Finite Group Databasebeta

← C11×#32917 #14610110

Subgroups — C11×#32917 #14610110

Order 2816.

1588 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×#518C211yesmaximal, characteristic, complemented
2C2×C11×#463C212yesmaximal, complemented
3C2×C11×#450C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic
5C11×#2620C211yesmaximal, characteristic, complemented
6C11×#1879C212yesmaximal, complemented
7C11×#1877C212yesmaximal, complemented
8C11×#1875C211yesmaximal, characteristic, complemented
9C11×#1873C211yesmaximal, characteristic, complemented
10C11×#1802C212yesmaximal, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C22×C11×D8C2212yes—
15C2×C11×#124C2211yescharacteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C11×#518—28no—
19C2×C4×D4×C11—22no—
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2212yes—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C22⋊C4—22no—
25C11×#463—28no—
26C11×#450—24no—
27C11×#447—24no—
28C2×C11×C4⋊C8C2212yescomplemented
29C2×C11×#103C2212yescomplemented
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yescomplemented
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#396—22no—
36C11×#394—22no—
37C11×#391C2211yescharacteristic, complemented
38C11×#390C2211yescharacteristic, complemented
39C11×#384C2211yescharacteristic, complemented
40C11×#340C2212yescomplemented
41C11×#340C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—24no—
46C22×D4×C11—24no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—22no—
50C22×D4×C11D414yes—
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2312yes—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11C2311yescharacteristic
56C2×C11×SD16—24no—
57C2×C11×SD16—24no—
58C2×C11×SD16—24no—
59C2×C11×D8—24no—
60C2×C11×D8—24no—
61C2×C11×D8—24no—
62C22×C8×C11C2312yes—
63C22×C8×C11C2312yes—
64C11×#124—24no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×#121—22no—
68C11×#121—22no—
69C4×D4×C11—216no—
70C4×D4×C11—24no—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C4×D4×C11D418yescomplemented
74C11×#117—24no—
75C11×#117—24no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4—216no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4D412yes—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C11×C4⋊C8—24no—
95C11×#103—24no—
96C11×#102—24no—
97C11×#102—24no—
98C11×#102—24no—
99C11×C22⋊C8—22no—
100C11×C22⋊C8—22no—
101C11×#95—22no—
102#32917C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—24no—
107C24×C11—21no—
108C24×C11—82no—
109C24×C11—82no—
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—216no—
118C2×D4×C11—216no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—42no—
128C2×D4×C11—82no—
129C2×D4×C11C2×D414yes—
130C2×D4×C11C2×D414yes—
131C2×D4×C11#4114yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—28no—
136C22×C4×C11—28no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—82no—
141C22×C4×C11—82no—
142C22×C4×C11—82no—
143C22×C4×C11—82no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C11×SD16—48no—
151C11×D8—48no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—82no—
166C11×C4⋊C4C2×D414yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—82no—
175C42×C11—24no—
176C42×C11—22no—
177C42×C11C2×D414yes—
178C2×#518C2×C1111yescharacteristic, complemented
179C2×#463C2×C1112yescomplemented
180C2×#450C2×C1111yescharacteristic, complemented
181C2×#447C2×C1111yescharacteristic
182#2620C2×C1111yescharacteristic, complemented
183#1879C2×C1112yescomplemented
184#1877C2×C1112yescomplemented
185#1875C2×C1111yescharacteristic, complemented
186#1873C2×C1111yescharacteristic, complemented
187#1802C2×C1112yescomplemented
188#1798C2×C1111yescharacteristic, complemented
189C23×C11—216no—
190C23×C11—21no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—21no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11—88no—
209C23×C11—88no—
210C23×C11#12112yes—
211C23×C11C22×D411yescharacteristic
212Q8×C11—42no—
213Q8×C11—42no—
214D4×C11—216no—
215D4×C11—24no—
216D4×C11—24no—
217D4×C11—24no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—84no—
221D4×C11#12118yes—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—88no—
242C2×C4×C11—88no—
243C2×C4×C11#12014yes—
244C2×C4×C11#12112yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D412yes—
247C2×C4×C11C2×#4112yes—
248C2×C4×C11C2×#4111yescharacteristic
249C8×C11—42no—
250C8×C11—42no—
251C23×D4C22×C1111yescharacteristic
252C22×SD16C22×C1112yes—
253C22×D8C22×C1112yes—
254C2×#124C22×C1111yescharacteristic, complemented
255C2×C22⋊Q8C22×C1111yescharacteristic
256C2×#121C22×C1111yescharacteristic
257#518—28no—
258C2×C4×D4—22no—
259C2×C4×D4C22×C1112yes—
260C2×C4×D4C22×C1112yes—
261C2×#117C22×C1111yescharacteristic
262C2×#117C22×C1111yescharacteristic
263C22×C22⋊C4—22no—
264#463—28no—
265#450—24no—
266#447—24no—
267C2×C4⋊C8C22×C1112yescomplemented
268C2×#103C22×C1112yescomplemented
269C2×#102C22×C1112yes—
270C2×#102C22×C1112yes—
271C2×#102C22×C1112yescomplemented
272C2×C22⋊C8C22×C1111yescharacteristic
273C2×C22⋊C8C22×C1111yescharacteristic
274#396—22no—
275#394—22no—
276#391C22×C1111yescharacteristic, complemented
277#390C22×C1111yescharacteristic, complemented
278#384C22×C1111yescharacteristic, complemented
279#340C22×C1112yescomplemented
280#340C22×C1112yescomplemented
281#336C22×C1112yescomplemented
282C22×C11—22no—
283C22×C11—28no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—42no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—816no—
295C22×C11—81no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11C2×#12011yescharacteristic
301C22×C11C2×#12111yescharacteristic
302C22×C11#52511yescharacteristic
303C22×C11#57612yes—
304C22×C11#57712yes—
305C4×C11—22no—
306C4×C11—24no—
307C4×C11—42no—
308C4×C11—44no—
309C4×C11—81no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11C2×#12112yes—
313C4×C11#52512yes—
314C25—21no—
315C22×Q8C23×C1111yescharacteristic
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—22no—
321C22×D4D4×C1114yes—
322C22×D4C23×C1111yescharacteristic
323C22×D4C23×C1112yes—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4C23×C1111yescharacteristic
327C2×SD16—24no—
328C2×SD16—24no—
329C2×SD16—24no—
330C2×D8—24no—
331C2×D8—24no—
332C2×D8—24no—
333C22×C8C23×C1112yes—
334C22×C8C23×C1112yes—
335#124—24no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338#121—22no—
339#121—22no—
340C4×D4—216no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4D4×C1118yescomplemented
345#117—24no—
346#117—24no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4D4×C1112yes—
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1112yes—
353C2×C22⋊C4—216no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4D4×C1112yes—
362C2×C42—21no—
363C2×C42C23×C1111yescharacteristic
364C2×C42C23×C1111yescharacteristic
365C4⋊C8—24no—
366#103—24no—
367#102—24no—
368#102—24no—
369#102—24no—
370C22⋊C8—22no—
371C22⋊C8—22no—
372#95—22no—
373C2×C11—42no—
374C2×C11—48no—
375C2×C11—161no—
376C2×C11#284711yescharacteristic
377C2×C11#301212yes—
378C2×C11#304111yescharacteristic
379C2×C11#304211yescharacteristic
380C2×C11#311812yes—
381C24—24no—
382C24—24no—
383C24—22no—
384C24—24no—
385C24—21no—
386C24—82no—
387C24—82no—
388C24C2×D4×C1111yescharacteristic
389C2×Q8—22no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—216no—
396C2×D4—216no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—42no—
406C2×D4—82no—
407C2×D4C2×D4×C1114yes—
408C2×D4C2×D4×C1114yes—
409C2×D4C11×#4114yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—82no—
419C22×C4—82no—
420C22×C4—82no—
421C22×C4—82no—
422C22×C4C2×D4×C1112yes—
423C22×C4C2×D4×C1112yes—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1112yes—
426C22×C4C11×#4112yes—
427C22×C4C24×C1111yescharacteristic
428SD16—48no—
429D8—48no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—42no—
443C4⋊C4—82no—
444C4⋊C4C2×D4×C1114yes—
445C22⋊C4—24no—
446C22⋊C4—28no—
447C22⋊C4—24no—
448C22⋊C4—28no—
449C22⋊C4—42no—
450C22⋊C4—44no—
451C22⋊C4—42no—
452C22⋊C4—82no—
453C42—24no—
454C42—22no—
455C42C2×D4×C1114yes—
456C11#3291711yescharacteristic, direct product factor, Sylow
457C23—216no—
458C23—21no—
459C23—24no—
460C23—24no—
461C23—21no—
462C23—24no—
463C23—22no—
464C23—22no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—84no—
475C23—84no—
476C23—88no—
477C23—88no—
478C23C11×#12112yes—
479C23C22×D4×C1111yescharacteristic
480Q8—42no—
481Q8—42no—
482D4—216no—
483D4—24no—
484D4—24no—
485D4—24no—
486D4—42no—
487D4—42no—
488D4—84no—
489D4C11×#12118yes—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—88no—
510C2×C4—88no—
511C2×C4C11×#12014yes—
512C2×C4C11×#12112yes—
513C2×C4C22×D4×C1111yescharacteristic
514C2×C4C22×D4×C1112yes—
515C2×C4C2×C11×#4112yes—
516C2×C4C2×C11×#4111yescharacteristic
517C8—42no—
518C8—42no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—28no—
523C22—44no—
524C22—44no—
525C22—42no—
526C22—44no—
527C22—44no—
528C22—42no—
529C22—44no—
530C22—44no—
531C22—816no—
532C22—82no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—82no—
537C22C2×C11×#12011yescharacteristic
538C22C2×C11×#12111yescharacteristic
539C22C11×#52511yescharacteristic
540C22C11×#57612yes—
541C22C11×#57712yes—
542C4—24no—
543C4—22no—
544C4—42no—
545C4—44no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4C2×C11×#12112yes—
550C4C11×#52512yes—
551C2—42no—
552C2—48no—
553C2—161no—
554C2C11×#284711yescharacteristic
555C2C11×#301212yes—
556C2C11×#304111yescharacteristic
557C2C11×#304211yescharacteristic
558C2C11×#311812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
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
1. C2×C11×#518C2semidirect
2. C2×C11×#463C2semidirect
3. C2×C11×#450C2semidirect
5. C11×#2620C2semidirect
6. C11×#1879C2semidirect
7. C11×#1877C2semidirect
8. C11×#1875C2semidirect
9. C11×#1873C2semidirect
10. C11×#1802C2semidirect
11. C11×#1798C2semidirect
15. C2×C11×#124C22semidirect
28. C2×C11×C4⋊C8C22semidirect
29. C2×C11×#103C22semidirect
32. C2×C11×#102C22semidirect
37. C11×#391C22semidirect
38. C11×#390C22semidirect
39. C11×#384C22semidirect
40. C11×#340C22semidirect
41. C11×#340C22semidirect
42. C11×#336C22semidirect
73. C4×D4×C11D4semidirect
102. #32917C11direct (N × H)
178. C2×#518C2×C11semidirect
179. C2×#463C2×C11semidirect
180. C2×#450C2×C11semidirect
182. #2620C2×C11semidirect
183. #1879C2×C11semidirect
184. #1877C2×C11semidirect
185. #1875C2×C11semidirect
186. #1873C2×C11semidirect
187. #1802C2×C11semidirect
188. #1798C2×C11semidirect
254. C2×#124C22×C11semidirect
267. C2×C4⋊C8C22×C11semidirect
268. C2×#103C22×C11semidirect
271. C2×#102C22×C11semidirect
276. #391C22×C11semidirect
277. #390C22×C11semidirect
278. #384C22×C11semidirect
279. #340C22×C11semidirect
280. #340C22×C11semidirect
281. #336C22×C11semidirect
344. C4×D4D4×C11semidirect
456. C11#32917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5182
C2×C11×#4632
C2×C11×#4502
C2×C11×#4472
C11×#26202
C11×#18792
C11×#18772
C11×#18752
C11×#18732
C11×#18022
C11×#17982
#3291711