Finite Group Databasebeta

← C11×#24158 #14601351

Subgroups — C11×#24158 #14601351

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic, complemented
3C2×C11×#463C211yesmaximal, characteristic, complemented
4C4×C11×#121C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2034C211yesmaximal, characteristic, complemented
7C11×#2000C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic
9C11×#1989C211yesmaximal, characteristic, complemented
10C11×#1983C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1797C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C11×#529—24no—
19C11×#529—24no—
20C2×C11×#126—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117—21no—
33C22×C42×C11C2211yescharacteristic
34C11×#478—24no—
35C11×#463—24no—
36C2×C11×#107C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#389C2211yescharacteristic
52C11×#388—21no—
53C11×#386—21no—
54C11×#380C2211yescharacteristic
55C4×C11×C4⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4—21no—
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11D411yescharacteristic
71C23×C4×C11D411yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—41no—
76C2×C11×D8—22no—
77C2×C11×D8—22no—
78C2×C11×D8—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×#126—28no—
84C11×#125—22no—
85C11×#125D414yescomplemented
86C11×#124—22no—
87C11×#124D414yescomplemented
88C11×#123—28no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×#121—22no—
92C11×#121—22no—
93C11×#121—22no—
94C11×#121—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×D4×C11—28no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—44no—
103C11×#117—28no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C42×C11—21no—
125C2×C42×C11—22no—
126C2×C42×C11—22no—
127C2×C42×C11—21no—
128C2×C42×C11D411yescharacteristic
129C2×C42×C11D411yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C2×C42×C11C2311yescharacteristic
132C11×#107—22no—
133C11×#106—22no—
134C11×C4⋊C8—22no—
135C11×C4⋊C8—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—41no—
139C11×#102—22no—
140C11×#102—22no—
141C11×#102—22no—
142C11×#102—22no—
143C11×#102—41no—
144C11×C22⋊C8—41no—
145C11×C22⋊C8—41no—
146C11×#95—21no—
147C11×#95—21no—
148C11×#95—21no—
149#24158C1111yesmaximal, characteristic, direct product factor, Sylow
150C24×C11—21no—
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11C2×D412yes—
159C2×D4×C11—24no—
160C2×D4×C11—24no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11C2×D412yes—
176C2×D4×C11#4112yes—
177C22×C4×C11—24no—
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—41no—
195C22×C4×C11—41no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11—42no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C11×SD16—44no—
208C11×D8—44no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—42no—
233C11×C4⋊C4C2×D412yes—
234C11×C4⋊C4C2×D412yes—
235C11×C4⋊C4#4112yes—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—42no—
245C11×C22⋊C4—42no—
246C42×C11—24no—
247C42×C11—22no—
248C42×C11—22no—
249C42×C11—21no—
250C42×C11—21no—
251C42×C11—42no—
252C42×C11C2×D412yes—
253C42×C11C2×D412yes—
254C2×#529C2×C1111yescharacteristic, complemented
255C2×#478C2×C1111yescharacteristic, complemented
256C2×#463C2×C1111yescharacteristic, complemented
257C4×#121C2×C1111yescharacteristic, complemented
258#2036C2×C1111yescharacteristic, complemented
259#2034C2×C1111yescharacteristic, complemented
260#2000C2×C1111yescharacteristic, complemented
261#1999C2×C1111yescharacteristic
262#1989C2×C1111yescharacteristic, complemented
263#1983C2×C1111yescharacteristic, complemented
264#1880C2×C1111yescharacteristic, complemented
265#1879C2×C1111yescharacteristic, complemented
266#1865C2×C1111yescharacteristic, complemented
267#1862C2×C1111yescharacteristic, complemented
268#1797C2×C1111yescharacteristic, complemented
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11#13512yes—
290C23×C11C22×D411yescharacteristic
291Q8×C11—22no—
292Q8×C11—22no—
293Q8×C11—41no—
294Q8×C11—41no—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—48no—
300D4×C11—48no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—41no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11—48no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—84no—
343C2×C4×C11#12012yes—
344C2×C4×C11#12012yes—
345C2×C4×C11AGL(1,ℤ/8)12yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4111yescharacteristic
349C2×C4×C11C2×#4111yescharacteristic
350C2×C4×C11H(5,𝔽2)11yescharacteristic
351C2×C4×C112−1+411yescharacteristic
352C8×C11—41no—
353C8×C11—41no—
354C8×C11—41no—
355C8×C11—41no—
356C22×SD16C22×C1111yescharacteristic
357C22×D8C22×C1111yescharacteristic
358#529—24no—
359#529—24no—
360C2×#126—21no—
361C2×#125C22×C1111yescharacteristic
362C2×#124C22×C1111yescharacteristic
363C2×#123—21no—
364C2×C22⋊Q8C22×C1111yescharacteristic
365C2×#121C22×C1111yescharacteristic
366C2×#121C22×C1111yescharacteristic
367C2×C4×Q8C22×C1111yescharacteristic
368C2×C4×D4—21no—
369C2×C4×D4—21no—
370C2×C4×D4C22×C1111yescharacteristic
371C2×C4×D4C22×C1111yescharacteristic
372C2×#117—21no—
373C22×C42C22×C1111yescharacteristic
374#478—24no—
375#463—24no—
376C2×#107C22×C1111yescharacteristic
377C2×#106C22×C1111yescharacteristic
378C2×C4⋊C8C22×C1111yescharacteristic
379C2×C4⋊C8C22×C1111yescharacteristic
380C2×#103C22×C1111yescharacteristic
381C2×#103C22×C1111yescharacteristic
382C2×#103C22×C1111yescharacteristic
383C2×#102C22×C1111yescharacteristic
384C2×#102C22×C1111yescharacteristic
385C2×#102C22×C1111yescharacteristic
386C2×#102C22×C1111yescharacteristic
387C2×#102C22×C1111yescharacteristic
388C2×C22⋊C8C22×C1111yescharacteristic
389C2×C22⋊C8C22×C1111yescharacteristic
390#390C22×C1111yescharacteristic
391#389C22×C1111yescharacteristic
392#388—21no—
393#386—21no—
394#380C22×C1111yescharacteristic
395C4×C4⋊C4C22×C1111yescharacteristic
396C4×C22⋊C4—21no—
397#340C22×C1111yescharacteristic
398#340C22×C1111yescharacteristic
399#340C22×C1111yescharacteristic
400#340C22×C1111yescharacteristic
401#336C22×C1111yescharacteristic
402#336C22×C1111yescharacteristic
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11C2×#12011yescharacteristic
425C22×C11#52511yescharacteristic
426C22×C11#53711yescharacteristic
427C22×C11C2×#13511yescharacteristic
428C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C11#57511yescharacteristic
430C22×C11#57511yescharacteristic
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—41no—
436C4×C11—42no—
437C4×C11—41no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11—81no—
441C4×C11—81no—
442C4×C11#54611yescharacteristic
443C4×C11#54711yescharacteristic
444C4×C11#54811yescharacteristic
445C4×C11#55011yescharacteristic
446C22×Q8C23×C1111yescharacteristic
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C1111yescharacteristic
450C22×D4C23×C1111yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4D4×C1111yescharacteristic
454C23×C4D4×C1111yescharacteristic
455C23×C4C23×C1111yescharacteristic
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—41no—
459C2×D8—22no—
460C2×D8—22no—
461C2×D8—41no—
462C22×C8C23×C1111yescharacteristic
463C22×C8C23×C1111yescharacteristic
464C22×C8C23×C1111yescharacteristic
465C22×C8C23×C1111yescharacteristic
466#126—28no—
467#125—22no—
468#125D4×C1114yescomplemented
469#124—22no—
470#124D4×C1114yescomplemented
471#123—28no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474#121—22no—
475#121—22no—
476#121—22no—
477#121—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×D4—28no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—44no—
486#117—28no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4C23×C1111yescharacteristic
493C2×C4⋊C4C23×C1111yescharacteristic
494C2×C4⋊C4C23×C1111yescharacteristic
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C4⋊C4C23×C1111yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C42—21no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—21no—
511C2×C42D4×C1111yescharacteristic
512C2×C42D4×C1111yescharacteristic
513C2×C42C23×C1111yescharacteristic
514C2×C42C23×C1111yescharacteristic
515#107—22no—
516#106—22no—
517C4⋊C8—22no—
518C4⋊C8—22no—
519#103—22no—
520#103—22no—
521#103—41no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—41no—
527C22⋊C8—41no—
528C22⋊C8—41no—
529#95—21no—
530#95—21no—
531#95—21no—
532C2×C11—42no—
533C2×C11—82no—
534C2×C11—82no—
535C2×C11#240711yescharacteristic
536C2×C11#300211yescharacteristic
537C2×C11#300611yescharacteristic
538C2×C11#310511yescharacteristic
539C2×C11#311111yescharacteristic
540C2×C11#325011yescharacteristic
541C2×C11#325111yescharacteristic
542C24—21no—
543C24—21no—
544C24C2×D4×C1111yescharacteristic
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8C2×D4×C1112yes—
551C2×D4—24no—
552C2×D4—24no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4C2×D4×C1112yes—
568C2×D4C11×#4112yes—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4C2×D4×C1111yescharacteristic
594C22×C4C2×D4×C1111yescharacteristic
595C22×C4C2×D4×C1111yescharacteristic
596C22×C4C2×D4×C1111yescharacteristic
597C22×C4C2×D4×C1111yescharacteristic
598C22×C4C24×C1111yescharacteristic
599SD16—44no—
600D8—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4C2×D4×C1112yes—
626C4⋊C4C2×D4×C1112yes—
627C4⋊C4C11×#4112yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C42—24no—
639C42—22no—
640C42—22no—
641C42—21no—
642C42—21no—
643C42—42no—
644C42C2×D4×C1112yes—
645C42C2×D4×C1112yes—
646C11#2415811yescharacteristic, direct product factor, Sylow
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C11×#13512yes—
668C23C22×D4×C1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—48no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—48no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—84no—
721C2×C4C11×#12012yes—
722C2×C4C11×#12012yes—
723C2×C4C11×AGL(1,ℤ/8)12yes—
724C2×C4C22×D4×C1111yescharacteristic
725C2×C4C22×D4×C1111yescharacteristic
726C2×C4C2×C11×#4111yescharacteristic
727C2×C4C2×C11×#4111yescharacteristic
728C2×C4C11×H(5,𝔽2)11yescharacteristic
729C2×C4C11×2−1+411yescharacteristic
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×C11×#12011yescharacteristic
756C22C11×#52511yescharacteristic
757C22C11×#53711yescharacteristic
758C22C2×C11×#13511yescharacteristic
759C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
760C22C11×#57511yescharacteristic
761C22C11×#57511yescharacteristic
762C4—22no—
763C4—22no—
764C4—22no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4C11×#54611yescharacteristic
774C4C11×#54711yescharacteristic
775C4C11×#54811yescharacteristic
776C4C11×#55011yescharacteristic
777C2—42no—
778C2—82no—
779C2—82no—
780C2C11×#240711yescharacteristic
781C2C11×#300211yescharacteristic
782C2C11×#300611yescharacteristic
783C2C11×#310511yescharacteristic
784C2C11×#311111yescharacteristic
785C2C11×#325011yescharacteristic
786C2C11×#325111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#529C2semidirect
2. C2×C11×#478C2semidirect
3. C2×C11×#463C2semidirect
4. C4×C11×#121C2semidirect
5. C11×#2036C2semidirect
6. C11×#2034C2semidirect
7. C11×#2000C2semidirect
9. C11×#1989C2semidirect
10. C11×#1983C2semidirect
11. C11×#1880C2semidirect
12. C11×#1879C2semidirect
13. C11×#1865C2semidirect
14. C11×#1862C2semidirect
15. C11×#1797C2semidirect
85. C11×#125D4semidirect
87. C11×#124D4semidirect
149. #24158C11direct (N × H)
254. C2×#529C2×C11semidirect
255. C2×#478C2×C11semidirect
256. C2×#463C2×C11semidirect
257. C4×#121C2×C11semidirect
258. #2036C2×C11semidirect
259. #2034C2×C11semidirect
260. #2000C2×C11semidirect
262. #1989C2×C11semidirect
263. #1983C2×C11semidirect
264. #1880C2×C11semidirect
265. #1879C2×C11semidirect
266. #1865C2×C11semidirect
267. #1862C2×C11semidirect
268. #1797C2×C11semidirect
468. #125D4×C11semidirect
470. #124D4×C11semidirect
646. C11#24158direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C11×#4782
C2×C11×#4632
C4×C11×#1212
C11×#20362
C11×#20342
C11×#20002
C11×#19992
C11×#19892
C11×#19832
C11×#18802
C11×#18792
C11×#18652
C11×#18622
C11×#17972
#2415811