Finite Group Databasebeta

← C11×#24265 #14601458

Subgroups — C11×#24265 #14601458

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic, complemented
2C2×C11×#465C212yesmaximal, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C11×#2407C212yesmaximal, complemented
5C11×#2056C211yesmaximal, characteristic, complemented
6C11×#2054C211yesmaximal, characteristic, complemented
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic, complemented
9C11×#1968C212yesmaximal, complemented
10C11×#1807C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C2×C11×#135—28no—
14C2×C11×#135—24no—
15C22×C11×Q16C2211yescharacteristic
16C22×C11×SD16C2212yes—
17C22×C11×D8C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#121C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C11×#465—28no—
24C8×D4×C11—24no—
25C2×C11×#106C2212yes—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C11×#394—22no—
35C11×#392—22no—
36C11×#391C2212yes—
37C11×#390C2212yes—
38C11×#386—22no—
39C11×#385—22no—
40C11×#380C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41—42no—
48C2×C11×#41—42no—
49C22×Q8×C11C2312yes—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11D411yescharacteristic
53C22×D4×C11C2312yes—
54C23×C4×C11—22no—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C11×#135—232no—
58C2×C11×Q16—24no—
59C2×C11×Q16—22no—
60C2×C11×SD16—24no—
61C2×C11×SD16—24no—
62C2×C11×SD16D418yescomplemented
63C2×C11×D8—24no—
64C2×C11×D8—22no—
65C22×C8×C11—24no—
66C22×C8×C11—22no—
67C22×C8×C11—24no—
68C22×C8×C11D414yescomplemented
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—42no—
75C11×#121—24no—
76C11×#121—42no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C11×#106—24no—
92C11×C4⋊C8—22no—
93C11×#103—24no—
94C11×#103—42no—
95C11×#102—24no—
96C11×#102—42no—
97C11×C22⋊C8—22no—
98C11×C22⋊C8—22no—
99C4×C8×C11—22no—
100C11×#95—22no—
101C11×#95—22no—
102C11×#95—22no—
103#24265C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—22no—
105C24×C11C2×D411yescharacteristic
106C24×C11C2×D411yescharacteristic
107C11×#41—216no—
108C11×#41—48no—
109C11×#41—48no—
110C11×#41—48no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11C2×D414yes—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—82no—
131C2×D4×C11C2×D414yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C11×Q16—28no—
152C11×SD16—216no—
153C11×D8—28no—
154C2×C8×C11—28no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—44no—
161C2×C8×C11C2×D412yes—
162C2×C8×C11C2×D412yes—
163C2×C8×C11C2×D414yes—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—44no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—44no—
175C11×C22⋊C4—82no—
176C11×C22⋊C4—82no—
177C42×C11—21no—
178C42×C11—21no—
179C22×#135C2×C1111yescharacteristic, complemented
180C2×#465C2×C1112yescomplemented
181C2×C8×D4C2×C1111yescharacteristic, complemented
182#2407C2×C1112yescomplemented
183#2056C2×C1111yescharacteristic, complemented
184#2054C2×C1111yescharacteristic, complemented
185#2001C2×C1111yescharacteristic, complemented
186#1999C2×C1111yescharacteristic, complemented
187#1968C2×C1112yescomplemented
188#1807C2×C1111yescharacteristic, complemented
189#1788C2×C1112yescomplemented
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11#12112yes—
206C23×C11#13512yescomplemented
207C23×C11C22×D411yescharacteristic
208Q8×C11—24no—
209Q8×C11—24no—
210Q8×C11—42no—
211Q8×C11—42no—
212D4×C11—28no—
213D4×C11—24no—
214D4×C11—24no—
215D4×C11—416no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—88no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—416no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11#12112yes—
243C2×C4×C11#13512yescomplemented
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D412yes—
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)12yes—
248C8×C11—22no—
249C8×C11—41no—
250C8×C11—41no—
251C8×C11#12014yes—
252C22×#41C22×C1112yes—
253C2×#135—28no—
254C2×#135—24no—
255C22×Q16C22×C1111yescharacteristic
256C22×SD16C22×C1112yes—
257C22×D8C22×C1111yescharacteristic
258C23×C8C22×C1111yescharacteristic
259C23×C8C22×C1111yescharacteristic
260C2×C22⋊Q8C22×C1112yes—
261C2×#121C22×C1112yes—
262C2×C4×D4C22×C1111yescharacteristic
263#465—28no—
264C8×D4—24no—
265C2×#106C22×C1112yes—
266C2×C4⋊C8C22×C1111yescharacteristic
267C2×#103C22×C1112yes—
268C2×#103C22×C1112yes—
269C2×#102C22×C1112yes—
270C2×#102C22×C1112yes—
271C2×C22⋊C8C22×C1111yescharacteristic
272C2×C22⋊C8C22×C1111yescharacteristic
273C2×C4×C8C22×C1111yescharacteristic
274#394—22no—
275#392—22no—
276#391C22×C1112yes—
277#390C22×C1112yes—
278#386—22no—
279#385—22no—
280#380C22×C1112yes—
281#340C22×C1111yescharacteristic
282#340C22×C1111yescharacteristic
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—41no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—41no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11C2×#12111yescharacteristic
301C22×C11D4212yes—
302C22×C11C2×#13511yescharacteristic
303C22×C11C2×#13511yescharacteristic
304C22×C11#57712yes—
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—41no—
308C4×C11—44no—
309C4×C11—41no—
310C4×C11—82no—
311C4×C11—82no—
312C4×C11C2×#12011yescharacteristic
313C4×C11#53511yescharacteristic
314C4×C11#54612yes—
315C2×#41—24no—
316C2×#41—24no—
317C2×#41—24no—
318C2×#41—24no—
319C2×#41—42no—
320C2×#41—42no—
321C22×Q8C23×C1112yes—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4D4×C1111yescharacteristic
325C22×D4C23×C1112yes—
326C23×C4—22no—
327C23×C4C23×C1111yescharacteristic
328C23×C4C23×C1111yescharacteristic
329#135—232no—
330C2×Q16—24no—
331C2×Q16—22no—
332C2×SD16—24no—
333C2×SD16—24no—
334C2×SD16D4×C1118yescomplemented
335C2×D8—24no—
336C2×D8—22no—
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—24no—
340C22×C8D4×C1114yescomplemented
341C22×C8C23×C1111yescharacteristic
342C22×C8C23×C1111yescharacteristic
343C22×C8C23×C1111yescharacteristic
344C22×C8C23×C1111yescharacteristic
345C22⋊Q8—24no—
346C22⋊Q8—42no—
347#121—24no—
348#121—42no—
349C4×D4—22no—
350C4×D4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4D4×C1111yescharacteristic
353C2×C4⋊C4C23×C1112yes—
354C2×C4⋊C4C23×C1112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4D4×C1111yescharacteristic
361C2×C22⋊C4D4×C1111yescharacteristic
362C2×C42C23×C1111yescharacteristic
363#106—24no—
364C4⋊C8—22no—
365#103—24no—
366#103—42no—
367#102—24no—
368#102—42no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C4×C8—22no—
372#95—22no—
373#95—22no—
374#95—22no—
375C2×C11—42no—
376C2×C11—42no—
377C2×C11—84no—
378C2×C11#240811yescharacteristic
379C2×C11#305011yescharacteristic
380C2×C11#306011yescharacteristic
381C2×C11#328212yes—
382C2×C11#328412yes—
383C24—22no—
384C24C2×D4×C1111yescharacteristic
385C24C2×D4×C1111yescharacteristic
386#41—216no—
387#41—48no—
388#41—48no—
389#41—48no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8C2×D4×C1114yes—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—82no—
410C2×D4C2×D4×C1114yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1112yes—
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C11×#4112yes—
429C22×C4C24×C1111yescharacteristic
430Q16—28no—
431SD16—216no—
432D8—28no—
433C2×C8—22no—
434C2×C8—28no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—44no—
440C2×C8C2×D4×C1112yes—
441C2×C8C2×D4×C1112yes—
442C2×C8C2×D4×C1114yes—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—44no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—82no—
455C22⋊C4—82no—
456C42—21no—
457C42—21no—
458C11#2426511yescharacteristic, direct product factor, Sylow
459C23—21no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—22no—
467C23—24no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23C11×#12112yes—
475C23C11×#13512yescomplemented
476C23C22×D4×C1111yescharacteristic
477Q8—24no—
478Q8—24no—
479Q8—42no—
480Q8—42no—
481D4—28no—
482D4—24no—
483D4—24no—
484D4—416no—
485D4—42no—
486D4—42no—
487D4—88no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—416no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4C11×#12112yes—
512C2×C4C11×#13512yescomplemented
513C2×C4C22×D4×C1111yescharacteristic
514C2×C4C22×D4×C1112yes—
515C2×C4C2×C11×#4111yescharacteristic
516C2×C4C11×H(5,𝔽2)12yes—
517C8—22no—
518C8—41no—
519C8—41no—
520C8C11×#12014yes—
521C22—22no—
522C22—24no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—41no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—41no—
531C22—44no—
532C22—44no—
533C22—44no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22—82no—
538C22C2×C11×#12111yescharacteristic
539C22D42×C1112yes—
540C22C2×C11×#13511yescharacteristic
541C22C2×C11×#13511yescharacteristic
542C22C11×#57712yes—
543C4—22no—
544C4—22no—
545C4—41no—
546C4—44no—
547C4—41no—
548C4—82no—
549C4—82no—
550C4C2×C11×#12011yescharacteristic
551C4C11×#53511yescharacteristic
552C4C11×#54612yes—
553C2—42no—
554C2—42no—
555C2—84no—
556C2C11×#240811yescharacteristic
557C2C11×#305011yescharacteristic
558C2C11×#306011yescharacteristic
559C2C11×#328212yes—
560C2C11×#328412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#135C2semidirect
2. C2×C11×#465C2semidirect
3. C2×C8×D4×C11C2semidirect
4. C11×#2407C2semidirect
5. C11×#2056C2semidirect
6. C11×#2054C2semidirect
7. C11×#2001C2semidirect
8. C11×#1999C2semidirect
9. C11×#1968C2semidirect
10. C11×#1807C2semidirect
11. C11×#1788C2semidirect
62. C2×C11×SD16D4semidirect
68. C22×C8×C11D4semidirect
103. #24265C11direct (N × H)
179. C22×#135C2×C11semidirect
180. C2×#465C2×C11semidirect
181. C2×C8×D4C2×C11semidirect
182. #2407C2×C11semidirect
183. #2056C2×C11semidirect
184. #2054C2×C11semidirect
185. #2001C2×C11semidirect
186. #1999C2×C11semidirect
187. #1968C2×C11semidirect
188. #1807C2×C11semidirect
189. #1788C2×C11semidirect
206. C23×C11#135semidirect
243. C2×C4×C11#135semidirect
334. C2×SD16D4×C11semidirect
340. C22×C8D4×C11semidirect
458. C11#24265direct (N × H)
475. C23C11×#135semidirect
512. C2×C4C11×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C2×C11×#4652
C2×C8×D4×C112
C11×#24072
C11×#20562
C11×#20542
C11×#20012
C11×#19992
C11×#19682
C11×#18072
C11×#17882
#2426511