Finite Group Databasebeta

← C11×#27038 #14604231

Subgroups — C11×#27038 #14604231

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2495C211yesmaximal, characteristic, complemented
2C11×#2363C211yesmaximal, characteristic
3C11×#2073C211yesmaximal, characteristic, complemented
4C11×#2067C211yesmaximal, characteristic, complemented
5C11×#2034C211yesmaximal, characteristic
6C11×#2033C211yesmaximal, characteristic
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1942C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1920C211yesmaximal, characteristic, complemented
11C11×#1920C211yesmaximal, characteristic, complemented
12C11×#1864C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1825C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#400—21no—
32C11×#397—21no—
33C11×#390—21no—
34C11×#390C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#388—21no—
39C11×#388—21no—
40C11×#386—21no—
41C11×#383—21no—
42C11×#382C2211yescharacteristic
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4—21no—
48C4×C11×C22⋊C4C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—22no—
68C11×#121—22no—
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C11×#117—22no—
72C11×#117—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#107—22no—
98C11×#107—41no—
99C11×#106—22no—
100C11×#106—22no—
101C11×C4⋊C8—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#102—41no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8—41no—
108C4×C8×C11—41no—
109C11×#95—21no—
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×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120#27038C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—81no—
130C2×D4×C11—81no—
131C2×D4×C11#4112yes—
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—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C8×C11—21no—
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#4112yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
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—81no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4#4112yes—
182C11×C4⋊C4#4112yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—81no—
191C11×C22⋊C4—81no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—42no—
197C42×C11—42no—
198C42×C11—81no—
199#2495C2×C1111yescharacteristic, complemented
200#2363C2×C1111yescharacteristic
201#2073C2×C1111yescharacteristic, complemented
202#2067C2×C1111yescharacteristic, complemented
203#2034C2×C1111yescharacteristic
204#2033C2×C1111yescharacteristic
205#1949C2×C1111yescharacteristic, complemented
206#1942C2×C1111yescharacteristic, complemented
207#1923C2×C1111yescharacteristic, complemented
208#1920C2×C1111yescharacteristic, complemented
209#1920C2×C1111yescharacteristic, complemented
210#1864C2×C1111yescharacteristic, complemented
211#1854C2×C1111yescharacteristic, complemented
212#1825C2×C1111yescharacteristic, complemented
213C4×#102C2×C1111yescharacteristic, complemented
214C23×C11—22no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C22×D411yescharacteristic
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—84no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
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—84no—
274C2×C4×C11#13512yes—
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C8×C11—22no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—41no—
285C2×#121C22×C1111yescharacteristic
286C2×C4×D4C22×C1111yescharacteristic
287C2×#117C22×C1111yescharacteristic
288C2×#107C22×C1111yescharacteristic
289C2×#107C22×C1111yescharacteristic
290C2×#106C22×C1111yescharacteristic
291C2×#106C22×C1111yescharacteristic
292C2×C4⋊C8C22×C1111yescharacteristic
293C2×#102C22×C1111yescharacteristic
294C2×#102C22×C1111yescharacteristic
295C2×#102C22×C1111yescharacteristic
296C2×#102C22×C1111yescharacteristic
297C2×C22⋊C8C22×C1111yescharacteristic
298C2×C22⋊C8C22×C1111yescharacteristic
299C2×C4×C8C22×C1111yescharacteristic
300#400—21no—
301#397—21no—
302#390—21no—
303#390C22×C1111yescharacteristic
304#389C22×C1111yescharacteristic
305#389C22×C1111yescharacteristic
306#389C22×C1111yescharacteristic
307#388—21no—
308#388—21no—
309#386—21no—
310#383—21no—
311#382C22×C1111yescharacteristic
312#380C22×C1111yescharacteristic
313#380C22×C1111yescharacteristic
314C4×C4⋊C4C22×C1111yescharacteristic
315C4×C4⋊C4C22×C1111yescharacteristic
316C4×C22⋊C4—21no—
317C4×C22⋊C4C22×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#336C22×C1111yescharacteristic
327#336C22×C1111yescharacteristic
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11—41no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11#52511yescharacteristic
343C22×C11#54611yescharacteristic
344C22×C11#54711yescharacteristic
345C22×C11C2×#13511yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57711yescharacteristic
349C4×C11—22no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11#52911yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11#55311yescharacteristic
364C4×C11#55611yescharacteristic
365C22×D4—21no—
366C22×D4C23×C1111yescharacteristic
367C23×C4—21no—
368C23×C4C23×C1111yescharacteristic
369C22×C8C23×C1111yescharacteristic
370C22×C8C23×C1111yescharacteristic
371C22×C8C23×C1111yescharacteristic
372C22×C8C23×C1111yescharacteristic
373#121—22no—
374#121—22no—
375C4×D4—22no—
376C4×D4—41no—
377#117—22no—
378#117—41no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4C23×C1111yescharacteristic
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C4⋊C4C23×C1111yescharacteristic
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4D4×C1111yescharacteristic
397C2×C22⋊C4D4×C1111yescharacteristic
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C23×C1111yescharacteristic
402C2×C42C23×C1111yescharacteristic
403#107—22no—
404#107—41no—
405#106—22no—
406#106—22no—
407C4⋊C8—22no—
408#102—22no—
409#102—22no—
410#102—22no—
411#102—41no—
412C22⋊C8—22no—
413C22⋊C8—41no—
414C4×C8—41no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95D4×C1111yescharacteristic
425#95D4×C1111yescharacteristic
426C2×C11—81no—
427C2×C11—82no—
428C2×C11#246611yescharacteristic
429C2×C11#310211yescharacteristic
430C2×C11#311811yescharacteristic
431C2×C11#329611yescharacteristic
432C2×C11#330911yescharacteristic
433C2×C11#334111yescharacteristic
434C2×C11#335111yescharacteristic
435C24—21no—
436C24C2×D4×C1111yescharacteristic
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—81no—
444C2×D4—81no—
445C2×D4C11×#4112yes—
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—42no—
460C22×C4—42no—
461C22×C4—81no—
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C24×C1111yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
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×C8C11×#4112yes—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
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—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4C11×#4112yes—
496C4⋊C4C11×#4112yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—42no—
512C42—81no—
513C11#2703811yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C22×D4×C1111yescharacteristic
529D4—22no—
530D4—22no—
531D4—41no—
532D4—41no—
533D4—84no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
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—84no—
574C2×C4C11×#13512yes—
575C2×C4C2×C11×#4111yescharacteristic
576C2×C4C2×C11×#4111yescharacteristic
577C2×C4C2×C11×#4111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C11×H(5,𝔽2)11yescharacteristic
580C2×C4C11×2−1+411yescharacteristic
581C8—22no—
582C8—41no—
583C8—41no—
584C8—41no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22C11×#52511yescharacteristic
600C22C11×#54611yescharacteristic
601C22C11×#54711yescharacteristic
602C22C2×C11×#13511yescharacteristic
603C22C11×#57511yescharacteristic
604C22C11×#57611yescharacteristic
605C22C11×#57711yescharacteristic
606C4—22no—
607C4—41no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—42no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4C11×#52911yescharacteristic
619C4C11×#53911yescharacteristic
620C4C11×#55311yescharacteristic
621C4C11×#55611yescharacteristic
622C2—81no—
623C2—82no—
624C2C11×#246611yescharacteristic
625C2C11×#310211yescharacteristic
626C2C11×#311811yescharacteristic
627C2C11×#329611yescharacteristic
628C2C11×#330911yescharacteristic
629C2C11×#334111yescharacteristic
630C2C11×#335111yescharacteristic
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. C11×#2495C2semidirect
3. C11×#2073C2semidirect
4. C11×#2067C2semidirect
7. C11×#1949C2semidirect
8. C11×#1942C2semidirect
9. C11×#1923C2semidirect
10. C11×#1920C2semidirect
11. C11×#1920C2semidirect
12. C11×#1864C2semidirect
13. C11×#1854C2semidirect
14. C11×#1825C2semidirect
15. C4×C11×#102C2semidirect
120. #27038C11direct (N × H)
199. #2495C2×C11semidirect
201. #2073C2×C11semidirect
202. #2067C2×C11semidirect
205. #1949C2×C11semidirect
206. #1942C2×C11semidirect
207. #1923C2×C11semidirect
208. #1920C2×C11semidirect
209. #1920C2×C11semidirect
210. #1864C2×C11semidirect
211. #1854C2×C11semidirect
212. #1825C2×C11semidirect
213. C4×#102C2×C11semidirect
513. C11#27038direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24952
C11×#23632
C11×#20732
C11×#20672
C11×#20342
C11×#20332
C11×#19492
C11×#19422
C11×#19232
C11×#19202
C11×#18642
C11×#18542
C11×#18252
C4×C11×#1022
#2703811