Finite Group Databasebeta

← C11×#24001 #14601194

Subgroups — C11×#24001 #14601194

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3509C211yesmaximal, characteristic, complemented
2C11×#3020C211yesmaximal, characteristic
3C2×C11×#456C211yesmaximal, characteristic, complemented
4C11×#2884C211yesmaximal, characteristic, complemented
5C11×#2031C212yesmaximal, complemented
6C11×#2009C212yesmaximal, complemented
7C11×#1912C211yesmaximal, characteristic, complemented
8C11×#1906C212yesmaximal, complemented
9C11×#1905C212yesmaximal, complemented
10C11×#1886C211yesmaximal, characteristic, complemented
11C11×#1830C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C11×#575C2212yes—
14C2×C11×#137C2212yes—
15C11×#557—22no—
16C11×#556—22no—
17C11×#552—24no—
18C11×#541—22no—
19C11×#536C2211yescharacteristic
20C11×#536C2211yescharacteristic
21C11×#533—22no—
22C11×#533C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#519C2211yescharacteristic
25C11×#519C2211yescharacteristic
26C11×#519C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic
28C11×#456—22no—
29C11×#456—22no—
30C11×#456—22no—
31C11×#454—22no—
32C11×#421C2212yes—
33C11×#421C2212yes—
34C2×C11×#104C2212yes—
35C11×#419C2212yes—
36C2×C11×#101C2211yescharacteristic
37C2×C11×#101C2211yescharacteristic
38C11×#410—24no—
39C11×#410C2212yes—
40C11×#410C2212yes—
41C11×#344C2212yes—
42C11×#344C2212yes—
43C11×#339C2212yes—
44C11×H(3,ℤ/4)C2212yes—
45C11×2−1+4—22no—
46C11×2−1+4—22no—
47C11×2−1+4—42no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41C2311yescharacteristic
51C2×C11×#41C2312yes—
52C22×Q8×C11—22no—
53C22×Q8×C11C2311yescharacteristic
54C22×Q8×C11C2311yescharacteristic
55C11×#137—24no—
56C11×#137—22no—
57C11×#137—22no—
58C11×#137—42no—
59C11×AGL(1,ℤ/8)—22no—
60C11×AGL(1,ℤ/8)—22no—
61C11×#135—42no—
62C2×C11×Q16—22no—
63C2×C11×SD16—22no—
64C2×C11×M16C2312yes—
65C2×C11×M16C2312yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8D412yes—
70C11×C4⋊Q8D412yes—
71C11×C4⋊Q8D412yes—
72C11×#126—24no—
73C11×#126—24no—
74C11×#125—24no—
75C11×#125—24no—
76C11×#125—24no—
77C11×#125—21no—
78C11×#124—21no—
79C11×#124D412yes—
80C11×#123—22no—
81C11×#123—22no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C4×Q8×C11—24no—
87C4×Q8×C11—21no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—42no—
94C4×D4×C11—21no—
95C4×D4×C11—22no—
96C11×#117—24no—
97C11×#117—22no—
98C11×#117—21no—
99C11×#117—22no—
100C11×#117D414yes—
101C11×#117C2312yes—
102C11×#117C2311yescharacteristic
103C11×#117C2311yescharacteristic
104C11×#117C2311yescharacteristic
105C2×C11×C4⋊C4—22no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#104—22no—
109C11×#104—22no—
110C11×#104—24no—
111C11×#104—42no—
112C11×#103—42no—
113C11×#101—22no—
114C11×#101—22no—
115C11×#99—24no—
116C11×#99—24no—
117#24001C1111yesmaximal, characteristic, direct product factor, Sylow
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—44no—
125C11×#41—44no—
126C11×#41—44no—
127C11×#41—44no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—44no—
136C2×Q8×C11—44no—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11C2×D411yescharacteristic
139C2×Q8×C11C2×D412yes—
140C2×Q8×C11C2×D412yes—
141C2×Q8×C11#4112yes—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—21no—
145C2×D4×C11C2×D411yescharacteristic
146C2×D4×C11#4112yes—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2411yescharacteristic
155C11×Q16—44no—
156C11×Q16—42no—
157C11×SD16—44no—
158C11×SD16—42no—
159C11×SD16—42no—
160C11×D8—42no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—42no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4C2×D412yes—
188C11×C22⋊C4C2×D412yes—
189C42×C11—22no—
190C42×C11—24no—
191C42×C11—24no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—22no—
196C42×C11—42no—
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D412yes—
200#3509C2×C1111yescharacteristic, complemented
201#3020C2×C1111yescharacteristic
202C2×#456C2×C1111yescharacteristic, complemented
203#2884C2×C1111yescharacteristic, complemented
204#2031C2×C1112yescomplemented
205#2009C2×C1112yescomplemented
206#1912C2×C1111yescharacteristic, complemented
207#1906C2×C1112yescomplemented
208#1905C2×C1112yescomplemented
209#1886C2×C1111yescharacteristic, complemented
210#1830C2×C1111yescharacteristic, complemented
211C23×C11—21no—
212C23×C11—22no—
213C23×C11C22×D411yescharacteristic
214Q8×C11—24no—
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—44no—
221Q8×C11—44no—
222Q8×C11—42no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—44no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—41no—
230D4×C11—42no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—42no—
242C2×C4×C11—44no—
243C2×C4×C11—48no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11#12014yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4112yes—
254C2×C4×C11H(5,𝔽2)12yes—
255C8×C11—42no—
256C8×C11—42no—
257C2×2−1+4C22×C1111yescharacteristic
258#575C22×C1112yes—
259C2×#137C22×C1112yes—
260#557—22no—
261#556—22no—
262#552—24no—
263#541—22no—
264#536C22×C1111yescharacteristic
265#536C22×C1111yescharacteristic
266#533—22no—
267#533C22×C1111yescharacteristic
268C2×C4⋊Q8C22×C1111yescharacteristic
269#519C22×C1111yescharacteristic
270#519C22×C1111yescharacteristic
271#519C22×C1111yescharacteristic
272C4×#41C22×C1111yescharacteristic
273#456—22no—
274#456—22no—
275#456—22no—
276#454—22no—
277#421C22×C1112yes—
278#421C22×C1112yes—
279C2×#104C22×C1112yes—
280#419C22×C1112yes—
281C2×#101C22×C1111yescharacteristic
282C2×#101C22×C1111yescharacteristic
283#410—24no—
284#410C22×C1112yes—
285#410C22×C1112yes—
286#344C22×C1112yes—
287#344C22×C1112yes—
288#339C22×C1112yes—
289H(3,ℤ/4)C22×C1112yes—
290C22×C11—41no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—41no—
294C22×C11—82no—
295C22×C11C2×#12011yescharacteristic
296C22×C11#52511yescharacteristic
297C22×C11#53511yescharacteristic
298C4×C11—22no—
299C4×C11—24no—
300C4×C11—42no—
301C4×C11—41no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—41no—
306C4×C11—42no—
307C4×C11—82no—
308C4×C11#54612yes—
309C4×C11#54612yes—
3102−1+4—22no—
3112−1+4—22no—
3122−1+4—42no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41C23×C1111yescharacteristic
316C2×#41C23×C1112yes—
317C22×Q8—22no—
318C22×Q8C23×C1111yescharacteristic
319C22×Q8C23×C1111yescharacteristic
320#137—24no—
321#137—22no—
322#137—22no—
323#137—42no—
324AGL(1,ℤ/8)—22no—
325AGL(1,ℤ/8)—22no—
326#135—42no—
327C2×Q16—22no—
328C2×SD16—22no—
329C2×M16C23×C1112yes—
330C2×M16C23×C1112yes—
331C4⋊Q8—22no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8D4×C1112yes—
335C4⋊Q8D4×C1112yes—
336C4⋊Q8D4×C1112yes—
337#126—24no—
338#126—24no—
339#125—24no—
340#125—24no—
341#125—24no—
342#125—21no—
343#124—21no—
344#124D4×C1112yes—
345#123—22no—
346#123—22no—
347C22⋊Q8—24no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C4×Q8—24no—
352C4×Q8—21no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—42no—
359C4×D4—21no—
360C4×D4—22no—
361#117—24no—
362#117—22no—
363#117—21no—
364#117—22no—
365#117D4×C1114yes—
366#117C23×C1112yes—
367#117C23×C1111yescharacteristic
368#117C23×C1111yescharacteristic
369#117C23×C1111yescharacteristic
370C2×C4⋊C4—22no—
371C2×C42—21no—
372C2×C42C23×C1111yescharacteristic
373#104—22no—
374#104—22no—
375#104—24no—
376#104—42no—
377#103—42no—
378#101—22no—
379#101—22no—
380#99—24no—
381#99—24no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—81no—
386C2×C11—82no—
387C2×C11#240411yescharacteristic
388#41—22no—
389#41—22no—
390#41—22no—
391#41—22no—
392#41—22no—
393#41—22no—
394#41—44no—
395#41—44no—
396#41—44no—
397#41—44no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—44no—
406C2×Q8—44no—
407C2×Q8C2×D4×C1112yes—
408C2×Q8C2×D4×C1111yescharacteristic
409C2×Q8C2×D4×C1112yes—
410C2×Q8C2×D4×C1112yes—
411C2×Q8C11×#4112yes—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4C2×D4×C1111yescharacteristic
416C2×D4C11×#4112yes—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4C2×D4×C1112yes—
424C22×C4C24×C1111yescharacteristic
425Q16—44no—
426Q16—42no—
427SD16—44no—
428SD16—42no—
429SD16—42no—
430D8—42no—
431M16—22no—
432M16—22no—
433M16—22no—
434M16—22no—
435C2×C8—22no—
436C2×C8—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C22⋊C4—22no—
453C22⋊C4—24no—
454C22⋊C4—21no—
455C22⋊C4—24no—
456C22⋊C4—22no—
457C22⋊C4C2×D4×C1112yes—
458C22⋊C4C2×D4×C1112yes—
459C42—22no—
460C42—24no—
461C42—24no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—22no—
466C42—42no—
467C42C2×D4×C1111yescharacteristic
468C42C2×D4×C1111yescharacteristic
469C42C2×D4×C1112yes—
470C11#2400111yescharacteristic, direct product factor, Sylow
471C23—21no—
472C23—22no—
473C23C22×D4×C1111yescharacteristic
474Q8—24no—
475Q8—24no—
476Q8—24no—
477Q8—22no—
478Q8—22no—
479Q8—22no—
480Q8—44no—
481Q8—44no—
482Q8—42no—
483D4—22no—
484D4—22no—
485D4—22no—
486D4—44no—
487D4—42no—
488D4—41no—
489D4—41no—
490D4—42no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—48no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4C11×#12014yes—
511C2×C4C22×D4×C1111yescharacteristic
512C2×C4C22×D4×C1111yescharacteristic
513C2×C4C2×C11×#4112yes—
514C2×C4C11×H(5,𝔽2)12yes—
515C8—42no—
516C8—42no—
517C22—41no—
518C22—42no—
519C22—42no—
520C22—41no—
521C22—82no—
522C22C2×C11×#12011yescharacteristic
523C22C11×#52511yescharacteristic
524C22C11×#53511yescharacteristic
525C4—22no—
526C4—24no—
527C4—42no—
528C4—41no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—41no—
533C4—42no—
534C4—82no—
535C4C11×#54612yes—
536C4C11×#54612yes—
537C2—21no—
538C2—21no—
539C2—21no—
540C2—81no—
541C2—82no—
542C2C11×#240411yescharacteristic
subgroupG/H
center, socleC2×C11#2404
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3020C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3509C2semidirect
3. C2×C11×#456C2semidirect
4. C11×#2884C2semidirect
5. C11×#2031C2semidirect
6. C11×#2009C2semidirect
7. C11×#1912C2semidirect
8. C11×#1906C2semidirect
9. C11×#1905C2semidirect
10. C11×#1886C2semidirect
11. C11×#1830C2semidirect
117. #24001C11direct (N × H)
200. #3509C2×C11semidirect
202. C2×#456C2×C11semidirect
203. #2884C2×C11semidirect
204. #2031C2×C11semidirect
205. #2009C2×C11semidirect
206. #1912C2×C11semidirect
207. #1906C2×C11semidirect
208. #1905C2×C11semidirect
209. #1886C2×C11semidirect
210. #1830C2×C11semidirect
470. C11#24001direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35092
C11×#30202
C2×C11×#4562
C11×#28842
C11×#20312
C11×#20092
C11×#19122
C11×#19062
C11×#19052
C11×#18862
C11×#18302
#2400111