Finite Group Databasebeta

← C11×#24304 #14601497

Subgroups — C11×#24304 #14601497

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C2×C11×#478C212yesmaximal, complemented
3C4×C11×#121C211yesmaximal, characteristic
4C11×#2058C211yesmaximal, characteristic, complemented
5C11×#2057C211yesmaximal, characteristic, complemented
6C11×#2023C211yesmaximal, characteristic, complemented
7C11×#2023C211yesmaximal, characteristic, complemented
8C11×#1989C212yesmaximal, complemented
9C11×#1875C212yesmaximal
10C11×#1854C212yesmaximal, complemented
11C11×#1797C211yesmaximal, characteristic, complemented
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×#121C2211yescharacteristic
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2212yes—
24C22×C42×C11C2211yescharacteristic
25C11×#478—28no—
26C2×C11×#107C2212yes—
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×C22⋊C8C2212yes—
32C11×#390C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#388—21no—
35C11×#386—21no—
36C11×#380C2211yescharacteristic
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×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—24no—
57C11×#125—24no—
58C11×#125D418yescomplemented
59C11×C22⋊Q8—28no—
60C11×C22⋊Q8—28no—
61C11×#121—22no—
62C11×#121Q814yescomplemented
63C4×Q8×C11—28no—
64C4×Q8×C11—28no—
65C4×D4×C11—24no—
66C4×D4×C11—44no—
67C11×#117—24no—
68C11×#117—24no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
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⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—22no—
86C2×C42×C11—24no—
87C2×C42×C11—21no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C11×#107—24no—
93C11×#106—24no—
94C11×C4⋊C8—24no—
95C11×#102—24no—
96C11×#102—24no—
97C11×C22⋊C8—24no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101#24304C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11C2×D411yescharacteristic
104C2×Q8×C11—24no—
105C2×Q8×C11—24no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11C2×Q812yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×Q812yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4C2×D414yes—
158C11×C4⋊C4C2×D414yes—
159C11×C4⋊C4C2×Q812yes—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C42×C11—28no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—42no—
171C42×C11C2×D414yes—
172C2×#533C2×C1111yescharacteristic, complemented
173C2×#478C2×C1112yescomplemented
174C4×#121C2×C1111yescharacteristic
175#2058C2×C1111yescharacteristic, complemented
176#2057C2×C1111yescharacteristic, complemented
177#2023C2×C1111yescharacteristic, complemented
178#2023C2×C1111yescharacteristic, complemented
179#1989C2×C1112yescomplemented
180#1875C2×C1112yes—
181#1854C2×C1112yescomplemented
182#1797C2×C1111yescharacteristic, complemented
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C22⋊Q812yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—48no—
199Q8×C11—48no—
200D4×C11—24no—
201D4×C11—48no—
202D4×C11—42no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—84no—
233C2×C4×C11#12012yes—
234C2×C4×C11#12012yes—
235C2×C4×C11C22⋊Q812yes—
236C2×C4×C11#13512yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C112−1+412yes—
242C8×C11—42no—
243C8×C11—42no—
244#533—28no—
245C2×C4⋊Q8C22×C1111yescharacteristic
246C2×C4⋊Q8C22×C1111yescharacteristic
247C2×#125C22×C1112yes—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250C2×#121C22×C1111yescharacteristic
251C2×C4×Q8—21no—
252C2×C4×Q8—21no—
253C2×C4×D4—21no—
254C2×C4×D4C22×C1111yescharacteristic
255C2×#117C22×C1112yes—
256C22×C42C22×C1111yescharacteristic
257#478—28no—
258C2×#107C22×C1112yes—
259C2×#106C22×C1112yes—
260C2×C4⋊C8C22×C1112yes—
261C2×#102C22×C1112yes—
262C2×#102C22×C1112yes—
263C2×C22⋊C8C22×C1112yes—
264#390C22×C1111yescharacteristic
265#389C22×C1111yescharacteristic
266#388—21no—
267#386—21no—
268#380C22×C1111yescharacteristic
269C4×C4⋊C4C22×C1111yescharacteristic
270C4×C22⋊C4—21no—
271#340C22×C1112yes—
272#340C22×C1112yes—
273#340C22×C1112yes—
274#340C22×C1112yes—
275#336C22×C1111yescharacteristic
276#336C22×C1111yescharacteristic
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11C2×#12011yescharacteristic
292C22×C11C2×C22⋊Q811yescharacteristic
293C22×C11#53611yescharacteristic
294C22×C11C2×#13511yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C11#57511yescharacteristic
297C22×C11#57511yescharacteristic
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—44no—
305C4×C11—44no—
306C4×C11—81no—
307C4×C11—81no—
308C4×C11#54812yes—
309C4×C11D4×Q812yes—
310C22×Q8—21no—
311C22×Q8—21no—
312C22×D4—21no—
313C22×D4C23×C1111yescharacteristic
314C23×C4—21no—
315C23×C4D4×C1111yescharacteristic
316C23×C4D4×C1111yescharacteristic
317C23×C4C23×C1111yescharacteristic
318C22×C8C23×C1112yes—
319C22×C8C23×C1112yes—
320C4⋊Q8—24no—
321C4⋊Q8—24no—
322#125—24no—
323#125D4×C1118yescomplemented
324C22⋊Q8—28no—
325C22⋊Q8—28no—
326#121—22no—
327#121Q8×C1114yescomplemented
328C4×Q8—28no—
329C4×Q8—28no—
330C4×D4—24no—
331C4×D4—44no—
332#117—24no—
333#117—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4C23×C1111yescharacteristic
340C2×C4⋊C4C23×C1111yescharacteristic
341C2×C4⋊C4C23×C1112yes—
342C2×C4⋊C4C23×C1112yes—
343C2×C4⋊C4C23×C1111yescharacteristic
344C2×C22⋊C4—22no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—21no—
353C2×C42D4×C1111yescharacteristic
354C2×C42D4×C1111yescharacteristic
355C2×C42C23×C1111yescharacteristic
356C2×C42C23×C1111yescharacteristic
357#107—24no—
358#106—24no—
359C4⋊C8—24no—
360#102—24no—
361#102—24no—
362C22⋊C8—24no—
363#95—21no—
364#95—21no—
365#95—21no—
366C2×C11—42no—
367C2×C11—82no—
368C2×C11#240911yescharacteristic
369C2×C11#300211yescharacteristic
370C2×C11#300611yescharacteristic
371C2×C11#307611yescharacteristic
372C2×C11#307711yescharacteristic
373C2×C11#322811yescharacteristic
374C2×C11#324011yescharacteristic
375C24—21no—
376C24C2×D4×C1111yescharacteristic
377C2×Q8—24no—
378C2×Q8—24no—
379C2×Q8—42no—
380C2×Q8—42no—
381C2×Q8—42no—
382C2×Q8—42no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4C2×Q8×C1112yes—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C2×D4×C1111yescharacteristic
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×Q8×C1112yes—
412C22×C4C11×#4112yes—
413C22×C4C24×C1111yescharacteristic
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—28no—
423C4⋊C4—28no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—42no—
430C4⋊C4C2×D4×C1114yes—
431C4⋊C4C2×D4×C1114yes—
432C4⋊C4C2×Q8×C1112yes—
433C22⋊C4—28no—
434C22⋊C4—24no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C42—28no—
440C42—22no—
441C42—22no—
442C42—22no—
443C42—42no—
444C42C2×D4×C1114yes—
445C11#2430411yescharacteristic, direct product factor, Sylow
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—22no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23C11×C22⋊Q812yes—
460C23C22×D4×C1111yescharacteristic
461Q8—48no—
462Q8—48no—
463D4—24no—
464D4—48no—
465D4—42no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—84no—
496C2×C4C11×#12012yes—
497C2×C4C11×#12012yes—
498C2×C4C11×C22⋊Q812yes—
499C2×C4C11×#13512yes—
500C2×C4C11×AGL(1,ℤ/8)12yes—
501C2×C4C22×D4×C1112yes—
502C2×C4C22×Q8×C1111yescharacteristic
503C2×C4C2×C11×#4111yescharacteristic
504C2×C4C11×2−1+412yes—
505C8—42no—
506C8—42no—
507C22—22no—
508C22—22no—
509C22—22no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22C2×C11×#12011yescharacteristic
522C22C2×C11×C22⋊Q811yescharacteristic
523C22C11×#53611yescharacteristic
524C22C2×C11×#13511yescharacteristic
525C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
526C22C11×#57511yescharacteristic
527C22C11×#57511yescharacteristic
528C4—22no—
529C4—22no—
530C4—22no—
531C4—22no—
532C4—22no—
533C4—44no—
534C4—44no—
535C4—42no—
536C4—81no—
537C4—81no—
538C4C11×#54812yes—
539C4D4×Q8×C1112yes—
540C2—42no—
541C2—82no—
542C2C11×#240911yescharacteristic
543C2C11×#300211yescharacteristic
544C2C11×#300611yescharacteristic
545C2C11×#307611yescharacteristic
546C2C11×#307711yescharacteristic
547C2C11×#322811yescharacteristic
548C2C11×#324011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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
1. C2×C11×#533C2semidirect
2. C2×C11×#478C2semidirect
4. C11×#2058C2semidirect
5. C11×#2057C2semidirect
6. C11×#2023C2semidirect
7. C11×#2023C2semidirect
8. C11×#1989C2semidirect
10. C11×#1854C2semidirect
11. C11×#1797C2semidirect
58. C11×#125D4semidirect
62. C11×#121Q8semidirect
101. #24304C11direct (N × H)
172. C2×#533C2×C11semidirect
173. C2×#478C2×C11semidirect
175. #2058C2×C11semidirect
176. #2057C2×C11semidirect
177. #2023C2×C11semidirect
178. #2023C2×C11semidirect
179. #1989C2×C11semidirect
181. #1854C2×C11semidirect
182. #1797C2×C11semidirect
323. #125D4×C11semidirect
327. #121Q8×C11semidirect
445. C11#24304direct (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×#4782
C4×C11×#1212
C11×#20582
C11×#20572
C11×#20232
C11×#19892
C11×#18752
C11×#18542
C11×#17972
#2430411