Finite Group Databasebeta

← C11×#24812 #14602005

Subgroups — C11×#24812 #14602005

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#476C211yesmaximal, characteristic, complemented
2C2×C4×C11×D8C211yesmaximal, characteristic
3C11×#2563C211yesmaximal, characteristic, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2085C212yesmaximal, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1939C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal
10C11×#1804C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C22×C11×C4⋊C4—21no—
18C11×#476—24no—
19C4×C11×D8—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29C11×#393—22no—
30C11×#390C2212yes—
31C11×#389C2212yes—
32C11×#385—22no—
33C11×#384C2211yescharacteristic
34C11×#382C2212yes—
35C11×#380—21no—
36C11×#380—21no—
37C11×#380—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11—22no—
49C2×C11×D8—22no—
50C2×C11×D8—22no—
51C2×C11×D8Q814yescomplemented
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—42no—
62C4×D4×C11D414yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—44no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C42×C11C2312yes—
80C2×C42×C11C2311yescharacteristic
81C11×#107—22no—
82C11×#106—24no—
83C11×C4⋊C8—22no—
84C11×C4⋊C8—42no—
85C11×#102—22no—
86C11×#102—24no—
87C11×#102—22no—
88C11×#102—42no—
89C4×C8×C11—22no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95D412yes—
94#24812C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C24×C11—21no—
97C2×Q8×C11—42no—
98C2×Q8×C11—81no—
99C2×Q8×C11—81no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11C2×D412yes—
109C2×D4×C11C2×Q812yes—
110C2×D4×C11C2×Q812yes—
111C2×D4×C11#4112yes—
112C22×C4×C11—21no—
113C22×C4×C11—24no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—44no—
118C22×C4×C11—44no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—82no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C11×D8—28no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11C2×Q812yes—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4C2×D412yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—82no—
158C11×C22⋊C4—82no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11C2×D412yes—
162C42×C11#4112yes—
163C2×#476C2×C1111yescharacteristic, complemented
164C2×C4×D8C2×C1111yescharacteristic
165#2563C2×C1111yescharacteristic, complemented
166D4×C4⋊C4C2×C1111yescharacteristic, complemented
167#2085C2×C1112yescomplemented
168#2065C2×C1112yescomplemented
169#1990C2×C1111yescharacteristic, complemented
170#1939C2×C1111yescharacteristic, complemented
171#1879C2×C1112yes—
172#1804C2×C1112yescomplemented
173#1802C2×C1111yescharacteristic, complemented
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11C22×D411yescharacteristic
189Q8×C11—84no—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11C22⋊Q814yes—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—48no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—88no—
220C2×C4×C11—84no—
221C2×C4×C11#12112yes—
222C2×C4×C11#12112yes—
223C2×C4×C11#13512yes—
224C2×C4×C11AGL(1,ℤ/8)12yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×Q811yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C8×C11—22no—
232C8×C11—41no—
233C8×C11—42no—
234C22×D8C22×C1111yescharacteristic
235C2×C4⋊Q8C22×C1111yescharacteristic
236C2×C4×D4C22×C1111yescharacteristic
237C2×C4×D4C22×C1112yes—
238C2×C4×D4C22×C1111yescharacteristic
239C22×C4⋊C4—21no—
240#476—24no—
241C4×D8—24no—
242C2×#107C22×C1111yescharacteristic
243C2×#106C22×C1112yes—
244C2×C4⋊C8C22×C1111yescharacteristic
245C2×C4⋊C8C22×C1112yes—
246C2×#102C22×C1111yescharacteristic
247C2×#102C22×C1112yes—
248C2×#102C22×C1111yescharacteristic
249C2×#102C22×C1112yes—
250C2×C4×C8C22×C1111yescharacteristic
251#393—22no—
252#390C22×C1112yes—
253#389C22×C1112yes—
254#385—22no—
255#384C22×C1111yescharacteristic
256#382C22×C1112yes—
257#380—21no—
258#380—21no—
259#380—21no—
260C4×C4⋊C4C22×C1111yescharacteristic
261#340C22×C1112yes—
262#340C22×C1112yes—
263#340C22×C1112yes—
264#336C22×C1112yes—
265C22×C11—24no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11C2×#12111yescharacteristic
280C22×C11#54611yescharacteristic
281C22×C11D4×Q811yescharacteristic
282C22×C11C2×#13511yescharacteristic
283C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C11#57611yescharacteristic
285C22×C11#57711yescharacteristic
286C4×C11—22no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—81no—
291C4×C11—82no—
292C4×C11—82no—
293C4×C11#46314yes—
294C4×C11C2×C22⋊Q811yescharacteristic
295C4×C11#53711yescharacteristic
296C4×C11#55211yescharacteristic
297C4×C11#55411yescharacteristic
298C22×Q8—21no—
299C22×D4C23×C1111yescharacteristic
300C22×D4C23×C1111yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—22no—
304C2×D8—22no—
305C2×D8—22no—
306C2×D8Q8×C1114yescomplemented
307C22×C8C23×C1112yes—
308C22×C8C23×C1111yescharacteristic
309C22×C8C23×C1111yescharacteristic
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—42no—
317C4×D4D4×C1114yes—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4D4×C1111yescharacteristic
324C2×C4⋊C4D4×C1111yescharacteristic
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1112yes—
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C42C23×C1112yes—
335C2×C42C23×C1111yescharacteristic
336#107—22no—
337#106—24no—
338C4⋊C8—22no—
339C4⋊C8—42no—
340#102—22no—
341#102—24no—
342#102—22no—
343#102—42no—
344C4×C8—22no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95D4×C1112yes—
349C2×C11—44no—
350C2×C11—82no—
351C2×C11#241711yescharacteristic
352C2×C11C2×#46311yescharacteristic
353C2×C11#304511yescharacteristic
354C2×C11#330311yescharacteristic
355C2×C11#332511yescharacteristic
356C2×C11#338011yescharacteristic
357C2×C11#338411yescharacteristic
358C24—21no—
359C24—21no—
360C2×Q8—42no—
361C2×Q8—81no—
362C2×Q8—81no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4C2×D4×C1112yes—
372C2×D4C2×Q8×C1112yes—
373C2×D4C2×Q8×C1112yes—
374C2×D4C11×#4112yes—
375C22×C4—21no—
376C22×C4—24no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—82no—
388C22×C4C2×D4×C1112yes—
389C22×C4C2×D4×C1112yes—
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C24×C1111yescharacteristic
393D8—28no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—21no—
400C2×C8—22no—
401C2×C8—21no—
402C2×C8C2×Q8×C1112yes—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—44no—
413C4⋊C4—42no—
414C4⋊C4—42no—
415C4⋊C4—81no—
416C4⋊C4C2×D4×C1112yes—
417C22⋊C4—24no—
418C22⋊C4—44no—
419C22⋊C4—42no—
420C22⋊C4—82no—
421C22⋊C4—82no—
422C42—22no—
423C42—22no—
424C42C2×D4×C1112yes—
425C42C11×#4112yes—
426C11#2481211yescharacteristic, direct product factor, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23C22×D4×C1111yescharacteristic
442Q8—84no—
443D4—22no—
444D4—22no—
445D4—22no—
446D4—22no—
447D4—22no—
448D4—41no—
449D4—41no—
450D4C11×C22⋊Q814yes—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—48no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—88no—
473C2×C4—84no—
474C2×C4C11×#12112yes—
475C2×C4C11×#12112yes—
476C2×C4C11×#13512yes—
477C2×C4C11×AGL(1,ℤ/8)12yes—
478C2×C4C22×D4×C1111yescharacteristic
479C2×C4C22×Q8×C1111yescharacteristic
480C2×C4C2×C11×#4111yescharacteristic
481C2×C4C2×C11×#4111yescharacteristic
482C2×C4C11×H(5,𝔽2)11yescharacteristic
483C2×C4C11×2−1+411yescharacteristic
484C8—22no—
485C8—41no—
486C8—42no—
487C22—24no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22C2×C11×#12111yescharacteristic
502C22C11×#54611yescharacteristic
503C22D4×Q8×C1111yescharacteristic
504C22C2×C11×#13511yescharacteristic
505C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
506C22C11×#57611yescharacteristic
507C22C11×#57711yescharacteristic
508C4—22no—
509C4—42no—
510C4—42no—
511C4—42no—
512C4—81no—
513C4—82no—
514C4—82no—
515C4C11×#46314yes—
516C4C2×C11×C22⋊Q811yescharacteristic
517C4C11×#53711yescharacteristic
518C4C11×#55211yescharacteristic
519C4C11×#55411yescharacteristic
520C2—44no—
521C2—82no—
522C2C11×#241711yescharacteristic
523C2C2×C11×#46311yescharacteristic
524C2C11×#304511yescharacteristic
525C2C11×#330311yescharacteristic
526C2C11×#332511yescharacteristic
527C2C11×#338011yescharacteristic
528C2C11×#338411yescharacteristic
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
1. C2×C11×#476C2semidirect
3. C11×#2563C2semidirect
4. D4×C11×C4⋊C4C2semidirect
5. C11×#2085C2semidirect
6. C11×#2065C2semidirect
7. C11×#1990C2semidirect
8. C11×#1939C2semidirect
10. C11×#1804C2semidirect
11. C11×#1802C2semidirect
51. C2×C11×D8Q8semidirect
94. #24812C11direct (N × H)
163. C2×#476C2×C11semidirect
165. #2563C2×C11semidirect
166. D4×C4⋊C4C2×C11semidirect
167. #2085C2×C11semidirect
168. #2065C2×C11semidirect
169. #1990C2×C11semidirect
170. #1939C2×C11semidirect
172. #1804C2×C11semidirect
173. #1802C2×C11semidirect
306. C2×D8Q8×C11semidirect
426. C11#24812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4762
C2×C4×C11×D82
C11×#25632
D4×C11×C4⋊C42
C11×#20852
C11×#20652
C11×#19902
C11×#19392
C11×#18792
C11×#18042
C11×#18022
#2481211