Finite Group Databasebeta

← C11×#26172 #14603365

Subgroups — C11×#26172 #14603365

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C11×#2448C211yesmaximal, characteristic, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2094C211yesmaximal, characteristic, complemented
6C11×#2088C211yesmaximal, characteristic, complemented
7C11×#2072C211yesmaximal, characteristic, complemented
8C11×#2042C211yesmaximal, characteristic, complemented
9C11×#1934C211yesmaximal, characteristic, complemented
10C11×#1916C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic
12C11×#1879C211yesmaximal, characteristic
13C11×#1877C211yesmaximal, characteristic, complemented
14C11×#1865C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4—21no—
24C11×#463—24no—
25C4×C11×SD16—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#399—21no—
39C11×#397—21no—
40C11×#391C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#388—21no—
47C11×#388—21no—
48C11×#385—21no—
49C11×#385—21no—
50C11×#384C2211yescharacteristic
51C11×#380—21no—
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16D414yes—
70C2×C11×D8—22no—
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#124—22no—
78C11×#124—41no—
79C4×Q8×C11—22no—
80C4×Q8×C11—41no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—41no—
86C4×D4×C11—41no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—44no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#106—22no—
115C11×#106—41no—
116C11×C4⋊C8—22no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—41no—
125C4×C8×C11—22no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95D411yescharacteristic
132C11×#95D411yescharacteristic
133#26172C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11—21no—
135C24×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11C2×D412yes—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C2×D412yes—
152C2×D4×C11#4112yes—
153C2×D4×C11#4112yes—
154C22×C4×C11—24no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C11×SD16—28no—
177C11×D8—44no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11C2×D412yes—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—42no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4—81no—
207C11×C4⋊C4#4112yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—81no—
216C11×C22⋊C4—81no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—42no—
224C2×#463C2×C1111yescharacteristic
225C2×C4×SD16C2×C1111yescharacteristic, complemented
226#2448C2×C1111yescharacteristic, complemented
227D4×C4⋊C4C2×C1111yescharacteristic, complemented
228#2094C2×C1111yescharacteristic, complemented
229#2088C2×C1111yescharacteristic, complemented
230#2072C2×C1111yescharacteristic, complemented
231#2042C2×C1111yescharacteristic, complemented
232#1934C2×C1111yescharacteristic, complemented
233#1916C2×C1111yescharacteristic, complemented
234#1879C2×C1111yescharacteristic
235#1879C2×C1111yescharacteristic
236#1877C2×C1111yescharacteristic, complemented
237#1865C2×C1111yescharacteristic, complemented
238#1864C2×C1111yescharacteristic, complemented
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11#12314yes—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—48no—
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—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—84no—
302C2×C4×C11—84no—
303C2×C4×C11#13512yes—
304C2×C4×C11AGL(1,ℤ/8)12yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C8×C11—22no—
312C8×C11—41no—
313C8×C11—41no—
314C8×C11—41no—
315C22×SD16C22×C1111yescharacteristic
316C22×D8C22×C1111yescharacteristic
317C2×#124C22×C1111yescharacteristic
318C2×C4×Q8C22×C1111yescharacteristic
319C2×C4×D4C22×C1111yescharacteristic
320C2×C4×D4C22×C1111yescharacteristic
321C2×C4×D4C22×C1111yescharacteristic
322C22×C4⋊C4—21no—
323#463—24no—
324C4×SD16—24no—
325C2×#106C22×C1111yescharacteristic
326C2×#106C22×C1111yescharacteristic
327C2×C4⋊C8C22×C1111yescharacteristic
328C2×#103C22×C1111yescharacteristic
329C2×#103C22×C1111yescharacteristic
330C2×#103C22×C1111yescharacteristic
331C2×#102C22×C1111yescharacteristic
332C2×#102C22×C1111yescharacteristic
333C2×#102C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×C4×C8C22×C1111yescharacteristic
337#399—21no—
338#397—21no—
339#391C22×C1111yescharacteristic
340#390C22×C1111yescharacteristic
341#390C22×C1111yescharacteristic
342#389C22×C1111yescharacteristic
343#389C22×C1111yescharacteristic
344#389C22×C1111yescharacteristic
345#388—21no—
346#388—21no—
347#385—21no—
348#385—21no—
349#384C22×C1111yescharacteristic
350#380—21no—
351C4×C4⋊C4C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#336C22×C1111yescharacteristic
357#336C22×C1111yescharacteristic
358#336C22×C1111yescharacteristic
359#336C22×C1111yescharacteristic
360C22×C11—24no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11#52511yescharacteristic
375C22×C11D4211yescharacteristic
376C22×C11#54811yescharacteristic
377C22×C11C2×#13511yescharacteristic
378C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C11#57711yescharacteristic
380C22×C11#57711yescharacteristic
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11C2×#12311yescharacteristic
394C4×C11#53911yescharacteristic
395C4×C11#54711yescharacteristic
396C4×C11#55311yescharacteristic
397C22×Q8C23×C1111yescharacteristic
398C22×D4C23×C1111yescharacteristic
399C22×D4C23×C1111yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4—21no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16D4×C1114yes—
406C2×D8—22no—
407C2×D8—22no—
408C2×D8—22no—
409C22×C8C23×C1111yescharacteristic
410C22×C8C23×C1111yescharacteristic
411C22×C8C23×C1111yescharacteristic
412C22×C8C23×C1111yescharacteristic
413#124—22no—
414#124—41no—
415C4×Q8—22no—
416C4×Q8—41no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—41no—
422C4×D4—41no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—44no—
430C2×C4⋊C4D4×C1111yescharacteristic
431C2×C4⋊C4D4×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42—21no—
447C2×C42C23×C1111yescharacteristic
448C2×C42C23×C1111yescharacteristic
449C2×C42C23×C1111yescharacteristic
450#106—22no—
451#106—41no—
452C4⋊C8—22no—
453#103—22no—
454#103—22no—
455#103—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—41no—
461C4×C8—22no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95D4×C1111yescharacteristic
468#95D4×C1111yescharacteristic
469C2×C11—44no—
470C2×C11—161no—
471C2×C11#244311yescharacteristic
472C2×C11#310511yescharacteristic
473C2×C11#312511yescharacteristic
474C2×C11#326511yescharacteristic
475C2×C11#328411yescharacteristic
476C2×C11#336011yescharacteristic
477C2×C11#337311yescharacteristic
478C24—21no—
479C24—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C2×D4×C1112yes—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4C2×D4×C1112yes—
496C2×D4C11×#4112yes—
497C2×D4C11×#4112yes—
498C22×C4—24no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C24×C1111yescharacteristic
520SD16—28no—
521D8—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8C2×D4×C1112yes—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4C11×#4112yes—
552C22⋊C4—24no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—42no—
568C11#2617211yescharacteristic, direct product factor, Sylow
569C23—22no—
570C23—22no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C22×D4×C1111yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588D4—22no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4C11×#12314yes—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—48no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4C11×#13512yes—
634C2×C4C11×AGL(1,ℤ/8)12yes—
635C2×C4C22×D4×C1111yescharacteristic
636C2×C4C2×C11×#4111yescharacteristic
637C2×C4C2×C11×#4111yescharacteristic
638C2×C4C2×C11×#4111yescharacteristic
639C2×C4C11×H(5,𝔽2)11yescharacteristic
640C2×C4C11×2−1+411yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8—41no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22C11×#52511yescharacteristic
660C22D42×C1111yescharacteristic
661C22C11×#54811yescharacteristic
662C22C2×C11×#13511yescharacteristic
663C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
664C22C11×#57711yescharacteristic
665C22C11×#57711yescharacteristic
666C4—22no—
667C4—22no—
668C4—42no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—42no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4C2×C11×#12311yescharacteristic
679C4C11×#53911yescharacteristic
680C4C11×#54711yescharacteristic
681C4C11×#55311yescharacteristic
682C2—44no—
683C2—161no—
684C2C11×#244311yescharacteristic
685C2C11×#310511yescharacteristic
686C2C11×#312511yescharacteristic
687C2C11×#326511yescharacteristic
688C2C11×#328411yescharacteristic
689C2C11×#336011yescharacteristic
690C2C11×#337311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
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. C2×C4×C11×SD16C2semidirect
3. C11×#2448C2semidirect
4. D4×C11×C4⋊C4C2semidirect
5. C11×#2094C2semidirect
6. C11×#2088C2semidirect
7. C11×#2072C2semidirect
8. C11×#2042C2semidirect
9. C11×#1934C2semidirect
10. C11×#1916C2semidirect
13. C11×#1877C2semidirect
14. C11×#1865C2semidirect
15. C11×#1864C2semidirect
133. #26172C11direct (N × H)
225. C2×C4×SD16C2×C11semidirect
226. #2448C2×C11semidirect
227. D4×C4⋊C4C2×C11semidirect
228. #2094C2×C11semidirect
229. #2088C2×C11semidirect
230. #2072C2×C11semidirect
231. #2042C2×C11semidirect
232. #1934C2×C11semidirect
233. #1916C2×C11semidirect
236. #1877C2×C11semidirect
237. #1865C2×C11semidirect
238. #1864C2×C11semidirect
568. C11#26172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C4×C11×SD162
C11×#24482
D4×C11×C4⋊C42
C11×#20942
C11×#20882
C11×#20722
C11×#20422
C11×#19342
C11×#19162
C11×#18792
C11×#18772
C11×#18652
C11×#18642
#2617211