Finite Group Databasebeta

← C11×#24361 #14601554

Subgroups — C11×#24361 #14601554

Order 2816.

1408 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×Q16C211yesmaximal, characteristic, complemented
2C2×C11×#464C212yesmaximal, complemented
3C2×C11×#448C211yesmaximal, characteristic
4C11×#2436C211yesmaximal, characteristic
5Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C11×#2056C212yesmaximal, complemented
7C11×#2015C212yesmaximal, complemented
8C11×#1893C211yesmaximal, characteristic
9C11×#1878C212yesmaximal, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C22×C11×Q16—24no—
15C22×C11×Q16—28no—
16C22×C11×Q16C2212yes—
17C22×C11×Q16C2212yes—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C11×#124C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C4×Q8×C11C2212yes—
24C11×#464—28no—
25C11×#448—24no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C11×#393—22no—
34C11×#391—22no—
35C11×#391C2212yes—
36C11×#391C2212yes—
37C11×#386—21no—
38C11×#386—21no—
39C11×#380—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
43C11×#340C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—24no—
49C22×Q8×C11—24no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—42no—
53C22×Q8×C11—42no—
54C22×Q8×C11D414yes—
55C22×Q8×C11C2312yes—
56C22×Q8×C11C2311yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C2×C11×Q16—232no—
64C2×C11×Q16—24no—
65C2×C11×Q16—24no—
66C2×C11×Q16—24no—
67C2×C11×Q16—24no—
68C2×C11×Q16—24no—
69C2×C11×Q16D418yescomplemented
70C2×C11×SD16—22no—
71C2×C11×SD16—22no—
72C2×C11×SD16—24no—
73C2×C11×SD16—42no—
74C22×C8×C11—22no—
75C22×C8×C11—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—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—22no—
95C2×C42×C11C2312yes—
96C11×C4⋊C8—24no—
97C11×#103—22no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#103—42no—
101C11×#102—24no—
102C11×C22⋊C8—22no—
103C11×#95—22no—
104C11×#95—22no—
105C11×#95—21no—
106C11×#95—22no—
107C11×#95—22no—
108C11×#95D412yes—
109#24361C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—21no—
111C24×C11C2×D411yescharacteristic
112C2×Q8×C11—24no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—28no—
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—44no—
127C2×Q8×C11—44no—
128C2×Q8×C11—48no—
129C2×Q8×C11—48no—
130C2×Q8×C11—44no—
131C2×Q8×C11—42no—
132C2×Q8×C11C2×D414yes—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D414yes—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—42no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C11×Q16—216no—
161C11×Q16—216no—
162C11×SD16—44no—
163C11×SD16—44no—
164C2×C8×C11—28no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11C2×D414yes—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—44no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—44no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—44no—
186C23×Q16C2×C1111yescharacteristic, complemented
187C2×#464C2×C1112yescomplemented
188C2×#448C2×C1111yescharacteristic
189#2436C2×C1111yescharacteristic
190Q8×C22⋊C4C2×C1111yescharacteristic, complemented
191#2056C2×C1112yescomplemented
192#2015C2×C1112yescomplemented
193#1893C2×C1111yescharacteristic
194#1878C2×C1112yescomplemented
195#1850C2×C1111yescharacteristic, complemented
196#1787C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11#12112yes—
205C23×C11#13512yes—
206C23×C11#13712yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—22no—
209Q8×C11—24no—
210Q8×C11—22no—
211Q8×C11—24no—
212Q8×C11—22no—
213Q8×C11—24no—
214Q8×C11—48no—
215Q8×C11—48no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—42no—
219Q8×C11#12014yes—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—42no—
223D4×C11—84no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—48no—
239C2×C4×C11—48no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11#12112yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D412yes—
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)12yes—
254C8×C11—24no—
255C8×C11—41no—
256C8×C11—41no—
257C23×Q8C22×C1111yescharacteristic
258C23×Q8C22×C1111yescharacteristic
259C22×Q16—24no—
260C22×Q16—28no—
261C22×Q16C22×C1112yes—
262C22×Q16C22×C1112yes—
263C22×SD16C22×C1111yescharacteristic
264C22×SD16C22×C1111yescharacteristic
265C23×C8C22×C1111yescharacteristic
266C2×#124C22×C1112yes—
267C2×#121C22×C1111yescharacteristic
268C2×C4×Q8C22×C1112yes—
269#464—28no—
270#448—24no—
271C2×C4⋊C8C22×C1112yes—
272C2×#103C22×C1111yescharacteristic
273C2×#103C22×C1112yes—
274C2×#103C22×C1111yescharacteristic
275C2×#103C22×C1112yes—
276C2×#102C22×C1112yes—
277C2×C22⋊C8C22×C1111yescharacteristic
278#393—22no—
279#391—22no—
280#391C22×C1112yes—
281#391C22×C1112yes—
282#386—21no—
283#386—21no—
284#380—21no—
285#380C22×C1111yescharacteristic
286C4×C22⋊C4—21no—
287C4×C22⋊C4C22×C1111yescharacteristic
288#340C22×C1112yes—
289#336C22×C1112yes—
290C22×C11—22no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—22no—
294C22×C11—81no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11#46414yescomplemented
300C22×C11C2×#12111yescharacteristic
301C22×C11D4212yes—
302C22×C11C2×#13511yescharacteristic
303C22×C11C2×#13711yescharacteristic
304C22×C11#57812yes—
305C4×C11—22no—
306C4×C11—24no—
307C4×C11—42no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—82no—
312C4×C11—81no—
313C4×C11C2×#12011yescharacteristic
314C4×C11#53411yescharacteristic
315C4×C11#54612yes—
316C22×Q8—21no—
317C22×Q8—21no—
318C22×Q8—22no—
319C22×Q8—24no—
320C22×Q8—24no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—42no—
324C22×Q8—42no—
325C22×Q8D4×C1114yes—
326C22×Q8C23×C1112yes—
327C22×Q8C23×C1111yescharacteristic
328C22×Q8C23×C1111yescharacteristic
329C22×D4—21no—
330C22×D4C23×C1111yescharacteristic
331C23×C4—21no—
332C23×C4—21no—
333C23×C4C23×C1111yescharacteristic
334C2×Q16—232no—
335C2×Q16—24no—
336C2×Q16—24no—
337C2×Q16—24no—
338C2×Q16—24no—
339C2×Q16—24no—
340C2×Q16D4×C1118yescomplemented
341C2×SD16—22no—
342C2×SD16—22no—
343C2×SD16—24no—
344C2×SD16—42no—
345C22×C8—22no—
346C22×C8—24no—
347C22×C8C23×C1111yescharacteristic
348C22×C8C23×C1111yescharacteristic
349C22×C8C23×C1112yes—
350#124—24no—
351#124—42no—
352#121—22no—
353#121—22no—
354C4×Q8—24no—
355C4×Q8—42no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4C23×C1112yes—
358C2×C4⋊C4C23×C1111yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4D4×C1111yescharacteristic
364C2×C22⋊C4D4×C1111yescharacteristic
365C2×C42—22no—
366C2×C42C23×C1112yes—
367C4⋊C8—24no—
368#103—22no—
369#103—22no—
370#103—24no—
371#103—42no—
372#102—24no—
373C22⋊C8—22no—
374#95—22no—
375#95—22no—
376#95—21no—
377#95—22no—
378#95—22no—
379#95D4×C1112yes—
380C2×C11—24no—
381C2×C11—161no—
382C2×C11#241011yescharacteristic
383C2×C11C2×#46411yescharacteristic
384C2×C11#304411yescharacteristic
385C2×C11#327012yes—
386C2×C11#328512yes—
387C24—21no—
388C24C2×D4×C1111yescharacteristic
389C2×Q8—24no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—28no—
395C2×Q8—28no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—44no—
403C2×Q8—44no—
404C2×Q8—44no—
405C2×Q8—48no—
406C2×Q8—48no—
407C2×Q8—44no—
408C2×Q8—42no—
409C2×Q8C2×D4×C1114yes—
410C2×Q8C2×D4×C1112yes—
411C2×Q8C2×D4×C1112yes—
412C2×Q8C2×D4×C1114yes—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4C2×D4×C1112yes—
432C22×C4C2×D4×C1112yes—
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1112yes—
435C22×C4C11×#4112yes—
436C22×C4C24×C1111yescharacteristic
437Q16—216no—
438Q16—216no—
439SD16—44no—
440SD16—44no—
441C2×C8—28no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8C2×D4×C1114yes—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—44no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—44no—
457C22⋊C4—44no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C42—22no—
461C42—22no—
462C42—44no—
463C11#2436111yescharacteristic, direct product factor, Sylow
464C23—22no—
465C23—22no—
466C23—41no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23—42no—
471C23C11×#12112yes—
472C23C11×#13512yes—
473C23C11×#13712yes—
474C23C22×D4×C1111yescharacteristic
475Q8—22no—
476Q8—24no—
477Q8—22no—
478Q8—24no—
479Q8—22no—
480Q8—24no—
481Q8—48no—
482Q8—48no—
483Q8—42no—
484Q8—42no—
485Q8—42no—
486Q8C11×#12014yes—
487D4—41no—
488D4—41no—
489D4—42no—
490D4—84no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—48no—
506C2×C4—48no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4C11×#12112yes—
517C2×C4C22×D4×C1111yescharacteristic
518C2×C4C22×D4×C1112yes—
519C2×C4C2×C11×#4111yescharacteristic
520C2×C4C11×H(5,𝔽2)12yes—
521C8—24no—
522C8—41no—
523C8—41no—
524C22—22no—
525C22—24no—
526C22—24no—
527C22—22no—
528C22—81no—
529C22—82no—
530C22—82no—
531C22—81no—
532C22—81no—
533C22C11×#46414yescomplemented
534C22C2×C11×#12111yescharacteristic
535C22D42×C1112yes—
536C22C2×C11×#13511yescharacteristic
537C22C2×C11×#13711yescharacteristic
538C22C11×#57812yes—
539C4—22no—
540C4—24no—
541C4—42no—
542C4—44no—
543C4—42no—
544C4—42no—
545C4—82no—
546C4—81no—
547C4C2×C11×#12011yescharacteristic
548C4C11×#53411yescharacteristic
549C4C11×#54612yes—
550C2—24no—
551C2—161no—
552C2C11×#241011yescharacteristic
553C2C2×C11×#46411yescharacteristic
554C2C11×#304411yescharacteristic
555C2C11×#327012yes—
556C2C11×#328512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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. C23×C11×Q16C2semidirect
2. C2×C11×#464C2semidirect
5. Q8×C11×C22⋊C4C2semidirect
6. C11×#2056C2semidirect
7. C11×#2015C2semidirect
9. C11×#1878C2semidirect
10. C11×#1850C2semidirect
11. C11×#1787C2semidirect
69. C2×C11×Q16D4semidirect
109. #24361C11direct (N × H)
186. C23×Q16C2×C11semidirect
187. C2×#464C2×C11semidirect
190. Q8×C22⋊C4C2×C11semidirect
191. #2056C2×C11semidirect
192. #2015C2×C11semidirect
194. #1878C2×C11semidirect
195. #1850C2×C11semidirect
196. #1787C2×C11semidirect
299. C22×C11#464semidirect
340. C2×Q16D4×C11semidirect
463. C11#24361direct (N × H)
533. C22C11×#464semidirect

Maximal subgroups

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

subgroupindex
C23×C11×Q162
C2×C11×#4642
C2×C11×#4482
C11×#24362
Q8×C11×C22⋊C42
C11×#20562
C11×#20152
C11×#18932
C11×#18782
C11×#18502
C11×#17872
#2436111