Finite Group Databasebeta

← C11×#21763 #14598956

Subgroups — C11×#21763 #14598956

Order 2816.

1590 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
1C2×C11×#525C211yesmaximal, characteristic
2C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×C11×#380C211yesmaximal, characteristic, complemented
4C11×#1893C212yesmaximal, complemented
5C11×#1892C212yesmaximal, complemented
6C11×#1874C212yesmaximal, complemented
7C11×#1872C212yesmaximal, complemented
8C11×#1825C212yesmaximal, complemented
9C11×#1788C212yesmaximal, complemented
10C22×C11×#41C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C23×C8×C11C2212yes—
13C11×#525—24no—
14C11×#525C418yescomplemented
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C22⋊C4—21no—
26C2×C11×#103C2214yescomplemented
27C2×C11×#102C2214yescomplemented
28C2×C11×C22⋊C8—24no—
29C2×C11×C22⋊C8C2212yes—
30C2×C11×C22⋊C8C2212yes—
31C11×#380—21no—
32C11×#380—21no—
33C11×#380C2212yes—
34C11×#380C2212yes—
35C2×C11×#95—21no—
36C11×#340C2214yescomplemented
37C11×#340C2214yescomplemented
38C25×C11D411yescharacteristic
39C2×C11×#41—22no—
40C2×C11×#41—44no—
41C2×C11×#41C2×C414yescomplemented
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—22no—
49C23×C4×C11—44no—
50C23×C4×C11C2×C414yes—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D414yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C8×C11—24no—
59C22×C8×C11—44no—
60C22×C8×C11C2314yes—
61C11×#123—28no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8C2×C414yes—
65C11×C22⋊Q8C2×C414yescomplemented
66C11×#121—22no—
67C11×#121—22no—
68C11×#121C2×C414yes—
69C11×#121C2×C414yescomplemented
70C11×#120—28no—
71C4×D4×C11—28no—
72C4×D4×C11—28no—
73C11×#117—22no—
74C11×#117C2×C414yescomplemented
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—44no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—44no—
90C2×C42×C11—21no—
91C11×#103—44no—
92C11×#102—44no—
93C11×C22⋊C8—24no—
94C11×C22⋊C8—24no—
95C11×#95—22no—
96C11×#95—22no—
97#21763C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—24no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—21no—
102C24×C11—42no—
103C24×C11C22⋊C414yes—
104C24×C11C2×D411yescharacteristic
105C24×C11C2×D411yescharacteristic
106C24×C11C2×D411yescharacteristic
107C11×#41—48no—
108C11×#41—48no—
109C2×Q8×C11—21no—
110C2×Q8×C11—24no—
111C2×Q8×C11C22×C412yes—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—21no—
116C2×D4×C11—24no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11C22×C412yes—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—48no—
131C22×C4×C11—48no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—44no—
136C22×C4×C11—44no—
137C22×C4×C11—44no—
138C22×C4×C11—44no—
139C22×C4×C11C22⋊C414yes—
140C22×C4×C11C22⋊C414yes—
141C22×C4×C11C22⋊C414yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2411yescharacteristic
152C2×C8×C11—24no—
153C2×C8×C11—24no—
154C2×C8×C11—24no—
155C2×C8×C11—48no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4C22×C412yes—
164C11×C4⋊C4C22×C412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—44no—
172C42×C11—24no—
173C2×#525C2×C1111yescharacteristic
174C22×C22⋊C8C2×C1111yescharacteristic, complemented
175C2×#380C2×C1111yescharacteristic, complemented
176#1893C2×C1112yescomplemented
177#1892C2×C1112yescomplemented
178#1874C2×C1112yescomplemented
179#1872C2×C1112yescomplemented
180#1825C2×C1112yescomplemented
181#1788C2×C1112yescomplemented
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—28no—
192C23×C11—28no—
193C23×C11—22no—
194C23×C11—44no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11C2×C22⋊C412yes—
202C23×C11C2×C22⋊C412yes—
203C23×C11C2×C22⋊C412yes—
204C23×C11#13514yes—
205C23×C11AGL(1,ℤ/8)12yes—
206C23×C11#13712yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—24no—
209Q8×C11—42no—
210D4×C11—24no—
211D4×C11—48no—
212D4×C11—48no—
213D4×C11—48no—
214D4×C11—42no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—44no—
236C2×C4×C11—44no—
237C2×C4×C11—44no—
238C2×C4×C11—88no—
239C2×C4×C11C2×C22⋊C412yes—
240C2×C4×C11C2×C22⋊C412yes—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11H(5,𝔽2)14yes—
245C8×C11—44no—
246C22×#41C22×C1111yescharacteristic
247C24×C4C22×C1111yescharacteristic
248C23×C8C22×C1112yes—
249#525—24no—
250#525C4×C1118yescomplemented
251C2×#123—21no—
252C2×C22⋊Q8C22×C1111yescharacteristic
253C2×C22⋊Q8C22×C1111yescharacteristic
254C2×#121C22×C1111yescharacteristic
255C2×#121C22×C1111yescharacteristic
256C2×#120—21no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×#117C22×C1111yescharacteristic
260C22×C4⋊C4C22×C1112yes—
261C22×C22⋊C4—21no—
262C2×#103C22×C1114yescomplemented
263C2×#102C22×C1114yescomplemented
264C2×C22⋊C8—24no—
265C2×C22⋊C8C22×C1112yes—
266C2×C22⋊C8C22×C1112yes—
267#380—21no—
268#380—21no—
269#380C22×C1112yes—
270#380C22×C1112yes—
271C2×#95—21no—
272#340C22×C1114yescomplemented
273#340C22×C1114yescomplemented
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—416no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11#41614yes—
294C22×C11#41714yes—
295C22×C11C22×C22⋊C411yescharacteristic
296C22×C11#53412yes—
297C22×C11C2×#13512yes—
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C11C2×#13711yescharacteristic
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—84no—
307C4×C11#51812yes—
308C4×C11#53412yes—
309C25D4×C1111yescharacteristic
310C2×#41—22no—
311C2×#41—44no—
312C2×#41C2×C4×C1114yescomplemented
313C22×Q8C23×C1111yescharacteristic
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C23×C1111yescharacteristic
318C23×C4—21no—
319C23×C4—22no—
320C23×C4—44no—
321C23×C4C2×C4×C1114yes—
322C23×C4D4×C1111yescharacteristic
323C23×C4D4×C1111yescharacteristic
324C23×C4D4×C1111yescharacteristic
325C23×C4D4×C1114yes—
326C23×C4C23×C1111yescharacteristic
327C23×C4C23×C1111yescharacteristic
328C23×C4C23×C1111yescharacteristic
329C22×C8—24no—
330C22×C8—44no—
331C22×C8C23×C1114yes—
332#123—28no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8C2×C4×C1114yes—
336C22⋊Q8C2×C4×C1114yescomplemented
337#121—22no—
338#121—22no—
339#121C2×C4×C1114yes—
340#121C2×C4×C1114yescomplemented
341#120—28no—
342C4×D4—28no—
343C4×D4—28no—
344#117—22no—
345#117C2×C4×C1114yescomplemented
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4C23×C1114yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C4⋊C4C23×C1111yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—44no—
361C2×C42—21no—
362#103—44no—
363#102—44no—
364C22⋊C8—24no—
365C22⋊C8—24no—
366#95—22no—
367#95—22no—
368C2×C11—24no—
369C2×C11—24no—
370C2×C11—42no—
371C2×C11—82no—
372C2×C11#230811yescharacteristic
373C2×C11C2×#41611yescharacteristic
374C2×C11C2×#41711yescharacteristic
375C2×C11#318812yes—
376C2×C11#319012yes—
377C24—24no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—42no—
382C24C11×C22⋊C414yes—
383C24C2×D4×C1111yescharacteristic
384C24C2×D4×C1111yescharacteristic
385C24C2×D4×C1111yescharacteristic
386#41—48no—
387#41—48no—
388C2×Q8—21no—
389C2×Q8—24no—
390C2×Q8C22×C4×C1112yes—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—21no—
395C2×D4—24no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4C22×C4×C1112yes—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—48no—
410C22×C4—48no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4C11×C22⋊C414yes—
419C22×C4C11×C22⋊C414yes—
420C22×C4C11×C22⋊C414yes—
421C22×C4C22×C4×C1112yes—
422C22×C4C22×C4×C1112yes—
423C22×C4C22×C4×C1112yes—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1112yes—
428C22×C4C2×D4×C1112yes—
429C22×C4C2×D4×C1112yes—
430C22×C4C24×C1111yescharacteristic
431C2×C8—24no—
432C2×C8—24no—
433C2×C8—24no—
434C2×C8—48no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—44no—
442C4⋊C4C22×C4×C1112yes—
443C4⋊C4C22×C4×C1112yes—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—44no—
450C22⋊C4—44no—
451C42—24no—
452C11#2176311yescharacteristic, direct product factor, Sylow
453C23—22no—
454C23—22no—
455C23—22no—
456C23—21no—
457C23—21no—
458C23—22no—
459C23—28no—
460C23—28no—
461C23—22no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—44no—
466C23—48no—
467C23—48no—
468C23—42no—
469C23—42no—
470C23—41no—
471C23—41no—
472C23C2×C11×C22⋊C412yes—
473C23C2×C11×C22⋊C412yes—
474C23C2×C11×C22⋊C412yes—
475C23C11×#13514yes—
476C23C11×AGL(1,ℤ/8)12yes—
477C23C11×#13712yes—
478C23C22×D4×C1111yescharacteristic
479Q8—24no—
480Q8—42no—
481D4—24no—
482D4—48no—
483D4—48no—
484D4—48no—
485D4—42no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—88no—
510C2×C4C2×C11×C22⋊C412yes—
511C2×C4C2×C11×C22⋊C412yes—
512C2×C4C2×C11×C22⋊C412yes—
513C2×C4C23×C4×C1111yescharacteristic
514C2×C4C22×D4×C1111yescharacteristic
515C2×C4C11×H(5,𝔽2)14yes—
516C8—44no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—24no—
521C22—24no—
522C22—24no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—416no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—82no—
535C22—82no—
536C22C11×#41614yes—
537C22C11×#41714yes—
538C22C22×C11×C22⋊C411yescharacteristic
539C22C11×#53412yes—
540C22C2×C11×#13512yes—
541C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
542C22C2×C11×#13711yescharacteristic
543C4—22no—
544C4—22no—
545C4—22no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—84no—
550C4C11×#51812yes—
551C4C11×#53412yes—
552C2—24no—
553C2—24no—
554C2—42no—
555C2—82no—
556C2C11×#230811yescharacteristic
557C2C2×C11×#41611yescharacteristic
558C2C2×C11×#41711yescharacteristic
559C2C11×#318812yes—
560C2C11×#319012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×C22⋊C8C2semidirect
3. C2×C11×#380C2semidirect
4. C11×#1893C2semidirect
5. C11×#1892C2semidirect
6. C11×#1874C2semidirect
7. C11×#1872C2semidirect
8. C11×#1825C2semidirect
9. C11×#1788C2semidirect
14. C11×#525C4semidirect
26. C2×C11×#103C22semidirect
27. C2×C11×#102C22semidirect
36. C11×#340C22semidirect
37. C11×#340C22semidirect
41. C2×C11×#41C2×C4semidirect
65. C11×C22⋊Q8C2×C4semidirect
69. C11×#121C2×C4semidirect
74. C11×#117C2×C4semidirect
97. #21763C11direct (N × H)
174. C22×C22⋊C8C2×C11semidirect
175. C2×#380C2×C11semidirect
176. #1893C2×C11semidirect
177. #1892C2×C11semidirect
178. #1874C2×C11semidirect
179. #1872C2×C11semidirect
180. #1825C2×C11semidirect
181. #1788C2×C11semidirect
250. #525C4×C11semidirect
262. C2×#103C22×C11semidirect
263. C2×#102C22×C11semidirect
272. #340C22×C11semidirect
273. #340C22×C11semidirect
312. C2×#41C2×C4×C11semidirect
336. C22⋊Q8C2×C4×C11semidirect
340. #121C2×C4×C11semidirect
345. #117C2×C4×C11semidirect
452. C11#21763direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C22×C11×C22⋊C82
C2×C11×#3802
C11×#18932
C11×#18922
C11×#18742
C11×#18722
C11×#18252
C11×#17882
#2176311