Finite Group Databasebeta

← C11×#23643 #14600836

Subgroups — C11×#23643 #14600836

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C2×C11×#408C211yesmaximal, characteristic
3C11×#2311C211yesmaximal, characteristic
4C11×#2311C211yesmaximal, characteristic
5C11×#2077C212yesmaximal, complemented
6C11×#2077C212yesmaximal, complemented
7C11×#2076C212yesmaximal, complemented
8C11×#2075C212yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C11×#1735C211yesmaximal, characteristic, complemented
11C2×C11×#340C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#428—24no—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22C11×#408—24no—
23C2×C11×C22⋊C8C2212yes—
24C2×C11×C22⋊C8C2212yes—
25C11×#391—21no—
26C11×#391—21no—
27C11×#390—21no—
28C11×#390—21no—
29C11×#386—22no—
30C11×#386—22no—
31C11×#380C2212yes—
32C11×#380C2212yes—
33C11×#380C2212yes—
34C11×#380C2212yes—
35C11×#340C2212yes—
36C11×#340C2212yes—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#340C2212yes—
42C11×#340C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11D412yes—
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C2×C11×M16—22no—
57C2×C11×M16—22no—
58C2×C11×M16D414yes—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2312yes—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C11×#107—24no—
90C11×#106—24no—
91C11×C22⋊C8—24no—
92C11×C22⋊C8—24no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—22no—
97#23643C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11C2×D412yes—
99C24×C11C2×D411yescharacteristic
100C11×#41—44no—
101C11×#41—44no—
102C11×#41—44no—
103C11×#41—44no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—81no—
128C22×C4×C11—81no—
129C22×C4×C11—81no—
130C22×C4×C11—81no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C11×M16—28no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—44no—
150C2×C8×C11C2×D414yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—82no—
168C11×C22⋊C4—82no—
169C11×C22⋊C4—82no—
170C11×C22⋊C4—82no—
171C42×C11—42no—
172C42×C11—42no—
173C2×#428C2×C1111yescharacteristic, complemented
174C2×#408C2×C1111yescharacteristic
175#2311C2×C1111yescharacteristic
176#2311C2×C1111yescharacteristic
177#2077C2×C1112yescomplemented
178#2077C2×C1112yescomplemented
179#2076C2×C1112yescomplemented
180#2075C2×C1112yescomplemented
181#1736C2×C1111yescharacteristic, complemented
182#1735C2×C1111yescharacteristic, complemented
183C2×#340C2×C1111yescharacteristic, complemented
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11#12112yes—
196C23×C11#12312yes—
197C23×C11#12312yes—
198C23×C11C22×D411yescharacteristic
199Q8×C11—44no—
200D4×C11—48no—
201D4×C11—44no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—84no—
228C2×C4×C11—84no—
229C2×C4×C11#12112yes—
230C2×C4×C11#12314yes—
231C2×C4×C11#12312yes—
232C2×C4×C11#12312yes—
233C2×C4×C11#12414yes—
234C2×C4×C11#12614yes—
235C2×C4×C11#12614yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C8×C11—24no—
243C8×C11—41no—
244C8×C11—41no—
245C22×#41C22×C1111yescharacteristic
246C22×M16C22×C1111yescharacteristic
247C23×C8C22×C1111yescharacteristic
248C2×#117C22×C1111yescharacteristic
249C2×#117C22×C1111yescharacteristic
250C22×C4⋊C4C22×C1111yescharacteristic
251C22×C4⋊C4C22×C1111yescharacteristic
252#428—24no—
253C2×#107C22×C1112yes—
254C2×#106C22×C1112yes—
255#408—24no—
256C2×C22⋊C8C22×C1112yes—
257C2×C22⋊C8C22×C1112yes—
258#391—21no—
259#391—21no—
260#390—21no—
261#390—21no—
262#386—22no—
263#386—22no—
264#380C22×C1112yes—
265#380C22×C1112yes—
266#380C22×C1112yes—
267#380C22×C1112yes—
268#340C22×C1111yescharacteristic
269#340C22×C1112yes—
270#340C22×C1112yes—
271#340C22×C1111yescharacteristic
272#340C22×C1112yes—
273#340C22×C1112yes—
274#340C22×C1111yescharacteristic
275#340C22×C1111yescharacteristic
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11#39714yes—
290C22×C11C2×#12111yescharacteristic
291C22×C11C2×#12311yescharacteristic
292C22×C11C2×#12311yescharacteristic
293C22×C11#57611yescharacteristic
294C22×C11#57711yescharacteristic
295C22×C11#57711yescharacteristic
296C22×C11#57811yescharacteristic
297C4×C11—42no—
298C4×C11—82no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11—82no—
303C4×C11—81no—
304C4×C11#39714yes—
305C4×C11C2×#12311yescharacteristic
306C4×C11C2×#12411yescharacteristic
307C4×C11C2×#12611yescharacteristic
308C4×C11C2×#12611yescharacteristic
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—22no—
315C22×Q8D4×C1111yescharacteristic
316C22×D4D4×C1112yes—
317C22×D4D4×C1111yescharacteristic
318C23×C4—21no—
319C23×C4—21no—
320C23×C4C23×C1112yes—
321C23×C4C23×C1111yescharacteristic
322C2×M16—22no—
323C2×M16—22no—
324C2×M16D4×C1114yes—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8C23×C1111yescharacteristic
329C22×C8C23×C1111yescharacteristic
330C22×C8C23×C1112yes—
331#117—22no—
332#117—22no—
333#117—22no—
334#117—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4C23×C1112yes—
342C2×C4⋊C4C23×C1112yes—
343C2×C4⋊C4C23×C1111yescharacteristic
344C2×C4⋊C4C23×C1111yescharacteristic
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C4⋊C4C23×C1111yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C42—21no—
354C2×C42—21no—
355#107—24no—
356#106—24no—
357C22⋊C8—24no—
358C22⋊C8—24no—
359#95—22no—
360#95—22no—
361#95—22no—
362#95—22no—
363C2×C11—24no—
364C2×C11—82no—
365C2×C11C2×#39711yescharacteristic
366C2×C11#306211yescharacteristic
367C2×C11#306311yescharacteristic
368C2×C11#309611yescharacteristic
369C2×C11#309711yescharacteristic
370C2×C11#309811yescharacteristic
371C2×C11#309911yescharacteristic
372C24C2×D4×C1112yes—
373C24C2×D4×C1111yescharacteristic
374#41—44no—
375#41—44no—
376#41—44no—
377#41—44no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×D4—24no—
382C2×D4—24no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—81no—
402C22×C4—81no—
403C22×C4—81no—
404C22×C4—81no—
405C22×C4C2×D4×C1112yes—
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1112yes—
408C22×C4C11×#4112yes—
409C22×C4C11×#4112yes—
410C22×C4C11×#4112yes—
411C22×C4C11×#4112yes—
412C22×C4C11×#4112yes—
413C22×C4C24×C1111yescharacteristic
414M16—28no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—44no—
424C2×C8C2×D4×C1114yes—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—42no—
438C4⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—82no—
442C22⋊C4—82no—
443C22⋊C4—82no—
444C22⋊C4—82no—
445C42—42no—
446C42—42no—
447C11#2364311yescharacteristic, direct product factor, Sylow
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23C11×#12112yes—
460C23C11×#12312yes—
461C23C11×#12312yes—
462C23C22×D4×C1111yescharacteristic
463Q8—44no—
464D4—48no—
465D4—44no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—84no—
492C2×C4—84no—
493C2×C4C11×#12112yes—
494C2×C4C11×#12314yes—
495C2×C4C11×#12312yes—
496C2×C4C11×#12312yes—
497C2×C4C11×#12414yes—
498C2×C4C11×#12614yes—
499C2×C4C11×#12614yes—
500C2×C4C22×D4×C1111yescharacteristic
501C2×C4C2×C11×#4111yescharacteristic
502C2×C4C2×C11×#4111yescharacteristic
503C2×C4C2×C11×#4111yescharacteristic
504C2×C4C2×C11×#4111yescharacteristic
505C2×C4C2×C11×#4111yescharacteristic
506C8—24no—
507C8—41no—
508C8—41no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22C11×#39714yes—
523C22C2×C11×#12111yescharacteristic
524C22C2×C11×#12311yescharacteristic
525C22C2×C11×#12311yescharacteristic
526C22C11×#57611yescharacteristic
527C22C11×#57711yescharacteristic
528C22C11×#57711yescharacteristic
529C22C11×#57811yescharacteristic
530C4—42no—
531C4—82no—
532C4—81no—
533C4—81no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4C11×#39714yes—
538C4C2×C11×#12311yescharacteristic
539C4C2×C11×#12411yescharacteristic
540C4C2×C11×#12611yescharacteristic
541C4C2×C11×#12611yescharacteristic
542C2—24no—
543C2—82no—
544C2C2×C11×#39711yescharacteristic
545C2C11×#306211yescharacteristic
546C2C11×#306311yescharacteristic
547C2C11×#309611yescharacteristic
548C2C11×#309711yescharacteristic
549C2C11×#309811yescharacteristic
550C2C11×#309911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
5. C11×#2077C2semidirect
6. C11×#2077C2semidirect
7. C11×#2076C2semidirect
8. C11×#2075C2semidirect
9. C11×#1736C2semidirect
10. C11×#1735C2semidirect
11. C2×C11×#340C2semidirect
97. #23643C11direct (N × H)
173. C2×#428C2×C11semidirect
177. #2077C2×C11semidirect
178. #2077C2×C11semidirect
179. #2076C2×C11semidirect
180. #2075C2×C11semidirect
181. #1736C2×C11semidirect
182. #1735C2×C11semidirect
183. C2×#340C2×C11semidirect
447. C11#23643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#4082
C11×#23112
C11×#20772
C11×#20762
C11×#20752
C11×#17362
C11×#17352
C2×C11×#3402
#2364311