Finite Group Databasebeta

← C11×#24128 #14601321

Subgroups — C11×#24128 #14601321

Order 2816.

1400 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C11×#442C211yesmaximal, characteristic, complemented
4C11×#2535C211yesmaximal, characteristic, complemented
5C11×#2034C212yesmaximal, complemented
6C11×#1999C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1955C211yesmaximal, characteristic, complemented
9C11×#1874C212yesmaximal, complemented
10C11×#1853C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×D8C2211yescharacteristic
14C11×#547—24no—
15C11×#547—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×#121C2212yes—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C11×#476—24no—
26C11×#442—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×#97C2211yescharacteristic
37C11×#397—21no—
38C11×#392—21no—
39C11×#386—22no—
40C11×#382C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—48no—
47C22×Q8×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11D411yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—22no—
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11C2312yes—
57C2×C11×D8—22no—
58C2×C11×D8—22no—
59C2×C11×D8—22no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8D414yescomplemented
65C11×#123—216no—
66C11×C22⋊Q8—28no—
67C11×#121—24no—
68C11×#121—24no—
69C11×#121—24no—
70C11×#121—42no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11D414yescomplemented
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4D412yes—
92C2×C42×C11C2311yescharacteristic
93C11×#106—22no—
94C11×#106—24no—
95C11×C4⋊C8—22no—
96C11×#102—22no—
97C11×#102—22no—
98C11×#102—24no—
99C11×#102—42no—
100C11×C22⋊C8—24no—
101C11×C22⋊C8—42no—
102C11×#97—22no—
103C11×#95—22no—
104C11×#95—21no—
105C11×#95—21no—
106#24128C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C24×C11C2×D412yes—
110C11×#41—432no—
111C2×Q8×C11—24no—
112C2×Q8×C11—44no—
113C2×D4×C11—24no—
114C2×D4×C11—28no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—82no—
131C2×D4×C11C2×D412yes—
132C2×D4×C11#4112yescomplemented
133C22×C4×C11—28no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—44no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11—42no—
149C22×C4×C11—82no—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C11×D8—28no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11—21no—
159C2×C8×C11—22no—
160C2×C8×C11—21no—
161C2×C8×C11—22no—
162C2×C8×C11—21no—
163C2×C8×C11#4112yescomplemented
164C11×C4⋊C4—28no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D414yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—44no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—82no—
181C42×C11C2×D412yes—
182C42×C11C2×D412yes—
183C2×#547C2×C1111yescharacteristic, complemented
184C2×#476C2×C1111yescharacteristic, complemented
185C2×#442C2×C1111yescharacteristic, complemented
186#2535C2×C1111yescharacteristic, complemented
187#2034C2×C1112yescomplemented
188#1999C2×C1112yescomplemented
189#1993C2×C1111yescharacteristic, complemented
190#1955C2×C1111yescharacteristic, complemented
191#1874C2×C1112yescomplemented
192#1853C2×C1112yescomplemented
193#1804C2×C1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11AGL(1,ℤ/8)14yes—
211C23×C11C22×D411yescharacteristic
212Q8×C11—48no—
213D4×C11—28no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—416no—
219D4×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—88no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—48no—
232C2×C4×C11—416no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—84no—
246C2×C4×C11#12012yes—
247C2×C4×C11#12012yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C8×C11—22no—
255C8×C11—41no—
256C8×C11—42no—
257C22×#41—21no—
258C22×D8C22×C1111yescharacteristic
259#547—24no—
260#547—24no—
261C2×C4⋊Q8C22×C1111yescharacteristic
262C2×#123—22no—
263C2×C22⋊Q8—21no—
264C2×#121C22×C1112yes—
265C2×#121C22×C1112yes—
266C2×C4×D4C22×C1111yescharacteristic
267C2×C4×D4C22×C1111yescharacteristic
268C2×C4×D4C22×C1111yescharacteristic
269C22×C4⋊C4C22×C1112yes—
270#476—24no—
271#442—24no—
272C2×#106C22×C1111yescharacteristic
273C2×#106C22×C1112yes—
274C2×C4⋊C8C22×C1111yescharacteristic
275C2×#102C22×C1111yescharacteristic
276C2×#102C22×C1112yes—
277C2×#102C22×C1111yescharacteristic
278C2×#102C22×C1112yes—
279C2×C22⋊C8C22×C1112yes—
280C2×C22⋊C8C22×C1112yes—
281C2×#97C22×C1111yescharacteristic
282#397—21no—
283#392—21no—
284#386—22no—
285#382C22×C1111yescharacteristic
286#380C22×C1112yes—
287#340C22×C1112yes—
288#340C22×C1112yes—
289#340C22×C1112yes—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—44no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—82no—
307C22×C11C2×#12011yescharacteristic
308C22×C11#54611yescharacteristic
309C22×C11#54711yescharacteristic
310C22×C11C2×AGL(1,ℤ/8)12yes—
311C22×C11#57712yes—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—44no—
317C4×C11—81no—
318C4×C11—82no—
319C4×C11#52511yescharacteristic
320C4×C11#53711yescharacteristic
321C4×C11#54811yescharacteristic
322C4×C11#55011yescharacteristic
323C2×#41—28no—
324C2×#41—48no—
325C22×Q8—21no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4D4×C1111yescharacteristic
329C22×D4C23×C1111yescharacteristic
330C22×D4C23×C1111yescharacteristic
331C23×C4—22no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4C23×C1112yes—
335C2×D8—22no—
336C2×D8—22no—
337C2×D8—22no—
338C22×C8C23×C1111yescharacteristic
339C22×C8C23×C1112yes—
340C22×C8C23×C1111yescharacteristic
341C4⋊Q8—22no—
342C4⋊Q8D4×C1114yescomplemented
343#123—216no—
344C22⋊Q8—28no—
345#121—24no—
346#121—24no—
347#121—24no—
348#121—42no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4D4×C1114yescomplemented
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4D4×C1111yescharacteristic
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1112yes—
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1112yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4D4×C1112yes—
370C2×C42C23×C1111yescharacteristic
371#106—22no—
372#106—24no—
373C4⋊C8—22no—
374#102—22no—
375#102—22no—
376#102—24no—
377#102—42no—
378C22⋊C8—24no—
379C22⋊C8—42no—
380#97—22no—
381#95—22no—
382#95—21no—
383#95—21no—
384C2×C11—44no—
385C2×C11—82no—
386C2×C11—82no—
387C2×C11#240711yescharacteristic
388C2×C11#300311yescharacteristic
389C2×C11#301011yescharacteristic
390C2×C11#330612yes—
391C2×C11#334512yes—
392C24—21no—
393C24—21no—
394C24C2×D4×C1112yes—
395#41—432no—
396C2×Q8—24no—
397C2×Q8—44no—
398C2×D4—24no—
399C2×D4—28no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—82no—
416C2×D4C2×D4×C1112yes—
417C2×D4C11×#4112yescomplemented
418C22×C4—28no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—42no—
434C22×C4—82no—
435C22×C4C2×D4×C1112yes—
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C24×C1111yescharacteristic
439D8—28no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—21no—
446C2×C8—22no—
447C2×C8—21no—
448C2×C8C11×#4112yescomplemented
449C4⋊C4—28no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4C2×D4×C1112yes—
459C4⋊C4C2×D4×C1114yes—
460C22⋊C4—28no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—44no—
464C22⋊C4—42no—
465C22⋊C4—82no—
466C42C2×D4×C1112yes—
467C42C2×D4×C1112yes—
468C11#2412811yescharacteristic, direct product factor, Sylow
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23C11×AGL(1,ℤ/8)14yes—
486C23C22×D4×C1111yescharacteristic
487Q8—48no—
488D4—28no—
489D4—22no—
490D4—22no—
491D4—22no—
492D4—22no—
493D4—416no—
494D4—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498D4—88no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—48no—
507C2×C4—416no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—84no—
521C2×C4C11×#12012yes—
522C2×C4C11×#12012yes—
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C2×C11×#4111yescharacteristic
526C2×C4C2×C11×#4111yescharacteristic
527C2×C4C11×H(5,𝔽2)11yescharacteristic
528C2×C4C11×2−1+411yescharacteristic
529C8—22no—
530C8—41no—
531C8—42no—
532C22—24no—
533C22—24no—
534C22—24no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—81no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22C2×C11×#12011yescharacteristic
550C22C11×#54611yescharacteristic
551C22C11×#54711yescharacteristic
552C22C2×C11×AGL(1,ℤ/8)12yes—
553C22C11×#57712yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—42no—
558C4—44no—
559C4—81no—
560C4—82no—
561C4C11×#52511yescharacteristic
562C4C11×#53711yescharacteristic
563C4C11×#54811yescharacteristic
564C4C11×#55011yescharacteristic
565C2—44no—
566C2—82no—
567C2—82no—
568C2C11×#240711yescharacteristic
569C2C11×#300311yescharacteristic
570C2C11×#301011yescharacteristic
571C2C11×#330612yes—
572C2C11×#334512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#547C2semidirect
2. C2×C11×#476C2semidirect
3. C2×C11×#442C2semidirect
4. C11×#2535C2semidirect
5. C11×#2034C2semidirect
6. C11×#1999C2semidirect
7. C11×#1993C2semidirect
8. C11×#1955C2semidirect
9. C11×#1874C2semidirect
10. C11×#1853C2semidirect
11. C11×#1804C2semidirect
64. C11×C4⋊Q8D4semidirect
76. C4×D4×C11D4semidirect
106. #24128C11direct (N × H)
132. C2×D4×C11#41semidirect
163. C2×C8×C11#41semidirect
183. C2×#547C2×C11semidirect
184. C2×#476C2×C11semidirect
185. C2×#442C2×C11semidirect
186. #2535C2×C11semidirect
187. #2034C2×C11semidirect
188. #1999C2×C11semidirect
189. #1993C2×C11semidirect
190. #1955C2×C11semidirect
191. #1874C2×C11semidirect
192. #1853C2×C11semidirect
193. #1804C2×C11semidirect
342. C4⋊Q8D4×C11semidirect
354. C4×D4D4×C11semidirect
417. C2×D4C11×#41semidirect
448. C2×C8C11×#41semidirect
468. C11#24128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4762
C2×C11×#4422
C11×#25352
C11×#20342
C11×#19992
C11×#19932
C11×#19552
C11×#18742
C11×#18532
C11×#18042
#2412811