Finite Group Databasebeta

← C11×#24538 #14601731

Subgroups — C11×#24538 #14601731

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#450C211yesmaximal, characteristic
2C2×C11×#418C211yesmaximal, characteristic
3C11×#2499C211yesmaximal, characteristic, complemented
4D4×C11×C22⋊C4C211yesmaximal, characteristic
5C11×#2073C211yesmaximal, characteristic, complemented
6C11×#2071C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1877C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C11×#450—24no—
26C2×C11×C4⋊C8C2211yescharacteristic, complemented
27C2×C11×C4⋊C8C2211yescharacteristic, complemented
28C11×#418—24no—
29C2×C11×#103C2211yescharacteristic, complemented
30C2×C11×#103C2211yescharacteristic, complemented
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#397—21no—
39C11×#397—21no—
40C11×#391C2211yescharacteristic, complemented
41C11×#391C2211yescharacteristic, complemented
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#387—21no—
45C11×#387—21no—
46C11×#386—21no—
47C11×#386—21no—
48C11×#384C2211yescharacteristic, complemented
49C11×#382C2211yescharacteristic, complemented
50C11×#380C2211yescharacteristic
51C11×#379—21no—
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic, complemented
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—41no—
68C22×D4×C11—41no—
69C22×D4×C11D414yes—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×SD16—22no—
79C2×C11×SD16—41no—
80C2×C11×SD16—41no—
81C2×C11×M16—22no—
82C2×C11×M16—41no—
83C2×C11×M16—41no—
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—41no—
93C4×D4×C11—41no—
94C11×#117—22no—
95C11×#117—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—44no—
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C11×C4⋊C8—41no—
120C11×C4⋊C8—41no—
121C11×#103—41no—
122C11×#103—41no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×C22⋊C8—22no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95D411yescharacteristic
138C11×#95D411yescharacteristic
139#24538C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—24no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—42no—
146C24×C11—42no—
147C24×C11—81no—
148C24×C11—81no—
149C24×C11C2×D411yescharacteristic
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×D4×C11—28no—
157C2×D4×C11—24no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—44no—
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11C2×D412yes—
172C2×D4×C11C2×D412yes—
173C2×D4×C11#4112yes—
174C2×D4×C11#4112yes—
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—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—81no—
190C22×C4×C11—81no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11#4112yes—
198C22×C4×C11C2411yescharacteristic
199C11×SD16—44no—
200C11×SD16—44no—
201C11×M16—44no—
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—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
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—42no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4—42no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—41no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—81no—
237C11×C22⋊C4—81no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—42no—
243C2×#450C2×C1111yescharacteristic
244C2×#418C2×C1111yescharacteristic
245#2499C2×C1111yescharacteristic, complemented
246D4×C22⋊C4C2×C1111yescharacteristic
247#2073C2×C1111yescharacteristic, complemented
248#2071C2×C1111yescharacteristic, complemented
249#2055C2×C1111yescharacteristic, complemented
250#2055C2×C1111yescharacteristic, complemented
251#1894C2×C1111yescharacteristic, complemented
252#1877C2×C1111yescharacteristic, complemented
253#1877C2×C1111yescharacteristic, complemented
254#1851C2×C1111yescharacteristic, complemented
255#1825C2×C1111yescharacteristic, complemented
256#1804C2×C1111yescharacteristic, complemented
257#1802C2×C1111yescharacteristic, complemented
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—48no—
269C23×C11—48no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—84no—
281C23×C11—84no—
282C23×C11—84no—
283C23×C11—84no—
284C23×C11—84no—
285C23×C11#12112yes—
286C23×C11C22×D411yescharacteristic
287Q8×C11—41no—
288Q8×C11—41no—
289Q8×C11—41no—
290Q8×C11—41no—
291D4×C11—22no—
292D4×C11—22no—
293D4×C11—22no—
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—48no—
297D4×C11—41no—
298D4×C11—41no—
299D4×C11#12314yes—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
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—84no—
336C2×C4×C11—84no—
337C2×C4×C11#12112yes—
338C2×C4×C11AGL(1,ℤ/8)12yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11C2×#4111yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C8×C11—41no—
346C8×C11—41no—
347C8×C11—41no—
348C8×C11—41no—
349C23×D4C22×C1111yescharacteristic
350C22×SD16C22×C1111yescharacteristic
351C22×SD16C22×C1111yescharacteristic
352C22×M16C22×C1111yescharacteristic
353C2×C22⋊Q8C22×C1111yescharacteristic
354C2×C4×D4C22×C1111yescharacteristic
355C2×C4×D4C22×C1111yescharacteristic
356C2×#117C22×C1111yescharacteristic
357C22×C22⋊C4—21no—
358#450—24no—
359C2×C4⋊C8C22×C1111yescharacteristic, complemented
360C2×C4⋊C8C22×C1111yescharacteristic, complemented
361#418—24no—
362C2×#103C22×C1111yescharacteristic, complemented
363C2×#103C22×C1111yescharacteristic, complemented
364C2×#102C22×C1111yescharacteristic
365C2×#102C22×C1111yescharacteristic
366C2×#102C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×#102C22×C1111yescharacteristic
369C2×#102C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1111yescharacteristic
371#397—21no—
372#397—21no—
373#391C22×C1111yescharacteristic, complemented
374#391C22×C1111yescharacteristic, complemented
375#390C22×C1111yescharacteristic
376#390C22×C1111yescharacteristic
377#387—21no—
378#387—21no—
379#386—21no—
380#386—21no—
381#384C22×C1111yescharacteristic, complemented
382#382C22×C1111yescharacteristic, complemented
383#380C22×C1111yescharacteristic
384#379—21no—
385C4×C22⋊C4C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic, complemented
387#340C22×C1111yescharacteristic, complemented
388#340C22×C1111yescharacteristic, complemented
389#340C22×C1111yescharacteristic, complemented
390#340C22×C1111yescharacteristic, complemented
391#340C22×C1111yescharacteristic, complemented
392#336C22×C1111yescharacteristic, complemented
393#336C22×C1111yescharacteristic, complemented
394C22×C11—22no—
395C22×C11—24no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—42no—
404C22×C11—41no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—41no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—816no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11C2×#12111yescharacteristic
417C22×C11#54611yescharacteristic
418C22×C11#54611yescharacteristic
419C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
420C22×C11#57511yescharacteristic
421C22×C11#57711yescharacteristic
422C22×C11#57711yescharacteristic
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—81no—
429C4×C11—81no—
430C4×C11—81no—
431C4×C11—81no—
432C4×C11—81no—
433C4×C11—81no—
434C4×C11C2×#12311yescharacteristic
435C4×C11#53411yescharacteristic
436C4×C11#55111yescharacteristic
437C4×C11#55111yescharacteristic
438C25—21no—
439C22×Q8C23×C1111yescharacteristic
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—21no—
443C22×D4—22no—
444C22×D4—41no—
445C22×D4—41no—
446C22×D4D4×C1114yes—
447C22×D4C23×C1111yescharacteristic
448C22×D4C23×C1111yescharacteristic
449C23×C4—21no—
450C23×C4—21no—
451C23×C4C23×C1111yescharacteristic
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—41no—
457C2×SD16—41no—
458C2×M16—22no—
459C2×M16—41no—
460C2×M16—41no—
461C22×C8C23×C1111yescharacteristic
462C22×C8C23×C1111yescharacteristic
463C22×C8C23×C1111yescharacteristic
464C22×C8C23×C1111yescharacteristic
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—41no—
470C4×D4—41no—
471#117—22no—
472#117—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1111yescharacteristic
479C2×C4⋊C4C23×C1111yescharacteristic
480C2×C4⋊C4C23×C1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—44no—
491C2×C22⋊C4D4×C1111yescharacteristic
492C2×C22⋊C4D4×C1111yescharacteristic
493C2×C42—21no—
494C2×C42C23×C1111yescharacteristic
495C2×C42C23×C1111yescharacteristic
496C4⋊C8—41no—
497C4⋊C8—41no—
498#103—41no—
499#103—41no—
500#102—22no—
501#102—22no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—22no—
506C22⋊C8—22no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95D4×C1111yescharacteristic
515#95D4×C1111yescharacteristic
516C2×C11—42no—
517C2×C11—44no—
518C2×C11—82no—
519C2×C11#241211yescharacteristic
520C2×C11#303611yescharacteristic
521C2×C11#304211yescharacteristic
522C2×C11#331011yescharacteristic
523C2×C11#331111yescharacteristic
524C2×C11#332311yescharacteristic
525C2×C11#332411yescharacteristic
526C24—21no—
527C24—21no—
528C24—24no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—81no—
534C24—81no—
535C24C2×D4×C1111yescharacteristic
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×D4—28no—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4C2×D4×C1112yes—
558C2×D4C2×D4×C1112yes—
559C2×D4C11×#4112yes—
560C2×D4C11×#4112yes—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4C2×D4×C1111yescharacteristic
578C22×C4C2×D4×C1111yescharacteristic
579C22×C4C2×D4×C1111yescharacteristic
580C22×C4C2×D4×C1111yescharacteristic
581C22×C4C2×D4×C1112yes—
582C22×C4C2×D4×C1111yescharacteristic
583C22×C4C11×#4112yes—
584C22×C4C24×C1111yescharacteristic
585SD16—44no—
586SD16—44no—
587M16—44no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—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—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C22⋊C4—22no—
614C22⋊C4—41no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—42no—
629C11#2453811yescharacteristic, direct product factor, Sylow
630C23—22no—
631C23—22no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—48no—
641C23—48no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23C11×#12112yes—
658C23C22×D4×C1111yescharacteristic
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—41no—
670D4—41no—
671D4C11×#12314yes—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
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×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—84no—
708C2×C4—84no—
709C2×C4C11×#12112yes—
710C2×C4C11×AGL(1,ℤ/8)12yes—
711C2×C4C22×D4×C1111yescharacteristic
712C2×C4C2×C11×#4111yescharacteristic
713C2×C4C2×C11×#4111yescharacteristic
714C2×C4C2×C11×#4111yescharacteristic
715C2×C4C11×H(5,𝔽2)11yescharacteristic
716C2×C4C11×H(5,𝔽2)11yescharacteristic
717C8—41no—
718C8—41no—
719C8—41no—
720C8—41no—
721C22—22no—
722C22—24no—
723C22—22no—
724C22—22no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—816no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×C11×#12111yescharacteristic
744C22C11×#54611yescharacteristic
745C22C11×#54611yescharacteristic
746C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
747C22C11×#57511yescharacteristic
748C22C11×#57711yescharacteristic
749C22C11×#57711yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—81no—
756C4—81no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4C2×C11×#12311yescharacteristic
762C4C11×#53411yescharacteristic
763C4C11×#55111yescharacteristic
764C4C11×#55111yescharacteristic
765C2—42no—
766C2—44no—
767C2—82no—
768C2C11×#241211yescharacteristic
769C2C11×#303611yescharacteristic
770C2C11×#304211yescharacteristic
771C2C11×#331011yescharacteristic
772C2C11×#331111yescharacteristic
773C2C11×#332311yescharacteristic
774C2C11×#332411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2499C2semidirect
5. C11×#2073C2semidirect
6. C11×#2071C2semidirect
7. C11×#2055C2semidirect
8. C11×#2055C2semidirect
9. C11×#1894C2semidirect
10. C11×#1877C2semidirect
11. C11×#1877C2semidirect
12. C11×#1851C2semidirect
13. C11×#1825C2semidirect
14. C11×#1804C2semidirect
15. C11×#1802C2semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×C11×C4⋊C8C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
40. C11×#391C22semidirect
41. C11×#391C22semidirect
48. C11×#384C22semidirect
49. C11×#382C22semidirect
53. C11×#340C22semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
139. #24538C11direct (N × H)
245. #2499C2×C11semidirect
247. #2073C2×C11semidirect
248. #2071C2×C11semidirect
249. #2055C2×C11semidirect
250. #2055C2×C11semidirect
251. #1894C2×C11semidirect
252. #1877C2×C11semidirect
253. #1877C2×C11semidirect
254. #1851C2×C11semidirect
255. #1825C2×C11semidirect
256. #1804C2×C11semidirect
257. #1802C2×C11semidirect
359. C2×C4⋊C8C22×C11semidirect
360. C2×C4⋊C8C22×C11semidirect
362. C2×#103C22×C11semidirect
363. C2×#103C22×C11semidirect
373. #391C22×C11semidirect
374. #391C22×C11semidirect
381. #384C22×C11semidirect
382. #382C22×C11semidirect
386. #340C22×C11semidirect
387. #340C22×C11semidirect
388. #340C22×C11semidirect
389. #340C22×C11semidirect
390. #340C22×C11semidirect
391. #340C22×C11semidirect
392. #336C22×C11semidirect
393. #336C22×C11semidirect
629. C11#24538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4502
C2×C11×#4182
C11×#24992
D4×C11×C22⋊C42
C11×#20732
C11×#20712
C11×#20552
C11×#18942
C11×#18772
C11×#18512
C11×#18252
C11×#18042
C11×#18022
#2453811