Finite Group Databasebeta

← C11×#24813 #14602006

Subgroups — C11×#24813 #14602006

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#475C211yesmaximal, characteristic, complemented
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2542C211yesmaximal, characteristic
4Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2084C212yesmaximal, complemented
6C11×#2065C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1939C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1803C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C4×Q8×C11C2212yes—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#475—24no—
20C4×C11×SD16—24no—
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2212yes—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C11×#399—22no—
31C11×#390C2212yes—
32C11×#389—22no—
33C11×#389C2212yes—
34C11×#384—21no—
35C11×#384C2211yescharacteristic
36C11×#384C2212yes—
37C4×C11×C4⋊C4—21no—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×SD16Q814yescomplemented
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×C22⋊Q8—44no—
56C11×C22⋊Q8—44no—
57C4×Q8×C11—22no—
58C4×Q8×C11—24no—
59C4×Q8×C11—42no—
60C4×Q8×C11D414yes—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—21no—
81C2×C42×C11—22no—
82C2×C42×C11C2312yes—
83C2×C42×C11C2311yescharacteristic
84C11×#106—22no—
85C11×#106—24no—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—42no—
88C11×#103—22no—
89C11×#103—24no—
90C11×#102—22no—
91C11×#102—42no—
92C4×C8×C11—22no—
93C11×#95—22no—
94C11×#95D412yes—
95#24813C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11C2×D412yes—
104C2×Q8×C11C2×Q812yes—
105C2×Q8×C11#4112yes—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11C2×Q812yes—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C11×SD16—28no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11C2×Q812yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—44no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—81no—
150C11×C4⋊C4—82no—
151C11×C4⋊C4SD1614yescomplemented
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—44no—
156C42×C11—24no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—44no—
160C42×C11C2×D412yes—
161C42×C11#4112yes—
162C2×#475C2×C1111yescharacteristic, complemented
163C2×C4×SD16C2×C1111yescharacteristic
164#2542C2×C1111yescharacteristic
165Q8×C4⋊C4C2×C1111yescharacteristic, complemented
166#2084C2×C1112yescomplemented
167#2065C2×C1112yes—
168#1990C2×C1111yescharacteristic, complemented
169#1939C2×C1111yescharacteristic, complemented
170#1880C2×C1112yes—
171#1803C2×C1112yescomplemented
172#1802C2×C1111yescharacteristic
173C23×C11—22no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11C22×D411yescharacteristic
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—84no—
185Q8×C11C22⋊Q814yescomplemented
186D4×C11—22no—
187D4×C11—22no—
188D4×C11—41no—
189D4×C11—41no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—84no—
213C2×C4×C11#12112yes—
214C2×C4×C11#12112yes—
215C2×C4×C11C2×SD1614yes—
216C2×C4×C11C2×SD1612yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×Q811yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C8×C11—22no—
225C8×C11—41no—
226C8×C11—42no—
227C22×SD16C22×C1111yescharacteristic
228C2×C4⋊Q8C22×C1111yescharacteristic
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C4×Q8C22×C1112yes—
232C2×C4×Q8C22×C1111yescharacteristic
233C2×C4×D4C22×C1111yescharacteristic
234#475—24no—
235C4×SD16—24no—
236C2×#106C22×C1112yes—
237C2×#106C22×C1111yescharacteristic
238C2×C4⋊C8C22×C1111yescharacteristic
239C2×C4⋊C8C22×C1112yes—
240C2×#103C22×C1112yes—
241C2×#103C22×C1111yescharacteristic
242C2×#102C22×C1111yescharacteristic
243C2×#102C22×C1112yes—
244C2×C4×C8C22×C1111yescharacteristic
245#399—22no—
246#390C22×C1112yes—
247#389—22no—
248#389C22×C1112yes—
249#384—21no—
250#384C22×C1111yescharacteristic
251#384C22×C1112yes—
252C4×C4⋊C4—21no—
253C4×C4⋊C4C22×C1111yescharacteristic
254#340C22×C1112yes—
255#340C22×C1112yes—
256#340C22×C1112yes—
257#336C22×C1112yes—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54611yescharacteristic
267C22×C11D4×Q811yescharacteristic
268C22×C11C22×SD1611yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11#57711yescharacteristic
271C22×C11#57811yescharacteristic
272C4×C11—24no—
273C4×C11—24no—
274C4×C11—22no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—82no—
278C4×C11—81no—
279C4×C11—82no—
280C4×C11#46014yes—
281C4×C11C2×C22⋊Q811yescharacteristic
282C4×C11#53711yescharacteristic
283C4×C11#55211yescharacteristic
284C4×C11#55411yescharacteristic
285C22×Q8—21no—
286C22×Q8C23×C1111yescharacteristic
287C22×D4C23×C1111yescharacteristic
288C23×C4—21no—
289C2×SD16—22no—
290C2×SD16—22no—
291C2×SD16Q8×C1114yescomplemented
292C22×C8C23×C1112yes—
293C22×C8C23×C1111yescharacteristic
294C22×C8C23×C1111yescharacteristic
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C22⋊Q8—44no—
298C22⋊Q8—44no—
299C4×Q8—22no—
300C4×Q8—24no—
301C4×Q8—42no—
302C4×Q8D4×C1114yes—
303C4×D4—22no—
304C4×D4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4D4×C1111yescharacteristic
314C2×C4⋊C4D4×C1111yescharacteristic
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C42—21no—
323C2×C42—22no—
324C2×C42C23×C1112yes—
325C2×C42C23×C1111yescharacteristic
326#106—22no—
327#106—24no—
328C4⋊C8—22no—
329C4⋊C8—42no—
330#103—22no—
331#103—24no—
332#102—22no—
333#102—42no—
334C4×C8—22no—
335#95—22no—
336#95D4×C1112yes—
337C2×C11—82no—
338C2×C11#241711yescharacteristic
339C2×C11C2×#46011yescharacteristic
340C2×C11#304611yescharacteristic
341C2×C11#329811yescharacteristic
342C2×C11#333211yescharacteristic
343C2×C11Q8×SD1611yescharacteristic
344C2×C11#338611yescharacteristic
345C24—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—42no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8C2×D4×C1112yes—
353C2×Q8C2×Q8×C1112yes—
354C2×Q8C11×#4112yes—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4C2×Q8×C1112yes—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1112yes—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C24×C1111yescharacteristic
374SD16—28no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8C2×Q8×C1112yes—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—42no—
396C4⋊C4—44no—
397C4⋊C4—42no—
398C4⋊C4—81no—
399C4⋊C4—82no—
400C4⋊C4C11×SD1614yescomplemented
401C4⋊C4C2×D4×C1112yes—
402C22⋊C4—44no—
403C22⋊C4—42no—
404C22⋊C4—44no—
405C42—24no—
406C42—22no—
407C42—22no—
408C42—44no—
409C42C2×D4×C1112yes—
410C42C11×#4112yes—
411C11#2481311yescharacteristic, direct product factor, Sylow
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23C22×D4×C1111yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—22no—
423Q8—84no—
424Q8C11×C22⋊Q814yescomplemented
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—84no—
452C2×C4C11×#12112yes—
453C2×C4C11×#12112yes—
454C2×C4C2×C11×SD1614yes—
455C2×C4C2×C11×SD1612yes—
456C2×C4C11×AGL(1,ℤ/8)12yes—
457C2×C4C22×D4×C1111yescharacteristic
458C2×C4C22×Q8×C1111yescharacteristic
459C2×C4C2×C11×#4111yescharacteristic
460C2×C4C2×C11×#4111yescharacteristic
461C2×C4C11×H(5,𝔽2)11yescharacteristic
462C2×C4C11×2−1+411yescharacteristic
463C8—22no—
464C8—41no—
465C8—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22C2×C11×#12111yescharacteristic
474C22C11×#54611yescharacteristic
475C22D4×Q8×C1111yescharacteristic
476C22C22×C11×SD1611yescharacteristic
477C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
478C22C11×#57711yescharacteristic
479C22C11×#57811yescharacteristic
480C4—24no—
481C4—24no—
482C4—22no—
483C4—42no—
484C4—42no—
485C4—81no—
486C4—82no—
487C4—82no—
488C4C11×#46014yes—
489C4C2×C11×C22⋊Q811yescharacteristic
490C4C11×#53711yescharacteristic
491C4C11×#55211yescharacteristic
492C4C11×#55411yescharacteristic
493C2—82no—
494C2C11×#241711yescharacteristic
495C2C2×C11×#46011yescharacteristic
496C2C11×#304611yescharacteristic
497C2C11×#329811yescharacteristic
498C2C11×#333211yescharacteristic
499C2Q8×C11×SD1611yescharacteristic
500C2C11×#338611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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×#475C2semidirect
4. Q8×C11×C4⋊C4C2semidirect
5. C11×#2084C2semidirect
7. C11×#1990C2semidirect
8. C11×#1939C2semidirect
10. C11×#1803C2semidirect
49. C2×C11×SD16Q8semidirect
95. #24813C11direct (N × H)
151. C11×C4⋊C4SD16semidirect
162. C2×#475C2×C11semidirect
165. Q8×C4⋊C4C2×C11semidirect
166. #2084C2×C11semidirect
168. #1990C2×C11semidirect
169. #1939C2×C11semidirect
171. #1803C2×C11semidirect
185. Q8×C11C22⋊Q8semidirect
291. C2×SD16Q8×C11semidirect
400. C4⋊C4C11×SD16semidirect
411. C11#24813direct (N × H)
424. Q8C11×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4752
C2×C4×C11×SD162
C11×#25422
Q8×C11×C4⋊C42
C11×#20842
C11×#20652
C11×#19902
C11×#19392
C11×#18802
C11×#18032
C11×#18022
#2481311