Finite Group Databasebeta

← C11×#23999 #14601192

Subgroups — C11×#23999 #14601192

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3510C211yesmaximal, characteristic, complemented
2C11×#3020C211yesmaximal, characteristic, complemented
3C2×C11×#454C211yesmaximal, characteristic, complemented
4C11×#2884C211yesmaximal, characteristic, complemented
5C11×#2031C212yesmaximal, complemented
6C11×#2008C212yesmaximal, complemented
7C11×#1912C211yesmaximal, characteristic, complemented
8C11×#1906C212yesmaximal, complemented
9C11×#1904C212yesmaximal, complemented
10C11×#1888C211yesmaximal, characteristic, complemented
11C11×#1830C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C11×#575C2212yes—
14C2×C11×AGL(1,ℤ/8)C2212yes—
15C11×#559—22no—
16C11×#556—22no—
17C11×#551—24no—
18C11×#542—22no—
19C11×#536C2211yescharacteristic
20C11×#535C2211yescharacteristic
21C11×#533C2211yescharacteristic
22C11×#529—22no—
23C2×C11×#124C2211yescharacteristic
24C11×#519C2211yescharacteristic
25C11×#519C2211yescharacteristic
26C11×#518C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic
28C11×#456—22no—
29C11×#454—22no—
30C11×#454—22no—
31C11×#454—22no—
32C11×#421C2212yes—
33C11×#421C2212yes—
34C2×C11×#104C2212yes—
35C11×#418C2212yes—
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×D4×C11C2311yescharacteristic
55C11×#137—22no—
56C11×#137—22no—
57C11×AGL(1,ℤ/8)—24no—
58C11×AGL(1,ℤ/8)—22no—
59C11×AGL(1,ℤ/8)—22no—
60C11×AGL(1,ℤ/8)—42no—
61C11×#135—42no—
62C2×C11×SD16—22no—
63C2×C11×D8—22no—
64C2×C11×M16C2312yes—
65C2×C11×M16C2312yes—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8D412yes—
68C11×#127—21no—
69C11×#126—24no—
70C11×#126—24no—
71C11×#125—21no—
72C11×#124—24no—
73C11×#124—22no—
74C11×#124—21no—
75C11×#124D412yes—
76C11×#124D412yes—
77C11×#124D412yes—
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×#120—22no—
86C4×Q8×C11—21no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—42no—
91C4×D4×C11—24no—
92C4×D4×C11—21no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C11×#117—24no—
97C11×#117—21no—
98C11×#117—22no—
99C11×#117D414yes—
100C11×#117C2312yes—
101C11×#117C2311yescharacteristic
102C11×#117C2311yescharacteristic
103C11×#117C2311yescharacteristic
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#104—22no—
109C11×#104—22no—
110C11×#104—24no—
111C11×#104—42no—
112C11×#102—42no—
113C11×#101—22no—
114C11×#101—22no—
115C11×#99—24no—
116C11×#99—24no—
117#23999C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—21no—
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—44no—
126C11×#41—44no—
127C11×#41—44no—
128C11×#41—44no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—44no—
134C2×Q8×C11—44no—
135C2×Q8×C11C2×D411yescharacteristic
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11#4112yes—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11C2×D412yes—
147C2×D4×C11C2×D411yescharacteristic
148C2×D4×C11#4112yes—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C11×Q16—42no—
158C11×SD16—44no—
159C11×SD16—42no—
160C11×SD16—42no—
161C11×D8—44no—
162C11×D8—42no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—42no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4C2×D412yes—
189C11×C22⋊C4C2×D412yes—
190C42×C11—22no—
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#3510C2×C1111yescharacteristic, complemented
201#3020C2×C1111yescharacteristic, complemented
202C2×#454C2×C1111yescharacteristic, complemented
203#2884C2×C1111yescharacteristic, complemented
204#2031C2×C1112yescomplemented
205#2008C2×C1112yescomplemented
206#1912C2×C1111yescharacteristic, complemented
207#1906C2×C1112yescomplemented
208#1904C2×C1112yescomplemented
209#1888C2×C1111yescharacteristic, complemented
210#1830C2×C1111yescharacteristic, complemented
211C23×C11—22no—
212C23×C11—21no—
213C23×C11—22no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—82no—
217C23×C11C22×D411yescharacteristic
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—44no—
224Q8×C11—82no—
225D4×C11—22no—
226D4×C11—24no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—44no—
230D4×C11—42no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—84no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—82no—
251C2×C4×C11—84no—
252C2×C4×C11—81no—
253C2×C4×C11#12014yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4112yes—
257C2×C4×C11H(5,𝔽2)12yes—
258C8×C11—42no—
259C8×C11—42no—
260C2×2−1+4C22×C1111yescharacteristic
261#575C22×C1112yes—
262C2×AGL(1,ℤ/8)C22×C1112yes—
263#559—22no—
264#556—22no—
265#551—24no—
266#542—22no—
267#536C22×C1111yescharacteristic
268#535C22×C1111yescharacteristic
269#533C22×C1111yescharacteristic
270#529—22no—
271C2×#124C22×C1111yescharacteristic
272#519C22×C1111yescharacteristic
273#519C22×C1111yescharacteristic
274#518C22×C1111yescharacteristic
275C4×#41C22×C1111yescharacteristic
276#456—22no—
277#454—22no—
278#454—22no—
279#454—22no—
280#421C22×C1112yes—
281#421C22×C1112yes—
282C2×#104C22×C1112yes—
283#418C22×C1112yes—
284C2×#101C22×C1111yescharacteristic
285C2×#101C22×C1111yescharacteristic
286#410—24no—
287#410C22×C1112yes—
288#410C22×C1112yes—
289#344C22×C1112yes—
290#344C22×C1112yes—
291#339C22×C1112yes—
292H(3,ℤ/4)C22×C1112yes—
293C22×C11—41no—
294C22×C11—42no—
295C22×C11—44no—
296C22×C11—42no—
297C22×C11—41no—
298C22×C11—42no—
299C22×C11—82no—
300C22×C11—161no—
301C22×C11—161no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#52511yescharacteristic
304C22×C11#53511yescharacteristic
305C4×C11—24no—
306C4×C11—42no—
307C4×C11—41no—
308C4×C11—42no—
309C4×C11—41no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—41no—
313C4×C11—82no—
314C4×C11#54612yes—
315C4×C11#54612yes—
3162−1+4—22no—
3172−1+4—22no—
3182−1+4—42no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41C23×C1111yescharacteristic
322C2×#41C23×C1112yes—
323C22×Q8—22no—
324C22×Q8C23×C1111yescharacteristic
325C22×D4C23×C1111yescharacteristic
326#137—22no—
327#137—22no—
328AGL(1,ℤ/8)—24no—
329AGL(1,ℤ/8)—22no—
330AGL(1,ℤ/8)—22no—
331AGL(1,ℤ/8)—42no—
332#135—42no—
333C2×SD16—22no—
334C2×D8—22no—
335C2×M16C23×C1112yes—
336C2×M16C23×C1112yes—
337C4⋊Q8—21no—
338C4⋊Q8D4×C1112yes—
339#127—21no—
340#126—24no—
341#126—24no—
342#125—21no—
343#124—24no—
344#124—22no—
345#124—21no—
346#124D4×C1112yes—
347#124D4×C1112yes—
348#124D4×C1112yes—
349#123—24no—
350#123—24no—
351#123—22no—
352C22⋊Q8—24no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355#121—22no—
356#120—22no—
357C4×Q8—21no—
358C4×Q8—22no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×Q8—42no—
362C4×D4—24no—
363C4×D4—21no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367#117—24no—
368#117—21no—
369#117—22no—
370#117D4×C1114yes—
371#117C23×C1112yes—
372#117C23×C1111yescharacteristic
373#117C23×C1111yescharacteristic
374#117C23×C1111yescharacteristic
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C42—21no—
378C2×C42C23×C1111yescharacteristic
379#104—22no—
380#104—22no—
381#104—24no—
382#104—42no—
383#102—42no—
384#101—22no—
385#101—22no—
386#99—24no—
387#99—24no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—81no—
392C2×C11—82no—
393C2×C11—82no—
394C2×C11#240411yescharacteristic
395C24—21no—
396#41—22no—
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—44no—
403#41—44no—
404#41—44no—
405#41—44no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—44no—
411C2×Q8—44no—
412C2×Q8C2×D4×C1111yescharacteristic
413C2×Q8C2×D4×C1112yes—
414C2×Q8C2×D4×C1112yes—
415C2×Q8C11×#4112yes—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—24no—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4C2×D4×C1112yes—
424C2×D4C2×D4×C1111yescharacteristic
425C2×D4C11×#4112yes—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4C2×D4×C1112yes—
433C22×C4C24×C1111yescharacteristic
434Q16—42no—
435SD16—44no—
436SD16—42no—
437SD16—42no—
438D8—44no—
439D8—42no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444C2×C8—22no—
445C2×C8—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—42no—
457C22⋊C4—24no—
458C22⋊C4—22no—
459C22⋊C4—24no—
460C22⋊C4—21no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—22no—
465C22⋊C4C2×D4×C1112yes—
466C22⋊C4C2×D4×C1112yes—
467C42—22no—
468C42—24no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—22no—
473C42—42no—
474C42C2×D4×C1111yescharacteristic
475C42C2×D4×C1111yescharacteristic
476C42C2×D4×C1112yes—
477C11#2399911yescharacteristic, direct product factor, Sylow
478C23—22no—
479C23—21no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—82no—
484C23C22×D4×C1111yescharacteristic
485Q8—24no—
486Q8—24no—
487Q8—22no—
488Q8—22no—
489Q8—22no—
490Q8—44no—
491Q8—82no—
492D4—22no—
493D4—24no—
494D4—22no—
495D4—22no—
496D4—44no—
497D4—42no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—42no—
502D4—84no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—82no—
518C2×C4—84no—
519C2×C4—81no—
520C2×C4C11×#12014yes—
521C2×C4C22×D4×C1111yescharacteristic
522C2×C4C22×D4×C1111yescharacteristic
523C2×C4C2×C11×#4112yes—
524C2×C4C11×H(5,𝔽2)12yes—
525C8—42no—
526C8—42no—
527C22—41no—
528C22—42no—
529C22—44no—
530C22—42no—
531C22—41no—
532C22—42no—
533C22—82no—
534C22—161no—
535C22—161no—
536C22C2×C11×#12011yescharacteristic
537C22C11×#52511yescharacteristic
538C22C11×#53511yescharacteristic
539C4—24no—
540C4—42no—
541C4—41no—
542C4—42no—
543C4—41no—
544C4—42no—
545C4—42no—
546C4—41no—
547C4—82no—
548C4C11×#54612yes—
549C4C11×#54612yes—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—82no—
554C2—81no—
555C2—82no—
556C2C11×#240411yescharacteristic
subgroupG/H
center, socleC2×C11#2404
commutator, Frattini, cosocleC22×C4C24×C11
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×#3020C2semidirect
3. C2×C11×#454C2semidirect
4. C11×#2884C2semidirect
5. C11×#2031C2semidirect
6. C11×#2008C2semidirect
7. C11×#1912C2semidirect
8. C11×#1906C2semidirect
9. C11×#1904C2semidirect
10. C11×#1888C2semidirect
11. C11×#1830C2semidirect
117. #23999C11direct (N × H)
200. #3510C2×C11semidirect
201. #3020C2×C11semidirect
202. C2×#454C2×C11semidirect
203. #2884C2×C11semidirect
204. #2031C2×C11semidirect
205. #2008C2×C11semidirect
206. #1912C2×C11semidirect
207. #1906C2×C11semidirect
208. #1904C2×C11semidirect
209. #1888C2×C11semidirect
210. #1830C2×C11semidirect
477. C11#23999direct (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×#30202
C2×C11×#4542
C11×#28842
C11×#20312
C11×#20082
C11×#19122
C11×#19062
C11×#19042
C11×#18882
C11×#18302
#2399911