Finite Group Databasebeta

← C11×#22787 #14599980

Subgroups — C11×#22787 #14599980

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C42×D4×C11C211yesmaximal, characteristic
2C11×#1924C212yesmaximal, complemented
3C11×#1917C212yesmaximal, complemented
4C11×#1869C212yesmaximal
5C11×#1839C211yesmaximal, characteristic, complemented
6C11×#1817C211yesmaximal, characteristic, complemented
7C11×#1797C211yesmaximal, characteristic, complemented
8C11×#1752C212yesmaximal, complemented
9C11×#1749C211yesmaximal, characteristic, complemented
10C11×#1745C211yesmaximal, characteristic, complemented
11C2×C11×#336C211yesmaximal, characteristic, complemented
12C23×C8×C11C2212yes—
13C2×C4×D4×C11C411yescharacteristic
14C2×C4×D4×C11C411yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C2×C11×C4⋊C8C2212yes—
19C2×C11×C22⋊C8C2212yes—
20C2×C11×C22⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22C2×C11×#97C2212yes—
23C2×C11×#97C2212yes—
24C4×C11×C4⋊C4C411yescharacteristic
25C4×C11×C4⋊C4C411yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4C411yescharacteristic
28C4×C11×C22⋊C4C411yescharacteristic
29C4×C11×C22⋊C4C411yescharacteristic
30C4×C11×C22⋊C4C411yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C43×C11C2211yescharacteristic
34C11×#336C2212yes—
35C11×#336C2212yes—
36C11×#336C2212yes—
37C11×#336C2212yes—
38C11×#336C2212yes—
39C11×#336C2211yescharacteristic
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C11×#336C2211yescharacteristic
43C22×D4×C11C2×C411yescharacteristic
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C8×C11—24no—
51C22×C8×C11—24no—
52C22×C8×C11—42no—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C11×C22⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C42×C11—42no—
71C2×C42×C11—42no—
72C2×C42×C11C2×C411yescharacteristic
73C2×C42×C11C2×C411yescharacteristic
74C2×C42×C11C2×C411yescharacteristic
75C2×C42×C11C2×C411yescharacteristic
76C2×C42×C11C2×C411yescharacteristic
77C2×C42×C11C2×C411yescharacteristic
78C2×C42×C11C2×C411yescharacteristic
79C2×C42×C11C2×C411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C11×C4⋊C8—42no—
86C11×C22⋊C8—24no—
87C11×C22⋊C8—24no—
88C11×C22⋊C8—42no—
89C11×#97—24no—
90C11×#97—42no—
91C11×#95C2×C411yescharacteristic
92C11×#95C2×C411yescharacteristic
93C11×#95C2×C411yescharacteristic
94C11×#95C2×C411yescharacteristic
95C11×#95C2×C411yescharacteristic
96C11×#95C2×C411yescharacteristic
97#22787C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11C22×C411yescharacteristic
99C24×C11C22×C411yescharacteristic
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11M1614yes—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11—41no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11M1614yes—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—48no—
148C2×C8×C11#4114yes—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—41no—
168C42×C11—41no—
169C42×C11—41no—
170C42×C11—41no—
171C42×C11—41no—
172C42×D4C2×C1111yescharacteristic
173#1924C2×C1112yescomplemented
174#1917C2×C1112yescomplemented
175#1869C2×C1112yes—
176#1839C2×C1111yescharacteristic, complemented
177#1817C2×C1111yescharacteristic, complemented
178#1797C2×C1111yescharacteristic, complemented
179#1752C2×C1112yescomplemented
180#1749C2×C1111yescharacteristic, complemented
181#1745C2×C1111yescharacteristic, complemented
182C2×#336C2×C1111yescharacteristic, complemented
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11#11712yes—
194C23×C11C2×M1612yes—
195C23×C11C2×M1612yes—
196C23×C11C2×M1612yes—
197C23×C11C23×C411yescharacteristic
198D4×C11—28no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11#11712yes—
239C2×C4×C11C2×M1612yes—
240C2×C4×C11C2×M1612yes—
241C2×C4×C11C2×M1612yes—
242C2×C4×C11#13112yes—
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4112yes—
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)12yes—
247C8×C11—24no—
248C8×C11—42no—
249C8×C11—42no—
250C8×C11—42no—
251C23×C8C22×C1112yes—
252C2×C4×D4C4×C1111yescharacteristic
253C2×C4×D4C4×C1111yescharacteristic
254C2×C4×D4C22×C1111yescharacteristic
255C22×C42C22×C1111yescharacteristic
256C22×C42C22×C1111yescharacteristic
257C2×C4⋊C8C22×C1112yes—
258C2×C22⋊C8C22×C1112yes—
259C2×C22⋊C8C22×C1112yes—
260C2×C22⋊C8C22×C1112yes—
261C2×#97C22×C1112yes—
262C2×#97C22×C1112yes—
263C4×C4⋊C4C4×C1111yescharacteristic
264C4×C4⋊C4C4×C1111yescharacteristic
265C4×C4⋊C4C22×C1111yescharacteristic
266C4×C22⋊C4C4×C1111yescharacteristic
267C4×C22⋊C4C4×C1111yescharacteristic
268C4×C22⋊C4C4×C1111yescharacteristic
269C4×C22⋊C4C4×C1111yescharacteristic
270C4×C22⋊C4C22×C1111yescharacteristic
271C4×C22⋊C4C22×C1111yescharacteristic
272C43C22×C1111yescharacteristic
273#336C22×C1111yescharacteristic
274#336C22×C1111yescharacteristic
275#336C22×C1111yescharacteristic
276#336C22×C1112yes—
277#336C22×C1112yes—
278#336C22×C1112yes—
279#336C22×C1112yes—
280#336C22×C1112yes—
281#336C22×C1111yescharacteristic
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11#43214yes—
296C22×C11C2×#11711yescharacteristic
297C22×C11C4×#4111yescharacteristic
298C22×C11#51811yescharacteristic
299C22×C11C22×M1611yescharacteristic
300C22×C11C22×M1611yescharacteristic
301C22×C11C2×#13111yescharacteristic
302C22×C11#56811yescharacteristic
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—41no—
309C4×C11—41no—
310C4×C11—41no—
311C4×C11—41no—
312C4×C11—41no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11#55112yes—
316C4×C11#55312yes—
317C22×D4C2×C4×C1111yescharacteristic
318C23×C4C2×C4×C1111yescharacteristic
319C23×C4C2×C4×C1111yescharacteristic
320C23×C4C2×C4×C1111yescharacteristic
321C23×C4C2×C4×C1111yescharacteristic
322C23×C4C23×C1111yescharacteristic
323C23×C4C23×C1111yescharacteristic
324C22×C8—24no—
325C22×C8—24no—
326C22×C8—42no—
327C22×C8C23×C1112yes—
328C22×C8C23×C1112yes—
329C22×C8C23×C1112yes—
330C22×C8C23×C1112yes—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—22no—
334C4×D4—22no—
335C2×C4⋊C4C2×C4×C1111yescharacteristic
336C2×C4⋊C4C2×C4×C1111yescharacteristic
337C2×C4⋊C4C2×C4×C1111yescharacteristic
338C2×C22⋊C4C2×C4×C1111yescharacteristic
339C2×C22⋊C4C2×C4×C1111yescharacteristic
340C2×C22⋊C4C2×C4×C1111yescharacteristic
341C2×C22⋊C4C2×C4×C1111yescharacteristic
342C2×C22⋊C4C2×C4×C1111yescharacteristic
343C2×C22⋊C4C2×C4×C1111yescharacteristic
344C2×C42—42no—
345C2×C42—42no—
346C2×C42C2×C4×C1111yescharacteristic
347C2×C42C2×C4×C1111yescharacteristic
348C2×C42C2×C4×C1111yescharacteristic
349C2×C42C2×C4×C1111yescharacteristic
350C2×C42C2×C4×C1111yescharacteristic
351C2×C42C2×C4×C1111yescharacteristic
352C2×C42C2×C4×C1111yescharacteristic
353C2×C42C2×C4×C1111yescharacteristic
354C2×C42C23×C1111yescharacteristic
355C2×C42C23×C1111yescharacteristic
356C2×C42C23×C1111yescharacteristic
357C2×C42C23×C1111yescharacteristic
358C2×C42C23×C1111yescharacteristic
359C4⋊C8—42no—
360C22⋊C8—24no—
361C22⋊C8—24no—
362C22⋊C8—42no—
363#97—24no—
364#97—42no—
365#95C2×C4×C1111yescharacteristic
366#95C2×C4×C1111yescharacteristic
367#95C2×C4×C1111yescharacteristic
368#95C2×C4×C1111yescharacteristic
369#95C2×C4×C1111yescharacteristic
370#95C2×C4×C1111yescharacteristic
371C2×C11—24no—
372C2×C11—42no—
373C2×C11#235311yescharacteristic
374C2×C11C2×#43211yescharacteristic
375C2×C11#292511yescharacteristic
376C2×C11#296511yescharacteristic
377C2×C11#297011yescharacteristic
378C2×C11#297311yescharacteristic
379C2×C11#297411yescharacteristic
380C24C22×C4×C1111yescharacteristic
381C24C22×C4×C1111yescharacteristic
382C2×D4—22no—
383C2×D4—22no—
384C2×D4C11×M1614yes—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4C11×M1614yes—
403C22×C4C22×C4×C1111yescharacteristic
404C22×C4C22×C4×C1111yescharacteristic
405C22×C4C22×C4×C1111yescharacteristic
406C22×C4C22×C4×C1111yescharacteristic
407C22×C4C22×C4×C1111yescharacteristic
408C22×C4C22×C4×C1111yescharacteristic
409C22×C4C22×C4×C1111yescharacteristic
410C22×C4C22×C4×C1111yescharacteristic
411C22×C4C22×C4×C1111yescharacteristic
412C22×C4C22×C4×C1111yescharacteristic
413C22×C4C22×C4×C1111yescharacteristic
414C22×C4C22×C4×C1111yescharacteristic
415C22×C4C11×#4112yes—
416C22×C4C11×#4112yes—
417C22×C4C24×C1111yescharacteristic
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—48no—
430C2×C8C11×#4114yes—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C42—22no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—21no—
445C42—21no—
446C42—22no—
447C42—22no—
448C42—22no—
449C42—41no—
450C42—41no—
451C42—41no—
452C42—41no—
453C42—41no—
454C11#2278711yescharacteristic, direct product factor, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23C11×#11712yes—
466C23C2×C11×M1612yes—
467C23C2×C11×M1612yes—
468C23C2×C11×M1612yes—
469C23C23×C4×C1111yescharacteristic
470D4—28no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4C11×#11712yes—
511C2×C4C2×C11×M1612yes—
512C2×C4C2×C11×M1612yes—
513C2×C4C2×C11×M1612yes—
514C2×C4C11×#13112yes—
515C2×C4C2×C11×#4111yescharacteristic
516C2×C4C2×C11×#4112yes—
517C2×C4C2×C11×#4111yescharacteristic
518C2×C4C11×H(5,𝔽2)12yes—
519C8—24no—
520C8—42no—
521C8—42no—
522C8—42no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22C11×#43214yes—
537C22C2×C11×#11711yescharacteristic
538C22C4×C11×#4111yescharacteristic
539C22C11×#51811yescharacteristic
540C22C22×C11×M1611yescharacteristic
541C22C22×C11×M1611yescharacteristic
542C22C2×C11×#13111yescharacteristic
543C22C11×#56811yescharacteristic
544C4—22no—
545C4—22no—
546C4—22no—
547C4—22no—
548C4—22no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4C11×#55112yes—
557C4C11×#55312yes—
558C2—24no—
559C2—42no—
560C2C11×#235311yescharacteristic
561C2C2×C11×#43211yescharacteristic
562C2C11×#292511yescharacteristic
563C2C11×#296511yescharacteristic
564C2C11×#297011yescharacteristic
565C2C11×#297311yescharacteristic
566C2C11×#297411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1924C2semidirect
3. C11×#1917C2semidirect
5. C11×#1839C2semidirect
6. C11×#1817C2semidirect
7. C11×#1797C2semidirect
8. C11×#1752C2semidirect
9. C11×#1749C2semidirect
10. C11×#1745C2semidirect
11. C2×C11×#336C2semidirect
97. #22787C11direct (N × H)
173. #1924C2×C11semidirect
174. #1917C2×C11semidirect
176. #1839C2×C11semidirect
177. #1817C2×C11semidirect
178. #1797C2×C11semidirect
179. #1752C2×C11semidirect
180. #1749C2×C11semidirect
181. #1745C2×C11semidirect
182. C2×#336C2×C11semidirect
454. C11#22787direct (N × H)

Maximal subgroups

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

subgroupindex
C42×D4×C112
C11×#19242
C11×#19172
C11×#18692
C11×#18392
C11×#18172
C11×#17972
C11×#17522
C11×#17492
C11×#17452
C2×C11×#3362
#2278711