Finite Group Databasebeta

← C11×#24456 #14601649

Subgroups — C11×#24456 #14601649

Order 2816.

1410 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#576C211yesmaximal, characteristic, complemented
2C2×C11×#472C211yesmaximal, characteristic, complemented
3C11×#3045C211yesmaximal, characteristic, complemented
4C2×C11×#453C211yesmaximal, characteristic, complemented
5C11×#3008C211yesmaximal, characteristic, complemented
6C11×#2897C211yesmaximal, characteristic, complemented
7C11×#2051C211yesmaximal, characteristic, complemented
8C11×#2045C211yesmaximal, characteristic, complemented
9C11×#2011C211yesmaximal, characteristic, complemented
10C11×#2002C211yesmaximal, characteristic, complemented
11C11×#1907C211yesmaximal, characteristic, complemented
12C11×#1883C211yesmaximal, characteristic, complemented
13C11×#1876C211yesmaximal, characteristic, complemented
14C11×#1866C211yesmaximal, characteristic, complemented
15C11×#1792C211yesmaximal, characteristic, complemented
16C2×C11×H(5,𝔽2)C2211yescharacteristic
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C11×#576—24no—
19C11×#576—24no—
20C2×C11×AGL(1,ℤ/8)—21no—
21C2×C11×AGL(1,ℤ/8)—21no—
22C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
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×D8—21no—
29C22×C11×D8C2211yescharacteristic
30C22×C11×D8C2211yescharacteristic, complemented
31C2×C11×#131C2211yescharacteristic
32C2×C11×#131C2211yescharacteristic, complemented
33C11×#535C2211yescharacteristic, complemented
34C2×C11×#127C2211yescharacteristic, complemented
35C11×#520C2211yescharacteristic, complemented
36C11×#472—24no—
37C11×#464—21no—
38C11×#463—21no—
39C11×#460—21no—
40C11×#459—21no—
41C11×#453—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, complemented
50C2×C11×#104C2211yescharacteristic, complemented
51C11×#418—21no—
52C11×#418C2211yescharacteristic, complemented
53C11×#418C2211yescharacteristic, complemented
54C11×#417—21no—
55C11×#417C2211yescharacteristic
56C11×#417C2211yescharacteristic, complemented
57C11×#416—21no—
58C11×#416C2211yescharacteristic
59C2×C11×#102—21no—
60C2×C11×#102C2211yescharacteristic, complemented
61C2×C11×#102C2211yescharacteristic, complemented
62C2×C11×#100C2211yescharacteristic, complemented
63C2×C11×#100C2211yescharacteristic, complemented
64C2×C11×#100C2211yescharacteristic, complemented
65C11×#408C2211yescharacteristic, complemented
66C11×#390C2211yescharacteristic, complemented
67C11×#343C2211yescharacteristic, complemented
68C11×#341C2211yescharacteristic, complemented
69C11×#339C2211yescharacteristic, complemented
70C11×#336C2211yescharacteristic, complemented
71C11×H(5,𝔽2)—22no—
72C11×H(5,𝔽2)—22no—
73C11×H(5,𝔽2)—22no—
74C11×H(5,𝔽2)—22no—
75C11×H(5,𝔽2)—22no—
76C11×H(5,𝔽2)—41no—
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×#41C2311yescharacteristic
84C2×C11×#41C2311yescharacteristic
85C2×C11×#41C2311yescharacteristic
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—41no—
91C22×D4×C11—41no—
92C22×D4×C11—41no—
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2311yescharacteristic
96C11×AGL(1,ℤ/8)—28no—
97C11×AGL(1,ℤ/8)—28no—
98C11×AGL(1,ℤ/8)—22no—
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)—22no—
105C11×AGL(1,ℤ/8)D414yescomplemented
106C11×#135—28no—
107C11×#135—22no—
108C11×#135—22no—
109C2×C11×Q16D411yescharacteristic, complemented
110C2×C11×SD16—21no—
111C2×C11×SD16—21no—
112C2×C11×SD16—21no—
113C2×C11×SD16—21no—
114C2×C11×SD16D411yescharacteristic, complemented
115C2×C11×SD16D411yescharacteristic, complemented
116C2×C11×D8—28no—
117C2×C11×D8—21no—
118C2×C11×D8—21no—
119C2×C11×D8—22no—
120C2×C11×D8—22no—
121C2×C11×D8—22no—
122C2×C11×D8—21no—
123C2×C11×D8—21no—
124C2×C11×D8—21no—
125C2×C11×D8—21no—
126C2×C11×D8—21no—
127C2×C11×D8—21no—
128C2×C11×D8—41no—
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×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×#103D411yescharacteristic, complemented
169C11×#103D411yescharacteristic, complemented
170C11×#102—21no—
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×#102—21no—
180C11×#102D411yescharacteristic, complemented
181C11×#102D411yescharacteristic, complemented
182C11×#100—22no—
183C11×#100—22no—
184C11×#100—22no—
185C11×C22⋊C8—21no—
186C11×C22⋊C8—21no—
187#24456C1111yesmaximal, characteristic, direct product factor, Sylow
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—41no—
192C24×C11—41no—
193C11×#41—21no—
194C11×#41—21no—
195C11×#41—21no—
196C11×#41—21no—
197C11×#41—24no—
198C11×#41—24no—
199C11×#41—24no—
200C11×#41—21no—
201C11×#41—21no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41—42no—
205C11×#41—42no—
206C11×#41—42no—
207C11×#41—42no—
208C11×#41—42no—
209C11×#41C2×D412yes—
210C11×#41C2×D412yes—
211C11×#41C2×D412yes—
212C11×#41#4112yes—
213C2×Q8×C11C2×D411yescharacteristic
214C2×Q8×C11C2×D411yescharacteristic
215C2×Q8×C11C2×D411yescharacteristic
216C2×D4×C11—21no—
217C2×D4×C11—21no—
218C2×D4×C11—24no—
219C2×D4×C11—24no—
220C2×D4×C11—24no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
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—42no—
239C2×D4×C11—42no—
240C2×D4×C11—42no—
241C2×D4×C11—41no—
242C2×D4×C11—41no—
243C2×D4×C11—41no—
244C2×D4×C11—41no—
245C2×D4×C11—41no—
246C2×D4×C11—41no—
247C2×D4×C11—44no—
248C2×D4×C11—42no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—44no—
252C2×D4×C11—42no—
253C2×D4×C11—44no—
254C2×D4×C11—82no—
255C2×D4×C11—82no—
256C2×D4×C11C2×D412yes—
257C2×D4×C11C2×D412yes—
258C2×D4×C11C2×D411yescharacteristic
259C2×D4×C11C2×D411yescharacteristic
260C2×D4×C11C2×D411yescharacteristic
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—41no—
267C22×C4×C11—41no—
268C22×C4×C11—41no—
269C22×C4×C11C2411yescharacteristic
270C11×Q16—22no—
271C11×SD16—24no—
272C11×SD16—24no—
273C11×SD16—22no—
274C11×SD16—22no—
275C11×SD16—42no—
276C11×SD16—42no—
277C11×D8—24no—
278C11×D8—24no—
279C11×D8—24no—
280C11×D8—22no—
281C11×D8—24no—
282C11×D8—42no—
283C11×D8—42no—
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—
319C11×C22⋊C4—82no—
320C42×C11—21no—
321C42×C11—21no—
322C42×C11—21no—
323C42×C11—41no—
324C2×#576C2×C1111yescharacteristic, complemented
325C2×#472C2×C1111yescharacteristic, complemented
326#3045C2×C1111yescharacteristic, complemented
327C2×#453C2×C1111yescharacteristic, complemented
328#3008C2×C1111yescharacteristic, complemented
329#2897C2×C1111yescharacteristic, complemented
330#2051C2×C1111yescharacteristic, complemented
331#2045C2×C1111yescharacteristic, complemented
332#2011C2×C1111yescharacteristic, complemented
333#2002C2×C1111yescharacteristic, complemented
334#1907C2×C1111yescharacteristic, complemented
335#1883C2×C1111yescharacteristic, complemented
336#1876C2×C1111yescharacteristic, complemented
337#1866C2×C1111yescharacteristic, complemented
338#1792C2×C1111yescharacteristic, complemented
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—81no—
354C23×C11—81no—
355C23×C11—81no—
356C23×C11—81no—
357C23×C11—81no—
358C23×C11—81no—
359C23×C11—161no—
360C23×C11—161no—
361C23×C11—161no—
362C23×C11—161no—
363C23×C11H(5,𝔽2)11yescharacteristic
364Q8×C11—21no—
365Q8×C11—21no—
366Q8×C11—21no—
367Q8×C11—21no—
368Q8×C11#12012yes—
369Q8×C11#12112yes—
370D4×C11—22no—
371D4×C11—22no—
372D4×C11—22no—
373D4×C11—22no—
374D4×C11—22no—
375D4×C11—22no—
376D4×C11—21no—
377D4×C11—22no—
378D4×C11—21no—
379D4×C11—22no—
380D4×C11—21no—
381D4×C11—21no—
382D4×C11—44no—
383D4×C11—44no—
384D4×C11—44no—
385D4×C11—44no—
386D4×C11—41no—
387D4×C11—41no—
388D4×C11—41no—
389D4×C11—41no—
390D4×C11—41no—
391D4×C11—41no—
392D4×C11—41no—
393D4×C11—41no—
394D4×C11—41no—
395D4×C11—41no—
396D4×C11—88no—
397D4×C11—161no—
398D4×C11—161no—
399D4×C11#12012yes—
400D4×C11#12112yes—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—44no—
412C2×C4×C11—44no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—81no—
419C2×C4×C11—161no—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C2×#4111yescharacteristic
425C2×C4×C11H(5,𝔽2)11yescharacteristic
426C8×C11—21no—
427C8×C11—22no—
428C8×C11—21no—
429C8×C11—21no—
430C8×C11—21no—
431C8×C11—41no—
432C8×C11—41no—
433C8×C11—41no—
434C2×H(5,𝔽2)C22×C1111yescharacteristic
435C2×H(5,𝔽2)C22×C1111yescharacteristic
436#576—24no—
437#576—24no—
438C2×AGL(1,ℤ/8)—21no—
439C2×AGL(1,ℤ/8)—21no—
440C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
441C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
442C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
443C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
444C2×#135—21no—
445C2×#135C22×C1111yescharacteristic
446C22×D8—21no—
447C22×D8C22×C1111yescharacteristic
448C22×D8C22×C1111yescharacteristic, complemented
449C2×#131C22×C1111yescharacteristic
450C2×#131C22×C1111yescharacteristic, complemented
451#535C22×C1111yescharacteristic, complemented
452C2×#127C22×C1111yescharacteristic, complemented
453#520C22×C1111yescharacteristic, complemented
454#472—24no—
455#464—21no—
456#463—21no—
457#460—21no—
458#459—21no—
459#453—24no—
460#449—21no—
461#449—21no—
462#447—21no—
463#447—21no—
464C2×#108C22×C1111yescharacteristic, complemented
465#424C22×C1111yescharacteristic, complemented
466C2×#104C22×C1111yescharacteristic
467C2×#104C22×C1111yescharacteristic, complemented
468C2×#104C22×C1111yescharacteristic, complemented
469#418—21no—
470#418C22×C1111yescharacteristic, complemented
471#418C22×C1111yescharacteristic, complemented
472#417—21no—
473#417C22×C1111yescharacteristic
474#417C22×C1111yescharacteristic, complemented
475#416—21no—
476#416C22×C1111yescharacteristic
477C2×#102—21no—
478C2×#102C22×C1111yescharacteristic, complemented
479C2×#102C22×C1111yescharacteristic, complemented
480C2×#100C22×C1111yescharacteristic, complemented
481C2×#100C22×C1111yescharacteristic, complemented
482C2×#100C22×C1111yescharacteristic, complemented
483#408C22×C1111yescharacteristic, complemented
484#390C22×C1111yescharacteristic, complemented
485#343C22×C1111yescharacteristic, complemented
486#341C22×C1111yescharacteristic, complemented
487#339C22×C1111yescharacteristic, complemented
488#336C22×C1111yescharacteristic, complemented
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11—41no—
497C22×C11—41no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—41no—
501C22×C11—41no—
502C22×C11—82no—
503C22×C11—82no—
504C22×C11—82no—
505C22×C11—81no—
506C22×C11—81no—
507C22×C11—81no—
508C22×C11—81no—
509C22×C11—81no—
510C22×C11—81no—
511C22×C11—81no—
512C22×C11—161no—
513C22×C11—161no—
514C22×C11—161no—
515C22×C11—164no—
516C22×C11—164no—
517C22×C11#53411yescharacteristic
518C22×C11D4211yescharacteristic
519C22×C11#54611yescharacteristic
520C4×C11—22no—
521C4×C11—22no—
522C4×C11—42no—
523C4×C11—41no—
524C4×C11—41no—
525C4×C11—41no—
526C4×C11—81no—
527C4×C11C2×#12011yescharacteristic
528C4×C11C2×#12111yescharacteristic
529C4×C11D4211yescharacteristic
530C4×C11#54611yescharacteristic
531H(5,𝔽2)—22no—
532H(5,𝔽2)—22no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—41no—
537H(5,𝔽2)—41no—
538H(5,𝔽2)D4×C1114yescomplemented
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41C23×C1111yescharacteristic
544C2×#41C23×C1111yescharacteristic
545C2×#41C23×C1111yescharacteristic
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4C23×C1111yescharacteristic
554C22×D4C23×C1111yescharacteristic
555C22×D4C23×C1111yescharacteristic
556AGL(1,ℤ/8)—28no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)D4×C1114yescomplemented
566#135—28no—
567#135—22no—
568#135—22no—
569C2×Q16D4×C1111yescharacteristic, complemented
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—21no—
574C2×SD16D4×C1111yescharacteristic, complemented
575C2×SD16D4×C1111yescharacteristic, complemented
576C2×D8—28no—
577C2×D8—21no—
578C2×D8—21no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8—21no—
587C2×D8—21no—
588C2×D8—41no—
589C2×D8D4×C1111yescharacteristic, complemented
590#131—22no—
591#131—22no—
592#131—22no—
593#131—41no—
594C2×M16—21no—
595C2×M16—21no—
596C2×M16C23×C1111yescharacteristic
597C2×M16C23×C1111yescharacteristic
598C2×M16C23×C1111yescharacteristic
599C2×M16C23×C1111yescharacteristic
600C22×C8—21no—
601C22×C8—21no—
602C22×C8C23×C1111yescharacteristic
603C22×C8C23×C1111yescharacteristic
604#127—22no—
605#127—21no—
606#127—41no—
607#124—21no—
608#121—21no—
609#121—21no—
610#120—41no—
611C4×Q8—21no—
612C4×D4—21no—
613C4×D4—41no—
614#117—21no—
615#117C23×C1111yescharacteristic
616C2×C4⋊C4—21no—
617C2×C4⋊C4C23×C1111yescharacteristic
618C2×C22⋊C4—41no—
619C2×C42C23×C1111yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103D4×C1111yescharacteristic, complemented
629#103D4×C1111yescharacteristic, complemented
630#102—21no—
631#102—21no—
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C1111yescharacteristic, complemented
641#102D4×C1111yescharacteristic, complemented
642#100—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C2×C11—21no—
648C2×C11—21no—
649C2×C11—42no—
650C2×C11—42no—
651C2×C11—81no—
652C2×C11—82no—
653C2×C11—82no—
654C2×C11—161no—
655C2×C11#241011yescharacteristic
656C2×C11#328811yescharacteristic
657C2×C11#329211yescharacteristic
658C24—21no—
659C24—21no—
660C24—21no—
661C24—41no—
662C24—41no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—24no—
668#41—24no—
669#41—24no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—42no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41C2×D4×C1112yes—
680#41C2×D4×C1112yes—
681#41C2×D4×C1112yes—
682#41C11×#4112yes—
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—24no—
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—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—41no—
717C2×D4—44no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—42no—
723C2×D4—44no—
724C2×D4—82no—
725C2×D4—82no—
726C2×D4C2×D4×C1112yes—
727C2×D4C2×D4×C1112yes—
728C2×D4C2×D4×C1111yescharacteristic
729C2×D4C2×D4×C1111yescharacteristic
730C2×D4C2×D4×C1111yescharacteristic
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4C24×C1111yescharacteristic
740Q16—22no—
741SD16—24no—
742SD16—24no—
743SD16—22no—
744SD16—22no—
745SD16—42no—
746SD16—42no—
747D8—24no—
748D8—24no—
749D8—24no—
750D8—22no—
751D8—24no—
752D8—42no—
753D8—42no—
754D8—42no—
755D8—42no—
756M16—24no—
757M16—21no—
758M16—21no—
759M16—21no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—42no—
765M16C2×D4×C1112yes—
766C2×C8—24no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—42no—
776C2×C8C2×D4×C1111yescharacteristic
777C2×C8C2×D4×C1111yescharacteristic
778C2×C8C2×D4×C1111yescharacteristic
779C2×C8C2×D4×C1111yescharacteristic
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—41no—
783C4⋊C4C2×D4×C1111yescharacteristic
784C4⋊C4C2×D4×C1111yescharacteristic
785C22⋊C4—21no—
786C22⋊C4—41no—
787C22⋊C4—41no—
788C22⋊C4—41no—
789C22⋊C4—82no—
790C42—21no—
791C42—21no—
792C42—21no—
793C42—41no—
794C11#2445611yescharacteristic, direct product factor, Sylow
795C23—21no—
796C23—21no—
797C23—21no—
798C23—22no—
799C23—22no—
800C23—44no—
801C23—44no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—81no—
810C23—81no—
811C23—81no—
812C23—81no—
813C23—81no—
814C23—81no—
815C23—161no—
816C23—161no—
817C23—161no—
818C23—161no—
819C23C11×H(5,𝔽2)11yescharacteristic
820Q8—21no—
821Q8—21no—
822Q8—21no—
823Q8—21no—
824Q8C11×#12012yes—
825Q8C11×#12112yes—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—21no—
833D4—22no—
834D4—21no—
835D4—22no—
836D4—21no—
837D4—21no—
838D4—44no—
839D4—44no—
840D4—44no—
841D4—44no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—88no—
853D4—161no—
854D4—161no—
855D4C11×#12012yes—
856D4C11×#12112yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—81no—
875C2×C4—161no—
876C2×C4C22×D4×C1111yescharacteristic
877C2×C4C22×D4×C1111yescharacteristic
878C2×C4C22×D4×C1111yescharacteristic
879C2×C4C22×D4×C1111yescharacteristic
880C2×C4C2×C11×#4111yescharacteristic
881C2×C4C11×H(5,𝔽2)11yescharacteristic
882C8—21no—
883C8—22no—
884C8—21no—
885C8—21no—
886C8—21no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—21no—
891C22—21no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—161no—
914C22—161no—
915C22—161no—
916C22—164no—
917C22—164no—
918C22C11×#53411yescharacteristic
919C22D42×C1111yescharacteristic
920C22C11×#54611yescharacteristic
921C4—22no—
922C4—22no—
923C4—42no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—81no—
928C4C2×C11×#12011yescharacteristic
929C4C2×C11×#12111yescharacteristic
930C4D42×C1111yescharacteristic
931C4C11×#54611yescharacteristic
932C2—21no—
933C2—21no—
934C2—42no—
935C2—42no—
936C2—81no—
937C2—82no—
938C2—82no—
939C2—161no—
940C2C11×#241011yescharacteristic
941C2C11×#328811yescharacteristic
942C2C11×#329211yescharacteristic
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×#576C2semidirect
2. C2×C11×#472C2semidirect
3. C11×#3045C2semidirect
4. C2×C11×#453C2semidirect
5. C11×#3008C2semidirect
6. C11×#2897C2semidirect
7. C11×#2051C2semidirect
8. C11×#2045C2semidirect
9. C11×#2011C2semidirect
10. C11×#2002C2semidirect
11. C11×#1907C2semidirect
12. C11×#1883C2semidirect
13. C11×#1876C2semidirect
14. C11×#1866C2semidirect
15. C11×#1792C2semidirect
25. C2×C11×AGL(1,ℤ/8)C22semidirect
30. C22×C11×D8C22semidirect
32. C2×C11×#131C22semidirect
33. C11×#535C22semidirect
34. C2×C11×#127C22semidirect
35. C11×#520C22semidirect
46. C2×C11×#108C22semidirect
47. C11×#424C22semidirect
49. C2×C11×#104C22semidirect
50. C2×C11×#104C22semidirect
52. C11×#418C22semidirect
53. C11×#418C22semidirect
56. C11×#417C22semidirect
60. C2×C11×#102C22semidirect
61. C2×C11×#102C22semidirect
62. C2×C11×#100C22semidirect
63. C2×C11×#100C22semidirect
64. C2×C11×#100C22semidirect
65. C11×#408C22semidirect
66. C11×#390C22semidirect
67. C11×#343C22semidirect
68. C11×#341C22semidirect
69. C11×#339C22semidirect
70. C11×#336C22semidirect
78. C11×H(5,𝔽2)D4semidirect
105. C11×AGL(1,ℤ/8)D4semidirect
109. C2×C11×Q16D4semidirect
114. C2×C11×SD16D4semidirect
115. C2×C11×SD16D4semidirect
129. C2×C11×D8D4semidirect
168. C11×#103D4semidirect
169. C11×#103D4semidirect
180. C11×#102D4semidirect
181. C11×#102D4semidirect
187. #24456C11direct (N × H)
324. C2×#576C2×C11semidirect
325. C2×#472C2×C11semidirect
326. #3045C2×C11semidirect
327. C2×#453C2×C11semidirect
328. #3008C2×C11semidirect
329. #2897C2×C11semidirect
330. #2051C2×C11semidirect
331. #2045C2×C11semidirect
332. #2011C2×C11semidirect
333. #2002C2×C11semidirect
334. #1907C2×C11semidirect
335. #1883C2×C11semidirect
336. #1876C2×C11semidirect
337. #1866C2×C11semidirect
338. #1792C2×C11semidirect
443. C2×AGL(1,ℤ/8)C22×C11semidirect
448. C22×D8C22×C11semidirect
450. C2×#131C22×C11semidirect
451. #535C22×C11semidirect
452. C2×#127C22×C11semidirect
453. #520C22×C11semidirect
464. C2×#108C22×C11semidirect
465. #424C22×C11semidirect
467. C2×#104C22×C11semidirect
468. C2×#104C22×C11semidirect
470. #418C22×C11semidirect
471. #418C22×C11semidirect
474. #417C22×C11semidirect
478. C2×#102C22×C11semidirect
479. C2×#102C22×C11semidirect
480. C2×#100C22×C11semidirect
481. C2×#100C22×C11semidirect
482. C2×#100C22×C11semidirect
483. #408C22×C11semidirect
484. #390C22×C11semidirect
485. #343C22×C11semidirect
486. #341C22×C11semidirect
487. #339C22×C11semidirect
488. #336C22×C11semidirect
538. H(5,𝔽2)D4×C11semidirect
565. AGL(1,ℤ/8)D4×C11semidirect
569. C2×Q16D4×C11semidirect
574. C2×SD16D4×C11semidirect
575. C2×SD16D4×C11semidirect
589. C2×D8D4×C11semidirect
628. #103D4×C11semidirect
629. #103D4×C11semidirect
640. #102D4×C11semidirect
641. #102D4×C11semidirect
794. C11#24456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5762
C2×C11×#4722
C11×#30452
C2×C11×#4532
C11×#30082
C11×#28972
C11×#20512
C11×#20452
C11×#20112
C11×#20022
C11×#19072
C11×#18832
C11×#18762
C11×#18662
C11×#17922
#2445611