Finite Group Databasebeta

← C11×#23991 #14601184

Subgroups — C11×#23991 #14601184

Order 2816.

1164 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3510C211yesmaximal, characteristic, complemented
2C11×#3027C211yesmaximal, characteristic
3C11×#3022C211yesmaximal, characteristic, complemented
4C11×#2901C211yesmaximal, characteristic, complemented
5C11×#2031C212yesmaximal, complemented
6C11×#2004C212yesmaximal, complemented
7C11×#1914C211yesmaximal, characteristic, complemented
8C11×#1911C212yesmaximal, complemented
9C11×#1909C211yesmaximal, characteristic, complemented
10C11×#1905C212yesmaximal, complemented
11C11×#1827C211yesmaximal, characteristic, complemented
12C11×#585C2211yescharacteristic
13C2×C11×#137C2212yes—
14C11×#568C2211yescharacteristic
15C11×#559—22no—
16C11×#556—22no—
17C11×#551—24no—
18C11×#542—22no—
19C11×#536C2211yescharacteristic
20C11×#535C2212yes—
21C11×#535C2211yescharacteristic
22C11×#533C2211yescharacteristic, complemented
23C11×#529—22no—
24C2×C11×#124C2211yescharacteristic, complemented
25C11×#519C2211yescharacteristic, complemented
26C11×#518C2211yescharacteristic, complemented
27C4×C11×#41C2211yescharacteristic
28C11×B(4,𝔽2)—24no—
29C11×#456—22no—
30C11×#455—22no—
31C11×#421—22no—
32C11×#421C2212yes—
33C11×#421C2212yes—
34C2×C11×#104—22no—
35C2×C11×#104C2212yes—
36C11×#419C2212yescomplemented
37C11×#413C2211yescharacteristic
38C2×C11×#100C2212yescomplemented
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×#137—24no—
57C11×#137—42no—
58C2×C11×Q16—22no—
59C2×C11×SD16—22no—
60C11×#131—42no—
61C2×C11×M16—22no—
62C2×C11×M16C2312yes—
63C2×C11×M16C2312yes—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8D412yescomplemented
66C11×#127—21no—
67C11×#127—22no—
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×#124D412yescomplemented
78C11×#123—24no—
79C11×#123—24no—
80C11×#123—22no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×#121—22no—
85C11×#121—42no—
86C11×#120—24no—
87C11×#120D414yes—
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×#117D412yescomplemented
100C11×#117C2312yes—
101C11×#117C2311yescharacteristic
102C11×#117C2311yescharacteristic
103C11×#117C2311yescharacteristic
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C42×C11D412yescomplemented
107C2×C42×C11C2311yescharacteristic
108C11×#104—22no—
109C11×#104—24no—
110C11×#104—22no—
111C11×#104—24no—
112C11×#103—42no—
113C11×#101—21no—
114C11×#100—21no—
115C11×#100—42no—
116C11×#99—22no—
117C11×#99—24no—
118#23991C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11C2×D412yes—
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—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—42no—
138C2×Q8×C11C2×D412yes—
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—21no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—42no—
149C2×D4×C11—44no—
150C2×D4×C11—42no—
151C2×D4×C11—44no—
152C2×D4×C11C2×D412yes—
153C2×D4×C11C2×D411yescharacteristic
154C2×D4×C11#4112yes—
155C22×C4×C11—21no—
156C22×C4×C11—24no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—42no—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2411yescharacteristic
163C11×Q16—44no—
164C11×SD16—44no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—42no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—42no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
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#3027C2×C1111yescharacteristic
205#3022C2×C1111yescharacteristic, complemented
206#2901C2×C1111yescharacteristic, complemented
207#2031C2×C1112yescomplemented
208#2004C2×C1112yescomplemented
209#1914C2×C1111yescharacteristic, complemented
210#1911C2×C1112yescomplemented
211#1909C2×C1111yescharacteristic, complemented
212#1905C2×C1112yescomplemented
213#1827C2×C1111yescharacteristic, complemented
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—82no—
219C23×C11#12012yes—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—24no—
224Q8×C11—22no—
225Q8×C11—42no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—82no—
229D4×C11—24no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—42no—
234D4×C11—44no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—42no—
240D4×C11—84no—
241D4×C11—164no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
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—42no—
257C2×C4×C11—82no—
258C2×C4×C11—84no—
259C2×C4×C11—81no—
260C2×C4×C11#12012yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4112yes—
264C2×C4×C11H(5,𝔽2)12yes—
265C8×C11—42no—
266C8×C11—42no—
267#585C22×C1111yescharacteristic
268C2×#137C22×C1112yes—
269#568C22×C1111yescharacteristic
270#559—22no—
271#556—22no—
272#551—24no—
273#542—22no—
274#536C22×C1111yescharacteristic
275#535C22×C1112yes—
276#535C22×C1111yescharacteristic
277#533C22×C1111yescharacteristic, complemented
278#529—22no—
279C2×#124C22×C1111yescharacteristic, complemented
280#519C22×C1111yescharacteristic, complemented
281#518C22×C1111yescharacteristic, complemented
282C4×#41C22×C1111yescharacteristic
283B(4,𝔽2)—24no—
284#456—22no—
285#455—22no—
286#421—22no—
287#421C22×C1112yes—
288#421C22×C1112yes—
289C2×#104—22no—
290C2×#104C22×C1112yes—
291#419C22×C1112yescomplemented
292#413C22×C1111yescharacteristic
293C2×#100C22×C1112yescomplemented
294#410C22×C1111yescharacteristic
295#410C22×C1112yes—
296#344C22×C1112yescomplemented
297#339C22×C1112yescomplemented
298H(3,ℤ/4)C22×C1112yescomplemented
299H(3,ℤ/4)C22×C1112yescomplemented
300C22×C11—22no—
301C22×C11—41no—
302C22×C11—42no—
303C22×C11—44no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—82no—
307C22×C11—84no—
308C22×C11—162no—
309C22×C11C2×#12011yescharacteristic
310C22×C11#54612yes—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—41no—
314C4×C11—42no—
315C4×C11—41no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—82no—
320C4×C11#52511yescharacteristic
321C4×C11#53511yescharacteristic
322C4×C11#54612yes—
3232−1+4—22no—
3242−1+4—21no—
325H(5,𝔽2)—22no—
326H(5,𝔽2)—22no—
327H(5,𝔽2)—21no—
328C2×#41—22no—
329C2×#41—42no—
330C2×#41C23×C1112yes—
331C2×#41C23×C1111yescharacteristic
332C22×Q8C23×C1111yescharacteristic
333C22×D4C23×C1111yescharacteristic
334#137—24no—
335#137—42no—
336C2×Q16—22no—
337C2×SD16—22no—
338#131—42no—
339C2×M16—22no—
340C2×M16C23×C1112yes—
341C2×M16C23×C1112yes—
342C4⋊Q8—21no—
343C4⋊Q8D4×C1112yescomplemented
344#127—21no—
345#127—22no—
346#126—24no—
347#126—24no—
348#125—21no—
349#124—24no—
350#124—22no—
351#124—21no—
352#124—22no—
353#124—21no—
354#124—21no—
355#124D4×C1112yescomplemented
356#123—24no—
357#123—24no—
358#123—22no—
359C22⋊Q8—24no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362#121—22no—
363#121—42no—
364#120—24no—
365#120D4×C1114yes—
366C4×Q8—21no—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×D4—24no—
371C4×D4—22no—
372C4×D4—21no—
373C4×D4—22no—
374C4×D4—22no—
375#117—24no—
376#117—22no—
377#117D4×C1112yescomplemented
378#117C23×C1112yes—
379#117C23×C1111yescharacteristic
380#117C23×C1111yescharacteristic
381#117C23×C1111yescharacteristic
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C42D4×C1112yescomplemented
385C2×C42C23×C1111yescharacteristic
386#104—22no—
387#104—24no—
388#104—22no—
389#104—24no—
390#103—42no—
391#101—21no—
392#100—21no—
393#100—42no—
394#99—22no—
395#99—24no—
396C2×C11—21no—
397C2×C11—22no—
398C2×C11—42no—
399C2×C11—82no—
400C2×C11—82no—
401C2×C11#240411yescharacteristic
402C24C2×D4×C1112yes—
403#41—22no—
404#41—22no—
405#41—24no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—44no—
411#41—42no—
412#41—42no—
413#41—42no—
414#41—42no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—42no—
421C2×Q8C2×D4×C1112yes—
422C2×Q8C2×D4×C1111yescharacteristic
423C2×Q8C11×#4112yes—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—24no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—42no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—44no—
435C2×D4C2×D4×C1112yes—
436C2×D4C2×D4×C1111yescharacteristic
437C2×D4C11×#4112yes—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—42no—
444C22×C4C2×D4×C1112yes—
445C22×C4C24×C1111yescharacteristic
446Q16—44no—
447SD16—44no—
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—42no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—42no—
456C4⋊C4—22no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—22no—
470C22⋊C4—24no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—24no—
474C22⋊C4—22no—
475C22⋊C4—44no—
476C22⋊C4C2×D4×C1112yes—
477C42—24no—
478C42—22no—
479C42—21no—
480C42—21no—
481C42—22no—
482C42C2×D4×C1111yescharacteristic
483C42C2×D4×C1112yes—
484C42C2×D4×C1111yescharacteristic
485C42C2×D4×C1112yes—
486C11#2399111yescharacteristic, direct product factor, Sylow
487C23—22no—
488C23—24no—
489C23—22no—
490C23—42no—
491C23—82no—
492C23C11×#12012yes—
493C23C22×D4×C1111yescharacteristic
494Q8—22no—
495Q8—22no—
496Q8—24no—
497Q8—22no—
498Q8—42no—
499Q8—41no—
500Q8—41no—
501Q8—82no—
502D4—24no—
503D4—22no—
504D4—22no—
505D4—22no—
506D4—42no—
507D4—44no—
508D4—42no—
509D4—42no—
510D4—41no—
511D4—41no—
512D4—42no—
513D4—84no—
514D4—164no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—82no—
531C2×C4—84no—
532C2×C4—81no—
533C2×C4C11×#12012yes—
534C2×C4C22×D4×C1111yescharacteristic
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C2×C11×#4112yes—
537C2×C4C11×H(5,𝔽2)12yes—
538C8—42no—
539C8—42no—
540C22—22no—
541C22—41no—
542C22—42no—
543C22—44no—
544C22—42no—
545C22—42no—
546C22—82no—
547C22—84no—
548C22—162no—
549C22C2×C11×#12011yescharacteristic
550C22C11×#54612yes—
551C4—22no—
552C4—42no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—82no—
560C4C11×#52511yescharacteristic
561C4C11×#53511yescharacteristic
562C4C11×#54612yes—
563C2—21no—
564C2—22no—
565C2—42no—
566C2—82no—
567C2—82no—
568C2C11×#240411yescharacteristic
subgroupG/H
center, socleC2×C11#2404
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3027C2
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
3. C11×#3022C2semidirect
4. C11×#2901C2semidirect
5. C11×#2031C2semidirect
6. C11×#2004C2semidirect
7. C11×#1914C2semidirect
8. C11×#1911C2semidirect
9. C11×#1909C2semidirect
10. C11×#1905C2semidirect
11. C11×#1827C2semidirect
22. C11×#533C22semidirect
24. C2×C11×#124C22semidirect
25. C11×#519C22semidirect
26. C11×#518C22semidirect
36. C11×#419C22semidirect
38. C2×C11×#100C22semidirect
41. C11×#344C22semidirect
42. C11×#339C22semidirect
43. C11×H(3,ℤ/4)C22semidirect
44. C11×H(3,ℤ/4)C22semidirect
65. C11×C4⋊Q8D4semidirect
77. C11×#124D4semidirect
99. C11×#117D4semidirect
106. C2×C42×C11D4semidirect
118. #23991C11direct (N × H)
203. #3510C2×C11semidirect
205. #3022C2×C11semidirect
206. #2901C2×C11semidirect
207. #2031C2×C11semidirect
208. #2004C2×C11semidirect
209. #1914C2×C11semidirect
210. #1911C2×C11semidirect
211. #1909C2×C11semidirect
212. #1905C2×C11semidirect
213. #1827C2×C11semidirect
277. #533C22×C11semidirect
279. C2×#124C22×C11semidirect
280. #519C22×C11semidirect
281. #518C22×C11semidirect
291. #419C22×C11semidirect
293. C2×#100C22×C11semidirect
296. #344C22×C11semidirect
297. #339C22×C11semidirect
298. H(3,ℤ/4)C22×C11semidirect
299. H(3,ℤ/4)C22×C11semidirect
343. C4⋊Q8D4×C11semidirect
355. #124D4×C11semidirect
377. #117D4×C11semidirect
384. C2×C42D4×C11semidirect
486. C11#23991direct (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×#30272
C11×#30222
C11×#29012
C11×#20312
C11×#20042
C11×#19142
C11×#19112
C11×#19092
C11×#19052
C11×#18272
#2399111