Finite Group Databasebeta

← C11×#24256 #14601449

Subgroups — C11×#24256 #14601449

Order 2816.

1510 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#548C211yesmaximal, characteristic, complemented
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#448C211yesmaximal, characteristic, complemented
5C2×C11×#440C211yesmaximal, characteristic, complemented
6C11×#2537C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C11×#1955C211yesmaximal, characteristic, complemented
13C11×#1803C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C11×#548—24no—
22C11×#548—24no—
23C2×C11×#124—21no—
24C2×C11×#124C2211yescharacteristic
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121—21no—
28C2×C11×#121—21no—
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C11×#463—24no—
37C11×#449—24no—
38C11×#448—24no—
39C11×#440—24no—
40C2×C11×#107C2211yescharacteristic
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×C22⋊C8C2211yescharacteristic
55C2×C11×C22⋊C8C2211yescharacteristic
56C2×C11×#97C2211yescharacteristic
57C11×#394—21no—
58C11×#394—21no—
59C11×#384C2211yescharacteristic
60C11×#380—21no—
61C11×#380C2211yescharacteristic
62C11×#380C2211yescharacteristic
63C11×#340C2211yescharacteristic
64C11×#340C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—21no—
74C22×Q8×C11—22no—
75C22×Q8×C11—22no—
76C22×Q8×C11—41no—
77C22×Q8×C11—41no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11D411yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—41no—
97C2×C11×SD16D414yescomplemented
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—41no—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×#124—28no—
106C11×#124—22no—
107C11×#124D414yescomplemented
108C11×C22⋊Q8—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—
119C4×Q8×C11—22no—
120C4×Q8×C11D414yescomplemented
121C4×D4×C11—28no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4D411yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
145C2×C11×C22⋊C4D411yescharacteristic
146C2×C42×C11—21no—
147C2×C42×C11C2311yescharacteristic
148C11×#107—22no—
149C11×C4⋊C8—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#103—41no—
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#24256C1111yesmaximal, characteristic, direct product factor, Sylow
168C24×C11—21no—
169C24×C11—21no—
170C24×C11C2×D411yescharacteristic
171C24×C11C2×D411yescharacteristic
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C2×Q8×C11—24no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—42no—
186C2×Q8×C11—42no—
187C2×Q8×C11—44no—
188C2×Q8×C11—44no—
189C2×Q8×C11—44no—
190C2×Q8×C11—44no—
191C2×Q8×C11C2×D412yes—
192C2×Q8×C11C2×D412yes—
193C2×Q8×C11C2×D412yes—
194C2×Q8×C11#4112yes—
195C2×D4×C11—24no—
196C2×D4×C11—24no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
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—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—42no—
217C2×D4×C11—42no—
218C2×D4×C11—81no—
219C2×D4×C11—81no—
220C2×D4×C11C2×D412yes—
221C2×D4×C11C2×D412yes—
222C22×C4×C11—21no—
223C22×C4×C11—24no—
224C22×C4×C11—24no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
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—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11—42no—
247C22×C4×C11—42no—
248C22×C4×C11—42no—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C11×SD16—28no—
255C11×SD16—44no—
256C11×D8—44no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11C2×D412yes—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—42no—
280C11×C4⋊C4—81no—
281C11×C4⋊C4C2×D412yes—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—22no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—42no—
289C11×C22⋊C4—42no—
290C11×C22⋊C4—42no—
291C11×C22⋊C4—42no—
292C11×C22⋊C4—42no—
293C42×C11—24no—
294C42×C11C2×D412yes—
295C42×C11C2×D412yes—
296C2×#548C2×C1111yescharacteristic, complemented
297C2×#463C2×C1111yescharacteristic, complemented
298C2×#449C2×C1111yescharacteristic, complemented
299C2×#448C2×C1111yescharacteristic, complemented
300C2×#440C2×C1111yescharacteristic, complemented
301#2537C2×C1111yescharacteristic, complemented
302#2036C2×C1111yescharacteristic, complemented
303#2033C2×C1111yescharacteristic, complemented
304#2000C2×C1111yescharacteristic, complemented
305#1999C2×C1111yescharacteristic, complemented
306#1959C2×C1111yescharacteristic, complemented
307#1955C2×C1111yescharacteristic, complemented
308#1803C2×C1111yescharacteristic, complemented
309#1788C2×C1111yescharacteristic, complemented
310#1787C2×C1111yescharacteristic, complemented
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11AGL(1,ℤ/8)12yes—
339C23×C11C22×D411yescharacteristic
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—22no—
343Q8×C11—22no—
344Q8×C11—22no—
345Q8×C11—48no—
346Q8×C11—41no—
347Q8×C11—41no—
348Q8×C11#12114yescomplemented
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—44no—
354D4×C11—48no—
355D4×C11—48no—
356D4×C11—41no—
357D4×C11—41no—
358D4×C11—41no—
359D4×C11—41no—
360D4×C11—84no—
361D4×C11—84no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—48no—
378C2×C4×C11—48no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—84no—
401C2×C4×C11#12012yes—
402C2×C4×C11#12012yes—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C2×#4111yescharacteristic
407C2×C4×C11H(5,𝔽2)11yescharacteristic
408C2×C4×C11H(5,𝔽2)11yescharacteristic
409C8×C11—22no—
410C8×C11—41no—
411C8×C11—41no—
412C8×C11—41no—
413C22×#41C22×C1111yescharacteristic
414C23×Q8C22×C1111yescharacteristic
415C22×SD16C22×C1111yescharacteristic
416C22×SD16C22×C1111yescharacteristic
417C22×D8C22×C1111yescharacteristic
418#548—24no—
419#548—24no—
420C2×#124—21no—
421C2×#124C22×C1111yescharacteristic
422C2×C22⋊Q8—21no—
423C2×C22⋊Q8C22×C1111yescharacteristic
424C2×#121—21no—
425C2×#121—21no—
426C2×#121C22×C1111yescharacteristic
427C2×#121C22×C1111yescharacteristic
428C2×#121C22×C1111yescharacteristic
429C2×C4×Q8C22×C1111yescharacteristic
430C2×C4×D4—21no—
431C2×C4×D4C22×C1111yescharacteristic
432C2×C4×D4C22×C1111yescharacteristic
433#463—24no—
434#449—24no—
435#448—24no—
436#440—24no—
437C2×#107C22×C1111yescharacteristic
438C2×C4⋊C8C22×C1111yescharacteristic
439C2×#103C22×C1111yescharacteristic
440C2×#103C22×C1111yescharacteristic
441C2×#103C22×C1111yescharacteristic
442C2×#103C22×C1111yescharacteristic
443C2×#103C22×C1111yescharacteristic
444C2×#103C22×C1111yescharacteristic
445C2×#102C22×C1111yescharacteristic
446C2×#102C22×C1111yescharacteristic
447C2×#102C22×C1111yescharacteristic
448C2×#102C22×C1111yescharacteristic
449C2×C22⋊C8C22×C1111yescharacteristic
450C2×C22⋊C8C22×C1111yescharacteristic
451C2×C22⋊C8C22×C1111yescharacteristic
452C2×C22⋊C8C22×C1111yescharacteristic
453C2×#97C22×C1111yescharacteristic
454#394—21no—
455#394—21no—
456#384C22×C1111yescharacteristic
457#380—21no—
458#380C22×C1111yescharacteristic
459#380C22×C1111yescharacteristic
460#340C22×C1111yescharacteristic
461#340C22×C1111yescharacteristic
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—41no—
469C22×C11—42no—
470C22×C11—41no—
471C22×C11—42no—
472C22×C11—41no—
473C22×C11—42no—
474C22×C11—41no—
475C22×C11—42no—
476C22×C11—41no—
477C22×C11—42no—
478C22×C11—41no—
479C22×C11—42no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—81no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11C2×#12011yescharacteristic
491C22×C11D4211yescharacteristic
492C22×C11#54611yescharacteristic
493C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
494C22×C11#57511yescharacteristic
495C22×C11#57711yescharacteristic
496C22×C11#57811yescharacteristic
497C4×C11—24no—
498C4×C11—22no—
499C4×C11—22no—
500C4×C11—41no—
501C4×C11—41no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—81no—
505C4×C11—81no—
506C4×C11—81no—
507C4×C11C2×#12111yescharacteristic
508C4×C11#53511yescharacteristic
509C4×C11D4211yescharacteristic
510C4×C11#54611yescharacteristic
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—41no—
516C2×#41—41no—
517C22×Q8—22no—
518C22×Q8—22no—
519C22×Q8—21no—
520C22×Q8—22no—
521C22×Q8—22no—
522C22×Q8—41no—
523C22×Q8—41no—
524C22×Q8C23×C1111yescharacteristic
525C22×Q8C23×C1111yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4D4×C1111yescharacteristic
531C22×D4C23×C1111yescharacteristic
532C22×D4C23×C1111yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C23×C1111yescharacteristic
537C23×C4C23×C1111yescharacteristic
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16D4×C1114yescomplemented
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C22×C8C23×C1111yescharacteristic
548C22×C8C23×C1111yescharacteristic
549C22×C8C23×C1111yescharacteristic
550C22×C8C23×C1111yescharacteristic
551#124—28no—
552#124—22no—
553#124D4×C1114yescomplemented
554C22⋊Q8—28no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557#121—28no—
558#121—22no—
559#121—22no—
560#121—22no—
561#121—22no—
562#121—41no—
563#121—41no—
564#121—44no—
565C4×Q8—22no—
566C4×Q8D4×C1114yescomplemented
567C4×D4—28no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4D4×C1111yescharacteristic
577C2×C4⋊C4C23×C1111yescharacteristic
578C2×C4⋊C4C23×C1111yescharacteristic
579C2×C4⋊C4C23×C1111yescharacteristic
580C2×C4⋊C4C23×C1111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C1111yescharacteristic
591C2×C22⋊C4D4×C1111yescharacteristic
592C2×C42—21no—
593C2×C42C23×C1111yescharacteristic
594#107—22no—
595C4⋊C8—22no—
596#103—22no—
597#103—22no—
598#103—22no—
599#103—22no—
600#103—22no—
601#103—41no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—41no—
606C22⋊C8—22no—
607C22⋊C8—22no—
608C22⋊C8—41no—
609C22⋊C8—41no—
610#97—22no—
611#95—21no—
612#95—21no—
613C2×C11—42no—
614C2×C11—81no—
615C2×C11—82no—
616C2×C11—82no—
617C2×C11#240811yescharacteristic
618C2×C11#300611yescharacteristic
619C2×C11#301311yescharacteristic
620C2×C11#326511yescharacteristic
621C2×C11#326911yescharacteristic
622C2×C11#330811yescharacteristic
623C2×C11#332111yescharacteristic
624C24—21no—
625C24—21no—
626C24C2×D4×C1111yescharacteristic
627C24C2×D4×C1111yescharacteristic
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632C2×Q8—24no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—42no—
642C2×Q8—42no—
643C2×Q8—44no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8C2×D4×C1112yes—
648C2×Q8C2×D4×C1112yes—
649C2×Q8C2×D4×C1112yes—
650C2×Q8C11×#4112yes—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—41no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4C2×D4×C1112yes—
677C2×D4C2×D4×C1112yes—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4C2×D4×C1111yescharacteristic
706C22×C4C2×D4×C1111yescharacteristic
707C22×C4C2×D4×C1111yescharacteristic
708C22×C4C2×D4×C1111yescharacteristic
709C22×C4C24×C1111yescharacteristic
710SD16—28no—
711SD16—44no—
712D8—44no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8C2×D4×C1112yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—22no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—81no—
737C4⋊C4C2×D4×C1112yes—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—24no—
750C42C2×D4×C1112yes—
751C42C2×D4×C1112yes—
752C11#2425611yescharacteristic, direct product factor, Sylow
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23C11×AGL(1,ℤ/8)12yes—
781C23C22×D4×C1111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—41no—
789Q8—41no—
790Q8C11×#12114yescomplemented
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—84no—
843C2×C4C11×#12012yes—
844C2×C4C11×#12012yes—
845C2×C4C22×D4×C1111yescharacteristic
846C2×C4C22×D4×C1111yescharacteristic
847C2×C4C22×D4×C1111yescharacteristic
848C2×C4C2×C11×#4111yescharacteristic
849C2×C4C11×H(5,𝔽2)11yescharacteristic
850C2×C4C11×H(5,𝔽2)11yescharacteristic
851C8—22no—
852C8—41no—
853C8—41no—
854C8—41no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×C11×#12011yescharacteristic
884C22D42×C1111yescharacteristic
885C22C11×#54611yescharacteristic
886C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
887C22C11×#57511yescharacteristic
888C22C11×#57711yescharacteristic
889C22C11×#57811yescharacteristic
890C4—24no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×C11×#12111yescharacteristic
901C4C11×#53511yescharacteristic
902C4D42×C1111yescharacteristic
903C4C11×#54611yescharacteristic
904C2—42no—
905C2—81no—
906C2—82no—
907C2—82no—
908C2C11×#240811yescharacteristic
909C2C11×#300611yescharacteristic
910C2C11×#301311yescharacteristic
911C2C11×#326511yescharacteristic
912C2C11×#326911yescharacteristic
913C2C11×#330811yescharacteristic
914C2C11×#332111yescharacteristic
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×#548C2semidirect
2. C2×C11×#463C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#448C2semidirect
5. C2×C11×#440C2semidirect
6. C11×#2537C2semidirect
7. C11×#2036C2semidirect
8. C11×#2033C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1959C2semidirect
12. C11×#1955C2semidirect
13. C11×#1803C2semidirect
14. C11×#1788C2semidirect
15. C11×#1787C2semidirect
97. C2×C11×SD16D4semidirect
107. C11×#124D4semidirect
120. C4×Q8×C11D4semidirect
167. #24256C11direct (N × H)
296. C2×#548C2×C11semidirect
297. C2×#463C2×C11semidirect
298. C2×#449C2×C11semidirect
299. C2×#448C2×C11semidirect
300. C2×#440C2×C11semidirect
301. #2537C2×C11semidirect
302. #2036C2×C11semidirect
303. #2033C2×C11semidirect
304. #2000C2×C11semidirect
305. #1999C2×C11semidirect
306. #1959C2×C11semidirect
307. #1955C2×C11semidirect
308. #1803C2×C11semidirect
309. #1788C2×C11semidirect
310. #1787C2×C11semidirect
348. Q8×C11#121semidirect
543. C2×SD16D4×C11semidirect
553. #124D4×C11semidirect
566. C4×Q8D4×C11semidirect
752. C11#24256direct (N × H)
790. Q8C11×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5482
C2×C11×#4632
C2×C11×#4492
C2×C11×#4482
C2×C11×#4402
C11×#25372
C11×#20362
C11×#20332
C11×#20002
C11×#19992
C11×#19592
C11×#19552
C11×#18032
C11×#17882
C11×#17872
#2425611