Finite Group Databasebeta

← C11×#24454 #14601647

Subgroups — C11×#24454 #14601647

Order 2816.

1528 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic, complemented
2C2×C11×#468C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C2×C11×#449C211yesmaximal, characteristic, complemented
5C2×C11×#417C211yesmaximal, characteristic, complemented
6C11×#2416C211yesmaximal, characteristic, complemented
7C11×#2043C211yesmaximal, characteristic, complemented
8C11×#2036C211yesmaximal, characteristic, complemented
9C11×#2013C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1872C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#547—24no—
23C11×#547—24no—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×#123—21no—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×#121—21no—
30C2×C11×#121—21no—
31C2×C11×#121C2211yescharacteristic
32C2×C11×#121C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C22×C11×C4⋊C4—21no—
36C22×C11×C4⋊C4C2211yescharacteristic
37C11×#468—24no—
38C11×#449—24no—
39C11×#449—24no—
40C2×C11×#107C2211yescharacteristic
41C11×#417—24no—
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
55C11×#396—21no—
56C11×#394—21no—
57C11×#390C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#386—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41D414yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
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—41no—
96C2×C11×SD16—41no—
97C2×C11×SD16—41no—
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—22no—
101C2×C11×M16—22no—
102C2×C11×M16—22no—
103C2×C11×M16—41no—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×C4⋊Q8—22no—
109C11×C4⋊Q8—22no—
110C11×#123—28no—
111C11×#123—28no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8D414yescomplemented
116C11×#121—28no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—41no—
121C11×#121—44no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C2×C11×C4⋊C4—28no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—22no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—41no—
135C2×C11×C4⋊C4D411yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
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×#107—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#103—22no—
156C11×#103—22no—
157C11×#103—41no—
158C11×#102—22no—
159C11×#102—22no—
160C11×#102—22no—
161C11×#102D414yescomplemented
162C11×C22⋊C8—22no—
163C11×C22⋊C8—22no—
164C11×C22⋊C8—41no—
165C11×#95—21no—
166C11×#95—21no—
167#24454C1111yesmaximal, characteristic, direct product factor, Sylow
168C24×C11—21no—
169C24×C11—21no—
170C24×C11C2×D411yescharacteristic
171C24×C11C2×D411yescharacteristic
172C11×#41—28no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C11×#41—44no—
177C11×#41—44no—
178C11×#41—44no—
179C11×#41—44no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11C2×D412yes—
191C2×Q8×C11C2×D412yes—
192C2×D4×C11—24no—
193C2×D4×C11—22no—
194C2×D4×C11—24no—
195C2×D4×C11—22no—
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—41no—
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—81no—
216C2×D4×C11C2×D412yes—
217C2×D4×C11C2×D412yes—
218C2×D4×C11#4112yes—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
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—24no—
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—42no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11—81no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D412yes—
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C11×SD16—44no—
255C11×SD16—44no—
256C11×D8—44no—
257C11×M16—44no—
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×C11—21no—
269C2×C8×C11C2×D412yes—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—24no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—24no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—42no—
282C11×C4⋊C4—42no—
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—42no—
291C11×C22⋊C4—42no—
292C11×C22⋊C4—42no—
293C11×C22⋊C4—42no—
294C11×C22⋊C4—81no—
295C42×C11—21no—
296C42×C11—21no—
297C2×#547C2×C1111yescharacteristic, complemented
298C2×#468C2×C1111yescharacteristic, complemented
299C2×#449C2×C1111yescharacteristic, complemented
300C2×#449C2×C1111yescharacteristic, complemented
301C2×#417C2×C1111yescharacteristic, complemented
302#2416C2×C1111yescharacteristic, complemented
303#2043C2×C1111yescharacteristic, complemented
304#2036C2×C1111yescharacteristic, complemented
305#2013C2×C1111yescharacteristic, complemented
306#2000C2×C1111yescharacteristic, complemented
307#1879C2×C1111yescharacteristic, complemented
308#1872C2×C1111yescharacteristic, complemented
309#1870C2×C1111yescharacteristic, complemented
310#1862C2×C1111yescharacteristic, complemented
311#1788C2×C1111yescharacteristic, complemented
312C23×C11—22no—
313C23×C11—21no—
314C23×C11—22no—
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—21no—
318C23×C11—21no—
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—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×C11—41no—
339C23×C11#12012yes—
340C23×C11C22×D411yescharacteristic
341Q8×C11—22no—
342Q8×C11—22no—
343Q8×C11—22no—
344Q8×C11—22no—
345Q8×C11—41no—
346Q8×C11—41no—
347Q8×C11—41no—
348Q8×C11—41no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—44no—
353D4×C11—48no—
354D4×C11—48no—
355D4×C11—41no—
356D4×C11—41no—
357D4×C11—41no—
358D4×C11—41no—
359D4×C11—84no—
360D4×C11—84no—
361D4×C11#12114yescomplemented
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—21no—
371C2×C4×C11—22no—
372C2×C4×C11—21no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—48no—
381C2×C4×C11—48no—
382C2×C4×C11—48no—
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—41no—
401C2×C4×C11—84no—
402C2×C4×C11#12012yes—
403C2×C4×C11AGL(1,ℤ/8)12yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C2×#4111yescharacteristic
408C2×C4×C11H(5,𝔽2)11yescharacteristic
409C2×C4×C11H(5,𝔽2)11yescharacteristic
410C8×C11—22no—
411C8×C11—41no—
412C8×C11—41no—
413C8×C11—41no—
414C22×#41C22×C1111yescharacteristic
415C22×#41C22×C1111yescharacteristic
416C22×SD16C22×C1111yescharacteristic
417C22×SD16C22×C1111yescharacteristic
418C22×D8C22×C1111yescharacteristic
419C22×M16C22×C1111yescharacteristic
420#547—24no—
421#547—24no—
422C2×C4⋊Q8C22×C1111yescharacteristic
423C2×#123—21no—
424C2×#123—21no—
425C2×C22⋊Q8C22×C1111yescharacteristic
426C2×C22⋊Q8C22×C1111yescharacteristic
427C2×#121—21no—
428C2×#121—21no—
429C2×#121C22×C1111yescharacteristic
430C2×#121C22×C1111yescharacteristic
431C2×C4×D4C22×C1111yescharacteristic
432C2×C4×D4C22×C1111yescharacteristic
433C22×C4⋊C4—21no—
434C22×C4⋊C4C22×C1111yescharacteristic
435#468—24no—
436#449—24no—
437#449—24no—
438C2×#107C22×C1111yescharacteristic
439#417—24no—
440C2×#103C22×C1111yescharacteristic
441C2×#103C22×C1111yescharacteristic
442C2×#103C22×C1111yescharacteristic
443C2×#103C22×C1111yescharacteristic
444C2×#103C22×C1111yescharacteristic
445C2×#103C22×C1111yescharacteristic
446C2×#102C22×C1111yescharacteristic
447C2×#102C22×C1111yescharacteristic
448C2×#102C22×C1111yescharacteristic
449C2×#102C22×C1111yescharacteristic
450C2×C22⋊C8C22×C1111yescharacteristic
451C2×C22⋊C8C22×C1111yescharacteristic
452C2×C22⋊C8C22×C1111yescharacteristic
453#396—21no—
454#394—21no—
455#390C22×C1111yescharacteristic
456#389C22×C1111yescharacteristic
457#386—21no—
458#380C22×C1111yescharacteristic
459#340C22×C1111yescharacteristic
460#340C22×C1111yescharacteristic
461#336C22×C1111yescharacteristic
462#336C22×C1111yescharacteristic
463C22×C11—22no—
464C22×C11—24no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—41no—
472C22×C11—42no—
473C22×C11—41no—
474C22×C11—42no—
475C22×C11—41no—
476C22×C11—42no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11C2×#12011yescharacteristic
492C22×C11D4211yescharacteristic
493C22×C11#54611yescharacteristic
494C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
495C22×C11#57511yescharacteristic
496C22×C11#57711yescharacteristic
497C22×C11#57811yescharacteristic
498C4×C11—22no—
499C4×C11—22no—
500C4×C11—41no—
501C4×C11—42no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—41no—
505C4×C11—42no—
506C4×C11—81no—
507C4×C11—81no—
508C4×C11C2×#12111yescharacteristic
509C4×C11#53411yescharacteristic
510C4×C11D4211yescharacteristic
511C4×C11#54611yescharacteristic
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41D4×C1114yescomplemented
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×C4—21no—
537C23×C4C23×C1111yescharacteristic
538C23×C4C23×C1111yescharacteristic
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—41no—
551C22×C8C23×C1111yescharacteristic
552C22×C8C23×C1111yescharacteristic
553C22×C8C23×C1111yescharacteristic
554C22×C8C23×C1111yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557#123—28no—
558#123—28no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8D4×C1114yescomplemented
563#121—28no—
564#121—22no—
565#121—22no—
566#121—22no—
567#121—41no—
568#121—44no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C2×C4⋊C4—28no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4D4×C1111yescharacteristic
583C2×C4⋊C4C23×C1111yescharacteristic
584C2×C4⋊C4C23×C1111yescharacteristic
585C2×C4⋊C4C23×C1111yescharacteristic
586C2×C4⋊C4C23×C1111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4D4×C1111yescharacteristic
596C2×C22⋊C4D4×C1111yescharacteristic
597C2×C42C23×C1111yescharacteristic
598#107—22no—
599#103—22no—
600#103—22no—
601#103—22no—
602#103—22no—
603#103—22no—
604#103—41no—
605#102—22no—
606#102—22no—
607#102—22no—
608#102D4×C1114yescomplemented
609C22⋊C8—22no—
610C22⋊C8—22no—
611C22⋊C8—41no—
612#95—21no—
613#95—21no—
614C2×C11—42no—
615C2×C11—44no—
616C2×C11—81no—
617C2×C11—161no—
618C2×C11#241011yescharacteristic
619C2×C11#300611yescharacteristic
620C2×C11#301311yescharacteristic
621C2×C11#326911yescharacteristic
622C2×C11#327211yescharacteristic
623C2×C11#330711yescharacteristic
624C2×C11#333011yescharacteristic
625C24—21no—
626C24—21no—
627C24C2×D4×C1111yescharacteristic
628C24C2×D4×C1111yescharacteristic
629#41—28no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8C2×D4×C1112yes—
648C2×Q8C2×D4×C1112yes—
649C2×D4—24no—
650C2×D4—22no—
651C2×D4—24no—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—41no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—81no—
673C2×D4C2×D4×C1112yes—
674C2×D4C2×D4×C1112yes—
675C2×D4C11×#4112yes—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
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—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—81no—
704C22×C4C2×D4×C1111yescharacteristic
705C22×C4C2×D4×C1111yescharacteristic
706C22×C4C2×D4×C1111yescharacteristic
707C22×C4C2×D4×C1112yes—
708C22×C4C2×D4×C1112yes—
709C22×C4C2×D4×C1111yescharacteristic
710C22×C4C24×C1111yescharacteristic
711SD16—44no—
712SD16—44no—
713D8—44no—
714M16—44no—
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×C8—21no—
725C2×C8—21no—
726C2×C8C2×D4×C1112yes—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—22no—
731C4⋊C4—24no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4C2×D4×C1112yes—
741C4⋊C4C2×D4×C1112yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C42—21no—
753C42—21no—
754C11#2445411yescharacteristic, direct product factor, Sylow
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23C11×#12012yes—
783C23C22×D4×C1111yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804D4C11×#12114yescomplemented
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—48no—
824C2×C4—48no—
825C2×C4—48no—
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—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4C11×#12012yes—
846C2×C4C11×AGL(1,ℤ/8)12yes—
847C2×C4C22×D4×C1111yescharacteristic
848C2×C4C22×D4×C1111yescharacteristic
849C2×C4C22×D4×C1111yescharacteristic
850C2×C4C2×C11×#4111yescharacteristic
851C2×C4C11×H(5,𝔽2)11yescharacteristic
852C2×C4C11×H(5,𝔽2)11yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×C11×#12011yescharacteristic
886C22D42×C1111yescharacteristic
887C22C11×#54611yescharacteristic
888C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
889C22C11×#57511yescharacteristic
890C22C11×#57711yescharacteristic
891C22C11×#57811yescharacteristic
892C4—22no—
893C4—22no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—41no—
899C4—42no—
900C4—81no—
901C4—81no—
902C4C2×C11×#12111yescharacteristic
903C4C11×#53411yescharacteristic
904C4D42×C1111yescharacteristic
905C4C11×#54611yescharacteristic
906C2—42no—
907C2—44no—
908C2—81no—
909C2—161no—
910C2C11×#241011yescharacteristic
911C2C11×#300611yescharacteristic
912C2C11×#301311yescharacteristic
913C2C11×#326911yescharacteristic
914C2C11×#327211yescharacteristic
915C2C11×#330711yescharacteristic
916C2C11×#333011yescharacteristic
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×#547C2semidirect
2. C2×C11×#468C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#449C2semidirect
5. C2×C11×#417C2semidirect
6. C11×#2416C2semidirect
7. C11×#2043C2semidirect
8. C11×#2036C2semidirect
9. C11×#2013C2semidirect
10. C11×#2000C2semidirect
11. C11×#1879C2semidirect
12. C11×#1872C2semidirect
13. C11×#1870C2semidirect
14. C11×#1862C2semidirect
15. C11×#1788C2semidirect
76. C2×C11×#41D4semidirect
115. C11×C22⋊Q8D4semidirect
161. C11×#102D4semidirect
167. #24454C11direct (N × H)
297. C2×#547C2×C11semidirect
298. C2×#468C2×C11semidirect
299. C2×#449C2×C11semidirect
300. C2×#449C2×C11semidirect
301. C2×#417C2×C11semidirect
302. #2416C2×C11semidirect
303. #2043C2×C11semidirect
304. #2036C2×C11semidirect
305. #2013C2×C11semidirect
306. #2000C2×C11semidirect
307. #1879C2×C11semidirect
308. #1872C2×C11semidirect
309. #1870C2×C11semidirect
310. #1862C2×C11semidirect
311. #1788C2×C11semidirect
361. D4×C11#121semidirect
523. C2×#41D4×C11semidirect
562. C22⋊Q8D4×C11semidirect
608. #102D4×C11semidirect
754. C11#24454direct (N × H)
804. D4C11×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4682
C2×C11×#4492
C2×C11×#4172
C11×#24162
C11×#20432
C11×#20362
C11×#20132
C11×#20002
C11×#18792
C11×#18722
C11×#18702
C11×#18622
C11×#17882
#2445411