Finite Group Databasebeta

← C11×#24823 #14602016

Subgroups — C11×#24823 #14602016

Order 2816.

928 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#478C211yesmaximal, characteristic, complemented
2C2×C11×#442C211yesmaximal, characteristic
3C11×#2566C211yesmaximal, characteristic, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2085C211yesmaximal, characteristic, complemented
6C11×#2084C211yesmaximal, characteristic, complemented
7C11×#2067C211yesmaximal, characteristic, complemented
8C11×#2065C211yesmaximal, characteristic, complemented
9C11×#1992C211yesmaximal, characteristic, complemented
10C11×#1940C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic
12C11×#1879C211yesmaximal, characteristic
13C11×#1804C211yesmaximal, characteristic, complemented
14C11×#1802C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4—21no—
23C11×#478—24no—
24C11×#442—24no—
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#97C2211yescharacteristic
38C11×#396—21no—
39C11×#396—21no—
40C11×#390C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#385—21no—
45C11×#385—21no—
46C11×#385—21no—
47C11×#385—21no—
48C11×#384C2211yescharacteristic
49C11×#384C2211yescharacteristic
50C11×#382C2211yescharacteristic
51C11×#380—21no—
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C2×C11×D8—22no—
68C2×C11×D8—22no—
69C2×C11×D8Q814yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#125—22no—
75C11×#125—22no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C4×D4×C11D414yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
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—44no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
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×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C11×#107—22no—
113C11×#106—22no—
114C11×#106—22no—
115C11×C4⋊C8—22no—
116C11×C4⋊C8—41no—
117C11×C4⋊C8—41no—
118C11×#102—22no—
119C11×#102—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—41no—
123C11×#102—41no—
124C11×#97—22no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95D411yescharacteristic
130C11×#95D411yescharacteristic
131#24823C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×Q812yes—
144C2×D4×C11C2×Q812yes—
145C2×D4×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—81no—
161C22×C4×C11—81no—
162C22×C4×C11—81no—
163C22×C4×C11—81no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C11×D8—28no—
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—
182C2×C8×C11—21no—
183C2×C8×C11C2×Q812yes—
184C11×C4⋊C4—22no—
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—41no—
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—81no—
204C11×C4⋊C4—81no—
205C11×C4⋊C4C2×D412yes—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—81no—
213C11×C22⋊C4—81no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11C2×D412yes—
219C42×C11#4112yes—
220C2×#478C2×C1111yescharacteristic, complemented
221C2×#442C2×C1111yescharacteristic
222#2566C2×C1111yescharacteristic, complemented
223D4×C4⋊C4C2×C1111yescharacteristic, complemented
224#2085C2×C1111yescharacteristic, complemented
225#2084C2×C1111yescharacteristic, complemented
226#2067C2×C1111yescharacteristic, complemented
227#2065C2×C1111yescharacteristic, complemented
228#1992C2×C1111yescharacteristic, complemented
229#1940C2×C1111yescharacteristic, complemented
230#1879C2×C1111yescharacteristic
231#1879C2×C1111yescharacteristic
232#1804C2×C1111yescharacteristic, complemented
233#1802C2×C1111yescharacteristic, complemented
234#1802C2×C1111yescharacteristic, complemented
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11C22×D411yescharacteristic
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11C22⋊Q814yes—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—48no—
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—84no—
293C2×C4×C11—84no—
294C2×C4×C11—84no—
295C2×C4×C11#12112yes—
296C2×C4×C11#12112yes—
297C2×C4×C11AGL(1,ℤ/8)12yes—
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×Q811yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C112−1+411yescharacteristic
304C8×C11—22no—
305C8×C11—41no—
306C8×C11—41no—
307C8×C11—41no—
308C22×D8C22×C1111yescharacteristic
309C2×#125C22×C1111yescharacteristic
310C2×C4×D4C22×C1111yescharacteristic
311C2×C4×D4C22×C1111yescharacteristic
312C2×C4×D4C22×C1111yescharacteristic
313C2×C4×D4C22×C1111yescharacteristic
314C22×C4⋊C4—21no—
315#478—24no—
316#442—24no—
317C2×#107C22×C1111yescharacteristic
318C2×#106C22×C1111yescharacteristic
319C2×#106C22×C1111yescharacteristic
320C2×C4⋊C8C22×C1111yescharacteristic
321C2×C4⋊C8C22×C1111yescharacteristic
322C2×C4⋊C8C22×C1111yescharacteristic
323C2×#102C22×C1111yescharacteristic
324C2×#102C22×C1111yescharacteristic
325C2×#102C22×C1111yescharacteristic
326C2×#102C22×C1111yescharacteristic
327C2×#102C22×C1111yescharacteristic
328C2×#102C22×C1111yescharacteristic
329C2×#97C22×C1111yescharacteristic
330#396—21no—
331#396—21no—
332#390C22×C1111yescharacteristic
333#390C22×C1111yescharacteristic
334#389C22×C1111yescharacteristic
335#389C22×C1111yescharacteristic
336#385—21no—
337#385—21no—
338#385—21no—
339#385—21no—
340#384C22×C1111yescharacteristic
341#384C22×C1111yescharacteristic
342#382C22×C1111yescharacteristic
343#380—21no—
344C4×C4⋊C4C22×C1111yescharacteristic
345#340C22×C1111yescharacteristic
346#340C22×C1111yescharacteristic
347#340C22×C1111yescharacteristic
348#340C22×C1111yescharacteristic
349#340C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351#336C22×C1111yescharacteristic
352#336C22×C1111yescharacteristic
353C22×C11—24no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11C2×#12111yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11D4×Q811yescharacteristic
370C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57611yescharacteristic
373C22×C11#57711yescharacteristic
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C2×C22⋊Q811yescharacteristic
387C4×C11#53711yescharacteristic
388C4×C11#55211yescharacteristic
389C4×C11#55411yescharacteristic
390C22×D4C23×C1111yescharacteristic
391C22×D4C23×C1111yescharacteristic
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—21no—
396C2×D8—22no—
397C2×D8—22no—
398C2×D8Q8×C1114yes—
399C22×C8C23×C1111yescharacteristic
400C22×C8C23×C1111yescharacteristic
401C22×C8C23×C1111yescharacteristic
402C22×C8C23×C1111yescharacteristic
403#125—22no—
404#125—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—41no—
411C4×D4—41no—
412C4×D4D4×C1114yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4D4×C1111yescharacteristic
423C2×C4⋊C4D4×C1111yescharacteristic
424C2×C4⋊C4C23×C1111yescharacteristic
425C2×C4⋊C4C23×C1111yescharacteristic
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C4⋊C4C23×C1111yescharacteristic
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C42C23×C1111yescharacteristic
439C2×C42C23×C1111yescharacteristic
440C2×C42C23×C1111yescharacteristic
441#107—22no—
442#106—22no—
443#106—22no—
444C4⋊C8—22no—
445C4⋊C8—41no—
446C4⋊C8—41no—
447#102—22no—
448#102—22no—
449#102—22no—
450#102—22no—
451#102—41no—
452#102—41no—
453#97—22no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95D4×C1111yescharacteristic
459#95D4×C1111yescharacteristic
460C2×C11—44no—
461C2×C11—82no—
462C2×C11#241711yescharacteristic
463C2×C11#303611yescharacteristic
464C2×C11#304511yescharacteristic
465C2×C11#330711yescharacteristic
466C2×C11#331811yescharacteristic
467C2×C11#338411yescharacteristic
468C2×C11#338911yescharacteristic
469C24—21no—
470C24—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4C2×D4×C1112yes—
480C2×D4C2×Q8×C1112yes—
481C2×D4C2×Q8×C1112yes—
482C2×D4C11×#4112yes—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4C2×D4×C1111yescharacteristic
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C2×D4×C1111yescharacteristic
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C24×C1111yescharacteristic
508D8—28no—
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—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C2×Q8×C1112yes—
521C4⋊C4—22no—
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—21no—
533C4⋊C4—41no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—81no—
540C4⋊C4—81no—
541C4⋊C4—81no—
542C4⋊C4C2×D4×C1112yes—
543C22⋊C4—24no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42C2×D4×C1112yes—
556C42C11×#4112yes—
557C11#2482311yescharacteristic, direct product factor, Sylow
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×D4×C1111yescharacteristic
573D4—22no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—41no—
579D4—41no—
580D4C11×C22⋊Q814yes—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—48no—
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×C4—84no—
618C2×C4C11×#12112yes—
619C2×C4C11×#12112yes—
620C2×C4C11×AGL(1,ℤ/8)12yes—
621C2×C4C22×D4×C1111yescharacteristic
622C2×C4C22×Q8×C1111yescharacteristic
623C2×C4C2×C11×#4111yescharacteristic
624C2×C4C2×C11×#4111yescharacteristic
625C2×C4C11×H(5,𝔽2)11yescharacteristic
626C2×C4C11×2−1+411yescharacteristic
627C8—22no—
628C8—41no—
629C8—41no—
630C8—41no—
631C22—24no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22C2×C11×#12111yescharacteristic
646C22C11×#54611yescharacteristic
647C22D4×Q8×C1111yescharacteristic
648C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
649C22C11×#57511yescharacteristic
650C22C11×#57611yescharacteristic
651C22C11×#57711yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—42no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4C2×C11×C22⋊Q811yescharacteristic
665C4C11×#53711yescharacteristic
666C4C11×#55211yescharacteristic
667C4C11×#55411yescharacteristic
668C2—44no—
669C2—82no—
670C2C11×#241711yescharacteristic
671C2C11×#303611yescharacteristic
672C2C11×#304511yescharacteristic
673C2C11×#330711yescharacteristic
674C2C11×#331811yescharacteristic
675C2C11×#338411yescharacteristic
676C2C11×#338911yescharacteristic
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
1. C2×C11×#478C2semidirect
3. C11×#2566C2semidirect
4. D4×C11×C4⋊C4C2semidirect
5. C11×#2085C2semidirect
6. C11×#2084C2semidirect
7. C11×#2067C2semidirect
8. C11×#2065C2semidirect
9. C11×#1992C2semidirect
10. C11×#1940C2semidirect
13. C11×#1804C2semidirect
14. C11×#1802C2semidirect
15. C11×#1802C2semidirect
131. #24823C11direct (N × H)
220. C2×#478C2×C11semidirect
222. #2566C2×C11semidirect
223. D4×C4⋊C4C2×C11semidirect
224. #2085C2×C11semidirect
225. #2084C2×C11semidirect
226. #2067C2×C11semidirect
227. #2065C2×C11semidirect
228. #1992C2×C11semidirect
229. #1940C2×C11semidirect
232. #1804C2×C11semidirect
233. #1802C2×C11semidirect
234. #1802C2×C11semidirect
557. C11#24823direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4782
C2×C11×#4422
C11×#25662
D4×C11×C4⋊C42
C11×#20852
C11×#20842
C11×#20672
C11×#20652
C11×#19922
C11×#19402
C11×#18792
C11×#18042
C11×#18022
#2482311