Finite Group Databasebeta

← C11×#24979 #14602172

Subgroups — C11×#24979 #14602172

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2536C211yesmaximal, characteristic
2D4×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#2077C211yesmaximal, characteristic, complemented
4C11×#2075C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2035C211yesmaximal, characteristic, complemented
7C11×#1955C211yesmaximal, characteristic
8C11×#1949C211yesmaximal, characteristic, complemented
9C11×#1872C211yesmaximal, characteristic, complemented
10C11×#1872C211yesmaximal, characteristic, complemented
11C11×#1836C211yesmaximal, characteristic, complemented
12C11×#1824C211yesmaximal, characteristic, complemented
13C11×#1823C211yesmaximal, characteristic, complemented
14C11×#1803C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C11×#398—21no—
36C11×#394—21no—
37C11×#389—21no—
38C11×#388—21no—
39C11×#388—21no—
40C11×#385—21no—
41C11×#385—21no—
42C11×#384C2211yescharacteristic
43C11×#382C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C11×#380C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11D411yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—41no—
72C11×C22⋊Q8—41no—
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—44no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—41no—
88C2×C11×C4⋊C4—41no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#107—41no—
109C11×#106—41no—
110C11×C4⋊C8—22no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#103—41no—
114C11×#103—41no—
115C11×C22⋊C8—41no—
116C11×C22⋊C8—41no—
117C11×C22⋊C8—41no—
118C11×C22⋊C8—41no—
119C11×#97—22no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127#24979C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11C2×D411yescharacteristic
129C24×C11C2×D411yescharacteristic
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11#4112yes—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
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—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—81no—
164C22×C4×C11—81no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—81no—
203C11×C4⋊C4#4112yes—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C42×C11—42no—
213C42×C11—42no—
214C42×C11#4112yes—
215C42×C11#4112yes—
216#2536C2×C1111yescharacteristic
217D4×C4⋊C4C2×C1111yescharacteristic
218#2077C2×C1111yescharacteristic, complemented
219#2075C2×C1111yescharacteristic, complemented
220#2036C2×C1111yescharacteristic, complemented
221#2035C2×C1111yescharacteristic, complemented
222#1955C2×C1111yescharacteristic
223#1949C2×C1111yescharacteristic, complemented
224#1872C2×C1111yescharacteristic, complemented
225#1872C2×C1111yescharacteristic, complemented
226#1836C2×C1111yescharacteristic, complemented
227#1824C2×C1111yescharacteristic, complemented
228#1823C2×C1111yescharacteristic, complemented
229#1803C2×C1111yescharacteristic, complemented
230#1763C2×C1111yescharacteristic, complemented
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11AGL(1,ℤ/8)12yes—
244C23×C11#13712yes—
245C23×C11C22×D411yescharacteristic
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—41no—
249Q8×C11—41no—
250D4×C11—28no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
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—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—84no—
294C2×C4×C11—84no—
295C2×C4×C11#12312yes—
296C2×C4×C11#12312yes—
297C2×C4×C11C2×#4111yescharacteristic
298C2×C4×C11C2×#4111yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C8×C11—41no—
304C8×C11—41no—
305C8×C11—41no—
306C8×C11—41no—
307C2×C22⋊Q8C22×C1111yescharacteristic
308C2×C22⋊Q8C22×C1111yescharacteristic
309C2×C4×Q8C22×C1111yescharacteristic
310C2×C4×D4—21no—
311C2×C4×D4C22×C1111yescharacteristic
312C22×C4⋊C4C22×C1111yescharacteristic
313C22×C4⋊C4C22×C1111yescharacteristic
314C2×#107C22×C1111yescharacteristic
315C2×#106C22×C1111yescharacteristic
316C2×C4⋊C8C22×C1111yescharacteristic
317C2×#103C22×C1111yescharacteristic
318C2×#103C22×C1111yescharacteristic
319C2×#103C22×C1111yescharacteristic
320C2×#103C22×C1111yescharacteristic
321C2×C22⋊C8C22×C1111yescharacteristic
322C2×C22⋊C8C22×C1111yescharacteristic
323C2×C22⋊C8C22×C1111yescharacteristic
324C2×C22⋊C8C22×C1111yescharacteristic
325C2×#97C22×C1111yescharacteristic
326#398—21no—
327#394—21no—
328#389—21no—
329#388—21no—
330#388—21no—
331#385—21no—
332#385—21no—
333#384C22×C1111yescharacteristic
334#382C22×C1111yescharacteristic
335#380C22×C1111yescharacteristic
336#380C22×C1111yescharacteristic
337#380C22×C1111yescharacteristic
338#380C22×C1111yescharacteristic
339C4×C4⋊C4C22×C1111yescharacteristic
340#340C22×C1111yescharacteristic
341#340C22×C1111yescharacteristic
342#340C22×C1111yescharacteristic
343#340C22×C1111yescharacteristic
344#340C22×C1111yescharacteristic
345#340C22×C1111yescharacteristic
346#340C22×C1111yescharacteristic
347#340C22×C1111yescharacteristic
348#340C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11C2×#12311yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C11C2×#13711yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11#52911yescharacteristic
384C4×C11#54011yescharacteristic
385C4×C11#55311yescharacteristic
386C4×C11#55511yescharacteristic
387C22×Q8C23×C1111yescharacteristic
388C22×D4D4×C1111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4C23×C1111yescharacteristic
392C23×C4C23×C1111yescharacteristic
393C22×C8C23×C1111yescharacteristic
394C22×C8C23×C1111yescharacteristic
395C22×C8C23×C1111yescharacteristic
396C22×C8C23×C1111yescharacteristic
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—41no—
400C22⋊Q8—41no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—44no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4D4×C1111yescharacteristic
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C4⋊C4C23×C1111yescharacteristic
422C2×C4⋊C4C23×C1111yescharacteristic
423C2×C4⋊C4C23×C1111yescharacteristic
424C2×C4⋊C4C23×C1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4D4×C1111yescharacteristic
432C2×C22⋊C4D4×C1111yescharacteristic
433C2×C42—21no—
434C2×C42—21no—
435C2×C42C23×C1111yescharacteristic
436#107—41no—
437#106—41no—
438C4⋊C8—22no—
439#103—22no—
440#103—22no—
441#103—41no—
442#103—41no—
443C22⋊C8—41no—
444C22⋊C8—41no—
445C22⋊C8—41no—
446C22⋊C8—41no—
447#97—22no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455C2×C11—42no—
456C2×C11—42no—
457C2×C11#242011yescharacteristic
458C2×C11#309211yescharacteristic
459C2×C11#309711yescharacteristic
460C2×C11#330811yescharacteristic
461C2×C11#331011yescharacteristic
462C2×C11#331211yescharacteristic
463C2×C11#331611yescharacteristic
464C24C2×D4×C1111yescharacteristic
465C24C2×D4×C1111yescharacteristic
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8C11×#4112yes—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4C2×D4×C1111yescharacteristic
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C24×C1111yescharacteristic
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—81no—
539C4⋊C4C11×#4112yes—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C42—42no—
549C42—42no—
550C42C11×#4112yes—
551C42C11×#4112yes—
552C11#2497911yescharacteristic, direct product factor, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23C11×AGL(1,ℤ/8)12yes—
566C23C11×#13712yes—
567C23C22×D4×C1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—84no—
616C2×C4—84no—
617C2×C4C11×#12312yes—
618C2×C4C11×#12312yes—
619C2×C4C2×C11×#4111yescharacteristic
620C2×C4C2×C11×#4111yescharacteristic
621C2×C4C2×C11×#4111yescharacteristic
622C2×C4C2×C11×#4111yescharacteristic
623C2×C4C11×H(5,𝔽2)11yescharacteristic
624C2×C4C11×H(5,𝔽2)11yescharacteristic
625C8—41no—
626C8—41no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22C2×C11×#12311yescharacteristic
644C22C11×#54611yescharacteristic
645C22C11×#54611yescharacteristic
646C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
647C22C2×C11×#13711yescharacteristic
648C22C11×#57711yescharacteristic
649C22C11×#57811yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4C11×#52911yescharacteristic
663C4C11×#54011yescharacteristic
664C4C11×#55311yescharacteristic
665C4C11×#55511yescharacteristic
666C2—42no—
667C2—42no—
668C2C11×#242011yescharacteristic
669C2C11×#309211yescharacteristic
670C2C11×#309711yescharacteristic
671C2C11×#330811yescharacteristic
672C2C11×#331011yescharacteristic
673C2C11×#331211yescharacteristic
674C2C11×#331611yescharacteristic
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×#2077C2semidirect
4. C11×#2075C2semidirect
5. C11×#2036C2semidirect
6. C11×#2035C2semidirect
8. C11×#1949C2semidirect
9. C11×#1872C2semidirect
10. C11×#1872C2semidirect
11. C11×#1836C2semidirect
12. C11×#1824C2semidirect
13. C11×#1823C2semidirect
14. C11×#1803C2semidirect
15. C11×#1763C2semidirect
127. #24979C11direct (N × H)
218. #2077C2×C11semidirect
219. #2075C2×C11semidirect
220. #2036C2×C11semidirect
221. #2035C2×C11semidirect
223. #1949C2×C11semidirect
224. #1872C2×C11semidirect
225. #1872C2×C11semidirect
226. #1836C2×C11semidirect
227. #1824C2×C11semidirect
228. #1823C2×C11semidirect
229. #1803C2×C11semidirect
230. #1763C2×C11semidirect
552. C11#24979direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25362
D4×C11×C4⋊C42
C11×#20772
C11×#20752
C11×#20362
C11×#20352
C11×#19552
C11×#19492
C11×#18722
C11×#18362
C11×#18242
C11×#18232
C11×#18032
C11×#17632
#2497911