Finite Group Databasebeta

← C11×#27139 #14604332

Subgroups — C11×#27139 #14604332

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2512C211yesmaximal, characteristic
2C11×#2370C211yesmaximal, characteristic, complemented
3C11×#2100C211yesmaximal, characteristic, complemented
4C11×#2065C211yesmaximal, characteristic
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2025C211yesmaximal, characteristic
7C11×#1948C211yesmaximal, characteristic, complemented
8C11×#1934C211yesmaximal, characteristic
9C11×#1926C211yesmaximal, characteristic
10C11×#1926C211yesmaximal, characteristic
11C11×#1925C211yesmaximal, characteristic
12C11×#1920C211yesmaximal, characteristic, complemented
13C11×#1918C211yesmaximal, characteristic, complemented
14C11×#1916C211yesmaximal, characteristic, complemented
15C4×C11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#126—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C11×#397—21no—
29C11×#396—21no—
30C11×#390C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#389—21no—
34C11×#389C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#388—21no—
38C11×#387—21no—
39C11×#387—21no—
40C11×#384C2211yescharacteristic
41C4×C11×C4⋊C4—21no—
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C4⋊C4C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#126—44no—
65C11×#125—22no—
66C11×#125—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
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×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C11×#107—22no—
97C11×#106—22no—
98C11×#106—22no—
99C11×#106—22no—
100C11×C4⋊C8—22no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—22no—
105C4×C8×C11—22no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#27139C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11#4112yes—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4#4112yes—
170C11×C4⋊C4#4112yes—
171C11×C4⋊C4#4112yes—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—81no—
177C11×C22⋊C4—81no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—42no—
185C42×C11—42no—
186C42×C11—81no—
187C42×C11—81no—
188#2512C2×C1111yescharacteristic
189#2370C2×C1111yescharacteristic, complemented
190#2100C2×C1111yescharacteristic, complemented
191#2065C2×C1111yescharacteristic
192#2059C2×C1111yescharacteristic, complemented
193#2025C2×C1111yescharacteristic
194#1948C2×C1111yescharacteristic, complemented
195#1934C2×C1111yescharacteristic
196#1926C2×C1111yescharacteristic
197#1926C2×C1111yescharacteristic
198#1925C2×C1111yescharacteristic
199#1920C2×C1111yescharacteristic, complemented
200#1918C2×C1111yescharacteristic, complemented
201#1916C2×C1111yescharacteristic, complemented
202C4×#106C2×C1111yescharacteristic, complemented
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11C22×D411yescharacteristic
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—41no—
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—22no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
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—21no—
233C2×C4×C11—21no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11#13512yes—
253C2×C4×C11AGL(1,ℤ/8)12yes—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C8×C11—22no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11—41no—
264C2×#126—21no—
265C2×#125C22×C1111yescharacteristic
266C2×#107C22×C1111yescharacteristic
267C2×#106C22×C1111yescharacteristic
268C2×#106C22×C1111yescharacteristic
269C2×#106C22×C1111yescharacteristic
270C2×C4⋊C8C22×C1111yescharacteristic
271C2×#102C22×C1111yescharacteristic
272C2×#102C22×C1111yescharacteristic
273C2×#102C22×C1111yescharacteristic
274C2×#102C22×C1111yescharacteristic
275C2×C4×C8C22×C1111yescharacteristic
276#397—21no—
277#396—21no—
278#390C22×C1111yescharacteristic
279#390C22×C1111yescharacteristic
280#390C22×C1111yescharacteristic
281#389—21no—
282#389C22×C1111yescharacteristic
283#389C22×C1111yescharacteristic
284#389C22×C1111yescharacteristic
285#388—21no—
286#387—21no—
287#387—21no—
288#384C22×C1111yescharacteristic
289C4×C4⋊C4—21no—
290C4×C4⋊C4C22×C1111yescharacteristic
291C4×C4⋊C4C22×C1111yescharacteristic
292C4×C4⋊C4C22×C1111yescharacteristic
293C4×C4⋊C4C22×C1111yescharacteristic
294C4×C4⋊C4C22×C1111yescharacteristic
295#340C22×C1111yescharacteristic
296#340C22×C1111yescharacteristic
297#340C22×C1111yescharacteristic
298#340C22×C1111yescharacteristic
299#340C22×C1111yescharacteristic
300#340C22×C1111yescharacteristic
301#340C22×C1111yescharacteristic
302#340C22×C1111yescharacteristic
303#336C22×C1111yescharacteristic
304#336C22×C1111yescharacteristic
305#336C22×C1111yescharacteristic
306#336C22×C1111yescharacteristic
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11#52511yescharacteristic
315C22×C11#54711yescharacteristic
316C22×C11#54811yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C11#57711yescharacteristic
320C22×C11#57711yescharacteristic
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—42no—
326C4×C11—41no—
327C4×C11—42no—
328C4×C11—41no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11#52911yescharacteristic
335C4×C11#54111yescharacteristic
336C4×C11#55611yescharacteristic
337C4×C11#55611yescharacteristic
338C22×D4C23×C1111yescharacteristic
339C22×C8C23×C1111yescharacteristic
340C22×C8C23×C1111yescharacteristic
341C22×C8C23×C1111yescharacteristic
342C22×C8C23×C1111yescharacteristic
343#126—44no—
344#125—22no—
345#125—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4D4×C1111yescharacteristic
354C2×C4⋊C4D4×C1111yescharacteristic
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C4⋊C4C23×C1111yescharacteristic
358C2×C4⋊C4C23×C1111yescharacteristic
359C2×C4⋊C4C23×C1111yescharacteristic
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42C23×C1111yescharacteristic
373C2×C42C23×C1111yescharacteristic
374C2×C42C23×C1111yescharacteristic
375#107—22no—
376#106—22no—
377#106—22no—
378#106—22no—
379C4⋊C8—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384C4×C8—22no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95D4×C1111yescharacteristic
393#95D4×C1111yescharacteristic
394C2×C11—161no—
395C2×C11#246911yescharacteristic
396C2×C11#310611yescharacteristic
397C2×C11#312511yescharacteristic
398C2×C11#333711yescharacteristic
399C2×C11#334511yescharacteristic
400C2×C11#336011yescharacteristic
401C2×C11#336811yescharacteristic
402C24—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C24×C1111yescharacteristic
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8C11×#4112yes—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C4⋊C4—81no—
454C4⋊C4—81no—
455C4⋊C4C11×#4112yes—
456C4⋊C4C11×#4112yes—
457C4⋊C4C11×#4112yes—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C22⋊C4—42no—
461C22⋊C4—42no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—42no—
471C42—42no—
472C42—81no—
473C42—81no—
474C11#2713911yescharacteristic, direct product factor, Sylow
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23C22×D4×C1111yescharacteristic
483D4—41no—
484D4—41no—
485D4—41no—
486D4—41no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4C11×#13512yes—
525C2×C4C11×AGL(1,ℤ/8)12yes—
526C2×C4C2×C11×#4111yescharacteristic
527C2×C4C2×C11×#4111yescharacteristic
528C2×C4C2×C11×#4111yescharacteristic
529C2×C4C2×C11×#4111yescharacteristic
530C2×C4C11×2−1+411yescharacteristic
531C2×C4C11×2−1+411yescharacteristic
532C8—22no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C11×#52511yescharacteristic
544C22C11×#54711yescharacteristic
545C22C11×#54811yescharacteristic
546C22C2×C11×#13511yescharacteristic
547C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
548C22C11×#57711yescharacteristic
549C22C11×#57711yescharacteristic
550C4—22no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—42no—
557C4—41no—
558C4—42no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4C11×#52911yescharacteristic
564C4C11×#54111yescharacteristic
565C4C11×#55611yescharacteristic
566C4C11×#55611yescharacteristic
567C2—161no—
568C2C11×#246911yescharacteristic
569C2C11×#310611yescharacteristic
570C2C11×#312511yescharacteristic
571C2C11×#333711yescharacteristic
572C2C11×#334511yescharacteristic
573C2C11×#336011yescharacteristic
574C2C11×#336811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2370C2semidirect
3. C11×#2100C2semidirect
5. C11×#2059C2semidirect
7. C11×#1948C2semidirect
12. C11×#1920C2semidirect
13. C11×#1918C2semidirect
14. C11×#1916C2semidirect
15. C4×C11×#106C2semidirect
115. #27139C11direct (N × H)
189. #2370C2×C11semidirect
190. #2100C2×C11semidirect
192. #2059C2×C11semidirect
194. #1948C2×C11semidirect
199. #1920C2×C11semidirect
200. #1918C2×C11semidirect
201. #1916C2×C11semidirect
202. C4×#106C2×C11semidirect
474. C11#27139direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25122
C11×#23702
C11×#21002
C11×#20652
C11×#20592
C11×#20252
C11×#19482
C11×#19342
C11×#19262
C11×#19252
C11×#19202
C11×#19182
C11×#19162
C4×C11×#1062
#2713911