Finite Group Databasebeta

← C11×#24369 #14601562

Subgroups — C11×#24369 #14601562

Order 2816.

1388 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic
2C2×C11×#464C211yesmaximal, characteristic, complemented
3C2×C11×#462C211yesmaximal, characteristic, complemented
4C2×C11×#451C211yesmaximal, characteristic, complemented
5C11×#2432C211yesmaximal, characteristic
6Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
7C11×#2056C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#2016C211yesmaximal, characteristic, complemented
10C11×#2015C211yesmaximal, characteristic, complemented
11C11×#1894C211yesmaximal, characteristic, complemented
12C11×#1880C211yesmaximal, characteristic, complemented
13C11×#1878C211yesmaximal, characteristic, complemented
14C11×#1851C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C2×C11×#137—24no—
19C2×C11×#137—24no—
20C2×C11×#137—24no—
21C22×C11×Q16C2211yescharacteristic
22C22×C11×Q16C2211yescharacteristic
23C22×C11×Q16C2211yescharacteristic
24C22×C11×Q16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic
26C22×C11×SD16C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C2×C11×#124C2211yescharacteristic
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C4×Q8×C11C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C11×#464—24no—
34C11×#462—24no—
35C11×#451—24no—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C11×#394—21no—
48C11×#394—21no—
49C11×#391—21no—
50C11×#391—21no—
51C11×#391C2211yescharacteristic
52C11×#391C2211yescharacteristic
53C11×#391C2211yescharacteristic
54C11×#390C2211yescharacteristic
55C11×#385—21no—
56C11×#385—21no—
57C11×#380—21no—
58C11×#380C2211yescharacteristic
59C4×C11×C22⋊C4—21no—
60C4×C11×C22⋊C4C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11—21no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—22no—
75C22×Q8×C11—41no—
76C22×Q8×C11—41no—
77C22×Q8×C11D414yes—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C11×#137—232no—
88C2×C11×Q16—22no—
89C2×C11×Q16—22no—
90C2×C11×Q16—22no—
91C2×C11×Q16—22no—
92C2×C11×Q16—22no—
93C2×C11×Q16—22no—
94C2×C11×Q16—22no—
95C2×C11×Q16—22no—
96C2×C11×Q16—22no—
97C2×C11×Q16—41no—
98C2×C11×Q16—41no—
99C2×C11×Q16D414yes—
100C2×C11×SD16—22no—
101C2×C11×SD16—22no—
102C2×C11×SD16—22no—
103C2×C11×SD16—22no—
104C2×C11×SD16—22no—
105C2×C11×SD16D414yes—
106C2×C11×M16—22no—
107C2×C11×M16—22no—
108C2×C11×M16—22no—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C11×C4⋊Q8—22no—
114C11×C4⋊Q8—41no—
115C11×#124—22no—
116C11×#124—41no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—22no—
119C4×Q8×C11—22no—
120C4×Q8×C11—22no—
121C4×Q8×C11—41no—
122C4×Q8×C11—41no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4D411yescharacteristic
138C2×C11×C22⋊C4D411yescharacteristic
139C2×C42×C11—21no—
140C2×C42×C11—21no—
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143C11×C4⋊C8—22no—
144C11×C4⋊C8—22no—
145C11×#103—22no—
146C11×#103—22no—
147C11×#103—22no—
148C11×#103—22no—
149C11×#103—22no—
150C11×#103—41no—
151C11×#102—22no—
152C11×#102—41no—
153C11×C22⋊C8—22no—
154C11×#95—21no—
155C11×#95—21no—
156C11×#95—21no—
157C11×#95—21no—
158C11×#95—21no—
159C11×#95—21no—
160C11×#95—21no—
161C11×#95D411yescharacteristic
162C11×#95D411yescharacteristic
163#24369C1111yesmaximal, characteristic, direct product factor, Sylow
164C24×C11—21no—
165C24×C11C2×D411yescharacteristic
166C11×#41—28no—
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C2×Q8×C11—24no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—28no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—42no—
192C2×Q8×C11—42no—
193C2×Q8×C11—44no—
194C2×Q8×C11—44no—
195C2×Q8×C11—44no—
196C2×Q8×C11C2×D412yes—
197C2×Q8×C11C2×D412yes—
198C2×Q8×C11C2×D412yes—
199C2×Q8×C11C2×D412yes—
200C2×Q8×C11C2×D412yes—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11C2×D412yes—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—24no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11#4112yes—
234C22×C4×C11C2411yescharacteristic
235C11×Q16—28no—
236C11×Q16—28no—
237C11×Q16—44no—
238C11×Q16—44no—
239C11×SD16—28no—
240C11×SD16—28no—
241C11×M16—28no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11C2×D412yes—
253C2×C8×C11C2×D412yes—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—42no—
261C11×C4⋊C4—42no—
262C11×C4⋊C4—42no—
263C11×C4⋊C4—42no—
264C11×C4⋊C4—42no—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—41no—
267C11×C22⋊C4—42no—
268C11×C22⋊C4—42no—
269C11×C22⋊C4—42no—
270C11×C22⋊C4—42no—
271C11×C22⋊C4—42no—
272C11×C22⋊C4—42no—
273C42×C11—21no—
274C42×C11—21no—
275C42×C11—21no—
276C42×C11—21no—
277C42×C11—42no—
278C42×C11—42no—
279C22×#137C2×C1111yescharacteristic
280C2×#464C2×C1111yescharacteristic, complemented
281C2×#462C2×C1111yescharacteristic, complemented
282C2×#451C2×C1111yescharacteristic, complemented
283#2432C2×C1111yescharacteristic
284Q8×C22⋊C4C2×C1111yescharacteristic, complemented
285#2056C2×C1111yescharacteristic, complemented
286#2055C2×C1111yescharacteristic, complemented
287#2016C2×C1111yescharacteristic, complemented
288#2015C2×C1111yescharacteristic, complemented
289#1894C2×C1111yescharacteristic, complemented
290#1880C2×C1111yescharacteristic, complemented
291#1878C2×C1111yescharacteristic, complemented
292#1851C2×C1111yescharacteristic, complemented
293#1788C2×C1111yescharacteristic
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—22no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11#12112yes—
308C23×C11C22×D411yescharacteristic
309Q8×C11—22no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—22no—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—48no—
317Q8×C11—41no—
318Q8×C11—41no—
319Q8×C11—41no—
320Q8×C11—41no—
321Q8×C11—41no—
322Q8×C11—41no—
323Q8×C11—41no—
324Q8×C11—41no—
325Q8×C11#12014yes—
326D4×C11—22no—
327D4×C11—22no—
328D4×C11—48no—
329D4×C11—41no—
330D4×C11—41no—
331C2×C4×C11—22no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—22no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—48no—
354C2×C4×C11—48no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11#12112yes—
372C2×C4×C11#13712yescomplemented
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C2×#4111yescharacteristic
377C2×C4×C11H(5,𝔽2)11yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C8×C11—22no—
380C8×C11—22no—
381C8×C11—41no—
382C8×C11—41no—
383C22×#41C22×C1111yescharacteristic
384C23×Q8C22×C1111yescharacteristic
385C2×#137—24no—
386C2×#137—24no—
387C2×#137—24no—
388C22×Q16C22×C1111yescharacteristic
389C22×Q16C22×C1111yescharacteristic
390C22×Q16C22×C1111yescharacteristic
391C22×Q16C22×C1111yescharacteristic
392C22×SD16C22×C1111yescharacteristic
393C22×SD16C22×C1111yescharacteristic
394C22×M16C22×C1111yescharacteristic
395C2×C4⋊Q8C22×C1111yescharacteristic
396C2×#124C22×C1111yescharacteristic
397C2×C22⋊Q8C22×C1111yescharacteristic
398C2×C4×Q8C22×C1111yescharacteristic
399C2×C4×Q8C22×C1111yescharacteristic
400#464—24no—
401#462—24no—
402#451—24no—
403C2×C4⋊C8C22×C1111yescharacteristic
404C2×C4⋊C8C22×C1111yescharacteristic
405C2×#103C22×C1111yescharacteristic
406C2×#103C22×C1111yescharacteristic
407C2×#103C22×C1111yescharacteristic
408C2×#103C22×C1111yescharacteristic
409C2×#103C22×C1111yescharacteristic
410C2×#103C22×C1111yescharacteristic
411C2×#102C22×C1111yescharacteristic
412C2×#102C22×C1111yescharacteristic
413C2×C22⋊C8C22×C1111yescharacteristic
414#394—21no—
415#394—21no—
416#391—21no—
417#391—21no—
418#391C22×C1111yescharacteristic
419#391C22×C1111yescharacteristic
420#391C22×C1111yescharacteristic
421#390C22×C1111yescharacteristic
422#385—21no—
423#385—21no—
424#380—21no—
425#380C22×C1111yescharacteristic
426C4×C22⋊C4—21no—
427C4×C22⋊C4C22×C1111yescharacteristic
428#340C22×C1111yescharacteristic
429#340C22×C1111yescharacteristic
430#336C22×C1111yescharacteristic
431#336C22×C1111yescharacteristic
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—81no—
443C22×C11—81no—
444C22×C11—81no—
445C22×C11—81no—
446C22×C11C2×#12111yescharacteristic
447C22×C11D4211yescharacteristic
448C22×C11D4211yescharacteristic
449C22×C11C2×#13711yescharacteristic
450C22×C11#57511yescharacteristic
451C22×C11#57811yescharacteristic
452C22×C11#57811yescharacteristic
453C4×C11—22no—
454C4×C11—24no—
455C4×C11—22no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11—41no—
459C4×C11—41no—
460C4×C11—41no—
461C4×C11—81no—
462C4×C11—81no—
463C4×C11—81no—
464C4×C11—81no—
465C4×C11C2×#12011yescharacteristic
466C4×C11#53411yescharacteristic
467C4×C11#54611yescharacteristic
468C4×C11#54611yescharacteristic
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—41no—
474C2×#41—41no—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—22no—
478C22×Q8—22no—
479C22×Q8—41no—
480C22×Q8—41no—
481C22×Q8D4×C1114yes—
482C22×Q8C23×C1111yescharacteristic
483C22×Q8C23×C1111yescharacteristic
484C22×Q8C23×C1111yescharacteristic
485C22×Q8C23×C1111yescharacteristic
486C22×D4—21no—
487C22×D4C23×C1111yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C23×C1111yescharacteristic
491#137—232no—
492C2×Q16—22no—
493C2×Q16—22no—
494C2×Q16—22no—
495C2×Q16—22no—
496C2×Q16—22no—
497C2×Q16—22no—
498C2×Q16—22no—
499C2×Q16—22no—
500C2×Q16—22no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×Q16D4×C1114yes—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C1114yes—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C22×C8C23×C1111yescharacteristic
514C22×C8C23×C1111yescharacteristic
515C22×C8C23×C1111yescharacteristic
516C22×C8C23×C1111yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519#124—22no—
520#124—41no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C4×Q8—22no—
524C4×Q8—22no—
525C4×Q8—41no—
526C4×Q8—41no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4C23×C1111yescharacteristic
533C2×C4⋊C4C23×C1111yescharacteristic
534C2×C4⋊C4C23×C1111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4D4×C1111yescharacteristic
542C2×C22⋊C4D4×C1111yescharacteristic
543C2×C42—21no—
544C2×C42—21no—
545C2×C42C23×C1111yescharacteristic
546C2×C42C23×C1111yescharacteristic
547C4⋊C8—22no—
548C4⋊C8—22no—
549#103—22no—
550#103—22no—
551#103—22no—
552#103—22no—
553#103—22no—
554#103—41no—
555#102—22no—
556#102—41no—
557C22⋊C8—22no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95D4×C1111yescharacteristic
566#95D4×C1111yescharacteristic
567C2×C11—42no—
568C2×C11—82no—
569C2×C11#241011yescharacteristic
570C2×C11#303711yescharacteristic
571C2×C11#304411yescharacteristic
572C2×C11#326911yescharacteristic
573C2×C11#327011yescharacteristic
574C2×C11#327611yescharacteristic
575C2×C11#327711yescharacteristic
576C24—21no—
577C24C2×D4×C1111yescharacteristic
578#41—28no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—24no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—28no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8C2×D4×C1112yes—
609C2×Q8C2×D4×C1112yes—
610C2×Q8C2×D4×C1112yes—
611C2×Q8C2×D4×C1112yes—
612C2×Q8C2×D4×C1112yes—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×D4×C1112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4C2×D4×C1111yescharacteristic
640C22×C4C2×D4×C1111yescharacteristic
641C22×C4C2×D4×C1111yescharacteristic
642C22×C4C2×D4×C1111yescharacteristic
643C22×C4C2×D4×C1112yes—
644C22×C4C2×D4×C1111yescharacteristic
645C22×C4C11×#4112yes—
646C22×C4C24×C1111yescharacteristic
647Q16—28no—
648Q16—28no—
649Q16—44no—
650Q16—44no—
651SD16—28no—
652SD16—28no—
653M16—28no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8C2×D4×C1112yes—
665C2×C8C2×D4×C1112yes—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—42no—
690C42—42no—
691C11#2436911yescharacteristic, direct product factor, Sylow
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23C11×#12112yes—
706C23C22×D4×C1111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—22no—
712Q8—22no—
713Q8—22no—
714Q8—48no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8C11×#12014yes—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4C11×#12112yes—
770C2×C4C11×#13712yescomplemented
771C2×C4C22×D4×C1111yescharacteristic
772C2×C4C22×D4×C1111yescharacteristic
773C2×C4C22×D4×C1111yescharacteristic
774C2×C4C2×C11×#4111yescharacteristic
775C2×C4C11×H(5,𝔽2)11yescharacteristic
776C2×C4C11×H(5,𝔽2)11yescharacteristic
777C8—22no—
778C8—22no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C11×#12111yescharacteristic
796C22D42×C1111yescharacteristic
797C22D42×C1111yescharacteristic
798C22C2×C11×#13711yescharacteristic
799C22C11×#57511yescharacteristic
800C22C11×#57811yescharacteristic
801C22C11×#57811yescharacteristic
802C4—22no—
803C4—24no—
804C4—22no—
805C4—42no—
806C4—42no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4C2×C11×#12011yescharacteristic
815C4C11×#53411yescharacteristic
816C4C11×#54611yescharacteristic
817C4C11×#54611yescharacteristic
818C2—42no—
819C2—82no—
820C2C11×#241011yescharacteristic
821C2C11×#303711yescharacteristic
822C2C11×#304411yescharacteristic
823C2C11×#326911yescharacteristic
824C2C11×#327011yescharacteristic
825C2C11×#327611yescharacteristic
826C2C11×#327711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
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
2. C2×C11×#464C2semidirect
3. C2×C11×#462C2semidirect
4. C2×C11×#451C2semidirect
6. Q8×C11×C22⋊C4C2semidirect
7. C11×#2056C2semidirect
8. C11×#2055C2semidirect
9. C11×#2016C2semidirect
10. C11×#2015C2semidirect
11. C11×#1894C2semidirect
12. C11×#1880C2semidirect
13. C11×#1878C2semidirect
14. C11×#1851C2semidirect
163. #24369C11direct (N × H)
280. C2×#464C2×C11semidirect
281. C2×#462C2×C11semidirect
282. C2×#451C2×C11semidirect
284. Q8×C22⋊C4C2×C11semidirect
285. #2056C2×C11semidirect
286. #2055C2×C11semidirect
287. #2016C2×C11semidirect
288. #2015C2×C11semidirect
289. #1894C2×C11semidirect
290. #1880C2×C11semidirect
291. #1878C2×C11semidirect
292. #1851C2×C11semidirect
372. C2×C4×C11#137semidirect
691. C11#24369direct (N × H)
770. C2×C4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#4642
C2×C11×#4622
C2×C11×#4512
C11×#24322
Q8×C11×C22⋊C42
C11×#20562
C11×#20552
C11×#20162
C11×#20152
C11×#18942
C11×#18802
C11×#18782
C11×#18512
C11×#17882
#2436911