Finite Group Databasebeta

← C11×#24670 #14601863

Subgroups — C11×#24670 #14601863

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3038C211yesmaximal, characteristic, complemented
2C2×C11×#459C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C11×#2925C211yesmaximal, characteristic, complemented
5C11×#2051C212yesmaximal, complemented
6C11×#2018C212yesmaximal, complemented
7C11×#1978C212yesmaximal, complemented
8C11×#1965C211yesmaximal, characteristic, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1931C212yesmaximal, complemented
11C11×#1800C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C22×C11×D8C2212yes—
15C2×C11×#127C2211yescharacteristic
16C4×C11×#41C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#460—21no—
19C11×#460—21no—
20C11×#459—21no—
21C11×#459—21no—
22C11×#459—21no—
23C11×#459—21no—
24C11×#459—22no—
25C11×#442—21no—
26C11×#440—21no—
27C4×C11×SD16—21no—
28C4×C11×D8—21no—
29C11×#433—22no—
30C11×#432—21no—
31C11×#431—21no—
32C2×C11×#108C2212yes—
33C11×#428C2211yescharacteristic
34C11×#423C2211yescharacteristic
35C11×#423C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C11×#418C2211yescharacteristic
38C11×#418C2212yes—
39C11×#417C2211yescharacteristic
40C2×C11×#102C2212yes—
41C2×C11×#100C2212yes—
42C2×C11×#100C2212yes—
43C2×C11×#100C2212yes—
44C11×#408C2212yes—
45C11×#405C2212yes—
46C4×C11×M16C2211yescharacteristic
47C11×#343C2212yes—
48C11×#341C2212yes—
49C2×C11×#41C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11C2312yes—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C11×AGL(1,ℤ/8)—22no—
56C11×AGL(1,ℤ/8)—22no—
57C11×AGL(1,ℤ/8)—42no—
58C11×AGL(1,ℤ/8)—42no—
59C2×C11×SD16—21no—
60C2×C11×SD16—22no—
61C2×C11×D8—21no—
62C2×C11×D8—22no—
63C2×C11×D8—24no—
64C2×C11×D8—22no—
65C2×C11×D8—22no—
66C2×C11×D8—42no—
67C2×C11×M16C2312yes—
68C2×C11×M16C2312yes—
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11C2312yes—
72C11×#127—21no—
73C11×#127—21no—
74C11×#127—21no—
75C11×#127—21no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11D411yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11D411yescharacteristic
85C4×D4×C11D411yescharacteristic
86C11×#117—21no—
87C11×#117C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×#108—42no—
93C11×#107—21no—
94C11×#106—21no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8D411yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C4⋊C8D412yes—
102C11×#103—21no—
103C11×#102—21no—
104C11×#102—22no—
105C11×#102—22no—
106C11×#102—21no—
107C11×#102—21no—
108C11×#102—22no—
109C11×#102—22no—
110C11×#100—24no—
111C11×#100—42no—
112C11×#100—42no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×#97—22no—
116C11×#97—21no—
117C4×C8×C11—22no—
118C4×C8×C11—21no—
119#24670C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C24×C11—22no—
122C11×#41—21no—
123C11×#41—21no—
124C11×#41—21no—
125C11×#41—21no—
126C2×Q8×C11C2×D411yescharacteristic
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—82no—
144C2×D4×C11—82no—
145C2×D4×C11C2×D411yescharacteristic
146C2×D4×C11#4112yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11—82no—
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C11×SD16—24no—
158C11×SD16—44no—
159C11×D8—24no—
160C11×D8—44no—
161C11×D8—44no—
162C11×D8—44no—
163C11×M16—21no—
164C11×M16—22no—
165C11×M16—21no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—21no—
169C11×M16—22no—
170C11×M16#4112yes—
171C2×C8×C11—21no—
172C2×C8×C11—22no—
173C2×C8×C11—21no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11C2×D412yes—
178C2×C8×C11C2×D412yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197#3038C2×C1111yescharacteristic, complemented
198C2×#459C2×C1111yescharacteristic, complemented
199C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
200#2925C2×C1111yescharacteristic, complemented
201#2051C2×C1112yescomplemented
202#2018C2×C1112yescomplemented
203#1978C2×C1112yescomplemented
204#1965C2×C1111yescharacteristic, complemented
205#1950C2×C1111yescharacteristic, complemented
206#1931C2×C1112yescomplemented
207#1800C2×C1111yescharacteristic, complemented
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—81no—
216C23×C11—81no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11C2×#4111yescharacteristic
220Q8×C11—21no—
221Q8×C11—21no—
222D4×C11—21no—
223D4×C11—22no—
224D4×C11—21no—
225D4×C11—22no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—42no—
229D4×C11—41no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—41no—
233D4×C11—42no—
234D4×C11—82no—
235D4×C11—82no—
236D4×C11—82no—
237D4×C11—82no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—81no—
248C2×C4×C11—82no—
249C2×C4×C11—82no—
250C2×C4×C11—81no—
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C8×C11—22no—
262C8×C11—22no—
263C8×C11—22no—
264C8×C11—41no—
265C8×C11—42no—
266C8×C11—42no—
267C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
268C2×AGL(1,ℤ/8)C22×C1112yes—
269C22×D8C22×C1112yes—
270C2×#127C22×C1111yescharacteristic
271C4×#41C22×C1111yescharacteristic
272C2×C4×D4C22×C1111yescharacteristic
273#460—21no—
274#460—21no—
275#459—21no—
276#459—21no—
277#459—21no—
278#459—21no—
279#459—22no—
280#442—21no—
281#440—21no—
282C4×SD16—21no—
283C4×D8—21no—
284#433—22no—
285#432—21no—
286#431—21no—
287C2×#108C22×C1112yes—
288#428C22×C1111yescharacteristic
289#423C22×C1111yescharacteristic
290#423C22×C1111yescharacteristic
291C2×C4⋊C8C22×C1111yescharacteristic
292#418C22×C1111yescharacteristic
293#418C22×C1112yes—
294#417C22×C1111yescharacteristic
295C2×#102C22×C1112yes—
296C2×#100C22×C1112yes—
297C2×#100C22×C1112yes—
298C2×#100C22×C1112yes—
299#408C22×C1112yes—
300#405C22×C1112yes—
301C4×M16C22×C1111yescharacteristic
302#343C22×C1112yes—
303#341C22×C1112yes—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—41no—
307C22×C11—42no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—162no—
318C22×C11—162no—
319C22×C11C2×#12111yescharacteristic
320C22×C11#55311yescharacteristic
321C22×C11#55511yescharacteristic
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—81no—
329C4×C11#47212yes—
330C4×C11#52511yescharacteristic
331C4×C11#53511yescharacteristic
332C4×C11#54611yescharacteristic
333C4×C11#55011yescharacteristic
334C2×#41C23×C1111yescharacteristic
335C22×D4—21no—
336C22×D4—21no—
337C22×D4C23×C1112yes—
338C22×D4C23×C1111yescharacteristic
339C23×C4—21no—
340AGL(1,ℤ/8)—22no—
341AGL(1,ℤ/8)—22no—
342AGL(1,ℤ/8)—42no—
343AGL(1,ℤ/8)—42no—
344C2×SD16—21no—
345C2×SD16—22no—
346C2×D8—21no—
347C2×D8—22no—
348C2×D8—24no—
349C2×D8—22no—
350C2×D8—22no—
351C2×D8—42no—
352C2×M16C23×C1112yes—
353C2×M16C23×C1112yes—
354C2×M16C23×C1111yescharacteristic
355C2×M16C23×C1111yescharacteristic
356C22×C8C23×C1112yes—
357#127—21no—
358#127—21no—
359#127—21no—
360#127—21no—
361C4×Q8D4×C1111yescharacteristic
362C4×Q8D4×C1111yescharacteristic
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4D4×C1111yescharacteristic
370C4×D4D4×C1111yescharacteristic
371#117—21no—
372#117C23×C1111yescharacteristic
373C2×C4⋊C4C23×C1111yescharacteristic
374C2×C22⋊C4—21no—
375C2×C42—21no—
376C2×C42C23×C1111yescharacteristic
377#108—42no—
378#107—21no—
379#106—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8D4×C1111yescharacteristic
385C4⋊C8D4×C1111yescharacteristic
386C4⋊C8D4×C1112yes—
387#103—21no—
388#102—21no—
389#102—22no—
390#102—22no—
391#102—21no—
392#102—21no—
393#102—22no—
394#102—22no—
395#100—24no—
396#100—42no—
397#100—42no—
398C22⋊C8—22no—
399C22⋊C8—22no—
400#97—22no—
401#97—21no—
402C4×C8—22no—
403C4×C8—21no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—81no—
407C2×C11—82no—
408C2×C11—162no—
409C2×C11#241411yescharacteristic
410C2×C11C2×#47211yescharacteristic
411C2×C11#306811yescharacteristic
412C24—21no—
413C24—22no—
414#41—21no—
415#41—21no—
416#41—21no—
417#41—21no—
418C2×Q8C2×D4×C1111yescharacteristic
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—82no—
436C2×D4—82no—
437C2×D4C2×D4×C1111yescharacteristic
438C2×D4C11×#4112yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—82no—
446C22×C4C11×#4111yescharacteristic
447C22×C4C11×#4111yescharacteristic
448C22×C4C24×C1111yescharacteristic
449SD16—24no—
450SD16—44no—
451D8—24no—
452D8—44no—
453D8—44no—
454D8—44no—
455M16—21no—
456M16—22no—
457M16—21no—
458M16—22no—
459M16—22no—
460M16—21no—
461M16—22no—
462M16C11×#4112yes—
463C2×C8—21no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—21no—
468C2×C8—22no—
469C2×C8C2×D4×C1112yes—
470C2×C8C2×D4×C1112yes—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4C2×D4×C1111yescharacteristic
476C4⋊C4C2×D4×C1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42C2×D4×C1111yescharacteristic
486C42C2×D4×C1111yescharacteristic
487C42C2×D4×C1111yescharacteristic
488C42C2×D4×C1111yescharacteristic
489C11#2467011yescharacteristic, direct product factor, Sylow
490C23—21no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—81no—
498C23—81no—
499C23—82no—
500C23—82no—
501C23C2×C11×#4111yescharacteristic
502Q8—21no—
503Q8—21no—
504D4—21no—
505D4—22no—
506D4—21no—
507D4—22no—
508D4—41no—
509D4—41no—
510D4—42no—
511D4—41no—
512D4—42no—
513D4—42no—
514D4—41no—
515D4—42no—
516D4—82no—
517D4—82no—
518D4—82no—
519D4—82no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—81no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—81no—
533C2×C4C11×#12111yescharacteristic
534C2×C4C11×#12111yescharacteristic
535C2×C4C11×#12111yescharacteristic
536C2×C4C11×#12111yescharacteristic
537C2×C4C22×D4×C1111yescharacteristic
538C2×C4C22×D4×C1111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C2×C4C2×C11×#4111yescharacteristic
541C2×C4C11×H(5,𝔽2)11yescharacteristic
542C2×C4C11×H(5,𝔽2)11yescharacteristic
543C8—22no—
544C8—22no—
545C8—22no—
546C8—42no—
547C8—41no—
548C8—42no—
549C22—21no—
550C22—21no—
551C22—41no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—82no—
556C22—82no—
557C22—81no—
558C22—81no—
559C22—82no—
560C22—82no—
561C22—82no—
562C22—162no—
563C22—162no—
564C22C2×C11×#12111yescharacteristic
565C22C11×#55311yescharacteristic
566C22C11×#55511yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4C11×#47212yes—
575C4C11×#52511yescharacteristic
576C4C11×#53511yescharacteristic
577C4C11×#54611yescharacteristic
578C4C11×#55011yescharacteristic
579C2—21no—
580C2—21no—
581C2—81no—
582C2—82no—
583C2—162no—
584C2C11×#241411yescharacteristic
585C2C2×C11×#47211yescharacteristic
586C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3038C2semidirect
2. C2×C11×#459C2semidirect
3. C4×C11×AGL(1,ℤ/8)C2semidirect
4. C11×#2925C2semidirect
5. C11×#2051C2semidirect
6. C11×#2018C2semidirect
7. C11×#1978C2semidirect
8. C11×#1965C2semidirect
9. C11×#1950C2semidirect
10. C11×#1931C2semidirect
11. C11×#1800C2semidirect
119. #24670C11direct (N × H)
197. #3038C2×C11semidirect
198. C2×#459C2×C11semidirect
199. C4×AGL(1,ℤ/8)C2×C11semidirect
200. #2925C2×C11semidirect
201. #2051C2×C11semidirect
202. #2018C2×C11semidirect
203. #1978C2×C11semidirect
204. #1965C2×C11semidirect
205. #1950C2×C11semidirect
206. #1931C2×C11semidirect
207. #1800C2×C11semidirect
489. C11#24670direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30382
C2×C11×#4592
C4×C11×AGL(1,ℤ/8)2
C11×#29252
C11×#20512
C11×#20182
C11×#19782
C11×#19652
C11×#19502
C11×#19312
C11×#18002
#2467011