Finite Group Databasebeta

← C11×#18993 #14596186

Subgroups — C11×#18993 #14596186

Order 2816.

1012 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
1C2×C11×#562C211yesmaximal, characteristic, complemented
2C11×#3234C211yesmaximal, characteristic, complemented
3C11×#3213C211yesmaximal, characteristic, complemented
4C11×#3153C211yesmaximal, characteristic, complemented
5C11×#1661C214yesmaximal, complemented
6C11×#1656C214yesmaximal, complemented
7C11×#1533C211yesmaximal, characteristic, complemented
8C11×#1528C211yesmaximal, characteristic, complemented
9C11×#1527C211yesmaximal, characteristic, complemented
10C2×C11×#137—21no—
11C2×C11×AGL(1,ℤ/8)—21no—
12C11×#562—22no—
13C11×#562—22no—
14C11×#562—22no—
15C11×#562C2214yes—
16C11×#532C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×#121—21no—
25C2×C11×#121—21no—
26C11×#501C2212yescomplemented
27C11×#497C2212yescomplemented
28C11×#496C2212yescomplemented
29C11×#496C2212yescomplemented
30C11×#495—22no—
31C11×#490C2212yescomplemented
32C11×#489C2212yescomplemented
33C11×#481—21no—
34C11×#480—21no—
35C11×#478—22no—
36C11×#463—22no—
37C11×#448—21no—
38C11×#447—21no—
39C11×#432C2211yescharacteristic
40C11×#432C2211yescharacteristic
41C4×C11×M16C2211yescharacteristic
42C11×#330C2214yescomplemented
43C11×#329C2214yescomplemented
44C11×#329C2214yescomplemented
45C2×C11×#41—21no—
46C22×Q8×C11D411yescharacteristic
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C11×#137—44no—
55C11×AGL(1,ℤ/8)—44no—
56C2×C11×Q16—22no—
57C2×C11×SD16—22no—
58C2×C11×SD16—22no—
59C2×C11×SD16—22no—
60C2×C11×D8—22no—
61C2×C11×D8—22no—
62C2×C11×M16—21no—
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127C2311yescharacteristic
65C11×#125—21no—
66C11×#125—21no—
67C11×#125D412yes—
68C11×#125C2312yes—
69C11×#124—21no—
70C11×#124—21no—
71C11×#124—21no—
72C11×#124—21no—
73C11×#124—21no—
74C11×#124D412yes—
75C11×#124D412yes—
76C11×#124C2312yes—
77C11×#124C2312yes—
78C11×#123—24no—
79C11×#123—24no—
80C11×#123—24no—
81C11×#123—24no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—24no—
85C11×C22⋊Q8—24no—
86C11×#121—24no—
87C11×#121—24no—
88C11×#121—24no—
89C11×#121—24no—
90C11×#121—21no—
91C11×#121—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4D411yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C42×C11C2311yescharacteristic
107C11×#107—22no—
108C11×#106—22no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×#103—22no—
112C11×#102—22no—
113C11×#102—22no—
114C11×#102—22no—
115C11×C22⋊C8—21no—
116C11×C22⋊C8—21no—
117C11×#97C2312yes—
118C11×#97C2312yes—
119C11×#97C2312yes—
120C4×C8×C11—21no—
121#18993C1111yesmaximal, characteristic, direct product factor, Sylow
122C24×C11—21no—
123C24×C11—21no—
124C11×#41—42no—
125C11×#41—42no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—42no—
130C2×Q8×C11—81no—
131C2×Q8×C11C2×D412yes—
132C2×Q8×C11C2×D412yes—
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—42no—
141C2×D4×C11—41no—
142C2×D4×C11—81no—
143C2×D4×C11—82no—
144C2×D4×C11—82no—
145C2×D4×C11C2×D412yes—
146C2×D4×C11C2×D412yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—41no—
154C22×C4×C11—82no—
155C22×C4×C11—82no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C11×Q16—44no—
160C11×SD16—44no—
161C11×SD16—44no—
162C11×SD16—82no—
163C11×D8—44no—
164C11×D8—82no—
165C11×M16—24no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4C2×D412yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2411yescharacteristic
197C2×#562C2×C1111yescharacteristic, complemented
198#3234C2×C1111yescharacteristic, complemented
199#3213C2×C1111yescharacteristic, complemented
200#3153C2×C1111yescharacteristic, complemented
201#1661C2×C1114yescomplemented
202#1656C2×C1114yescomplemented
203#1533C2×C1111yescharacteristic, complemented
204#1528C2×C1111yescharacteristic, complemented
205#1527C2×C1111yescharacteristic, complemented
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—41no—
215C23×C11#12011yescharacteristic
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—41no—
219Q8×C11—41no—
220Q8×C11—81no—
221Q8×C11—81no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—41no—
225D4×C11—42no—
226D4×C11—41no—
227D4×C11—42no—
228D4×C11—81no—
229D4×C11—81no—
230D4×C11—84no—
231D4×C11—84no—
232D4×C11—82no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—82no—
246C2×C4×C11—84no—
247C2×C4×C11—84no—
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C8×C11—24no—
255C8×C11—42no—
256C8×C11—42no—
257C2×#137—21no—
258C2×AGL(1,ℤ/8)—21no—
259#562—22no—
260#562—22no—
261#562—22no—
262#562C22×C1114yes—
263#532C22×C1111yescharacteristic
264C2×#125C22×C1111yescharacteristic
265C2×#124C22×C1111yescharacteristic
266C2×#124C22×C1111yescharacteristic
267C2×#123—21no—
268C2×#123—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8—21no—
271C2×#121—21no—
272C2×#121—21no—
273#501C22×C1112yescomplemented
274#497C22×C1112yescomplemented
275#496C22×C1112yescomplemented
276#496C22×C1112yescomplemented
277#495—22no—
278#490C22×C1112yescomplemented
279#489C22×C1112yescomplemented
280#481—21no—
281#480—21no—
282#478—22no—
283#463—22no—
284#448—21no—
285#447—21no—
286#432C22×C1111yescharacteristic
287#432C22×C1111yescharacteristic
288C4×M16C22×C1111yescharacteristic
289#330C22×C1114yescomplemented
290#329C22×C1114yescomplemented
291#329C22×C1114yescomplemented
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—84no—
301C22×C11—84no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11#45312yes—
306C22×C11C2×#12011yescharacteristic
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—81no—
318C2×#41—21no—
319C22×Q8D4×C1111yescharacteristic
320C22×Q8D4×C1111yescharacteristic
321C22×D4—21no—
322C22×D4—21no—
323C22×D4D4×C1111yescharacteristic
324C22×D4D4×C1111yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327#137—44no—
328AGL(1,ℤ/8)—44no—
329C2×Q16—22no—
330C2×SD16—22no—
331C2×SD16—22no—
332C2×SD16—22no—
333C2×D8—22no—
334C2×D8—22no—
335C2×M16—21no—
336C4⋊Q8C23×C1111yescharacteristic
337#127C23×C1111yescharacteristic
338#125—21no—
339#125—21no—
340#125D4×C1112yes—
341#125C23×C1112yes—
342#124—21no—
343#124—21no—
344#124—21no—
345#124—21no—
346#124—21no—
347#124D4×C1112yes—
348#124D4×C1112yes—
349#124C23×C1112yes—
350#124C23×C1112yes—
351#123—24no—
352#123—24no—
353#123—24no—
354#123—24no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359#121—24no—
360#121—24no—
361#121—24no—
362#121—24no—
363#121—21no—
364#121—21no—
365C4×D4—21no—
366C4×D4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4D4×C1111yescharacteristic
372C2×C4⋊C4D4×C1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C42C23×C1111yescharacteristic
380#107—22no—
381#106—22no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384#103—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390#97C23×C1112yes—
391#97C23×C1112yes—
392#97C23×C1112yes—
393C4×C8—21no—
394C2×C11—22no—
395C2×C11—82no—
396C2×C11—82no—
397C2×C11—161no—
398C2×C11C2×#45311yescharacteristic
399C2×C11#301911yescharacteristic
400C2×C11#302011yescharacteristic
401C24—21no—
402C24—21no—
403#41—42no—
404#41—42no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—42no—
409C2×Q8—81no—
410C2×Q8C2×D4×C1112yes—
411C2×Q8C2×D4×C1112yes—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—42no—
420C2×D4—41no—
421C2×D4—81no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4C2×D4×C1112yes—
425C2×D4C2×D4×C1112yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—41no—
433C22×C4—82no—
434C22×C4—82no—
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438Q16—44no—
439SD16—44no—
440SD16—44no—
441SD16—82no—
442D8—44no—
443D8—82no—
444M16—24no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4C2×D4×C1112yes—
459C4⋊C4C2×D4×C1112yes—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C42C2×D4×C1111yescharacteristic
473C42C2×D4×C1111yescharacteristic
474C42C2×D4×C1111yescharacteristic
475C42C24×C1111yescharacteristic
476C11#1899311yescharacteristic, direct product factor, Sylow
477C23—22no—
478C23—22no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23C11×#12011yescharacteristic
487Q8—42no—
488Q8—42no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—81no—
493D4—42no—
494D4—42no—
495D4—41no—
496D4—42no—
497D4—41no—
498D4—42no—
499D4—81no—
500D4—81no—
501D4—84no—
502D4—84no—
503D4—82no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4C11×#12011yescharacteristic
520C2×C4C11×#12011yescharacteristic
521C2×C4C11×#12011yescharacteristic
522C2×C4C22×D4×C1111yescharacteristic
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C8—24no—
526C8—42no—
527C8—42no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—84no—
537C22—84no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22C11×#45312yes—
542C22C2×C11×#12011yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—42no—
553C4—81no—
554C2—22no—
555C2—82no—
556C2—82no—
557C2—161no—
558C2C2×C11×#45311yescharacteristic
559C2C11×#301911yescharacteristic
560C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#562C2semidirect
2. C11×#3234C2semidirect
3. C11×#3213C2semidirect
4. C11×#3153C2semidirect
5. C11×#1661C2semidirect
6. C11×#1656C2semidirect
7. C11×#1533C2semidirect
8. C11×#1528C2semidirect
9. C11×#1527C2semidirect
26. C11×#501C22semidirect
27. C11×#497C22semidirect
28. C11×#496C22semidirect
29. C11×#496C22semidirect
31. C11×#490C22semidirect
32. C11×#489C22semidirect
42. C11×#330C22semidirect
43. C11×#329C22semidirect
44. C11×#329C22semidirect
121. #18993C11direct (N × H)
197. C2×#562C2×C11semidirect
198. #3234C2×C11semidirect
199. #3213C2×C11semidirect
200. #3153C2×C11semidirect
201. #1661C2×C11semidirect
202. #1656C2×C11semidirect
203. #1533C2×C11semidirect
204. #1528C2×C11semidirect
205. #1527C2×C11semidirect
273. #501C22×C11semidirect
274. #497C22×C11semidirect
275. #496C22×C11semidirect
276. #496C22×C11semidirect
278. #490C22×C11semidirect
279. #489C22×C11semidirect
289. #330C22×C11semidirect
290. #329C22×C11semidirect
291. #329C22×C11semidirect
476. C11#18993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5622
C11×#32342
C11×#32132
C11×#31532
C11×#16612
C11×#16562
C11×#15332
C11×#15282
C11×#15272
#1899311