Finite Group Databasebeta

← C11×#23993 #14601186

Subgroups — C11×#23993 #14601186

Order 2816.

1152 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3510C211yesmaximal, characteristic, complemented
2C11×#3028C211yesmaximal, characteristic, complemented
3C11×#3021C211yesmaximal, characteristic
4C11×#2901C211yesmaximal, characteristic, complemented
5C11×#2031C212yesmaximal, complemented
6C11×#2003C212yesmaximal, complemented
7C11×#1915C211yesmaximal, characteristic, complemented
8C11×#1912C212yesmaximal, complemented
9C11×#1910C211yesmaximal, characteristic, complemented
10C11×#1904C212yesmaximal, complemented
11C11×#1827C211yesmaximal, characteristic, complemented
12C11×#585C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C11×#568C2211yescharacteristic
15C11×#559—22no—
16C11×#556—22no—
17C11×#551—24no—
18C11×#542—22no—
19C11×#536C2211yescharacteristic
20C11×#536C2212yes—
21C11×#535C2211yescharacteristic
22C11×#533C2211yescharacteristic, complemented
23C11×#529—22no—
24C2×C11×#124C2211yescharacteristic, complemented
25C11×#519C2211yescharacteristic, complemented
26C11×#518C2211yescharacteristic, complemented
27C4×C11×#41C2211yescharacteristic
28C11×#458—24no—
29C11×#454—22no—
30C11×#453—22no—
31C11×#421—22no—
32C11×#421C2212yes—
33C11×#421C2212yes—
34C2×C11×#104—22no—
35C2×C11×#104C2212yes—
36C11×#418C2212yescomplemented
37C11×#413C2211yescharacteristic
38C2×C11×#101C2212yescomplemented
39C11×#410C2212yes—
40C11×#410C2211yescharacteristic
41C11×#344C2212yescomplemented
42C11×#339C2212yescomplemented
43C11×H(3,ℤ/4)C2212yescomplemented
44C11×H(3,ℤ/4)C2212yescomplemented
45C11×2−1+4—22no—
46C11×2−1+4—21no—
47C11×H(5,𝔽2)—22no—
48C11×H(5,𝔽2)—22no—
49C11×H(5,𝔽2)—21no—
50C2×C11×#41—22no—
51C2×C11×#41—42no—
52C2×C11×#41C2312yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11C2311yescharacteristic
56C11×AGL(1,ℤ/8)—24no—
57C11×AGL(1,ℤ/8)—42no—
58C2×C11×SD16—22no—
59C2×C11×D8—22no—
60C11×#131—42no—
61C2×C11×M16—22no—
62C2×C11×M16C2312yes—
63C2×C11×M16C2312yes—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—21no—
67C11×#127D412yes—
68C11×#126—24no—
69C11×#126—24no—
70C11×#125—21no—
71C11×#124—24no—
72C11×#124—22no—
73C11×#124—21no—
74C11×#124—22no—
75C11×#124—21no—
76C11×#124—21no—
77C11×#124D412yes—
78C11×#123—24no—
79C11×#123—24no—
80C11×#123—24no—
81C11×#123D414yes—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—42no—
86C11×#121—22no—
87C11×#120—22no—
88C4×Q8×C11—21no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×D4×C11—24no—
93C4×D4×C11—22no—
94C4×D4×C11—21no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C11×#117—24no—
98C11×#117—22no—
99C11×#117D412yes—
100C11×#117C2312yes—
101C11×#117C2311yescharacteristic
102C11×#117C2311yescharacteristic
103C11×#117C2311yescharacteristic
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C42×C11D412yes—
107C2×C42×C11C2311yescharacteristic
108C11×#104—22no—
109C11×#104—24no—
110C11×#104—22no—
111C11×#104—24no—
112C11×#102—42no—
113C11×#101—21no—
114C11×#101—42no—
115C11×#100—21no—
116C11×#99—22no—
117C11×#99—24no—
118#23993C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—24no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—44no—
128C11×#41—42no—
129C11×#41—42no—
130C11×#41—42no—
131C11×#41—42no—
132C2×Q8×C11—22no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11—42no—
139C2×Q8×C11C2×D411yescharacteristic
140C2×Q8×C11#4112yes—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—42no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D412yes—
151C2×D4×C11C2×D412yes—
152C2×D4×C11C2×D411yescharacteristic
153C2×D4×C11#4112yes—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—42no—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2411yescharacteristic
162C11×SD16—44no—
163C11×D8—44no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—42no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—42no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—44no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—44no—
193C11×C22⋊C4C2×D412yes—
194C42×C11—24no—
195C42×C11—22no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—22no—
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D412yes—
201C42×C11C2×D411yescharacteristic
202C42×C11C2×D412yes—
203#3510C2×C1111yescharacteristic, complemented
204#3028C2×C1111yescharacteristic, complemented
205#3021C2×C1111yescharacteristic
206#2901C2×C1111yescharacteristic, complemented
207#2031C2×C1112yescomplemented
208#2003C2×C1112yescomplemented
209#1915C2×C1111yescharacteristic, complemented
210#1912C2×C1112yescomplemented
211#1910C2×C1111yescharacteristic, complemented
212#1904C2×C1112yescomplemented
213#1827C2×C1111yescharacteristic, complemented
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—82no—
219C23×C11#12012yes—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—42no—
225Q8×C11—41no—
226Q8×C11—41no—
227Q8×C11—42no—
228Q8×C11—82no—
229D4×C11—24no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—24no—
234D4×C11—42no—
235D4×C11—44no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—84no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—44no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—82no—
257C2×C4×C11—84no—
258C2×C4×C11—81no—
259C2×C4×C11#12012yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4112yes—
263C2×C4×C11H(5,𝔽2)12yes—
264C8×C11—42no—
265C8×C11—42no—
266#585C22×C1111yescharacteristic
267C2×AGL(1,ℤ/8)C22×C1112yes—
268#568C22×C1111yescharacteristic
269#559—22no—
270#556—22no—
271#551—24no—
272#542—22no—
273#536C22×C1111yescharacteristic
274#536C22×C1112yes—
275#535C22×C1111yescharacteristic
276#533C22×C1111yescharacteristic, complemented
277#529—22no—
278C2×#124C22×C1111yescharacteristic, complemented
279#519C22×C1111yescharacteristic, complemented
280#518C22×C1111yescharacteristic, complemented
281C4×#41C22×C1111yescharacteristic
282#458—24no—
283#454—22no—
284#453—22no—
285#421—22no—
286#421C22×C1112yes—
287#421C22×C1112yes—
288C2×#104—22no—
289C2×#104C22×C1112yes—
290#418C22×C1112yescomplemented
291#413C22×C1111yescharacteristic
292C2×#101C22×C1112yescomplemented
293#410C22×C1111yescharacteristic
294#410C22×C1112yes—
295#344C22×C1112yescomplemented
296#339C22×C1112yescomplemented
297H(3,ℤ/4)C22×C1112yescomplemented
298H(3,ℤ/4)C22×C1112yescomplemented
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—82no—
306C22×C11—162no—
307C22×C11—162no—
308C22×C11C2×#12011yescharacteristic
309C22×C11#54612yes—
310C4×C11—22no—
311C4×C11—42no—
312C4×C11—41no—
313C4×C11—42no—
314C4×C11—41no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—82no—
319C4×C11#52511yescharacteristic
320C4×C11#53511yescharacteristic
321C4×C11#54612yes—
3222−1+4—22no—
3232−1+4—21no—
324H(5,𝔽2)—22no—
325H(5,𝔽2)—22no—
326H(5,𝔽2)—21no—
327C2×#41—22no—
328C2×#41—42no—
329C2×#41C23×C1112yes—
330C2×#41C23×C1111yescharacteristic
331C22×Q8C23×C1111yescharacteristic
332C22×D4C23×C1111yescharacteristic
333AGL(1,ℤ/8)—24no—
334AGL(1,ℤ/8)—42no—
335C2×SD16—22no—
336C2×D8—22no—
337#131—42no—
338C2×M16—22no—
339C2×M16C23×C1112yes—
340C2×M16C23×C1112yes—
341C4⋊Q8—21no—
342C4⋊Q8—22no—
343C4⋊Q8—21no—
344#127D4×C1112yes—
345#126—24no—
346#126—24no—
347#125—21no—
348#124—24no—
349#124—22no—
350#124—21no—
351#124—22no—
352#124—21no—
353#124—21no—
354#124D4×C1112yes—
355#123—24no—
356#123—24no—
357#123—24no—
358#123D4×C1114yes—
359C22⋊Q8—24no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—42no—
363#121—22no—
364#120—22no—
365C4×Q8—21no—
366C4×Q8—22no—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×D4—24no—
370C4×D4—22no—
371C4×D4—21no—
372C4×D4—22no—
373C4×D4—22no—
374#117—24no—
375#117—22no—
376#117D4×C1112yes—
377#117C23×C1112yes—
378#117C23×C1111yescharacteristic
379#117C23×C1111yescharacteristic
380#117C23×C1111yescharacteristic
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C42D4×C1112yes—
384C2×C42C23×C1111yescharacteristic
385#104—22no—
386#104—24no—
387#104—22no—
388#104—24no—
389#102—42no—
390#101—21no—
391#101—42no—
392#100—21no—
393#99—22no—
394#99—24no—
395C2×C11—21no—
396C2×C11—22no—
397C2×C11—42no—
398C2×C11—82no—
399C2×C11—82no—
400C2×C11#240411yescharacteristic
401C24—21no—
402#41—22no—
403#41—22no—
404#41—24no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—44no—
410#41—42no—
411#41—42no—
412#41—42no—
413#41—42no—
414C2×Q8—22no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—42no—
421C2×Q8C2×D4×C1111yescharacteristic
422C2×Q8C11×#4112yes—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—42no—
430C2×D4—44no—
431C2×D4—42no—
432C2×D4C2×D4×C1112yes—
433C2×D4C2×D4×C1112yes—
434C2×D4C2×D4×C1111yescharacteristic
435C2×D4C11×#4112yes—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4C2×D4×C1112yes—
442C22×C4C2×D4×C1112yes—
443C22×C4C24×C1111yescharacteristic
444SD16—44no—
445D8—44no—
446M16—22no—
447M16—22no—
448M16—22no—
449M16—22no—
450M16—42no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—42no—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—44no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—24no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—44no—
475C22⋊C4C2×D4×C1112yes—
476C42—24no—
477C42—22no—
478C42—21no—
479C42—21no—
480C42—22no—
481C42C2×D4×C1111yescharacteristic
482C42C2×D4×C1112yes—
483C42C2×D4×C1111yescharacteristic
484C42C2×D4×C1112yes—
485C11#2399311yescharacteristic, direct product factor, Sylow
486C23—22no—
487C23—22no—
488C23—42no—
489C23—42no—
490C23—82no—
491C23C11×#12012yes—
492C23C22×D4×C1111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—22no—
496Q8—42no—
497Q8—41no—
498Q8—41no—
499Q8—42no—
500Q8—82no—
501D4—24no—
502D4—22no—
503D4—22no—
504D4—22no—
505D4—24no—
506D4—42no—
507D4—44no—
508D4—42no—
509D4—42no—
510D4—41no—
511D4—41no—
512D4—84no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—84no—
530C2×C4—81no—
531C2×C4C11×#12012yes—
532C2×C4C22×D4×C1111yescharacteristic
533C2×C4C22×D4×C1111yescharacteristic
534C2×C4C2×C11×#4112yes—
535C2×C4C11×H(5,𝔽2)12yes—
536C8—42no—
537C8—42no—
538C22—22no—
539C22—41no—
540C22—42no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—82no—
545C22—162no—
546C22—162no—
547C22C2×C11×#12011yescharacteristic
548C22C11×#54612yes—
549C4—22no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—41no—
554C4—42no—
555C4—42no—
556C4—42no—
557C4—82no—
558C4C11×#52511yescharacteristic
559C4C11×#53511yescharacteristic
560C4C11×#54612yes—
561C2—21no—
562C2—22no—
563C2—42no—
564C2—82no—
565C2—82no—
566C2C11×#240411yescharacteristic
subgroupG/H
center, socleC2×C11#2404
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3021C2
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×#3510C2semidirect
2. C11×#3028C2semidirect
4. C11×#2901C2semidirect
5. C11×#2031C2semidirect
6. C11×#2003C2semidirect
7. C11×#1915C2semidirect
8. C11×#1912C2semidirect
9. C11×#1910C2semidirect
10. C11×#1904C2semidirect
11. C11×#1827C2semidirect
22. C11×#533C22semidirect
24. C2×C11×#124C22semidirect
25. C11×#519C22semidirect
26. C11×#518C22semidirect
36. C11×#418C22semidirect
38. C2×C11×#101C22semidirect
41. C11×#344C22semidirect
42. C11×#339C22semidirect
43. C11×H(3,ℤ/4)C22semidirect
44. C11×H(3,ℤ/4)C22semidirect
118. #23993C11direct (N × H)
203. #3510C2×C11semidirect
204. #3028C2×C11semidirect
206. #2901C2×C11semidirect
207. #2031C2×C11semidirect
208. #2003C2×C11semidirect
209. #1915C2×C11semidirect
210. #1912C2×C11semidirect
211. #1910C2×C11semidirect
212. #1904C2×C11semidirect
213. #1827C2×C11semidirect
276. #533C22×C11semidirect
278. C2×#124C22×C11semidirect
279. #519C22×C11semidirect
280. #518C22×C11semidirect
290. #418C22×C11semidirect
292. C2×#101C22×C11semidirect
295. #344C22×C11semidirect
296. #339C22×C11semidirect
297. H(3,ℤ/4)C22×C11semidirect
298. H(3,ℤ/4)C22×C11semidirect
485. C11#23993direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35102
C11×#30282
C11×#30212
C11×#29012
C11×#20312
C11×#20032
C11×#19152
C11×#19122
C11×#19102
C11×#19042
C11×#18272
#2399311