Finite Group Databasebeta

← C11×#61058 #14638251

Subgroups — C11×#61058 #14638251

Order 2816.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#576C211yesmaximal, characteristic, complemented
2C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C11×#3485C211yesmaximal, characteristic, complemented
4C11×#3484C211yesmaximal, characteristic, complemented
5C11×#3273C214yesmaximal, complemented
6C11×#3272C214yesmaximal, complemented
7C11×#3267C214yesmaximal, complemented
8C11×#3264C214yesmaximal, complemented
9C11×#3154C211yesmaximal, characteristic, complemented
10C11×#3057C211yesmaximal, characteristic, complemented
11C11×#3054C211yesmaximal, characteristic, complemented
12C11×#3042C211yesmaximal, characteristic, complemented
13C11×#3041C211yesmaximal, characteristic, complemented
14C11×#3009C211yesmaximal, characteristic, complemented
15C11×#3008C211yesmaximal, characteristic, complemented
16C11×#3005C211yesmaximal, characteristic, complemented
17C11×#3003C211yesmaximal, characteristic, complemented
18C11×#2948C211yesmaximal, characteristic, complemented
19C11×#2930C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2211yescharacteristic
21C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
22C22×C11×#41C2211yescharacteristic, complemented
23C23×D4×C11C2211yescharacteristic, complemented
24C11×#576—28no—
25C2×C11×#137C2211yescharacteristic, complemented
26C2×C11×AGL(1,ℤ/8)—28no—
27C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C11×AGL(1,ℤ/8)C2214yescomplemented
29C2×C11×AGL(1,ℤ/8)C2214yescomplemented
30C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
31C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
32C2×C11×AGL(1,ℤ/8)C2212yescomplemented
33C2×C11×AGL(1,ℤ/8)C2212yescomplemented
34C2×C11×#135C2211yescharacteristic, complemented
35C2×C11×#135C2212yescomplemented
36C22×C11×SD16C2211yescharacteristic, complemented
37C22×C11×SD16C2211yescharacteristic, complemented
38C22×C11×D8C2211yescharacteristic
39C22×C11×D8C2211yescharacteristic, complemented
40C22×C11×D8C2212yescomplemented
41C2×C11×#131C2211yescharacteristic, complemented
42C22×C11×M16C2211yescharacteristic, complemented
43C11×#547—22no—
44C11×#547C2214yescomplemented
45C11×#546—22no—
46C11×#546—22no—
47C11×#546C2214yescomplemented
48C11×#546C2214yescomplemented
49D42×C11—22no—
50D42×C11C2214yescomplemented
51C11×#536C2211yescharacteristic, complemented
52C11×#536C2211yescharacteristic, complemented
53C11×#535C2211yescharacteristic
54C11×#535C2211yescharacteristic, complemented
55C11×#534—22no—
56C11×#534—22no—
57C11×#525C2211yescharacteristic
58C11×#525C2211yescharacteristic, complemented
59C11×#525C2211yescharacteristic, complemented
60C2×C11×#123—22no—
61C2×C11×#120—22no—
62C11×#518C2211yescharacteristic, complemented
63C11×#518C2211yescharacteristic, complemented
64C11×#497C2212yescomplemented
65C11×#496C2212yescomplemented
66C11×#495C2212yescomplemented
67C11×#492C2212yescomplemented
68C11×#470C2212yescomplemented
69C11×#469C2212yescomplemented
70C11×#468C2214yescomplemented
71C11×#468C2212yescomplemented
72C11×#468C2212yescomplemented
73C11×#465C2214yescomplemented
74C11×#463C2214yescomplemented
75C11×#463C2214yescomplemented
76C11×#461C2214yescomplemented
77C11×#459C2214yescomplemented
78C11×#452C2214yescomplemented
79C11×#452C2214yescomplemented
80C11×#450C2214yescomplemented
81C11×#450C2214yescomplemented
82C11×#449C2214yescomplemented
83C11×#449C2214yescomplemented
84C11×#447C2214yescomplemented
85C11×#447C2214yescomplemented
86C11×#442C2214yescomplemented
87C4×C11×D8C2214yescomplemented
88C11×#436C2214yescomplemented
89C11×#435C2214yescomplemented
90C11×#427C2211yescharacteristic, complemented
91C11×#424C2211yescharacteristic, complemented
92C11×#419C2211yescharacteristic, complemented
93C11×#418C2211yescharacteristic, complemented
94C11×#418C2211yescharacteristic, complemented
95C11×#418C2211yescharacteristic, complemented
96C11×#416C2211yescharacteristic, complemented
97C11×#416C2211yescharacteristic, complemented
98C11×#408C2211yescharacteristic, complemented
99C11×#407C2211yescharacteristic, complemented
100C11×#405C2211yescharacteristic, complemented
101C25×C11—21no—
102C11×H(5,𝔽2)—24no—
103C11×H(5,𝔽2)—24no—
104C11×H(5,𝔽2)—42no—
105C11×H(5,𝔽2)—42no—
106C2×C11×#41—21no—
107C2×C11×#41—21no—
108C2×C11×#41—22no—
109C2×C11×#41—24no—
110C2×C11×#41—42no—
111C2×C11×#41C2311yescharacteristic
112C2×C11×#41C2311yescharacteristic
113C2×C11×#41C2312yes—
114C2×C11×#41C2314yes—
115C2×C11×#41C2311yescharacteristic
116C2×C11×#41C2312yescomplemented
117C22×Q8×C11C2311yescharacteristic
118C22×D4×C11—24no—
119C22×D4×C11—21no—
120C22×D4×C11—22no—
121C22×D4×C11—22no—
122C22×D4×C11—21no—
123C22×D4×C11—21no—
124C22×D4×C11—24no—
125C22×D4×C11—21no—
126C22×D4×C11—22no—
127C22×D4×C11—42no—
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2312yes—
130C22×D4×C11C2314yes—
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2312yescomplemented
134C23×C4×C11—21no—
135C23×C4×C11C2311yescharacteristic
136C11×#137—42no—
137C11×AGL(1,ℤ/8)—24no—
138C11×AGL(1,ℤ/8)—24no—
139C11×AGL(1,ℤ/8)—216no—
140C11×AGL(1,ℤ/8)—216no—
141C11×AGL(1,ℤ/8)—28no—
142C11×AGL(1,ℤ/8)—28no—
143C11×AGL(1,ℤ/8)—42no—
144C11×#135—28no—
145C11×#135—24no—
146C2×C11×Q16C2311yescharacteristic, complemented
147C2×C11×Q16C2312yescomplemented
148C2×C11×SD16—24no—
149C2×C11×SD16—24no—
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2314yes—
153C2×C11×SD16C2312yes—
154C2×C11×SD16C2312yes—
155C2×C11×SD16C2311yescharacteristic, complemented
156C2×C11×SD16C2311yescharacteristic, complemented
157C2×C11×SD16C2312yescomplemented
158C2×C11×SD16C2312yescomplemented
159C2×C11×D8—24no—
160C2×C11×D8—28no—
161C2×C11×D8D418yescomplemented
162C2×C11×D8C2312yes—
163C2×C11×D8C2314yes—
164C2×C11×D8C2312yes—
165C2×C11×D8C2312yes—
166C2×C11×D8C2312yes—
167C2×C11×D8C2311yescharacteristic, complemented
168C2×C11×D8C2312yescomplemented
169C11×#131—24no—
170C2×C11×M16—24no—
171C2×C11×M16C2311yescharacteristic
172C2×C11×M16C2311yescharacteristic
173C2×C11×M16C2312yes—
174C2×C11×M16C2312yes—
175C2×C11×M16C2312yescomplemented
176C22×C8×C11C2311yescharacteristic
177C22×C8×C11C2311yescharacteristic
178C22×C8×C11C2312yescomplemented
179C11×C4⋊Q8—21no—
180C11×C4⋊Q8C2312yescomplemented
181C11×#127—21no—
182C11×#127C2312yes—
183C11×#124—21no—
184C11×#124—21no—
185C11×#124C2312yes—
186C11×#124C2312yescomplemented
187C11×#123—22no—
188C11×#123—21no—
189C11×#123—21no—
190C11×#123—24no—
191C11×#123—24no—
192C11×#123—22no—
193C11×#123—24no—
194C11×#123—24no—
195C11×#123D412yes—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8D412yes—
198C11×C22⋊Q8C2312yes—
199C11×C22⋊Q8C2312yes—
200C11×C22⋊Q8C2314yescomplemented
201C11×#121—24no—
202C11×#121—24no—
203C11×#121—22no—
204C11×#121—24no—
205C11×#121—24no—
206C11×#121D412yes—
207C11×#121C2312yes—
208C11×#121C2312yes—
209C11×#121C2314yes—
210C11×#120—21no—
211C11×#120—21no—
212C11×#120—22no—
213C11×#120—24no—
214C11×#120—24no—
215C11×#120—22no—
216C11×#120—24no—
217C11×#120—24no—
218C11×#120D412yes—
219C4×D4×C11—22no—
220C4×D4×C11—22no—
221C4×D4×C11—22no—
222C4×D4×C11—22no—
223C4×D4×C11C2314yes—
224C4×D4×C11C2314yes—
225C4×D4×C11C2314yescomplemented
226C11×#117C2311yescharacteristic
227C11×#117C2311yescharacteristic
228C11×#117C2311yescharacteristic
229C2×C11×C4⋊C4—24no—
230C2×C11×C22⋊C4—22no—
231C2×C11×C22⋊C4—22no—
232C2×C11×C22⋊C4—24no—
233C2×C11×C22⋊C4—24no—
234C11×#107C2312yescomplemented
235C11×#106C2312yescomplemented
236C11×C4⋊C8C2314yescomplemented
237C11×#103C2312yescomplemented
238C11×#103C2312yescomplemented
239C11×#103C2314yescomplemented
240C11×#102C2314yes—
241C11×#102C2314yes—
242C11×#102C2312yescomplemented
243C11×#102C2312yescomplemented
244C11×#102C2314yescomplemented
245C11×C22⋊C8C2314yes—
246C11×C22⋊C8C2314yescomplemented
247C11×#97C2312yescomplemented
248C4×C8×C11C2312yescomplemented
249#61058C1111yesmaximal, characteristic, direct product factor, Sylow
250C24×C11—21no—
251C24×C11—21no—
252C24×C11—24no—
253C24×C11—22no—
254C24×C11—21no—
255C24×C11—22no—
256C24×C11—44no—
257C24×C11—84no—
258C24×C11C2×D411yescharacteristic
259C11×#41—22no—
260C11×#41—22no—
261C11×#41—24no—
262C11×#41—24no—
263C11×#41—28no—
264C11×#41—22no—
265C11×#41—22no—
266C11×#41—22no—
267C11×#41—22no—
268C11×#41—44no—
269C11×#41—42no—
270C11×#41—42no—
271C11×#41—48no—
272C11×#41—44no—
273C11×#41—44no—
274C2×Q8×C11—21no—
275C2×Q8×C11—22no—
276C2×Q8×C11—22no—
277C2×Q8×C11C2×D411yescharacteristic
278C2×Q8×C11C2411yescharacteristic
279C2×Q8×C11C2411yescharacteristic
280C2×Q8×C11C2412yes—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—28no—
284C2×D4×C11—22no—
285C2×D4×C11—21no—
286C2×D4×C11—22no—
287C2×D4×C11—24no—
288C2×D4×C11—21no—
289C2×D4×C11—22no—
290C2×D4×C11—22no—
291C2×D4×C11—24no—
292C2×D4×C11—21no—
293C2×D4×C11—21no—
294C2×D4×C11—22no—
295C2×D4×C11—22no—
296C2×D4×C11—24no—
297C2×D4×C11—22no—
298C2×D4×C11—21no—
299C2×D4×C11—24no—
300C2×D4×C11—22no—
301C2×D4×C11—22no—
302C2×D4×C11—22no—
303C2×D4×C11—44no—
304C2×D4×C11—42no—
305C2×D4×C11—42no—
306C2×D4×C11—48no—
307C2×D4×C11—44no—
308C2×D4×C11—44no—
309C2×D4×C11—44no—
310C2×D4×C11—48no—
311C2×D4×C11—48no—
312C2×D4×C11—44no—
313C2×D4×C11—88no—
314C2×D4×C11C2×D412yes—
315C2×D4×C11C2×D411yescharacteristic
316C2×D4×C11C2×D414yes—
317C2×D4×C11C2×D414yes—
318C2×D4×C11C2×D414yescomplemented
319C2×D4×C11C2412yes—
320C2×D4×C11C2411yescharacteristic
321C2×D4×C11C2411yescharacteristic
322C2×D4×C11C2412yes—
323C2×D4×C11C2412yes—
324C22×C4×C11—22no—
325C22×C4×C11—22no—
326C22×C4×C11—21no—
327C22×C4×C11—22no—
328C22×C4×C11—24no—
329C22×C4×C11—22no—
330C22×C4×C11—21no—
331C22×C4×C11—21no—
332C22×C4×C11—24no—
333C22×C4×C11—24no—
334C22×C4×C11—44no—
335C22×C4×C11C2×D412yes—
336C22×C4×C11C2×D411yescharacteristic
337C22×C4×C11C2412yes—
338C22×C4×C11C2412yes—
339C22×C4×C11C2411yescharacteristic
340C11×Q16—22no—
341C11×Q16—42no—
342C11×SD16—24no—
343C11×SD16—24no—
344C11×SD16—22no—
345C11×SD16—22no—
346C11×SD16—28no—
347C11×SD16—24no—
348C11×SD16—24no—
349C11×SD16—42no—
350C11×SD16—42no—
351C11×D8—22no—
352C11×D8—24no—
353C11×D8—28no—
354C11×D8—24no—
355C11×D8—42no—
356C11×D8C2×D418yescomplemented
357C11×D8C2×D418yescomplemented
358C11×M16—24no—
359C11×M16—24no—
360C11×M16—24no—
361C11×M16—22no—
362C11×M16—22no—
363C2×C8×C11—24no—
364C2×C8×C11—22no—
365C2×C8×C11C2×D414yescomplemented
366C2×C8×C11C2412yes—
367C2×C8×C11C2412yes—
368C2×C8×C11C2412yes—
369C2×C8×C11C2411yescharacteristic
370C2×C8×C11C2411yescharacteristic
371C11×C4⋊C4—22no—
372C11×C4⋊C4—24no—
373C11×C4⋊C4—24no—
374C11×C4⋊C4—22no—
375C11×C4⋊C4C2×D414yes—
376C11×C4⋊C4C2×D412yes—
377C11×C4⋊C4C2412yes—
378C11×C4⋊C4C2412yes—
379C11×C22⋊C4—21no—
380C11×C22⋊C4—21no—
381C11×C22⋊C4—22no—
382C11×C22⋊C4—24no—
383C11×C22⋊C4—22no—
384C11×C22⋊C4—22no—
385C11×C22⋊C4—24no—
386C11×C22⋊C4—24no—
387C11×C22⋊C4—24no—
388C11×C22⋊C4—24no—
389C11×C22⋊C4—24no—
390C11×C22⋊C4—22no—
391C11×C22⋊C4C2×D412yes—
392C11×C22⋊C4C2×D414yes—
393C11×C22⋊C4C2×D414yes—
394C42×C11—21no—
395C42×C11—21no—
396C42×C11C2412yes—
397C2×#576C2×C1111yescharacteristic, complemented
398C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
399#3485C2×C1111yescharacteristic, complemented
400#3484C2×C1111yescharacteristic, complemented
401#3273C2×C1114yescomplemented
402#3272C2×C1114yescomplemented
403#3267C2×C1114yescomplemented
404#3264C2×C1114yescomplemented
405#3154C2×C1111yescharacteristic, complemented
406#3057C2×C1111yescharacteristic, complemented
407#3054C2×C1111yescharacteristic, complemented
408#3042C2×C1111yescharacteristic, complemented
409#3041C2×C1111yescharacteristic, complemented
410#3009C2×C1111yescharacteristic, complemented
411#3008C2×C1111yescharacteristic, complemented
412#3005C2×C1111yescharacteristic, complemented
413#3003C2×C1111yescharacteristic, complemented
414#2948C2×C1111yescharacteristic, complemented
415#2930C2×C1111yescharacteristic, complemented
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—24no—
420C23×C11—24no—
421C23×C11—21no—
422C23×C11—22no—
423C23×C11—21no—
424C23×C11—42no—
425C23×C11—48no—
426C23×C11—44no—
427C23×C11—44no—
428C23×C11—48no—
429C23×C11—42no—
430C23×C11—82no—
431C23×C11—82no—
432C23×C11—82no—
433C23×C11—84no—
434C23×C11—84no—
435C23×C11—84no—
436C23×C11—816no—
437C23×C11C22×D412yes—
438C23×C11C22×D412yes—
439C23×C11C22×D411yescharacteristic
440Q8×C11—22no—
441Q8×C11—22no—
442Q8×C11—21no—
443Q8×C11—21no—
444Q8×C11—21no—
445Q8×C11—22no—
446Q8×C11—21no—
447Q8×C11—42no—
448D4×C11—24no—
449D4×C11—24no—
450D4×C11—24no—
451D4×C11—22no—
452D4×C11—21no—
453D4×C11—21no—
454D4×C11—22no—
455D4×C11—22no—
456D4×C11—22no—
457D4×C11—21no—
458D4×C11—22no—
459D4×C11—21no—
460D4×C11—44no—
461D4×C11—48no—
462D4×C11—44no—
463D4×C11—44no—
464D4×C11—44no—
465D4×C11—44no—
466D4×C11—48no—
467D4×C11—44no—
468D4×C11—42no—
469D4×C11—42no—
470D4×C11—42no—
471D4×C11—84no—
472D4×C11—82no—
473D4×C11—84no—
474D4×C11C22×D414yes—
475D4×C11C22×D414yes—
476C2×C4×C11—22no—
477C2×C4×C11—24no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—48no—
488C2×C4×C11—44no—
489C2×C4×C11—44no—
490C2×C4×C11—42no—
491C2×C4×C11—42no—
492C2×C4×C11—42no—
493C2×C4×C11—84no—
494C2×C4×C11—84no—
495C2×C4×C11C22×D414yes—
496C2×C4×C11C22×D412yes—
497C2×C4×C11C22×D412yes—
498C2×C4×C11C22×D411yescharacteristic
499C2×C4×C11C22×D412yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C2×C4×C11C2511yescharacteristic
502C8×C11—22no—
503C8×C11—22no—
504C8×C11—22no—
505C8×C11C22×D412yes—
506C8×C11C22×D412yes—
507C2×H(5,𝔽2)C22×C1111yescharacteristic
508C2×H(5,𝔽2)C22×C1111yescharacteristic, complemented
509C22×#41C22×C1111yescharacteristic, complemented
510C23×D4C22×C1111yescharacteristic, complemented
511#576—28no—
512C2×#137C22×C1111yescharacteristic, complemented
513C2×AGL(1,ℤ/8)—28no—
514C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
515C2×AGL(1,ℤ/8)C22×C1114yescomplemented
516C2×AGL(1,ℤ/8)C22×C1114yescomplemented
517C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
518C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
519C2×AGL(1,ℤ/8)C22×C1112yescomplemented
520C2×AGL(1,ℤ/8)C22×C1112yescomplemented
521C2×#135C22×C1111yescharacteristic, complemented
522C2×#135C22×C1112yescomplemented
523C22×SD16C22×C1111yescharacteristic, complemented
524C22×SD16C22×C1111yescharacteristic, complemented
525C22×D8C22×C1111yescharacteristic
526C22×D8C22×C1111yescharacteristic, complemented
527C22×D8C22×C1112yescomplemented
528C2×#131C22×C1111yescharacteristic, complemented
529C22×M16C22×C1111yescharacteristic, complemented
530#547—22no—
531#547C22×C1114yescomplemented
532#546—22no—
533#546—22no—
534#546C22×C1114yescomplemented
535#546C22×C1114yescomplemented
536D42—22no—
537D42C22×C1114yescomplemented
538#536C22×C1111yescharacteristic, complemented
539#536C22×C1111yescharacteristic, complemented
540#535C22×C1111yescharacteristic
541#535C22×C1111yescharacteristic, complemented
542#534—22no—
543#534—22no—
544#525C22×C1111yescharacteristic
545#525C22×C1111yescharacteristic, complemented
546#525C22×C1111yescharacteristic, complemented
547C2×#123—22no—
548C2×#120—22no—
549#518C22×C1111yescharacteristic, complemented
550#518C22×C1111yescharacteristic, complemented
551#497C22×C1112yescomplemented
552#496C22×C1112yescomplemented
553#495C22×C1112yescomplemented
554#492C22×C1112yescomplemented
555#470C22×C1112yescomplemented
556#469C22×C1112yescomplemented
557#468C22×C1114yescomplemented
558#468C22×C1112yescomplemented
559#468C22×C1112yescomplemented
560#465C22×C1114yescomplemented
561#463C22×C1114yescomplemented
562#463C22×C1114yescomplemented
563#461C22×C1114yescomplemented
564#459C22×C1114yescomplemented
565#452C22×C1114yescomplemented
566#452C22×C1114yescomplemented
567#450C22×C1114yescomplemented
568#450C22×C1114yescomplemented
569#449C22×C1114yescomplemented
570#449C22×C1114yescomplemented
571#447C22×C1114yescomplemented
572#447C22×C1114yescomplemented
573#442C22×C1114yescomplemented
574C4×D8C22×C1114yescomplemented
575#436C22×C1114yescomplemented
576#435C22×C1114yescomplemented
577#427C22×C1111yescharacteristic, complemented
578#424C22×C1111yescharacteristic, complemented
579#419C22×C1111yescharacteristic, complemented
580#418C22×C1111yescharacteristic, complemented
581#418C22×C1111yescharacteristic, complemented
582#418C22×C1111yescharacteristic, complemented
583#416C22×C1111yescharacteristic, complemented
584#416C22×C1111yescharacteristic, complemented
585#408C22×C1111yescharacteristic, complemented
586#407C22×C1111yescharacteristic, complemented
587#405C22×C1111yescharacteristic, complemented
588C22×C11—22no—
589C22×C11—22no—
590C22×C11—24no—
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—22no—
594C22×C11—24no—
595C22×C11—24no—
596C22×C11—44no—
597C22×C11—44no—
598C22×C11—44no—
599C22×C11—42no—
600C22×C11—44no—
601C22×C11—42no—
602C22×C11—41no—
603C22×C11—41no—
604C22×C11—42no—
605C22×C11—84no—
606C22×C11—84no—
607C22×C11—84no—
608C22×C11—816no—
609C22×C11—164no—
610C22×C11—164no—
611C22×C11D4212yes—
612C22×C11C23×D411yescharacteristic
613C4×C11—24no—
614C4×C11—22no—
615C4×C11—22no—
616C4×C11—42no—
617C4×C11—42no—
618C4×C11—41no—
619C4×C11—41no—
620C4×C11—42no—
621C4×C11D4212yes—
622C4×C11C23×D411yescharacteristic
623C4×C11C2×H(5,𝔽2)11yescharacteristic
624C25—21no—
625H(5,𝔽2)—24no—
626H(5,𝔽2)—24no—
627H(5,𝔽2)—42no—
628H(5,𝔽2)—42no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—24no—
633C2×#41—42no—
634C2×#41C23×C1111yescharacteristic
635C2×#41C23×C1111yescharacteristic
636C2×#41C23×C1112yes—
637C2×#41C23×C1114yes—
638C2×#41C23×C1111yescharacteristic
639C2×#41C23×C1112yescomplemented
640C22×Q8C23×C1111yescharacteristic
641C22×D4—24no—
642C22×D4—21no—
643C22×D4—22no—
644C22×D4—22no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—24no—
648C22×D4—21no—
649C22×D4—22no—
650C22×D4—42no—
651C22×D4C23×C1111yescharacteristic
652C22×D4C23×C1112yes—
653C22×D4C23×C1114yes—
654C22×D4C23×C1111yescharacteristic
655C22×D4C23×C1111yescharacteristic
656C22×D4C23×C1112yescomplemented
657C23×C4—21no—
658C23×C4C23×C1111yescharacteristic
659#137—42no—
660AGL(1,ℤ/8)—24no—
661AGL(1,ℤ/8)—24no—
662AGL(1,ℤ/8)—216no—
663AGL(1,ℤ/8)—216no—
664AGL(1,ℤ/8)—28no—
665AGL(1,ℤ/8)—28no—
666AGL(1,ℤ/8)—42no—
667#135—28no—
668#135—24no—
669C2×Q16C23×C1111yescharacteristic, complemented
670C2×Q16C23×C1112yescomplemented
671C2×SD16—24no—
672C2×SD16—24no—
673C2×SD16C23×C1114yes—
674C2×SD16C23×C1112yes—
675C2×SD16C23×C1112yes—
676C2×SD16C23×C1112yes—
677C2×SD16C23×C1112yes—
678C2×SD16C23×C1112yescomplemented
679C2×SD16C23×C1111yescharacteristic, complemented
680C2×SD16C23×C1111yescharacteristic, complemented
681C2×SD16C23×C1112yescomplemented
682C2×D8—24no—
683C2×D8—28no—
684C2×D8D4×C1118yescomplemented
685C2×D8C23×C1112yes—
686C2×D8C23×C1114yes—
687C2×D8C23×C1112yes—
688C2×D8C23×C1112yes—
689C2×D8C23×C1112yes—
690C2×D8C23×C1111yescharacteristic, complemented
691C2×D8C23×C1112yescomplemented
692#131—24no—
693C2×M16—24no—
694C2×M16C23×C1112yes—
695C2×M16C23×C1112yes—
696C2×M16C23×C1111yescharacteristic
697C2×M16C23×C1111yescharacteristic
698C2×M16C23×C1112yescomplemented
699C22×C8C23×C1111yescharacteristic
700C22×C8C23×C1111yescharacteristic
701C22×C8C23×C1112yescomplemented
702C4⋊Q8—21no—
703C4⋊Q8C23×C1112yescomplemented
704#127—21no—
705#127C23×C1112yes—
706#124—21no—
707#124—21no—
708#124C23×C1112yes—
709#124C23×C1112yescomplemented
710#123—22no—
711#123—21no—
712#123—21no—
713#123—24no—
714#123—24no—
715#123—22no—
716#123—24no—
717#123—24no—
718#123D4×C1112yes—
719C22⋊Q8—22no—
720C22⋊Q8D4×C1112yes—
721C22⋊Q8C23×C1112yes—
722C22⋊Q8C23×C1112yes—
723C22⋊Q8C23×C1114yescomplemented
724#121—24no—
725#121—24no—
726#121—22no—
727#121—24no—
728#121—24no—
729#121D4×C1112yes—
730#121C23×C1112yes—
731#121C23×C1112yes—
732#121C23×C1114yes—
733#120—21no—
734#120—21no—
735#120—22no—
736#120—24no—
737#120—24no—
738#120—22no—
739#120—24no—
740#120—24no—
741#120D4×C1112yes—
742C4×D4—22no—
743C4×D4—22no—
744C4×D4—22no—
745C4×D4—22no—
746C4×D4C23×C1114yes—
747C4×D4C23×C1114yes—
748C4×D4C23×C1114yescomplemented
749#117C23×C1111yescharacteristic
750#117C23×C1111yescharacteristic
751#117C23×C1111yescharacteristic
752C2×C4⋊C4—24no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—24no—
756C2×C22⋊C4—24no—
757#107C23×C1112yescomplemented
758#106C23×C1112yescomplemented
759C4⋊C8C23×C1114yescomplemented
760#103C23×C1112yescomplemented
761#103C23×C1112yescomplemented
762#103C23×C1114yescomplemented
763#102C23×C1114yes—
764#102C23×C1114yes—
765#102C23×C1112yescomplemented
766#102C23×C1112yescomplemented
767#102C23×C1114yescomplemented
768C22⋊C8C23×C1114yes—
769C22⋊C8C23×C1114yescomplemented
770#97C23×C1112yescomplemented
771C4×C8C23×C1112yescomplemented
772C2×C11—22no—
773C2×C11—42no—
774C2×C11—42no—
775C2×C11—44no—
776C2×C11—44no—
777C2×C11—82no—
778C2×C11—81no—
779C2×C11—81no—
780C2×C11C2×D4211yescharacteristic
781C2×C11#358512yes—
782C24—21no—
783C24—21no—
784C24—24no—
785C24—22no—
786C24—21no—
787C24—22no—
788C24—44no—
789C24—84no—
790C24C2×D4×C1111yescharacteristic
791#41—22no—
792#41—22no—
793#41—24no—
794#41—24no—
795#41—28no—
796#41—22no—
797#41—22no—
798#41—22no—
799#41—22no—
800#41—44no—
801#41—42no—
802#41—42no—
803#41—48no—
804#41—44no—
805#41—44no—
806C2×Q8—21no—
807C2×Q8—22no—
808C2×Q8—22no—
809C2×Q8C2×D4×C1111yescharacteristic
810C2×Q8C24×C1111yescharacteristic
811C2×Q8C24×C1111yescharacteristic
812C2×Q8C24×C1112yes—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—28no—
816C2×D4—22no—
817C2×D4—21no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—21no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—24no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—24no—
829C2×D4—22no—
830C2×D4—21no—
831C2×D4—24no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—44no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—48no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—48no—
843C2×D4—48no—
844C2×D4—44no—
845C2×D4—88no—
846C2×D4C2×D4×C1112yes—
847C2×D4C2×D4×C1111yescharacteristic
848C2×D4C2×D4×C1114yes—
849C2×D4C2×D4×C1114yes—
850C2×D4C2×D4×C1114yescomplemented
851C2×D4C24×C1112yes—
852C2×D4C24×C1111yescharacteristic
853C2×D4C24×C1111yescharacteristic
854C2×D4C24×C1112yes—
855C2×D4C24×C1112yes—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—22no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—44no—
867C22×C4C2×D4×C1112yes—
868C22×C4C2×D4×C1111yescharacteristic
869C22×C4C24×C1112yes—
870C22×C4C24×C1112yes—
871C22×C4C24×C1111yescharacteristic
872Q16—22no—
873Q16—42no—
874SD16—28no—
875SD16—24no—
876SD16—24no—
877SD16—24no—
878SD16—24no—
879SD16—22no—
880SD16—22no—
881SD16—42no—
882SD16—42no—
883D8—24no—
884D8—28no—
885D8—24no—
886D8—22no—
887D8—42no—
888D8C2×D4×C1118yescomplemented
889D8C2×D4×C1118yescomplemented
890M16—22no—
891M16—22no—
892M16—24no—
893M16—24no—
894M16—24no—
895C2×C8—22no—
896C2×C8—24no—
897C2×C8C2×D4×C1114yescomplemented
898C2×C8C24×C1112yes—
899C2×C8C24×C1112yes—
900C2×C8C24×C1112yes—
901C2×C8C24×C1111yescharacteristic
902C2×C8C24×C1111yescharacteristic
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4C2×D4×C1114yes—
908C4⋊C4C2×D4×C1112yes—
909C4⋊C4C24×C1112yes—
910C4⋊C4C24×C1112yes—
911C22⋊C4—21no—
912C22⋊C4—21no—
913C22⋊C4—22no—
914C22⋊C4—24no—
915C22⋊C4—22no—
916C22⋊C4—22no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—22no—
923C22⋊C4C2×D4×C1112yes—
924C22⋊C4C2×D4×C1114yes—
925C22⋊C4C2×D4×C1114yes—
926C42—21no—
927C42—21no—
928C42C24×C1112yes—
929C11#6105811yescharacteristic, direct product factor, Sylow
930C23—22no—
931C23—22no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—21no—
936C23—22no—
937C23—21no—
938C23—42no—
939C23—48no—
940C23—44no—
941C23—44no—
942C23—48no—
943C23—42no—
944C23—82no—
945C23—82no—
946C23—82no—
947C23—84no—
948C23—84no—
949C23—84no—
950C23—816no—
951C23C22×D4×C1112yes—
952C23C22×D4×C1112yes—
953C23C22×D4×C1111yescharacteristic
954Q8—22no—
955Q8—22no—
956Q8—21no—
957Q8—21no—
958Q8—21no—
959Q8—22no—
960Q8—21no—
961Q8—42no—
962D4—24no—
963D4—24no—
964D4—24no—
965D4—22no—
966D4—21no—
967D4—21no—
968D4—22no—
969D4—22no—
970D4—22no—
971D4—21no—
972D4—22no—
973D4—21no—
974D4—44no—
975D4—48no—
976D4—44no—
977D4—44no—
978D4—44no—
979D4—44no—
980D4—48no—
981D4—44no—
982D4—42no—
983D4—42no—
984D4—42no—
985D4—84no—
986D4—82no—
987D4—84no—
988D4C22×D4×C1114yes—
989D4C22×D4×C1114yes—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—48no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—84no—
1008C2×C4—84no—
1009C2×C4C22×D4×C1114yes—
1010C2×C4C22×D4×C1112yes—
1011C2×C4C22×D4×C1112yes—
1012C2×C4C22×D4×C1111yescharacteristic
1013C2×C4C22×D4×C1112yes—
1014C2×C4C11×H(5,𝔽2)12yes—
1015C2×C4C25×C1111yescharacteristic
1016C8—22no—
1017C8—22no—
1018C8—22no—
1019C8C22×D4×C1112yes—
1020C8C22×D4×C1112yes—
1021C22—22no—
1022C22—22no—
1023C22—22no—
1024C22—24no—
1025C22—24no—
1026C22—22no—
1027C22—24no—
1028C22—22no—
1029C22—44no—
1030C22—44no—
1031C22—44no—
1032C22—41no—
1033C22—41no—
1034C22—42no—
1035C22—42no—
1036C22—44no—
1037C22—42no—
1038C22—84no—
1039C22—84no—
1040C22—84no—
1041C22—816no—
1042C22—164no—
1043C22—164no—
1044C22D42×C1112yes—
1045C22C23×D4×C1111yescharacteristic
1046C4—22no—
1047C4—22no—
1048C4—24no—
1049C4—41no—
1050C4—41no—
1051C4—42no—
1052C4—42no—
1053C4—42no—
1054C4D42×C1112yes—
1055C4C23×D4×C1111yescharacteristic
1056C4C2×C11×H(5,𝔽2)11yescharacteristic
1057C2—22no—
1058C2—42no—
1059C2—42no—
1060C2—44no—
1061C2—44no—
1062C2—82no—
1063C2—81no—
1064C2—81no—
1065C2C2×D42×C1111yescharacteristic
1066C2C11×#358512yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#576C2semidirect
2. C22×C11×AGL(1,ℤ/8)C2semidirect
3. C11×#3485C2semidirect
4. C11×#3484C2semidirect
5. C11×#3273C2semidirect
6. C11×#3272C2semidirect
7. C11×#3267C2semidirect
8. C11×#3264C2semidirect
9. C11×#3154C2semidirect
10. C11×#3057C2semidirect
11. C11×#3054C2semidirect
12. C11×#3042C2semidirect
13. C11×#3041C2semidirect
14. C11×#3009C2semidirect
15. C11×#3008C2semidirect
16. C11×#3005C2semidirect
17. C11×#3003C2semidirect
18. C11×#2948C2semidirect
19. C11×#2930C2semidirect
21. C2×C11×H(5,𝔽2)C22semidirect
22. C22×C11×#41C22semidirect
23. C23×D4×C11C22semidirect
25. C2×C11×#137C22semidirect
28. C2×C11×AGL(1,ℤ/8)C22semidirect
29. C2×C11×AGL(1,ℤ/8)C22semidirect
30. C2×C11×AGL(1,ℤ/8)C22semidirect
31. C2×C11×AGL(1,ℤ/8)C22semidirect
32. C2×C11×AGL(1,ℤ/8)C22semidirect
33. C2×C11×AGL(1,ℤ/8)C22semidirect
34. C2×C11×#135C22semidirect
35. C2×C11×#135C22semidirect
36. C22×C11×SD16C22semidirect
37. C22×C11×SD16C22semidirect
39. C22×C11×D8C22semidirect
40. C22×C11×D8C22semidirect
41. C2×C11×#131C22semidirect
42. C22×C11×M16C22semidirect
44. C11×#547C22semidirect
47. C11×#546C22semidirect
48. C11×#546C22semidirect
50. D42×C11C22semidirect
51. C11×#536C22semidirect
52. C11×#536C22semidirect
54. C11×#535C22semidirect
58. C11×#525C22semidirect
59. C11×#525C22semidirect
62. C11×#518C22semidirect
63. C11×#518C22semidirect
64. C11×#497C22semidirect
65. C11×#496C22semidirect
66. C11×#495C22semidirect
67. C11×#492C22semidirect
68. C11×#470C22semidirect
69. C11×#469C22semidirect
70. C11×#468C22semidirect
71. C11×#468C22semidirect
72. C11×#468C22semidirect
73. C11×#465C22semidirect
74. C11×#463C22semidirect
75. C11×#463C22semidirect
76. C11×#461C22semidirect
77. C11×#459C22semidirect
78. C11×#452C22semidirect
79. C11×#452C22semidirect
80. C11×#450C22semidirect
81. C11×#450C22semidirect
82. C11×#449C22semidirect
83. C11×#449C22semidirect
84. C11×#447C22semidirect
85. C11×#447C22semidirect
86. C11×#442C22semidirect
87. C4×C11×D8C22semidirect
88. C11×#436C22semidirect
89. C11×#435C22semidirect
90. C11×#427C22semidirect
91. C11×#424C22semidirect
92. C11×#419C22semidirect
93. C11×#418C22semidirect
94. C11×#418C22semidirect
95. C11×#418C22semidirect
96. C11×#416C22semidirect
97. C11×#416C22semidirect
98. C11×#408C22semidirect
99. C11×#407C22semidirect
100. C11×#405C22semidirect
116. C2×C11×#41C23semidirect
133. C22×D4×C11C23semidirect
146. C2×C11×Q16C23semidirect
147. C2×C11×Q16C23semidirect
155. C2×C11×SD16C23semidirect
156. C2×C11×SD16C23semidirect
157. C2×C11×SD16C23semidirect
158. C2×C11×SD16C23semidirect
161. C2×C11×D8D4semidirect
167. C2×C11×D8C23semidirect
168. C2×C11×D8C23semidirect
175. C2×C11×M16C23semidirect
178. C22×C8×C11C23semidirect
180. C11×C4⋊Q8C23semidirect
186. C11×#124C23semidirect
200. C11×C22⋊Q8C23semidirect
225. C4×D4×C11C23semidirect
234. C11×#107C23semidirect
235. C11×#106C23semidirect
236. C11×C4⋊C8C23semidirect
237. C11×#103C23semidirect
238. C11×#103C23semidirect
239. C11×#103C23semidirect
242. C11×#102C23semidirect
243. C11×#102C23semidirect
244. C11×#102C23semidirect
246. C11×C22⋊C8C23semidirect
247. C11×#97C23semidirect
248. C4×C8×C11C23semidirect
249. #61058C11direct (N × H)
318. C2×D4×C11C2×D4semidirect
356. C11×D8C2×D4semidirect
357. C11×D8C2×D4semidirect
365. C2×C8×C11C2×D4semidirect
397. C2×#576C2×C11semidirect
398. C22×AGL(1,ℤ/8)C2×C11semidirect
399. #3485C2×C11semidirect
400. #3484C2×C11semidirect
401. #3273C2×C11semidirect
402. #3272C2×C11semidirect
403. #3267C2×C11semidirect
404. #3264C2×C11semidirect
405. #3154C2×C11semidirect
406. #3057C2×C11semidirect
407. #3054C2×C11semidirect
408. #3042C2×C11semidirect
409. #3041C2×C11semidirect
410. #3009C2×C11semidirect
411. #3008C2×C11semidirect
412. #3005C2×C11semidirect
413. #3003C2×C11semidirect
414. #2948C2×C11semidirect
415. #2930C2×C11semidirect
508. C2×H(5,𝔽2)C22×C11semidirect
509. C22×#41C22×C11semidirect
510. C23×D4C22×C11semidirect
512. C2×#137C22×C11semidirect
515. C2×AGL(1,ℤ/8)C22×C11semidirect
516. C2×AGL(1,ℤ/8)C22×C11semidirect
517. C2×AGL(1,ℤ/8)C22×C11semidirect
518. C2×AGL(1,ℤ/8)C22×C11semidirect
519. C2×AGL(1,ℤ/8)C22×C11semidirect
520. C2×AGL(1,ℤ/8)C22×C11semidirect
521. C2×#135C22×C11semidirect
522. C2×#135C22×C11semidirect
523. C22×SD16C22×C11semidirect
524. C22×SD16C22×C11semidirect
526. C22×D8C22×C11semidirect
527. C22×D8C22×C11semidirect
528. C2×#131C22×C11semidirect
529. C22×M16C22×C11semidirect
531. #547C22×C11semidirect
534. #546C22×C11semidirect
535. #546C22×C11semidirect
537. D42C22×C11semidirect
538. #536C22×C11semidirect
539. #536C22×C11semidirect
541. #535C22×C11semidirect
545. #525C22×C11semidirect
546. #525C22×C11semidirect
549. #518C22×C11semidirect
550. #518C22×C11semidirect
551. #497C22×C11semidirect
552. #496C22×C11semidirect
553. #495C22×C11semidirect
554. #492C22×C11semidirect
555. #470C22×C11semidirect
556. #469C22×C11semidirect
557. #468C22×C11semidirect
558. #468C22×C11semidirect
559. #468C22×C11semidirect
560. #465C22×C11semidirect
561. #463C22×C11semidirect
562. #463C22×C11semidirect
563. #461C22×C11semidirect
564. #459C22×C11semidirect
565. #452C22×C11semidirect
566. #452C22×C11semidirect
567. #450C22×C11semidirect
568. #450C22×C11semidirect
569. #449C22×C11semidirect
570. #449C22×C11semidirect
571. #447C22×C11semidirect
572. #447C22×C11semidirect
573. #442C22×C11semidirect
574. C4×D8C22×C11semidirect
575. #436C22×C11semidirect
576. #435C22×C11semidirect
577. #427C22×C11semidirect
578. #424C22×C11semidirect
579. #419C22×C11semidirect
580. #418C22×C11semidirect
581. #418C22×C11semidirect
582. #418C22×C11semidirect
583. #416C22×C11semidirect
584. #416C22×C11semidirect
585. #408C22×C11semidirect
586. #407C22×C11semidirect
587. #405C22×C11semidirect
639. C2×#41C23×C11semidirect
656. C22×D4C23×C11semidirect
669. C2×Q16C23×C11semidirect
670. C2×Q16C23×C11semidirect
678. C2×SD16C23×C11semidirect
679. C2×SD16C23×C11semidirect
680. C2×SD16C23×C11semidirect
681. C2×SD16C23×C11semidirect
684. C2×D8D4×C11semidirect
690. C2×D8C23×C11semidirect
691. C2×D8C23×C11semidirect
698. C2×M16C23×C11semidirect
701. C22×C8C23×C11semidirect
703. C4⋊Q8C23×C11semidirect
709. #124C23×C11semidirect
723. C22⋊Q8C23×C11semidirect
748. C4×D4C23×C11semidirect
757. #107C23×C11semidirect
758. #106C23×C11semidirect
759. C4⋊C8C23×C11semidirect
760. #103C23×C11semidirect
761. #103C23×C11semidirect
762. #103C23×C11semidirect
765. #102C23×C11semidirect
766. #102C23×C11semidirect
767. #102C23×C11semidirect
769. C22⋊C8C23×C11semidirect
770. #97C23×C11semidirect
771. C4×C8C23×C11semidirect
850. C2×D4C2×D4×C11semidirect
888. D8C2×D4×C11semidirect
889. D8C2×D4×C11semidirect
897. C2×C8C2×D4×C11semidirect
929. C11#61058direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5762
C22×C11×AGL(1,ℤ/8)2
C11×#34852
C11×#34842
C11×#32732
C11×#32722
C11×#32672
C11×#32642
C11×#31542
C11×#30572
C11×#30542
C11×#30422
C11×#30412
C11×#30092
C11×#30082
C11×#30052
C11×#30032
C11×#29482
C11×#29302
#6105811