Finite Group Databasebeta

← C11×#22414 #14599607

Subgroups — C11×#22414 #14599607

Order 2816.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic
2C2×C8×D4×C11C211yesmaximal, characteristic, complemented
3C2×C11×#416C211yesmaximal, characteristic, complemented
4C22×C11×#102C211yesmaximal, characteristic, complemented
5C11×#2352C211yesmaximal, characteristic, complemented
6C11×#1983C211yesmaximal, characteristic, complemented
7C11×#1958C211yesmaximal, characteristic, complemented
8C11×#1893C211yesmaximal, characteristic, complemented
9C11×#1892C211yesmaximal, characteristic, complemented
10C11×#1875C211yesmaximal, characteristic, complemented
11C11×#1872C211yesmaximal, characteristic, complemented
12C11×#1804C211yesmaximal, characteristic, complemented
13C11×#1788C211yesmaximal, characteristic, complemented
14C11×#1786C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic, complemented
20C11×#546—24no—
21C11×#546C418yescomplemented
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#120—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic, complemented
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4—21no—
33C8×D4×C11—24no—
34C2×C11×C4⋊C8C2211yescharacteristic, complemented
35C11×#416—24no—
36C2×C11×#103C2211yescharacteristic, complemented
37C2×C11×#103C2211yescharacteristic, complemented
38C2×C11×#103C2211yescharacteristic, complemented
39C2×C11×#103C2211yescharacteristic, complemented
40C2×C11×#102—24no—
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51C2×C4×C8×C11C2211yescharacteristic, complemented
52C11×#388—21no—
53C11×#387—21no—
54C11×#386—21no—
55C11×#382C2211yescharacteristic, complemented
56C11×#380C2211yescharacteristic
57C11×#380C2211yescharacteristic, complemented
58C4×C11×C4⋊C4C2211yescharacteristic, complemented
59C4×C11×C22⋊C4—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#340C2211yescharacteristic, complemented
64C25×C11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—22no—
73C22×D4×C11—22no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—22no—
78C22×D4×C11—41no—
79C22×D4×C11—41no—
80C22×D4×C11C2×C414yes—
81C22×D4×C11D411yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C8×C11—22no—
90C22×C8×C11—22no—
91C22×C8×C11—22no—
92C22×C8×C11—22no—
93C22×C8×C11—41no—
94C22×C8×C11—41no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C11×#124—22no—
100C11×#124C2×C414yescomplemented
101C11×#123—28no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8C2×C414yes—
104C11×#121—22no—
105C11×#121—28no—
106C11×#121C2×C414yescomplemented
107C11×#120—28no—
108C4×D4×C11—22no—
109C4×D4×C11C2×C414yes—
110C4×D4×C11C2×C414yescomplemented
111C4×D4×C11D414yes—
112C11×#117—22no—
113C11×#117—41no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—41no—
118C2×C11×C4⋊C4D411yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—28no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4D411yescharacteristic
134C2×C11×C22⋊C4D411yescharacteristic
135C2×C42×C11—21no—
136C2×C42×C11—21no—
137C2×C42×C11C2311yescharacteristic
138C11×C4⋊C8—22no—
139C11×#103—22no—
140C11×#103—22no—
141C11×#103—41no—
142C11×#103—41no—
143C11×#102—22no—
144C11×#102—22no—
145C11×#102—22no—
146C11×#102—22no—
147C11×#102—22no—
148C11×#102—41no—
149C11×#102—41no—
150C11×#102D414yescomplemented
151C11×C22⋊C8—22no—
152C11×C22⋊C8—22no—
153C4×C8×C11—22no—
154C11×#95—21no—
155C11×#95—21no—
156C11×#95—21no—
157C11×#95—21no—
158C11×#95—21no—
159#22414C1111yesmaximal, characteristic, direct product factor, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—24no—
163C24×C11—42no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—81no—
168C24×C11—81no—
169C24×C11C2×D411yescharacteristic
170C24×C11C2×D411yescharacteristic
171C11×#41—28no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11C22×C412yes—
181C2×D4×C11—22no—
182C2×D4×C11—22no—
183C2×D4×C11—28no—
184C2×D4×C11—24no—
185C2×D4×C11—24no—
186C2×D4×C11—24no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11—42no—
199C2×D4×C11—42no—
200C2×D4×C11—42no—
201C2×D4×C11—42no—
202C2×D4×C11—81no—
203C2×D4×C11—81no—
204C2×D4×C11C22⋊C414yes—
205C2×D4×C11C22×C412yes—
206C2×D4×C11C22×C412yes—
207C2×D4×C11C2×D412yes—
208C2×D4×C11#4112yes—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—24no—
221C22×C4×C11—24no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11—42no—
228C22×C4×C11—42no—
229C22×C4×C11—81no—
230C22×C4×C11—81no—
231C22×C4×C11—81no—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2411yescharacteristic
241C2×C8×C11—21no—
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×C11—44no—
253C2×C8×C11—44no—
254C2×C8×C11C2×D412yes—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—42no—
265C11×C4⋊C4C22⋊C414yes—
266C11×C4⋊C4C22×C412yes—
267C11×C4⋊C4C2×D412yes—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—42no—
274C11×C22⋊C4—42no—
275C11×C22⋊C4—81no—
276C11×C22⋊C4C22⋊C414yes—
277C11×C22⋊C4C22⋊C414yes—
278C42×C11—42no—
279C42×C11—81no—
280C42×C11C22×C412yes—
281C42×C11C2×D412yes—
282C2×#546C2×C1111yescharacteristic
283C2×C8×D4C2×C1111yescharacteristic, complemented
284C2×#416C2×C1111yescharacteristic, complemented
285C22×#102C2×C1111yescharacteristic, complemented
286#2352C2×C1111yescharacteristic, complemented
287#1983C2×C1111yescharacteristic, complemented
288#1958C2×C1111yescharacteristic, complemented
289#1893C2×C1111yescharacteristic, complemented
290#1892C2×C1111yescharacteristic, complemented
291#1875C2×C1111yescharacteristic, complemented
292#1872C2×C1111yescharacteristic, complemented
293#1804C2×C1111yescharacteristic, complemented
294#1788C2×C1111yescharacteristic, complemented
295#1786C2×C1111yescharacteristic, complemented
296C4×#102C2×C1111yescharacteristic, complemented
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—22no—
302C23×C11—21no—
303C23×C11—22no—
304C23×C11—21no—
305C23×C11—22no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—22no—
311C23×C11—48no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—48no—
323C23×C11—84no—
324C23×C11—84no—
325C23×C11—84no—
326C23×C11—84no—
327C23×C11—84no—
328C23×C11C2×C22⋊C412yes—
329C23×C11C2×C22⋊C412yes—
330C23×C11#13512yes—
331C23×C11#13512yes—
332C23×C11C22×D411yescharacteristic
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—41no—
336Q8×C11—41no—
337D4×C11—28no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—48no—
344D4×C11—48no—
345D4×C11—41no—
346D4×C11—41no—
347D4×C11—84no—
348D4×C11C4×D414yes—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—48no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—84no—
385C2×C4×C11—84no—
386C2×C4×C11C2×C22⋊C412yes—
387C2×C4×C11C2×C22⋊C412yes—
388C2×C4×C11C2×C22⋊C412yes—
389C2×C4×C11C2×C22⋊C412yes—
390C2×C4×C11C23×C411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C2×#4111yescharacteristic
394C2×C4×C11H(5,𝔽2)11yescharacteristic
395C2×C4×C11H(5,𝔽2)11yescharacteristic
396C8×C11—22no—
397C8×C11—41no—
398C8×C11—41no—
399C8×C11—41no—
400C22×#41C22×C1111yescharacteristic
401C23×D4C22×C1111yescharacteristic
402C23×C8C22×C1111yescharacteristic
403C23×C8C22×C1111yescharacteristic, complemented
404#546—24no—
405#546C4×C1118yescomplemented
406C2×#124C22×C1111yescharacteristic
407C2×#123—21no—
408C2×C22⋊Q8C22×C1111yescharacteristic
409C2×#121—21no—
410C2×#121C22×C1111yescharacteristic
411C2×#120—21no—
412C2×C4×D4C22×C1111yescharacteristic
413C2×C4×D4C22×C1111yescharacteristic
414C2×#117C22×C1111yescharacteristic, complemented
415C22×C4⋊C4C22×C1111yescharacteristic
416C22×C22⋊C4—21no—
417C8×D4—24no—
418C2×C4⋊C8C22×C1111yescharacteristic, complemented
419#416—24no—
420C2×#103C22×C1111yescharacteristic, complemented
421C2×#103C22×C1111yescharacteristic, complemented
422C2×#103C22×C1111yescharacteristic, complemented
423C2×#103C22×C1111yescharacteristic, complemented
424C2×#102—24no—
425C2×#102C22×C1111yescharacteristic
426C2×#102C22×C1111yescharacteristic
427C2×#102C22×C1111yescharacteristic
428C2×#102C22×C1111yescharacteristic
429C2×#102C22×C1111yescharacteristic
430C2×#102C22×C1111yescharacteristic
431C2×#102C22×C1111yescharacteristic
432C2×#102C22×C1111yescharacteristic
433C2×C22⋊C8C22×C1111yescharacteristic
434C2×C22⋊C8C22×C1111yescharacteristic, complemented
435C2×C4×C8C22×C1111yescharacteristic, complemented
436#388—21no—
437#387—21no—
438#386—21no—
439#382C22×C1111yescharacteristic, complemented
440#380C22×C1111yescharacteristic
441#380C22×C1111yescharacteristic, complemented
442C4×C4⋊C4C22×C1111yescharacteristic, complemented
443C4×C22⋊C4—21no—
444#340C22×C1111yescharacteristic, complemented
445#340C22×C1111yescharacteristic, complemented
446#340C22×C1111yescharacteristic, complemented
447#340C22×C1111yescharacteristic, complemented
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—24no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—41no—
461C22×C11—42no—
462C22×C11—41no—
463C22×C11—42no—
464C22×C11—41no—
465C22×C11—42no—
466C22×C11—41no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—816no—
472C22×C11—81no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11—81no—
476C22×C11#41614yescomplemented
477C22×C11C22×C22⋊C411yescharacteristic
478C22×C11D4211yescharacteristic
479C22×C11#54611yescharacteristic
480C22×C11C2×#13511yescharacteristic
481C22×C11C2×#13511yescharacteristic
482C22×C11#57611yescharacteristic
483C22×C11#57711yescharacteristic
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—81no—
492C4×C11—81no—
493C4×C11—81no—
494C4×C11C2×C4×D411yescharacteristic
495C4×C11#51811yescharacteristic
496C4×C11D4211yescharacteristic
497C4×C11#54611yescharacteristic
498C25—21no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41C2×C4×C1114yescomplemented
505C22×Q8C23×C1111yescharacteristic
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×C4×C1114yes—
515C22×D4D4×C1111yescharacteristic
516C22×D4C23×C1111yescharacteristic
517C22×D4C23×C1111yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C1111yescharacteristic
522C23×C4C23×C1111yescharacteristic
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8C23×C1111yescharacteristic
530C22×C8C23×C1111yescharacteristic
531C22×C8C23×C1111yescharacteristic
532C22×C8C23×C1111yescharacteristic
533#124—22no—
534#124C2×C4×C1114yescomplemented
535#123—28no—
536C22⋊Q8—22no—
537C22⋊Q8C2×C4×C1114yes—
538#121—22no—
539#121—28no—
540#121C2×C4×C1114yescomplemented
541#120—28no—
542C4×D4—22no—
543C4×D4C2×C4×C1114yes—
544C4×D4C2×C4×C1114yescomplemented
545C4×D4D4×C1114yes—
546#117—22no—
547#117—41no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4D4×C1111yescharacteristic
553C2×C4⋊C4C23×C1111yescharacteristic
554C2×C4⋊C4C23×C1111yescharacteristic
555C2×C4⋊C4C23×C1111yescharacteristic
556C2×C4⋊C4C23×C1111yescharacteristic
557C2×C4⋊C4C23×C1111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—28no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4D4×C1111yescharacteristic
568C2×C22⋊C4D4×C1111yescharacteristic
569C2×C42—21no—
570C2×C42—21no—
571C2×C42C23×C1111yescharacteristic
572C4⋊C8—22no—
573#103—22no—
574#103—22no—
575#103—41no—
576#103—41no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—22no—
582#102—41no—
583#102—41no—
584#102D4×C1114yescomplemented
585C22⋊C8—22no—
586C22⋊C8—22no—
587C4×C8—22no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—21no—
593C2×C11—24no—
594C2×C11—42no—
595C2×C11—44no—
596C2×C11—82no—
597C2×C11D4×C22⋊C411yescharacteristic
598C2×C11C2×#41611yescharacteristic
599C2×C11#289711yescharacteristic
600C2×C11#328011yescharacteristic
601C2×C11#328211yescharacteristic
602C2×C11#329611yescharacteristic
603C2×C11#329711yescharacteristic
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C1111yescharacteristic
614C24C2×D4×C1111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C1112yes—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—28no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C11×C22⋊C414yes—
649C2×D4C22×C4×C1112yes—
650C2×D4C22×C4×C1112yes—
651C2×D4C2×D4×C1112yes—
652C2×D4C11×#4112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4C22×C4×C1112yes—
677C22×C4C22×C4×C1112yes—
678C22×C4C2×D4×C1111yescharacteristic
679C22×C4C2×D4×C1111yescharacteristic
680C22×C4C2×D4×C1111yescharacteristic
681C22×C4C2×D4×C1111yescharacteristic
682C22×C4C2×D4×C1112yes—
683C22×C4C2×D4×C1112yes—
684C22×C4C24×C1111yescharacteristic
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—44no—
697C2×C8—44no—
698C2×C8C2×D4×C1112yes—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—42no—
709C4⋊C4C11×C22⋊C414yes—
710C4⋊C4C22×C4×C1112yes—
711C4⋊C4C2×D4×C1112yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4C11×C22⋊C414yes—
721C22⋊C4C11×C22⋊C414yes—
722C42—42no—
723C42—81no—
724C42C22×C4×C1112yes—
725C42C2×D4×C1112yes—
726C11#2241411yescharacteristic, direct product factor, Sylow
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—48no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23C2×C11×C22⋊C412yes—
759C23C2×C11×C22⋊C412yes—
760C23C11×#13512yes—
761C23C11×#13512yes—
762C23C22×D4×C1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—28no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4C4×D4×C1114yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×C11×C22⋊C412yes—
817C2×C4C2×C11×C22⋊C412yes—
818C2×C4C2×C11×C22⋊C412yes—
819C2×C4C2×C11×C22⋊C412yes—
820C2×C4C23×C4×C1111yescharacteristic
821C2×C4C22×D4×C1111yescharacteristic
822C2×C4C22×D4×C1111yescharacteristic
823C2×C4C2×C11×#4111yescharacteristic
824C2×C4C11×H(5,𝔽2)11yescharacteristic
825C2×C4C11×H(5,𝔽2)11yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—24no—
840C22—42no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—816no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22C11×#41614yescomplemented
859C22C22×C11×C22⋊C411yescharacteristic
860C22D42×C1111yescharacteristic
861C22C11×#54611yescharacteristic
862C22C2×C11×#13511yescharacteristic
863C22C2×C11×#13511yescharacteristic
864C22C11×#57611yescharacteristic
865C22C11×#57711yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4C2×C4×D4×C1111yescharacteristic
877C4C11×#51811yescharacteristic
878C4D42×C1111yescharacteristic
879C4C11×#54611yescharacteristic
880C2—24no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C11×C22⋊C411yescharacteristic
885C2C2×C11×#41611yescharacteristic
886C2C11×#289711yescharacteristic
887C2C11×#328011yescharacteristic
888C2C11×#328211yescharacteristic
889C2C11×#329611yescharacteristic
890C2C11×#329711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#546C2
LCSG ▷ C2×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×C8×D4×C11C2semidirect
3. C2×C11×#416C2semidirect
4. C22×C11×#102C2semidirect
5. C11×#2352C2semidirect
6. C11×#1983C2semidirect
7. C11×#1958C2semidirect
8. C11×#1893C2semidirect
9. C11×#1892C2semidirect
10. C11×#1875C2semidirect
11. C11×#1872C2semidirect
12. C11×#1804C2semidirect
13. C11×#1788C2semidirect
14. C11×#1786C2semidirect
15. C4×C11×#102C2semidirect
19. C23×C8×C11C22semidirect
21. C11×#546C4semidirect
30. C2×C11×#117C22semidirect
34. C2×C11×C4⋊C8C22semidirect
36. C2×C11×#103C22semidirect
37. C2×C11×#103C22semidirect
38. C2×C11×#103C22semidirect
39. C2×C11×#103C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. C2×C4×C8×C11C22semidirect
55. C11×#382C22semidirect
57. C11×#380C22semidirect
58. C4×C11×C4⋊C4C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#340C22semidirect
70. C2×C11×#41C2×C4semidirect
100. C11×#124C2×C4semidirect
106. C11×#121C2×C4semidirect
110. C4×D4×C11C2×C4semidirect
150. C11×#102D4semidirect
159. #22414C11direct (N × H)
283. C2×C8×D4C2×C11semidirect
284. C2×#416C2×C11semidirect
285. C22×#102C2×C11semidirect
286. #2352C2×C11semidirect
287. #1983C2×C11semidirect
288. #1958C2×C11semidirect
289. #1893C2×C11semidirect
290. #1892C2×C11semidirect
291. #1875C2×C11semidirect
292. #1872C2×C11semidirect
293. #1804C2×C11semidirect
294. #1788C2×C11semidirect
295. #1786C2×C11semidirect
296. C4×#102C2×C11semidirect
403. C23×C8C22×C11semidirect
405. #546C4×C11semidirect
414. C2×#117C22×C11semidirect
418. C2×C4⋊C8C22×C11semidirect
420. C2×#103C22×C11semidirect
421. C2×#103C22×C11semidirect
422. C2×#103C22×C11semidirect
423. C2×#103C22×C11semidirect
434. C2×C22⋊C8C22×C11semidirect
435. C2×C4×C8C22×C11semidirect
439. #382C22×C11semidirect
441. #380C22×C11semidirect
442. C4×C4⋊C4C22×C11semidirect
444. #340C22×C11semidirect
445. #340C22×C11semidirect
446. #340C22×C11semidirect
447. #340C22×C11semidirect
476. C22×C11#416semidirect
504. C2×#41C2×C4×C11semidirect
534. #124C2×C4×C11semidirect
540. #121C2×C4×C11semidirect
544. C4×D4C2×C4×C11semidirect
584. #102D4×C11semidirect
726. C11#22414direct (N × H)
858. C22C11×#416semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5462
C2×C8×D4×C112
C2×C11×#4162
C22×C11×#1022
C11×#23522
C11×#19832
C11×#19582
C11×#18932
C11×#18922
C11×#18752
C11×#18722
C11×#18042
C11×#17882
C11×#17862
C4×C11×#1022
#2241411