Finite Group Databasebeta

← C11×#24275 #14601468

Subgroups — C11×#24275 #14601468

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C11×#466C211yesmaximal, characteristic, complemented
3C2×C11×#465C211yesmaximal, characteristic, complemented
4C2×C11×#435C211yesmaximal, characteristic, complemented
5C11×#2408C211yesmaximal, characteristic, complemented
6C11×#2407C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2054C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1973C211yesmaximal, characteristic, complemented
12C11×#1972C211yesmaximal, characteristic, complemented
13C11×#1809C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)—24no—
19C2×C11×AGL(1,ℤ/8)—24no—
20C2×C11×AGL(1,ℤ/8)—24no—
21C22×C11×SD16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C22×C11×D8C2211yescharacteristic
24C22×C11×D8C2211yescharacteristic
25C22×C11×M16C2211yescharacteristic
26C23×C8×C11C2211yescharacteristic, complemented
27C2×C11×C22⋊Q8C2211yescharacteristic, complemented
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic, complemented
31C2×C11×#120—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C11×#466—24no—
34C11×#465—24no—
35C11×#435—24no—
36C2×C11×#107C2211yescharacteristic, complemented
37C2×C11×#106C2211yescharacteristic, complemented
38C2×C11×C4⋊C8C2211yescharacteristic, complemented
39C2×C11×#103C2211yescharacteristic, complemented
40C2×C11×#103C2211yescharacteristic, complemented
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic, complemented
46C2×C11×#102C2211yescharacteristic, complemented
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic, complemented
49C2×C11×#97C2211yescharacteristic, complemented
50C11×#394—21no—
51C11×#394—21no—
52C11×#392—21no—
53C11×#392—21no—
54C11×#391C2211yescharacteristic, complemented
55C11×#390C2211yescharacteristic
56C11×#390C2211yescharacteristic
57C11×#390C2211yescharacteristic, complemented
58C11×#386—21no—
59C11×#385—21no—
60C11×#380C2211yescharacteristic
61C11×#380C2211yescharacteristic
62C11×#379—21no—
63C11×#340C2211yescharacteristic, complemented
64C11×#340C2211yescharacteristic, complemented
65C25×C11—21no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—22no—
80C22×D4×C11—21no—
81C22×D4×C11—22no—
82C22×D4×C11—41no—
83C22×D4×C11—41no—
84C22×D4×C11D411yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C11×AGL(1,ℤ/8)—232no—
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16D414yescomplemented
98C2×C11×D8—22no—
99C2×C11×D8—22no—
100C2×C11×D8—22no—
101C2×C11×D8—22no—
102C2×C11×D8—22no—
103C2×C11×D8D414yescomplemented
104C2×C11×M16—22no—
105C2×C11×M16—22no—
106C2×C11×M16D414yescomplemented
107C22×C8×C11—22no—
108C22×C8×C11—22no—
109C22×C8×C11—22no—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—41no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—22no—
119C11×#121—41no—
120C11×#121—41no—
121C11×#121—41no—
122C11×#120—44no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4D411yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4D411yescharacteristic
144C2×C11×C22⋊C4D411yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C11×#107—22no—
147C11×#106—22no—
148C11×C4⋊C8—22no—
149C11×#103—22no—
150C11×#103—41no—
151C11×#102—22no—
152C11×#102—22no—
153C11×#102—22no—
154C11×#102—41no—
155C11×#102—41no—
156C11×#102—41no—
157C11×C22⋊C8—22no—
158C11×C22⋊C8—22no—
159C11×#97—22no—
160C11×#95—21no—
161C11×#95—21no—
162C11×#95—21no—
163C11×#95—21no—
164#24275C1111yesmaximal, characteristic, direct product factor, Sylow
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11—42no—
172C24×C11—42no—
173C24×C11—81no—
174C24×C11—81no—
175C24×C11C2×D411yescharacteristic
176C24×C11C2×D411yescharacteristic
177C11×#41—28no—
178C11×#41—44no—
179C11×#41—44no—
180C11×#41—44no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11C2×D412yes—
187C2×D4×C11—28no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
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—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—44no—
206C2×D4×C11—44no—
207C2×D4×C11—41no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—44no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—42no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C2×D4×C11—42no—
220C2×D4×C11—42no—
221C2×D4×C11—81no—
222C2×D4×C11—81no—
223C2×D4×C11—81no—
224C2×D4×C11C2×D412yes—
225C2×D4×C11C2×D412yes—
226C2×D4×C11C2×D412yes—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
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—21no—
241C22×C4×C11—21no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11—42no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D412yes—
250C22×C4×C11#4112yes—
251C22×C4×C11C2411yescharacteristic
252C11×SD16—28no—
253C11×SD16—28no—
254C11×D8—28no—
255C11×D8—28no—
256C11×M16—28no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—44no—
266C2×C8×C11C2×D412yes—
267C2×C8×C11C2×D412yes—
268C2×C8×C11C2×D412yes—
269C2×C8×C11C2×D412yes—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—42no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—42no—
283C11×C22⋊C4—42no—
284C11×C22⋊C4—42no—
285C11×C22⋊C4—42no—
286C11×C22⋊C4—42no—
287C11×C22⋊C4—42no—
288C11×C22⋊C4—42no—
289C11×C22⋊C4—42no—
290C11×C22⋊C4—81no—
291C11×C22⋊C4—81no—
292C11×C22⋊C4—81no—
293C11×C22⋊C4—81no—
294C42×C11—21no—
295C42×C11—21no—
296C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
297C2×#466C2×C1111yescharacteristic, complemented
298C2×#465C2×C1111yescharacteristic, complemented
299C2×#435C2×C1111yescharacteristic, complemented
300#2408C2×C1111yescharacteristic, complemented
301#2407C2×C1111yescharacteristic, complemented
302#2055C2×C1111yescharacteristic, complemented
303#2054C2×C1111yescharacteristic, complemented
304#2000C2×C1111yescharacteristic, complemented
305#1999C2×C1111yescharacteristic, complemented
306#1973C2×C1111yescharacteristic, complemented
307#1972C2×C1111yescharacteristic, complemented
308#1809C2×C1111yescharacteristic, complemented
309#1788C2×C1111yescharacteristic, complemented
310#1786C2×C1111yescharacteristic, complemented
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—48no—
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—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—84no—
346C23×C11—84no—
347C23×C11—84no—
348C23×C11—84no—
349C23×C11—84no—
350C23×C11—84no—
351C23×C11#12112yes—
352C23×C11AGL(1,ℤ/8)12yescomplemented
353C23×C11C22×D411yescharacteristic
354Q8×C11—22no—
355Q8×C11—22no—
356Q8×C11—41no—
357Q8×C11—41no—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—22no—
364D4×C11—48no—
365D4×C11—44no—
366D4×C11—48no—
367D4×C11—41no—
368D4×C11—41no—
369D4×C11—41no—
370D4×C11—41no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—84no—
374D4×C11—84no—
375D4×C11—84no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—22no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—48no—
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—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11#12112yes—
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C2×#4111yescharacteristic
416C2×C4×C11H(5,𝔽2)11yescharacteristic
417C2×C4×C11H(5,𝔽2)11yescharacteristic
418C8×C11—22no—
419C8×C11—41no—
420C8×C11—41no—
421C8×C11#12014yescomplemented
422C22×#41C22×C1111yescharacteristic
423C23×D4C22×C1111yescharacteristic
424C2×AGL(1,ℤ/8)—24no—
425C2×AGL(1,ℤ/8)—24no—
426C2×AGL(1,ℤ/8)—24no—
427C22×SD16C22×C1111yescharacteristic
428C22×SD16C22×C1111yescharacteristic
429C22×D8C22×C1111yescharacteristic
430C22×D8C22×C1111yescharacteristic
431C22×M16C22×C1111yescharacteristic
432C23×C8C22×C1111yescharacteristic, complemented
433C2×C22⋊Q8C22×C1111yescharacteristic, complemented
434C2×#121C22×C1111yescharacteristic
435C2×#121C22×C1111yescharacteristic
436C2×#121C22×C1111yescharacteristic, complemented
437C2×#120—21no—
438C2×C4×D4C22×C1111yescharacteristic
439#466—24no—
440#465—24no—
441#435—24no—
442C2×#107C22×C1111yescharacteristic, complemented
443C2×#106C22×C1111yescharacteristic, complemented
444C2×C4⋊C8C22×C1111yescharacteristic, complemented
445C2×#103C22×C1111yescharacteristic, complemented
446C2×#103C22×C1111yescharacteristic, complemented
447C2×#102C22×C1111yescharacteristic
448C2×#102C22×C1111yescharacteristic
449C2×#102C22×C1111yescharacteristic
450C2×#102C22×C1111yescharacteristic
451C2×#102C22×C1111yescharacteristic, complemented
452C2×#102C22×C1111yescharacteristic, complemented
453C2×C22⋊C8C22×C1111yescharacteristic
454C2×C22⋊C8C22×C1111yescharacteristic, complemented
455C2×#97C22×C1111yescharacteristic, complemented
456#394—21no—
457#394—21no—
458#392—21no—
459#392—21no—
460#391C22×C1111yescharacteristic, complemented
461#390C22×C1111yescharacteristic
462#390C22×C1111yescharacteristic
463#390C22×C1111yescharacteristic, complemented
464#386—21no—
465#385—21no—
466#380C22×C1111yescharacteristic
467#380C22×C1111yescharacteristic
468#379—21no—
469#340C22×C1111yescharacteristic, complemented
470#340C22×C1111yescharacteristic, complemented
471C22×C11—22no—
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—816no—
495C22×C11—81no—
496C22×C11—81no—
497C22×C11—81no—
498C22×C11—81no—
499C22×C11—81no—
500C22×C11—81no—
501C22×C11—81no—
502C22×C11—81no—
503C22×C11—81no—
504C22×C11—81no—
505C22×C11—81no—
506C22×C11—81no—
507C22×C11C2×#12111yescharacteristic
508C22×C11D4211yescharacteristic
509C22×C11D4211yescharacteristic
510C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
511C22×C11#57511yescharacteristic
512C22×C11#57611yescharacteristic
513C22×C11#57711yescharacteristic
514C4×C11—22no—
515C4×C11—41no—
516C4×C11—42no—
517C4×C11—41no—
518C4×C11—41no—
519C4×C11—81no—
520C4×C11—81no—
521C4×C11—81no—
522C4×C11—81no—
523C4×C11C2×#12011yescharacteristic
524C4×C11#53511yescharacteristic
525C4×C11#54611yescharacteristic
526C4×C11#54611yescharacteristic
527C25—21no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8C23×C1111yescharacteristic
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4D4×C1111yescharacteristic
547C22×D4C23×C1111yescharacteristic
548C22×D4C23×C1111yescharacteristic
549C22×D4C23×C1111yescharacteristic
550C23×C4—21no—
551C23×C4C23×C1111yescharacteristic
552C23×C4C23×C1111yescharacteristic
553AGL(1,ℤ/8)—232no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16D4×C1114yescomplemented
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8D4×C1114yescomplemented
566C2×M16—22no—
567C2×M16—22no—
568C2×M16D4×C1114yescomplemented
569C22×C8—22no—
570C22×C8—22no—
571C22×C8—22no—
572C22×C8C23×C1111yescharacteristic
573C22×C8C23×C1111yescharacteristic
574C22×C8C23×C1111yescharacteristic
575C22×C8C23×C1111yescharacteristic
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—41no—
582#121—41no—
583#121—41no—
584#120—44no—
585C4×D4—22no—
586C4×D4—22no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C1111yescharacteristic
589C2×C4⋊C4C23×C1111yescharacteristic
590C2×C4⋊C4C23×C1111yescharacteristic
591C2×C4⋊C4C23×C1111yescharacteristic
592C2×C4⋊C4C23×C1111yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C1111yescharacteristic
606C2×C22⋊C4D4×C1111yescharacteristic
607C2×C42C23×C1111yescharacteristic
608#107—22no—
609#106—22no—
610C4⋊C8—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—22no—
621#97—22no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C2×C11—42no—
627C2×C11—42no—
628C2×C11—82no—
629C2×C11—82no—
630C2×C11—82no—
631C2×C11#240811yescharacteristic
632C2×C11#305511yescharacteristic
633C2×C11#306211yescharacteristic
634C2×C11#326411yescharacteristic
635C2×C11#326511yescharacteristic
636C2×C11#326711yescharacteristic
637C2×C11#326811yescharacteristic
638C24—21no—
639C24—21no—
640C24—21no—
641C24—42no—
642C24—42no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—81no—
647C24—81no—
648C24C2×D4×C1111yescharacteristic
649C24C2×D4×C1111yescharacteristic
650#41—28no—
651#41—44no—
652#41—44no—
653#41—44no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C1112yes—
660C2×D4—28no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—41no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4C2×D4×C1112yes—
698C2×D4C2×D4×C1112yes—
699C2×D4C2×D4×C1112yes—
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—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4C2×D4×C1111yescharacteristic
719C22×C4C2×D4×C1111yescharacteristic
720C22×C4C2×D4×C1111yescharacteristic
721C22×C4C2×D4×C1111yescharacteristic
722C22×C4C2×D4×C1112yes—
723C22×C4C11×#4112yes—
724C22×C4C24×C1111yescharacteristic
725SD16—28no—
726SD16—28no—
727D8—28no—
728D8—28no—
729M16—28no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—44no—
739C2×C8C2×D4×C1112yes—
740C2×C8C2×D4×C1112yes—
741C2×C8C2×D4×C1112yes—
742C2×C8C2×D4×C1112yes—
743C4⋊C4—22no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—42no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—81no—
764C22⋊C4—81no—
765C22⋊C4—81no—
766C22⋊C4—81no—
767C42—21no—
768C42—21no—
769C11#2427511yescharacteristic, direct product factor, Sylow
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—48no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23C11×#12112yes—
811C23C11×AGL(1,ℤ/8)12yescomplemented
812C23C22×D4×C1111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—41no—
816Q8—41no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—48no—
824D4—44no—
825D4—48no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—48no—
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×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C11×#12112yes—
871C2×C4C22×D4×C1111yescharacteristic
872C2×C4C22×D4×C1111yescharacteristic
873C2×C4C22×D4×C1111yescharacteristic
874C2×C4C2×C11×#4111yescharacteristic
875C2×C4C11×H(5,𝔽2)11yescharacteristic
876C2×C4C11×H(5,𝔽2)11yescharacteristic
877C8—22no—
878C8—41no—
879C8—41no—
880C8C11×#12014yescomplemented
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—816no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×C11×#12111yescharacteristic
918C22D42×C1111yescharacteristic
919C22D42×C1111yescharacteristic
920C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
921C22C11×#57511yescharacteristic
922C22C11×#57611yescharacteristic
923C22C11×#57711yescharacteristic
924C4—22no—
925C4—41no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4C2×C11×#12011yescharacteristic
934C4C11×#53511yescharacteristic
935C4C11×#54611yescharacteristic
936C4C11×#54611yescharacteristic
937C2—42no—
938C2—42no—
939C2—82no—
940C2—82no—
941C2—82no—
942C2C11×#240811yescharacteristic
943C2C11×#305511yescharacteristic
944C2C11×#306211yescharacteristic
945C2C11×#326411yescharacteristic
946C2C11×#326511yescharacteristic
947C2C11×#326711yescharacteristic
948C2C11×#326811yescharacteristic
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. C22×C11×AGL(1,ℤ/8)C2semidirect
2. C2×C11×#466C2semidirect
3. C2×C11×#465C2semidirect
4. C2×C11×#435C2semidirect
5. C11×#2408C2semidirect
6. C11×#2407C2semidirect
7. C11×#2055C2semidirect
8. C11×#2054C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1973C2semidirect
12. C11×#1972C2semidirect
13. C11×#1809C2semidirect
14. C11×#1788C2semidirect
15. C11×#1786C2semidirect
26. C23×C8×C11C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
30. C2×C11×#121C22semidirect
36. C2×C11×#107C22semidirect
37. C2×C11×#106C22semidirect
38. C2×C11×C4⋊C8C22semidirect
39. C2×C11×#103C22semidirect
40. C2×C11×#103C22semidirect
45. C2×C11×#102C22semidirect
46. C2×C11×#102C22semidirect
48. C2×C11×C22⋊C8C22semidirect
49. C2×C11×#97C22semidirect
54. C11×#391C22semidirect
57. C11×#390C22semidirect
63. C11×#340C22semidirect
64. C11×#340C22semidirect
97. C2×C11×SD16D4semidirect
103. C2×C11×D8D4semidirect
106. C2×C11×M16D4semidirect
164. #24275C11direct (N × H)
296. C22×AGL(1,ℤ/8)C2×C11semidirect
297. C2×#466C2×C11semidirect
298. C2×#465C2×C11semidirect
299. C2×#435C2×C11semidirect
300. #2408C2×C11semidirect
301. #2407C2×C11semidirect
302. #2055C2×C11semidirect
303. #2054C2×C11semidirect
304. #2000C2×C11semidirect
305. #1999C2×C11semidirect
306. #1973C2×C11semidirect
307. #1972C2×C11semidirect
308. #1809C2×C11semidirect
309. #1788C2×C11semidirect
310. #1786C2×C11semidirect
352. C23×C11AGL(1,ℤ/8)semidirect
421. C8×C11#120semidirect
432. C23×C8C22×C11semidirect
433. C2×C22⋊Q8C22×C11semidirect
436. C2×#121C22×C11semidirect
442. C2×#107C22×C11semidirect
443. C2×#106C22×C11semidirect
444. C2×C4⋊C8C22×C11semidirect
445. C2×#103C22×C11semidirect
446. C2×#103C22×C11semidirect
451. C2×#102C22×C11semidirect
452. C2×#102C22×C11semidirect
454. C2×C22⋊C8C22×C11semidirect
455. C2×#97C22×C11semidirect
460. #391C22×C11semidirect
463. #390C22×C11semidirect
469. #340C22×C11semidirect
470. #340C22×C11semidirect
559. C2×SD16D4×C11semidirect
565. C2×D8D4×C11semidirect
568. C2×M16D4×C11semidirect
769. C11#24275direct (N × H)
811. C23C11×AGL(1,ℤ/8)semidirect
880. C8C11×#120semidirect

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C2×C11×#4662
C2×C11×#4652
C2×C11×#4352
C11×#24082
C11×#24072
C11×#20552
C11×#20542
C11×#20002
C11×#19992
C11×#19732
C11×#19722
C11×#18092
C11×#17882
C11×#17862
#2427511