Finite Group Databasebeta

← C11×#24377 #14601570

Subgroups — C11×#24377 #14601570

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic, complemented
2C2×C11×#463C212yesmaximal, complemented
3C2×C11×#449C211yesmaximal, characteristic
4C11×#2436C211yesmaximal, characteristic, complemented
5C11×#2339C211yesmaximal, characteristic, complemented
6C11×#2056C212yesmaximal, complemented
7C11×#2015C212yesmaximal, complemented
8C11×#1895C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C2×C11×#137—24no—
15C2×C11×#137—28no—
16C22×C11×Q16C2212yes—
17C22×C11×SD16C2212yes—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C2×C11×#124C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C4×D4×C11C2212yes—
24C11×#463—28no—
25C11×#449—24no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#393—21no—
34C11×#393—21no—
35C11×#391C2212yes—
36C11×#391C2212yes—
37C11×#386—22no—
38C11×#386—22no—
39C11×#381—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4C2211yescharacteristic
42C2×C11×#95—21no—
43C11×#340C2212yes—
44C11×#336C2212yes—
45C2×C11×#41—22no—
46C2×C11×#41—24no—
47C2×C11×#41—42no—
48C2×C11×#41D414yes—
49C22×Q8×C11—21no—
50C22×Q8×C11—24no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—42no—
54C22×Q8×C11C2312yes—
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11—22no—
63C23×C4×C11C2311yescharacteristic
64C11×#137—232no—
65C2×C11×Q16—24no—
66C2×C11×Q16—24no—
67C2×C11×Q16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—24no—
70C2×C11×SD16—22no—
71C2×C11×SD16—42no—
72C2×C11×SD16D418yescomplemented
73C2×C11×D8—22no—
74C2×C11×D8—24no—
75C2×C11×M16—22no—
76C2×C11×M16—24no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2312yes—
80C11×#124—24no—
81C11×#124—42no—
82C11×#121—22no—
83C11×#121—22no—
84C4×D4×C11—24no—
85C4×D4×C11—42no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D412yes—
94C2×C42×C11C2312yes—
95C11×C4⋊C8—24no—
96C11×#103—22no—
97C11×#103—24no—
98C11×#103—42no—
99C11×#102—22no—
100C11×#102—24no—
101C11×C22⋊C8—22no—
102C11×#95—21no—
103C11×#95—22no—
104C11×#95—22no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#24377C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—21no—
111C24×C11—21no—
112C24×C11C2×D411yescharacteristic
113C11×#41—28no—
114C11×#41—44no—
115C11×#41—48no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—44no—
126C2×Q8×C11—48no—
127C2×Q8×C11—44no—
128C2×Q8×C11—42no—
129C2×Q8×C11C2×D414yes—
130C2×Q8×C11C2×D412yes—
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11—42no—
141C2×D4×C11C2×D412yes—
142C2×D4×C11C2×D414yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11—42no—
155C22×C4×C11—82no—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C11×Q16—216no—
163C11×SD16—216no—
164C11×SD16—44no—
165C11×D8—44no—
166C11×M16—28no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11C2×D414yes—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—44no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C42×C11—22no—
185C42×C11—22no—
186C22×#137C2×C1111yescharacteristic, complemented
187C2×#463C2×C1112yescomplemented
188C2×#449C2×C1111yescharacteristic
189#2436C2×C1111yescharacteristic, complemented
190#2339C2×C1111yescharacteristic, complemented
191#2056C2×C1112yescomplemented
192#2015C2×C1112yescomplemented
193#1895C2×C1111yescharacteristic, complemented
194#1877C2×C1112yescomplemented
195#1851C2×C1111yescharacteristic, complemented
196#1787C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—42no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11#12112yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—24no—
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—24no—
217Q8×C11—48no—
218Q8×C11—42no—
219Q8×C11—42no—
220Q8×C11—42no—
221D4×C11—22no—
222D4×C11—24no—
223D4×C11—48no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—42no—
227D4×C11—84no—
228D4×C11#12014yes—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—48no—
242C2×C4×C11—48no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—88no—
252C2×C4×C11#12112yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D412yes—
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)12yes—
257C8×C11—24no—
258C8×C11—41no—
259C8×C11—41no—
260C22×#41C22×C1111yescharacteristic
261C23×Q8C22×C1111yescharacteristic
262C2×#137—24no—
263C2×#137—28no—
264C22×Q16C22×C1112yes—
265C22×SD16C22×C1112yes—
266C22×SD16C22×C1111yescharacteristic
267C22×D8C22×C1111yescharacteristic
268C22×M16C22×C1111yescharacteristic
269C2×#124C22×C1112yes—
270C2×#121C22×C1111yescharacteristic
271C2×C4×D4C22×C1112yes—
272#463—28no—
273#449—24no—
274C2×C4⋊C8C22×C1112yes—
275C2×#103C22×C1111yescharacteristic
276C2×#103C22×C1112yes—
277C2×#103C22×C1112yes—
278C2×#102C22×C1111yescharacteristic
279C2×#102C22×C1112yes—
280C2×C22⋊C8C22×C1111yescharacteristic
281#393—21no—
282#393—21no—
283#391C22×C1112yes—
284#391C22×C1112yes—
285#386—22no—
286#386—22no—
287#381—21no—
288#380C22×C1111yescharacteristic
289C4×C22⋊C4C22×C1111yescharacteristic
290C2×#95—21no—
291#340C22×C1112yes—
292#336C22×C1112yes—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—81no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11C2×#12111yescharacteristic
309C22×C11D4212yes—
310C22×C11#57512yes—
311C22×C11#57711yescharacteristic
312C22×C11#57811yescharacteristic
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—44no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—82no—
319C4×C11—81no—
320C4×C11C2×#12011yescharacteristic
321C4×C11#53411yescharacteristic
322C4×C11#54612yes—
323C2×#41—22no—
324C2×#41—24no—
325C2×#41—42no—
326C2×#41D4×C1114yes—
327C22×Q8—21no—
328C22×Q8—24no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—42no—
332C22×Q8C23×C1112yes—
333C22×Q8C23×C1111yescharacteristic
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C23×C1111yescharacteristic
337C22×D4C23×C1111yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4C23×C1111yescharacteristic
342#137—232no—
343C2×Q16—24no—
344C2×Q16—24no—
345C2×Q16—24no—
346C2×SD16—24no—
347C2×SD16—24no—
348C2×SD16—22no—
349C2×SD16—42no—
350C2×SD16D4×C1118yescomplemented
351C2×D8—22no—
352C2×D8—24no—
353C2×M16—22no—
354C2×M16—24no—
355C22×C8C23×C1111yescharacteristic
356C22×C8C23×C1111yescharacteristic
357C22×C8C23×C1112yes—
358#124—24no—
359#124—42no—
360#121—22no—
361#121—22no—
362C4×D4—24no—
363C4×D4—42no—
364C2×C4⋊C4C23×C1112yes—
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4D4×C1112yes—
372C2×C42C23×C1112yes—
373C4⋊C8—24no—
374#103—22no—
375#103—24no—
376#103—42no—
377#102—22no—
378#102—24no—
379C22⋊C8—22no—
380#95—21no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—22no—
385#95D4×C1111yescharacteristic
386#95D4×C1111yescharacteristic
387C2×C11—42no—
388C2×C11—44no—
389C2×C11—161no—
390C2×C11#241011yescharacteristic
391C2×C11#304011yescharacteristic
392C2×C11#304611yescharacteristic
393C2×C11#326912yes—
394C2×C11#327512yes—
395C24—21no—
396C24—21no—
397C24C2×D4×C1111yescharacteristic
398#41—28no—
399#41—44no—
400#41—48no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—28no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—44no—
411C2×Q8—48no—
412C2×Q8—44no—
413C2×Q8—42no—
414C2×Q8C2×D4×C1114yes—
415C2×Q8C2×D4×C1112yes—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4C2×D4×C1112yes—
427C2×D4C2×D4×C1114yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—82no—
441C22×C4C2×D4×C1112yes—
442C22×C4C2×D4×C1112yes—
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1112yes—
445C22×C4C11×#4112yes—
446C22×C4C24×C1111yescharacteristic
447Q16—216no—
448SD16—216no—
449SD16—44no—
450D8—44no—
451M16—28no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8C2×D4×C1114yes—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C22⋊C4—42no—
464C22⋊C4—44no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C22⋊C4—42no—
468C22⋊C4—81no—
469C42—22no—
470C42—22no—
471C11#2437711yescharacteristic, direct product factor, Sylow
472C23—22no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—41no—
485C23—41no—
486C23C11×#12112yes—
487C23C22×D4×C1111yescharacteristic
488Q8—24no—
489Q8—22no—
490Q8—22no—
491Q8—24no—
492Q8—48no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496D4—22no—
497D4—24no—
498D4—48no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—84no—
503D4C11×#12014yes—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—48no—
517C2×C4—48no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—88no—
527C2×C4C11×#12112yes—
528C2×C4C22×D4×C1111yescharacteristic
529C2×C4C22×D4×C1112yes—
530C2×C4C2×C11×#4111yescharacteristic
531C2×C4C11×H(5,𝔽2)12yes—
532C8—24no—
533C8—41no—
534C8—41no—
535C22—22no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—42no—
540C22—44no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—81no—
549C22—81no—
550C22C2×C11×#12111yescharacteristic
551C22D42×C1112yes—
552C22C11×#57512yes—
553C22C11×#57711yescharacteristic
554C22C11×#57811yescharacteristic
555C4—22no—
556C4—42no—
557C4—44no—
558C4—42no—
559C4—42no—
560C4—82no—
561C4—81no—
562C4C2×C11×#12011yescharacteristic
563C4C11×#53411yescharacteristic
564C4C11×#54612yes—
565C2—42no—
566C2—44no—
567C2—161no—
568C2C11×#241011yescharacteristic
569C2C11×#304011yescharacteristic
570C2C11×#304611yescharacteristic
571C2C11×#326912yes—
572C2C11×#327512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#137C2semidirect
2. C2×C11×#463C2semidirect
4. C11×#2436C2semidirect
5. C11×#2339C2semidirect
6. C11×#2056C2semidirect
7. C11×#2015C2semidirect
8. C11×#1895C2semidirect
9. C11×#1877C2semidirect
10. C11×#1851C2semidirect
11. C11×#1787C2semidirect
72. C2×C11×SD16D4semidirect
109. #24377C11direct (N × H)
186. C22×#137C2×C11semidirect
187. C2×#463C2×C11semidirect
189. #2436C2×C11semidirect
190. #2339C2×C11semidirect
191. #2056C2×C11semidirect
192. #2015C2×C11semidirect
193. #1895C2×C11semidirect
194. #1877C2×C11semidirect
195. #1851C2×C11semidirect
196. #1787C2×C11semidirect
350. C2×SD16D4×C11semidirect
471. C11#24377direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#4632
C2×C11×#4492
C11×#24362
C11×#23392
C11×#20562
C11×#20152
C11×#18952
C11×#18772
C11×#18512
C11×#17872
#2437711