Finite Group Databasebeta

← C11×#23590 #14600783

Subgroups — C11×#23590 #14600783

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3461C211yesmaximal, characteristic
2C4×C11×#137C212yesmaximal, complemented
3C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
4C11×#2060C211yesmaximal, characteristic, complemented
5C11×#2039C211yesmaximal, characteristic
6C11×#2038C212yesmaximal, complemented
7C11×#2028C211yesmaximal, characteristic, complemented
8C11×#2007C211yesmaximal, characteristic
9C11×#2005C212yesmaximal, complemented
10C4×C11×#104C212yesmaximal, complemented
11C4×C11×#101C211yesmaximal, characteristic, complemented
12C2×C11×#137C2212yes—
13C11×#544C2211yescharacteristic
14C11×#542—22no—
15C11×#541—22no—
16C11×#539—22no—
17C11×#537C2211yescharacteristic
18C11×#536C2212yes—
19C11×#533—22no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C11×#529—22no—
22C11×#529—22no—
23C4×C11×#41C2212yes—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C11×#441—22no—
27C11×#440—22no—
28C4×C11×Q16—22no—
29C4×C11×SD16—22no—
30C11×#428C2212yes—
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#419C2212yes—
34C11×#417C2212yes—
35C2×C11×#101C2212yes—
36C4×C11×M16C2212yes—
37C11×#391C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#389—22no—
40C11×#384C2211yescharacteristic
41C4×C11×C4⋊C4—22no—
42C43×C11C2211yescharacteristic
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#339C2212yes—
46C11×#339C2212yes—
47C2×C11×#41C2312yes—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C11×#137—24no—
51C11×#137—24no—
52C2×C11×Q16—22no—
53C2×C11×SD16—22no—
54C2×C11×M16C2312yes—
55C2×C11×M16C2312yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—22no—
60C11×#126—24no—
61C11×#126—24no—
62C11×#125—22no—
63C11×#125—24no—
64C11×#125—22no—
65C11×#124—22no—
66C11×#124—22no—
67C11×#123—24no—
68C11×#123—24no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×#121—22no—
75C11×#121—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11D412yes—
82C4×Q8×C11D412yes—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11D412yes—
87C4×D4×C11D412yes—
88C11×#117—24no—
89C11×#117—22no—
90C11×#117C2312yes—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D412yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C42×C11—21no—
98C2×C42×C11—22no—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11D412yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C11×#107—22no—
106C11×#106—22no—
107C11×#104—24no—
108C11×#104—24no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#103—22no—
112C11×#102—22no—
113C11×#101—24no—
114C11×#97—22no—
115C4×C8×C11—22no—
116C11×#95—22no—
117C11×#95—22no—
118#23590C1111yesmaximal, characteristic, direct product factor, Sylow
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2×D412yes—
132C2×Q8×C11#4112yes—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11C2×D412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C11×Q16—28no—
149C11×SD16—28no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16#4114yes—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—44no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11—24no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—21no—
184C42×C11—22no—
185C42×C11—42no—
186C42×C11—41no—
187C42×C11—41no—
188C42×C11C2×D412yes—
189C42×C11C2×D412yes—
190C42×C11#4112yes—
191#3461C2×C1111yescharacteristic
192C4×#137C2×C1112yescomplemented
193C4×C4⋊Q8C2×C1111yescharacteristic, complemented
194#2060C2×C1111yescharacteristic, complemented
195#2039C2×C1111yescharacteristic
196#2038C2×C1112yescomplemented
197#2028C2×C1111yescharacteristic, complemented
198#2007C2×C1111yescharacteristic
199#2005C2×C1112yescomplemented
200C4×#104C2×C1112yescomplemented
201C4×#101C2×C1111yescharacteristic, complemented
202C23×C11—22no—
203C23×C11C22×D411yescharacteristic
204Q8×C11—24no—
205Q8×C11—22no—
206Q8×C11—22no—
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—82no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—82no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—82no—
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12012yes—
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4112yes—
247C2×C4×C11C2×#4111yescharacteristic
248C8×C11—24no—
249C8×C11—42no—
250C2×#137C22×C1112yes—
251#544C22×C1111yescharacteristic
252#542—22no—
253#541—22no—
254#539—22no—
255#537C22×C1111yescharacteristic
256#536C22×C1112yes—
257#533—22no—
258C2×C4⋊Q8C22×C1111yescharacteristic
259#529—22no—
260#529—22no—
261C4×#41C22×C1112yes—
262C2×C4×Q8C22×C1111yescharacteristic
263C2×C4×Q8C22×C1111yescharacteristic
264#441—22no—
265#440—22no—
266C4×Q16—22no—
267C4×SD16—22no—
268#428C22×C1112yes—
269C2×#104C22×C1112yes—
270C2×#104C22×C1112yes—
271#419C22×C1112yes—
272#417C22×C1112yes—
273C2×#101C22×C1112yes—
274C4×M16C22×C1112yes—
275#391C22×C1111yescharacteristic
276#391C22×C1111yescharacteristic
277#389—22no—
278#384C22×C1111yescharacteristic
279C4×C4⋊C4—22no—
280C43C22×C1111yescharacteristic
281#343C22×C1111yescharacteristic
282#343C22×C1111yescharacteristic
283#339C22×C1112yes—
284#339C22×C1112yes—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11C2×#12011yescharacteristic
291C22×C11#52511yescharacteristic
292C22×C11#53211yescharacteristic
293C4×C11—24no—
294C4×C11—21no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—81no—
304C4×C11#45612yes—
305C4×C11#52512yes—
306C4×C11#53212yes—
307C2×#41C23×C1112yes—
308C22×Q8C23×C1111yescharacteristic
309C22×Q8C23×C1111yescharacteristic
310#137—24no—
311#137—24no—
312C2×Q16—22no—
313C2×SD16—22no—
314C2×M16C23×C1112yes—
315C2×M16C23×C1112yes—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320#126—24no—
321#126—24no—
322#125—22no—
323#125—24no—
324#125—22no—
325#124—22no—
326#124—22no—
327#123—24no—
328#123—24no—
329C22⋊Q8—24no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334#121—22no—
335#121—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8D4×C1112yes—
342C4×Q8D4×C1112yes—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4D4×C1112yes—
347C4×D4D4×C1112yes—
348#117—24no—
349#117—22no—
350#117C23×C1112yes—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4D4×C1112yes—
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C42—21no—
358C2×C42—22no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42D4×C1112yes—
362C2×C42C23×C1111yescharacteristic
363C2×C42C23×C1111yescharacteristic
364C2×C42C23×C1111yescharacteristic
365#107—22no—
366#106—22no—
367#104—24no—
368#104—24no—
369#103—22no—
370#103—22no—
371#103—22no—
372#102—22no—
373#101—24no—
374#97—22no—
375C4×C8—22no—
376#95—22no—
377#95—22no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—82no—
381C2×C11#238811yescharacteristic
382C2×C11C2×#45611yescharacteristic
383C2×C11#301811yescharacteristic
384#41—22no—
385#41—22no—
386#41—22no—
387#41—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8C2×D4×C1112yes—
397C2×Q8C11×#4112yes—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4C2×D4×C1112yes—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4C2×D4×C1112yes—
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1112yes—
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C24×C1111yescharacteristic
413Q16—28no—
414SD16—28no—
415M16—22no—
416M16—22no—
417M16—22no—
418M16C11×#4114yes—
419C2×C8—22no—
420C2×C8—22no—
421C4⋊C4—28no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—44no—
433C4⋊C4—42no—
434C4⋊C4C2×D4×C1112yes—
435C4⋊C4C2×D4×C1112yes—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C42—24no—
443C42—22no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42—21no—
449C42—22no—
450C42—42no—
451C42—41no—
452C42—41no—
453C42C2×D4×C1112yes—
454C42C2×D4×C1112yes—
455C42C11×#4112yes—
456C11#2359011yescharacteristic, direct product factor, Sylow
457C23—22no—
458C23C22×D4×C1111yescharacteristic
459Q8—24no—
460Q8—22no—
461Q8—22no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—82no—
466D4—22no—
467D4—22no—
468D4—42no—
469D4—42no—
470D4—82no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—82no—
496C2×C4C11×#12011yescharacteristic
497C2×C4C11×#12012yes—
498C2×C4C11×#12011yescharacteristic
499C2×C4C22×D4×C1112yes—
500C2×C4C2×C11×#4111yescharacteristic
501C2×C4C2×C11×#4112yes—
502C2×C4C2×C11×#4111yescharacteristic
503C8—24no—
504C8—42no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22C2×C11×#12011yescharacteristic
511C22C11×#52511yescharacteristic
512C22C11×#53211yescharacteristic
513C4—24no—
514C4—21no—
515C4—22no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—42no—
523C4—81no—
524C4C11×#45612yes—
525C4C11×#52512yes—
526C4C11×#53212yes—
527C2—21no—
528C2—21no—
529C2—82no—
530C2C11×#238811yescharacteristic
531C2C2×C11×#45611yescharacteristic
532C2C11×#301811yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutator, Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×#120
prime radicalC11×#537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#137C2semidirect
3. C4×C11×C4⋊Q8C2semidirect
4. C11×#2060C2semidirect
6. C11×#2038C2semidirect
7. C11×#2028C2semidirect
9. C11×#2005C2semidirect
10. C4×C11×#104C2semidirect
11. C4×C11×#101C2semidirect
118. #23590C11direct (N × H)
192. C4×#137C2×C11semidirect
193. C4×C4⋊Q8C2×C11semidirect
194. #2060C2×C11semidirect
196. #2038C2×C11semidirect
197. #2028C2×C11semidirect
199. #2005C2×C11semidirect
200. C4×#104C2×C11semidirect
201. C4×#101C2×C11semidirect
456. C11#23590direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34612
C4×C11×#1372
C4×C11×C4⋊Q82
C11×#20602
C11×#20392
C11×#20382
C11×#20282
C11×#20072
C11×#20052
C4×C11×#1042
C4×C11×#1012
#2359011