24no—
320C2×SD16—24no—
321C2×D8—22no—
322C2×D8—22no—
323C2×D8D4×C1114yes—
324C22×C8C23×C1112yes—
325C22×C8C23×C1111yescharacteristic
326C22×C8C23×C1111yescharacteristic
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329#124—24no—
330#124—42no—
331C4×D4—24no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—42no—
336C4×D4D4×C1114yes—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4D4×C1111yescharacteristic
344C2×C4⋊C4D4×C1111yescharacteristic
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C4⋊C4C23×C1112yes—
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C42C23×C1112yes—
354C2×C42C23×C1111yescharacteristic
355#107—22no—
356C4⋊C8—24no—
357C4⋊C8—22no—
358#103—24no—
359#103—24no—
360#103—42no—
361#102—22no—
362#102—24no—
363#102—22no—
364C4×C8—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95D4×C1112yes—
369C2×C11—44no—
370C2×C11—82no—
371C2×C11#241611yescharacteristic
372C2×C11C2×#46311yescharacteristic
373C2×C11#304611yescharacteristic
374C2×C11#327211yescharacteristic
375C2×C11#328311yescharacteristic
376C2×C11#336011yescharacteristic
377C2×C11#336711yescharacteristic
378C24—21no—
379C24—21no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C2×D4×C1112yes—
395C2×D4C2×D4×C1112yes—
396C2×D4C2×D4×C1112yes—
397C2×D4C11×#4112yes—
398C22×C4—21no—
399C22×C4—24no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—82no—
411C22×C4C2×D4×C1112yes—
412C22×C4C2×D4×C1112yes—
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C24×C1111yescharacteristic
416SD16—48no—
417D8—28no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8C2×D4×C1112yes—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—44no—
435C4⋊C4—42no—
436C4⋊C4—42no—
437C4⋊C4—42no—
438C4⋊C4—81no—
439C4⋊C4C2×D4×C1112yes—
440C22⋊C4—24no—
441C22⋊C4—44no—
442C22⋊C4—44no—
443C22⋊C4—44no—
444C22⋊C4—42no—
445C42—22no—
446C42—22no—
447C42C2×D4×C1112yes—
448C42C11×#4112yes—
449C11#2472711yescharacteristic, direct product factor, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23C22×D4×C1111yescharacteristic
465Q8—42no—
466Q8—42no—
467Q8—42no—
468Q8—42no—
469D4—22no—
470D4—22no—
471D4—22no—
472D4—22no—
473D4—22no—
474D4—41no—
475D4—41no—
476D4C11×#12114yes—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—48no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—88no—
499C2×C4—84no—
500C2×C4C11×#12112yes—
501C2×C4C11×#12112yes—
502C2×C4C11×#13512yes—
503C2×C4C11×AGL(1,ℤ/8)12yes—
504C2×C4C22×D4×C1111yescharacteristic
505C2×C4C22×D4×C1111yescharacteristic
506C2×C4C2×C11×#4111yescharacteristic
507C2×C4C2×C11×#4111yescharacteristic
508C2×C4C11×H(5,𝔽2)11yescharacteristic
509C2×C4C11×2−1+411yescharacteristic
510C8—22no—
511C8—42no—
512C8—41no—
513C22—24no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22C2×C11×#12111yescharacteristic
528C22D42×C1111yescharacteristic
529C22C11×#54811yescharacteristic
530C22C2×C11×#13511yescharacteristic
531C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
532C22C11×#57711yescharacteristic
533C22C11×#57811yescharacteristic
534C4—22no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—82no—
539C4—82no—
540C4—81no—
541C4C11×#46314yescomplemented
542C4C2×C11×#12111yescharacteristic
543C4C11×#53711yescharacteristic
544C4C11×#54711yescharacteristic
545C4C11×#55311yescharacteristic
546C2—44no—
547C2—82no—
548C2C11×#241611yescharacteristic
549C2C2×C11×#46311yescharacteristic
550C2C11×#304611yescharacteristic
551C2C11×#327211yescharacteristic
552C2C11×#328311yescharacteristic
553C2C11×#336011yescharacteristic
554C2C11×#336711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#461C2semidirect
4. C11×#2547C2semidirect
5. D4×C11×C4⋊C4C2semidirect
6. C11×#2068C2semidirect
7. C11×#2042C2semidirect
8. C11×#1956C2semidirect
9. C11×#1939C2semidirect
10. C11×#1877C2semidirect
11. C11×#1802C2semidirect
101. #24727C11direct (N × H)
174. C2×#461C2×C11semidirect
176. #2547C2×C11semidirect
177. D4×C4⋊C4C2×C11semidirect
178. #2068C2×C11semidirect
179. #2042C2×C11semidirect
180. #1956C2×C11semidirect
181. #1939C2×C11semidirect
182. #1877C2×C11semidirect
183. #1802C2×C11semidirect
307. C4×C11#463semidirect
449. C11#24727direct (N × H)
541. C4C11×#463semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C11×#4612
C2×C4×C11×D82
C11×#25472
D4×C11×C4⋊C42
C11×#20682
C11×#20422
C11×#19562
C11×#19392
C11×#18772
C11×#18022
#2472711