Finite Group Databasebeta

← C11×#24457 #14601650

Subgroups — C11×#24457 #14601650

Order 2816.

1376 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#577C211yesmaximal, characteristic, complemented
2C2×C11×#471C211yesmaximal, characteristic, complemented
3C11×#3045C211yesmaximal, characteristic, complemented
4C2×C11×#453C211yesmaximal, characteristic, complemented
5C11×#3010C211yesmaximal, characteristic, complemented
6C11×#2897C211yesmaximal, characteristic, complemented
7C11×#2051C211yesmaximal, characteristic, complemented
8C11×#2046C211yesmaximal, characteristic, complemented
9C11×#2014C211yesmaximal, characteristic, complemented
10C11×#2002C211yesmaximal, characteristic, complemented
11C11×#1907C211yesmaximal, characteristic, complemented
12C11×#1882C211yesmaximal, characteristic, complemented
13C11×#1876C211yesmaximal, characteristic, complemented
14C11×#1866C211yesmaximal, characteristic, complemented
15C11×#1793C211yesmaximal, 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
26C2×C11×#135—21no—
27C2×C11×#135C2211yescharacteristic
28C22×C11×SD16—21no—
29C22×C11×SD16C2211yescharacteristic
30C22×C11×SD16C2211yescharacteristic, complemented
31C2×C11×#131C2211yescharacteristic
32C2×C11×#131C2211yescharacteristic
33C11×#535C2211yescharacteristic, complemented
34C2×C11×#127C2211yescharacteristic
35C11×#520C2211yescharacteristic
36C11×#471—24no—
37C11×#464—21no—
38C11×#463—21no—
39C11×#460—21no—
40C11×#459—21no—
41C11×#453—24no—
42C11×#449—21no—
43C11×#449—21no—
44C11×#448—21no—
45C11×#448—21no—
46C2×C11×#108C2211yescharacteristic, complemented
47C11×#424C2211yescharacteristic, complemented
48C2×C11×#104C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic, complemented
51C11×#419C2211yescharacteristic, complemented
52C11×#418—21no—
53C11×#418C2211yescharacteristic
54C11×#417—21no—
55C11×#417C2211yescharacteristic
56C11×#417C2211yescharacteristic, complemented
57C11×#416—21no—
58C11×#416C2211yescharacteristic
59C2×C11×#102—21no—
60C2×C11×#102C2211yescharacteristic
61C2×C11×#102C2211yescharacteristic, complemented
62C2×C11×#101C2211yescharacteristic, complemented
63C2×C11×#100C2211yescharacteristic
64C2×C11×#100C2211yescharacteristic, complemented
65C11×#408C2211yescharacteristic, complemented
66C11×#391C2211yescharacteristic, complemented
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—22no—
74C11×2−1+4—41no—
75C11×H(5,𝔽2)—22no—
76C11×H(5,𝔽2)—22no—
77C11×H(5,𝔽2)—41no—
78C11×H(5,𝔽2)D414yescomplemented
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×C11—41no—
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2311yescharacteristic
96C11×#137—28no—
97C11×#137—22no—
98C11×#137D414yescomplemented
99C11×AGL(1,ℤ/8)—28no—
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)—22no—
105C11×AGL(1,ℤ/8)—22no—
106C11×#135—28no—
107C11×#135—22no—
108C11×#135—22no—
109C2×C11×Q16—21no—
110C2×C11×Q16D411yescharacteristic, complemented
111C2×C11×SD16—28no—
112C2×C11×SD16—21no—
113C2×C11×SD16—22no—
114C2×C11×SD16—21no—
115C2×C11×SD16—22no—
116C2×C11×SD16—22no—
117C2×C11×SD16—21no—
118C2×C11×SD16—21no—
119C2×C11×SD16—21no—
120C2×C11×SD16—21no—
121C2×C11×SD16—21no—
122C2×C11×SD16—21no—
123C2×C11×SD16—41no—
124C2×C11×SD16D411yescharacteristic, complemented
125C2×C11×SD16D411yescharacteristic, complemented
126C2×C11×D8—21no—
127C2×C11×D8—21no—
128C2×C11×D8—21no—
129C2×C11×D8D411yescharacteristic, complemented
130C11×#131—22no—
131C11×#131—22no—
132C11×#131—22no—
133C11×#131—41no—
134C2×C11×M16—21no—
135C2×C11×M16—21no—
136C2×C11×M16C2311yescharacteristic
137C2×C11×M16C2311yescharacteristic
138C2×C11×M16C2311yescharacteristic
139C2×C11×M16C2311yescharacteristic
140C22×C8×C11—21no—
141C22×C8×C11—21no—
142C22×C8×C11C2311yescharacteristic
143C22×C8×C11C2311yescharacteristic
144C11×#127—22no—
145C11×#127—21no—
146C11×#127—41no—
147C11×#124—21no—
148C11×#121—21no—
149C11×#121—21no—
150C11×#120—41no—
151C4×Q8×C11—21no—
152C4×D4×C11—21no—
153C4×D4×C11—41no—
154C11×#117—21no—
155C11×#117C2311yescharacteristic
156C2×C11×C4⋊C4—21no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159C11×#108—22no—
160C11×C4⋊C8—21no—
161C11×C4⋊C8—21no—
162C11×#104—22no—
163C11×#104—22no—
164C11×#104—41no—
165C11×#103—21no—
166C11×#103—21no—
167C11×#103—21no—
168C11×#103—21no—
169C11×#103D411yescharacteristic, complemented
170C11×#103D411yescharacteristic, complemented
171C11×#102—21no—
172C11×#102—21no—
173C11×#102—21no—
174C11×#102—21no—
175C11×#102—21no—
176C11×#102—21no—
177C11×#102—21no—
178C11×#102—21no—
179C11×#102D411yescharacteristic, complemented
180C11×#102D411yescharacteristic, complemented
181C11×#101—22no—
182C11×#100—22no—
183C11×#100—22no—
184C11×C22⋊C8—21no—
185C11×C22⋊C8—21no—
186C11×#95—41no—
187#24457C1111yesmaximal, 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—42no—
203C11×#41—44no—
204C11×#41—42no—
205C11×#41—42no—
206C11×#41—42no—
207C11×#41—44no—
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—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11—21no—
218C2×Q8×C11—21no—
219C2×Q8×C11—41no—
220C2×Q8×C11—42no—
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—24no—
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—21no—
243C2×D4×C11—42no—
244C2×D4×C11—42no—
245C2×D4×C11—41no—
246C2×D4×C11—41no—
247C2×D4×C11—41no—
248C2×D4×C11—41no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—41no—
252C2×D4×C11—44no—
253C2×D4×C11—82no—
254C2×D4×C11—82no—
255C2×D4×C11C2×D412yes—
256C2×D4×C11C2×D411yescharacteristic
257C2×D4×C11C2×D411yescharacteristic
258C2×D4×C11C2×D411yescharacteristic
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—41no—
266C22×C4×C11—41no—
267C22×C4×C11—41no—
268C22×C4×C11—41no—
269C22×C4×C11C2411yescharacteristic
270C11×Q16—24no—
271C11×Q16—22no—
272C11×SD16—24no—
273C11×SD16—24no—
274C11×SD16—24no—
275C11×SD16—22no—
276C11×SD16—22no—
277C11×SD16—24no—
278C11×SD16—42no—
279C11×SD16—42no—
280C11×SD16—42no—
281C11×SD16—42no—
282C11×D8—24no—
283C11×D8—22no—
284C11×D8—42no—
285C11×D8—42no—
286C11×M16—24no—
287C11×M16—21no—
288C11×M16—21no—
289C11×M16—21no—
290C11×M16—21no—
291C11×M16—21no—
292C11×M16—21no—
293C11×M16—21no—
294C11×M16—42no—
295C11×M16C2×D412yes—
296C2×C8×C11—24no—
297C2×C8×C11—21no—
298C2×C8×C11—21no—
299C2×C8×C11—21no—
300C2×C8×C11—21no—
301C2×C8×C11—21no—
302C2×C8×C11—21no—
303C2×C8×C11—21no—
304C2×C8×C11—21no—
305C2×C8×C11—42no—
306C2×C8×C11C2×D411yescharacteristic
307C2×C8×C11C2×D411yescharacteristic
308C2×C8×C11C2×D411yescharacteristic
309C2×C8×C11C2×D411yescharacteristic
310C11×C4⋊C4—21no—
311C11×C4⋊C4—21no—
312C11×C4⋊C4—41no—
313C11×C4⋊C4C2×D411yescharacteristic
314C11×C4⋊C4C2×D411yescharacteristic
315C11×C22⋊C4—21no—
316C11×C22⋊C4—41no—
317C11×C22⋊C4—41no—
318C11×C22⋊C4—41no—
319C42×C11—21no—
320C42×C11—21no—
321C42×C11—21no—
322C42×C11—41no—
323C2×#577C2×C1111yescharacteristic, complemented
324C2×#471C2×C1111yescharacteristic, complemented
325#3045C2×C1111yescharacteristic, complemented
326C2×#453C2×C1111yescharacteristic, complemented
327#3010C2×C1111yescharacteristic, complemented
328#2897C2×C1111yescharacteristic, complemented
329#2051C2×C1111yescharacteristic, complemented
330#2046C2×C1111yescharacteristic, complemented
331#2014C2×C1111yescharacteristic, complemented
332#2002C2×C1111yescharacteristic, complemented
333#1907C2×C1111yescharacteristic, complemented
334#1882C2×C1111yescharacteristic, complemented
335#1876C2×C1111yescharacteristic, complemented
336#1866C2×C1111yescharacteristic, complemented
337#1793C2×C1111yescharacteristic, complemented
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—22no—
342C23×C11—44no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—81no—
349C23×C11—81no—
350C23×C11—81no—
351C23×C11—81no—
352C23×C11—161no—
353C23×C11—161no—
354C23×C11H(5,𝔽2)11yescharacteristic
355Q8×C11—21no—
356Q8×C11—21no—
357Q8×C11—22no—
358Q8×C11—21no—
359Q8×C11—22no—
360Q8×C11—21no—
361Q8×C11—44no—
362Q8×C11—41no—
363Q8×C11—41no—
364Q8×C11#12012yes—
365Q8×C11#12112yes—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—22no—
369D4×C11—22no—
370D4×C11—21no—
371D4×C11—22no—
372D4×C11—22no—
373D4×C11—21no—
374D4×C11—21no—
375D4×C11—21no—
376D4×C11—44no—
377D4×C11—44no—
378D4×C11—44no—
379D4×C11—41no—
380D4×C11—41no—
381D4×C11—41no—
382D4×C11—41no—
383D4×C11—41no—
384D4×C11—41no—
385D4×C11—41no—
386D4×C11—41no—
387D4×C11—88no—
388D4×C11—161no—
389D4×C11—161no—
390D4×C11#12012yes—
391D4×C11#12112yes—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—22no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11—41no—
406C2×C4×C11—44no—
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—81no—
414C2×C4×C11—161no—
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C2×#4111yescharacteristic
420C2×C4×C11H(5,𝔽2)11yescharacteristic
421C8×C11—21no—
422C8×C11—22no—
423C8×C11—21no—
424C8×C11—21no—
425C8×C11—21no—
426C8×C11—41no—
427C8×C11—41no—
428C8×C11—41no—
429C2×2−1+4C22×C1111yescharacteristic
430C2×H(5,𝔽2)C22×C1111yescharacteristic
431#577—24no—
432#577—24no—
433C2×#137—21no—
434C2×#137C22×C1111yescharacteristic
435C2×AGL(1,ℤ/8)—21no—
436C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
437C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
438C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
439C2×#135—21no—
440C2×#135C22×C1111yescharacteristic
441C22×SD16—21no—
442C22×SD16C22×C1111yescharacteristic
443C22×SD16C22×C1111yescharacteristic, complemented
444C2×#131C22×C1111yescharacteristic
445C2×#131C22×C1111yescharacteristic
446#535C22×C1111yescharacteristic, complemented
447C2×#127C22×C1111yescharacteristic
448#520C22×C1111yescharacteristic
449#471—24no—
450#464—21no—
451#463—21no—
452#460—21no—
453#459—21no—
454#453—24no—
455#449—21no—
456#449—21no—
457#448—21no—
458#448—21no—
459C2×#108C22×C1111yescharacteristic, complemented
460#424C22×C1111yescharacteristic, complemented
461C2×#104C22×C1111yescharacteristic
462C2×#104C22×C1111yescharacteristic
463C2×#104C22×C1111yescharacteristic, complemented
464#419C22×C1111yescharacteristic, complemented
465#418—21no—
466#418C22×C1111yescharacteristic
467#417—21no—
468#417C22×C1111yescharacteristic
469#417C22×C1111yescharacteristic, complemented
470#416—21no—
471#416C22×C1111yescharacteristic
472C2×#102—21no—
473C2×#102C22×C1111yescharacteristic
474C2×#102C22×C1111yescharacteristic, complemented
475C2×#101C22×C1111yescharacteristic, complemented
476C2×#100C22×C1111yescharacteristic
477C2×#100C22×C1111yescharacteristic, complemented
478#408C22×C1111yescharacteristic, complemented
479#391C22×C1111yescharacteristic, complemented
480#343C22×C1111yescharacteristic, complemented
481#341C22×C1111yescharacteristic, complemented
482#339C22×C1111yescharacteristic, complemented
483#336C22×C1111yescharacteristic, complemented
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—22no—
487C22×C11—22no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11—41no—
491C22×C11—41no—
492C22×C11—41no—
493C22×C11—42no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—82no—
497C22×C11—82no—
498C22×C11—81no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11—81no—
502C22×C11—81no—
503C22×C11—161no—
504C22×C11—161no—
505C22×C11—164no—
506C22×C11#53411yescharacteristic
507C22×C11D4211yescharacteristic
508C22×C11#54611yescharacteristic
509C4×C11—22no—
510C4×C11—22no—
511C4×C11—42no—
512C4×C11—41no—
513C4×C11—42no—
514C4×C11—41no—
515C4×C11—41no—
516C4×C11—81no—
517C4×C11C2×#12011yescharacteristic
518C4×C11C2×#12111yescharacteristic
519C4×C11D4211yescharacteristic
520C4×C11#54611yescharacteristic
5212−1+4—22no—
5222−1+4—22no—
5232−1+4—22no—
5242−1+4—41no—
525H(5,𝔽2)—22no—
526H(5,𝔽2)—22no—
527H(5,𝔽2)—41no—
528H(5,𝔽2)D4×C1114yescomplemented
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—41no—
534C2×#41C23×C1111yescharacteristic
535C2×#41C23×C1111yescharacteristic
536C2×#41C23×C1111yescharacteristic
537C22×Q8—21no—
538C22×Q8—21no—
539C22×Q8C23×C1111yescharacteristic
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4C23×C1111yescharacteristic
545C22×D4C23×C1111yescharacteristic
546#137—28no—
547#137—22no—
548#137D4×C1114yescomplemented
549AGL(1,ℤ/8)—28no—
550AGL(1,ℤ/8)—22no—
551AGL(1,ℤ/8)—22no—
552AGL(1,ℤ/8)—22no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—22no—
556#135—28no—
557#135—22no—
558#135—22no—
559C2×Q16—21no—
560C2×Q16D4×C1111yescharacteristic, complemented
561C2×SD16—28no—
562C2×SD16—21no—
563C2×SD16—22no—
564C2×SD16—21no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—41no—
574C2×SD16D4×C1111yescharacteristic, complemented
575C2×SD16D4×C1111yescharacteristic, complemented
576C2×D8—21no—
577C2×D8—21no—
578C2×D8—21no—
579C2×D8D4×C1111yescharacteristic, complemented
580#131—22no—
581#131—22no—
582#131—22no—
583#131—41no—
584C2×M16—21no—
585C2×M16—21no—
586C2×M16C23×C1111yescharacteristic
587C2×M16C23×C1111yescharacteristic
588C2×M16C23×C1111yescharacteristic
589C2×M16C23×C1111yescharacteristic
590C22×C8—21no—
591C22×C8—21no—
592C22×C8C23×C1111yescharacteristic
593C22×C8C23×C1111yescharacteristic
594#127—22no—
595#127—21no—
596#127—41no—
597#124—21no—
598#121—21no—
599#121—21no—
600#120—41no—
601C4×Q8—21no—
602C4×D4—21no—
603C4×D4—41no—
604#117—21no—
605#117C23×C1111yescharacteristic
606C2×C4⋊C4—21no—
607C2×C4⋊C4C23×C1111yescharacteristic
608C2×C42C23×C1111yescharacteristic
609#108—22no—
610C4⋊C8—21no—
611C4⋊C8—21no—
612#104—22no—
613#104—22no—
614#104—41no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103D4×C1111yescharacteristic, complemented
620#103D4×C1111yescharacteristic, complemented
621#102—21no—
622#102—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627#102—21no—
628#102—21no—
629#102D4×C1111yescharacteristic, complemented
630#102D4×C1111yescharacteristic, complemented
631#101—22no—
632#100—22no—
633#100—22no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636#95—41no—
637C2×C11—21no—
638C2×C11—21no—
639C2×C11—42no—
640C2×C11—42no—
641C2×C11—81no—
642C2×C11—82no—
643C2×C11—161no—
644C2×C11#241011yescharacteristic
645C2×C11#328811yescharacteristic
646C2×C11#329111yescharacteristic
647C24—21no—
648C24—21no—
649C24—41no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—24no—
655#41—24no—
656#41—24no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—42no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41—42no—
666#41—44no—
667#41—42no—
668#41C2×D4×C1112yes—
669#41C2×D4×C1112yes—
670#41C2×D4×C1112yes—
671#41C11×#4112yes—
672C2×Q8—21no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8C2×D4×C1112yes—
683C2×Q8C2×D4×C1111yescharacteristic
684C2×Q8C2×D4×C1111yescharacteristic
685C2×Q8C2×D4×C1111yescharacteristic
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—24no—
689C2×D4—24no—
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—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—41no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—41no—
711C2×D4—44no—
712C2×D4—82no—
713C2×D4—82no—
714C2×D4C2×D4×C1112yes—
715C2×D4C2×D4×C1111yescharacteristic
716C2×D4C2×D4×C1111yescharacteristic
717C2×D4C2×D4×C1111yescharacteristic
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—41no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4C24×C1111yescharacteristic
729Q16—24no—
730Q16—22no—
731SD16—24no—
732SD16—24no—
733SD16—24no—
734SD16—22no—
735SD16—22no—
736SD16—24no—
737SD16—42no—
738SD16—42no—
739SD16—42no—
740SD16—42no—
741D8—24no—
742D8—22no—
743D8—42no—
744D8—42no—
745M16—24no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—21no—
753M16—42no—
754M16C2×D4×C1112yes—
755C2×C8—24no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—42no—
765C2×C8C2×D4×C1111yescharacteristic
766C2×C8C2×D4×C1111yescharacteristic
767C2×C8C2×D4×C1111yescharacteristic
768C2×C8C2×D4×C1111yescharacteristic
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—41no—
772C4⋊C4C2×D4×C1111yescharacteristic
773C4⋊C4C2×D4×C1111yescharacteristic
774C22⋊C4—21no—
775C22⋊C4—41no—
776C22⋊C4—41no—
777C22⋊C4—41no—
778C42—21no—
779C42—21no—
780C42—21no—
781C42—41no—
782C11#2445711yescharacteristic, direct product factor, Sylow
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—81no—
797C23—161no—
798C23—161no—
799C23C11×H(5,𝔽2)11yescharacteristic
800Q8—21no—
801Q8—21no—
802Q8—22no—
803Q8—21no—
804Q8—22no—
805Q8—21no—
806Q8—44no—
807Q8—41no—
808Q8—41no—
809Q8C11×#12012yes—
810Q8C11×#12112yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—21no—
816D4—22no—
817D4—22no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—88no—
833D4—161no—
834D4—161no—
835D4C11×#12012yes—
836D4C11×#12112yes—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—41no—
851C2×C4—44no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—81no—
859C2×C4—161no—
860C2×C4C22×D4×C1111yescharacteristic
861C2×C4C22×D4×C1111yescharacteristic
862C2×C4C22×D4×C1111yescharacteristic
863C2×C4C22×D4×C1111yescharacteristic
864C2×C4C2×C11×#4111yescharacteristic
865C2×C4C11×H(5,𝔽2)11yescharacteristic
866C8—21no—
867C8—22no—
868C8—21no—
869C8—21no—
870C8—21no—
871C8—41no—
872C8—41no—
873C8—41no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—22no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—82no—
887C22—82no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—161no—
894C22—161no—
895C22—164no—
896C22C11×#53411yescharacteristic
897C22D42×C1111yescharacteristic
898C22C11×#54611yescharacteristic
899C4—22no—
900C4—22no—
901C4—42no—
902C4—41no—
903C4—42no—
904C4—41no—
905C4—41no—
906C4—81no—
907C4C2×C11×#12011yescharacteristic
908C4C2×C11×#12111yescharacteristic
909C4D42×C1111yescharacteristic
910C4C11×#54611yescharacteristic
911C2—21no—
912C2—21no—
913C2—42no—
914C2—42no—
915C2—81no—
916C2—82no—
917C2—161no—
918C2C11×#241011yescharacteristic
919C2C11×#328811yescharacteristic
920C2C11×#329111yescharacteristic
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×#471C2semidirect
3. C11×#3045C2semidirect
4. C2×C11×#453C2semidirect
5. C11×#3010C2semidirect
6. C11×#2897C2semidirect
7. C11×#2051C2semidirect
8. C11×#2046C2semidirect
9. C11×#2014C2semidirect
10. C11×#2002C2semidirect
11. C11×#1907C2semidirect
12. C11×#1882C2semidirect
13. C11×#1876C2semidirect
14. C11×#1866C2semidirect
15. C11×#1793C2semidirect
30. C22×C11×SD16C22semidirect
33. C11×#535C22semidirect
46. C2×C11×#108C22semidirect
47. C11×#424C22semidirect
50. C2×C11×#104C22semidirect
51. C11×#419C22semidirect
56. C11×#417C22semidirect
61. C2×C11×#102C22semidirect
62. C2×C11×#101C22semidirect
64. C2×C11×#100C22semidirect
65. C11×#408C22semidirect
66. C11×#391C22semidirect
67. C11×#343C22semidirect
68. C11×#341C22semidirect
69. C11×#339C22semidirect
70. C11×#336C22semidirect
78. C11×H(5,𝔽2)D4semidirect
98. C11×#137D4semidirect
110. C2×C11×Q16D4semidirect
124. C2×C11×SD16D4semidirect
125. C2×C11×SD16D4semidirect
129. C2×C11×D8D4semidirect
169. C11×#103D4semidirect
170. C11×#103D4semidirect
179. C11×#102D4semidirect
180. C11×#102D4semidirect
187. #24457C11direct (N × H)
323. C2×#577C2×C11semidirect
324. C2×#471C2×C11semidirect
325. #3045C2×C11semidirect
326. C2×#453C2×C11semidirect
327. #3010C2×C11semidirect
328. #2897C2×C11semidirect
329. #2051C2×C11semidirect
330. #2046C2×C11semidirect
331. #2014C2×C11semidirect
332. #2002C2×C11semidirect
333. #1907C2×C11semidirect
334. #1882C2×C11semidirect
335. #1876C2×C11semidirect
336. #1866C2×C11semidirect
337. #1793C2×C11semidirect
443. C22×SD16C22×C11semidirect
446. #535C22×C11semidirect
459. C2×#108C22×C11semidirect
460. #424C22×C11semidirect
463. C2×#104C22×C11semidirect
464. #419C22×C11semidirect
469. #417C22×C11semidirect
474. C2×#102C22×C11semidirect
475. C2×#101C22×C11semidirect
477. C2×#100C22×C11semidirect
478. #408C22×C11semidirect
479. #391C22×C11semidirect
480. #343C22×C11semidirect
481. #341C22×C11semidirect
482. #339C22×C11semidirect
483. #336C22×C11semidirect
528. H(5,𝔽2)D4×C11semidirect
548. #137D4×C11semidirect
560. C2×Q16D4×C11semidirect
574. C2×SD16D4×C11semidirect
575. C2×SD16D4×C11semidirect
579. C2×D8D4×C11semidirect
619. #103D4×C11semidirect
620. #103D4×C11semidirect
629. #102D4×C11semidirect
630. #102D4×C11semidirect
782. C11#24457direct (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×#4712
C11×#30452
C2×C11×#4532
C11×#30102
C11×#28972
C11×#20512
C11×#20462
C11×#20142
C11×#20022
C11×#19072
C11×#18822
C11×#18762
C11×#18662
C11×#17932
#2445711