Finite Group Databasebeta

← C11×#24100 #14601293

Subgroups — C11×#24100 #14601293

Order 2816.

1300 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic
2C2×C11×#482C211yesmaximal, characteristic, complemented
3C2×C11×#428C211yesmaximal, characteristic, complemented
4C11×#2485C211yesmaximal, characteristic, complemented
5C11×#2058C211yesmaximal, characteristic, complemented
6C11×#2057C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1895C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1864C211yesmaximal, characteristic, complemented
12C11×#1862C211yesmaximal, characteristic, complemented
13C11×#1853C211yesmaximal, characteristic, complemented
14C11×#1852C211yesmaximal, characteristic, complemented
15C11×#1824C211yesmaximal, characteristic, complemented
16C22×C11×#41—21no—
17C22×C11×M16C2211yescharacteristic
18C11×#547—24no—
19C11×#547—24no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C11×#482—24no—
32C11×#428—24no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#107C2211yescharacteristic
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×#106C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C11×#397—21no—
47C11×#394—21no—
48C11×#389C2211yescharacteristic
49C11×#389C2211yescharacteristic
50C11×#388—21no—
51C11×#387—21no—
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C11×#380C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C2×C11×#41—28no—
64C2×C11×#41—44no—
65C2×C11×#41—44no—
66C22×Q8×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11D411yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8—22no—
85C11×#123—28no—
86C11×#123—28no—
87C11×C22⋊Q8—28no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121D414yes—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C11×#117—22no—
97C11×#117—22no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4D414yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C42×C11—21no—
125C2×C42×C11C2311yescharacteristic
126C11×#107—22no—
127C11×#107—22no—
128C11×#107—22no—
129C11×#106—22no—
130C11×#106—22no—
131C11×#106—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#102—22no—
136C11×C22⋊C8—22no—
137C11×C22⋊C8—22no—
138C11×C22⋊C8—22no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144#24100C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C24×C11C2×D411yescharacteristic
148C11×#41—432no—
149C2×Q8×C11—24no—
150C2×Q8×C11—42no—
151C2×Q8×C11—42no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11C2×D412yes—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—21no—
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—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C11×M16—28no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
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#4112yescomplemented
212C2×C8×C11#4112yescomplemented
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—42no—
229C11×C4⋊C4—81no—
230C11×C4⋊C4C2×D412yes—
231C11×C4⋊C4C2×D412yes—
232C11×C4⋊C4C2×D412yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—81no—
241C11×C22⋊C4—81no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—42no—
245C2×#547C2×C1111yescharacteristic
246C2×#482C2×C1111yescharacteristic, complemented
247C2×#428C2×C1111yescharacteristic, complemented
248#2485C2×C1111yescharacteristic, complemented
249#2058C2×C1111yescharacteristic, complemented
250#2057C2×C1111yescharacteristic, complemented
251#2034C2×C1111yescharacteristic, complemented
252#2033C2×C1111yescharacteristic, complemented
253#1895C2×C1111yescharacteristic, complemented
254#1870C2×C1111yescharacteristic, complemented
255#1864C2×C1111yescharacteristic, complemented
256#1862C2×C1111yescharacteristic, complemented
257#1853C2×C1111yescharacteristic, complemented
258#1852C2×C1111yescharacteristic, complemented
259#1824C2×C1111yescharacteristic, complemented
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—22no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11#12012yes—
280C23×C11AGL(1,ℤ/8)12yes—
281C23×C11C22×D411yescharacteristic
282Q8×C11—48no—
283D4×C11—28no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—48no—
287D4×C11—48no—
288D4×C11—41no—
289D4×C11—41no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—48no—
308C2×C4×C11—48no—
309C2×C4×C11—48no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
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#12012yes—
333C2×C4×C11AGL(1,ℤ/8)12yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C112−1+411yescharacteristic
339C2×C4×C112−1+411yescharacteristic
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—41no—
343C8×C11—41no—
344C22×#41—21no—
345C22×M16C22×C1111yescharacteristic
346#547—24no—
347#547—24no—
348C2×C4⋊Q8C22×C1111yescharacteristic
349C2×#123—21no—
350C2×#123—21no—
351C2×C22⋊Q8—21no—
352C2×#121C22×C1111yescharacteristic
353C2×#121C22×C1111yescharacteristic
354C2×C4×D4C22×C1111yescharacteristic
355C2×C4×D4C22×C1111yescharacteristic
356C2×#117C22×C1111yescharacteristic
357C22×C4⋊C4C22×C1111yescharacteristic
358C22×C4⋊C4C22×C1111yescharacteristic
359#482—24no—
360#428—24no—
361C2×#107C22×C1111yescharacteristic
362C2×#107C22×C1111yescharacteristic
363C2×#107C22×C1111yescharacteristic
364C2×#106C22×C1111yescharacteristic
365C2×#106C22×C1111yescharacteristic
366C2×#106C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×#102C22×C1111yescharacteristic
369C2×#102C22×C1111yescharacteristic
370C2×#102C22×C1111yescharacteristic
371C2×C22⋊C8C22×C1111yescharacteristic
372C2×C22⋊C8C22×C1111yescharacteristic
373C2×C22⋊C8C22×C1111yescharacteristic
374#397—21no—
375#394—21no—
376#389C22×C1111yescharacteristic
377#389C22×C1111yescharacteristic
378#388—21no—
379#387—21no—
380#380C22×C1111yescharacteristic
381#380C22×C1111yescharacteristic
382#380C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384#340C22×C1111yescharacteristic
385#340C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic
387#340C22×C1111yescharacteristic
388#340C22×C1111yescharacteristic
389#336C22×C1111yescharacteristic
390#336C22×C1111yescharacteristic
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11C2×#12011yescharacteristic
413C22×C11#54711yescharacteristic
414C22×C11#54711yescharacteristic
415C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C11#57711yescharacteristic
418C22×C11#57811yescharacteristic
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—41no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—41no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11—81no—
430C4×C11#52511yescharacteristic
431C4×C11#53611yescharacteristic
432C4×C11#54711yescharacteristic
433C4×C11#54711yescharacteristic
434C2×#41—28no—
435C2×#41—44no—
436C2×#41—44no—
437C22×Q8—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4D4×C1111yescharacteristic
441C22×D4C23×C1111yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—21no—
445C23×C4C23×C1111yescharacteristic
446C23×C4C23×C1111yescharacteristic
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—22no—
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C4⋊Q8—22no—
455C4⋊Q8—22no—
456#123—28no—
457#123—28no—
458C22⋊Q8—28no—
459#121—22no—
460#121—22no—
461#121—22no—
462#121D4×C1114yes—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—22no—
467#117—22no—
468#117—22no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4D4×C1111yescharacteristic
478C2×C4⋊C4D4×C1114yes—
479C2×C4⋊C4C23×C1111yescharacteristic
480C2×C4⋊C4C23×C1111yescharacteristic
481C2×C4⋊C4C23×C1111yescharacteristic
482C2×C4⋊C4C23×C1111yescharacteristic
483C2×C4⋊C4C23×C1111yescharacteristic
484C2×C4⋊C4C23×C1111yescharacteristic
485C2×C4⋊C4C23×C1111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4D4×C1111yescharacteristic
494C2×C22⋊C4D4×C1111yescharacteristic
495C2×C42—21no—
496C2×C42C23×C1111yescharacteristic
497#107—22no—
498#107—22no—
499#107—22no—
500#106—22no—
501#106—22no—
502#106—22no—
503#102—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515C2×C11—42no—
516C2×C11—42no—
517C2×C11—82no—
518C2×C11#240611yescharacteristic
519C2×C11#300311yescharacteristic
520C2×C11#301311yescharacteristic
521C2×C11#334311yescharacteristic
522C2×C11#334511yescharacteristic
523C2×C11#335311yescharacteristic
524C2×C11#335411yescharacteristic
525C24—21no—
526C24C2×D4×C1111yescharacteristic
527C24C2×D4×C1111yescharacteristic
528#41—432no—
529C2×Q8—24no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—22no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4C2×D4×C1112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4C2×D4×C1111yescharacteristic
574C22×C4C2×D4×C1111yescharacteristic
575C22×C4C2×D4×C1111yescharacteristic
576C22×C4C2×D4×C1112yes—
577C22×C4C2×D4×C1112yes—
578C22×C4C2×D4×C1111yescharacteristic
579C22×C4C24×C1111yescharacteristic
580M16—28no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8C11×#4112yescomplemented
592C2×C8C11×#4112yescomplemented
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—42no—
609C4⋊C4—81no—
610C4⋊C4C2×D4×C1112yes—
611C4⋊C4C2×D4×C1112yes—
612C4⋊C4C2×D4×C1112yes—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—24no—
617C22⋊C4—22no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C42—21no—
623C42—21no—
624C42—42no—
625C11#2410011yescharacteristic, direct product factor, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C11×#12012yes—
646C23C11×AGL(1,ℤ/8)12yes—
647C23C22×D4×C1111yescharacteristic
648Q8—48no—
649D4—28no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—48no—
654D4—41no—
655D4—41no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
674C2×C4—48no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
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×C4C11×#12012yes—
699C2×C4C11×AGL(1,ℤ/8)12yes—
700C2×C4C22×D4×C1111yescharacteristic
701C2×C4C22×D4×C1111yescharacteristic
702C2×C4C2×C11×#4111yescharacteristic
703C2×C4C2×C11×#4111yescharacteristic
704C2×C4C11×2−1+411yescharacteristic
705C2×C4C11×2−1+411yescharacteristic
706C8—22no—
707C8—22no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×C11×#12011yescharacteristic
732C22C11×#54711yescharacteristic
733C22C11×#54711yescharacteristic
734C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
735C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
736C22C11×#57711yescharacteristic
737C22C11×#57811yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C11×#52511yescharacteristic
750C4C11×#53611yescharacteristic
751C4C11×#54711yescharacteristic
752C4C11×#54711yescharacteristic
753C2—42no—
754C2—42no—
755C2—82no—
756C2C11×#240611yescharacteristic
757C2C11×#300311yescharacteristic
758C2C11×#301311yescharacteristic
759C2C11×#334311yescharacteristic
760C2C11×#334511yescharacteristic
761C2C11×#335311yescharacteristic
762C2C11×#335411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#547C2
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
2. C2×C11×#482C2semidirect
3. C2×C11×#428C2semidirect
4. C11×#2485C2semidirect
5. C11×#2058C2semidirect
6. C11×#2057C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1895C2semidirect
10. C11×#1870C2semidirect
11. C11×#1864C2semidirect
12. C11×#1862C2semidirect
13. C11×#1853C2semidirect
14. C11×#1852C2semidirect
15. C11×#1824C2semidirect
144. #24100C11direct (N × H)
211. C2×C8×C11#41semidirect
212. C2×C8×C11#41semidirect
246. C2×#482C2×C11semidirect
247. C2×#428C2×C11semidirect
248. #2485C2×C11semidirect
249. #2058C2×C11semidirect
250. #2057C2×C11semidirect
251. #2034C2×C11semidirect
252. #2033C2×C11semidirect
253. #1895C2×C11semidirect
254. #1870C2×C11semidirect
255. #1864C2×C11semidirect
256. #1862C2×C11semidirect
257. #1853C2×C11semidirect
258. #1852C2×C11semidirect
259. #1824C2×C11semidirect
591. C2×C8C11×#41semidirect
592. C2×C8C11×#41semidirect
625. C11#24100direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4822
C2×C11×#4282
C11×#24852
C11×#20582
C11×#20572
C11×#20342
C11×#20332
C11×#18952
C11×#18702
C11×#18642
C11×#18622
C11×#18532
C11×#18522
C11×#18242
#2410011