Finite Group Databasebeta

← C11×#24628 #14601821

Subgroups — C11×#24628 #14601821

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C211yesmaximal, characteristic, complemented
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C11×#2541C211yesmaximal, characteristic
4C11×#2355C211yesmaximal, characteristic, complemented
5C11×#2055C212yesmaximal, complemented
6C11×#2014C212yesmaximal, complemented
7C11×#1982C212yesmaximal, complemented
8C11×#1957C211yesmaximal, characteristic, complemented
9C11×#1939C211yesmaximal, characteristic, complemented
10C11×#1926C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#127C2212yes—
16C2×C11×#121—21no—
17C2×C11×#121—21no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C11×#460—24no—
21C4×C11×SD16—24no—
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#392—22no—
33C11×#391C2212yes—
34C11×#390C2212yes—
35C11×#387—22no—
36C11×#384C2211yescharacteristic
37C11×#382—21no—
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16—24no—
54C2×C11×SD16—22no—
55C2×C11×SD16—42no—
56C2×C11×SD16—42no—
57C22×C8×C11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#127—24no—
61C11×#127—22no—
62C11×#127—22no—
63C11×#127—42no—
64C11×#121—44no—
65C11×#121—44no—
66C4×Q8×C11—22no—
67C4×Q8×C11D414yescomplemented
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C42×C11—21no—
82C2×C42×C11—22no—
83C2×C42×C11C2312yes—
84C2×C42×C11C2311yescharacteristic
85C11×#106—22no—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—42no—
88C11×#103—22no—
89C11×#102—24no—
90C11×#102—22no—
91C11×#102—24no—
92C11×#102—42no—
93C11×#102—42no—
94C4×C8×C11—22no—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—22no—
98C11×#95D412yes—
99#24628C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
101C24×C11—22no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11C2×D412yes—
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—82no—
128C2×D4×C11—81no—
129C2×D4×C11—81no—
130C2×D4×C11—82no—
131C2×D4×C11#4112yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C11×SD16—28no—
145C11×SD16—48no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11#4112yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—81no—
164C11×C4⋊C4SD1614yescomplemented
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—44no—
169C42×C11—24no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—82no—
173C42×C11C2×D412yes—
174C42×C11#4112yes—
175C2×#460C2×C1111yescharacteristic, complemented
176C2×C4×SD16C2×C1111yescharacteristic, complemented
177#2541C2×C1111yescharacteristic
178#2355C2×C1111yescharacteristic, complemented
179#2055C2×C1112yescomplemented
180#2014C2×C1112yescomplemented
181#1982C2×C1112yescomplemented
182#1957C2×C1111yescharacteristic, complemented
183#1939C2×C1111yescharacteristic, complemented
184#1926C2×C1112yescomplemented
185#1802C2×C1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11C22×D411yescharacteristic
201Q8×C11—22no—
202Q8×C11—22no—
203Q8×C11—41no—
204Q8×C11—41no—
205D4×C11—22no—
206D4×C11—22no—
207D4×C11—42no—
208D4×C11—41no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—41no—
212D4×C11—42no—
213D4×C11—88no—
214D4×C11—84no—
215D4×C11—88no—
216D4×C11—84no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—84no—
237C2×C4×C11#12112yes—
238C2×C4×C11#12112yes—
239C2×C4×C11C2×SD1614yes—
240C2×C4×C11C2×SD1612yes—
241C2×C4×C11AGL(1,ℤ/8)12yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C8×C11—22no—
249C8×C11—41no—
250C8×C11—42no—
251C22×SD16C22×C1111yescharacteristic
252C22×SD16C22×C1112yes—
253C2×#127C22×C1111yescharacteristic
254C2×#127C22×C1112yes—
255C2×#121—21no—
256C2×#121—21no—
257C2×C4×Q8C22×C1111yescharacteristic
258C2×C4×D4C22×C1111yescharacteristic
259#460—24no—
260C4×SD16—24no—
261C2×#106C22×C1111yescharacteristic
262C2×C4⋊C8C22×C1111yescharacteristic
263C2×C4⋊C8C22×C1112yes—
264C2×#103C22×C1111yescharacteristic
265C2×#102C22×C1111yescharacteristic
266C2×#102C22×C1112yes—
267C2×#102C22×C1112yes—
268C2×#102C22×C1112yes—
269C2×#102C22×C1112yes—
270C2×C4×C8C22×C1111yescharacteristic
271#392—22no—
272#391C22×C1112yes—
273#390C22×C1112yes—
274#387—22no—
275#384C22×C1111yescharacteristic
276#382—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4C22×C1112yes—
279C4×C4⋊C4C22×C1111yescharacteristic
280#340C22×C1112yes—
281#336C22×C1112yes—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11—82no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11C2×#12111yescharacteristic
297C22×C11#54611yescharacteristic
298C22×C11#55011yescharacteristic
299C22×C11C22×SD1611yescharacteristic
300C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C11#57611yescharacteristic
302C22×C11#57711yescharacteristic
303C4×C11—24no—
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—82no—
309C4×C11—81no—
310C4×C11#46014yes—
311C4×C11#52511yescharacteristic
312C4×C11#53511yescharacteristic
313C4×C11#55311yescharacteristic
314C4×C11#55511yescharacteristic
315C22×Q8C23×C1111yescharacteristic
316C22×D4—21no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—21no—
320C22×D4C23×C1112yes—
321C22×D4C23×C1111yescharacteristic
322C23×C4—21no—
323C2×SD16—22no—
324C2×SD16—22no—
325C2×SD16—24no—
326C2×SD16—22no—
327C2×SD16—42no—
328C2×SD16—42no—
329C22×C8C23×C1112yes—
330C22×C8C23×C1111yescharacteristic
331C22×C8C23×C1111yescharacteristic
332#127—24no—
333#127—22no—
334#127—22no—
335#127—42no—
336#121—44no—
337#121—44no—
338C4×Q8—22no—
339C4×Q8D4×C1114yescomplemented
340C4×D4—22no—
341C4×D4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4D4×C1111yescharacteristic
346C2×C4⋊C4D4×C1111yescharacteristic
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C4⋊C4C23×C1112yes—
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C42—21no—
354C2×C42—22no—
355C2×C42C23×C1112yes—
356C2×C42C23×C1111yescharacteristic
357#106—22no—
358C4⋊C8—22no—
359C4⋊C8—42no—
360#103—22no—
361#102—24no—
362#102—22no—
363#102—24no—
364#102—42no—
365#102—42no—
366C4×C8—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95D4×C1112yes—
371C2×C11—82no—
372C2×C11—162no—
373C2×C11#241411yescharacteristic
374C2×C11C2×#46011yescharacteristic
375C2×C11#304511yescharacteristic
376C2×C11#329511yescharacteristic
377C2×C11#332411yescharacteristic
378C2×C11#339211yescharacteristic
379C2×C11#339911yescharacteristic
380C24—21no—
381C24—22no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8C2×D4×C1112yes—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—44no—
400C2×D4—44no—
401C2×D4—44no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—44no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—82no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—82no—
411C2×D4C11×#4112yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4C2×D4×C1112yes—
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1112yes—
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C24×C1111yescharacteristic
424SD16—28no—
425SD16—48no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8—21no—
433C2×C8—22no—
434C2×C8C11×#4112yes—
435C4⋊C4—24no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—42no—
443C4⋊C4—81no—
444C4⋊C4C11×SD1614yescomplemented
445C4⋊C4C2×D4×C1112yes—
446C22⋊C4—44no—
447C22⋊C4—42no—
448C22⋊C4—44no—
449C42—24no—
450C42—22no—
451C42—22no—
452C42—82no—
453C42C2×D4×C1112yes—
454C42C11×#4112yes—
455C11#2462811yescharacteristic, direct product factor, Sylow
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23C22×D4×C1111yescharacteristic
471Q8—22no—
472Q8—22no—
473Q8—41no—
474Q8—41no—
475D4—22no—
476D4—22no—
477D4—42no—
478D4—41no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—42no—
483D4—88no—
484D4—84no—
485D4—88no—
486D4—84no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4C11×#12112yes—
508C2×C4C11×#12112yes—
509C2×C4C2×C11×SD1614yes—
510C2×C4C2×C11×SD1612yes—
511C2×C4C11×AGL(1,ℤ/8)12yes—
512C2×C4C22×D4×C1111yescharacteristic
513C2×C4C2×C11×#4111yescharacteristic
514C2×C4C2×C11×#4111yescharacteristic
515C2×C4C2×C11×#4111yescharacteristic
516C2×C4C11×H(5,𝔽2)11yescharacteristic
517C2×C4C11×H(5,𝔽2)11yescharacteristic
518C8—22no—
519C8—42no—
520C8—41no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22C2×C11×#12111yescharacteristic
536C22C11×#54611yescharacteristic
537C22C11×#55011yescharacteristic
538C22C22×C11×SD1611yescharacteristic
539C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
540C22C11×#57611yescharacteristic
541C22C11×#57711yescharacteristic
542C4—24no—
543C4—22no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—81no—
548C4—82no—
549C4C11×#46014yes—
550C4C11×#52511yescharacteristic
551C4C11×#53511yescharacteristic
552C4C11×#55311yescharacteristic
553C4C11×#55511yescharacteristic
554C2—82no—
555C2—162no—
556C2C11×#241411yescharacteristic
557C2C2×C11×#46011yescharacteristic
558C2C11×#304511yescharacteristic
559C2C11×#329511yescharacteristic
560C2C11×#332411yescharacteristic
561C2C11×#339211yescharacteristic
562C2C11×#339911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2541C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#460C2semidirect
2. C2×C4×C11×SD16C2semidirect
4. C11×#2355C2semidirect
5. C11×#2055C2semidirect
6. C11×#2014C2semidirect
7. C11×#1982C2semidirect
8. C11×#1957C2semidirect
9. C11×#1939C2semidirect
10. C11×#1926C2semidirect
11. C11×#1802C2semidirect
67. C4×Q8×C11D4semidirect
99. #24628C11direct (N × H)
164. C11×C4⋊C4SD16semidirect
175. C2×#460C2×C11semidirect
176. C2×C4×SD16C2×C11semidirect
178. #2355C2×C11semidirect
179. #2055C2×C11semidirect
180. #2014C2×C11semidirect
181. #1982C2×C11semidirect
182. #1957C2×C11semidirect
183. #1939C2×C11semidirect
184. #1926C2×C11semidirect
185. #1802C2×C11semidirect
339. C4×Q8D4×C11semidirect
444. C4⋊C4C11×SD16semidirect
455. C11#24628direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C2×C4×C11×SD162
C11×#25412
C11×#23552
C11×#20552
C11×#20142
C11×#19822
C11×#19572
C11×#19392
C11×#19262
C11×#18022
#2462811