Finite Group Databasebeta

← C11×#24375 #14601568

Subgroups — C11×#24375 #14601568

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic, complemented
2C2×C11×#464C212yesmaximal, complemented
3C2×C11×#449C211yesmaximal, characteristic
4C11×#2436C211yesmaximal, characteristic, complemented
5C11×#2341C211yesmaximal, characteristic, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#2012C212yesmaximal, complemented
8C11×#1895C211yesmaximal, characteristic, complemented
9C11×#1878C212yesmaximal, 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×SD16C2211yescharacteristic
18C22×C11×SD16C2212yes—
19C22×C11×D8C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C2×C11×#124C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C4×Q8×C11C2212yes—
24C11×#464—28no—
25C11×#449—24no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#393—21no—
34C11×#393—21no—
35C11×#391C2212yes—
36C11×#390—22no—
37C11×#390C2212yes—
38C11×#386—22no—
39C11×#380—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
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×C11C2311yescharacteristic
63C11×#137—232no—
64C2×C11×Q16—24no—
65C2×C11×Q16—24no—
66C2×C11×Q16D418yescomplemented
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—22no—
70C2×C11×SD16—24no—
71C2×C11×SD16—24no—
72C2×C11×D8—22no—
73C2×C11×D8—42no—
74C2×C11×M16—22no—
75C2×C11×M16—24no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2312yes—
79C11×#124—24no—
80C11×#124—42no—
81C11×#121—22no—
82C11×#121—22no—
83C4×Q8×C11—24no—
84C4×Q8×C11—42no—
85C2×C11×C4⋊C4—22no—
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⋊C4—22no—
94C2×C11×C22⋊C4D412yes—
95C2×C42×C11—22no—
96C2×C42×C11C2312yes—
97C11×C4⋊C8—24no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#103—42no—
101C11×#102—22no—
102C11×#102—24no—
103C11×C22⋊C8—22no—
104C11×#95—21no—
105C11×#95—22no—
106C11×#95—22no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#24375C1111yesmaximal, 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—22no—
119C2×Q8×C11—28no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—44no—
125C2×Q8×C11—48no—
126C2×Q8×C11—44no—
127C2×Q8×C11—42no—
128C2×Q8×C11C2×D414yes—
129C2×Q8×C11C2×D412yes—
130C2×Q8×C11C2×D414yes—
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—42no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
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—42no—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C11×Q16—216no—
160C11×SD16—216no—
161C11×SD16—44no—
162C11×D8—44no—
163C11×M16—28no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11C2×D414yes—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—44no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—44no—
178C11×C22⋊C4—44no—
179C11×C22⋊C4—44no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—82no—
182C11×C22⋊C4—81no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—44no—
186C22×#137C2×C1111yescharacteristic, complemented
187C2×#464C2×C1112yescomplemented
188C2×#449C2×C1111yescharacteristic
189#2436C2×C1111yescharacteristic, complemented
190#2341C2×C1111yescharacteristic, complemented
191#2055C2×C1112yescomplemented
192#2012C2×C1112yescomplemented
193#1895C2×C1111yescharacteristic, complemented
194#1878C2×C1112yescomplemented
195#1851C2×C1111yescharacteristic, complemented
196#1787C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—22no—
202C23×C11—42no—
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—22no—
214Q8×C11—24no—
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—48no—
218Q8×C11—42no—
219Q8×C11—42no—
220Q8×C11#12014yes—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—48no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—84no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—48no—
243C2×C4×C11—48no—
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#12112yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D412yes—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)12yes—
256C8×C11—24no—
257C8×C11—41no—
258C8×C11—41no—
259C22×#41C22×C1111yescharacteristic
260C23×Q8C22×C1111yescharacteristic
261C2×#137—24no—
262C2×#137—28no—
263C22×Q16C22×C1112yes—
264C22×SD16C22×C1112yes—
265C22×SD16C22×C1111yescharacteristic
266C22×D8C22×C1111yescharacteristic
267C22×M16C22×C1111yescharacteristic
268C2×#124C22×C1112yes—
269C2×#121C22×C1111yescharacteristic
270C2×C4×Q8C22×C1112yes—
271#464—28no—
272#449—24no—
273C2×C4⋊C8C22×C1112yes—
274C2×#103C22×C1112yes—
275C2×#103C22×C1111yescharacteristic
276C2×#103C22×C1112yes—
277C2×#102C22×C1111yescharacteristic
278C2×#102C22×C1112yes—
279C2×C22⋊C8C22×C1111yescharacteristic
280#393—21no—
281#393—21no—
282#391C22×C1112yes—
283#390—22no—
284#390C22×C1112yes—
285#386—22no—
286#380—21no—
287#380C22×C1111yescharacteristic
288C4×C22⋊C4—21no—
289C4×C22⋊C4C22×C1111yescharacteristic
290#340C22×C1112yes—
291#336C22×C1112yes—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—81no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11C2×#12111yescharacteristic
308C22×C11D4212yes—
309C22×C11#57512yes—
310C22×C11#57711yescharacteristic
311C22×C11#57811yescharacteristic
312C4×C11—22no—
313C4×C11—24no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—82no—
318C4×C11—81no—
319C4×C11C2×#12011yescharacteristic
320C4×C11#53411yescharacteristic
321C4×C11#54612yes—
322C2×#41—22no—
323C2×#41—24no—
324C2×#41—42no—
325C2×#41D4×C1114yes—
326C22×Q8—21no—
327C22×Q8—24no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—42no—
331C22×Q8C23×C1112yes—
332C22×Q8C23×C1111yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4C23×C1111yescharacteristic
336C22×D4C23×C1111yescharacteristic
337C23×C4—21no—
338C23×C4—21no—
339C23×C4C23×C1111yescharacteristic
340#137—232no—
341C2×Q16—24no—
342C2×Q16—24no—
343C2×Q16D4×C1118yescomplemented
344C2×SD16—24no—
345C2×SD16—24no—
346C2×SD16—22no—
347C2×SD16—24no—
348C2×SD16—24no—
349C2×D8—22no—
350C2×D8—42no—
351C2×M16—22no—
352C2×M16—24no—
353C22×C8C23×C1111yescharacteristic
354C22×C8C23×C1111yescharacteristic
355C22×C8C23×C1112yes—
356#124—24no—
357#124—42no—
358#121—22no—
359#121—22no—
360C4×Q8—24no—
361C4×Q8—42no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4C23×C1112yes—
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4D4×C1112yes—
372C2×C42—22no—
373C2×C42C23×C1112yes—
374C4⋊C8—24no—
375#103—22no—
376#103—24no—
377#103—42no—
378#102—22no—
379#102—24no—
380C22⋊C8—22no—
381#95—21no—
382#95—22no—
383#95—22no—
384#95D4×C1111yescharacteristic
385#95D4×C1111yescharacteristic
386C2×C11—42no—
387C2×C11—82no—
388C2×C11—161no—
389C2×C11#241011yescharacteristic
390C2×C11#304011yescharacteristic
391C2×C11#304611yescharacteristic
392C2×C11#327112yes—
393C2×C11#327712yes—
394C24—21no—
395C24—21no—
396C24C2×D4×C1111yescharacteristic
397#41—28no—
398#41—44no—
399#41—48no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—28no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—44no—
409C2×Q8—48no—
410C2×Q8—44no—
411C2×Q8—42no—
412C2×Q8C2×D4×C1114yes—
413C2×Q8C2×D4×C1112yes—
414C2×Q8C2×D4×C1114yes—
415C2×D4—24no—
416C2×D4—22no—
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—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—42no—
437C22×C4C2×D4×C1112yes—
438C22×C4C2×D4×C1112yes—
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1112yes—
441C22×C4C11×#4112yes—
442C22×C4C24×C1111yescharacteristic
443Q16—216no—
444SD16—216no—
445SD16—44no—
446D8—44no—
447M16—28no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8C2×D4×C1114yes—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—44no—
460C22⋊C4—42no—
461C22⋊C4—44no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C22⋊C4—42no—
465C22⋊C4—82no—
466C22⋊C4—81no—
467C42—22no—
468C42—22no—
469C42—44no—
470C11#2437511yescharacteristic, direct product factor, Sylow
471C23—22no—
472C23—22no—
473C23—21no—
474C23—21no—
475C23—22no—
476C23—42no—
477C23—42no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—42no—
482C23—42no—
483C23—41no—
484C23—41no—
485C23C11×#12112yes—
486C23C22×D4×C1111yescharacteristic
487Q8—22no—
488Q8—24no—
489Q8—24no—
490Q8—24no—
491Q8—48no—
492Q8—42no—
493Q8—42no—
494Q8C11×#12014yes—
495D4—22no—
496D4—22no—
497D4—48no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—42no—
502D4—84no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
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—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4C11×#12112yes—
526C2×C4C22×D4×C1111yescharacteristic
527C2×C4C22×D4×C1112yes—
528C2×C4C2×C11×#4111yescharacteristic
529C2×C4C11×H(5,𝔽2)12yes—
530C8—24no—
531C8—41no—
532C8—41no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—82no—
542C22—82no—
543C22—81no—
544C22—82no—
545C22—82no—
546C22—81no—
547C22—81no—
548C22C2×C11×#12111yescharacteristic
549C22D42×C1112yes—
550C22C11×#57512yes—
551C22C11×#57711yescharacteristic
552C22C11×#57811yescharacteristic
553C4—22no—
554C4—24no—
555C4—44no—
556C4—42no—
557C4—42no—
558C4—82no—
559C4—81no—
560C4C2×C11×#12011yescharacteristic
561C4C11×#53411yescharacteristic
562C4C11×#54612yes—
563C2—42no—
564C2—82no—
565C2—161no—
566C2C11×#241011yescharacteristic
567C2C11×#304011yescharacteristic
568C2C11×#304611yescharacteristic
569C2C11×#327112yes—
570C2C11×#327712yes—
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×#464C2semidirect
4. C11×#2436C2semidirect
5. C11×#2341C2semidirect
6. C11×#2055C2semidirect
7. C11×#2012C2semidirect
8. C11×#1895C2semidirect
9. C11×#1878C2semidirect
10. C11×#1851C2semidirect
11. C11×#1787C2semidirect
66. C2×C11×Q16D4semidirect
109. #24375C11direct (N × H)
186. C22×#137C2×C11semidirect
187. C2×#464C2×C11semidirect
189. #2436C2×C11semidirect
190. #2341C2×C11semidirect
191. #2055C2×C11semidirect
192. #2012C2×C11semidirect
193. #1895C2×C11semidirect
194. #1878C2×C11semidirect
195. #1851C2×C11semidirect
196. #1787C2×C11semidirect
343. C2×Q16D4×C11semidirect
470. C11#24375direct (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×#4642
C2×C11×#4492
C11×#24362
C11×#23412
C11×#20552
C11×#20122
C11×#18952
C11×#18782
C11×#18512
C11×#17872
#2437511