Finite Group Databasebeta

← C11×#24460 #14601653

Subgroups — C11×#24460 #14601653

Order 2816.

1352 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×#577C211yesmaximal, characteristic, complemented
2C2×C11×#472C211yesmaximal, characteristic, complemented
3C11×#3045C211yesmaximal, characteristic, complemented
4C2×C11×#454C211yesmaximal, characteristic, complemented
5C11×#3008C211yesmaximal, characteristic, complemented
6C11×#2898C211yesmaximal, characteristic, complemented
7C11×#2052C211yesmaximal, characteristic, complemented
8C11×#2046C211yesmaximal, characteristic, complemented
9C11×#2012C211yesmaximal, characteristic, complemented
10C11×#2004C211yesmaximal, characteristic, complemented
11C11×#1907C211yesmaximal, characteristic, complemented
12C11×#1883C211yesmaximal, characteristic, complemented
13C11×#1876C211yesmaximal, characteristic, complemented
14C11×#1866C211yesmaximal, characteristic, complemented
15C11×#1792C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C11×#577—24no—
19C11×#577—24no—
20C2×C11×#137—21no—
21C2×C11×#137C2211yescharacteristic
22C2×C11×AGL(1,ℤ/8)—21no—
23C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
24C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
26C2×C11×#135—21no—
27C2×C11×#135C2211yescharacteristic
28C22×C11×SD16—21no—
29C22×C11×SD16C2211yescharacteristic
30C22×C11×D8C2211yescharacteristic
31C2×C11×#131C2211yescharacteristic
32C2×C11×#131C2211yescharacteristic, complemented
33C11×#535C2211yescharacteristic
34C2×C11×#124C2211yescharacteristic, complemented
35C11×#520C2211yescharacteristic, complemented
36C11×#472—24no—
37C11×#464—21no—
38C11×#463—21no—
39C11×#460—21no—
40C11×#459—21no—
41C11×#454—24no—
42C11×#449—21no—
43C11×#449—21no—
44C11×#447—21no—
45C11×#447—21no—
46C2×C11×#108C2211yescharacteristic, complemented
47C11×#424C2211yescharacteristic, complemented
48C2×C11×#104C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic, complemented
51C11×#419—21no—
52C11×#419C2211yescharacteristic, complemented
53C11×#418C2211yescharacteristic
54C11×#417—21no—
55C11×#417C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C11×#416—21no—
58C11×#416C2211yescharacteristic
59C2×C11×#103—21no—
60C2×C11×#103C2211yescharacteristic, complemented
61C2×C11×#102C2211yescharacteristic, complemented
62C2×C11×#101C2211yescharacteristic, complemented
63C2×C11×#100C2211yescharacteristic
64C2×C11×#100C2211yescharacteristic, complemented
65C11×#408C2211yescharacteristic
66C11×#390C2211yescharacteristic
67C11×#343C2211yescharacteristic, complemented
68C11×#341C2211yescharacteristic, complemented
69C11×#339C2211yescharacteristic, complemented
70C11×#336C2211yescharacteristic, complemented
71C11×2−1+4—22no—
72C11×2−1+4—22no—
73C11×2−1+4—41no—
74C11×2−1+4D414yescomplemented
75C11×H(5,𝔽2)—22no—
76C11×H(5,𝔽2)—22no—
77C11×H(5,𝔽2)—22no—
78C11×H(5,𝔽2)—41no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—21no—
83C2×C11×#41—41no—
84C2×C11×#41C2311yescharacteristic
85C2×C11×#41C2311yescharacteristic
86C2×C11×#41C2311yescharacteristic
87C22×Q8×C11—21no—
88C22×Q8×C11—21no—
89C22×Q8×C11C2311yescharacteristic
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—41no—
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C11×#137—28no—
96C11×#137—22no—
97C11×#137—22no—
98C11×AGL(1,ℤ/8)—28no—
99C11×AGL(1,ℤ/8)—22no—
100C11×AGL(1,ℤ/8)—22no—
101C11×AGL(1,ℤ/8)—22no—
102C11×AGL(1,ℤ/8)—22no—
103C11×AGL(1,ℤ/8)—22no—
104C11×AGL(1,ℤ/8)D414yescomplemented
105C11×#135—28no—
106C11×#135—22no—
107C11×#135—22no—
108C2×C11×Q16—21no—
109C2×C11×Q16D411yescharacteristic
110C2×C11×SD16—28no—
111C2×C11×SD16—21no—
112C2×C11×SD16—22no—
113C2×C11×SD16—21no—
114C2×C11×SD16—22no—
115C2×C11×SD16—21no—
116C2×C11×SD16—21no—
117C2×C11×SD16—21no—
118C2×C11×SD16—21no—
119C2×C11×SD16D411yescharacteristic
120C2×C11×SD16D411yescharacteristic
121C2×C11×D8—21no—
122C2×C11×D8—22no—
123C2×C11×D8—21no—
124C2×C11×D8—21no—
125C2×C11×D8—21no—
126C2×C11×D8—21no—
127C2×C11×D8—41no—
128C2×C11×D8D411yescharacteristic
129C11×#131—22no—
130C11×#131—22no—
131C11×#131—22no—
132C11×#131—41no—
133C2×C11×M16—21no—
134C2×C11×M16—21no—
135C2×C11×M16C2311yescharacteristic
136C2×C11×M16C2311yescharacteristic
137C2×C11×M16C2311yescharacteristic
138C2×C11×M16C2311yescharacteristic
139C22×C8×C11—21no—
140C22×C8×C11—21no—
141C22×C8×C11C2311yescharacteristic
142C22×C8×C11C2311yescharacteristic
143C11×#127—21no—
144C11×#124—22no—
145C11×#124—21no—
146C11×#124—41no—
147C11×#121—21no—
148C11×#121—21no—
149C11×#120—41no—
150C4×Q8×C11—21no—
151C4×D4×C11—21no—
152C4×D4×C11—41no—
153C11×#117—21no—
154C11×#117C2311yescharacteristic
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—41no—
158C2×C11×C22⋊C4—41no—
159C2×C42×C11C2311yescharacteristic
160C11×#108—22no—
161C11×C4⋊C8—21no—
162C11×C4⋊C8—21no—
163C11×#104—22no—
164C11×#104—22no—
165C11×#104—41no—
166C11×#103—21no—
167C11×#103—21no—
168C11×#103—21no—
169C11×#103—21no—
170C11×#103—21no—
171C11×#103—21no—
172C11×#103D411yescharacteristic
173C11×#103D411yescharacteristic
174C11×#102—21no—
175C11×#102—21no—
176C11×#102—21no—
177C11×#102—21no—
178C11×#102—21no—
179C11×#102—21no—
180C11×#102D411yescharacteristic
181C11×#102D411yescharacteristic
182C11×#101—22no—
183C11×#100—22no—
184C11×#100—22no—
185C11×C22⋊C8—21no—
186C11×C22⋊C8—21no—
187#24460C1111yesmaximal, characteristic, direct product factor, Sylow
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—41no—
191C11×#41—21no—
192C11×#41—21no—
193C11×#41—21no—
194C11×#41—21no—
195C11×#41—24no—
196C11×#41—24no—
197C11×#41—24no—
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—21no—
201C11×#41—21no—
202C11×#41—44no—
203C11×#41—42no—
204C11×#41—42no—
205C11×#41—42no—
206C11×#41—44no—
207C11×#41—42no—
208C11×#41—42no—
209C11×#41C2×D412yes—
210C11×#41C2×D412yes—
211C11×#41C2×D412yes—
212C11×#41#4112yes—
213C2×Q8×C11—21no—
214C2×Q8×C11—24no—
215C2×Q8×C11—24no—
216C2×Q8×C11—21no—
217C2×Q8×C11—21no—
218C2×Q8×C11—21no—
219C2×Q8×C11—21no—
220C2×Q8×C11—41no—
221C2×Q8×C11—42no—
222C2×Q8×C11—42no—
223C2×Q8×C11C2×D412yes—
224C2×Q8×C11C2×D411yescharacteristic
225C2×Q8×C11C2×D411yescharacteristic
226C2×Q8×C11C2×D411yescharacteristic
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—24no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—21no—
235C2×D4×C11—21no—
236C2×D4×C11—21no—
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11—21no—
241C2×D4×C11—21no—
242C2×D4×C11—42no—
243C2×D4×C11—41no—
244C2×D4×C11—41no—
245C2×D4×C11—41no—
246C2×D4×C11—41no—
247C2×D4×C11—42no—
248C2×D4×C11—44no—
249C2×D4×C11—44no—
250C2×D4×C11—41no—
251C2×D4×C11—42no—
252C2×D4×C11C2×D412yes—
253C2×D4×C11C2×D411yescharacteristic
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11C2×D411yescharacteristic
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11—41no—
265C22×C4×C11—41no—
266C22×C4×C11C2411yescharacteristic
267C11×Q16—24no—
268C11×Q16—22no—
269C11×SD16—24no—
270C11×SD16—24no—
271C11×SD16—24no—
272C11×SD16—22no—
273C11×SD16—24no—
274C11×SD16—22no—
275C11×SD16—42no—
276C11×SD16—42no—
277C11×D8—24no—
278C11×D8—22no—
279C11×D8—42no—
280C11×D8—42no—
281C11×D8—42no—
282C11×D8—42no—
283C11×M16—24no—
284C11×M16—21no—
285C11×M16—21no—
286C11×M16—21no—
287C11×M16—21no—
288C11×M16—21no—
289C11×M16—21no—
290C11×M16—21no—
291C11×M16—42no—
292C11×M16C2×D412yes—
293C2×C8×C11—24no—
294C2×C8×C11—21no—
295C2×C8×C11—21no—
296C2×C8×C11—21no—
297C2×C8×C11—21no—
298C2×C8×C11—21no—
299C2×C8×C11—21no—
300C2×C8×C11—21no—
301C2×C8×C11—21no—
302C2×C8×C11—42no—
303C2×C8×C11C2×D411yescharacteristic
304C2×C8×C11C2×D411yescharacteristic
305C2×C8×C11C2×D411yescharacteristic
306C2×C8×C11C2×D411yescharacteristic
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4—41no—
310C11×C4⋊C4C2×D411yescharacteristic
311C11×C4⋊C4C2×D411yescharacteristic
312C11×C22⋊C4—21no—
313C11×C22⋊C4—41no—
314C11×C22⋊C4—41no—
315C11×C22⋊C4—41no—
316C11×C22⋊C4—44no—
317C11×C22⋊C4—82no—
318C42×C11—21no—
319C42×C11—21no—
320C42×C11—21no—
321C42×C11—41no—
322C2×#577C2×C1111yescharacteristic, complemented
323C2×#472C2×C1111yescharacteristic, complemented
324#3045C2×C1111yescharacteristic, complemented
325C2×#454C2×C1111yescharacteristic, complemented
326#3008C2×C1111yescharacteristic, complemented
327#2898C2×C1111yescharacteristic, complemented
328#2052C2×C1111yescharacteristic, complemented
329#2046C2×C1111yescharacteristic, complemented
330#2012C2×C1111yescharacteristic, complemented
331#2004C2×C1111yescharacteristic, complemented
332#1907C2×C1111yescharacteristic, complemented
333#1883C2×C1111yescharacteristic, complemented
334#1876C2×C1111yescharacteristic, complemented
335#1866C2×C1111yescharacteristic, complemented
336#1792C2×C1111yescharacteristic, complemented
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—22no—
341C23×C11—44no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—81no—
348C23×C11—81no—
349C23×C11—81no—
350C23×C11—81no—
351C23×C11—161no—
352C23×C11—161no—
353C23×C11H(5,𝔽2)11yescharacteristic
354Q8×C11—21no—
355Q8×C11—21no—
356Q8×C11—22no—
357Q8×C11—21no—
358Q8×C11—22no—
359Q8×C11—21no—
360Q8×C11—44no—
361Q8×C11—41no—
362Q8×C11—41no—
363Q8×C11#12012yes—
364Q8×C11#12112yes—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—22no—
370D4×C11—21no—
371D4×C11—21no—
372D4×C11—22no—
373D4×C11—21no—
374D4×C11—21no—
375D4×C11—44no—
376D4×C11—44no—
377D4×C11—44no—
378D4×C11—41no—
379D4×C11—41no—
380D4×C11—41no—
381D4×C11—41no—
382D4×C11—41no—
383D4×C11—41no—
384D4×C11—41no—
385D4×C11—41no—
386D4×C11—161no—
387D4×C11—161no—
388D4×C11#12012yes—
389D4×C11#12112yes—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—44no—
401C2×C4×C11—44no—
402C2×C4×C11—44no—
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—81no—
412C2×C4×C11—161no—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C2×#4111yescharacteristic
418C2×C4×C11H(5,𝔽2)11yescharacteristic
419C8×C11—21no—
420C8×C11—22no—
421C8×C11—21no—
422C8×C11—21no—
423C8×C11—21no—
424C8×C11—41no—
425C8×C11—41no—
426C8×C11—41no—
427C2×2−1+4C22×C1111yescharacteristic
428C2×H(5,𝔽2)C22×C1111yescharacteristic
429#577—24no—
430#577—24no—
431C2×#137—21no—
432C2×#137C22×C1111yescharacteristic
433C2×AGL(1,ℤ/8)—21no—
434C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
435C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
436C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
437C2×#135—21no—
438C2×#135C22×C1111yescharacteristic
439C22×SD16—21no—
440C22×SD16C22×C1111yescharacteristic
441C22×D8C22×C1111yescharacteristic
442C2×#131C22×C1111yescharacteristic
443C2×#131C22×C1111yescharacteristic, complemented
444#535C22×C1111yescharacteristic
445C2×#124C22×C1111yescharacteristic, complemented
446#520C22×C1111yescharacteristic, complemented
447#472—24no—
448#464—21no—
449#463—21no—
450#460—21no—
451#459—21no—
452#454—24no—
453#449—21no—
454#449—21no—
455#447—21no—
456#447—21no—
457C2×#108C22×C1111yescharacteristic, complemented
458#424C22×C1111yescharacteristic, complemented
459C2×#104C22×C1111yescharacteristic
460C2×#104C22×C1111yescharacteristic
461C2×#104C22×C1111yescharacteristic, complemented
462#419—21no—
463#419C22×C1111yescharacteristic, complemented
464#418C22×C1111yescharacteristic
465#417—21no—
466#417C22×C1111yescharacteristic
467#417C22×C1111yescharacteristic
468#416—21no—
469#416C22×C1111yescharacteristic
470C2×#103—21no—
471C2×#103C22×C1111yescharacteristic, complemented
472C2×#102C22×C1111yescharacteristic, complemented
473C2×#101C22×C1111yescharacteristic, complemented
474C2×#100C22×C1111yescharacteristic
475C2×#100C22×C1111yescharacteristic, complemented
476#408C22×C1111yescharacteristic
477#390C22×C1111yescharacteristic
478#343C22×C1111yescharacteristic, complemented
479#341C22×C1111yescharacteristic, complemented
480#339C22×C1111yescharacteristic, complemented
481#336C22×C1111yescharacteristic, complemented
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11—41no—
491C22×C11—42no—
492C22×C11—41no—
493C22×C11—41no—
494C22×C11—82no—
495C22×C11—82no—
496C22×C11—81no—
497C22×C11—81no—
498C22×C11—81no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11—161no—
502C22×C11—161no—
503C22×C11—164no—
504C22×C11#53411yescharacteristic
505C22×C11D4211yescharacteristic
506C22×C11#54611yescharacteristic
507C4×C11—22no—
508C4×C11—22no—
509C4×C11—41no—
510C4×C11—42no—
511C4×C11—41no—
512C4×C11—41no—
513C4×C11—81no—
514C4×C11—81no—
515C4×C11C2×#12011yescharacteristic
516C4×C11C2×#12111yescharacteristic
517C4×C11D4211yescharacteristic
518C4×C11#54611yescharacteristic
5192−1+4—22no—
5202−1+4—22no—
5212−1+4—41no—
5222−1+4D4×C1114yescomplemented
523H(5,𝔽2)—22no—
524H(5,𝔽2)—22no—
525H(5,𝔽2)—22no—
526H(5,𝔽2)—41no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—41no—
532C2×#41C23×C1111yescharacteristic
533C2×#41C23×C1111yescharacteristic
534C2×#41C23×C1111yescharacteristic
535C22×Q8—21no—
536C22×Q8—21no—
537C22×Q8C23×C1111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—41no—
541C22×D4C23×C1111yescharacteristic
542C22×D4C23×C1111yescharacteristic
543#137—28no—
544#137—22no—
545#137—22no—
546AGL(1,ℤ/8)—28no—
547AGL(1,ℤ/8)—22no—
548AGL(1,ℤ/8)—22no—
549AGL(1,ℤ/8)—22no—
550AGL(1,ℤ/8)—22no—
551AGL(1,ℤ/8)—22no—
552AGL(1,ℤ/8)D4×C1114yescomplemented
553#135—28no—
554#135—22no—
555#135—22no—
556C2×Q16—21no—
557C2×Q16D4×C1111yescharacteristic
558C2×SD16—28no—
559C2×SD16—21no—
560C2×SD16—22no—
561C2×SD16—21no—
562C2×SD16—22no—
563C2×SD16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16D4×C1111yescharacteristic
568C2×SD16D4×C1111yescharacteristic
569C2×D8—21no—
570C2×D8—22no—
571C2×D8—21no—
572C2×D8—21no—
573C2×D8—21no—
574C2×D8—21no—
575C2×D8—41no—
576C2×D8D4×C1111yescharacteristic
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—21no—
582C2×M16—21no—
583C2×M16C23×C1111yescharacteristic
584C2×M16C23×C1111yescharacteristic
585C2×M16C23×C1111yescharacteristic
586C2×M16C23×C1111yescharacteristic
587C22×C8—21no—
588C22×C8—21no—
589C22×C8C23×C1111yescharacteristic
590C22×C8C23×C1111yescharacteristic
591#127—21no—
592#124—22no—
593#124—21no—
594#124—41no—
595#121—21no—
596#121—21no—
597#120—41no—
598C4×Q8—21no—
599C4×D4—21no—
600C4×D4—41no—
601#117—21no—
602#117C23×C1111yescharacteristic
603C2×C4⋊C4—21no—
604C2×C4⋊C4C23×C1111yescharacteristic
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C42C23×C1111yescharacteristic
608#108—22no—
609C4⋊C8—21no—
610C4⋊C8—21no—
611#104—22no—
612#104—22no—
613#104—41no—
614#103—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103D4×C1111yescharacteristic
621#103D4×C1111yescharacteristic
622#102—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627#102—21no—
628#102D4×C1111yescharacteristic
629#102D4×C1111yescharacteristic
630#101—22no—
631#100—22no—
632#100—22no—
633C22⋊C8—21no—
634C22⋊C8—21no—
635C2×C11—21no—
636C2×C11—21no—
637C2×C11—42no—
638C2×C11—42no—
639C2×C11—81no—
640C2×C11—82no—
641C2×C11—161no—
642C2×C11#241011yescharacteristic
643C2×C11#328811yescharacteristic
644C2×C11#329011yescharacteristic
645C24—21no—
646C24—21no—
647C24—41no—
648#41—21no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—24no—
653#41—24no—
654#41—24no—
655#41—21no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—44no—
660#41—42no—
661#41—42no—
662#41—42no—
663#41—44no—
664#41—42no—
665#41—42no—
666#41C2×D4×C1112yes—
667#41C2×D4×C1112yes—
668#41C2×D4×C1112yes—
669#41C11×#4112yes—
670C2×Q8—21no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—41no—
678C2×Q8—42no—
679C2×Q8—42no—
680C2×Q8C2×D4×C1112yes—
681C2×Q8C2×D4×C1111yescharacteristic
682C2×Q8C2×D4×C1111yescharacteristic
683C2×Q8C2×D4×C1111yescharacteristic
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—24no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—42no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4C2×D4×C1112yes—
710C2×D4C2×D4×C1111yescharacteristic
711C2×D4C2×D4×C1111yescharacteristic
712C2×D4C2×D4×C1111yescharacteristic
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4C24×C1111yescharacteristic
724Q16—24no—
725Q16—22no—
726SD16—24no—
727SD16—24no—
728SD16—24no—
729SD16—22no—
730SD16—24no—
731SD16—22no—
732SD16—42no—
733SD16—42no—
734D8—24no—
735D8—22no—
736D8—42no—
737D8—42no—
738D8—42no—
739D8—42no—
740M16—24no—
741M16—21no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—42no—
749M16C2×D4×C1112yes—
750C2×C8—24no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—42no—
760C2×C8C2×D4×C1111yescharacteristic
761C2×C8C2×D4×C1111yescharacteristic
762C2×C8C2×D4×C1111yescharacteristic
763C2×C8C2×D4×C1111yescharacteristic
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—41no—
767C4⋊C4C2×D4×C1111yescharacteristic
768C4⋊C4C2×D4×C1111yescharacteristic
769C22⋊C4—21no—
770C22⋊C4—41no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—44no—
774C22⋊C4—82no—
775C42—21no—
776C42—21no—
777C42—21no—
778C42—41no—
779C11#2446011yescharacteristic, direct product factor, Sylow
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—44no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—161no—
795C23—161no—
796C23C11×H(5,𝔽2)11yescharacteristic
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—22no—
802Q8—21no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8C11×#12012yes—
807Q8C11×#12112yes—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—21no—
814D4—21no—
815D4—22no—
816D4—21no—
817D4—21no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—161no—
830D4—161no—
831D4C11×#12012yes—
832D4C11×#12112yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—161no—
856C2×C4C22×D4×C1111yescharacteristic
857C2×C4C22×D4×C1111yescharacteristic
858C2×C4C22×D4×C1111yescharacteristic
859C2×C4C22×D4×C1111yescharacteristic
860C2×C4C2×C11×#4111yescharacteristic
861C2×C4C11×H(5,𝔽2)11yescharacteristic
862C8—21no—
863C8—22no—
864C8—21no—
865C8—21no—
866C8—21no—
867C8—41no—
868C8—41no—
869C8—41no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—161no—
890C22—161no—
891C22—164no—
892C22C11×#53411yescharacteristic
893C22D42×C1111yescharacteristic
894C22C11×#54611yescharacteristic
895C4—22no—
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—81no—
902C4—81no—
903C4C2×C11×#12011yescharacteristic
904C4C2×C11×#12111yescharacteristic
905C4D42×C1111yescharacteristic
906C4C11×#54611yescharacteristic
907C2—21no—
908C2—21no—
909C2—42no—
910C2—42no—
911C2—81no—
912C2—82no—
913C2—161no—
914C2C11×#241011yescharacteristic
915C2C11×#328811yescharacteristic
916C2C11×#329011yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#577C2semidirect
2. C2×C11×#472C2semidirect
3. C11×#3045C2semidirect
4. C2×C11×#454C2semidirect
5. C11×#3008C2semidirect
6. C11×#2898C2semidirect
7. C11×#2052C2semidirect
8. C11×#2046C2semidirect
9. C11×#2012C2semidirect
10. C11×#2004C2semidirect
11. C11×#1907C2semidirect
12. C11×#1883C2semidirect
13. C11×#1876C2semidirect
14. C11×#1866C2semidirect
15. C11×#1792C2semidirect
25. C2×C11×AGL(1,ℤ/8)C22semidirect
32. C2×C11×#131C22semidirect
34. C2×C11×#124C22semidirect
35. C11×#520C22semidirect
46. C2×C11×#108C22semidirect
47. C11×#424C22semidirect
50. C2×C11×#104C22semidirect
52. C11×#419C22semidirect
60. C2×C11×#103C22semidirect
61. C2×C11×#102C22semidirect
62. C2×C11×#101C22semidirect
64. C2×C11×#100C22semidirect
67. C11×#343C22semidirect
68. C11×#341C22semidirect
69. C11×#339C22semidirect
70. C11×#336C22semidirect
74. C11×2−1+4D4semidirect
104. C11×AGL(1,ℤ/8)D4semidirect
187. #24460C11direct (N × H)
322. C2×#577C2×C11semidirect
323. C2×#472C2×C11semidirect
324. #3045C2×C11semidirect
325. C2×#454C2×C11semidirect
326. #3008C2×C11semidirect
327. #2898C2×C11semidirect
328. #2052C2×C11semidirect
329. #2046C2×C11semidirect
330. #2012C2×C11semidirect
331. #2004C2×C11semidirect
332. #1907C2×C11semidirect
333. #1883C2×C11semidirect
334. #1876C2×C11semidirect
335. #1866C2×C11semidirect
336. #1792C2×C11semidirect
436. C2×AGL(1,ℤ/8)C22×C11semidirect
443. C2×#131C22×C11semidirect
445. C2×#124C22×C11semidirect
446. #520C22×C11semidirect
457. C2×#108C22×C11semidirect
458. #424C22×C11semidirect
461. C2×#104C22×C11semidirect
463. #419C22×C11semidirect
471. C2×#103C22×C11semidirect
472. C2×#102C22×C11semidirect
473. C2×#101C22×C11semidirect
475. C2×#100C22×C11semidirect
478. #343C22×C11semidirect
479. #341C22×C11semidirect
480. #339C22×C11semidirect
481. #336C22×C11semidirect
522. 2−1+4D4×C11semidirect
552. AGL(1,ℤ/8)D4×C11semidirect
779. C11#24460direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5772
C2×C11×#4722
C11×#30452
C2×C11×#4542
C11×#30082
C11×#28982
C11×#20522
C11×#20462
C11×#20122
C11×#20042
C11×#19072
C11×#18832
C11×#18762
C11×#18662
C11×#17922
#2446011