Finite Group Databasebeta

← C11×#24137 #14601330

Subgroups — C11×#24137 #14601330

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic, complemented
3C2×C11×#440C211yesmaximal, characteristic, complemented
4C11×#2537C211yesmaximal, characteristic
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2035C211yesmaximal, characteristic, complemented
7C11×#2000C211yesmaximal, characteristic, complemented
8C11×#2000C211yesmaximal, characteristic, complemented
9C11×#1992C211yesmaximal, characteristic, complemented
10C11×#1955C211yesmaximal, characteristic, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1852C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C11×#552—24no—
18C11×#552—24no—
19C2×C11×#126—21no—
20C2×C11×#125—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117—21no—
32C2×C11×#117C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C11×#478—24no—
35C11×#440—24no—
36C2×C11×#107C2211yescharacteristic
37C2×C11×#107C2211yescharacteristic
38C2×C11×#106C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C11×#394—21no—
52C11×#394—21no—
53C11×#384C2211yescharacteristic
54C11×#380—21no—
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11D411yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C2×C11×SD16—22no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×#126—28no—
80C11×#125—28no—
81C11×#125—22no—
82C11×#125D414yescomplemented
83C11×#123—28no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—41no—
91C11×#121—41no—
92C11×#121—44no—
93C4×Q8×C11—22no—
94C4×Q8×C11D414yescomplemented
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C11×#117—28no—
100C11×#117—22no—
101C11×#117—22no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4D411yescharacteristic
128C2×C11×C22⋊C4D411yescharacteristic
129C2×C42×C11—21no—
130C2×C42×C11—21no—
131C2×C42×C11C2311yescharacteristic
132C11×#107—22no—
133C11×#107—22no—
134C11×#106—22no—
135C11×C4⋊C8—22no—
136C11×#103—22no—
137C11×#103—41no—
138C11×#103—41no—
139C11×#102—22no—
140C11×#102—22no—
141C11×#102—22no—
142C11×C22⋊C8—22no—
143C11×C22⋊C8—22no—
144C11×C22⋊C8—41no—
145C11×C22⋊C8—41no—
146C11×#97—22no—
147C11×#95—21no—
148C11×#95—21no—
149#24137C1111yesmaximal, characteristic, direct product factor, Sylow
150C24×C11—21no—
151C24×C11C2×D411yescharacteristic
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—22no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—41no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—81no—
172C2×D4×C11—81no—
173C2×D4×C11#4112yes—
174C22×C4×C11—24no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
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—42no—
195C22×C4×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—42no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C11×SD16—28no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
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#4112yes—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—21no—
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—21no—
233C11×C4⋊C4—42no—
234C11×C4⋊C4—81no—
235C11×C4⋊C4C2×D412yes—
236C11×C4⋊C4C2×D412yes—
237C11×C4⋊C4C2×D412yes—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—42no—
245C11×C22⋊C4—42no—
246C11×C22⋊C4—42no—
247C11×C22⋊C4—42no—
248C42×C11—24no—
249C42×C11—24no—
250C42×C11C2×D412yes—
251C42×C11C2×D412yes—
252C2×#552C2×C1111yescharacteristic, complemented
253C2×#478C2×C1111yescharacteristic, complemented
254C2×#440C2×C1111yescharacteristic, complemented
255#2537C2×C1111yescharacteristic
256#2036C2×C1111yescharacteristic, complemented
257#2035C2×C1111yescharacteristic, complemented
258#2000C2×C1111yescharacteristic, complemented
259#2000C2×C1111yescharacteristic, complemented
260#1992C2×C1111yescharacteristic, complemented
261#1955C2×C1111yescharacteristic, complemented
262#1875C2×C1111yescharacteristic, complemented
263#1874C2×C1111yescharacteristic, complemented
264#1854C2×C1111yescharacteristic, complemented
265#1852C2×C1111yescharacteristic, complemented
266#1803C2×C1111yescharacteristic, complemented
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—22no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11AGL(1,ℤ/8)12yes—
288C23×C11C22×D411yescharacteristic
289Q8×C11—22no—
290Q8×C11—22no—
291Q8×C11—41no—
292Q8×C11—41no—
293D4×C11—22no—
294D4×C11—22no—
295D4×C11—44no—
296D4×C11—41no—
297D4×C11—41no—
298D4×C11—84no—
299D4×C11—84no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—48no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
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—84no—
341C2×C4×C11#12012yes—
342C2×C4×C11#12012yes—
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C2×#4111yescharacteristic
346C2×C4×C11C2×#4111yescharacteristic
347C2×C4×C11H(5,𝔽2)11yescharacteristic
348C2×C4×C112−1+411yescharacteristic
349C8×C11—22no—
350C8×C11—41no—
351C8×C11—41no—
352C8×C11—41no—
353C22×SD16C22×C1111yescharacteristic
354#552—24no—
355#552—24no—
356C2×#126—21no—
357C2×#125—21no—
358C2×#125C22×C1111yescharacteristic
359C2×#123—21no—
360C2×C22⋊Q8C22×C1111yescharacteristic
361C2×C22⋊Q8C22×C1111yescharacteristic
362C2×#121—21no—
363C2×#121C22×C1111yescharacteristic
364C2×#121C22×C1111yescharacteristic
365C2×C4×Q8C22×C1111yescharacteristic
366C2×C4×D4C22×C1111yescharacteristic
367C2×C4×D4C22×C1111yescharacteristic
368C2×#117—21no—
369C2×#117C22×C1111yescharacteristic
370C22×C4⋊C4C22×C1111yescharacteristic
371#478—24no—
372#440—24no—
373C2×#107C22×C1111yescharacteristic
374C2×#107C22×C1111yescharacteristic
375C2×#106C22×C1111yescharacteristic
376C2×C4⋊C8C22×C1111yescharacteristic
377C2×#103C22×C1111yescharacteristic
378C2×#103C22×C1111yescharacteristic
379C2×#103C22×C1111yescharacteristic
380C2×#102C22×C1111yescharacteristic
381C2×#102C22×C1111yescharacteristic
382C2×#102C22×C1111yescharacteristic
383C2×C22⋊C8C22×C1111yescharacteristic
384C2×C22⋊C8C22×C1111yescharacteristic
385C2×C22⋊C8C22×C1111yescharacteristic
386C2×C22⋊C8C22×C1111yescharacteristic
387C2×#97C22×C1111yescharacteristic
388#394—21no—
389#394—21no—
390#384C22×C1111yescharacteristic
391#380—21no—
392#380C22×C1111yescharacteristic
393#380C22×C1111yescharacteristic
394#340C22×C1111yescharacteristic
395#340C22×C1111yescharacteristic
396#340C22×C1111yescharacteristic
397#340C22×C1111yescharacteristic
398#340C22×C1111yescharacteristic
399#340C22×C1111yescharacteristic
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—42no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—42no—
415C22×C11—41no—
416C22×C11—42no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11C2×#12011yescharacteristic
422C22×C11#54611yescharacteristic
423C22×C11#54711yescharacteristic
424C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
425C22×C11#57511yescharacteristic
426C22×C11#57711yescharacteristic
427C22×C11#57811yescharacteristic
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—81no—
437C4×C11—81no—
438C4×C11—81no—
439C4×C11#52511yescharacteristic
440C4×C11#53711yescharacteristic
441C4×C11#54811yescharacteristic
442C4×C11#55011yescharacteristic
443C22×Q8C23×C1111yescharacteristic
444C22×D4—21no—
445C22×D4—21no—
446C22×D4D4×C1111yescharacteristic
447C22×D4C23×C1111yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4C23×C1111yescharacteristic
451C23×C4C23×C1111yescharacteristic
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457C22×C8C23×C1111yescharacteristic
458C22×C8C23×C1111yescharacteristic
459#126—28no—
460#125—28no—
461#125—22no—
462#125D4×C1114yescomplemented
463#123—28no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468#121—22no—
469#121—22no—
470#121—41no—
471#121—41no—
472#121—44no—
473C4×Q8—22no—
474C4×Q8D4×C1114yescomplemented
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479#117—28no—
480#117—22no—
481#117—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C1111yescharacteristic
493C2×C4⋊C4C23×C1111yescharacteristic
494C2×C4⋊C4C23×C1111yescharacteristic
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C4⋊C4C23×C1111yescharacteristic
497C2×C4⋊C4C23×C1111yescharacteristic
498C2×C4⋊C4C23×C1111yescharacteristic
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×C22⋊C4D4×C1111yescharacteristic
508C2×C22⋊C4D4×C1111yescharacteristic
509C2×C42—21no—
510C2×C42—21no—
511C2×C42C23×C1111yescharacteristic
512#107—22no—
513#107—22no—
514#106—22no—
515C4⋊C8—22no—
516#103—22no—
517#103—41no—
518#103—41no—
519#102—22no—
520#102—22no—
521#102—22no—
522C22⋊C8—22no—
523C22⋊C8—22no—
524C22⋊C8—41no—
525C22⋊C8—41no—
526#97—22no—
527#95—21no—
528#95—21no—
529C2×C11—42no—
530C2×C11—81no—
531C2×C11—82no—
532C2×C11#240711yescharacteristic
533C2×C11#300611yescharacteristic
534C2×C11#301311yescharacteristic
535C2×C11#331011yescharacteristic
536C2×C11#331511yescharacteristic
537C2×C11#334311yescharacteristic
538C2×C11#334811yescharacteristic
539C24—21no—
540C24C2×D4×C1111yescharacteristic
541C24C2×D4×C1111yescharacteristic
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8C2×D4×C1112yes—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—41no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4C11×#4112yes—
563C22×C4—24no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4C2×D4×C1111yescharacteristic
589C22×C4C2×D4×C1111yescharacteristic
590C22×C4C2×D4×C1111yescharacteristic
591C22×C4C2×D4×C1111yescharacteristic
592C22×C4C24×C1111yescharacteristic
593SD16—28no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8C11×#4112yes—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—81no—
624C4⋊C4C2×D4×C1112yes—
625C4⋊C4C2×D4×C1112yes—
626C4⋊C4C2×D4×C1112yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C42—24no—
638C42—24no—
639C42C2×D4×C1112yes—
640C42C2×D4×C1112yes—
641C11#2413711yescharacteristic, direct product factor, Sylow
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—22no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23C11×AGL(1,ℤ/8)12yes—
663C23C22×D4×C1111yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—41no—
667Q8—41no—
668D4—22no—
669D4—22no—
670D4—44no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—48no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
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—84no—
716C2×C4C11×#12012yes—
717C2×C4C11×#12012yes—
718C2×C4C22×D4×C1111yescharacteristic
719C2×C4C22×D4×C1111yescharacteristic
720C2×C4C2×C11×#4111yescharacteristic
721C2×C4C2×C11×#4111yescharacteristic
722C2×C4C11×H(5,𝔽2)11yescharacteristic
723C2×C4C11×2−1+411yescharacteristic
724C8—22no—
725C8—41no—
726C8—41no—
727C8—41no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—41no—
742C22—42no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22C2×C11×#12011yescharacteristic
750C22C11×#54611yescharacteristic
751C22C11×#54711yescharacteristic
752C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
753C22C11×#57511yescharacteristic
754C22C11×#57711yescharacteristic
755C22C11×#57811yescharacteristic
756C4—22no—
757C4—22no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4C11×#52511yescharacteristic
768C4C11×#53711yescharacteristic
769C4C11×#54811yescharacteristic
770C4C11×#55011yescharacteristic
771C2—42no—
772C2—81no—
773C2—82no—
774C2C11×#240711yescharacteristic
775C2C11×#300611yescharacteristic
776C2C11×#301311yescharacteristic
777C2C11×#331011yescharacteristic
778C2C11×#331511yescharacteristic
779C2C11×#334311yescharacteristic
780C2C11×#334811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2537C2
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×#552C2semidirect
2. C2×C11×#478C2semidirect
3. C2×C11×#440C2semidirect
5. C11×#2036C2semidirect
6. C11×#2035C2semidirect
7. C11×#2000C2semidirect
8. C11×#2000C2semidirect
9. C11×#1992C2semidirect
10. C11×#1955C2semidirect
11. C11×#1875C2semidirect
12. C11×#1874C2semidirect
13. C11×#1854C2semidirect
14. C11×#1852C2semidirect
15. C11×#1803C2semidirect
82. C11×#125D4semidirect
94. C4×Q8×C11D4semidirect
149. #24137C11direct (N × H)
252. C2×#552C2×C11semidirect
253. C2×#478C2×C11semidirect
254. C2×#440C2×C11semidirect
256. #2036C2×C11semidirect
257. #2035C2×C11semidirect
258. #2000C2×C11semidirect
259. #2000C2×C11semidirect
260. #1992C2×C11semidirect
261. #1955C2×C11semidirect
262. #1875C2×C11semidirect
263. #1874C2×C11semidirect
264. #1854C2×C11semidirect
265. #1852C2×C11semidirect
266. #1803C2×C11semidirect
462. #125D4×C11semidirect
474. C4×Q8D4×C11semidirect
641. C11#24137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#4782
C2×C11×#4402
C11×#25372
C11×#20362
C11×#20352
C11×#20002
C11×#19922
C11×#19552
C11×#18752
C11×#18742
C11×#18542
C11×#18522
C11×#18032
#2413711