Finite Group Databasebeta

← C11×#24444 #14601637

Subgroups — C11×#24444 #14601637

Order 2816.

1662 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic, complemented
2C2×C11×#469C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C2×C11×#417C211yesmaximal, characteristic, complemented
6C11×#2416C211yesmaximal, characteristic, complemented
7C11×#2042C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#2012C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1864C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic, complemented
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic, complemented
22C11×#546—24no—
23C11×#546—24no—
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121—21no—
28C2×C11×#121—21no—
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic, complemented
32C2×C11×#120—21no—
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic, complemented
36C22×C11×C22⋊C4—21no—
37C11×#469—24no—
38C11×#449—24no—
39C11×#447—24no—
40C2×C11×#106C2211yescharacteristic, complemented
41C11×#417—24no—
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
55C11×#396—21no—
56C11×#394—21no—
57C11×#390C2211yescharacteristic, complemented
58C11×#389C2211yescharacteristic, complemented
59C11×#386—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#336C2211yescharacteristic, complemented
64C11×#336C2211yescharacteristic, complemented
65C25×C11—21no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C2×C11×#41D414yescomplemented
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—41no—
95C2×C11×SD16—41no—
96C2×C11×D8—22no—
97C2×C11×D8—22no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—22no—
101C2×C11×D8—41no—
102C2×C11×M16—22no—
103C2×C11×M16—22no—
104C2×C11×M16—41no—
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×#124—22no—
110C11×#124—22no—
111C11×#123—28no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×#121—28no—
115C11×#121—22no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—41no—
120C11×#121—44no—
121C11×#121D414yescomplemented
122C11×#120—28no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—22no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—41no—
132C2×C11×C4⋊C4D411yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4—28no—
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⋊C4D411yescharacteristic
149C2×C11×C22⋊C4D411yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C11×#106—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—22no—
159C11×#102—22no—
160C11×#102—41no—
161C11×#102D414yescomplemented
162C11×C22⋊C8—22no—
163C11×C22⋊C8—22no—
164C11×C22⋊C8—41no—
165C11×#95—21no—
166C11×#95—21no—
167#24444C1111yesmaximal, 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—28no—
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—22no—
192C2×D4×C11—24no—
193C2×D4×C11—22no—
194C2×D4×C11—24no—
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—21no—
209C2×D4×C11—41no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—42no—
217C2×D4×C11—42no—
218C2×D4×C11—44no—
219C2×D4×C11—42no—
220C2×D4×C11—42no—
221C2×D4×C11—42no—
222C2×D4×C11—42no—
223C2×D4×C11—81no—
224C2×D4×C11—81no—
225C2×D4×C11—81no—
226C2×D4×C11C2×D412yes—
227C2×D4×C11C2×D412yes—
228C2×D4×C11C2×D412yes—
229C2×D4×C11#4112yes—
230C22×C4×C11—21no—
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—24no—
238C22×C4×C11—24no—
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—42no—
248C22×C4×C11—42no—
249C22×C4×C11—42no—
250C22×C4×C11—42no—
251C22×C4×C11—81no—
252C22×C4×C11—81no—
253C22×C4×C11—81no—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2411yescharacteristic
261C11×SD16—44no—
262C11×D8—44no—
263C11×D8—44no—
264C11×M16—44no—
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×C11—21no—
276C2×C8×C11C2×D412yes—
277C11×C4⋊C4—24no—
278C11×C4⋊C4—22no—
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—42no—
287C11×C4⋊C4C2×D412yes—
288C11×C4⋊C4C2×D412yes—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—42no—
297C11×C22⋊C4—42no—
298C11×C22⋊C4—42no—
299C11×C22⋊C4—42no—
300C11×C22⋊C4—81no—
301C42×C11—21no—
302C42×C11—21no—
303C2×#546C2×C1111yescharacteristic, complemented
304C2×#469C2×C1111yescharacteristic, complemented
305C2×#449C2×C1111yescharacteristic, complemented
306C2×#447C2×C1111yescharacteristic, complemented
307C2×#417C2×C1111yescharacteristic, complemented
308#2416C2×C1111yescharacteristic, complemented
309#2042C2×C1111yescharacteristic, complemented
310#2035C2×C1111yescharacteristic, complemented
311#2012C2×C1111yescharacteristic, complemented
312#2000C2×C1111yescharacteristic, complemented
313#1879C2×C1111yescharacteristic, complemented
314#1874C2×C1111yescharacteristic, complemented
315#1870C2×C1111yescharacteristic, complemented
316#1864C2×C1111yescharacteristic, complemented
317#1786C2×C1111yescharacteristic, complemented
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—22no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—22no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—22no—
334C23×C11—48no—
335C23×C11—48no—
336C23×C11—41no—
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×C11#12012yes—
359C23×C11AGL(1,ℤ/8)12yes—
360C23×C11C22×D411yescharacteristic
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—41no—
364Q8×C11—41no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—22no—
370D4×C11—44no—
371D4×C11—48no—
372D4×C11—48no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—41no—
377D4×C11—41no—
378D4×C11—41no—
379D4×C11—84no—
380D4×C11—84no—
381D4×C11—84no—
382D4×C11#12114yescomplemented
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
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—84no—
419C2×C4×C11—84no—
420C2×C4×C11#12012yes—
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C2×#4111yescharacteristic
425C2×C4×C11H(5,𝔽2)11yescharacteristic
426C2×C4×C11H(5,𝔽2)11yescharacteristic
427C8×C11—22no—
428C8×C11—41no—
429C8×C11—41no—
430C8×C11—41no—
431C22×#41C22×C1111yescharacteristic
432C23×D4C22×C1111yescharacteristic
433C22×SD16C22×C1111yescharacteristic, complemented
434C22×D8C22×C1111yescharacteristic
435C22×D8C22×C1111yescharacteristic
436C22×M16C22×C1111yescharacteristic, complemented
437#546—24no—
438#546—24no—
439C2×#124C22×C1111yescharacteristic
440C2×#123—21no—
441C2×C22⋊Q8C22×C1111yescharacteristic
442C2×#121—21no—
443C2×#121—21no—
444C2×#121C22×C1111yescharacteristic
445C2×#121C22×C1111yescharacteristic
446C2×#121C22×C1111yescharacteristic, complemented
447C2×#120—21no—
448C2×C4×D4C22×C1111yescharacteristic
449C2×C4×D4C22×C1111yescharacteristic
450C22×C4⋊C4C22×C1111yescharacteristic, complemented
451C22×C22⋊C4—21no—
452#469—24no—
453#449—24no—
454#447—24no—
455C2×#106C22×C1111yescharacteristic, complemented
456#417—24no—
457C2×#103C22×C1111yescharacteristic, complemented
458C2×#103C22×C1111yescharacteristic, complemented
459C2×#103C22×C1111yescharacteristic, complemented
460C2×#102C22×C1111yescharacteristic
461C2×#102C22×C1111yescharacteristic
462C2×#102C22×C1111yescharacteristic
463C2×#102C22×C1111yescharacteristic
464C2×#102C22×C1111yescharacteristic
465C2×#102C22×C1111yescharacteristic
466C2×#102C22×C1111yescharacteristic, complemented
467C2×C22⋊C8C22×C1111yescharacteristic
468C2×C22⋊C8C22×C1111yescharacteristic
469C2×C22⋊C8C22×C1111yescharacteristic, complemented
470#396—21no—
471#394—21no—
472#390C22×C1111yescharacteristic, complemented
473#389C22×C1111yescharacteristic, complemented
474#386—21no—
475#380C22×C1111yescharacteristic
476#340C22×C1111yescharacteristic, complemented
477#340C22×C1111yescharacteristic, complemented
478#336C22×C1111yescharacteristic, complemented
479#336C22×C1111yescharacteristic, complemented
480C22×C11—22no—
481C22×C11—24no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—41no—
488C22×C11—42no—
489C22×C11—41no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—41no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—42no—
496C22×C11—41no—
497C22×C11—42no—
498C22×C11—41no—
499C22×C11—41no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—816no—
505C22×C11—81no—
506C22×C11—81no—
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×C11C2×#12011yescharacteristic
517C22×C11D4211yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
520C22×C11#57511yescharacteristic
521C22×C11#57611yescharacteristic
522C22×C11#57711yescharacteristic
523C4×C11—22no—
524C4×C11—41no—
525C4×C11—42no—
526C4×C11—41no—
527C4×C11—42no—
528C4×C11—41no—
529C4×C11—42no—
530C4×C11—81no—
531C4×C11—81no—
532C4×C11C2×#12111yescharacteristic
533C4×C11#53411yescharacteristic
534C4×C11D4211yescharacteristic
535C4×C11#54611yescharacteristic
536C25—21no—
537C2×#41—22no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—41no—
541C2×#41—41no—
542C2×#41D4×C1114yescomplemented
543C22×Q8C23×C1111yescharacteristic
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4—41no—
555C22×D4D4×C1111yescharacteristic
556C22×D4C23×C1111yescharacteristic
557C22×D4C23×C1111yescharacteristic
558C22×D4C23×C1111yescharacteristic
559C23×C4—21no—
560C23×C4—21no—
561C23×C4—21no—
562C23×C4C23×C1111yescharacteristic
563C23×C4C23×C1111yescharacteristic
564C2×SD16—22no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×D8—22no—
568C2×D8—22no—
569C2×D8—22no—
570C2×D8—22no—
571C2×D8—22no—
572C2×D8—41no—
573C2×M16—22no—
574C2×M16—22no—
575C2×M16—41no—
576C22×C8C23×C1111yescharacteristic
577C22×C8C23×C1111yescharacteristic
578C22×C8C23×C1111yescharacteristic
579C22×C8C23×C1111yescharacteristic
580#124—22no—
581#124—22no—
582#123—28no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585#121—28no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—41no—
591#121—44no—
592#121D4×C1114yescomplemented
593#120—28no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4D4×C1111yescharacteristic
604C2×C4⋊C4C23×C1111yescharacteristic
605C2×C4⋊C4C23×C1111yescharacteristic
606C2×C4⋊C4C23×C1111yescharacteristic
607C2×C4⋊C4C23×C1111yescharacteristic
608C2×C22⋊C4—28no—
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⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4D4×C1111yescharacteristic
620C2×C22⋊C4D4×C1111yescharacteristic
621C2×C42C23×C1111yescharacteristic
622#106—22no—
623#103—22no—
624#103—22no—
625#103—22no—
626#102—22no—
627#102—22no—
628#102—22no—
629#102—22no—
630#102—22no—
631#102—41no—
632#102D4×C1114yescomplemented
633C22⋊C8—22no—
634C22⋊C8—22no—
635C22⋊C8—41no—
636#95—21no—
637#95—21no—
638C2×C11—42no—
639C2×C11—42no—
640C2×C11—44no—
641C2×C11—82no—
642C2×C11—161no—
643C2×C11#241011yescharacteristic
644C2×C11#300611yescharacteristic
645C2×C11#301211yescharacteristic
646C2×C11#326411yescharacteristic
647C2×C11#327511yescharacteristic
648C2×C11#330611yescharacteristic
649C2×C11#332211yescharacteristic
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C1111yescharacteristic
661C24C2×D4×C1111yescharacteristic
662#41—28no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C1112yes—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—24no—
675C2×D4—22no—
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—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—41no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4C2×D4×C1112yes—
709C2×D4C2×D4×C1112yes—
710C2×D4C2×D4×C1112yes—
711C2×D4C11×#4112yes—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4C2×D4×C1111yescharacteristic
737C22×C4C2×D4×C1111yescharacteristic
738C22×C4C2×D4×C1111yescharacteristic
739C22×C4C2×D4×C1111yescharacteristic
740C22×C4C2×D4×C1112yes—
741C22×C4C2×D4×C1112yes—
742C22×C4C24×C1111yescharacteristic
743SD16—44no—
744D8—44no—
745D8—44no—
746M16—44no—
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×C8—21no—
757C2×C8—21no—
758C2×C8C2×D4×C1112yes—
759C4⋊C4—24no—
760C4⋊C4—22no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—42no—
769C4⋊C4C2×D4×C1112yes—
770C4⋊C4C2×D4×C1112yes—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—24no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—81no—
783C42—21no—
784C42—21no—
785C11#2444411yescharacteristic, direct product factor, Sylow
786C23—21no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—22no—
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—41no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23—84no—
826C23C11×#12012yes—
827C23C11×AGL(1,ℤ/8)12yes—
828C23C22×D4×C1111yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
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—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4C11×#12114yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4C11×#12012yes—
889C2×C4C22×D4×C1111yescharacteristic
890C2×C4C22×D4×C1111yescharacteristic
891C2×C4C22×D4×C1111yescharacteristic
892C2×C4C2×C11×#4111yescharacteristic
893C2×C4C11×H(5,𝔽2)11yescharacteristic
894C2×C4C11×H(5,𝔽2)11yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—24no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—41no—
916C22—42no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—816no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22C2×C11×#12011yescharacteristic
936C22D42×C1111yescharacteristic
937C22C11×#54611yescharacteristic
938C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
939C22C11×#57511yescharacteristic
940C22C11×#57611yescharacteristic
941C22C11×#57711yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×C11×#12111yescharacteristic
952C4C11×#53411yescharacteristic
953C4D42×C1111yescharacteristic
954C4C11×#54611yescharacteristic
955C2—42no—
956C2—42no—
957C2—44no—
958C2—82no—
959C2—161no—
960C2C11×#241011yescharacteristic
961C2C11×#300611yescharacteristic
962C2C11×#301211yescharacteristic
963C2C11×#326411yescharacteristic
964C2C11×#327511yescharacteristic
965C2C11×#330611yescharacteristic
966C2C11×#332211yescharacteristic
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×#469C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#447C2semidirect
5. C2×C11×#417C2semidirect
6. C11×#2416C2semidirect
7. C11×#2042C2semidirect
8. C11×#2035C2semidirect
9. C11×#2012C2semidirect
10. C11×#2000C2semidirect
11. C11×#1879C2semidirect
12. C11×#1874C2semidirect
13. C11×#1870C2semidirect
14. C11×#1864C2semidirect
15. C11×#1786C2semidirect
18. C22×C11×SD16C22semidirect
21. C22×C11×M16C22semidirect
31. C2×C11×#121C22semidirect
35. C22×C11×C4⋊C4C22semidirect
40. C2×C11×#106C22semidirect
42. C2×C11×#103C22semidirect
43. C2×C11×#103C22semidirect
44. C2×C11×#103C22semidirect
51. C2×C11×#102C22semidirect
54. C2×C11×C22⋊C8C22semidirect
57. C11×#390C22semidirect
58. C11×#389C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
71. C2×C11×#41D4semidirect
121. C11×#121D4semidirect
161. C11×#102D4semidirect
167. #24444C11direct (N × H)
303. C2×#546C2×C11semidirect
304. C2×#469C2×C11semidirect
305. C2×#449C2×C11semidirect
306. C2×#447C2×C11semidirect
307. C2×#417C2×C11semidirect
308. #2416C2×C11semidirect
309. #2042C2×C11semidirect
310. #2035C2×C11semidirect
311. #2012C2×C11semidirect
312. #2000C2×C11semidirect
313. #1879C2×C11semidirect
314. #1874C2×C11semidirect
315. #1870C2×C11semidirect
316. #1864C2×C11semidirect
317. #1786C2×C11semidirect
382. D4×C11#121semidirect
433. C22×SD16C22×C11semidirect
436. C22×M16C22×C11semidirect
446. C2×#121C22×C11semidirect
450. C22×C4⋊C4C22×C11semidirect
455. C2×#106C22×C11semidirect
457. C2×#103C22×C11semidirect
458. C2×#103C22×C11semidirect
459. C2×#103C22×C11semidirect
466. C2×#102C22×C11semidirect
469. C2×C22⋊C8C22×C11semidirect
472. #390C22×C11semidirect
473. #389C22×C11semidirect
476. #340C22×C11semidirect
477. #340C22×C11semidirect
478. #336C22×C11semidirect
479. #336C22×C11semidirect
542. C2×#41D4×C11semidirect
592. #121D4×C11semidirect
632. #102D4×C11semidirect
785. C11#24444direct (N × H)
850. 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×#4692
C2×C11×#4492
C2×C11×#4472
C2×C11×#4172
C11×#24162
C11×#20422
C11×#20352
C11×#20122
C11×#20002
C11×#18792
C11×#18742
C11×#18702
C11×#18642
C11×#17862
#2444411