Finite Group Databasebeta

← C11×#24677 #14601870

Subgroups — C11×#24677 #14601870

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 520 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
4C11×#2354C211yesmaximal, characteristic, complemented
5C11×#2073C212yesmaximal, complemented
6C11×#2054C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1949C212yesmaximal, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1926C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C11×#117—21no—
17C11×#476—24no—
18C4×C11×D8—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#393—22no—
29C11×#390C2212yes—
30C11×#390C2212yes—
31C11×#388—22no—
32C11×#384C2211yescharacteristic
33C11×#382C2212yes—
34C11×#380—21no—
35C11×#380—21no—
36C11×#380—21no—
37C4×C11×C4⋊C4C2212yes—
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—
48C2×C11×D8—22no—
49C2×C11×D8—22no—
50C2×C11×D8—22no—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11D414yes—
60C11×#117—44no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—22no—
77C2×C42×C11C2312yes—
78C2×C42×C11C2311yescharacteristic
79C11×#107—22no—
80C11×#106—24no—
81C11×C4⋊C8—24no—
82C11×C4⋊C8—22no—
83C11×#102—22no—
84C11×#102—24no—
85C11×#102—24no—
86C11×#102—22no—
87C4×C8×C11—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95D412yes—
92#24677C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—21no—
94C24×C11—21no—
95C2×Q8×C11—42no—
96C2×Q8×C11—81no—
97C2×Q8×C11—81no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
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×C11#4112yes—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C11×D8—28no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11#4112yes—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—81no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—42no—
151C11×C22⋊C4—82no—
152C11×C22⋊C4—82no—
153C11×C22⋊C4—82no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—44no—
157C42×C11C2×D412yes—
158C42×C11#4112yes—
159C2×#476C2×C1111yescharacteristic, complemented
160C2×C4×D8C2×C1111yescharacteristic
161#2563C2×C1111yescharacteristic, complemented
162#2354C2×C1111yescharacteristic, complemented
163#2073C2×C1112yescomplemented
164#2054C2×C1112yes—
165#1990C2×C1111yescharacteristic, complemented
166#1949C2×C1112yescomplemented
167#1939C2×C1111yescharacteristic, complemented
168#1926C2×C1112yescomplemented
169#1802C2×C1111yescharacteristic, complemented
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11C22×D411yescharacteristic
185Q8×C11—84no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—41no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—48no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—84no—
216C2×C4×C11#12112yes—
217C2×C4×C11#12112yes—
218C2×C4×C11#13512yes—
219C2×C4×C11AGL(1,ℤ/8)12yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C8×C11—22no—
227C8×C11—42no—
228C8×C11—41no—
229C22×D8C22×C1111yescharacteristic
230C2×C4⋊Q8C22×C1111yescharacteristic
231C2×C4×D4C22×C1111yescharacteristic
232C2×C4×D4C22×C1111yescharacteristic
233C2×#117—21no—
234#476—24no—
235C4×D8—24no—
236C2×#107C22×C1111yescharacteristic
237C2×#106C22×C1112yes—
238C2×C4⋊C8C22×C1112yes—
239C2×C4⋊C8C22×C1111yescharacteristic
240C2×#102C22×C1112yes—
241C2×#102C22×C1112yes—
242C2×#102C22×C1111yescharacteristic
243C2×#102C22×C1111yescharacteristic
244C2×C4×C8C22×C1111yescharacteristic
245#393—22no—
246#390C22×C1112yes—
247#390C22×C1112yes—
248#388—22no—
249#384C22×C1111yescharacteristic
250#382C22×C1112yes—
251#380—21no—
252#380—21no—
253#380—21no—
254C4×C4⋊C4C22×C1112yes—
255C4×C4⋊C4C22×C1111yescharacteristic
256#340C22×C1112yes—
257#340C22×C1112yes—
258#340C22×C1112yes—
259#336C22×C1112yes—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C2×#12111yescharacteristic
275C22×C11#54711yescharacteristic
276C22×C11#54811yescharacteristic
277C22×C11C2×#13511yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57711yescharacteristic
281C4×C11—22no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—82no—
286C4×C11—81no—
287C4×C11—82no—
288C4×C11#46314yes—
289C4×C11#52511yescharacteristic
290C4×C11#53611yescharacteristic
291C4×C11#55211yescharacteristic
292C4×C11#55611yescharacteristic
293C22×Q8—21no—
294C22×D4C23×C1111yescharacteristic
295C22×D4C23×C1111yescharacteristic
296C23×C4—21no—
297C23×C4—21no—
298C2×D8—22no—
299C2×D8—22no—
300C2×D8—22no—
301C22×C8C23×C1111yescharacteristic
302C22×C8C23×C1112yes—
303C22×C8C23×C1111yescharacteristic
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306C4×D4—22no—
307C4×D4—22no—
308C4×D4—22no—
309C4×D4D4×C1114yes—
310#117—44no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4D4×C1111yescharacteristic
315C2×C4⋊C4D4×C1111yescharacteristic
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1112yes—
319C2×C4⋊C4C23×C1111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C42—22no—
327C2×C42C23×C1112yes—
328C2×C42C23×C1111yescharacteristic
329#107—22no—
330#106—24no—
331C4⋊C8—24no—
332C4⋊C8—22no—
333#102—22no—
334#102—24no—
335#102—24no—
336#102—22no—
337C4×C8—22no—
338#95—22no—
339#95—22no—
340#95—22no—
341#95D4×C1112yes—
342C2×C11—82no—
343C2×C11—82no—
344C2×C11#241511yescharacteristic
345C2×C11C2×#46311yescharacteristic
346C2×C11#304511yescharacteristic
347C2×C11#334111yescharacteristic
348C2×C11#335411yescharacteristic
349C2×C11#336011yescharacteristic
350C2×C11#336611yescharacteristic
351C24—21no—
352C24—21no—
353C2×Q8—42no—
354C2×Q8—81no—
355C2×Q8—81no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4C2×D4×C1112yes—
367C2×D4C11×#4112yes—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4C2×D4×C1112yes—
379C22×C4C2×D4×C1112yes—
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C24×C1111yescharacteristic
383D8—28no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8C11×#4112yes—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—81no—
405C4⋊C4C2×D4×C1112yes—
406C22⋊C4—24no—
407C22⋊C4—44no—
408C22⋊C4—42no—
409C22⋊C4—82no—
410C22⋊C4—82no—
411C22⋊C4—82no—
412C42—22no—
413C42—22no—
414C42—44no—
415C42C2×D4×C1112yes—
416C42C11×#4112yes—
417C11#2467711yescharacteristic, direct product factor, Sylow
418C23—22no—
419C23—22no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23C22×D4×C1111yescharacteristic
433Q8—84no—
434D4—22no—
435D4—22no—
436D4—22no—
437D4—22no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—41no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—48no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—84no—
464C2×C4C11×#12112yes—
465C2×C4C11×#12112yes—
466C2×C4C11×#13512yes—
467C2×C4C11×AGL(1,ℤ/8)12yes—
468C2×C4C22×D4×C1111yescharacteristic
469C2×C4C2×C11×#4111yescharacteristic
470C2×C4C2×C11×#4111yescharacteristic
471C2×C4C2×C11×#4111yescharacteristic
472C2×C4C11×2−1+411yescharacteristic
473C2×C4C11×2−1+411yescharacteristic
474C8—22no—
475C8—42no—
476C8—41no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C2×C11×#12111yescharacteristic
492C22C11×#54711yescharacteristic
493C22C11×#54811yescharacteristic
494C22C2×C11×#13511yescharacteristic
495C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
496C22C11×#57611yescharacteristic
497C22C11×#57711yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—81no—
503C4—82no—
504C4—82no—
505C4C11×#46314yes—
506C4C11×#52511yescharacteristic
507C4C11×#53611yescharacteristic
508C4C11×#55211yescharacteristic
509C4C11×#55611yescharacteristic
510C2—82no—
511C2—82no—
512C2C11×#241511yescharacteristic
513C2C2×C11×#46311yescharacteristic
514C2C11×#304511yescharacteristic
515C2C11×#334111yescharacteristic
516C2C11×#335411yescharacteristic
517C2C11×#336011yescharacteristic
518C2C11×#336611yescharacteristic
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. C11×#2354C2semidirect
5. C11×#2073C2semidirect
7. C11×#1990C2semidirect
8. C11×#1949C2semidirect
9. C11×#1939C2semidirect
10. C11×#1926C2semidirect
11. C11×#1802C2semidirect
92. #24677C11direct (N × H)
159. C2×#476C2×C11semidirect
161. #2563C2×C11semidirect
162. #2354C2×C11semidirect
163. #2073C2×C11semidirect
165. #1990C2×C11semidirect
166. #1949C2×C11semidirect
167. #1939C2×C11semidirect
168. #1926C2×C11semidirect
169. #1802C2×C11semidirect
417. C11#24677direct (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
C11×#23542
C11×#20732
C11×#20542
C11×#19902
C11×#19492
C11×#19392
C11×#19262
C11×#18022
#2467711