Finite Group Databasebeta

← C11×#22544 #14599737

Subgroups — C11×#22544 #14599737

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic
2C2×C11×#446C211yesmaximal, characteristic, complemented
3Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4C11×#1983C212yesmaximal
5C11×#1981C211yesmaximal, characteristic, complemented
6C11×#1959C212yesmaximal
7C11×#1956C211yesmaximal, characteristic, complemented
8C11×#1803C212yesmaximal, complemented
9C11×#1802C211yesmaximal, characteristic
10C11×#1763C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C11×#556—24no—
13C11×#556C418yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C11×#446—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2212yes—
33C2×C11×#97C2212yes—
34C2×C4×C8×C11C2211yescharacteristic
35C11×#389—21no—
36C11×#389—22no—
37C11×#384C2211yescharacteristic
38C11×#384C2212yes—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C4⋊C4C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C11×#340C2212yes—
44C22×Q8×C11D411yescharacteristic
45C22×Q8×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yes—
53C11×#126—216no—
54C11×#124—24no—
55C11×#124C2×C418yes—
56C11×C22⋊Q8—28no—
57C4×Q8×C11—24no—
58C4×Q8×C11—44no—
59C4×Q8×C11C2×C418yes—
60C4×Q8×C11C2×C414yes—
61C4×Q8×C11D414yes—
62C4×D4×C11—22no—
63C4×D4×C11C2×C414yes—
64C11×#117—28no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D412yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2312yes—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—24no—
88C11×#103—24no—
89C11×#103—24no—
90C11×#103—42no—
91C11×#103—42no—
92C11×#102—22no—
93C11×#102—22no—
94C11×#102—42no—
95C11×#97—24no—
96C4×C8×C11—22no—
97C11×#95—22no—
98C11×#95—21no—
99#22544C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
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×Q8×C11—22no—
108C2×Q8×C11C22⋊C414yes—
109C2×Q8×C11C22×C414yes—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C22×C412yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11#4112yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—44no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—82no—
150C11×C4⋊C4—81no—
151C11×C4⋊C4C22⋊C414yes—
152C11×C4⋊C4C22⋊C418yes—
153C11×C4⋊C4C22×C412yes—
154C11×C4⋊C4#4112yes—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—28no—
158C42×C11—28no—
159C42×C11—44no—
160C42×C11—42no—
161C42×C11C22×C412yes—
162C42×C11C22×C414yes—
163C42×C11C2×D412yes—
164C42×C11C2×D414yes—
165C2×#556C2×C1111yescharacteristic
166C2×#446C2×C1111yescharacteristic, complemented
167Q8×C4⋊C4C2×C1111yescharacteristic, complemented
168#1983C2×C1112yes—
169#1981C2×C1111yescharacteristic, complemented
170#1959C2×C1112yes—
171#1956C2×C1111yescharacteristic, complemented
172#1803C2×C1112yescomplemented
173#1802C2×C1111yescharacteristic
174#1763C2×C1112yescomplemented
175C4×#102C2×C1111yescharacteristic
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11C22×D411yescharacteristic
184Q8×C11—28no—
185Q8×C11—24no—
186Q8×C11—24no—
187Q8×C11—42no—
188Q8×C11—42no—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11—41no—
192D4×C11—41no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—48no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11C2×C22⋊C414yes—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C2×C22⋊C414yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11AGL(1,ℤ/8)12yes—
220C2×C4×C11#13712yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C8×C11—22no—
228C8×C11—41no—
229C8×C11—42no—
230#556—24no—
231#556C4×C1118yescomplemented
232C2×C4⋊Q8C22×C1111yescharacteristic
233C2×#126—22no—
234C2×#124C22×C1112yes—
235C2×C22⋊Q8—21no—
236C2×C4×Q8—21no—
237C2×C4×Q8C22×C1112yes—
238C2×C4×Q8C22×C1111yescharacteristic
239C2×C4×D4C22×C1111yescharacteristic
240C2×#117—21no—
241#446—24no—
242C2×C4⋊C8C22×C1111yescharacteristic
243C2×C4⋊C8C22×C1112yes—
244C2×#103C22×C1112yes—
245C2×#103C22×C1112yes—
246C2×#103C22×C1112yes—
247C2×#103C22×C1112yes—
248C2×#102C22×C1111yescharacteristic
249C2×#102C22×C1111yescharacteristic
250C2×#102C22×C1112yes—
251C2×#97C22×C1112yes—
252C2×C4×C8C22×C1111yescharacteristic
253#389—21no—
254#389—22no—
255#384C22×C1111yescharacteristic
256#384C22×C1112yes—
257C4×C4⋊C4C22×C1111yescharacteristic
258C4×C4⋊C4C22×C1112yes—
259#340C22×C1112yes—
260#340C22×C1111yescharacteristic
261#340C22×C1111yescharacteristic
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#54811yescharacteristic
271C22×C11#55011yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—24no—
277C4×C11—24no—
278C4×C11—22no—
279C4×C11—44no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—81no—
283C4×C11—82no—
284C4×C11#41714yes—
285C4×C11C4×#4111yescharacteristic
286C4×C11#52011yescharacteristic
287C4×C11#54811yescharacteristic
288C4×C11#55011yescharacteristic
289C22×Q8D4×C1111yescharacteristic
290C22×Q8C23×C1112yes—
291C22×D4C23×C1111yescharacteristic
292C23×C4—21no—
293C22×C8C23×C1111yescharacteristic
294C22×C8C23×C1112yes—
295C22×C8C23×C1111yescharacteristic
296C4⋊Q8—22no—
297C4⋊Q8C2×C4×C1114yes—
298#126—216no—
299#124—24no—
300#124C2×C4×C1118yes—
301C22⋊Q8—28no—
302C4×Q8—24no—
303C4×Q8—44no—
304C4×Q8C2×C4×C1118yes—
305C4×Q8C2×C4×C1114yes—
306C4×Q8D4×C1114yes—
307C4×D4—22no—
308C4×D4C2×C4×C1114yes—
309#117—28no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4D4×C1111yescharacteristic
318C2×C4⋊C4D4×C1112yes—
319C2×C4⋊C4C23×C1111yescharacteristic
320C2×C4⋊C4C23×C1112yes—
321C2×C4⋊C4C23×C1111yescharacteristic
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C22⋊C4—22no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—22no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—21no—
329C2×C42C23×C1111yescharacteristic
330C2×C42C23×C1112yes—
331C4⋊C8—22no—
332C4⋊C8—24no—
333#103—24no—
334#103—24no—
335#103—42no—
336#103—42no—
337#102—22no—
338#102—22no—
339#102—42no—
340#97—24no—
341C4×C8—22no—
342#95—22no—
343#95—21no—
344C2×C11—82no—
345C2×C11#234111yescharacteristic
346C2×C11C2×#41711yescharacteristic
347C2×C11#289811yescharacteristic
348C2×C11#336711yescharacteristic
349C2×C11#336911yescharacteristic
350C2×C11#339711yescharacteristic
351C2×C11#339811yescharacteristic
352C24—21no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8C11×C22⋊C414yes—
361C2×Q8C22×C4×C1114yes—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C22×C4×C1112yes—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4C2×D4×C1112yes—
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1112yes—
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C24×C1111yescharacteristic
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—22no—
385C2×C8—21no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—21no—
389C2×C8C11×#4112yes—
390C4⋊C4—24no—
391C4⋊C4—28no—
392C4⋊C4—24no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—44no—
400C4⋊C4—42no—
401C4⋊C4—82no—
402C4⋊C4—81no—
403C4⋊C4C11×C22⋊C414yes—
404C4⋊C4C11×C22⋊C418yes—
405C4⋊C4C22×C4×C1112yes—
406C4⋊C4C11×#4112yes—
407C22⋊C4—28no—
408C22⋊C4—24no—
409C22⋊C4—28no—
410C42—28no—
411C42—44no—
412C42—42no—
413C42C22×C4×C1112yes—
414C42C22×C4×C1114yes—
415C42C2×D4×C1112yes—
416C42C2×D4×C1114yes—
417C11#2254411yescharacteristic, direct product factor, Sylow
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C22×D4×C1111yescharacteristic
426Q8—28no—
427Q8—24no—
428Q8—24no—
429Q8—42no—
430Q8—42no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—48no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4C2×C11×C22⋊C414yes—
458C2×C4C2×C11×C22⋊C412yes—
459C2×C4C2×C11×C22⋊C414yes—
460C2×C4C2×C11×C22⋊C412yes—
461C2×C4C11×AGL(1,ℤ/8)12yes—
462C2×C4C11×#13712yes—
463C2×C4C23×C4×C1111yescharacteristic
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C2×C11×#4111yescharacteristic
466C2×C4C2×C11×#4111yescharacteristic
467C2×C4C11×H(5,𝔽2)11yescharacteristic
468C2×C4C11×2−1+411yescharacteristic
469C8—22no—
470C8—41no—
471C8—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22C22×C11×C22⋊C411yescharacteristic
480C22C11×#54811yescharacteristic
481C22C11×#55011yescharacteristic
482C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
483C22C2×C11×#13711yescharacteristic
484C22C11×#57711yescharacteristic
485C22C11×#57811yescharacteristic
486C4—24no—
487C4—24no—
488C4—22no—
489C4—42no—
490C4—44no—
491C4—42no—
492C4—81no—
493C4—82no—
494C4C11×#41714yes—
495C4C4×C11×#4111yescharacteristic
496C4C11×#52011yescharacteristic
497C4C11×#54811yescharacteristic
498C4C11×#55011yescharacteristic
499C2—82no—
500C2C11×#234111yescharacteristic
501C2C2×C11×#41711yescharacteristic
502C2C11×#289811yescharacteristic
503C2C11×#336711yescharacteristic
504C2C11×#336911yescharacteristic
505C2C11×#339711yescharacteristic
506C2C11×#339811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×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
2. C2×C11×#446C2semidirect
3. Q8×C11×C4⋊C4C2semidirect
5. C11×#1981C2semidirect
7. C11×#1956C2semidirect
8. C11×#1803C2semidirect
10. C11×#1763C2semidirect
13. C11×#556C4semidirect
99. #22544C11direct (N × H)
166. C2×#446C2×C11semidirect
167. Q8×C4⋊C4C2×C11semidirect
169. #1981C2×C11semidirect
171. #1956C2×C11semidirect
172. #1803C2×C11semidirect
174. #1763C2×C11semidirect
231. #556C4×C11semidirect
417. C11#22544direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4462
Q8×C11×C4⋊C42
C11×#19832
C11×#19812
C11×#19592
C11×#19562
C11×#18032
C11×#18022
C11×#17632
C4×C11×#1022
#2254411