Finite Group Databasebeta

← C11×#24448 #14601641

Subgroups — C11×#24448 #14601641

Order 2816.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C11C211yesmaximal, characteristic
2C2×C11×#468C211yesmaximal, characteristic, complemented
3C2×C11×#450C211yesmaximal, characteristic, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C2×C11×#418C211yesmaximal, characteristic, complemented
6C11×#2415C211yesmaximal, characteristic, complemented
7C11×#2041C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2014C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1875C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11—21no—
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic, complemented
21C22×C11×SD16C2211yescharacteristic, complemented
22C22×C11×M16C2211yescharacteristic, complemented
23D42×C11—24no—
24D42×C11—24no—
25C2×C11×#127C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic, complemented
27C2×C11×C22⋊Q8C2211yescharacteristic, complemented
28C2×C11×#121—21no—
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#120—21no—
32C2×C11×#120—21no—
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C2×C11×#117C2211yescharacteristic, complemented
36C11×#468—24no—
37C11×#450—24no—
38C11×#450—24no—
39C2×C11×#107C2211yescharacteristic, complemented
40C11×#418—24no—
41C2×C11×#103C2211yescharacteristic, complemented
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic, complemented
47C2×C11×#102C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×C22⋊C8C2211yescharacteristic, complemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C11×#397—21no—
55C11×#394—21no—
56C11×#391C2211yescharacteristic, complemented
57C11×#389—21no—
58C11×#389C2211yescharacteristic, complemented
59C11×#388—21no—
60C11×#380C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#336C2211yescharacteristic, complemented
64C11×#336C2211yescharacteristic, complemented
65C25×C11—21no—
66C25×C11—21no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—22no—
69C22×D4×C11—22no—
70C22×D4×C11—28no—
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—22no—
81C22×D4×C11—21no—
82C22×D4×C11—41no—
83C22×D4×C11—41no—
84C22×D4×C11—41no—
85C22×D4×C11—41no—
86C22×D4×C11—44no—
87C22×D4×C11—44no—
88C22×D4×C11D411yescharacteristic
89C22×D4×C11D414yes—
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11—21no—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—22no—
100C2×C11×SD16—22no—
101C2×C11×SD16—22no—
102C2×C11×SD16—41no—
103C2×C11×SD16—41no—
104C2×C11×SD16—41no—
105C2×C11×M16—22no—
106C2×C11×M16—22no—
107C2×C11×M16—41no—
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#127—22no—
113C11×#127—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—41no—
118C11×#121—28no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121D414yes—
123C11×#120—28no—
124C11×#120—28no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C11×#117—22no—
130C11×#117—41no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4D411yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
146C2×C11×C22⋊C4D411yescharacteristic
147C2×C11×C22⋊C4D411yescharacteristic
148C2×C42×C11—21no—
149C2×C42×C11C2311yescharacteristic
150C11×#107—22no—
151C11×#103—22no—
152C11×#102—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—22no—
159C11×#102—41no—
160C11×#102D414yescomplemented
161C11×C22⋊C8—22no—
162C11×C22⋊C8—22no—
163C11×C22⋊C8—41no—
164C11×#95—21no—
165C11×#95—21no—
166C11×#95—21no—
167C11×#95—21no—
168#24448C1111yesmaximal, characteristic, direct product factor, Sylow
169C24×C11—21no—
170C24×C11—24no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—24no—
174C24×C11—42no—
175C24×C11—42no—
176C24×C11—42no—
177C24×C11—42no—
178C24×C11—42no—
179C24×C11—42no—
180C24×C11—42no—
181C24×C11—42no—
182C24×C11—81no—
183C24×C11—81no—
184C24×C11—81no—
185C24×C11—81no—
186C24×C11C2×D411yescharacteristic
187C24×C11C2×D411yescharacteristic
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—28no—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—24no—
202C2×D4×C11—24no—
203C2×D4×C11—22no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11—44no—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—42no—
221C2×D4×C11—42no—
222C2×D4×C11—42no—
223C2×D4×C11—42no—
224C2×D4×C11—42no—
225C2×D4×C11—44no—
226C2×D4×C11—44no—
227C2×D4×C11—432no—
228C2×D4×C11—44no—
229C2×D4×C11—42no—
230C2×D4×C11—42no—
231C2×D4×C11—42no—
232C2×D4×C11—42no—
233C2×D4×C11—44no—
234C2×D4×C11—42no—
235C2×D4×C11—81no—
236C2×D4×C11—81no—
237C2×D4×C11C2×D412yes—
238C2×D4×C11C2×D412yes—
239C2×D4×C11C2×D412yes—
240C2×D4×C11C2×D412yes—
241C2×D4×C11#4112yes—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—24no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—42no—
259C22×C4×C11—42no—
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C11×SD16—44no—
268C11×SD16—44no—
269C11×SD16—44no—
270C11×M16—44no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11—21no—
276C2×C8×C11—21no—
277C2×C8×C11—21no—
278C2×C8×C11—21no—
279C2×C8×C11—21no—
280C2×C8×C11—21no—
281C2×C8×C11—21no—
282C2×C8×C11C2×D412yescomplemented
283C11×C4⋊C4—22no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—42no—
291C11×C4⋊C4—42no—
292C11×C4⋊C4—42no—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2×D412yescomplemented
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—42no—
301C11×C22⋊C4—42no—
302C11×C22⋊C4—42no—
303C11×C22⋊C4—42no—
304C42×C11—21no—
305C42×C11—21no—
306C42×C11—42no—
307C2×D42C2×C1111yescharacteristic
308C2×#468C2×C1111yescharacteristic, complemented
309C2×#450C2×C1111yescharacteristic, complemented
310C2×#450C2×C1111yescharacteristic, complemented
311C2×#418C2×C1111yescharacteristic, complemented
312#2415C2×C1111yescharacteristic, complemented
313#2041C2×C1111yescharacteristic, complemented
314#2033C2×C1111yescharacteristic, complemented
315#2014C2×C1111yescharacteristic, complemented
316#2000C2×C1111yescharacteristic, complemented
317#1877C2×C1111yescharacteristic, complemented
318#1875C2×C1111yescharacteristic, complemented
319#1870C2×C1111yescharacteristic, complemented
320#1862C2×C1111yescharacteristic, complemented
321#1786C2×C1111yescharacteristic, complemented
322C23×C11—21no—
323C23×C11—22no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—22no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—22no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—21no—
336C23×C11—21no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—48no—
340C23×C11—48no—
341C23×C11—48no—
342C23×C11—48no—
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—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—84no—
360C23×C11—84no—
361C23×C11—84no—
362C23×C11—84no—
363C23×C11—84no—
364C23×C11—84no—
365C23×C11—84no—
366C23×C11—84no—
367C23×C11—84no—
368C23×C11—84no—
369C23×C11#12012yes—
370C23×C11AGL(1,ℤ/8)12yes—
371C23×C11C22×D411yescharacteristic
372Q8×C11—41no—
373Q8×C11—41no—
374Q8×C11—41no—
375Q8×C11—41no—
376D4×C11—28no—
377D4×C11—22no—
378D4×C11—22no—
379D4×C11—22no—
380D4×C11—22no—
381D4×C11—22no—
382D4×C11—22no—
383D4×C11—22no—
384D4×C11—48no—
385D4×C11—48no—
386D4×C11—48no—
387D4×C11—48no—
388D4×C11—48no—
389D4×C11—41no—
390D4×C11—41no—
391D4×C11—41no—
392D4×C11—41no—
393D4×C11—84no—
394D4×C11#12114yes—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—48no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11#12012yes—
430C2×C4×C11AGL(1,ℤ/8)12yes—
431C2×C4×C11C22×D411yescharacteristic
432C2×C4×C11C22×D411yescharacteristic
433C2×C4×C11C22×D411yescharacteristic
434C2×C4×C11C2×#4111yescharacteristic
435C2×C4×C11H(5,𝔽2)11yescharacteristic
436C2×C4×C11H(5,𝔽2)11yescharacteristic
437C8×C11—22no—
438C8×C11—41no—
439C8×C11—41no—
440C8×C11—41no—
441C23×D4—21no—
442C23×D4C22×C1111yescharacteristic
443C23×D4C22×C1111yescharacteristic
444C22×SD16C22×C1111yescharacteristic
445C22×SD16C22×C1111yescharacteristic, complemented
446C22×SD16C22×C1111yescharacteristic, complemented
447C22×M16C22×C1111yescharacteristic, complemented
448D42—24no—
449D42—24no—
450C2×#127C22×C1111yescharacteristic
451C2×C22⋊Q8C22×C1111yescharacteristic, complemented
452C2×C22⋊Q8C22×C1111yescharacteristic, complemented
453C2×#121—21no—
454C2×#121C22×C1111yescharacteristic
455C2×#121C22×C1111yescharacteristic
456C2×#120—21no—
457C2×#120—21no—
458C2×C4×D4C22×C1111yescharacteristic
459C2×C4×D4C22×C1111yescharacteristic
460C2×#117C22×C1111yescharacteristic, complemented
461#468—24no—
462#450—24no—
463#450—24no—
464C2×#107C22×C1111yescharacteristic, complemented
465#418—24no—
466C2×#103C22×C1111yescharacteristic, complemented
467C2×#102C22×C1111yescharacteristic
468C2×#102C22×C1111yescharacteristic
469C2×#102C22×C1111yescharacteristic
470C2×#102C22×C1111yescharacteristic, complemented
471C2×#102C22×C1111yescharacteristic, complemented
472C2×#102C22×C1111yescharacteristic, complemented
473C2×#102C22×C1111yescharacteristic, complemented
474C2×#102C22×C1111yescharacteristic, complemented
475C2×#102C22×C1111yescharacteristic, complemented
476C2×C22⋊C8C22×C1111yescharacteristic, complemented
477C2×C22⋊C8C22×C1111yescharacteristic, complemented
478C2×C22⋊C8C22×C1111yescharacteristic, complemented
479#397—21no—
480#394—21no—
481#391C22×C1111yescharacteristic, complemented
482#389—21no—
483#389C22×C1111yescharacteristic, complemented
484#388—21no—
485#380C22×C1111yescharacteristic, complemented
486#340C22×C1111yescharacteristic, complemented
487#340C22×C1111yescharacteristic, complemented
488#336C22×C1111yescharacteristic, complemented
489#336C22×C1111yescharacteristic, complemented
490C22×C11—22no—
491C22×C11—24no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—22no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11—41no—
498C22×C11—42no—
499C22×C11—41no—
500C22×C11—42no—
501C22×C11—41no—
502C22×C11—42no—
503C22×C11—41no—
504C22×C11—41no—
505C22×C11—42no—
506C22×C11—41no—
507C22×C11—42no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—816no—
518C22×C11—816no—
519C22×C11—81no—
520C22×C11—81no—
521C22×C11—81no—
522C22×C11—81no—
523C22×C11—81no—
524C22×C11—81no—
525C22×C11—81no—
526C22×C11—81no—
527C22×C11C2×#12011yescharacteristic
528C22×C11D4211yescharacteristic
529C22×C11#54611yescharacteristic
530C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
531C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
532C22×C11#57711yescharacteristic
533C22×C11#57711yescharacteristic
534C4×C11—22no—
535C4×C11—22no—
536C4×C11—41no—
537C4×C11—42no—
538C4×C11—41no—
539C4×C11—42no—
540C4×C11—81no—
541C4×C11—81no—
542C4×C11—81no—
543C4×C11C2×#12111yescharacteristic
544C4×C11#53411yescharacteristic
545C4×C11D4211yescharacteristic
546C4×C11#54611yescharacteristic
547C25—21no—
548C25—21no—
549C22×Q8C23×C1111yescharacteristic
550C22×D4—22no—
551C22×D4—22no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—22no—
563C22×D4—21no—
564C22×D4—41no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4—44no—
569C22×D4—44no—
570C22×D4D4×C1111yescharacteristic
571C22×D4D4×C1114yes—
572C22×D4C23×C1111yescharacteristic
573C22×D4C23×C1111yescharacteristic
574C22×D4C23×C1111yescharacteristic
575C23×C4—21no—
576C23×C4C23×C1111yescharacteristic
577C23×C4C23×C1111yescharacteristic
578C2×SD16—22no—
579C2×SD16—22no—
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—22no—
583C2×SD16—22no—
584C2×SD16—41no—
585C2×SD16—41no—
586C2×SD16—41no—
587C2×M16—22no—
588C2×M16—22no—
589C2×M16—41no—
590C22×C8C23×C1111yescharacteristic
591C22×C8C23×C1111yescharacteristic
592C22×C8C23×C1111yescharacteristic
593C22×C8C23×C1111yescharacteristic
594#127—22no—
595#127—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—41no—
600#121—28no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121D4×C1114yes—
605#120—28no—
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611#117—22no—
612#117—41no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4D4×C1111yescharacteristic
617C2×C4⋊C4C23×C1111yescharacteristic
618C2×C4⋊C4C23×C1111yescharacteristic
619C2×C4⋊C4C23×C1111yescharacteristic
620C2×C4⋊C4C23×C1111yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C1111yescharacteristic
629C2×C22⋊C4D4×C1111yescharacteristic
630C2×C42—21no—
631C2×C42C23×C1111yescharacteristic
632#107—22no—
633#103—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—41no—
642#102D4×C1114yescomplemented
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646#95—21no—
647#95—21no—
648#95—21no—
649#95—21no—
650C2×C11—42no—
651C2×C11—42no—
652C2×C11—44no—
653C2×C11—82no—
654C2×C11—82no—
655C2×C11#241011yescharacteristic
656C2×C11#300311yescharacteristic
657C2×C11#300911yescharacteristic
658C2×C11#326511yescharacteristic
659C2×C11#327211yescharacteristic
660C2×C11#331011yescharacteristic
661C2×C11#332411yescharacteristic
662C24—21no—
663C24—24no—
664C24—21no—
665C24—21no—
666C24—24no—
667C24—42no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24—81no—
679C24C2×D4×C1111yescharacteristic
680C24C2×D4×C1111yescharacteristic
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—28no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—432no—
721C2×D4—44no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—44no—
727C2×D4—42no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4C2×D4×C1112yes—
731C2×D4C2×D4×C1112yes—
732C2×D4C2×D4×C1112yes—
733C2×D4C2×D4×C1112yes—
734C2×D4C11×#4112yes—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—24no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C1111yescharacteristic
754C22×C4C2×D4×C1111yescharacteristic
755C22×C4C2×D4×C1111yescharacteristic
756C22×C4C2×D4×C1112yes—
757C22×C4C2×D4×C1112yes—
758C22×C4C2×D4×C1111yescharacteristic
759C22×C4C24×C1111yescharacteristic
760SD16—44no—
761SD16—44no—
762SD16—44no—
763M16—44no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8C2×D4×C1112yescomplemented
776C4⋊C4—22no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—42no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4C2×D4×C1112yes—
787C4⋊C4C2×D4×C1112yescomplemented
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—22no—
791C22⋊C4—24no—
792C22⋊C4—22no—
793C22⋊C4—42no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C42—21no—
798C42—21no—
799C42—42no—
800C11#2444811yescharacteristic, direct product factor, Sylow
801C23—21no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—21no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—22no—
818C23—48no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23C11×#12012yes—
849C23C11×AGL(1,ℤ/8)12yes—
850C23C22×D4×C1111yescharacteristic
851Q8—41no—
852Q8—41no—
853Q8—41no—
854Q8—41no—
855D4—28no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—84no—
873D4C11×#12114yes—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4C11×#12012yes—
909C2×C4C11×AGL(1,ℤ/8)12yes—
910C2×C4C22×D4×C1111yescharacteristic
911C2×C4C22×D4×C1111yescharacteristic
912C2×C4C22×D4×C1111yescharacteristic
913C2×C4C2×C11×#4111yescharacteristic
914C2×C4C11×H(5,𝔽2)11yescharacteristic
915C2×C4C11×H(5,𝔽2)11yescharacteristic
916C8—22no—
917C8—41no—
918C8—41no—
919C8—41no—
920C22—22no—
921C22—24no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—42no—
931C22—41no—
932C22—42no—
933C22—41no—
934C22—41no—
935C22—42no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—816no—
948C22—816no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22C2×C11×#12011yescharacteristic
958C22D42×C1111yescharacteristic
959C22C11×#54611yescharacteristic
960C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
961C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
962C22C11×#57711yescharacteristic
963C22C11×#57711yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—42no—
968C4—41no—
969C4—42no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4C2×C11×#12111yescharacteristic
974C4C11×#53411yescharacteristic
975C4D42×C1111yescharacteristic
976C4C11×#54611yescharacteristic
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2—82no—
982C2C11×#241011yescharacteristic
983C2C11×#300311yescharacteristic
984C2C11×#300911yescharacteristic
985C2C11×#326511yescharacteristic
986C2C11×#327211yescharacteristic
987C2C11×#331011yescharacteristic
988C2C11×#332411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×D42×C11C2
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
2. C2×C11×#468C2semidirect
3. C2×C11×#450C2semidirect
4. C2×C11×#450C2semidirect
5. C2×C11×#418C2semidirect
6. C11×#2415C2semidirect
7. C11×#2041C2semidirect
8. C11×#2033C2semidirect
9. C11×#2014C2semidirect
10. C11×#2000C2semidirect
11. C11×#1877C2semidirect
12. C11×#1875C2semidirect
13. C11×#1870C2semidirect
14. C11×#1862C2semidirect
15. C11×#1786C2semidirect
20. C22×C11×SD16C22semidirect
21. C22×C11×SD16C22semidirect
22. C22×C11×M16C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
35. C2×C11×#117C22semidirect
39. C2×C11×#107C22semidirect
41. C2×C11×#103C22semidirect
45. C2×C11×#102C22semidirect
46. C2×C11×#102C22semidirect
47. C2×C11×#102C22semidirect
48. C2×C11×#102C22semidirect
49. C2×C11×#102C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×C22⋊C8C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. C2×C11×C22⋊C8C22semidirect
56. C11×#391C22semidirect
58. C11×#389C22semidirect
60. C11×#380C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
160. C11×#102D4semidirect
168. #24448C11direct (N × H)
282. C2×C8×C11C2×D4semidirect
294. C11×C4⋊C4C2×D4semidirect
308. C2×#468C2×C11semidirect
309. C2×#450C2×C11semidirect
310. C2×#450C2×C11semidirect
311. C2×#418C2×C11semidirect
312. #2415C2×C11semidirect
313. #2041C2×C11semidirect
314. #2033C2×C11semidirect
315. #2014C2×C11semidirect
316. #2000C2×C11semidirect
317. #1877C2×C11semidirect
318. #1875C2×C11semidirect
319. #1870C2×C11semidirect
320. #1862C2×C11semidirect
321. #1786C2×C11semidirect
445. C22×SD16C22×C11semidirect
446. C22×SD16C22×C11semidirect
447. C22×M16C22×C11semidirect
451. C2×C22⋊Q8C22×C11semidirect
452. C2×C22⋊Q8C22×C11semidirect
460. C2×#117C22×C11semidirect
464. C2×#107C22×C11semidirect
466. C2×#103C22×C11semidirect
470. C2×#102C22×C11semidirect
471. C2×#102C22×C11semidirect
472. C2×#102C22×C11semidirect
473. C2×#102C22×C11semidirect
474. C2×#102C22×C11semidirect
475. C2×#102C22×C11semidirect
476. C2×C22⋊C8C22×C11semidirect
477. C2×C22⋊C8C22×C11semidirect
478. C2×C22⋊C8C22×C11semidirect
481. #391C22×C11semidirect
483. #389C22×C11semidirect
485. #380C22×C11semidirect
486. #340C22×C11semidirect
487. #340C22×C11semidirect
488. #336C22×C11semidirect
489. #336C22×C11semidirect
642. #102D4×C11semidirect
775. C2×C8C2×D4×C11semidirect
787. C4⋊C4C2×D4×C11semidirect
800. C11#24448direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D42×C112
C2×C11×#4682
C2×C11×#4502
C2×C11×#4182
C11×#24152
C11×#20412
C11×#20332
C11×#20142
C11×#20002
C11×#18772
C11×#18752
C11×#18702
C11×#18622
C11×#17862
#2444811