Finite Group Databasebeta

← C11×#24671 #14601864

Subgroups — C11×#24671 #14601864

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3039C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C11×#2925C211yesmaximal, characteristic, complemented
5C11×#2052C212yesmaximal, complemented
6C11×#2019C212yesmaximal
7C11×#1977C212yesmaximal, complemented
8C11×#1966C211yesmaximal, characteristic, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1930C212yesmaximal, complemented
11C11×#1800C211yesmaximal, characteristic, complemented
12C2×C11×#137C2212yes—
13C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C4×C11×#41C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#462—21no—
19C11×#462—21no—
20C11×#461—21no—
21C11×#461—21no—
22C11×#461—21no—
23C11×#461—21no—
24C11×#461—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×#419C2212yes—
38C11×#418C2211yescharacteristic
39C11×#417C2211yescharacteristic
40C2×C11×#103C2212yes—
41C2×C11×#101C2212yes—
42C2×C11×#101C2212yes—
43C2×C11×#100C2212yes—
44C11×#408C2212yes—
45C11×#405C2212yes—
46C4×C11×M16C2211yescharacteristic
47C11×#343C2212yes—
48C11×#341C2212yes—
49C2×C11×#41C2311yescharacteristic
50C22×Q8×C11C2312yes—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C11×#137—42no—
54C11×#137—42no—
55C11×AGL(1,ℤ/8)—22no—
56C11×AGL(1,ℤ/8)—22no—
57C2×C11×Q16—22no—
58C2×C11×SD16—21no—
59C2×C11×SD16—22no—
60C2×C11×SD16—24no—
61C2×C11×SD16—22no—
62C2×C11×SD16—22no—
63C2×C11×SD16—42no—
64C2×C11×D8—21no—
65C2×C11×M16C2312yes—
66C2×C11×M16C2312yes—
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C22×C8×C11C2312yes—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C4×Q8×C11D411yescharacteristic
75C4×Q8×C11D411yescharacteristic
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11D411yescharacteristic
84C11×#117—21no—
85C11×#117C2311yescharacteristic
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
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×#103—22no—
104C11×#103—22no—
105C11×#103—22no—
106C11×#103—22no—
107C11×#102—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×#101—24no—
111C11×#101—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#24671C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C11×#41—21no—
122C11×#41—21no—
123C11×#41—21no—
124C11×#41—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2×D411yescharacteristic
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C2×D411yescharacteristic
139C2×D4×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—82no—
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C11×Q16—44no—
152C11×SD16—24no—
153C11×SD16—44no—
154C11×SD16—44no—
155C11×SD16—44no—
156C11×D8—24no—
157C11×M16—21no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—21no—
162C11×M16—21no—
163C11×M16—22no—
164C11×M16#4112yes—
165C2×C8×C11—21no—
166C2×C8×C11—22no—
167C2×C8×C11—21no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11C2×D412yes—
172C2×C8×C11C2×D412yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195#3039C2×C1111yescharacteristic, complemented
196C2×#461C2×C1111yescharacteristic, complemented
197C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
198#2925C2×C1111yescharacteristic, complemented
199#2052C2×C1112yescomplemented
200#2019C2×C1112yes—
201#1977C2×C1112yescomplemented
202#1966C2×C1111yescharacteristic, complemented
203#1950C2×C1111yescharacteristic, complemented
204#1930C2×C1112yescomplemented
205#1800C2×C1111yescharacteristic, complemented
206C23×C11—21no—
207C23×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—81no—
211C23×C11—81no—
212C23×C11C2×#4111yescharacteristic
213Q8×C11—21no—
214Q8×C11—21no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—42no—
219D4×C11—21no—
220D4×C11—22no—
221D4×C11—21no—
222D4×C11—22no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—81no—
240C2×C4×C11—82no—
241C2×C4×C11—82no—
242C2×C4×C11—81no—
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C8×C11—22no—
254C8×C11—22no—
255C8×C11—22no—
256C8×C11—41no—
257C8×C11—42no—
258C8×C11—42no—
259C2×#137C22×C1112yes—
260C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
261C22×SD16C22×C1112yes—
262C2×C4⋊Q8C22×C1111yescharacteristic
263C4×#41C22×C1111yescharacteristic
264C2×C4×D4C22×C1111yescharacteristic
265#462—21no—
266#462—21no—
267#461—21no—
268#461—21no—
269#461—21no—
270#461—21no—
271#461—22no—
272#442—21no—
273#440—21no—
274C4×SD16—21no—
275C4×D8—21no—
276#433—22no—
277#432—21no—
278#431—21no—
279C2×#108C22×C1112yes—
280#428C22×C1111yescharacteristic
281#423C22×C1111yescharacteristic
282#423C22×C1111yescharacteristic
283C2×C4⋊C8C22×C1111yescharacteristic
284#419C22×C1112yes—
285#418C22×C1111yescharacteristic
286#417C22×C1111yescharacteristic
287C2×#103C22×C1112yes—
288C2×#101C22×C1112yes—
289C2×#101C22×C1112yes—
290C2×#100C22×C1112yes—
291#408C22×C1112yes—
292#405C22×C1112yes—
293C4×M16C22×C1111yescharacteristic
294#343C22×C1112yes—
295#341C22×C1112yes—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—41no—
299C22×C11—42no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11C2×#12111yescharacteristic
307C22×C11#55311yescharacteristic
308C22×C11#55511yescharacteristic
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—41no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11—82no—
316C4×C11—81no—
317C4×C11#47112yes—
318C4×C11#52511yescharacteristic
319C4×C11#53511yescharacteristic
320C4×C11#54611yescharacteristic
321C4×C11#55011yescharacteristic
322C2×#41C23×C1111yescharacteristic
323C22×Q8C23×C1112yes—
324C22×D4C23×C1111yescharacteristic
325C23×C4—21no—
326#137—42no—
327#137—42no—
328AGL(1,ℤ/8)—22no—
329AGL(1,ℤ/8)—22no—
330C2×Q16—22no—
331C2×SD16—21no—
332C2×SD16—22no—
333C2×SD16—24no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×SD16—42no—
337C2×D8—21no—
338C2×M16C23×C1112yes—
339C2×M16C23×C1112yes—
340C2×M16C23×C1111yescharacteristic
341C2×M16C23×C1111yescharacteristic
342C22×C8C23×C1112yes—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4×Q8D4×C1111yescharacteristic
348C4×Q8D4×C1111yescharacteristic
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4D4×C1111yescharacteristic
356C4×D4D4×C1111yescharacteristic
357#117—21no—
358#117C23×C1111yescharacteristic
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C22⋊C4—21no—
363C2×C42—21no—
364C2×C42C23×C1111yescharacteristic
365#108—42no—
366#107—21no—
367#106—21no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8D4×C1111yescharacteristic
373C4⋊C8D4×C1111yescharacteristic
374C4⋊C8D4×C1112yes—
375#103—21no—
376#103—22no—
377#103—22no—
378#103—22no—
379#103—22no—
380#102—21no—
381#102—21no—
382#102—21no—
383#101—24no—
384#101—42no—
385#100—42no—
386C22⋊C8—22no—
387C22⋊C8—22no—
388#97—22no—
389#97—21no—
390C4×C8—22no—
391C4×C8—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—81no—
395C2×C11—82no—
396C2×C11#241411yescharacteristic
397C2×C11C2×#47111yescharacteristic
398C2×C11#306911yescharacteristic
399C24—21no—
400#41—21no—
401#41—21no—
402#41—21no—
403#41—21no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8C2×D4×C1111yescharacteristic
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C2×D4×C1111yescharacteristic
418C2×D4C11×#4112yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—82no—
427C22×C4C11×#4111yescharacteristic
428C22×C4C11×#4111yescharacteristic
429C22×C4C24×C1111yescharacteristic
430Q16—44no—
431SD16—24no—
432SD16—44no—
433SD16—44no—
434SD16—44no—
435D8—24no—
436M16—21no—
437M16—22no—
438M16—22no—
439M16—22no—
440M16—21no—
441M16—21no—
442M16—22no—
443M16C11×#4112yes—
444C2×C8—21no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—21no—
449C2×C8—22no—
450C2×C8C2×D4×C1112yes—
451C2×C8C2×D4×C1112yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4C2×D4×C1111yescharacteristic
461C4⋊C4C2×D4×C1111yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42C2×D4×C1111yescharacteristic
471C42C2×D4×C1111yescharacteristic
472C42C2×D4×C1111yescharacteristic
473C42C2×D4×C1111yescharacteristic
474C11#2467111yescharacteristic, direct product factor, Sylow
475C23—21no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—81no—
480C23—81no—
481C23C2×C11×#4111yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—42no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488D4—21no—
489D4—22no—
490D4—21no—
491D4—22no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—81no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—81no—
512C2×C4C11×#12111yescharacteristic
513C2×C4C11×#12111yescharacteristic
514C2×C4C11×#12111yescharacteristic
515C2×C4C11×#12111yescharacteristic
516C2×C4C22×D4×C1111yescharacteristic
517C2×C4C22×D4×C1111yescharacteristic
518C2×C4C2×C11×#4111yescharacteristic
519C2×C4C2×C11×#4111yescharacteristic
520C2×C4C11×H(5,𝔽2)11yescharacteristic
521C2×C4C11×H(5,𝔽2)11yescharacteristic
522C8—22no—
523C8—22no—
524C8—22no—
525C8—42no—
526C8—41no—
527C8—42no—
528C22—21no—
529C22—21no—
530C22—41no—
531C22—42no—
532C22—41no—
533C22—41no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22C2×C11×#12111yescharacteristic
539C22C11×#55311yescharacteristic
540C22C11×#55511yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—82no—
548C4—81no—
549C4C11×#47112yes—
550C4C11×#52511yescharacteristic
551C4C11×#53511yescharacteristic
552C4C11×#54611yescharacteristic
553C4C11×#55011yescharacteristic
554C2—21no—
555C2—21no—
556C2—81no—
557C2—82no—
558C2C11×#241411yescharacteristic
559C2C2×C11×#47111yescharacteristic
560C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×AGL(1,ℤ/8)C22
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×#3039C2semidirect
2. C2×C11×#461C2semidirect
4. C11×#2925C2semidirect
5. C11×#2052C2semidirect
7. C11×#1977C2semidirect
8. C11×#1966C2semidirect
9. C11×#1950C2semidirect
10. C11×#1930C2semidirect
11. C11×#1800C2semidirect
119. #24671C11direct (N × H)
195. #3039C2×C11semidirect
196. C2×#461C2×C11semidirect
198. #2925C2×C11semidirect
199. #2052C2×C11semidirect
201. #1977C2×C11semidirect
202. #1966C2×C11semidirect
203. #1950C2×C11semidirect
204. #1930C2×C11semidirect
205. #1800C2×C11semidirect
474. C11#24671direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30392
C2×C11×#4612
C4×C11×AGL(1,ℤ/8)2
C11×#29252
C11×#20522
C11×#20192
C11×#19772
C11×#19662
C11×#19502
C11×#19302
C11×#18002
#2467111