Finite Group Databasebeta

← C11×#24244 #14601437

Subgroups — C11×#24244 #14601437

Order 2816.

1488 conjugacy classes of subgroups.

The subgroup lattice has 910 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×C4×C11×SD16C211yesmaximal, characteristic, complemented
6C11×#2535C211yesmaximal, characteristic, complemented
7C11×#2035C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1958C211yesmaximal, characteristic, complemented
12C11×#1954C211yesmaximal, characteristic, complemented
13C11×#1805C211yesmaximal, 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×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C4×Q8×C11C2211yescharacteristic
32C2×C4×D4×C11—21no—
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C11×#463—24no—
36C11×#449—24no—
37C11×#448—24no—
38C4×C11×SD16—24no—
39C2×C11×#106C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×C22⋊C8C2211yescharacteristic
55C2×C4×C8×C11C2211yescharacteristic
56C11×#397—21no—
57C11×#392—21no—
58C11×#386—21no—
59C11×#386—21no—
60C11×#382C2211yescharacteristic
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—
118C4×Q8×C11—22no—
119C4×Q8×C11D414yescomplemented
120C4×D4×C11—28no—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4D411yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
142C2×C11×C22⋊C4D411yescharacteristic
143C2×C42×C11—21no—
144C2×C42×C11C2311yescharacteristic
145C11×#106—22no—
146C11×C4⋊C8—22no—
147C11×#103—22no—
148C11×#103—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103—41no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—41no—
157C11×C22⋊C8—22no—
158C11×C22⋊C8—22no—
159C11×C22⋊C8—41no—
160C11×C22⋊C8—41no—
161C4×C8×C11—22no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24244C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—21no—
169C24×C11C2×D411yescharacteristic
170C24×C11C2×D411yescharacteristic
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C2×Q8×C11—24no—
176C2×Q8×C11—21no—
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—42no—
185C2×Q8×C11—42no—
186C2×Q8×C11—44no—
187C2×Q8×C11—44no—
188C2×Q8×C11—44no—
189C2×Q8×C11—44no—
190C2×Q8×C11C2×D412yes—
191C2×Q8×C11C2×D412yes—
192C2×Q8×C11C2×D412yes—
193C2×Q8×C11#4112yes—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
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—41no—
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—81no—
218C2×D4×C11—81no—
219C2×D4×C11C2×D412yes—
220C2×D4×C11C2×D412yes—
221C22×C4×C11—21no—
222C22×C4×C11—24no—
223C22×C4×C11—24no—
224C22×C4×C11—21no—
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—42no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11—81no—
247C22×C4×C11—81no—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C11×SD16—28no—
254C11×SD16—44no—
255C11×D8—44no—
256C2×C8×C11—21no—
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×C11C2×D412yes—
268C11×C4⋊C4—24no—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—21no—
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⋊C4C2×D412yes—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4—42no—
286C11×C22⋊C4—42no—
287C11×C22⋊C4—42no—
288C11×C22⋊C4—81no—
289C11×C22⋊C4—81no—
290C42×C11—24no—
291C42×C11C2×D412yes—
292C42×C11C2×D412yes—
293C2×#548C2×C1111yescharacteristic, complemented
294C2×#463C2×C1111yescharacteristic, complemented
295C2×#449C2×C1111yescharacteristic, complemented
296C2×#448C2×C1111yescharacteristic, complemented
297C2×C4×SD16C2×C1111yescharacteristic, complemented
298#2535C2×C1111yescharacteristic, complemented
299#2035C2×C1111yescharacteristic, complemented
300#2034C2×C1111yescharacteristic, complemented
301#2000C2×C1111yescharacteristic, complemented
302#1999C2×C1111yescharacteristic, complemented
303#1958C2×C1111yescharacteristic, complemented
304#1954C2×C1111yescharacteristic, complemented
305#1805C2×C1111yescharacteristic, complemented
306#1788C2×C1111yescharacteristic, complemented
307#1787C2×C1111yescharacteristic, complemented
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
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#13512yes—
336C23×C11C22×D411yescharacteristic
337Q8×C11—22no—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—48no—
343Q8×C11—41no—
344Q8×C11—41no—
345Q8×C11#12114yes—
346D4×C11—22no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—44no—
351D4×C11—48no—
352D4×C11—48no—
353D4×C11—41no—
354D4×C11—41no—
355D4×C11—41no—
356D4×C11—41no—
357D4×C11—84no—
358D4×C11—84no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
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—21no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—48no—
375C2×C4×C11—48no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
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—84no—
398C2×C4×C11#12012yes—
399C2×C4×C11#12012yes—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C2×#4111yescharacteristic
404C2×C4×C11H(5,𝔽2)11yescharacteristic
405C2×C4×C11H(5,𝔽2)11yescharacteristic
406C8×C11—22no—
407C8×C11—41no—
408C8×C11—41no—
409C8×C11—41no—
410C22×#41C22×C1111yescharacteristic
411C23×Q8C22×C1111yescharacteristic
412C22×SD16C22×C1111yescharacteristic
413C22×SD16C22×C1111yescharacteristic
414C22×D8C22×C1111yescharacteristic
415#548—24no—
416#548—24no—
417C2×#124—21no—
418C2×#124C22×C1111yescharacteristic
419C2×C22⋊Q8—21no—
420C2×C22⋊Q8C22×C1111yescharacteristic
421C2×#121—21no—
422C2×#121C22×C1111yescharacteristic
423C2×#121C22×C1111yescharacteristic
424C2×#121C22×C1111yescharacteristic
425C2×C4×Q8C22×C1111yescharacteristic
426C2×C4×D4—21no—
427C2×C4×D4C22×C1111yescharacteristic
428C2×C4×D4C22×C1111yescharacteristic
429#463—24no—
430#449—24no—
431#448—24no—
432C4×SD16—24no—
433C2×#106C22×C1111yescharacteristic
434C2×C4⋊C8C22×C1111yescharacteristic
435C2×#103C22×C1111yescharacteristic
436C2×#103C22×C1111yescharacteristic
437C2×#103C22×C1111yescharacteristic
438C2×#103C22×C1111yescharacteristic
439C2×#103C22×C1111yescharacteristic
440C2×#103C22×C1111yescharacteristic
441C2×#102C22×C1111yescharacteristic
442C2×#102C22×C1111yescharacteristic
443C2×#102C22×C1111yescharacteristic
444C2×#102C22×C1111yescharacteristic
445C2×C22⋊C8C22×C1111yescharacteristic
446C2×C22⋊C8C22×C1111yescharacteristic
447C2×C22⋊C8C22×C1111yescharacteristic
448C2×C22⋊C8C22×C1111yescharacteristic
449C2×C4×C8C22×C1111yescharacteristic
450#397—21no—
451#392—21no—
452#386—21no—
453#386—21no—
454#382C22×C1111yescharacteristic
455#380C22×C1111yescharacteristic
456#380C22×C1111yescharacteristic
457#340C22×C1111yescharacteristic
458#340C22×C1111yescharacteristic
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—42no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—41no—
470C22×C11—42no—
471C22×C11—41no—
472C22×C11—42no—
473C22×C11—41no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—41no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—81no—
480C22×C11—81no—
481C22×C11—81no—
482C22×C11—81no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11C2×#12011yescharacteristic
488C22×C11D4211yescharacteristic
489C22×C11#54611yescharacteristic
490C22×C11C2×#13511yescharacteristic
491C22×C11#57511yescharacteristic
492C22×C11#57711yescharacteristic
493C22×C11#57711yescharacteristic
494C4×C11—24no—
495C4×C11—22no—
496C4×C11—22no—
497C4×C11—41no—
498C4×C11—41no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11—81no—
502C4×C11—81no—
503C4×C11—81no—
504C4×C11C2×#12111yescharacteristic
505C4×C11#53511yescharacteristic
506C4×C11D4211yescharacteristic
507C4×C11#54611yescharacteristic
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C22×Q8—22no—
515C22×Q8—22no—
516C22×Q8—21no—
517C22×Q8—22no—
518C22×Q8—22no—
519C22×Q8—41no—
520C22×Q8—41no—
521C22×Q8C23×C1111yescharacteristic
522C22×Q8C23×C1111yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4D4×C1111yescharacteristic
528C22×D4C23×C1111yescharacteristic
529C22×D4C23×C1111yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C23×C1111yescharacteristic
534C23×C4C23×C1111yescharacteristic
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16D4×C1114yescomplemented
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C22×C8C23×C1111yescharacteristic
545C22×C8C23×C1111yescharacteristic
546C22×C8C23×C1111yescharacteristic
547C22×C8C23×C1111yescharacteristic
548#124—28no—
549#124—22no—
550#124D4×C1114yescomplemented
551C22⋊Q8—28no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554#121—28no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121—22no—
559#121—41no—
560#121—41no—
561C4×Q8—22no—
562C4×Q8D4×C1114yescomplemented
563C4×D4—28no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4D4×C1111yescharacteristic
571C2×C4⋊C4C23×C1111yescharacteristic
572C2×C4⋊C4C23×C1111yescharacteristic
573C2×C4⋊C4C23×C1111yescharacteristic
574C2×C4⋊C4C23×C1111yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4D4×C1111yescharacteristic
585C2×C22⋊C4D4×C1111yescharacteristic
586C2×C42—21no—
587C2×C42C23×C1111yescharacteristic
588#106—22no—
589C4⋊C8—22no—
590#103—22no—
591#103—22no—
592#103—22no—
593#103—22no—
594#103—22no—
595#103—41no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—41no—
600C22⋊C8—22no—
601C22⋊C8—22no—
602C22⋊C8—41no—
603C22⋊C8—41no—
604C4×C8—22no—
605#95—21no—
606#95—21no—
607#95—21no—
608#95—21no—
609C2×C11—42no—
610C2×C11—81no—
611C2×C11—82no—
612C2×C11—82no—
613C2×C11#240811yescharacteristic
614C2×C11#300211yescharacteristic
615C2×C11#301011yescharacteristic
616C2×C11#327511yescharacteristic
617C2×C11#328211yescharacteristic
618C2×C11#330111yescharacteristic
619C2×C11#332611yescharacteristic
620C24—21no—
621C24—21no—
622C24C2×D4×C1111yescharacteristic
623C24C2×D4×C1111yescharacteristic
624#41—44no—
625#41—44no—
626#41—44no—
627#41—44no—
628C2×Q8—24no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—42no—
638C2×Q8—42no—
639C2×Q8—44no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8C2×D4×C1112yes—
644C2×Q8C2×D4×C1112yes—
645C2×Q8C2×D4×C1112yes—
646C2×Q8C11×#4112yes—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
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—41no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—81no—
671C2×D4—81no—
672C2×D4C2×D4×C1112yes—
673C2×D4C2×D4×C1112yes—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
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—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C2×D4×C1111yescharacteristic
702C22×C4C2×D4×C1111yescharacteristic
703C22×C4C2×D4×C1111yescharacteristic
704C22×C4C2×D4×C1111yescharacteristic
705C22×C4C24×C1111yescharacteristic
706SD16—28no—
707SD16—44no—
708D8—44no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8C2×D4×C1112yes—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—22no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4C2×D4×C1112yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—81no—
742C22⋊C4—81no—
743C42—24no—
744C42C2×D4×C1112yes—
745C42C2×D4×C1112yes—
746C11#2424411yescharacteristic, direct product factor, Sylow
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—22no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23C11×#13512yes—
775C23C22×D4×C1111yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—48no—
782Q8—41no—
783Q8—41no—
784Q8C11×#12114yes—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—44no—
790D4—48no—
791D4—48no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—84no—
797D4—84no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
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—84no—
837C2×C4C11×#12012yes—
838C2×C4C11×#12012yes—
839C2×C4C22×D4×C1111yescharacteristic
840C2×C4C22×D4×C1111yescharacteristic
841C2×C4C22×D4×C1111yescharacteristic
842C2×C4C2×C11×#4111yescharacteristic
843C2×C4C11×H(5,𝔽2)11yescharacteristic
844C2×C4C11×H(5,𝔽2)11yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×C11×#12011yescharacteristic
878C22D42×C1111yescharacteristic
879C22C11×#54611yescharacteristic
880C22C2×C11×#13511yescharacteristic
881C22C11×#57511yescharacteristic
882C22C11×#57711yescharacteristic
883C22C11×#57711yescharacteristic
884C4—24no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4C2×C11×#12111yescharacteristic
895C4C11×#53511yescharacteristic
896C4D42×C1111yescharacteristic
897C4C11×#54611yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—82no—
902C2C11×#240811yescharacteristic
903C2C11×#300211yescharacteristic
904C2C11×#301011yescharacteristic
905C2C11×#327511yescharacteristic
906C2C11×#328211yescharacteristic
907C2C11×#330111yescharacteristic
908C2C11×#332611yescharacteristic
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×C4×C11×SD16C2semidirect
6. C11×#2535C2semidirect
7. C11×#2035C2semidirect
8. C11×#2034C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1958C2semidirect
12. C11×#1954C2semidirect
13. C11×#1805C2semidirect
14. C11×#1788C2semidirect
15. C11×#1787C2semidirect
97. C2×C11×SD16D4semidirect
107. C11×#124D4semidirect
119. C4×Q8×C11D4semidirect
166. #24244C11direct (N × H)
293. C2×#548C2×C11semidirect
294. C2×#463C2×C11semidirect
295. C2×#449C2×C11semidirect
296. C2×#448C2×C11semidirect
297. C2×C4×SD16C2×C11semidirect
298. #2535C2×C11semidirect
299. #2035C2×C11semidirect
300. #2034C2×C11semidirect
301. #2000C2×C11semidirect
302. #1999C2×C11semidirect
303. #1958C2×C11semidirect
304. #1954C2×C11semidirect
305. #1805C2×C11semidirect
306. #1788C2×C11semidirect
307. #1787C2×C11semidirect
540. C2×SD16D4×C11semidirect
550. #124D4×C11semidirect
562. C4×Q8D4×C11semidirect
746. C11#24244direct (N × H)

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×C4×C11×SD162
C11×#25352
C11×#20352
C11×#20342
C11×#20002
C11×#19992
C11×#19582
C11×#19542
C11×#18052
C11×#17882
C11×#17872
#2424411