Finite Group Databasebeta

← C11×#23929 #14601122

Subgroups — C11×#23929 #14601122

Order 2816.

1824 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C212yesmaximal, complemented
2C2×C11×#452C212yesmaximal, complemented
3C2×C11×#449C212yesmaximal, complemented
4C11×#2001C211yesmaximal, characteristic, complemented
5C11×#2000C212yesmaximal, complemented
6C11×#1999C211yesmaximal, characteristic, complemented
7C11×#1874C212yesmaximal, complemented
8C11×#1872C212yesmaximal, complemented
9C11×#1780C211yesmaximal, characteristic, complemented
10C22×C11×#41C2212yes—
11C22×C11×#41C2211yescharacteristic
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C22×C11×D8C2211yescharacteristic
15C11×#537—28no—
16C11×#537—28no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121—22no—
21C2×C11×#121—22no—
22C2×C11×#121—22no—
23C2×C11×#121C2212yes—
24C2×C11×#121C2212yes—
25C22×C11×C4⋊C4C2212yes—
26C11×#452—28no—
27C11×#449—28no—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×C22⋊C8C2212yes—
33C2×C11×C22⋊C8C2212yes—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#340C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2211yescharacteristic
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—24no—
42C2×C11×#41—24no—
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—41no—
46C2×C11×#41—41no—
47C2×C11×#41—42no—
48C2×C11×#41—42no—
49C22×Q8×C11D411yescharacteristic
50C22×Q8×C11C2312yes—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11D411yescharacteristic
55C22×D4×C11D412yes—
56C22×D4×C11C2312yes—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C2×C11×Q16—24no—
62C2×C11×Q16—41no—
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×SD16—42no—
66C2×C11×D8—24no—
67C2×C11×D8—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2312yes—
70C22×C8×C11C2311yescharacteristic
71C11×C22⋊Q8—216no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8D418yescomplemented
76C11×#121—216no—
77C11×#121—216no—
78C11×#121—216no—
79C11×#121—24no—
80C11×#121—24no—
81C11×#121—24no—
82C11×#121D418yescomplemented
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C11×#103—24no—
95C11×#103—24no—
96C11×#102—24no—
97C11×#102—24no—
98C11×C22⋊C8—24no—
99C11×C22⋊C8—24no—
100C11×C22⋊C8—41no—
101C11×C22⋊C8—41no—
102#23929C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—22no—
104C24×C11C2×D411yescharacteristic
105C24×C11C2×D412yes—
106C11×#41—44no—
107C11×#41—48no—
108C11×#41—44no—
109C11×#41—48no—
110C11×#41—48no—
111C11×#41—48no—
112C11×#41—48no—
113C2×Q8×C11—24no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—41no—
120C2×Q8×C11C2×D414yes—
121C2×D4×C11—28no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11—24no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—42no—
133C2×D4×C11—41no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—82no—
137C2×D4×C11—82no—
138C2×D4×C11—82no—
139C2×D4×C11—82no—
140C2×D4×C11C2×D414yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—28no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—28no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11—82no—
157C22×C4×C11—82no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2411yescharacteristic
163C11×Q16—44no—
164C11×SD16—48no—
165C11×D8—44no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—21no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C2×D414yes—
179C11×C4⋊C4C2×D414yes—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—28no—
184C2×#537C2×C1112yescomplemented
185C2×#452C2×C1112yescomplemented
186C2×#449C2×C1112yescomplemented
187#2001C2×C1111yescharacteristic, complemented
188#2000C2×C1112yescomplemented
189#1999C2×C1111yescharacteristic, complemented
190#1874C2×C1112yescomplemented
191#1872C2×C1112yescomplemented
192#1780C2×C1111yescharacteristic, complemented
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11—21no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11#12014yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—44no—
216Q8×C11—42no—
217Q8×C11—42no—
218D4×C11—24no—
219D4×C11—24no—
220D4×C11—48no—
221D4×C11—44no—
222D4×C11—416no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—88no—
226D4×C11—88no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—416no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—88no—
249C2×C4×C11#12014yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C8×C11—41no—
255C8×C11—42no—
256C8×C11—41no—
257C22×#41C22×C1112yes—
258C22×#41C22×C1111yescharacteristic
259C22×Q16C22×C1111yescharacteristic
260C22×SD16C22×C1112yes—
261C22×D8C22×C1111yescharacteristic
262#537—28no—
263#537—28no—
264C2×C22⋊Q8—22no—
265C2×C22⋊Q8C22×C1112yes—
266C2×C22⋊Q8C22×C1112yes—
267C2×#121—22no—
268C2×#121—22no—
269C2×#121—22no—
270C2×#121C22×C1112yes—
271C2×#121C22×C1112yes—
272C22×C4⋊C4C22×C1112yes—
273#452—28no—
274#449—28no—
275C2×#103C22×C1112yes—
276C2×#103C22×C1112yes—
277C2×#102C22×C1112yes—
278C2×#102C22×C1112yes—
279C2×C22⋊C8C22×C1112yes—
280C2×C22⋊C8C22×C1112yes—
281C2×C22⋊C8C22×C1111yescharacteristic
282C2×C22⋊C8C22×C1111yescharacteristic
283#340C22×C1111yescharacteristic
284#340C22×C1112yes—
285#340C22×C1111yescharacteristic
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—44no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—42no—
300C22×C11—44no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11C2×#12012yes—
306C22×C11#53411yescharacteristic
307C22×C11#57611yescharacteristic
308C22×C11#57712yes—
309C22×C11#57811yescharacteristic
310C4×C11—24no—
311C4×C11—41no—
312C4×C11—44no—
313C4×C11—44no—
314C4×C11—44no—
315C4×C11D4211yescharacteristic
316C4×C11D4212yes—
317C4×C11D4211yescharacteristic
318C2×#41—24no—
319C2×#41—24no—
320C2×#41—24no—
321C2×#41—24no—
322C2×#41—24no—
323C2×#41—24no—
324C2×#41—41no—
325C2×#41—41no—
326C2×#41—42no—
327C2×#41—42no—
328C22×Q8D4×C1111yescharacteristic
329C22×Q8C23×C1112yes—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4D4×C1111yescharacteristic
334C22×D4D4×C1112yes—
335C22×D4C23×C1112yes—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4C23×C1111yescharacteristic
339C23×C4C23×C1112yes—
340C2×Q16—24no—
341C2×Q16—41no—
342C2×SD16—24no—
343C2×SD16—24no—
344C2×SD16—42no—
345C2×D8—24no—
346C2×D8—41no—
347C22×C8C23×C1111yescharacteristic
348C22×C8C23×C1112yes—
349C22×C8C23×C1111yescharacteristic
350C22⋊Q8—216no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353C22⋊Q8—24no—
354C22⋊Q8D4×C1118yescomplemented
355#121—216no—
356#121—216no—
357#121—216no—
358#121—24no—
359#121—24no—
360#121—24no—
361#121D4×C1118yescomplemented
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4C23×C1112yes—
368C2×C4⋊C4C23×C1112yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373#103—24no—
374#103—24no—
375#102—24no—
376#102—24no—
377C22⋊C8—24no—
378C22⋊C8—24no—
379C22⋊C8—41no—
380C22⋊C8—41no—
381C2×C11—44no—
382C2×C11—81no—
383C2×C11—84no—
384C2×C11#240311yescharacteristic
385C2×C11#301212yes—
386C2×C11#301312yes—
387C2×C11#320311yescharacteristic
388C2×C11#320411yescharacteristic
389C24—22no—
390C24C2×D4×C1111yescharacteristic
391C24C2×D4×C1112yes—
392#41—44no—
393#41—48no—
394#41—44no—
395#41—48no—
396#41—48no—
397#41—48no—
398#41—48no—
399C2×Q8—24no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—41no—
406C2×Q8C2×D4×C1114yes—
407C2×D4—28no—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4—82no—
426C2×D4C2×D4×C1114yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—28no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—28no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1112yes—
446C22×C4C2×D4×C1114yes—
447C22×C4C2×D4×C1114yes—
448C22×C4C24×C1111yescharacteristic
449Q16—44no—
450SD16—48no—
451D8—44no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8—21no—
459C4⋊C4—28no—
460C4⋊C4—28no—
461C4⋊C4—28no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4C2×D4×C1114yes—
465C4⋊C4C2×D4×C1114yes—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—28no—
469C22⋊C4—28no—
470C11#2392911yescharacteristic, direct product factor, Sylow
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—24no—
479C23—21no—
480C23—21no—
481C23—22no—
482C23—21no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23C11×#12014yes—
490C23C22×D4×C1111yescharacteristic
491Q8—24no—
492Q8—24no—
493Q8—44no—
494Q8—42no—
495Q8—42no—
496D4—24no—
497D4—24no—
498D4—48no—
499D4—44no—
500D4—416no—
501D4—42no—
502D4—42no—
503D4—88no—
504D4—88no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—416no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—88no—
527C2×C4C11×#12014yes—
528C2×C4C22×D4×C1112yes—
529C2×C4C22×D4×C1112yes—
530C2×C4C11×H(5,𝔽2)11yescharacteristic
531C2×C4C11×H(5,𝔽2)11yescharacteristic
532C8—41no—
533C8—42no—
534C8—41no—
535C22—24no—
536C22—24no—
537C22—24no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—42no—
547C22—44no—
548C22—42no—
549C22—44no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22C2×C11×#12012yes—
555C22C11×#53411yescharacteristic
556C22C11×#57611yescharacteristic
557C22C11×#57712yes—
558C22C11×#57811yescharacteristic
559C4—24no—
560C4—41no—
561C4—44no—
562C4—44no—
563C4—44no—
564C4D42×C1111yescharacteristic
565C4D42×C1112yes—
566C4D42×C1111yescharacteristic
567C2—44no—
568C2—81no—
569C2—84no—
570C2C11×#240311yescharacteristic
571C2C11×#301212yes—
572C2C11×#301312yes—
573C2C11×#320311yescharacteristic
574C2C11×#320411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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×#537C2semidirect
2. C2×C11×#452C2semidirect
3. C2×C11×#449C2semidirect
4. C11×#2001C2semidirect
5. C11×#2000C2semidirect
6. C11×#1999C2semidirect
7. C11×#1874C2semidirect
8. C11×#1872C2semidirect
9. C11×#1780C2semidirect
75. C11×C22⋊Q8D4semidirect
82. C11×#121D4semidirect
102. #23929C11direct (N × H)
184. C2×#537C2×C11semidirect
185. C2×#452C2×C11semidirect
186. C2×#449C2×C11semidirect
187. #2001C2×C11semidirect
188. #2000C2×C11semidirect
189. #1999C2×C11semidirect
190. #1874C2×C11semidirect
191. #1872C2×C11semidirect
192. #1780C2×C11semidirect
354. C22⋊Q8D4×C11semidirect
361. #121D4×C11semidirect
470. C11#23929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#4522
C2×C11×#4492
C11×#20012
C11×#20002
C11×#19992
C11×#18742
C11×#18722
C11×#17802
#2392911