Finite Group Databasebeta

← C11×#24521 #14601714

Subgroups — C11×#24521 #14601714

Order 2816.

976 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
1C11×#3095C211yesmaximal, characteristic, complemented
2C2×C11×#450C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic, complemented
4C2×C11×#418C211yesmaximal, characteristic
5C11×#2063C212yesmaximal, complemented
6C11×#2046C212yesmaximal, complemented
7C11×#1977C212yesmaximal, complemented
8C11×#1931C212yesmaximal, complemented
9C11×#1901C211yesmaximal, characteristic, complemented
10C11×#1855C211yesmaximal, characteristic, complemented
11C11×#1783C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C22×C11×M16C2211yescharacteristic
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C11×#485—21no—
18C11×#485—21no—
19C11×#484—21no—
20C11×#483—21no—
21C11×#450—21no—
22C11×#450—21no—
23C11×#450—22no—
24C11×#433—22no—
25C11×#432—21no—
26C11×#431—21no—
27C2×C11×#108C2212yescomplemented
28C11×#428C2211yescharacteristic, complemented
29C11×#428C2211yescharacteristic, complemented
30C11×#424C2212yescomplemented
31C11×#419C2211yescharacteristic, complemented
32C11×#419C2211yescharacteristic, complemented
33C11×#418—21no—
34C11×#418—21no—
35C11×#418C2212yes—
36C11×#418C2212yes—
37C2×C11×#102—21no—
38C2×C11×#102—21no—
39C2×C11×#102C2212yes—
40C2×C11×#101C2212yescomplemented
41C2×C11×#100C2212yes—
42C2×C11×#100C2212yes—
43C11×#407C2211yescharacteristic
44C11×#407C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C11×#405C2212yescomplemented
47C11×#343C2212yescomplemented
48C11×#341C2212yescomplemented
49C25×C11—21no—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—42no—
58C22×D4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C2×C11×SD16—24no—
61C2×C11×SD16—22no—
62C2×C11×SD16—22no—
63C2×C11×SD16—42no—
64C2×C11×M16—21no—
65C2×C11×M16—42no—
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2312yes—
68C2×C11×M16C2312yes—
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11—21no—
71C22×C8×C11C2312yes—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117D411yescharacteristic
79C11×#117D411yescharacteristic
80C11×#117C2311yescharacteristic
81C11×#117C2311yescharacteristic
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C11×#108—42no—
90C11×#107—21no—
91C11×#107—21no—
92C11×#106—21no—
93C11×#106—21no—
94C11×C4⋊C8—22no—
95C11×C4⋊C8—22no—
96C11×#103—21no—
97C11×#103—21no—
98C11×#103—21no—
99C11×#103—21no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#102—22no—
106C11×#101—42no—
107C11×#100—24no—
108C11×#100—42no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8D411yescharacteristic
114C11×C22⋊C8D411yescharacteristic
115C11×C22⋊C8D412yes—
116C11×#97—22no—
117C4×C8×C11—22no—
118#24521C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—22no—
120C24×C11—44no—
121C24×C11—41no—
122C24×C11—41no—
123C24×C11—82no—
124C24×C11—82no—
125C24×C11#4111yescharacteristic
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—44no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11#4114yes—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C11×SD16—44no—
158C11×SD16—44no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—42no—
166C2×C8×C11—22no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—42no—
173C2×C8×C11C2×D412yes—
174C2×C8×C11C2×D412yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195#3095C2×C1111yescharacteristic, complemented
196C2×#450C2×C1111yescharacteristic
197#2924C2×C1111yescharacteristic, complemented
198C2×#418C2×C1111yescharacteristic
199#2063C2×C1112yescomplemented
200#2046C2×C1112yescomplemented
201#1977C2×C1112yescomplemented
202#1931C2×C1112yescomplemented
203#1901C2×C1111yescharacteristic, complemented
204#1855C2×C1111yescharacteristic, complemented
205#1783C2×C1111yescharacteristic
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—41no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—82no—
215C23×C11—82no—
216C23×C11—82no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—816no—
220C23×C11—82no—
221C23×C11#12111yescharacteristic
222C23×C11#12111yescharacteristic
223C23×C11C2×#4111yescharacteristic
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—42no—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—44no—
230D4×C11—44no—
231D4×C11—42no—
232D4×C11—42no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—81no—
249C2×C4×C11—81no—
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4112yes—
255C2×C4×C11H(5,𝔽2)12yes—
256C8×C11—22no—
257C8×C11—22no—
258C8×C11—41no—
259C8×C11—42no—
260C8×C11—41no—
261C8×C11—42no—
262C23×D4C22×C1111yescharacteristic
263C22×SD16C22×C1112yes—
264C22×M16C22×C1111yescharacteristic
265C2×C22⋊Q8C22×C1111yescharacteristic
266C2×#117C22×C1111yescharacteristic
267#485—21no—
268#485—21no—
269#484—21no—
270#483—21no—
271#450—21no—
272#450—21no—
273#450—22no—
274#433—22no—
275#432—21no—
276#431—21no—
277C2×#108C22×C1112yescomplemented
278#428C22×C1111yescharacteristic, complemented
279#428C22×C1111yescharacteristic, complemented
280#424C22×C1112yescomplemented
281#419C22×C1111yescharacteristic, complemented
282#419C22×C1111yescharacteristic, complemented
283#418—21no—
284#418—21no—
285#418C22×C1112yes—
286#418C22×C1112yes—
287C2×#102—21no—
288C2×#102—21no—
289C2×#102C22×C1112yes—
290C2×#101C22×C1112yescomplemented
291C2×#100C22×C1112yes—
292C2×#100C22×C1112yes—
293#407C22×C1111yescharacteristic
294#407C22×C1111yescharacteristic
295C2×C22⋊C8C22×C1111yescharacteristic
296#405C22×C1112yescomplemented
297#343C22×C1112yescomplemented
298#341C22×C1112yescomplemented
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—84no—
309C22×C11—84no—
310C22×C11—88no—
311C22×C11—88no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11#47112yes—
315C22×C11C2×#12111yescharacteristic
316C22×C11#55112yes—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—41no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11—41no—
323C4×C11—81no—
324C4×C11—81no—
325C4×C11#52511yescharacteristic
326C4×C11#53511yescharacteristic
327C4×C11#54612yes—
328C25—21no—
329C22×Q8C23×C1111yescharacteristic
330C22×D4—24no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—42no—
337C22×D4C23×C1112yes—
338C23×C4C23×C1111yescharacteristic
339C2×SD16—24no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16—42no—
343C2×M16—21no—
344C2×M16—42no—
345C2×M16C23×C1112yes—
346C2×M16C23×C1111yescharacteristic
347C2×M16C23×C1112yes—
348C2×M16C23×C1111yescharacteristic
349C22×C8—21no—
350C22×C8C23×C1112yes—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355#117—21no—
356#117—21no—
357#117D4×C1111yescharacteristic
358#117D4×C1111yescharacteristic
359#117C23×C1111yescharacteristic
360#117C23×C1111yescharacteristic
361C2×C4⋊C4—21no—
362C2×C4⋊C4D4×C1111yescharacteristic
363C2×C4⋊C4D4×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C42—21no—
368#108—42no—
369#107—21no—
370#107—21no—
371#106—21no—
372#106—21no—
373C4⋊C8—22no—
374C4⋊C8—22no—
375#103—21no—
376#103—21no—
377#103—21no—
378#103—21no—
379#102—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385#101—42no—
386#100—24no—
387#100—42no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8D4×C1111yescharacteristic
393C22⋊C8D4×C1111yescharacteristic
394C22⋊C8D4×C1112yes—
395#97—22no—
396C4×C8—22no—
397C2×C11—22no—
398C2×C11—22no—
399C2×C11—41no—
400C2×C11—84no—
401C2×C11#241111yescharacteristic
402C2×C11C2×#47111yescharacteristic
403C2×C11#306811yescharacteristic
404C24—22no—
405C24—44no—
406C24—41no—
407C24—41no—
408C24—82no—
409C24—82no—
410C24C11×#4111yescharacteristic
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4C11×#4114yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C11×#4111yescharacteristic
441C22×C4C24×C1111yescharacteristic
442SD16—44no—
443SD16—44no—
444M16—22no—
445M16—22no—
446M16—22no—
447M16—22no—
448M16—22no—
449M16—22no—
450M16—42no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—22no—
457C2×C8—42no—
458C2×C8C2×D4×C1112yes—
459C2×C8C2×D4×C1112yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×D4×C1111yescharacteristic
467C4⋊C4C2×D4×C1111yescharacteristic
468C4⋊C4C2×D4×C1111yescharacteristic
469C4⋊C4C2×D4×C1111yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C11#2452111yescharacteristic, direct product factor, Sylow
481C23—22no—
482C23—22no—
483C23—24no—
484C23—41no—
485C23—44no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—82no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23—82no—
494C23—816no—
495C23—82no—
496C23C11×#12111yescharacteristic
497C23C11×#12111yescharacteristic
498C23C2×C11×#4111yescharacteristic
499Q8—41no—
500Q8—41no—
501Q8—42no—
502D4—24no—
503D4—24no—
504D4—44no—
505D4—44no—
506D4—42no—
507D4—42no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—81no—
524C2×C4—81no—
525C2×C4C11×#12111yescharacteristic
526C2×C4C11×#12111yescharacteristic
527C2×C4C22×D4×C1111yescharacteristic
528C2×C4C22×D4×C1111yescharacteristic
529C2×C4C2×C11×#4112yes—
530C2×C4C11×H(5,𝔽2)12yes—
531C8—22no—
532C8—22no—
533C8—41no—
534C8—42no—
535C8—41no—
536C8—42no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—44no—
545C22—44no—
546C22—84no—
547C22—84no—
548C22—88no—
549C22—88no—
550C22—82no—
551C22—82no—
552C22C11×#47112yes—
553C22C2×C11×#12111yescharacteristic
554C22C11×#55112yes—
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4C11×#52511yescharacteristic
564C4C11×#53511yescharacteristic
565C4C11×#54612yes—
566C2—22no—
567C2—22no—
568C2—41no—
569C2—84no—
570C2C11×#241111yescharacteristic
571C2C2×C11×#47111yescharacteristic
572C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3095C2semidirect
3. C11×#2924C2semidirect
5. C11×#2063C2semidirect
6. C11×#2046C2semidirect
7. C11×#1977C2semidirect
8. C11×#1931C2semidirect
9. C11×#1901C2semidirect
10. C11×#1855C2semidirect
27. C2×C11×#108C22semidirect
28. C11×#428C22semidirect
29. C11×#428C22semidirect
30. C11×#424C22semidirect
31. C11×#419C22semidirect
32. C11×#419C22semidirect
40. C2×C11×#101C22semidirect
46. C11×#405C22semidirect
47. C11×#343C22semidirect
48. C11×#341C22semidirect
118. #24521C11direct (N × H)
195. #3095C2×C11semidirect
197. #2924C2×C11semidirect
199. #2063C2×C11semidirect
200. #2046C2×C11semidirect
201. #1977C2×C11semidirect
202. #1931C2×C11semidirect
203. #1901C2×C11semidirect
204. #1855C2×C11semidirect
277. C2×#108C22×C11semidirect
278. #428C22×C11semidirect
279. #428C22×C11semidirect
280. #424C22×C11semidirect
281. #419C22×C11semidirect
282. #419C22×C11semidirect
290. C2×#101C22×C11semidirect
296. #405C22×C11semidirect
297. #343C22×C11semidirect
298. #341C22×C11semidirect
480. C11#24521direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30952
C2×C11×#4502
C11×#29242
C2×C11×#4182
C11×#20632
C11×#20462
C11×#19772
C11×#19312
C11×#19012
C11×#18552
C11×#17832
#2452111