Finite Group Databasebeta

← C11×#24065 #14601258

Subgroups — C11×#24065 #14601258

Order 2816.

1072 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C2×C11×#485C212yesmaximal
3C11×#2296C211yesmaximal, characteristic
4C11×#2058C211yesmaximal, characteristic, complemented
5C11×#2057C211yesmaximal, characteristic, complemented
6C11×#2043C211yesmaximal, characteristic, complemented
7C11×#2043C211yesmaximal, characteristic, complemented
8C11×#1873C212yesmaximal
9C11×#1865C212yesmaximal, complemented
10C11×#1863C212yesmaximal, complemented
11C11×#1817C211yesmaximal, characteristic
12C11×#533—28no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C11×#117—21no—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C11×#485—28no—
25C2×C11×#107C2212yes—
26C2×C11×#106C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×C22⋊C8C2212yes—
32C11×#389C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#385—21no—
37C11×#385—21no—
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2211yescharacteristic
43C11×#336C2211yescharacteristic
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2312yes—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8—24no—
54C11×#125—28no—
55C11×C22⋊Q8—28no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8D418yes—
58C4×Q8×C11—28no—
59C4×Q8×C11—24no—
60C4×Q8×C11—24no—
61C11×#117—28no—
62C11×#117—22no—
63C11×#117—22no—
64C11×#117—24no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—24no—
83C2×C42×C11—22no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C11×#107—24no—
91C11×#106—24no—
92C11×#103—24no—
93C11×#103—24no—
94C11×#103—24no—
95C11×#103—24no—
96C11×C22⋊C8—24no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101#24065C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11C2×D411yescharacteristic
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×Q8×C11C2×D414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
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—24no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4C2×D414yes—
155C11×C4⋊C4#4112yes—
156C11×C4⋊C4#4112yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—42no—
160C42×C11—24no—
161C42×C11—28no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—42no—
167C2×#533C2×C1111yescharacteristic
168C2×#485C2×C1112yes—
169#2296C2×C1111yescharacteristic
170#2058C2×C1111yescharacteristic, complemented
171#2057C2×C1111yescharacteristic, complemented
172#2043C2×C1111yescharacteristic, complemented
173#2043C2×C1111yescharacteristic, complemented
174#1873C2×C1112yes—
175#1865C2×C1112yescomplemented
176#1863C2×C1112yescomplemented
177#1817C2×C1111yescharacteristic
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11#12012yes—
185C23×C11C22×D411yescharacteristic
186Q8×C11—24no—
187Q8×C11—24no—
188Q8×C11—48no—
189Q8×C11—42no—
190Q8×C11—42no—
191C2×C4×C11—28no—
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—21no—
199C2×C4×C11—21no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—21no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11#12012yes—
225C2×C4×C11#13512yes—
226C2×C4×C11#13712yes—
227C2×C4×C11#13712yes—
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C112−1+412yes—
232C8×C11—42no—
233C8×C11—42no—
234#533—28no—
235C2×C4⋊Q8C22×C1111yescharacteristic
236C2×C4⋊Q8C22×C1111yescharacteristic
237C2×#125—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C22×C1112yes—
240C2×C4×Q8—21no—
241C2×C4×Q8C22×C1112yes—
242C2×#117—21no—
243C2×#117C22×C1111yescharacteristic
244C2×#117C22×C1111yescharacteristic
245C22×C42C22×C1111yescharacteristic
246#485—28no—
247C2×#107C22×C1112yes—
248C2×#106C22×C1112yes—
249C2×#103C22×C1112yes—
250C2×#103C22×C1112yes—
251C2×#103C22×C1112yes—
252C2×#103C22×C1112yes—
253C2×C22⋊C8C22×C1112yes—
254#389C22×C1111yescharacteristic
255#389C22×C1111yescharacteristic
256#389C22×C1111yescharacteristic
257#389C22×C1111yescharacteristic
258#385—21no—
259#385—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262#340C22×C1112yes—
263#340C22×C1112yes—
264#336C22×C1111yescharacteristic
265#336C22×C1111yescharacteristic
266#336C22×C1112yes—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11C2×#12011yescharacteristic
275C22×C11#52511yescharacteristic
276C22×C11#53611yescharacteristic
277C22×C11C2×#13511yescharacteristic
278C22×C11C2×#13711yescharacteristic
279C22×C11C2×#13711yescharacteristic
280C22×C11#57511yescharacteristic
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—44no—
288C4×C11—41no—
289C4×C11—44no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11#54712yes—
293C4×C11#54712yes—
294C22×Q8—21no—
295C22×Q8C23×C1112yes—
296C23×C4D4×C1111yescharacteristic
297C23×C4D4×C1111yescharacteristic
298C23×C4C23×C1111yescharacteristic
299C22×C8C23×C1112yes—
300C22×C8C23×C1112yes—
301C4⋊Q8—24no—
302C4⋊Q8—24no—
303#125—28no—
304C22⋊Q8—28no—
305C22⋊Q8—24no—
306C22⋊Q8D4×C1118yes—
307C4×Q8—28no—
308C4×Q8—24no—
309C4×Q8—24no—
310#117—28no—
311#117—22no—
312#117—22no—
313#117—24no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4C23×C1111yescharacteristic
324C2×C4⋊C4C23×C1111yescharacteristic
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C22⋊C4—22no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C42—22no—
332C2×C42—21no—
333C2×C42—24no—
334C2×C42—21no—
335C2×C42D4×C1111yescharacteristic
336C2×C42D4×C1111yescharacteristic
337C2×C42C23×C1111yescharacteristic
338C2×C42C23×C1111yescharacteristic
339#107—24no—
340#106—24no—
341#103—24no—
342#103—24no—
343#103—24no—
344#103—24no—
345C22⋊C8—24no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350C2×C11—42no—
351C2×C11#240611yescharacteristic
352C2×C11#300211yescharacteristic
353C2×C11#300411yescharacteristic
354C2×C11#310711yescharacteristic
355C2×C11#311611yescharacteristic
356C2×C11#323111yescharacteristic
357C2×C11#323711yescharacteristic
358C24C2×D4×C1111yescharacteristic
359C2×Q8—24no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8C2×D4×C1114yes—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—41no—
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1114yes—
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C24×C1111yescharacteristic
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—28no—
399C4⋊C4—24no—
400C4⋊C4—28no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—42no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4C2×D4×C1114yes—
411C4⋊C4C11×#4112yes—
412C4⋊C4C11×#4112yes—
413C22⋊C4—24no—
414C22⋊C4—28no—
415C22⋊C4—42no—
416C42—28no—
417C42—24no—
418C42—22no—
419C42—22no—
420C42—22no—
421C42—22no—
422C42—42no—
423C11#2406511yescharacteristic, direct product factor, Sylow
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23C11×#12012yes—
431C23C22×D4×C1111yescharacteristic
432Q8—24no—
433Q8—24no—
434Q8—48no—
435Q8—42no—
436Q8—42no—
437C2×C4—28no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—44no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4C11×#12012yes—
471C2×C4C11×#13512yes—
472C2×C4C11×#13712yes—
473C2×C4C11×#13712yes—
474C2×C4C22×D4×C1112yes—
475C2×C4C2×C11×#4111yescharacteristic
476C2×C4C2×C11×#4111yescharacteristic
477C2×C4C11×2−1+412yes—
478C8—42no—
479C8—42no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22C2×C11×#12011yescharacteristic
488C22C11×#52511yescharacteristic
489C22C11×#53611yescharacteristic
490C22C2×C11×#13511yescharacteristic
491C22C2×C11×#13711yescharacteristic
492C22C2×C11×#13711yescharacteristic
493C22C11×#57511yescharacteristic
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—44no—
499C4—41no—
500C4—44no—
501C4—42no—
502C4—42no—
503C4—81no—
504C4—81no—
505C4C11×#54712yes—
506C4C11×#54712yes—
507C2—42no—
508C2C11×#240611yescharacteristic
509C2C11×#300211yescharacteristic
510C2C11×#300411yescharacteristic
511C2C11×#310711yescharacteristic
512C2C11×#311611yescharacteristic
513C2C11×#323111yescharacteristic
514C2C11×#323711yescharacteristic
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
4. C11×#2058C2semidirect
5. C11×#2057C2semidirect
6. C11×#2043C2semidirect
7. C11×#2043C2semidirect
9. C11×#1865C2semidirect
10. C11×#1863C2semidirect
101. #24065C11direct (N × H)
170. #2058C2×C11semidirect
171. #2057C2×C11semidirect
172. #2043C2×C11semidirect
173. #2043C2×C11semidirect
175. #1865C2×C11semidirect
176. #1863C2×C11semidirect
423. C11#24065direct (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×#4852
C11×#22962
C11×#20582
C11×#20572
C11×#20432
C11×#18732
C11×#18652
C11×#18632
C11×#18172
#2406511