Finite Group Databasebeta

← C11×#24351 #14601544

Subgroups — C11×#24351 #14601544

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C11×#2855C212yesmaximal, complemented
3C4×C11×#123C211yesmaximal, characteristic
4C11×#2062C212yesmaximal, complemented
5C11×#2030C212yesmaximal, complemented
6C11×#1996C212yesmaximal, complemented
7C11×#1890C212yesmaximal
8C11×#1867C212yesmaximal
9C11×#1799C211yesmaximal, characteristic
10C11×#554—24no—
11C11×#554—22no—
12D4×Q8×C11—22no—
13C11×#544—21no—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—21no—
17C2×C11×#123C2211yescharacteristic
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C11×#518C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C2×C11×#99C2212yes—
24C11×#391—22no—
25C11×#389—22no—
26C11×#388—21no—
27C11×#387—21no—
28C11×#387—24no—
29C11×#386C2211yescharacteristic
30C11×#385C2214yes—
31C11×#385C2211yescharacteristic
32C11×#381C2214yes—
33C11×#381C2211yescharacteristic
34C11×#380C2212yes—
35C4×C11×C4⋊C4—21no—
36C4×C11×C22⋊C4—21no—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#342C2214yes—
39C11×#342C2214yes—
40C11×#342C2212yes—
41C22×Q8×C11—21no—
42C22×Q8×C11D412yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—24no—
51C11×#125—22no—
52C11×#125—24no—
53C11×#123—22no—
54C11×#123Q814yescomplemented
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C11×#117—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D414yes—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C11×C22⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2311yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11—22no—
94C2×C42×C11—21no—
95C2×C42×C11—22no—
96C2×C42×C11—21no—
97C2×C42×C11D411yescharacteristic
98C11×#99—24no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—22no—
105C11×#95—24no—
106C11×#95—24no—
107C11×#95—24no—
108#24351C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11C2×D411yescharacteristic
110C24×C11C2411yescharacteristic
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—44no—
116C2×Q8×C11—82no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11C2×Q812yes—
120C2×D4×C11#4112yes—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×Q812yescomplemented
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—44no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—48no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4C2×Q812yescomplemented
174C42×C11—24no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—42no—
178C42×C11—41no—
179C42×C11—42no—
180C42×C11—41no—
181#3501C2×C1111yescharacteristic
182#2855C2×C1112yescomplemented
183C4×#123C2×C1111yescharacteristic
184#2062C2×C1112yescomplemented
185#2030C2×C1112yescomplemented
186#1996C2×C1112yescomplemented
187#1890C2×C1112yes—
188#1867C2×C1112yes—
189#1799C2×C1111yescharacteristic
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C22⋊Q812yes—
197C23×C11C22×D411yescharacteristic
198C23×C11C22×D412yes—
199C23×C11C22×Q811yescharacteristic
200C23×C11C2×#4111yescharacteristic
201C23×C112−1+412yes—
202Q8×C11—44no—
203Q8×C11—82no—
204Q8×C11—82no—
205Q8×C11—82no—
206D4×C11—24no—
207D4×C11—24no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—21no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—41no—
241C2×C4×C11—44no—
242C2×C4×C11—81no—
243C2×C4×C11—82no—
244C2×C4×C11—82no—
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12012yes—
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11C22⋊Q812yes—
249#554—24no—
250#554—22no—
251D4×Q8—22no—
252#544—21no—
253#543—21no—
254#543C22×C1112yes—
255#533—21no—
256C2×#123C22×C1111yescharacteristic
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C22×C1112yes—
259#518C22×C1112yes—
260C2×C4×D4C22×C1111yescharacteristic
261C22×C42C22×C1111yescharacteristic
262C2×#99C22×C1112yes—
263#391—22no—
264#389—22no—
265#388—21no—
266#387—24no—
267#387—21no—
268#386C22×C1111yescharacteristic
269#385C22×C1111yescharacteristic
270#385C22×C1114yes—
271#381C22×C1114yes—
272#381C22×C1111yescharacteristic
273#380C22×C1112yes—
274C4×C4⋊C4—21no—
275C4×C22⋊C4—21no—
276C4×C22⋊C4C22×C1111yescharacteristic
277#342C22×C1112yes—
278#342C22×C1114yes—
279#342C22×C1114yes—
280C22×C11—22no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—81no—
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×C22⋊Q811yescharacteristic
294C22×C11#53611yescharacteristic
295C22×C11#54812yes—
296C22×C11D4×Q812yes—
297C4×C11—22no—
298C4×C11—21no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—41no—
303C4×C11—44no—
304C4×C11—42no—
305C4×C11—44no—
306C4×C11—41no—
307C4×C11—84no—
308C4×C11—81no—
309C4×C11#45812yes—
310C22×Q8—21no—
311C22×Q8D4×C1112yes—
312C22×D4C23×C1111yescharacteristic
313C23×C4D4×C1111yescharacteristic
314C23×C4C23×C1111yescharacteristic
315C23×C4C23×C1111yescharacteristic
316C23×C4C23×C1111yescharacteristic
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—24no—
320#125—22no—
321#125—24no—
322#123—22no—
323#123Q8×C1114yescomplemented
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—24no—
341C4×D4—24no—
342#117—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4D4×C1111yescharacteristic
350C2×C4⋊C4D4×C1114yes—
351C2×C4⋊C4D4×C1112yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4D4×C1111yescharacteristic
356C2×C22⋊C4C23×C1111yescharacteristic
357C2×C22⋊C4C23×C1114yes—
358C2×C22⋊C4C23×C1111yescharacteristic
359C2×C22⋊C4C23×C1114yes—
360C2×C22⋊C4C23×C1111yescharacteristic
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—22no—
364C2×C42—21no—
365C2×C42—22no—
366C2×C42D4×C1111yescharacteristic
367#99—24no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—22no—
374#95—24no—
375#95—24no—
376#95—24no—
377C2×C11—21no—
378C2×C11—22no—
379C2×C11—21no—
380C2×C11—22no—
381C2×C11—42no—
382C2×C11#240911yescharacteristic
383C2×C11C2×#45811yescharacteristic
384C2×C11#302511yescharacteristic
385C24C2×D4×C1111yescharacteristic
386C24C24×C1111yescharacteristic
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—44no—
392C2×Q8—82no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4C2×Q8×C1112yes—
396C2×D4C11×#4112yes—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—24no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4C2×D4×C1111yescharacteristic
414C22×C4C2×D4×C1112yes—
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1114yes—
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1114yes—
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1112yes—
422C22×C4C2×Q8×C1112yescomplemented
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—44no—
436C4⋊C4—42no—
437C4⋊C4—48no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—22no—
442C22⋊C4—24no—
443C22⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C22⋊C4—24no—
448C22⋊C4—42no—
449C22⋊C4C2×Q8×C1112yescomplemented
450C42—24no—
451C42—21no—
452C42—21no—
453C42—42no—
454C42—41no—
455C42—42no—
456C42—41no—
457C11#2435111yescharacteristic, direct product factor, Sylow
458C23—21no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23C11×C22⋊Q812yes—
465C23C22×D4×C1111yescharacteristic
466C23C22×D4×C1112yes—
467C23C22×Q8×C1111yescharacteristic
468C23C2×C11×#4111yescharacteristic
469C23C11×2−1+412yes—
470Q8—44no—
471Q8—82no—
472Q8—82no—
473Q8—82no—
474D4—24no—
475D4—24no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—21no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—44no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—41no—
509C2×C4—44no—
510C2×C4—81no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4C11×#12011yescharacteristic
514C2×C4C11×#12012yes—
515C2×C4C11×#12011yescharacteristic
516C2×C4C11×C22⋊Q812yes—
517C22—22no—
518C22—21no—
519C22—22no—
520C22—21no—
521C22—22no—
522C22—41no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22—81no—
529C22C2×C11×#12011yescharacteristic
530C22C2×C11×C22⋊Q811yescharacteristic
531C22C11×#53611yescharacteristic
532C22C11×#54812yes—
533C22D4×Q8×C1112yes—
534C4—22no—
535C4—21no—
536C4—22no—
537C4—42no—
538C4—42no—
539C4—41no—
540C4—44no—
541C4—42no—
542C4—44no—
543C4—41no—
544C4—84no—
545C4—81no—
546C4C11×#45812yes—
547C2—21no—
548C2—22no—
549C2—21no—
550C2—22no—
551C2—42no—
552C2C11×#240911yescharacteristic
553C2C2×C11×#45811yescharacteristic
554C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2855C2semidirect
4. C11×#2062C2semidirect
5. C11×#2030C2semidirect
6. C11×#1996C2semidirect
54. C11×#123Q8semidirect
108. #24351C11direct (N × H)
146. C22×C4×C11C2×Q8semidirect
173. C11×C22⋊C4C2×Q8semidirect
182. #2855C2×C11semidirect
184. #2062C2×C11semidirect
185. #2030C2×C11semidirect
186. #1996C2×C11semidirect
323. #123Q8×C11semidirect
422. C22×C4C2×Q8×C11semidirect
449. C22⋊C4C2×Q8×C11semidirect
457. C11#24351direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#28552
C4×C11×#1232
C11×#20622
C11×#20302
C11×#19962
C11×#18902
C11×#18672
C11×#17992
#2435111