Finite Group Databasebeta

← C11×#24257 #14601450

Subgroups — C11×#24257 #14601450

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic, complemented
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C2×C11×#442C211yesmaximal, characteristic, complemented
6C11×#2537C211yesmaximal, characteristic, complemented
7C11×#2035C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C11×#1955C211yesmaximal, characteristic, complemented
13C11×#1802C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic, complemented
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C11×#546—24no—
22C11×#546—24no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C11×#121—21no—
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic, complemented
31C2×C11×#120—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic, complemented
35C22×C11×C22⋊C4—21no—
36C11×#463—24no—
37C11×#449—24no—
38C11×#447—24no—
39C11×#442—24no—
40C2×C11×#106C2211yescharacteristic, complemented
41C2×C11×C4⋊C8C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#103C2211yescharacteristic, complemented
44C2×C11×#103C2211yescharacteristic, complemented
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×C22⋊C8C2211yescharacteristic, complemented
55C2×C11×C22⋊C8C2211yescharacteristic, complemented
56C2×C11×#97C2211yescharacteristic, complemented
57C11×#394—21no—
58C11×#394—21no—
59C11×#384C2211yescharacteristic, complemented
60C11×#380—21no—
61C11×#380C2211yescharacteristic
62C11×#380C2211yescharacteristic, complemented
63C11×#340C2211yescharacteristic, complemented
64C11×#340C2211yescharacteristic, complemented
65C25×C11—21no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—21no—
74C22×D4×C11—21no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—22no—
78C22×D4×C11—22no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—41no—
83C22×D4×C11—41no—
84C22×D4×C11D411yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—41no—
96C2×C11×D8—22no—
97C2×C11×D8—22no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—41no—
101C2×C11×D8D414yescomplemented
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#124—22no—
107C11×#124D414yescomplemented
108C11×#123—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×#121—28no—
112C11×#121—22no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121—22no—
116C11×#121—41no—
117C11×#121—41no—
118C11×#121—44no—
119C11×#120—28no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11D414yescomplemented
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4D411yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C22⋊C4—28no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4D411yescharacteristic
146C2×C11×C22⋊C4D411yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C11×#106—22no—
149C11×C4⋊C8—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—41no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—22no—
159C11×#102—41no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8—41no—
163C11×C22⋊C8—41no—
164C11×#97—22no—
165C11×#95—21no—
166C11×#95—21no—
167#24257C1111yesmaximal, characteristic, direct product factor, Sylow
168C24×C11—21no—
169C24×C11—24no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—42no—
173C24×C11—42no—
174C24×C11—42no—
175C24×C11—42no—
176C24×C11—81no—
177C24×C11—81no—
178C24×C11C2×D411yescharacteristic
179C24×C11C2×D411yescharacteristic
180C11×#41—44no—
181C11×#41—44no—
182C11×#41—44no—
183C11×#41—44no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11C2×D412yes—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—22no—
193C2×D4×C11—24no—
194C2×D4×C11—22no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—41no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—44no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—44no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C2×D4×C11—42no—
220C2×D4×C11—42no—
221C2×D4×C11—81no—
222C2×D4×C11—81no—
223C2×D4×C11—81no—
224C2×D4×C11—81no—
225C2×D4×C11C2×D412yes—
226C2×D4×C11C2×D412yes—
227C2×D4×C11C2×D412yes—
228C2×D4×C11C2×D412yes—
229C2×D4×C11#4112yes—
230C22×C4×C11—24no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—24no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—42no—
250C22×C4×C11—42no—
251C22×C4×C11—42no—
252C22×C4×C11—42no—
253C22×C4×C11—42no—
254C22×C4×C11—81no—
255C22×C4×C11—81no—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C11×SD16—44no—
262C11×D8—28no—
263C11×D8—44no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11C2×D412yes—
276C11×C4⋊C4—24no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—42no—
286C11×C4⋊C4—81no—
287C11×C4⋊C4C2×D412yes—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—42no—
296C11×C22⋊C4—42no—
297C11×C22⋊C4—42no—
298C11×C22⋊C4—42no—
299C11×C22⋊C4—42no—
300C42×C11C2×D412yes—
301C42×C11C2×D412yes—
302C2×#546C2×C1111yescharacteristic, complemented
303C2×#463C2×C1111yescharacteristic, complemented
304C2×#449C2×C1111yescharacteristic, complemented
305C2×#447C2×C1111yescharacteristic, complemented
306C2×#442C2×C1111yescharacteristic, complemented
307#2537C2×C1111yescharacteristic, complemented
308#2035C2×C1111yescharacteristic, complemented
309#2034C2×C1111yescharacteristic, complemented
310#2000C2×C1111yescharacteristic, complemented
311#1999C2×C1111yescharacteristic, complemented
312#1959C2×C1111yescharacteristic, complemented
313#1955C2×C1111yescharacteristic, complemented
314#1802C2×C1111yescharacteristic, complemented
315#1788C2×C1111yescharacteristic, complemented
316#1786C2×C1111yescharacteristic, complemented
317C23×C11—21no—
318C23×C11—22no—
319C23×C11—21no—
320C23×C11—22no—
321C23×C11—21no—
322C23×C11—22no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—22no—
327C23×C11—21no—
328C23×C11—22no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—48no—
336C23×C11—48no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—84no—
354C23×C11—84no—
355C23×C11—84no—
356C23×C11—84no—
357C23×C11—84no—
358C23×C11AGL(1,ℤ/8)12yes—
359C23×C11C22×D411yescharacteristic
360Q8×C11—22no—
361Q8×C11—22no—
362Q8×C11—41no—
363Q8×C11—41no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—22no—
370D4×C11—22no—
371D4×C11—44no—
372D4×C11—48no—
373D4×C11—48no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—41no—
377D4×C11—41no—
378D4×C11—84no—
379D4×C11—84no—
380D4×C11—84no—
381D4×C11#12114yescomplemented
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—22no—
387C2×C4×C11—21no—
388C2×C4×C11—22no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—48no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—84no—
417C2×C4×C11—84no—
418C2×C4×C11#12012yes—
419C2×C4×C11#12012yes—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C2×#4111yescharacteristic
424C2×C4×C11H(5,𝔽2)11yescharacteristic
425C2×C4×C11H(5,𝔽2)11yescharacteristic
426C8×C11—22no—
427C8×C11—41no—
428C8×C11—41no—
429C8×C11—41no—
430C22×#41C22×C1111yescharacteristic
431C23×D4C22×C1111yescharacteristic
432C22×SD16C22×C1111yescharacteristic, complemented
433C22×D8C22×C1111yescharacteristic
434C22×D8C22×C1111yescharacteristic
435#546—24no—
436#546—24no—
437C2×#124C22×C1111yescharacteristic
438C2×#123—21no—
439C2×C22⋊Q8C22×C1111yescharacteristic
440C2×#121—21no—
441C2×#121—21no—
442C2×#121C22×C1111yescharacteristic
443C2×#121C22×C1111yescharacteristic
444C2×#121C22×C1111yescharacteristic, complemented
445C2×#120—21no—
446C2×C4×D4C22×C1111yescharacteristic
447C2×C4×D4C22×C1111yescharacteristic
448C2×C4×D4C22×C1111yescharacteristic, complemented
449C22×C22⋊C4—21no—
450#463—24no—
451#449—24no—
452#447—24no—
453#442—24no—
454C2×#106C22×C1111yescharacteristic, complemented
455C2×C4⋊C8C22×C1111yescharacteristic, complemented
456C2×#103C22×C1111yescharacteristic, complemented
457C2×#103C22×C1111yescharacteristic, complemented
458C2×#103C22×C1111yescharacteristic, complemented
459C2×#102C22×C1111yescharacteristic
460C2×#102C22×C1111yescharacteristic
461C2×#102C22×C1111yescharacteristic
462C2×#102C22×C1111yescharacteristic
463C2×#102C22×C1111yescharacteristic
464C2×#102C22×C1111yescharacteristic
465C2×#102C22×C1111yescharacteristic, complemented
466C2×C22⋊C8C22×C1111yescharacteristic
467C2×C22⋊C8C22×C1111yescharacteristic
468C2×C22⋊C8C22×C1111yescharacteristic, complemented
469C2×C22⋊C8C22×C1111yescharacteristic, complemented
470C2×#97C22×C1111yescharacteristic, complemented
471#394—21no—
472#394—21no—
473#384C22×C1111yescharacteristic, complemented
474#380—21no—
475#380C22×C1111yescharacteristic
476#380C22×C1111yescharacteristic, complemented
477#340C22×C1111yescharacteristic, complemented
478#340C22×C1111yescharacteristic, complemented
479C22×C11—24no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—41no—
490C22×C11—42no—
491C22×C11—41no—
492C22×C11—42no—
493C22×C11—41no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—41no—
497C22×C11—42no—
498C22×C11—41no—
499C22×C11—42no—
500C22×C11—41no—
501C22×C11—42no—
502C22×C11—41no—
503C22×C11—42no—
504C22×C11—41no—
505C22×C11—41no—
506C22×C11—816no—
507C22×C11—81no—
508C22×C11—81no—
509C22×C11—81no—
510C22×C11—81no—
511C22×C11—81no—
512C22×C11—81no—
513C22×C11—81no—
514C22×C11—81no—
515C22×C11C2×#12011yescharacteristic
516C22×C11D4211yescharacteristic
517C22×C11#54611yescharacteristic
518C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
519C22×C11#57511yescharacteristic
520C22×C11#57611yescharacteristic
521C22×C11#57711yescharacteristic
522C4×C11—22no—
523C4×C11—22no—
524C4×C11—41no—
525C4×C11—41no—
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—81no—
529C4×C11—81no—
530C4×C11—81no—
531C4×C11C2×#12111yescharacteristic
532C4×C11#53511yescharacteristic
533C4×C11D4211yescharacteristic
534C4×C11#54611yescharacteristic
535C25—21no—
536C2×#41—22no—
537C2×#41—22no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—41no—
541C2×#41—41no—
542C22×Q8C23×C1111yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4D4×C1111yescharacteristic
555C22×D4C23×C1111yescharacteristic
556C22×D4C23×C1111yescharacteristic
557C22×D4C23×C1111yescharacteristic
558C23×C4—21no—
559C23×C4—21no—
560C23×C4—21no—
561C23×C4C23×C1111yescharacteristic
562C23×C4C23×C1111yescharacteristic
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—41no—
566C2×D8—22no—
567C2×D8—22no—
568C2×D8—22no—
569C2×D8—22no—
570C2×D8—41no—
571C2×D8D4×C1114yescomplemented
572C22×C8C23×C1111yescharacteristic
573C22×C8C23×C1111yescharacteristic
574C22×C8C23×C1111yescharacteristic
575C22×C8C23×C1111yescharacteristic
576#124—22no—
577#124D4×C1114yescomplemented
578#123—28no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581#121—28no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—41no—
587#121—41no—
588#121—44no—
589#120—28no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4D4×C1114yescomplemented
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4D4×C1111yescharacteristic
600C2×C4⋊C4C23×C1111yescharacteristic
601C2×C4⋊C4C23×C1111yescharacteristic
602C2×C4⋊C4C23×C1111yescharacteristic
603C2×C4⋊C4C23×C1111yescharacteristic
604C2×C22⋊C4—28no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4D4×C1111yescharacteristic
616C2×C22⋊C4D4×C1111yescharacteristic
617C2×C42C23×C1111yescharacteristic
618#106—22no—
619C4⋊C8—22no—
620#103—22no—
621#103—22no—
622#103—41no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—22no—
629#102—41no—
630C22⋊C8—22no—
631C22⋊C8—22no—
632C22⋊C8—41no—
633C22⋊C8—41no—
634#97—22no—
635#95—21no—
636#95—21no—
637C2×C11—42no—
638C2×C11—44no—
639C2×C11—81no—
640C2×C11—82no—
641C2×C11—82no—
642C2×C11#240811yescharacteristic
643C2×C11#300611yescharacteristic
644C2×C11#301211yescharacteristic
645C2×C11#326411yescharacteristic
646C2×C11#326711yescharacteristic
647C2×C11#330611yescharacteristic
648C2×C11#331911yescharacteristic
649C24—21no—
650C24—24no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—81no—
658C24—81no—
659C24C2×D4×C1111yescharacteristic
660C24C2×D4×C1111yescharacteristic
661#41—44no—
662#41—44no—
663#41—44no—
664#41—44no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8C2×D4×C1112yes—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—44no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4C2×D4×C1112yes—
707C2×D4C2×D4×C1112yes—
708C2×D4C2×D4×C1112yes—
709C2×D4C2×D4×C1112yes—
710C2×D4C11×#4112yes—
711C22×C4—24no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—24no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C1111yescharacteristic
738C22×C4C2×D4×C1111yescharacteristic
739C22×C4C2×D4×C1111yescharacteristic
740C22×C4C2×D4×C1111yescharacteristic
741C22×C4C24×C1111yescharacteristic
742SD16—44no—
743D8—28no—
744D8—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8C2×D4×C1112yes—
757C4⋊C4—24no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—42no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C1112yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—22no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C42C2×D4×C1112yes—
782C42C2×D4×C1112yes—
783C11#2425711yescharacteristic, direct product factor, Sylow
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23C11×AGL(1,ℤ/8)12yes—
826C23C22×D4×C1111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4C11×#12114yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4C11×#12012yes—
886C2×C4C11×#12012yes—
887C2×C4C22×D4×C1111yescharacteristic
888C2×C4C22×D4×C1111yescharacteristic
889C2×C4C22×D4×C1111yescharacteristic
890C2×C4C2×C11×#4111yescharacteristic
891C2×C4C11×H(5,𝔽2)11yescharacteristic
892C2×C4C11×H(5,𝔽2)11yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×C11×#12011yescharacteristic
934C22D42×C1111yescharacteristic
935C22C11×#54611yescharacteristic
936C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
937C22C11×#57511yescharacteristic
938C22C11×#57611yescharacteristic
939C22C11×#57711yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×C11×#12111yescharacteristic
950C4C11×#53511yescharacteristic
951C4D42×C1111yescharacteristic
952C4C11×#54611yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C11×#240811yescharacteristic
959C2C11×#300611yescharacteristic
960C2C11×#301211yescharacteristic
961C2C11×#326411yescharacteristic
962C2C11×#326711yescharacteristic
963C2C11×#330611yescharacteristic
964C2C11×#331911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#546C2semidirect
2. C2×C11×#463C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#447C2semidirect
5. C2×C11×#442C2semidirect
6. C11×#2537C2semidirect
7. C11×#2035C2semidirect
8. C11×#2034C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1959C2semidirect
12. C11×#1955C2semidirect
13. C11×#1802C2semidirect
14. C11×#1788C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×SD16C22semidirect
30. C2×C11×#121C22semidirect
34. C2×C4×D4×C11C22semidirect
40. C2×C11×#106C22semidirect
41. C2×C11×C4⋊C8C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
44. C2×C11×#103C22semidirect
51. C2×C11×#102C22semidirect
54. C2×C11×C22⋊C8C22semidirect
55. C2×C11×C22⋊C8C22semidirect
56. C2×C11×#97C22semidirect
59. C11×#384C22semidirect
62. C11×#380C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
101. C2×C11×D8D4semidirect
107. C11×#124D4semidirect
125. C4×D4×C11D4semidirect
167. #24257C11direct (N × H)
302. C2×#546C2×C11semidirect
303. C2×#463C2×C11semidirect
304. C2×#449C2×C11semidirect
305. C2×#447C2×C11semidirect
306. C2×#442C2×C11semidirect
307. #2537C2×C11semidirect
308. #2035C2×C11semidirect
309. #2034C2×C11semidirect
310. #2000C2×C11semidirect
311. #1999C2×C11semidirect
312. #1959C2×C11semidirect
313. #1955C2×C11semidirect
314. #1802C2×C11semidirect
315. #1788C2×C11semidirect
316. #1786C2×C11semidirect
381. D4×C11#121semidirect
432. C22×SD16C22×C11semidirect
444. C2×#121C22×C11semidirect
448. C2×C4×D4C22×C11semidirect
454. C2×#106C22×C11semidirect
455. C2×C4⋊C8C22×C11semidirect
456. C2×#103C22×C11semidirect
457. C2×#103C22×C11semidirect
458. C2×#103C22×C11semidirect
465. C2×#102C22×C11semidirect
468. C2×C22⋊C8C22×C11semidirect
469. C2×C22⋊C8C22×C11semidirect
470. C2×#97C22×C11semidirect
473. #384C22×C11semidirect
476. #380C22×C11semidirect
477. #340C22×C11semidirect
478. #340C22×C11semidirect
571. C2×D8D4×C11semidirect
577. #124D4×C11semidirect
595. C4×D4D4×C11semidirect
783. C11#24257direct (N × H)
848. D4C11×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5462
C2×C11×#4632
C2×C11×#4492
C2×C11×#4472
C2×C11×#4422
C11×#25372
C11×#20352
C11×#20342
C11×#20002
C11×#19992
C11×#19592
C11×#19552
C11×#18022
C11×#17882
C11×#17862
#2425711