Finite Group Databasebeta

← C11×#23511 #14600704

Subgroups — C11×#23511 #14600704

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic, complemented
5C22×C11×#102C211yesmaximal, characteristic, complemented
6C11×#2316C211yesmaximal, characteristic, complemented
7C11×#2042C214yesmaximal, complemented
8C11×#2041C214yesmaximal, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#535—24no—
15C11×#535—24no—
16C2×C11×#127C2212yes—
17C2×C11×#124C2212yes—
18C2×C11×#121—22no—
19C2×C11×#120—22no—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#418—24no—
24C11×#417—24no—
25C11×#416—24no—
26C2×C11×#103C2212yescomplemented
27C2×C11×#103C2212yescomplemented
28C2×C11×#102—24no—
29C2×C11×#102C2214yes—
30C2×C11×#102C2214yes—
31C2×C11×#102C2212yescomplemented
32C2×C11×#102C2212yescomplemented
33C11×#389—22no—
34C11×#389C2214yescomplemented
35C11×#380—22no—
36C11×#336C2214yescomplemented
37C25×C11—21no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41D414yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—24no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11D414yes—
54C22×D4×C11C2312yes—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C2×C11×M16—22no—
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11C2312yes—
66C22×C8×C11C2312yes—
67C11×#127—24no—
68C11×#127—24no—
69C11×#124—24no—
70C11×#124—24no—
71C11×#121—216no—
72C11×#120—216no—
73C11×#117—22no—
74C11×#117—22no—
75C11×#117—22no—
76C11×#117—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4D414yescomplemented
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—21no—
88C2×C42×C11C2312yes—
89C11×#103—24no—
90C11×#103—24no—
91C11×#102—28no—
92C11×#102—24no—
93C11×#102—28no—
94C11×#102—24no—
95C11×#95—24no—
96#23511C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—22no—
98C24×C11—21no—
99C24×C11—24no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11—82no—
103C24×C11—82no—
104C24×C11C2×D411yescharacteristic
105C11×#41—28no—
106C11×#41—28no—
107C11×#41—44no—
108C11×#41—44no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11C2×D412yes—
115C2×D4×C11—24no—
116C2×D4×C11—216no—
117C2×D4×C11—24no—
118C2×D4×C11—28no—
119C2×D4×C11—28no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11—44no—
133C2×D4×C11—42no—
134C2×D4×C11—44no—
135C2×D4×C11—42no—
136C2×D4×C11—84no—
137C2×D4×C11—84no—
138C2×D4×C11C2×D414yes—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—82no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C11×M16—44no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—44no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—84no—
171C11×C4⋊C4C2×D414yes—
172C11×C22⋊C4—216no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—42no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—42no—
178C2×#535C2×C1111yescharacteristic
179C2×#417C2×C1111yescharacteristic, complemented
180C2×#418C2×C1111yescharacteristic, complemented
181C2×#416C2×C1111yescharacteristic, complemented
182C22×#102C2×C1111yescharacteristic, complemented
183#2316C2×C1111yescharacteristic, complemented
184#2042C2×C1114yescomplemented
185#2041C2×C1114yescomplemented
186#1729C2×C1111yescharacteristic, complemented
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—42no—
193C23×C11—41no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—44no—
197C23×C11—42no—
198C23×C11—44no—
199C23×C11—48no—
200C23×C11—88no—
201C23×C11—88no—
202C23×C11—84no—
203C23×C11—84no—
204C23×C11#12012yes—
205C23×C11#12112yes—
206C23×C11#12412yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—41no—
211Q8×C11—41no—
212D4×C11—24no—
213D4×C11—22no—
214D4×C11—24no—
215D4×C11—22no—
216D4×C11—48no—
217D4×C11—42no—
218D4×C11—41no—
219D4×C11—42no—
220D4×C11—41no—
221D4×C11—48no—
222D4×C11—816no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—44no—
231C2×C4×C11—48no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—84no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12114yes—
238C2×C4×C11#12114yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12314yes—
241C2×C4×C11#12314yes—
242C2×C4×C11#12412yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C8×C11—42no—
250C8×C11—42no—
251C22×#41C22×C1111yescharacteristic
252C23×D4C22×C1111yescharacteristic
253C22×M16C22×C1111yescharacteristic
254C23×C8C22×C1111yescharacteristic
255#535—24no—
256#535—24no—
257C2×#127C22×C1112yes—
258C2×#124C22×C1112yes—
259C2×#121—22no—
260C2×#120—22no—
261C2×#117C22×C1111yescharacteristic
262C2×#117C22×C1111yescharacteristic
263C22×C4⋊C4C22×C1111yescharacteristic
264#418—24no—
265#417—24no—
266#416—24no—
267C2×#103C22×C1112yescomplemented
268C2×#103C22×C1112yescomplemented
269C2×#102—24no—
270C2×#102C22×C1114yes—
271C2×#102C22×C1114yes—
272C2×#102C22×C1112yescomplemented
273C2×#102C22×C1112yescomplemented
274#389—22no—
275#389C22×C1114yescomplemented
276#380—22no—
277#336C22×C1114yescomplemented
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—42no—
283C22×C11—44no—
284C22×C11—44no—
285C22×C11—48no—
286C22×C11—816no—
287C22×C11—82no—
288C22×C11—84no—
289C22×C11—81no—
290C22×C11—82no—
291C22×C11—81no—
292C22×C11—82no—
293C22×C11#39414yes—
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×#12111yescharacteristic
296C22×C11C2×#12411yescharacteristic
297C22×C11#57612yes—
298C22×C11#57712yes—
299C4×C11—42no—
300C4×C11—44no—
301C4×C11—44no—
302C4×C11—82no—
303C4×C11#39414yes—
304C4×C11C2×#12111yescharacteristic
305C4×C11C2×#12111yescharacteristic
306C4×C11C2×#12311yescharacteristic
307C4×C11C2×#12311yescharacteristic
308C25—21no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41D4×C1114yes—
315C22×Q8C23×C1111yescharacteristic
316C22×D4—21no—
317C22×D4—22no—
318C22×D4—21no—
319C22×D4—22no—
320C22×D4—24no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4D4×C1114yes—
325C22×D4C23×C1112yes—
326C22×D4C23×C1111yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4C23×C1111yescharacteristic
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8C23×C1112yes—
337C22×C8C23×C1112yes—
338#127—24no—
339#127—24no—
340#124—24no—
341#124—24no—
342#121—216no—
343#120—216no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4D4×C1112yes—
352C2×C4⋊C4D4×C1114yescomplemented
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1112yes—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4D4×C1112yes—
358C2×C42—21no—
359C2×C42C23×C1112yes—
360#103—24no—
361#103—24no—
362#102—28no—
363#102—24no—
364#102—28no—
365#102—24no—
366#95—24no—
367C2×C11—24no—
368C2×C11—82no—
369C2×C11—84no—
370C2×C11C2×#39411yescharacteristic
371C2×C11#301212yes—
372C2×C11#304111yescharacteristic
373C2×C11#304311yescharacteristic
374C2×C11#313612yes—
375C24—22no—
376C24—21no—
377C24—24no—
378C24—42no—
379C24—42no—
380C24—82no—
381C24—82no—
382C24C2×D4×C1111yescharacteristic
383#41—28no—
384#41—28no—
385#41—44no—
386#41—44no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8C2×D4×C1112yes—
393C2×D4—24no—
394C2×D4—216no—
395C2×D4—24no—
396C2×D4—28no—
397C2×D4—28no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—44no—
411C2×D4—42no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—84no—
415C2×D4—84no—
416C2×D4C2×D4×C1114yes—
417C2×D4C2×D4×C1112yes—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—82no—
426C22×C4C2×D4×C1114yes—
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1112yes—
429C22×C4C2×D4×C1112yes—
430C22×C4C2×D4×C1112yes—
431C22×C4C11×#4112yes—
432C22×C4C11×#4112yes—
433C22×C4C11×#4112yes—
434C22×C4C24×C1111yescharacteristic
435M16—44no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—44no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—84no—
449C4⋊C4C2×D4×C1114yes—
450C22⋊C4—216no—
451C22⋊C4—24no—
452C22⋊C4—42no—
453C42—22no—
454C42—22no—
455C42—42no—
456C11#2351111yescharacteristic, direct product factor, Sylow
457C23—22no—
458C23—22no—
459C23—24no—
460C23—22no—
461C23—41no—
462C23—42no—
463C23—41no—
464C23—42no—
465C23—48no—
466C23—42no—
467C23—44no—
468C23—42no—
469C23—44no—
470C23—88no—
471C23—84no—
472C23—84no—
473C23—88no—
474C23C11×#12012yes—
475C23C11×#12112yes—
476C23C11×#12412yes—
477C23C22×D4×C1111yescharacteristic
478Q8—22no—
479Q8—22no—
480Q8—41no—
481Q8—41no—
482D4—24no—
483D4—22no—
484D4—24no—
485D4—22no—
486D4—48no—
487D4—42no—
488D4—41no—
489D4—42no—
490D4—41no—
491D4—48no—
492D4—816no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—44no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—84no—
506C2×C4C11×#12012yes—
507C2×C4C11×#12114yes—
508C2×C4C11×#12114yes—
509C2×C4C11×#12112yes—
510C2×C4C11×#12314yes—
511C2×C4C11×#12314yes—
512C2×C4C11×#12412yes—
513C2×C4C22×D4×C1111yescharacteristic
514C2×C4C22×D4×C1111yescharacteristic
515C2×C4C22×D4×C1111yescharacteristic
516C2×C4C2×C11×#4111yescharacteristic
517C2×C4C2×C11×#4111yescharacteristic
518C2×C4C2×C11×#4111yescharacteristic
519C8—42no—
520C8—42no—
521C22—24no—
522C22—22no—
523C22—22no—
524C22—24no—
525C22—42no—
526C22—44no—
527C22—44no—
528C22—48no—
529C22—816no—
530C22—82no—
531C22—81no—
532C22—82no—
533C22—81no—
534C22—84no—
535C22—82no—
536C22C11×#39414yes—
537C22C2×C11×#12011yescharacteristic
538C22C2×C11×#12111yescharacteristic
539C22C2×C11×#12411yescharacteristic
540C22C11×#57612yes—
541C22C11×#57712yes—
542C4—42no—
543C4—44no—
544C4—44no—
545C4—82no—
546C4C11×#39414yes—
547C4C2×C11×#12111yescharacteristic
548C4C2×C11×#12111yescharacteristic
549C4C2×C11×#12311yescharacteristic
550C4C2×C11×#12311yescharacteristic
551C2—24no—
552C2—84no—
553C2—82no—
554C2C2×C11×#39411yescharacteristic
555C2C11×#301212yes—
556C2C11×#304111yescharacteristic
557C2C11×#304311yescharacteristic
558C2C11×#313612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#417C2semidirect
3. C2×C11×#418C2semidirect
4. C2×C11×#416C2semidirect
5. C22×C11×#102C2semidirect
6. C11×#2316C2semidirect
7. C11×#2042C2semidirect
8. C11×#2041C2semidirect
9. C11×#1729C2semidirect
26. C2×C11×#103C22semidirect
27. C2×C11×#103C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
34. C11×#389C22semidirect
36. C11×#336C22semidirect
81. C2×C11×C4⋊C4D4semidirect
96. #23511C11direct (N × H)
179. C2×#417C2×C11semidirect
180. C2×#418C2×C11semidirect
181. C2×#416C2×C11semidirect
182. C22×#102C2×C11semidirect
183. #2316C2×C11semidirect
184. #2042C2×C11semidirect
185. #2041C2×C11semidirect
186. #1729C2×C11semidirect
267. C2×#103C22×C11semidirect
268. C2×#103C22×C11semidirect
272. C2×#102C22×C11semidirect
273. C2×#102C22×C11semidirect
275. #389C22×C11semidirect
277. #336C22×C11semidirect
352. C2×C4⋊C4D4×C11semidirect
456. C11#23511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4172
C2×C11×#4182
C2×C11×#4162
C22×C11×#1022
C11×#23162
C11×#20422
C11×#20412
C11×#17292
#2351111