Finite Group Databasebeta

← C11×#24440 #14601633

Subgroups — C11×#24440 #14601633

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C11C211yesmaximal, characteristic, complemented
2C2×C11×#469C211yesmaximal, characteristic, complemented
3C2×C11×#447C211yesmaximal, characteristic, complemented
4C2×C11×#447C211yesmaximal, characteristic, complemented
5C2×C11×#418C211yesmaximal, characteristic, complemented
6C11×#2414C211yesmaximal, characteristic, complemented
7C11×#2041C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic, complemented
9C11×#2011C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1875C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1864C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11—21no—
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic, complemented
21C22×C11×D8C2211yescharacteristic, complemented
22C22×C11×M16C2211yescharacteristic, complemented
23D42×C11—24no—
24D42×C11—24no—
25C2×C11×#127C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic, complemented
30C2×C11×#121C2211yescharacteristic, complemented
31C2×C11×#120—21no—
32C2×C11×#120—21no—
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C2×C11×#117C2211yescharacteristic, complemented
36C11×#469—24no—
37C11×#447—24no—
38C11×#447—24no—
39C2×C11×#106C2211yescharacteristic, complemented
40C11×#418—24no—
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic, complemented
45C2×C11×#102C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic, complemented
47C2×C11×#102C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×C22⋊C8C2211yescharacteristic, complemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C11×#394—21no—
55C11×#392—21no—
56C11×#390—21no—
57C11×#390C2211yescharacteristic, complemented
58C11×#389C2211yescharacteristic, complemented
59C11×#388—21no—
60C11×#380C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62C11×#340C2211yescharacteristic, complemented
63C11×#336C2211yescharacteristic, complemented
64C11×#336C2211yescharacteristic, complemented
65C25×C11—21no—
66C25×C11—21no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—28no—
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11—22no—
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—22no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—22no—
82C22×D4×C11—21no—
83C22×D4×C11—41no—
84C22×D4×C11—41no—
85C22×D4×C11—41no—
86C22×D4×C11—41no—
87C22×D4×C11—44no—
88C22×D4×C11—44no—
89C22×D4×C11D411yescharacteristic
90C22×D4×C11D414yescomplemented
91C22×D4×C11C2311yescharacteristic
92C22×D4×C11C2311yescharacteristic
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—22no—
101C2×C11×D8—22no—
102C2×C11×D8—22no—
103C2×C11×D8—22no—
104C2×C11×D8—41no—
105C2×C11×D8—41no—
106C2×C11×D8—41no—
107C2×C11×M16—22no—
108C2×C11×M16—22no—
109C2×C11×M16—41no—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×#127—22no—
115C11×#127—22no—
116C11×#121—28no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—41no—
124C11×#121D414yescomplemented
125C11×#120—28no—
126C11×#120—28no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C11×#117—22no—
132C11×#117—41no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4D411yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C11×C22⋊C4D411yescharacteristic
149C2×C11×C22⋊C4D411yescharacteristic
150C2×C42×C11—21no—
151C2×C42×C11C2311yescharacteristic
152C11×#106—22no—
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—22no—
159C11×#102—22no—
160C11×#102—22no—
161C11×#102—41no—
162C11×#102D414yescomplemented
163C11×C22⋊C8—22no—
164C11×C22⋊C8—22no—
165C11×C22⋊C8—41no—
166C11×#95—21no—
167C11×#95—21no—
168#24440C1111yesmaximal, characteristic, direct product factor, Sylow
169C24×C11—21no—
170C24×C11—24no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—24no—
174C24×C11—21no—
175C24×C11—42no—
176C24×C11—42no—
177C24×C11—42no—
178C24×C11—42no—
179C24×C11—42no—
180C24×C11—42no—
181C24×C11—42no—
182C24×C11—42no—
183C24×C11—81no—
184C24×C11—81no—
185C24×C11—81no—
186C24×C11—81no—
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—28no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—24no—
197C2×D4×C11—24no—
198C2×D4×C11—22no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11—21no—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—44no—
221C2×D4×C11—42no—
222C2×D4×C11—42no—
223C2×D4×C11—42no—
224C2×D4×C11—42no—
225C2×D4×C11—42no—
226C2×D4×C11—42no—
227C2×D4×C11—44no—
228C2×D4×C11—44no—
229C2×D4×C11—432no—
230C2×D4×C11—44no—
231C2×D4×C11—42no—
232C2×D4×C11—42no—
233C2×D4×C11—42no—
234C2×D4×C11—42no—
235C2×D4×C11—44no—
236C2×D4×C11—42no—
237C2×D4×C11—42no—
238C2×D4×C11—42no—
239C2×D4×C11—81no—
240C2×D4×C11—81no—
241C2×D4×C11—81no—
242C2×D4×C11—81no—
243C2×D4×C11—81no—
244C2×D4×C11C2×D412yes—
245C2×D4×C11C2×D412yes—
246C2×D4×C11C2×D412yes—
247C2×D4×C11C2×D412yes—
248C2×D4×C11#4112yes—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—24no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—42no—
265C22×C4×C11—42no—
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2×D412yes—
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2411yescharacteristic
273C11×D8—44no—
274C11×D8—44no—
275C11×D8—44no—
276C11×M16—44no—
277C2×C8×C11—21no—
278C2×C8×C11—21no—
279C2×C8×C11—21no—
280C2×C8×C11—21no—
281C2×C8×C11—21no—
282C2×C8×C11—21no—
283C2×C8×C11—21no—
284C2×C8×C11—21no—
285C2×C8×C11—21no—
286C2×C8×C11—21no—
287C2×C8×C11—21no—
288C2×C8×C11C2×D412yescomplemented
289C11×C4⋊C4—22no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—81no—
297C11×C4⋊C4C2×D412yes—
298C11×C4⋊C4C2×D412yescomplemented
299C11×C22⋊C4—24no—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—24no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—42no—
305C11×C22⋊C4—42no—
306C11×C22⋊C4—42no—
307C11×C22⋊C4—42no—
308C11×C22⋊C4—81no—
309C11×C22⋊C4—81no—
310C42×C11—21no—
311C42×C11—21no—
312C42×C11—42no—
313C2×D42C2×C1111yescharacteristic, complemented
314C2×#469C2×C1111yescharacteristic, complemented
315C2×#447C2×C1111yescharacteristic, complemented
316C2×#447C2×C1111yescharacteristic, complemented
317C2×#418C2×C1111yescharacteristic, complemented
318#2414C2×C1111yescharacteristic, complemented
319#2041C2×C1111yescharacteristic, complemented
320#2034C2×C1111yescharacteristic, complemented
321#2011C2×C1111yescharacteristic, complemented
322#1999C2×C1111yescharacteristic, complemented
323#1879C2×C1111yescharacteristic, complemented
324#1875C2×C1111yescharacteristic, complemented
325#1870C2×C1111yescharacteristic, complemented
326#1864C2×C1111yescharacteristic, complemented
327#1786C2×C1111yescharacteristic, complemented
328C23×C11—21no—
329C23×C11—22no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11—22no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—22no—
336C23×C11—21no—
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—21no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—48no—
346C23×C11—48no—
347C23×C11—48no—
348C23×C11—48no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—84no—
373C23×C11—84no—
374C23×C11—84no—
375C23×C11—84no—
376C23×C11—84no—
377C23×C11—84no—
378C23×C11—84no—
379C23×C11—84no—
380C23×C11—84no—
381C23×C11—84no—
382C23×C11#12012yes—
383C23×C11AGL(1,ℤ/8)12yes—
384C23×C11C22×D411yescharacteristic
385D4×C11—28no—
386D4×C11—22no—
387D4×C11—22no—
388D4×C11—22no—
389D4×C11—22no—
390D4×C11—22no—
391D4×C11—22no—
392D4×C11—22no—
393D4×C11—48no—
394D4×C11—48no—
395D4×C11—48no—
396D4×C11—48no—
397D4×C11—48no—
398D4×C11—41no—
399D4×C11—41no—
400D4×C11—41no—
401D4×C11—41no—
402D4×C11—41no—
403D4×C11—41no—
404D4×C11—41no—
405D4×C11—41no—
406D4×C11—84no—
407D4×C11—84no—
408D4×C11—84no—
409D4×C11#12114yes—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—48no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11#12012yes—
442C2×C4×C11AGL(1,ℤ/8)12yes—
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11C22×D411yescharacteristic
446C2×C4×C11C2×#4111yescharacteristic
447C2×C4×C11H(5,𝔽2)11yescharacteristic
448C2×C4×C11H(5,𝔽2)11yescharacteristic
449C8×C11—22no—
450C8×C11—41no—
451C8×C11—41no—
452C8×C11—41no—
453C23×D4—21no—
454C23×D4C22×C1111yescharacteristic
455C23×D4C22×C1111yescharacteristic
456C22×D8C22×C1111yescharacteristic
457C22×D8C22×C1111yescharacteristic, complemented
458C22×D8C22×C1111yescharacteristic, complemented
459C22×M16C22×C1111yescharacteristic, complemented
460D42—24no—
461D42—24no—
462C2×#127C22×C1111yescharacteristic
463C2×#121—21no—
464C2×#121C22×C1111yescharacteristic
465C2×#121C22×C1111yescharacteristic
466C2×#121C22×C1111yescharacteristic, complemented
467C2×#121C22×C1111yescharacteristic, complemented
468C2×#120—21no—
469C2×#120—21no—
470C2×C4×D4C22×C1111yescharacteristic
471C2×C4×D4C22×C1111yescharacteristic
472C2×#117C22×C1111yescharacteristic, complemented
473#469—24no—
474#447—24no—
475#447—24no—
476C2×#106C22×C1111yescharacteristic, complemented
477#418—24no—
478C2×#102C22×C1111yescharacteristic
479C2×#102C22×C1111yescharacteristic
480C2×#102C22×C1111yescharacteristic
481C2×#102C22×C1111yescharacteristic, complemented
482C2×#102C22×C1111yescharacteristic, complemented
483C2×#102C22×C1111yescharacteristic, complemented
484C2×#102C22×C1111yescharacteristic, complemented
485C2×#102C22×C1111yescharacteristic, complemented
486C2×#102C22×C1111yescharacteristic, complemented
487C2×#102C22×C1111yescharacteristic, complemented
488C2×C22⋊C8C22×C1111yescharacteristic, complemented
489C2×C22⋊C8C22×C1111yescharacteristic, complemented
490C2×C22⋊C8C22×C1111yescharacteristic, complemented
491#394—21no—
492#392—21no—
493#390—21no—
494#390C22×C1111yescharacteristic, complemented
495#389C22×C1111yescharacteristic, complemented
496#388—21no—
497#380C22×C1111yescharacteristic, complemented
498#340C22×C1111yescharacteristic, complemented
499#340C22×C1111yescharacteristic, complemented
500#336C22×C1111yescharacteristic, complemented
501#336C22×C1111yescharacteristic, complemented
502C22×C11—22no—
503C22×C11—24no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—22no—
509C22×C11—41no—
510C22×C11—42no—
511C22×C11—41no—
512C22×C11—42no—
513C22×C11—41no—
514C22×C11—42no—
515C22×C11—41no—
516C22×C11—41no—
517C22×C11—42no—
518C22×C11—41no—
519C22×C11—42no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—816no—
530C22×C11—816no—
531C22×C11—81no—
532C22×C11—81no—
533C22×C11—81no—
534C22×C11—81no—
535C22×C11—81no—
536C22×C11—81no—
537C22×C11—81no—
538C22×C11—81no—
539C22×C11—81no—
540C22×C11—81no—
541C22×C11—81no—
542C22×C11—81no—
543C22×C11—81no—
544C22×C11—81no—
545C22×C11—81no—
546C22×C11C2×#12011yescharacteristic
547C22×C11D4211yescharacteristic
548C22×C11#54611yescharacteristic
549C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
550C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
551C22×C11#57611yescharacteristic
552C22×C11#57611yescharacteristic
553C4×C11—22no—
554C4×C11—22no—
555C4×C11—41no—
556C4×C11—42no—
557C4×C11—41no—
558C4×C11—42no—
559C4×C11—81no—
560C4×C11—81no—
561C4×C11C2×#12111yescharacteristic
562C4×C11#53411yescharacteristic
563C4×C11D4211yescharacteristic
564C4×C11#54611yescharacteristic
565C25—21no—
566C25—21no—
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—28no—
570C22×D4—21no—
571C22×D4—21no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—22no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—22no—
582C22×D4—21no—
583C22×D4—41no—
584C22×D4—41no—
585C22×D4—41no—
586C22×D4—41no—
587C22×D4—44no—
588C22×D4—44no—
589C22×D4D4×C1111yescharacteristic
590C22×D4D4×C1114yescomplemented
591C22×D4C23×C1111yescharacteristic
592C22×D4C23×C1111yescharacteristic
593C22×D4C23×C1111yescharacteristic
594C22×D4C23×C1111yescharacteristic
595C23×C4—21no—
596C23×C4C23×C1111yescharacteristic
597C23×C4C23×C1111yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—41no—
605C2×D8—41no—
606C2×D8—41no—
607C2×M16—22no—
608C2×M16—22no—
609C2×M16—41no—
610C22×C8C23×C1111yescharacteristic
611C22×C8C23×C1111yescharacteristic
612C22×C8C23×C1111yescharacteristic
613C22×C8C23×C1111yescharacteristic
614#127—22no—
615#127—22no—
616#121—28no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—41no—
624#121D4×C1114yescomplemented
625#120—28no—
626#120—28no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631#117—22no—
632#117—41no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4D4×C1111yescharacteristic
635C2×C4⋊C4C23×C1111yescharacteristic
636C2×C4⋊C4C23×C1111yescharacteristic
637C2×C4⋊C4C23×C1111yescharacteristic
638C2×C4⋊C4C23×C1111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4D4×C1111yescharacteristic
649C2×C22⋊C4D4×C1111yescharacteristic
650C2×C42—21no—
651C2×C42C23×C1111yescharacteristic
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—22no—
660#102—22no—
661#102—41no—
662#102D4×C1114yescomplemented
663C22⋊C8—22no—
664C22⋊C8—22no—
665C22⋊C8—41no—
666#95—21no—
667#95—21no—
668C2×C11—42no—
669C2×C11—42no—
670C2×C11—44no—
671C2×C11—82no—
672C2×C11—82no—
673C2×C11—161no—
674C2×C11#241011yescharacteristic
675C2×C11#300311yescharacteristic
676C2×C11#300811yescharacteristic
677C2×C11#326411yescharacteristic
678C2×C11#327411yescharacteristic
679C2×C11#331811yescharacteristic
680C2×C11#332511yescharacteristic
681C24—21no—
682C24—24no—
683C24—21no—
684C24—21no—
685C24—24no—
686C24—21no—
687C24—42no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—81no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C1111yescharacteristic
700C24C2×D4×C1111yescharacteristic
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—28no—
704C2×D4—24no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—22no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—432no—
742C2×D4—44no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C1112yes—
757C2×D4C2×D4×C1112yes—
758C2×D4C2×D4×C1112yes—
759C2×D4C2×D4×C1112yes—
760C2×D4C11×#4112yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—24no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4C2×D4×C1111yescharacteristic
779C22×C4C2×D4×C1111yescharacteristic
780C22×C4C2×D4×C1111yescharacteristic
781C22×C4C2×D4×C1112yes—
782C22×C4C2×D4×C1112yes—
783C22×C4C2×D4×C1111yescharacteristic
784C22×C4C24×C1111yescharacteristic
785D8—44no—
786D8—44no—
787D8—44no—
788M16—44no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8C2×D4×C1112yescomplemented
801C4⋊C4—22no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—81no—
809C4⋊C4C2×D4×C1112yes—
810C4⋊C4C2×D4×C1112yescomplemented
811C22⋊C4—24no—
812C22⋊C4—24no—
813C22⋊C4—22no—
814C22⋊C4—24no—
815C22⋊C4—22no—
816C22⋊C4—42no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—81no—
821C22⋊C4—81no—
822C42—21no—
823C42—21no—
824C42—42no—
825C11#2444011yescharacteristic, direct product factor, Sylow
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23C11×#12012yes—
881C23C11×AGL(1,ℤ/8)12yes—
882C23C22×D4×C1111yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4C11×#12114yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4C11×#12012yes—
940C2×C4C11×AGL(1,ℤ/8)12yes—
941C2×C4C22×D4×C1111yescharacteristic
942C2×C4C22×D4×C1111yescharacteristic
943C2×C4C22×D4×C1111yescharacteristic
944C2×C4C2×C11×#4111yescharacteristic
945C2×C4C11×H(5,𝔽2)11yescharacteristic
946C2×C4C11×H(5,𝔽2)11yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—42no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×C11×#12011yescharacteristic
996C22D42×C1111yescharacteristic
997C22C11×#54611yescharacteristic
998C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
999C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
1000C22C11×#57611yescharacteristic
1001C22C11×#57611yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—41no—
1005C4—42no—
1006C4—41no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4C2×C11×#12111yescharacteristic
1011C4C11×#53411yescharacteristic
1012C4D42×C1111yescharacteristic
1013C4C11×#54611yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2C11×#241011yescharacteristic
1021C2C11×#300311yescharacteristic
1022C2C11×#300811yescharacteristic
1023C2C11×#326411yescharacteristic
1024C2C11×#327411yescharacteristic
1025C2C11×#331811yescharacteristic
1026C2C11×#332511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×D42×C11C2semidirect
2. C2×C11×#469C2semidirect
3. C2×C11×#447C2semidirect
4. C2×C11×#447C2semidirect
5. C2×C11×#418C2semidirect
6. C11×#2414C2semidirect
7. C11×#2041C2semidirect
8. C11×#2034C2semidirect
9. C11×#2011C2semidirect
10. C11×#1999C2semidirect
11. C11×#1879C2semidirect
12. C11×#1875C2semidirect
13. C11×#1870C2semidirect
14. C11×#1864C2semidirect
15. C11×#1786C2semidirect
20. C22×C11×D8C22semidirect
21. C22×C11×D8C22semidirect
22. C22×C11×M16C22semidirect
29. C2×C11×#121C22semidirect
30. C2×C11×#121C22semidirect
35. C2×C11×#117C22semidirect
39. C2×C11×#106C22semidirect
44. C2×C11×#102C22semidirect
45. C2×C11×#102C22semidirect
46. C2×C11×#102C22semidirect
47. C2×C11×#102C22semidirect
48. C2×C11×#102C22semidirect
49. C2×C11×#102C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×C22⋊C8C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. C2×C11×C22⋊C8C22semidirect
57. C11×#390C22semidirect
58. C11×#389C22semidirect
60. C11×#380C22semidirect
61. C11×#340C22semidirect
62. C11×#340C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
90. C22×D4×C11D4semidirect
124. C11×#121D4semidirect
162. C11×#102D4semidirect
168. #24440C11direct (N × H)
288. C2×C8×C11C2×D4semidirect
298. C11×C4⋊C4C2×D4semidirect
313. C2×D42C2×C11semidirect
314. C2×#469C2×C11semidirect
315. C2×#447C2×C11semidirect
316. C2×#447C2×C11semidirect
317. C2×#418C2×C11semidirect
318. #2414C2×C11semidirect
319. #2041C2×C11semidirect
320. #2034C2×C11semidirect
321. #2011C2×C11semidirect
322. #1999C2×C11semidirect
323. #1879C2×C11semidirect
324. #1875C2×C11semidirect
325. #1870C2×C11semidirect
326. #1864C2×C11semidirect
327. #1786C2×C11semidirect
457. C22×D8C22×C11semidirect
458. C22×D8C22×C11semidirect
459. C22×M16C22×C11semidirect
466. C2×#121C22×C11semidirect
467. C2×#121C22×C11semidirect
472. C2×#117C22×C11semidirect
476. C2×#106C22×C11semidirect
481. C2×#102C22×C11semidirect
482. C2×#102C22×C11semidirect
483. C2×#102C22×C11semidirect
484. C2×#102C22×C11semidirect
485. C2×#102C22×C11semidirect
486. C2×#102C22×C11semidirect
487. C2×#102C22×C11semidirect
488. C2×C22⋊C8C22×C11semidirect
489. C2×C22⋊C8C22×C11semidirect
490. C2×C22⋊C8C22×C11semidirect
494. #390C22×C11semidirect
495. #389C22×C11semidirect
497. #380C22×C11semidirect
498. #340C22×C11semidirect
499. #340C22×C11semidirect
500. #336C22×C11semidirect
501. #336C22×C11semidirect
590. C22×D4D4×C11semidirect
624. #121D4×C11semidirect
662. #102D4×C11semidirect
800. C2×C8C2×D4×C11semidirect
810. C4⋊C4C2×D4×C11semidirect
825. C11#24440direct (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×#4692
C2×C11×#4472
C2×C11×#4182
C11×#24142
C11×#20412
C11×#20342
C11×#20112
C11×#19992
C11×#18792
C11×#18752
C11×#18702
C11×#18642
C11×#17862
#2444011