Finite Group Databasebeta

← C11×#24044 #14601237

Subgroups — C11×#24044 #14601237

Order 2816.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C11C211yesmaximal, characteristic
2C2×C11×#482C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C11×#2485C211yesmaximal, characteristic, complemented
5C11×#2041C211yesmaximal, characteristic, complemented
6C11×#2041C211yesmaximal, 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×#1786C211yesmaximal, characteristic, complemented
14C11×#1786C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11—21no—
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic, complemented
20D42×C11—24no—
21D42×C11—24no—
22C2×C11×#127C2211yescharacteristic
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#120—21no—
27C2×C11×#120—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic, complemented
31C11×#482—24no—
32C2×C11×#107C2211yescharacteristic, complemented
33C2×C11×#106C2211yescharacteristic, complemented
34C11×#418—24no—
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic, complemented
40C2×C11×#102C2211yescharacteristic, complemented
41C2×C11×#102C2211yescharacteristic, complemented
42C2×C11×#102C2211yescharacteristic, complemented
43C2×C11×#102C2211yescharacteristic, complemented
44C2×C11×#102C2211yescharacteristic, complemented
45C2×C11×#102C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic, complemented
47C2×C11×C22⋊C8C2211yescharacteristic, complemented
48C2×C11×C22⋊C8C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic, complemented
50C11×#397—21no—
51C11×#394—21no—
52C11×#389C2211yescharacteristic, complemented
53C11×#389C2211yescharacteristic, complemented
54C11×#388—21no—
55C11×#387—21no—
56C11×#380C2211yescharacteristic, complemented
57C11×#380C2211yescharacteristic, complemented
58C11×#380C2211yescharacteristic, complemented
59C11×#340C2211yescharacteristic, complemented
60C11×#340C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63C25×C11—21no—
64C25×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—28no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C22×D4×C11—22no—
71C22×D4×C11—22no—
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—21no—
79C22×D4×C11—41no—
80C22×D4×C11—41no—
81C22×D4×C11—41no—
82C22×D4×C11—41no—
83C22×D4×C11—44no—
84C22×D4×C11—44no—
85C22×D4×C11D411yescharacteristic
86C22×D4×C11D414yes—
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C2×C11×M16—22no—
94C2×C11×M16—41no—
95C2×C11×M16—41no—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#127—22no—
101C11×#127—22no—
102C11×#121—28no—
103C11×#121—22no—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121D414yes—
107C11×#120—28no—
108C11×#120—28no—
109C4×D4×C11—22no—
110C4×D4×C11—22no—
111C4×D4×C11—22no—
112C4×D4×C11—22no—
113C11×#117—22no—
114C11×#117—22no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—21no—
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—21no—
130C2×C11×C22⋊C4D411yescharacteristic
131C2×C11×C22⋊C4D411yescharacteristic
132C2×C42×C11—21no—
133C2×C42×C11C2311yescharacteristic
134C11×#107—22no—
135C11×#106—22no—
136C11×#102—22no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—22no—
141C11×#102—22no—
142C11×#102—22no—
143C11×#102—22no—
144C11×#102—41no—
145C11×#102—41no—
146C11×#102—41no—
147C11×#102—41no—
148C11×C22⋊C8—22no—
149C11×C22⋊C8—41no—
150C11×C22⋊C8—41no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154C11×#95—21no—
155C11×#95—21no—
156#24044C1111yesmaximal, characteristic, direct product factor, Sylow
157C24×C11—21no—
158C24×C11—24no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—24no—
162C24×C11—42no—
163C24×C11—42no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—81no—
171C24×C11—81no—
172C24×C11—81no—
173C24×C11—81no—
174C24×C11C2×D411yescharacteristic
175C24×C11C2×D411yescharacteristic
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11—28no—
179C2×D4×C11—24no—
180C2×D4×C11—24no—
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—22no—
186C2×D4×C11—21no—
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—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—44no—
200C2×D4×C11—44no—
201C2×D4×C11—44no—
202C2×D4×C11—42no—
203C2×D4×C11—42no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—44no—
208C2×D4×C11—44no—
209C2×D4×C11—432no—
210C2×D4×C11—44no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—44no—
216C2×D4×C11—42no—
217C2×D4×C11—81no—
218C2×D4×C11—81no—
219C2×D4×C11C2×D412yes—
220C2×D4×C11C2×D412yes—
221C2×D4×C11C2×D412yes—
222C2×D4×C11#4112yes—
223C2×D4×C11#4112yes—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—24no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—42no—
241C22×C4×C11—42no—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C11×M16—44no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C11×C4⋊C4—22no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—42no—
273C11×C4⋊C4—81no—
274C11×C4⋊C4C2×D412yes—
275C11×C22⋊C4—24no—
276C11×C22⋊C4—24no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—24no—
279C11×C22⋊C4—22no—
280C11×C22⋊C4—42no—
281C11×C22⋊C4—42no—
282C11×C22⋊C4—81no—
283C11×C22⋊C4—81no—
284C42×C11—21no—
285C42×C11—21no—
286C42×C11—42no—
287C2×D42C2×C1111yescharacteristic
288C2×#482C2×C1111yescharacteristic, complemented
289C2×#418C2×C1111yescharacteristic, complemented
290#2485C2×C1111yescharacteristic, complemented
291#2041C2×C1111yescharacteristic, complemented
292#2041C2×C1111yescharacteristic, complemented
293#2034C2×C1111yescharacteristic, complemented
294#2033C2×C1111yescharacteristic, complemented
295#1895C2×C1111yescharacteristic, complemented
296#1870C2×C1111yescharacteristic, complemented
297#1864C2×C1111yescharacteristic, complemented
298#1862C2×C1111yescharacteristic, complemented
299#1786C2×C1111yescharacteristic, complemented
300#1786C2×C1111yescharacteristic, complemented
301#1786C2×C1111yescharacteristic, complemented
302C23×C11—21no—
303C23×C11—22no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—48no—
320C23×C11—48no—
321C23×C11—48no—
322C23×C11—48no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—84no—
340C23×C11—84no—
341C23×C11—84no—
342C23×C11—84no—
343C23×C11—84no—
344C23×C11—84no—
345C23×C11—84no—
346C23×C11—84no—
347C23×C11—84no—
348C23×C11—84no—
349C23×C11#12012yes—
350C23×C11AGL(1,ℤ/8)12yes—
351C23×C11C22×D411yescharacteristic
352D4×C11—28no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—48no—
361D4×C11—48no—
362D4×C11—48no—
363D4×C11—48no—
364D4×C11—48no—
365D4×C11—41no—
366D4×C11—41no—
367D4×C11—41no—
368D4×C11—41no—
369D4×C11—84no—
370D4×C11#12314yes—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—48no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11#12012yes—
406C2×C4×C11AGL(1,ℤ/8)12yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C2×#4111yescharacteristic
410C2×C4×C11C2×#4111yescharacteristic
411C2×C4×C11H(5,𝔽2)11yescharacteristic
412C2×C4×C11H(5,𝔽2)11yescharacteristic
413C8×C11—41no—
414C8×C11—41no—
415C8×C11—41no—
416C8×C11—41no—
417C23×D4—21no—
418C23×D4C22×C1111yescharacteristic
419C23×D4C22×C1111yescharacteristic
420C22×M16C22×C1111yescharacteristic, complemented
421D42—24no—
422D42—24no—
423C2×#127C22×C1111yescharacteristic
424C2×#121—21no—
425C2×#121C22×C1111yescharacteristic
426C2×#121C22×C1111yescharacteristic
427C2×#120—21no—
428C2×#120—21no—
429C2×C4×D4C22×C1111yescharacteristic
430C2×C4×D4C22×C1111yescharacteristic
431C2×#117C22×C1111yescharacteristic, complemented
432#482—24no—
433C2×#107C22×C1111yescharacteristic, complemented
434C2×#106C22×C1111yescharacteristic, complemented
435#418—24no—
436C2×#102C22×C1111yescharacteristic
437C2×#102C22×C1111yescharacteristic
438C2×#102C22×C1111yescharacteristic
439C2×#102C22×C1111yescharacteristic
440C2×#102C22×C1111yescharacteristic, complemented
441C2×#102C22×C1111yescharacteristic, complemented
442C2×#102C22×C1111yescharacteristic, complemented
443C2×#102C22×C1111yescharacteristic, complemented
444C2×#102C22×C1111yescharacteristic, complemented
445C2×#102C22×C1111yescharacteristic, complemented
446C2×#102C22×C1111yescharacteristic, complemented
447C2×#102C22×C1111yescharacteristic, complemented
448C2×C22⋊C8C22×C1111yescharacteristic, complemented
449C2×C22⋊C8C22×C1111yescharacteristic, complemented
450C2×C22⋊C8C22×C1111yescharacteristic, complemented
451#397—21no—
452#394—21no—
453#389C22×C1111yescharacteristic, complemented
454#389C22×C1111yescharacteristic, complemented
455#388—21no—
456#387—21no—
457#380C22×C1111yescharacteristic, complemented
458#380C22×C1111yescharacteristic, complemented
459#380C22×C1111yescharacteristic, complemented
460#340C22×C1111yescharacteristic, complemented
461#340C22×C1111yescharacteristic, complemented
462#336C22×C1111yescharacteristic, complemented
463#336C22×C1111yescharacteristic, complemented
464C22×C11—22no—
465C22×C11—24no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—41no—
472C22×C11—42no—
473C22×C11—41no—
474C22×C11—42no—
475C22×C11—41no—
476C22×C11—42no—
477C22×C11—41no—
478C22×C11—42no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—42no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—816no—
492C22×C11—816no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11—81no—
496C22×C11—81no—
497C22×C11—81no—
498C22×C11—81no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11C2×#12011yescharacteristic
502C22×C11#54611yescharacteristic
503C22×C11#54611yescharacteristic
504C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
505C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
506C22×C11#57611yescharacteristic
507C22×C11#57711yescharacteristic
508C4×C11—22no—
509C4×C11—22no—
510C4×C11—41no—
511C4×C11—42no—
512C4×C11—41no—
513C4×C11—81no—
514C4×C11—81no—
515C4×C11—81no—
516C4×C11—81no—
517C4×C11C2×#12311yescharacteristic
518C4×C11#53411yescharacteristic
519C4×C11#54611yescharacteristic
520C4×C11#54611yescharacteristic
521C25—21no—
522C25—21no—
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—28no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—22no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4—41no—
540C22×D4—41no—
541C22×D4—44no—
542C22×D4—44no—
543C22×D4D4×C1111yescharacteristic
544C22×D4D4×C1114yes—
545C22×D4C23×C1111yescharacteristic
546C22×D4C23×C1111yescharacteristic
547C22×D4C23×C1111yescharacteristic
548C23×C4—21no—
549C23×C4C23×C1111yescharacteristic
550C23×C4C23×C1111yescharacteristic
551C2×M16—22no—
552C2×M16—41no—
553C2×M16—41no—
554C22×C8C23×C1111yescharacteristic
555C22×C8C23×C1111yescharacteristic
556C22×C8C23×C1111yescharacteristic
557C22×C8C23×C1111yescharacteristic
558#127—22no—
559#127—22no—
560#121—28no—
561#121—22no—
562#121—22no—
563#121—22no—
564#121D4×C1114yes—
565#120—28no—
566#120—28no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571#117—22no—
572#117—22no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4D4×C1111yescharacteristic
576C2×C4⋊C4C23×C1111yescharacteristic
577C2×C4⋊C4C23×C1111yescharacteristic
578C2×C4⋊C4C23×C1111yescharacteristic
579C2×C4⋊C4C23×C1111yescharacteristic
580C2×C4⋊C4C23×C1111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4D4×C1111yescharacteristic
589C2×C22⋊C4D4×C1111yescharacteristic
590C2×C42—21no—
591C2×C42C23×C1111yescharacteristic
592#107—22no—
593#106—22no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102—41no—
604#102—41no—
605#102—41no—
606C22⋊C8—22no—
607C22⋊C8—41no—
608C22⋊C8—41no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95—21no—
613#95—21no—
614C2×C11—42no—
615C2×C11—42no—
616C2×C11—44no—
617C2×C11—82no—
618C2×C11—82no—
619C2×C11#240511yescharacteristic
620C2×C11#300311yescharacteristic
621C2×C11#301211yescharacteristic
622C2×C11#331011yescharacteristic
623C2×C11#331811yescharacteristic
624C2×C11#332411yescharacteristic
625C2×C11#332511yescharacteristic
626C24—21no—
627C24—24no—
628C24—21no—
629C24—21no—
630C24—24no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—81no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24C2×D4×C1111yescharacteristic
644C24C2×D4×C1111yescharacteristic
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—28no—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—432no—
679C2×D4—44no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4C2×D4×C1112yes—
689C2×D4C2×D4×C1112yes—
690C2×D4C2×D4×C1112yes—
691C2×D4C11×#4112yes—
692C2×D4C11×#4112yes—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4C2×D4×C1111yescharacteristic
712C22×C4C2×D4×C1111yescharacteristic
713C22×C4C2×D4×C1111yescharacteristic
714C22×C4C2×D4×C1112yes—
715C22×C4C2×D4×C1112yes—
716C22×C4C2×D4×C1111yescharacteristic
717C22×C4C24×C1111yescharacteristic
718M16—44no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—81no—
743C4⋊C4C2×D4×C1112yes—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C22⋊C4—81no—
753C42—21no—
754C42—21no—
755C42—42no—
756C11#2404411yescharacteristic, direct product factor, Sylow
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23C11×#12012yes—
805C23C11×AGL(1,ℤ/8)12yes—
806C23C22×D4×C1111yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4C11×#12314yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4C11×#12012yes—
861C2×C4C11×AGL(1,ℤ/8)12yes—
862C2×C4C22×D4×C1111yescharacteristic
863C2×C4C22×D4×C1111yescharacteristic
864C2×C4C2×C11×#4111yescharacteristic
865C2×C4C2×C11×#4111yescharacteristic
866C2×C4C11×H(5,𝔽2)11yescharacteristic
867C2×C4C11×H(5,𝔽2)11yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—42no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×C11×#12011yescharacteristic
910C22C11×#54611yescharacteristic
911C22C11×#54611yescharacteristic
912C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
913C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
914C22C11×#57611yescharacteristic
915C22C11×#57711yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×C11×#12311yescharacteristic
926C4C11×#53411yescharacteristic
927C4C11×#54611yescharacteristic
928C4C11×#54611yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C11×#240511yescharacteristic
935C2C11×#300311yescharacteristic
936C2C11×#301211yescharacteristic
937C2C11×#331011yescharacteristic
938C2C11×#331811yescharacteristic
939C2C11×#332411yescharacteristic
940C2C11×#332511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×D42×C11C2
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×#418C2semidirect
4. C11×#2485C2semidirect
5. C11×#2041C2semidirect
6. C11×#2041C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1895C2semidirect
10. C11×#1870C2semidirect
11. C11×#1864C2semidirect
12. C11×#1862C2semidirect
13. C11×#1786C2semidirect
14. C11×#1786C2semidirect
15. C11×#1786C2semidirect
19. C22×C11×M16C22semidirect
30. C2×C11×#117C22semidirect
32. C2×C11×#107C22semidirect
33. C2×C11×#106C22semidirect
39. C2×C11×#102C22semidirect
40. C2×C11×#102C22semidirect
41. C2×C11×#102C22semidirect
42. C2×C11×#102C22semidirect
43. C2×C11×#102C22semidirect
44. C2×C11×#102C22semidirect
45. C2×C11×#102C22semidirect
46. C2×C11×#102C22semidirect
47. C2×C11×C22⋊C8C22semidirect
48. C2×C11×C22⋊C8C22semidirect
49. C2×C11×C22⋊C8C22semidirect
52. C11×#389C22semidirect
53. C11×#389C22semidirect
56. C11×#380C22semidirect
57. C11×#380C22semidirect
58. C11×#380C22semidirect
59. C11×#340C22semidirect
60. C11×#340C22semidirect
61. C11×#336C22semidirect
62. C11×#336C22semidirect
156. #24044C11direct (N × H)
288. C2×#482C2×C11semidirect
289. C2×#418C2×C11semidirect
290. #2485C2×C11semidirect
291. #2041C2×C11semidirect
292. #2041C2×C11semidirect
293. #2034C2×C11semidirect
294. #2033C2×C11semidirect
295. #1895C2×C11semidirect
296. #1870C2×C11semidirect
297. #1864C2×C11semidirect
298. #1862C2×C11semidirect
299. #1786C2×C11semidirect
300. #1786C2×C11semidirect
301. #1786C2×C11semidirect
420. C22×M16C22×C11semidirect
431. C2×#117C22×C11semidirect
433. C2×#107C22×C11semidirect
434. C2×#106C22×C11semidirect
440. C2×#102C22×C11semidirect
441. C2×#102C22×C11semidirect
442. C2×#102C22×C11semidirect
443. C2×#102C22×C11semidirect
444. C2×#102C22×C11semidirect
445. C2×#102C22×C11semidirect
446. C2×#102C22×C11semidirect
447. C2×#102C22×C11semidirect
448. C2×C22⋊C8C22×C11semidirect
449. C2×C22⋊C8C22×C11semidirect
450. C2×C22⋊C8C22×C11semidirect
453. #389C22×C11semidirect
454. #389C22×C11semidirect
457. #380C22×C11semidirect
458. #380C22×C11semidirect
459. #380C22×C11semidirect
460. #340C22×C11semidirect
461. #340C22×C11semidirect
462. #336C22×C11semidirect
463. #336C22×C11semidirect
756. C11#24044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D42×C112
C2×C11×#4822
C2×C11×#4182
C11×#24852
C11×#20412
C11×#20342
C11×#20332
C11×#18952
C11×#18702
C11×#18642
C11×#18622
C11×#17862
#2404411