Finite Group Databasebeta

← C11×#24306 #14601499

Subgroups — C11×#24306 #14601499

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C2×C11×#479C212yesmaximal, complemented
3C4×C11×C22⋊Q8C211yesmaximal, characteristic
4C11×#2058C211yesmaximal, characteristic, complemented
5C11×#2057C211yesmaximal, characteristic, complemented
6C11×#2024C211yesmaximal, characteristic, complemented
7C11×#2024C211yesmaximal, characteristic, complemented
8C11×#1989C212yesmaximal, complemented
9C11×#1873C212yesmaximal
10C11×#1854C212yesmaximal
11C11×#1797C211yesmaximal, characteristic
12C11×#533—28no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C11×#117C2212yes—
23C22×C42×C11C2211yescharacteristic
24C11×#479—28no—
25C2×C11×#107C2212yes—
26C2×C11×#106C2212yes—
27C2×C11×C4⋊C8C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×C22⋊C8C2212yes—
31C11×#391C2211yescharacteristic
32C11×#389C2211yescharacteristic
33C11×#387—21no—
34C11×#385—21no—
35C11×#380C2211yescharacteristic
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4—21no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—24no—
55C11×#125—24no—
56C11×#125D418yes—
57C11×C22⋊Q8—28no—
58C11×C22⋊Q8—28no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8Q814yescomplemented
61C4×Q8×C11—28no—
62C4×Q8×C11—28no—
63C4×Q8×C11—24no—
64C11×#117—24no—
65C11×#117—24no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—22no—
82C2×C42×C11—24no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11D411yescharacteristic
86C2×C42×C11D411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C11×#107—24no—
90C11×#106—24no—
91C11×C4⋊C8—24no—
92C11×#103—24no—
93C11×#103—24no—
94C11×C22⋊C8—24no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100#24306C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11C2×D411yescharacteristic
102C2×Q8×C11—24no—
103C2×Q8×C11—24no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×Q8×C11C2×Q812yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×Q812yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4C2×D414yes—
153C11×C4⋊C4C2×D414yes—
154C11×C4⋊C4C2×Q812yes—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—42no—
158C42×C11—28no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—42no—
163C42×C11—42no—
164C42×C11C2×D414yes—
165C2×#533C2×C1111yescharacteristic
166C2×#479C2×C1112yescomplemented
167C4×C22⋊Q8C2×C1111yescharacteristic
168#2058C2×C1111yescharacteristic, complemented
169#2057C2×C1111yescharacteristic, complemented
170#2024C2×C1111yescharacteristic, complemented
171#2024C2×C1111yescharacteristic, complemented
172#1989C2×C1112yescomplemented
173#1873C2×C1112yes—
174#1854C2×C1112yes—
175#1797C2×C1111yescharacteristic
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11C22⋊Q812yes—
183C23×C11C22×D411yescharacteristic
184Q8×C11—24no—
185Q8×C11—48no—
186Q8×C11—48no—
187Q8×C11—42no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—44no—
205C2×C4×C11—44no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11#12012yes—
221C2×C4×C11#12012yes—
222C2×C4×C11C22⋊Q812yes—
223C2×C4×C11#13512yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×Q811yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C112−1+412yes—
229C8×C11—42no—
230C8×C11—42no—
231#533—28no—
232C2×C4⋊Q8C22×C1111yescharacteristic
233C2×C4⋊Q8C22×C1111yescharacteristic
234C2×#125C22×C1112yes—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8C22×C1111yescharacteristic
238C2×C4×Q8—21no—
239C2×C4×Q8—21no—
240C2×C4×Q8C22×C1111yescharacteristic
241C2×#117C22×C1112yes—
242C22×C42C22×C1111yescharacteristic
243#479—28no—
244C2×#107C22×C1112yes—
245C2×#106C22×C1112yes—
246C2×C4⋊C8C22×C1112yes—
247C2×#103C22×C1112yes—
248C2×#103C22×C1112yes—
249C2×C22⋊C8C22×C1112yes—
250#391C22×C1111yescharacteristic
251#389C22×C1111yescharacteristic
252#387—21no—
253#385—21no—
254#380C22×C1111yescharacteristic
255C4×C4⋊C4—21no—
256C4×C4⋊C4C22×C1111yescharacteristic
257C4×C22⋊C4—21no—
258#340C22×C1112yes—
259#340C22×C1112yes—
260#340C22×C1112yes—
261#340C22×C1112yes—
262#336C22×C1111yescharacteristic
263#336C22×C1111yescharacteristic
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11C2×#12011yescharacteristic
272C22×C11C2×C22⋊Q811yescharacteristic
273C22×C11#53611yescharacteristic
274C22×C11C2×#13511yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C22×C11#57511yescharacteristic
277C22×C11#57511yescharacteristic
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—44no—
286C4×C11—44no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11#54812yes—
290C4×C11D4×Q812yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8C23×C1111yescharacteristic
294C23×C4D4×C1111yescharacteristic
295C23×C4D4×C1111yescharacteristic
296C23×C4C23×C1111yescharacteristic
297C22×C8C23×C1112yes—
298C22×C8C23×C1112yes—
299C4⋊Q8—24no—
300C4⋊Q8—24no—
301#125—24no—
302#125D4×C1118yes—
303C22⋊Q8—28no—
304C22⋊Q8—28no—
305C22⋊Q8—22no—
306C22⋊Q8Q8×C1114yescomplemented
307C4×Q8—28no—
308C4×Q8—28no—
309C4×Q8—24no—
310#117—24no—
311#117—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4C23×C1111yescharacteristic
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C4⋊C4C23×C1112yes—
322C2×C4⋊C4C23×C1112yes—
323C2×C4⋊C4C23×C1111yescharacteristic
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C42—22no—
328C2×C42—24no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42D4×C1111yescharacteristic
332C2×C42D4×C1111yescharacteristic
333C2×C42C23×C1111yescharacteristic
334C2×C42C23×C1111yescharacteristic
335#107—24no—
336#106—24no—
337C4⋊C8—24no—
338#103—24no—
339#103—24no—
340C22⋊C8—24no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346C2×C11—42no—
347C2×C11#240911yescharacteristic
348C2×C11#300211yescharacteristic
349C2×C11#300711yescharacteristic
350C2×C11#307611yescharacteristic
351C2×C11#307811yescharacteristic
352C2×C11#323111yescharacteristic
353C2×C11#324011yescharacteristic
354C24C2×D4×C1111yescharacteristic
355C2×Q8—24no—
356C2×Q8—24no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—42no—
363C2×Q8—42no—
364C2×Q8C2×Q8×C1112yes—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×Q8×C1112yes—
385C22×C4C11×#4112yes—
386C22×C4C24×C1111yescharacteristic
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—28no—
396C4⋊C4—28no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4C2×D4×C1114yes—
406C4⋊C4C2×D4×C1114yes—
407C4⋊C4C2×Q8×C1112yes—
408C22⋊C4—28no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C42—28no—
412C42—22no—
413C42—22no—
414C42—22no—
415C42—42no—
416C42—42no—
417C42C2×D4×C1114yes—
418C11#2430611yescharacteristic, direct product factor, Sylow
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23C11×C22⋊Q812yes—
426C23C22×D4×C1111yescharacteristic
427Q8—24no—
428Q8—48no—
429Q8—48no—
430Q8—42no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4C11×#12012yes—
464C2×C4C11×#12012yes—
465C2×C4C11×C22⋊Q812yes—
466C2×C4C11×#13512yes—
467C2×C4C11×#13712yes—
468C2×C4C22×D4×C1112yes—
469C2×C4C22×Q8×C1111yescharacteristic
470C2×C4C2×C11×#4111yescharacteristic
471C2×C4C11×2−1+412yes—
472C8—42no—
473C8—42no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22C2×C11×#12011yescharacteristic
482C22C2×C11×C22⋊Q811yescharacteristic
483C22C11×#53611yescharacteristic
484C22C2×C11×#13511yescharacteristic
485C22C2×C11×#13711yescharacteristic
486C22C11×#57511yescharacteristic
487C22C11×#57511yescharacteristic
488C4—22no—
489C4—22no—
490C4—22no—
491C4—22no—
492C4—22no—
493C4—42no—
494C4—44no—
495C4—44no—
496C4—42no—
497C4—81no—
498C4—81no—
499C4C11×#54812yes—
500C4D4×Q8×C1112yes—
501C2—42no—
502C2C11×#240911yescharacteristic
503C2C11×#300211yescharacteristic
504C2C11×#300711yescharacteristic
505C2C11×#307611yescharacteristic
506C2C11×#307811yescharacteristic
507C2C11×#323111yescharacteristic
508C2C11×#324011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#479C2semidirect
4. C11×#2058C2semidirect
5. C11×#2057C2semidirect
6. C11×#2024C2semidirect
7. C11×#2024C2semidirect
8. C11×#1989C2semidirect
60. C11×C22⋊Q8Q8semidirect
100. #24306C11direct (N × H)
166. C2×#479C2×C11semidirect
168. #2058C2×C11semidirect
169. #2057C2×C11semidirect
170. #2024C2×C11semidirect
171. #2024C2×C11semidirect
172. #1989C2×C11semidirect
306. C22⋊Q8Q8×C11semidirect
418. C11#24306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C2×C11×#4792
C4×C11×C22⋊Q82
C11×#20582
C11×#20572
C11×#20242
C11×#19892
C11×#18732
C11×#18542
C11×#17972
#2430611