Finite Group Databasebeta

← C11×#24388 #14601581

Subgroups — C11×#24388 #14601581

Order 2816.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic, complemented
2C2×C11×#469C211yesmaximal, characteristic, complemented
3C2×C11×#468C211yesmaximal, characteristic, complemented
4C2×C11×#449C211yesmaximal, characteristic, complemented
5C2×C11×#407C211yesmaximal, characteristic, complemented
6C11×#2847C211yesmaximal, characteristic, complemented
7C11×#2035C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C11×#1894C211yesmaximal, characteristic, complemented
13C11×#1875C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic, complemented
19C22×C11×D8C2211yescharacteristic, complemented
20C22×C11×M16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#525—24no—
23C11×#525—24no—
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C11×#120—21no—
33C2×C11×#120—21no—
34C2×C4×D4×C11—21no—
35C2×C4×D4×C11—21no—
36C2×C11×#117C2211yescharacteristic
37C11×#469—24no—
38C11×#468—24no—
39C11×#449—24no—
40C2×C11×#107C2211yescharacteristic, complemented
41C2×C11×#106C2211yescharacteristic, complemented
42C2×C11×#103C2211yescharacteristic, complemented
43C2×C11×#103C2211yescharacteristic, complemented
44C2×C11×#103C2211yescharacteristic, complemented
45C2×C11×#102C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic, complemented
47C2×C11×#102C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic, complemented
50C11×#407—24no—
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×C22⋊C8C2211yescharacteristic
55C11×#386—21no—
56C11×#386—21no—
57C11×#386—21no—
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#340C2211yescharacteristic, complemented
64C11×#340C2211yescharacteristic, complemented
65C25×C11D411yescharacteristic
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—21no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—22no—
83C23×C4×C11—22no—
84C23×C4×C11—22no—
85C23×C4×C11—22no—
86C23×C4×C11—41no—
87C23×C4×C11—41no—
88C23×C4×C11D411yescharacteristic
89C23×C4×C11D411yescharacteristic
90C23×C4×C11D411yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—41no—
97C2×C11×D8—22no—
98C2×C11×D8—22no—
99C2×C11×D8—41no—
100C2×C11×M16—22no—
101C2×C11×M16—22no—
102C2×C11×M16—22no—
103C2×C11×M16—22no—
104C2×C11×M16—41no—
105C2×C11×M16—41no—
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C11×#123—28no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8D414yescomplemented
115C11×#121—22no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—41no—
123C11×#121—41no—
124C11×#121D414yescomplemented
125C11×#120—28no—
126C11×#120—44no—
127C4×D4×C11—28no—
128C4×D4×C11—28no—
129C11×#117—22no—
130C11×#117—22no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C11×C22⋊C4—21no—
149C2×C42×C11—21no—
150C11×#107—22no—
151C11×#106—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—41no—
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—22no—
163C11×C22⋊C8D414yescomplemented
164C11×#95—21no—
165C11×#95—21no—
166C11×#95—21no—
167#24388C1111yesmaximal, characteristic, direct product factor, Sylow
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—41no—
174C24×C11—41no—
175C24×C11—41no—
176C24×C11—41no—
177C24×C11C2×D411yescharacteristic
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—24no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
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—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—42no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C2×D4×C11C2×D412yes—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—24no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
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—21no—
246C22×C4×C11—21no—
247C22×C4×C11—41no—
248C22×C4×C11—41no—
249C22×C4×C11—41no—
250C22×C4×C11—44no—
251C22×C4×C11—44no—
252C22×C4×C11—44no—
253C22×C4×C11—44no—
254C22×C4×C11—42no—
255C22×C4×C11—42no—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D412yes—
262C22×C4×C11#4112yes—
263C22×C4×C11C2411yescharacteristic
264C11×SD16—44no—
265C11×D8—44no—
266C11×M16—44no—
267C11×M16—44no—
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×C11—21no—
276C2×C8×C11—21no—
277C2×C8×C11—21no—
278C2×C8×C11C2×D412yes—
279C2×C8×C11C2×D412yes—
280C11×C4⋊C4—24no—
281C11×C4⋊C4—24no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
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⋊C4C2×D412yes—
291C11×C4⋊C4C2×D412yes—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—24no—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4—42no—
298C11×C22⋊C4—42no—
299C11×C22⋊C4—42no—
300C11×C22⋊C4—42no—
301C11×C22⋊C4—42no—
302C11×C22⋊C4—42no—
303C42×C11—24no—
304C2×#525C2×C1111yescharacteristic, complemented
305C2×#469C2×C1111yescharacteristic, complemented
306C2×#468C2×C1111yescharacteristic, complemented
307C2×#449C2×C1111yescharacteristic, complemented
308C2×#407C2×C1111yescharacteristic, complemented
309#2847C2×C1111yescharacteristic, complemented
310#2035C2×C1111yescharacteristic, complemented
311#2033C2×C1111yescharacteristic, complemented
312#2000C2×C1111yescharacteristic, complemented
313#1999C2×C1111yescharacteristic, complemented
314#1895C2×C1111yescharacteristic, complemented
315#1894C2×C1111yescharacteristic, complemented
316#1875C2×C1111yescharacteristic, complemented
317#1854C2×C1111yescharacteristic, complemented
318#1788C2×C1111yescharacteristic, complemented
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
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—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
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#12012yes—
359C23×C11#12112yes—
360C23×C11AGL(1,ℤ/8)12yes—
361C23×C11C22×D411yescharacteristic
362Q8×C11—22no—
363Q8×C11—22no—
364Q8×C11—41no—
365Q8×C11—41no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—48no—
369D4×C11—48no—
370D4×C11—48no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—41no—
377D4×C11—84no—
378D4×C11—84no—
379D4×C11—84no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—21no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—44no—
399C2×C4×C11—44no—
400C2×C4×C11—44no—
401C2×C4×C11—48no—
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—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11#12012yes—
422C2×C4×C11#12112yes—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C2×#4111yescharacteristic
427C2×C4×C11H(5,𝔽2)11yescharacteristic
428C2×C4×C11H(5,𝔽2)11yescharacteristic
429C8×C11—22no—
430C8×C11—22no—
431C8×C11—41no—
432C8×C11—41no—
433C22×#41C22×C1111yescharacteristic
434C24×C4C22×C1111yescharacteristic
435C22×SD16C22×C1111yescharacteristic, complemented
436C22×D8C22×C1111yescharacteristic, complemented
437C22×M16C22×C1111yescharacteristic
438C22×M16C22×C1111yescharacteristic
439#525—24no—
440#525—24no—
441C2×#123—21no—
442C2×C22⋊Q8C22×C1111yescharacteristic
443C2×C22⋊Q8C22×C1111yescharacteristic
444C2×#121C22×C1111yescharacteristic
445C2×#121C22×C1111yescharacteristic
446C2×#121C22×C1111yescharacteristic
447C2×#121C22×C1111yescharacteristic
448C2×#121C22×C1111yescharacteristic
449C2×#120—21no—
450C2×#120—21no—
451C2×C4×D4—21no—
452C2×C4×D4—21no—
453C2×#117C22×C1111yescharacteristic
454#469—24no—
455#468—24no—
456#449—24no—
457C2×#107C22×C1111yescharacteristic, complemented
458C2×#106C22×C1111yescharacteristic, complemented
459C2×#103C22×C1111yescharacteristic, complemented
460C2×#103C22×C1111yescharacteristic, complemented
461C2×#103C22×C1111yescharacteristic, complemented
462C2×#102C22×C1111yescharacteristic, complemented
463C2×#102C22×C1111yescharacteristic, complemented
464C2×#102C22×C1111yescharacteristic, complemented
465C2×#102C22×C1111yescharacteristic, complemented
466C2×#102C22×C1111yescharacteristic, complemented
467#407—24no—
468C2×C22⋊C8C22×C1111yescharacteristic
469C2×C22⋊C8C22×C1111yescharacteristic
470C2×C22⋊C8C22×C1111yescharacteristic
471C2×C22⋊C8C22×C1111yescharacteristic
472#386—21no—
473#386—21no—
474#386—21no—
475#380C22×C1111yescharacteristic
476#380C22×C1111yescharacteristic
477#380C22×C1111yescharacteristic
478#340C22×C1111yescharacteristic, complemented
479#340C22×C1111yescharacteristic, complemented
480#340C22×C1111yescharacteristic, complemented
481#340C22×C1111yescharacteristic, complemented
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—22no—
488C22×C11—22no—
489C22×C11—22no—
490C22×C11—22no—
491C22×C11—416no—
492C22×C11—41no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—41no—
499C22×C11—41no—
500C22×C11—41no—
501C22×C11—41no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
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×C11—81no—
516C22×C11—81no—
517C22×C11—81no—
518C22×C11C2×#12011yescharacteristic
519C22×C11C2×#12111yescharacteristic
520C22×C11#53411yescharacteristic
521C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
522C22×C11#57511yescharacteristic
523C22×C11#57511yescharacteristic
524C22×C11#57511yescharacteristic
525C4×C11—22no—
526C4×C11—22no—
527C4×C11—41no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—81no—
532C4×C11—81no—
533C4×C11—81no—
534C4×C11D4211yescharacteristic
535C4×C11D4211yescharacteristic
536C4×C11#54611yescharacteristic
537C4×C11#54611yescharacteristic
538C25D4×C1111yescharacteristic
539C2×#41—22no—
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—41no—
544C2×#41—41no—
545C22×Q8C23×C1111yescharacteristic
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4C23×C1111yescharacteristic
553C22×D4C23×C1111yescharacteristic
554C23×C4—21no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—41no—
560C23×C4—41no—
561C23×C4D4×C1111yescharacteristic
562C23×C4D4×C1111yescharacteristic
563C23×C4D4×C1111yescharacteristic
564C23×C4C23×C1111yescharacteristic
565C23×C4C23×C1111yescharacteristic
566C23×C4C23×C1111yescharacteristic
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—41no—
570C2×D8—22no—
571C2×D8—22no—
572C2×D8—41no—
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C2×M16—41no—
579C22×C8C23×C1111yescharacteristic
580C22×C8C23×C1111yescharacteristic
581C22×C8C23×C1111yescharacteristic
582C22×C8C23×C1111yescharacteristic
583#123—28no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8D4×C1114yescomplemented
588#121—22no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—41no—
596#121—41no—
597#121D4×C1114yescomplemented
598#120—28no—
599#120—44no—
600C4×D4—28no—
601C4×D4—28no—
602#117—22no—
603#117—22no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4C23×C1111yescharacteristic
607C2×C4⋊C4C23×C1111yescharacteristic
608C2×C4⋊C4C23×C1111yescharacteristic
609C2×C4⋊C4C23×C1111yescharacteristic
610C2×C4⋊C4C23×C1111yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C42—21no—
623#107—22no—
624#106—22no—
625#103—22no—
626#103—22no—
627#103—41no—
628#102—22no—
629#102—22no—
630#102—22no—
631#102—22no—
632#102—41no—
633C22⋊C8—22no—
634C22⋊C8—22no—
635C22⋊C8—22no—
636C22⋊C8D4×C1114yescomplemented
637#95—21no—
638#95—21no—
639#95—21no—
640C2×C11—42no—
641C2×C11—42no—
642C2×C11—42no—
643C2×C11—82no—
644C2×C11—161no—
645C2×C11#241011yescharacteristic
646C2×C11#300511yescharacteristic
647C2×C11#300611yescharacteristic
648C2×C11#305411yescharacteristic
649C2×C11#305511yescharacteristic
650C2×C11#319411yescharacteristic
651C2×C11#319711yescharacteristic
652C24—22no—
653C24—22no—
654C24—22no—
655C24—21no—
656C24—21no—
657C24—41no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24C2×D4×C1111yescharacteristic
662C24C2×D4×C1111yescharacteristic
663C24C2×D4×C1111yescharacteristic
664#41—44no—
665#41—44no—
666#41—44no—
667#41—44no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8C2×D4×C1112yes—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
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—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4C2×D4×C1112yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—41no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4C2×D4×C1111yescharacteristic
741C22×C4C2×D4×C1111yescharacteristic
742C22×C4C2×D4×C1112yes—
743C22×C4C2×D4×C1112yes—
744C22×C4C2×D4×C1111yescharacteristic
745C22×C4C2×D4×C1112yes—
746C22×C4C11×#4112yes—
747C22×C4C24×C1111yescharacteristic
748SD16—44no—
749D8—44no—
750M16—44no—
751M16—44no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8C2×D4×C1112yes—
763C2×C8C2×D4×C1112yes—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4C2×D4×C1112yes—
775C4⋊C4C2×D4×C1112yes—
776C22⋊C4—24no—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C42—24no—
788C11#2438811yescharacteristic, direct product factor, Sylow
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—22no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23C11×#12012yes—
829C23C11×#12112yes—
830C23C11×AGL(1,ℤ/8)12yes—
831C23C22×D4×C1111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4C11×#12012yes—
892C2×C4C11×#12112yes—
893C2×C4C22×D4×C1111yescharacteristic
894C2×C4C22×D4×C1111yescharacteristic
895C2×C4C22×D4×C1111yescharacteristic
896C2×C4C2×C11×#4111yescharacteristic
897C2×C4C11×H(5,𝔽2)11yescharacteristic
898C2×C4C11×H(5,𝔽2)11yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—416no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22C2×C11×#12011yescharacteristic
940C22C2×C11×#12111yescharacteristic
941C22C11×#53411yescharacteristic
942C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
943C22C11×#57511yescharacteristic
944C22C11×#57511yescharacteristic
945C22C11×#57511yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C1111yescharacteristic
956C4D42×C1111yescharacteristic
957C4C11×#54611yescharacteristic
958C4C11×#54611yescharacteristic
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C11×#241011yescharacteristic
965C2C11×#300511yescharacteristic
966C2C11×#300611yescharacteristic
967C2C11×#305411yescharacteristic
968C2C11×#305511yescharacteristic
969C2C11×#319411yescharacteristic
970C2C11×#319711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#525C2semidirect
2. C2×C11×#469C2semidirect
3. C2×C11×#468C2semidirect
4. C2×C11×#449C2semidirect
5. C2×C11×#407C2semidirect
6. C11×#2847C2semidirect
7. C11×#2035C2semidirect
8. C11×#2033C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1895C2semidirect
12. C11×#1894C2semidirect
13. C11×#1875C2semidirect
14. C11×#1854C2semidirect
15. C11×#1788C2semidirect
18. C22×C11×SD16C22semidirect
19. C22×C11×D8C22semidirect
40. C2×C11×#107C22semidirect
41. C2×C11×#106C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
44. C2×C11×#103C22semidirect
45. C2×C11×#102C22semidirect
46. C2×C11×#102C22semidirect
47. C2×C11×#102C22semidirect
48. C2×C11×#102C22semidirect
49. C2×C11×#102C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
114. C11×C22⋊Q8D4semidirect
124. C11×#121D4semidirect
163. C11×C22⋊C8D4semidirect
167. #24388C11direct (N × H)
304. C2×#525C2×C11semidirect
305. C2×#469C2×C11semidirect
306. C2×#468C2×C11semidirect
307. C2×#449C2×C11semidirect
308. C2×#407C2×C11semidirect
309. #2847C2×C11semidirect
310. #2035C2×C11semidirect
311. #2033C2×C11semidirect
312. #2000C2×C11semidirect
313. #1999C2×C11semidirect
314. #1895C2×C11semidirect
315. #1894C2×C11semidirect
316. #1875C2×C11semidirect
317. #1854C2×C11semidirect
318. #1788C2×C11semidirect
435. C22×SD16C22×C11semidirect
436. C22×D8C22×C11semidirect
457. C2×#107C22×C11semidirect
458. C2×#106C22×C11semidirect
459. C2×#103C22×C11semidirect
460. C2×#103C22×C11semidirect
461. C2×#103C22×C11semidirect
462. C2×#102C22×C11semidirect
463. C2×#102C22×C11semidirect
464. C2×#102C22×C11semidirect
465. C2×#102C22×C11semidirect
466. C2×#102C22×C11semidirect
478. #340C22×C11semidirect
479. #340C22×C11semidirect
480. #340C22×C11semidirect
481. #340C22×C11semidirect
587. C22⋊Q8D4×C11semidirect
597. #121D4×C11semidirect
636. C22⋊C8D4×C11semidirect
788. C11#24388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C2×C11×#4692
C2×C11×#4682
C2×C11×#4492
C2×C11×#4072
C11×#28472
C11×#20352
C11×#20332
C11×#20002
C11×#19992
C11×#18952
C11×#18942
C11×#18752
C11×#18542
C11×#17882
#2438811