Finite Group Databasebeta

← C11×#24961 #14602154

Subgroups — C11×#24961 #14602154

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2485C211yesmaximal, characteristic
2C11×#2352C211yesmaximal, characteristic
3C11×#2101C211yesmaximal, characteristic, complemented
4C11×#2085C211yesmaximal, characteristic, complemented
5C11×#2077C211yesmaximal, characteristic, complemented
6C11×#2077C211yesmaximal, characteristic, complemented
7C11×#1920C211yesmaximal, characteristic, complemented
8C11×#1919C211yesmaximal, characteristic, complemented
9C11×#1870C211yesmaximal, characteristic
10C11×#1854C211yesmaximal, characteristic, complemented
11C11×#1853C211yesmaximal, characteristic, complemented
12C11×#1825C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1809C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#397—21no—
29C11×#394—21no—
30C11×#389C2211yescharacteristic
31C11×#389C2211yescharacteristic
32C11×#388—21no—
33C11×#388—21no—
34C11×#387—21no—
35C11×#387—21no—
36C11×#386—21no—
37C11×#382C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#380C2211yescharacteristic
40C11×#380C2211yescharacteristic
41C11×#380C2211yescharacteristic
42C11×#380C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C22⋊C4—21no—
45C11×#340C2211yescharacteristic
46C11×#340C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—41no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C11×#117—22no—
73C11×#117—22no—
74C11×#117—22no—
75C11×#117—41no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C11×#107—41no—
104C11×#106—22no—
105C11×#106—22no—
106C11×#106—41no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×C22⋊C8—41no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120#24961C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11C2×D411yescharacteristic
122C24×C11C2×D411yescharacteristic
123C2×D4×C11—22no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C11×M16—44no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11#4112yes—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—81no—
186C11×C4⋊C4#4112yes—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—81no—
194C11×C22⋊C4—81no—
195C11×C22⋊C4—81no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—42no—
199C42×C11—42no—
200C42×C11—81no—
201#2485C2×C1111yescharacteristic
202#2352C2×C1111yescharacteristic
203#2101C2×C1111yescharacteristic, complemented
204#2085C2×C1111yescharacteristic, complemented
205#2077C2×C1111yescharacteristic, complemented
206#2077C2×C1111yescharacteristic, complemented
207#1920C2×C1111yescharacteristic, complemented
208#1919C2×C1111yescharacteristic, complemented
209#1870C2×C1111yescharacteristic
210#1854C2×C1111yescharacteristic, complemented
211#1853C2×C1111yescharacteristic, complemented
212#1825C2×C1111yescharacteristic, complemented
213#1825C2×C1111yescharacteristic, complemented
214#1809C2×C1111yescharacteristic, complemented
215#1736C2×C1111yescharacteristic, complemented
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11#12312yes—
230C23×C11C22×D411yescharacteristic
231D4×C11—44no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—84no—
276C2×C4×C11#12312yes—
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C8×C11—22no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—41no—
287C22×M16C22×C1111yescharacteristic
288C2×C4×D4C22×C1111yescharacteristic
289C2×#117C22×C1111yescharacteristic
290C2×#117C22×C1111yescharacteristic
291C22×C4⋊C4C22×C1111yescharacteristic
292C2×#107C22×C1111yescharacteristic
293C2×#106C22×C1111yescharacteristic
294C2×#106C22×C1111yescharacteristic
295C2×#106C22×C1111yescharacteristic
296C2×C22⋊C8C22×C1111yescharacteristic
297C2×C22⋊C8C22×C1111yescharacteristic
298C2×C22⋊C8C22×C1111yescharacteristic
299#397—21no—
300#394—21no—
301#389C22×C1111yescharacteristic
302#389C22×C1111yescharacteristic
303#388—21no—
304#388—21no—
305#387—21no—
306#387—21no—
307#386—21no—
308#382C22×C1111yescharacteristic
309#380C22×C1111yescharacteristic
310#380C22×C1111yescharacteristic
311#380C22×C1111yescharacteristic
312#380C22×C1111yescharacteristic
313#380C22×C1111yescharacteristic
314C4×C4⋊C4C22×C1111yescharacteristic
315C4×C22⋊C4—21no—
316#340C22×C1111yescharacteristic
317#340C22×C1111yescharacteristic
318#340C22×C1111yescharacteristic
319#340C22×C1111yescharacteristic
320#340C22×C1111yescharacteristic
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#340C22×C1111yescharacteristic
324#340C22×C1111yescharacteristic
325#340C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#336C22×C1111yescharacteristic
329#336C22×C1111yescharacteristic
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11C2×#12311yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#54711yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57711yescharacteristic
351C4×C11—22no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11#52911yescharacteristic
364C4×C11#53911yescharacteristic
365C4×C11#55111yescharacteristic
366C4×C11#55211yescharacteristic
367C22×D4D4×C1111yescharacteristic
368C23×C4—21no—
369C23×C4C23×C1111yescharacteristic
370C23×C4C23×C1111yescharacteristic
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—41no—
374C22×C8C23×C1111yescharacteristic
375C22×C8C23×C1111yescharacteristic
376C22×C8C23×C1111yescharacteristic
377C22×C8C23×C1111yescharacteristic
378C4×D4—22no—
379C4×D4—22no—
380#117—22no—
381#117—22no—
382#117—22no—
383#117—41no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4D4×C1111yescharacteristic
390C2×C4⋊C4C23×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C4⋊C4C23×C1111yescharacteristic
396C2×C4⋊C4C23×C1111yescharacteristic
397C2×C4⋊C4C23×C1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4D4×C1111yescharacteristic
406C2×C22⋊C4D4×C1111yescharacteristic
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42C23×C1111yescharacteristic
411#107—41no—
412#106—22no—
413#106—22no—
414#106—41no—
415C22⋊C8—22no—
416C22⋊C8—22no—
417C22⋊C8—41no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428C2×C11—42no—
429C2×C11—81no—
430C2×C11#241911yescharacteristic
431C2×C11#309311yescharacteristic
432C2×C11#309911yescharacteristic
433C2×C11#332111yescharacteristic
434C2×C11#332311yescharacteristic
435C2×C11#335011yescharacteristic
436C2×C11#335111yescharacteristic
437C24C2×D4×C1111yescharacteristic
438C24C2×D4×C1111yescharacteristic
439C2×D4—22no—
440C2×D4—41no—
441C2×D4—41no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C11×#4112yes—
468C22×C4C11×#4112yes—
469C22×C4C24×C1111yescharacteristic
470M16—44no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8C11×#4112yes—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—81no—
502C4⋊C4C11×#4112yes—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C22⋊C4—81no—
512C42—21no—
513C42—21no—
514C42—42no—
515C42—42no—
516C42—81no—
517C11#2496111yescharacteristic, direct product factor, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23C11×#12312yes—
532C23C22×D4×C1111yescharacteristic
533D4—44no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4C11×#12312yes—
579C2×C4C2×C11×#4111yescharacteristic
580C2×C4C2×C11×#4111yescharacteristic
581C2×C4C2×C11×#4111yescharacteristic
582C2×C4C2×C11×#4111yescharacteristic
583C2×C4C11×H(5,𝔽2)11yescharacteristic
584C2×C4C11×2−1+411yescharacteristic
585C8—22no—
586C8—41no—
587C8—41no—
588C8—41no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22C2×C11×#12311yescharacteristic
604C22C11×#54611yescharacteristic
605C22C11×#54711yescharacteristic
606C22C11×#57511yescharacteristic
607C22C11×#57511yescharacteristic
608C22C11×#57711yescharacteristic
609C22C11×#57711yescharacteristic
610C4—22no—
611C4—41no—
612C4—42no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4C11×#52911yescharacteristic
623C4C11×#53911yescharacteristic
624C4C11×#55111yescharacteristic
625C4C11×#55211yescharacteristic
626C2—42no—
627C2—81no—
628C2C11×#241911yescharacteristic
629C2C11×#309311yescharacteristic
630C2C11×#309911yescharacteristic
631C2C11×#332111yescharacteristic
632C2C11×#332311yescharacteristic
633C2C11×#335011yescharacteristic
634C2C11×#335111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
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
3. C11×#2101C2semidirect
4. C11×#2085C2semidirect
5. C11×#2077C2semidirect
6. C11×#2077C2semidirect
7. C11×#1920C2semidirect
8. C11×#1919C2semidirect
10. C11×#1854C2semidirect
11. C11×#1853C2semidirect
12. C11×#1825C2semidirect
13. C11×#1825C2semidirect
14. C11×#1809C2semidirect
15. C11×#1736C2semidirect
120. #24961C11direct (N × H)
203. #2101C2×C11semidirect
204. #2085C2×C11semidirect
205. #2077C2×C11semidirect
206. #2077C2×C11semidirect
207. #1920C2×C11semidirect
208. #1919C2×C11semidirect
210. #1854C2×C11semidirect
211. #1853C2×C11semidirect
212. #1825C2×C11semidirect
213. #1825C2×C11semidirect
214. #1809C2×C11semidirect
215. #1736C2×C11semidirect
517. C11#24961direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24852
C11×#23522
C11×#21012
C11×#20852
C11×#20772
C11×#19202
C11×#19192
C11×#18702
C11×#18542
C11×#18532
C11×#18252
C11×#18092
C11×#17362
#2496111