Finite Group Databasebeta

← C11×#61643 #14638836

Subgroups — C11×#61643 #14638836

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3539C211yesmaximal, characteristic, complemented
2C11×#3484C211yesmaximal, characteristic, complemented
3C11×#3323C212yesmaximal, complemented
4C11×#3322C212yesmaximal, complemented
5C11×#3318C212yesmaximal, complemented
6C11×#3310C212yesmaximal, complemented
7C11×#3274C212yesmaximal, complemented
8C11×#3272C212yesmaximal, complemented
9C11×#3268C212yesmaximal, complemented
10C11×#3267C212yesmaximal, complemented
11C11×#3222C211yesmaximal, characteristic, complemented
12C11×#3220C211yesmaximal, characteristic, complemented
13C11×#3198C212yesmaximal, complemented
14C11×#3197C212yesmaximal, complemented
15C11×#3123C211yesmaximal, characteristic, complemented
16C11×#3122C211yesmaximal, characteristic, complemented
17C11×#3012C212yesmaximal, complemented
18C11×#3003C212yesmaximal, complemented
19C11×#2978C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2211yescharacteristic
21C23×D4×C11C2211yescharacteristic
22C2×C11×AGL(1,ℤ/8)C2212yescomplemented
23C2×C11×AGL(1,ℤ/8)C2212yescomplemented
24C2×C11×AGL(1,ℤ/8)C2212yescomplemented
25C2×C11×#135C2212yescomplemented
26C11×#560—22no—
27C11×#553—22no—
28C11×#553C2212yescomplemented
29C11×#552C2212yescomplemented
30C11×#550C2212yescomplemented
31C11×#547C2212yescomplemented
32C11×#546—22no—
33C11×#546C2212yes—
34C11×#546C2212yes—
35D42×C11—22no—
36D42×C11C2212yes—
37D42×C11C2212yes—
38C11×#541C2211yescharacteristic, complemented
39C11×#540—22no—
40C11×#540C2211yescharacteristic, complemented
41C11×#539—22no—
42C11×#537C2212yescomplemented
43C11×#535C2211yescharacteristic
44C11×#535C2211yescharacteristic
45C11×#534—22no—
46C11×#525C2211yescharacteristic
47C11×#525C2211yescharacteristic
48C11×#525C2212yescomplemented
49C2×C11×#120—22no—
50C11×#518C2211yescharacteristic
51C11×#497C2211yescharacteristic, complemented
52C11×#496C2211yescharacteristic, complemented
53C11×#493C2211yescharacteristic, complemented
54C11×#492C2211yescharacteristic, complemented
55C11×#490C2211yescharacteristic, complemented
56C11×#490C2211yescharacteristic, complemented
57C11×#488C2211yescharacteristic, complemented
58C11×#488C2211yescharacteristic, complemented
59C11×#485C2212yescomplemented
60C11×#485C2212yescomplemented
61C11×#482C2212yescomplemented
62C11×#482C2212yescomplemented
63C11×#481C2212yescomplemented
64C11×#480C2212yescomplemented
65C11×#478C2212yescomplemented
66C11×#478C2212yescomplemented
67C11×#470C2212yescomplemented
68C11×#469C2212yescomplemented
69C11×#469C2212yescomplemented
70C11×#468C2212yescomplemented
71C11×#468C2212yescomplemented
72C11×#468C2212yescomplemented
73C11×#466C2212yescomplemented
74C11×#465C2212yescomplemented
75C11×#464C2212yescomplemented
76C11×#463C2212yescomplemented
77C11×#461C2212yescomplemented
78C11×#460C2212yescomplemented
79C11×#459C2212yescomplemented
80C11×#459C2212yescomplemented
81C11×#452C2212yescomplemented
82C11×#452C2212yescomplemented
83C11×#452C2212yescomplemented
84C11×#450C2212yes—
85C11×#450C2212yescomplemented
86C11×#450C2212yescomplemented
87C11×#450C2212yescomplemented
88C11×#450C2212yescomplemented
89C11×#449C2212yescomplemented
90C11×#449C2212yescomplemented
91C11×#449C2212yescomplemented
92C11×#449C2212yescomplemented
93C11×#449C2212yescomplemented
94C11×#447C2212yes—
95C11×#447C2212yescomplemented
96C11×#447C2212yescomplemented
97C11×#447C2212yescomplemented
98C11×#447C2212yescomplemented
99C11×#442C2212yescomplemented
100C11×#440C2212yescomplemented
101C4×C11×SD16C2212yescomplemented
102C4×C11×D8C2212yescomplemented
103C11×#436C2212yescomplemented
104C11×#436C2212yescomplemented
105C11×#435C2212yescomplemented
106C11×#435C2212yescomplemented
107C11×#433C2211yescharacteristic, complemented
108C11×#433C2211yescharacteristic, complemented
109C11×#418C2212yescomplemented
110C11×#418C2212yescomplemented
111C11×#417C2212yescomplemented
112C2×C11×#102C2212yescomplemented
113C11×#408C2212yescomplemented
114C11×#407C2212yescomplemented
115C25×C11—21no—
116C11×H(5,𝔽2)—44no—
117C2×C11×#41—21no—
118C2×C11×#41C2312yes—
119C2×C11×#41C2311yescharacteristic
120C2×C11×#41C2312yes—
121C2×C11×#41C2311yescharacteristic
122C2×C11×#41C2312yescomplemented
123C22×D4×C11—22no—
124C22×D4×C11—21no—
125C22×D4×C11—22no—
126C22×D4×C11—22no—
127C22×D4×C11—21no—
128C22×D4×C11—22no—
129C22×D4×C11—44no—
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2312yes—
132C22×D4×C11C2312yes—
133C22×D4×C11C2312yes—
134C22×D4×C11C2311yescharacteristic
135C23×C4×C11C2311yescharacteristic
136C11×AGL(1,ℤ/8)—44no—
137C11×AGL(1,ℤ/8)—44no—
138C11×AGL(1,ℤ/8)—44no—
139C11×#135—44no—
140C2×C11×Q16C2312yescomplemented
141C2×C11×SD16C2312yes—
142C2×C11×SD16C2312yes—
143C2×C11×SD16C2312yes—
144C2×C11×SD16C2312yes—
145C2×C11×SD16C2312yescomplemented
146C2×C11×SD16C2312yescomplemented
147C2×C11×D8C2312yes—
148C2×C11×D8C2312yes—
149C2×C11×D8C2312yes—
150C2×C11×D8C2312yes—
151C2×C11×D8C2312yescomplemented
152C2×C11×M16C2312yes—
153C2×C11×M16C2312yes—
154C2×C11×M16C2312yescomplemented
155C22×C8×C11C2312yescomplemented
156C11×C4⋊Q8C2311yescharacteristic, complemented
157C11×#127—21no—
158C11×#127—22no—
159C11×#127C2311yescharacteristic
160C11×#127C2311yescharacteristic
161C11×#127C2311yescharacteristic, complemented
162C11×#126—22no—
163C11×#126—22no—
164C11×#126—22no—
165C11×#125—22no—
166C11×#125—22no—
167C11×#125C2311yescharacteristic, complemented
168C11×#125C2311yescharacteristic, complemented
169C11×#124—21no—
170C11×#124C2311yescharacteristic
171C11×#124C2311yescharacteristic
172C11×#123—22no—
173C11×#123—21no—
174C11×#123—22no—
175C11×#123—22no—
176C11×#123—22no—
177C11×#123—22no—
178C11×#123—22no—
179C11×#123—22no—
180C11×#123—22no—
181C11×#123D412yes—
182C11×C22⋊Q8—22no—
183C11×C22⋊Q8D412yes—
184C11×C22⋊Q8C2312yes—
185C11×C22⋊Q8C2312yes—
186C11×C22⋊Q8C2312yes—
187C11×C22⋊Q8C2312yescomplemented
188C11×#121—22no—
189C11×#121—22no—
190C11×#121—22no—
191C11×#121—22no—
192C11×#121—22no—
193C11×#121—22no—
194C11×#121—22no—
195C11×#121—22no—
196C11×#121—22no—
197C11×#121—22no—
198C11×#121—22no—
199C11×#121—22no—
200C11×#121—22no—
201C11×#121D412yes—
202C11×#121C2312yes—
203C11×#121C2312yes—
204C11×#121C2312yes—
205C11×#121C2312yes—
206C11×#121C2312yes—
207C11×#121C2312yescomplemented
208C11×#120—21no—
209C11×#120—22no—
210C11×#120—22no—
211C11×#120—22no—
212C11×#120—22no—
213C11×#120—22no—
214C11×#120—22no—
215C11×#120—22no—
216C11×#120—22no—
217C11×#120—22no—
218C11×#120D412yes—
219C4×Q8×C11C2312yescomplemented
220C4×D4×C11—22no—
221C4×D4×C11—22no—
222C4×D4×C11—22no—
223C4×D4×C11—22no—
224C4×D4×C11—22no—
225C4×D4×C11—22no—
226C4×D4×C11C2312yes—
227C4×D4×C11C2312yes—
228C4×D4×C11C2312yes—
229C4×D4×C11C2312yes—
230C4×D4×C11C2312yescomplemented
231C11×#117—22no—
232C11×#117C2311yescharacteristic
233C11×#117C2312yes—
234C11×#117C2311yescharacteristic
235C2×C11×C4⋊C4—22no—
236C2×C11×C4⋊C4C2312yescomplemented
237C2×C11×C22⋊C4—22no—
238C2×C11×C22⋊C4—22no—
239C2×C11×C22⋊C4—22no—
240C11×#107C2312yescomplemented
241C11×#107C2312yescomplemented
242C11×#106C2312yescomplemented
243C11×#106C2312yescomplemented
244C11×C4⋊C8C2312yescomplemented
245C11×C4⋊C8C2312yescomplemented
246C11×#103C2312yescomplemented
247C11×#103C2312yescomplemented
248C11×#103C2312yescomplemented
249C11×#103C2312yescomplemented
250C11×#102C2312yes—
251C11×#102C2312yes—
252C11×#102C2312yes—
253C11×#102C2312yes—
254C11×#102C2312yes—
255C11×#102C2312yes—
256C11×#102C2312yes—
257C11×#102C2312yes—
258C11×#102C2312yescomplemented
259C11×#102C2312yescomplemented
260C11×#102C2312yescomplemented
261C11×#102C2312yescomplemented
262C11×C22⋊C8C2312yes—
263C11×C22⋊C8C2312yes—
264C11×C22⋊C8C2312yes—
265C11×C22⋊C8C2312yes—
266C11×C22⋊C8C2312yescomplemented
267C11×C22⋊C8C2312yescomplemented
268C11×#97C2311yescharacteristic, complemented
269C11×#97C2311yescharacteristic, complemented
270C4×C8×C11C2311yescharacteristic, complemented
271C4×C8×C11C2311yescharacteristic, complemented
272#61643C1111yesmaximal, characteristic, direct product factor, Sylow
273C24×C11—21no—
274C24×C11—22no—
275C24×C11—22no—
276C24×C11—21no—
277C24×C11—22no—
278C24×C11—44no—
279C24×C11—84no—
280C24×C11C2×D411yescharacteristic
281C11×#41—24no—
282C11×#41—42no—
283C11×#41—42no—
284C11×#41—42no—
285C11×#41—42no—
286C11×#41—42no—
287C11×#41—42no—
288C11×#41—42no—
289C11×#41—44no—
290C2×Q8×C11C2×D411yescharacteristic
291C2×Q8×C11C2411yescharacteristic
292C2×Q8×C11C2412yes—
293C2×D4×C11—24no—
294C2×D4×C11—24no—
295C2×D4×C11—24no—
296C2×D4×C11—24no—
297C2×D4×C11—22no—
298C2×D4×C11—21no—
299C2×D4×C11—22no—
300C2×D4×C11—22no—
301C2×D4×C11—22no—
302C2×D4×C11—22no—
303C2×D4×C11—22no—
304C2×D4×C11—22no—
305C2×D4×C11—22no—
306C2×D4×C11—22no—
307C2×D4×C11—21no—
308C2×D4×C11—22no—
309C2×D4×C11—22no—
310C2×D4×C11—22no—
311C2×D4×C11—21no—
312C2×D4×C11—22no—
313C2×D4×C11—22no—
314C2×D4×C11—22no—
315C2×D4×C11—42no—
316C2×D4×C11—42no—
317C2×D4×C11—42no—
318C2×D4×C11—42no—
319C2×D4×C11—48no—
320C2×D4×C11—44no—
321C2×D4×C11—44no—
322C2×D4×C11—48no—
323C2×D4×C11—84no—
324C2×D4×C11—84no—
325C2×D4×C11C2×D412yes—
326C2×D4×C11C2×D412yes—
327C2×D4×C11C2×D412yes—
328C2×D4×C11C2×D411yescharacteristic
329C2×D4×C11C2411yescharacteristic
330C2×D4×C11C2411yescharacteristic
331C2×D4×C11C2411yescharacteristic
332C2×D4×C11C2412yes—
333C2×D4×C11C2412yes—
334C22×C4×C11—22no—
335C22×C4×C11—22no—
336C22×C4×C11—21no—
337C22×C4×C11—22no—
338C22×C4×C11—22no—
339C22×C4×C11—22no—
340C22×C4×C11—22no—
341C22×C4×C11—22no—
342C22×C4×C11—42no—
343C22×C4×C11C2×D412yes—
344C22×C4×C11C2×D411yescharacteristic
345C22×C4×C11C2411yescharacteristic
346C22×C4×C11C2412yes—
347C22×C4×C11C2412yes—
348C11×Q16—42no—
349C11×SD16—24no—
350C11×SD16—24no—
351C11×SD16—42no—
352C11×SD16—42no—
353C11×SD16—42no—
354C11×SD16—42no—
355C11×D8—24no—
356C11×D8—24no—
357C11×D8—42no—
358C11×D8—42no—
359C11×D8—42no—
360C11×M16—42no—
361C11×M16—42no—
362C11×M16—42no—
363C2×C8×C11—42no—
364C2×C8×C11C2412yes—
365C2×C8×C11C2412yes—
366C2×C8×C11C2412yes—
367C2×C8×C11C2412yes—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—22no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—22no—
372C11×C4⋊C4—22no—
373C11×C4⋊C4—22no—
374C11×C4⋊C4—22no—
375C11×C4⋊C4—22no—
376C11×C4⋊C4—22no—
377C11×C4⋊C4C2×D412yes—
378C11×C4⋊C4C2×D412yes—
379C11×C4⋊C4C2×D412yes—
380C11×C4⋊C4C2412yes—
381C11×C4⋊C4C2412yes—
382C11×C4⋊C4C2412yes—
383C11×C22⋊C4—21no—
384C11×C22⋊C4—22no—
385C11×C22⋊C4—22no—
386C11×C22⋊C4—22no—
387C11×C22⋊C4—22no—
388C11×C22⋊C4—22no—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—22no—
391C11×C22⋊C4—22no—
392C11×C22⋊C4—22no—
393C11×C22⋊C4—22no—
394C11×C22⋊C4—22no—
395C11×C22⋊C4—22no—
396C11×C22⋊C4—22no—
397C11×C22⋊C4—22no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—22no—
400C11×C22⋊C4C2×D412yes—
401C11×C22⋊C4C2×D412yes—
402C11×C22⋊C4C2×D412yes—
403C11×C22⋊C4C2×D412yes—
404C11×C22⋊C4C2×D412yes—
405C42×C11—22no—
406C42×C11—22no—
407C42×C11—21no—
408C42×C11C2411yescharacteristic
409C42×C11C2411yescharacteristic
410#3539C2×C1111yescharacteristic, complemented
411#3484C2×C1111yescharacteristic, complemented
412#3323C2×C1112yescomplemented
413#3322C2×C1112yescomplemented
414#3318C2×C1112yescomplemented
415#3310C2×C1112yescomplemented
416#3274C2×C1112yescomplemented
417#3272C2×C1112yescomplemented
418#3268C2×C1112yescomplemented
419#3267C2×C1112yescomplemented
420#3222C2×C1111yescharacteristic, complemented
421#3220C2×C1111yescharacteristic, complemented
422#3198C2×C1112yescomplemented
423#3197C2×C1112yescomplemented
424#3123C2×C1111yescharacteristic, complemented
425#3122C2×C1111yescharacteristic, complemented
426#3012C2×C1112yescomplemented
427#3003C2×C1112yescomplemented
428#2978C2×C1111yescharacteristic, complemented
429C23×C11—24no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11—21no—
435C23×C11—41no—
436C23×C11—42no—
437C23×C11—44no—
438C23×C11—44no—
439C23×C11—44no—
440C23×C11—42no—
441C23×C11—44no—
442C23×C11—44no—
443C23×C11—82no—
444C23×C11—82no—
445C23×C11—82no—
446C23×C11—82no—
447C23×C11—82no—
448C23×C11—82no—
449C23×C11—816no—
450C23×C11C22×D412yes—
451C23×C11C22×D411yescharacteristic
452C23×C11C22×D412yes—
453Q8×C11—22no—
454Q8×C11—22no—
455Q8×C11—22no—
456Q8×C11—41no—
457D4×C11—24no—
458D4×C11—22no—
459D4×C11—22no—
460D4×C11—22no—
461D4×C11—22no—
462D4×C11—22no—
463D4×C11—22no—
464D4×C11—41no—
465D4×C11—42no—
466D4×C11—42no—
467D4×C11—42no—
468D4×C11—44no—
469D4×C11—44no—
470D4×C11—44no—
471D4×C11—42no—
472D4×C11—44no—
473D4×C11—42no—
474D4×C11—44no—
475D4×C11—82no—
476D4×C11—82no—
477D4×C11—82no—
478D4×C11—82no—
479D4×C11—82no—
480D4×C11—82no—
481D4×C11—82no—
482D4×C11—82no—
483D4×C11—82no—
484D4×C11—82no—
485D4×C11H(5,𝔽2)14yes—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—42no—
497C2×C4×C11—41no—
498C2×C4×C11—44no—
499C2×C4×C11—42no—
500C2×C4×C11—82no—
501C2×C4×C11—82no—
502C2×C4×C11—82no—
503C2×C4×C11—82no—
504C2×C4×C11—82no—
505C2×C4×C11—82no—
506C2×C4×C11C22×D412yes—
507C2×C4×C11C22×D412yes—
508C2×C4×C11C22×D411yescharacteristic
509C2×C4×C11C22×D412yes—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C2511yescharacteristic
512C8×C11—22no—
513C8×C11—22no—
514C8×C11—22no—
515C8×C11—22no—
516C2×H(5,𝔽2)C22×C1111yescharacteristic
517C23×D4C22×C1111yescharacteristic
518C2×AGL(1,ℤ/8)C22×C1112yescomplemented
519C2×AGL(1,ℤ/8)C22×C1112yescomplemented
520C2×AGL(1,ℤ/8)C22×C1112yescomplemented
521C2×#135C22×C1112yescomplemented
522#560—22no—
523#553—22no—
524#553C22×C1112yescomplemented
525#552C22×C1112yescomplemented
526#550C22×C1112yescomplemented
527#547C22×C1112yescomplemented
528#546—22no—
529#546C22×C1112yes—
530#546C22×C1112yes—
531D42—22no—
532D42C22×C1112yes—
533D42C22×C1112yes—
534#541C22×C1111yescharacteristic, complemented
535#540—22no—
536#540C22×C1111yescharacteristic, complemented
537#539—22no—
538#537C22×C1112yescomplemented
539#535C22×C1111yescharacteristic
540#535C22×C1111yescharacteristic
541#534—22no—
542#525C22×C1111yescharacteristic
543#525C22×C1111yescharacteristic
544#525C22×C1112yescomplemented
545C2×#120—22no—
546#518C22×C1111yescharacteristic
547#497C22×C1111yescharacteristic, complemented
548#496C22×C1111yescharacteristic, complemented
549#493C22×C1111yescharacteristic, complemented
550#492C22×C1111yescharacteristic, complemented
551#490C22×C1111yescharacteristic, complemented
552#490C22×C1111yescharacteristic, complemented
553#488C22×C1111yescharacteristic, complemented
554#488C22×C1111yescharacteristic, complemented
555#485C22×C1112yescomplemented
556#485C22×C1112yescomplemented
557#482C22×C1112yescomplemented
558#482C22×C1112yescomplemented
559#481C22×C1112yescomplemented
560#480C22×C1112yescomplemented
561#478C22×C1112yescomplemented
562#478C22×C1112yescomplemented
563#470C22×C1112yescomplemented
564#469C22×C1112yescomplemented
565#469C22×C1112yescomplemented
566#468C22×C1112yescomplemented
567#468C22×C1112yescomplemented
568#468C22×C1112yescomplemented
569#466C22×C1112yescomplemented
570#465C22×C1112yescomplemented
571#464C22×C1112yescomplemented
572#463C22×C1112yescomplemented
573#461C22×C1112yescomplemented
574#460C22×C1112yescomplemented
575#459C22×C1112yescomplemented
576#459C22×C1112yescomplemented
577#452C22×C1112yescomplemented
578#452C22×C1112yescomplemented
579#452C22×C1112yescomplemented
580#450C22×C1112yes—
581#450C22×C1112yescomplemented
582#450C22×C1112yescomplemented
583#450C22×C1112yescomplemented
584#450C22×C1112yescomplemented
585#449C22×C1112yescomplemented
586#449C22×C1112yescomplemented
587#449C22×C1112yescomplemented
588#449C22×C1112yescomplemented
589#449C22×C1112yescomplemented
590#447C22×C1112yes—
591#447C22×C1112yescomplemented
592#447C22×C1112yescomplemented
593#447C22×C1112yescomplemented
594#447C22×C1112yescomplemented
595#442C22×C1112yescomplemented
596#440C22×C1112yescomplemented
597C4×SD16C22×C1112yescomplemented
598C4×D8C22×C1112yescomplemented
599#436C22×C1112yescomplemented
600#436C22×C1112yescomplemented
601#435C22×C1112yescomplemented
602#435C22×C1112yescomplemented
603#433C22×C1111yescharacteristic, complemented
604#433C22×C1111yescharacteristic, complemented
605#418C22×C1112yescomplemented
606#418C22×C1112yescomplemented
607#417C22×C1112yescomplemented
608C2×#102C22×C1112yescomplemented
609#408C22×C1112yescomplemented
610#407C22×C1112yescomplemented
611C22×C11—22no—
612C22×C11—22no—
613C22×C11—22no—
614C22×C11—22no—
615C22×C11—22no—
616C22×C11—21no—
617C22×C11—22no—
618C22×C11—22no—
619C22×C11—24no—
620C22×C11—44no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11—42no—
628C22×C11—41no—
629C22×C11—42no—
630C22×C11—41no—
631C22×C11—41no—
632C22×C11—84no—
633C22×C11—88no—
634C22×C11—88no—
635C22×C11—84no—
636C22×C11—164no—
637C22×C11C23×D411yescharacteristic
638C4×C11—22no—
639C4×C11—22no—
640C4×C11—21no—
641C4×C11—22no—
642C4×C11—22no—
643C4×C11—42no—
644C4×C11—42no—
645C4×C11—42no—
646C4×C11—41no—
647C4×C11—42no—
648C4×C11C2×H(5,𝔽2)12yes—
649C25—21no—
650H(5,𝔽2)—44no—
651C2×#41—21no—
652C2×#41C23×C1112yes—
653C2×#41C23×C1111yescharacteristic
654C2×#41C23×C1112yes—
655C2×#41C23×C1111yescharacteristic
656C2×#41C23×C1112yescomplemented
657C22×D4—22no—
658C22×D4—21no—
659C22×D4—22no—
660C22×D4—22no—
661C22×D4—21no—
662C22×D4—22no—
663C22×D4—44no—
664C22×D4C23×C1111yescharacteristic
665C22×D4C23×C1112yes—
666C22×D4C23×C1112yes—
667C22×D4C23×C1112yes—
668C22×D4C23×C1111yescharacteristic
669C23×C4C23×C1111yescharacteristic
670AGL(1,ℤ/8)—44no—
671AGL(1,ℤ/8)—44no—
672AGL(1,ℤ/8)—44no—
673#135—44no—
674C2×Q16C23×C1112yescomplemented
675C2×SD16C23×C1112yes—
676C2×SD16C23×C1112yes—
677C2×SD16C23×C1112yes—
678C2×SD16C23×C1112yes—
679C2×SD16C23×C1112yescomplemented
680C2×SD16C23×C1112yescomplemented
681C2×D8C23×C1112yes—
682C2×D8C23×C1112yes—
683C2×D8C23×C1112yes—
684C2×D8C23×C1112yes—
685C2×D8C23×C1112yescomplemented
686C2×M16C23×C1112yes—
687C2×M16C23×C1112yes—
688C2×M16C23×C1112yescomplemented
689C22×C8C23×C1112yescomplemented
690C4⋊Q8C23×C1111yescharacteristic, complemented
691#127—21no—
692#127—22no—
693#127C23×C1111yescharacteristic
694#127C23×C1111yescharacteristic
695#127C23×C1111yescharacteristic, complemented
696#126—22no—
697#126—22no—
698#126—22no—
699#125—22no—
700#125—22no—
701#125C23×C1111yescharacteristic, complemented
702#125C23×C1111yescharacteristic, complemented
703#124—21no—
704#124C23×C1111yescharacteristic
705#124C23×C1111yescharacteristic
706#123—22no—
707#123—21no—
708#123—22no—
709#123—22no—
710#123—22no—
711#123—22no—
712#123—22no—
713#123—22no—
714#123—22no—
715#123D4×C1112yes—
716C22⋊Q8—22no—
717C22⋊Q8D4×C1112yes—
718C22⋊Q8C23×C1112yes—
719C22⋊Q8C23×C1112yes—
720C22⋊Q8C23×C1112yes—
721C22⋊Q8C23×C1112yescomplemented
722#121—22no—
723#121—22no—
724#121—22no—
725#121—22no—
726#121—22no—
727#121—22no—
728#121—22no—
729#121—22no—
730#121—22no—
731#121—22no—
732#121—22no—
733#121—22no—
734#121—22no—
735#121D4×C1112yes—
736#121C23×C1112yes—
737#121C23×C1112yes—
738#121C23×C1112yes—
739#121C23×C1112yes—
740#121C23×C1112yes—
741#121C23×C1112yescomplemented
742#120—21no—
743#120—22no—
744#120—22no—
745#120—22no—
746#120—22no—
747#120—22no—
748#120—22no—
749#120—22no—
750#120—22no—
751#120—22no—
752#120D4×C1112yes—
753C4×Q8C23×C1112yescomplemented
754C4×D4—22no—
755C4×D4—22no—
756C4×D4—22no—
757C4×D4—22no—
758C4×D4—22no—
759C4×D4—22no—
760C4×D4C23×C1112yes—
761C4×D4C23×C1112yes—
762C4×D4C23×C1112yes—
763C4×D4C23×C1112yes—
764C4×D4C23×C1112yescomplemented
765#117—22no—
766#117C23×C1111yescharacteristic
767#117C23×C1112yes—
768#117C23×C1111yescharacteristic
769C2×C4⋊C4—22no—
770C2×C4⋊C4C23×C1112yescomplemented
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774#107C23×C1112yescomplemented
775#107C23×C1112yescomplemented
776#106C23×C1112yescomplemented
777#106C23×C1112yescomplemented
778C4⋊C8C23×C1112yescomplemented
779C4⋊C8C23×C1112yescomplemented
780#103C23×C1112yescomplemented
781#103C23×C1112yescomplemented
782#103C23×C1112yescomplemented
783#103C23×C1112yescomplemented
784#102C23×C1112yes—
785#102C23×C1112yes—
786#102C23×C1112yes—
787#102C23×C1112yes—
788#102C23×C1112yes—
789#102C23×C1112yes—
790#102C23×C1112yes—
791#102C23×C1112yes—
792#102C23×C1112yescomplemented
793#102C23×C1112yescomplemented
794#102C23×C1112yescomplemented
795#102C23×C1112yescomplemented
796C22⋊C8C23×C1112yes—
797C22⋊C8C23×C1112yes—
798C22⋊C8C23×C1112yes—
799C22⋊C8C23×C1112yes—
800C22⋊C8C23×C1112yescomplemented
801C22⋊C8C23×C1112yescomplemented
802#97C23×C1111yescharacteristic, complemented
803#97C23×C1111yescharacteristic, complemented
804C4×C8C23×C1111yescharacteristic, complemented
805C4×C8C23×C1111yescharacteristic, complemented
806C2×C11—42no—
807C2×C11—41no—
808C2×C11—42no—
809C2×C11—44no—
810C2×C11—82no—
811C2×C11—81no—
812C2×C11—81no—
813C2×C11—81no—
814C2×C11#348411yescharacteristic
815C2×C11#358512yes—
816C24—21no—
817C24—22no—
818C24—22no—
819C24—21no—
820C24—22no—
821C24—44no—
822C24—84no—
823C24C2×D4×C1111yescharacteristic
824#41—24no—
825#41—42no—
826#41—42no—
827#41—42no—
828#41—42no—
829#41—42no—
830#41—42no—
831#41—42no—
832#41—44no—
833C2×Q8C2×D4×C1111yescharacteristic
834C2×Q8C24×C1111yescharacteristic
835C2×Q8C24×C1112yes—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—24no—
840C2×D4—22no—
841C2×D4—21no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—21no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—48no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—48no—
866C2×D4—84no—
867C2×D4—84no—
868C2×D4C2×D4×C1112yes—
869C2×D4C2×D4×C1112yes—
870C2×D4C2×D4×C1112yes—
871C2×D4C2×D4×C1111yescharacteristic
872C2×D4C24×C1111yescharacteristic
873C2×D4C24×C1111yescharacteristic
874C2×D4C24×C1111yescharacteristic
875C2×D4C24×C1112yes—
876C2×D4C24×C1112yes—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—21no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—42no—
886C22×C4C2×D4×C1112yes—
887C22×C4C2×D4×C1111yescharacteristic
888C22×C4C24×C1111yescharacteristic
889C22×C4C24×C1112yes—
890C22×C4C24×C1112yes—
891Q16—42no—
892SD16—24no—
893SD16—24no—
894SD16—42no—
895SD16—42no—
896SD16—42no—
897SD16—42no—
898D8—24no—
899D8—24no—
900D8—42no—
901D8—42no—
902D8—42no—
903M16—42no—
904M16—42no—
905M16—42no—
906C2×C8—42no—
907C2×C8C24×C1112yes—
908C2×C8C24×C1112yes—
909C2×C8C24×C1112yes—
910C2×C8C24×C1112yes—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—22no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4C2×D4×C1112yes—
921C4⋊C4C2×D4×C1112yes—
922C4⋊C4C2×D4×C1112yes—
923C4⋊C4C24×C1112yes—
924C4⋊C4C24×C1112yes—
925C4⋊C4C24×C1112yes—
926C22⋊C4—21no—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—22no—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4—22no—
933C22⋊C4—22no—
934C22⋊C4—22no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4C2×D4×C1112yes—
944C22⋊C4C2×D4×C1112yes—
945C22⋊C4C2×D4×C1112yes—
946C22⋊C4C2×D4×C1112yes—
947C22⋊C4C2×D4×C1112yes—
948C42—22no—
949C42—22no—
950C42—21no—
951C42C24×C1111yescharacteristic
952C42C24×C1111yescharacteristic
953C11#6164311yescharacteristic, direct product factor, Sylow
954C23—24no—
955C23—22no—
956C23—22no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—41no—
961C23—42no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—42no—
966C23—44no—
967C23—44no—
968C23—82no—
969C23—82no—
970C23—82no—
971C23—82no—
972C23—82no—
973C23—82no—
974C23—816no—
975C23C22×D4×C1111yescharacteristic
976C23C22×D4×C1112yes—
977C23C22×D4×C1112yes—
978Q8—22no—
979Q8—22no—
980Q8—22no—
981Q8—41no—
982D4—24no—
983D4—22no—
984D4—22no—
985D4—22no—
986D4—22no—
987D4—22no—
988D4—22no—
989D4—41no—
990D4—42no—
991D4—42no—
992D4—42no—
993D4—44no—
994D4—44no—
995D4—44no—
996D4—42no—
997D4—44no—
998D4—42no—
999D4—44no—
1000D4—82no—
1001D4—82no—
1002D4—82no—
1003D4—82no—
1004D4—82no—
1005D4—82no—
1006D4—82no—
1007D4—82no—
1008D4—82no—
1009D4—82no—
1010D4C11×H(5,𝔽2)14yes—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—42no—
1022C2×C4—41no—
1023C2×C4—44no—
1024C2×C4—42no—
1025C2×C4—82no—
1026C2×C4—82no—
1027C2×C4—82no—
1028C2×C4—82no—
1029C2×C4—82no—
1030C2×C4—82no—
1031C2×C4C22×D4×C1112yes—
1032C2×C4C22×D4×C1112yes—
1033C2×C4C22×D4×C1111yescharacteristic
1034C2×C4C22×D4×C1112yes—
1035C2×C4C22×D4×C1112yes—
1036C2×C4C25×C1111yescharacteristic
1037C8—22no—
1038C8—22no—
1039C8—22no—
1040C8—22no—
1041C22—21no—
1042C22—22no—
1043C22—22no—
1044C22—24no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—22no—
1050C22—44no—
1051C22—42no—
1052C22—42no—
1053C22—41no—
1054C22—42no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—84no—
1063C22—88no—
1064C22—88no—
1065C22—84no—
1066C22—164no—
1067C22C23×D4×C1111yescharacteristic
1068C4—21no—
1069C4—22no—
1070C4—22no—
1071C4—22no—
1072C4—22no—
1073C4—41no—
1074C4—42no—
1075C4—42no—
1076C4—42no—
1077C4—42no—
1078C4C2×C11×H(5,𝔽2)12yes—
1079C2—41no—
1080C2—42no—
1081C2—42no—
1082C2—44no—
1083C2—81no—
1084C2—81no—
1085C2—81no—
1086C2—82no—
1087C2C11×#348411yescharacteristic
1088C2C11×#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. C11×#3539C2semidirect
2. C11×#3484C2semidirect
3. C11×#3323C2semidirect
4. C11×#3322C2semidirect
5. C11×#3318C2semidirect
6. C11×#3310C2semidirect
7. C11×#3274C2semidirect
8. C11×#3272C2semidirect
9. C11×#3268C2semidirect
10. C11×#3267C2semidirect
11. C11×#3222C2semidirect
12. C11×#3220C2semidirect
13. C11×#3198C2semidirect
14. C11×#3197C2semidirect
15. C11×#3123C2semidirect
16. C11×#3122C2semidirect
17. C11×#3012C2semidirect
18. C11×#3003C2semidirect
19. C11×#2978C2semidirect
22. C2×C11×AGL(1,ℤ/8)C22semidirect
23. C2×C11×AGL(1,ℤ/8)C22semidirect
24. C2×C11×AGL(1,ℤ/8)C22semidirect
25. C2×C11×#135C22semidirect
28. C11×#553C22semidirect
29. C11×#552C22semidirect
30. C11×#550C22semidirect
31. C11×#547C22semidirect
38. C11×#541C22semidirect
40. C11×#540C22semidirect
42. C11×#537C22semidirect
48. C11×#525C22semidirect
51. C11×#497C22semidirect
52. C11×#496C22semidirect
53. C11×#493C22semidirect
54. C11×#492C22semidirect
55. C11×#490C22semidirect
56. C11×#490C22semidirect
57. C11×#488C22semidirect
58. C11×#488C22semidirect
59. C11×#485C22semidirect
60. C11×#485C22semidirect
61. C11×#482C22semidirect
62. C11×#482C22semidirect
63. C11×#481C22semidirect
64. C11×#480C22semidirect
65. C11×#478C22semidirect
66. C11×#478C22semidirect
67. C11×#470C22semidirect
68. C11×#469C22semidirect
69. C11×#469C22semidirect
70. C11×#468C22semidirect
71. C11×#468C22semidirect
72. C11×#468C22semidirect
73. C11×#466C22semidirect
74. C11×#465C22semidirect
75. C11×#464C22semidirect
76. C11×#463C22semidirect
77. C11×#461C22semidirect
78. C11×#460C22semidirect
79. C11×#459C22semidirect
80. C11×#459C22semidirect
81. C11×#452C22semidirect
82. C11×#452C22semidirect
83. C11×#452C22semidirect
85. C11×#450C22semidirect
86. C11×#450C22semidirect
87. C11×#450C22semidirect
88. C11×#450C22semidirect
89. C11×#449C22semidirect
90. C11×#449C22semidirect
91. C11×#449C22semidirect
92. C11×#449C22semidirect
93. C11×#449C22semidirect
95. C11×#447C22semidirect
96. C11×#447C22semidirect
97. C11×#447C22semidirect
98. C11×#447C22semidirect
99. C11×#442C22semidirect
100. C11×#440C22semidirect
101. C4×C11×SD16C22semidirect
102. C4×C11×D8C22semidirect
103. C11×#436C22semidirect
104. C11×#436C22semidirect
105. C11×#435C22semidirect
106. C11×#435C22semidirect
107. C11×#433C22semidirect
108. C11×#433C22semidirect
109. C11×#418C22semidirect
110. C11×#418C22semidirect
111. C11×#417C22semidirect
112. C2×C11×#102C22semidirect
113. C11×#408C22semidirect
114. C11×#407C22semidirect
122. C2×C11×#41C23semidirect
140. C2×C11×Q16C23semidirect
145. C2×C11×SD16C23semidirect
146. C2×C11×SD16C23semidirect
151. C2×C11×D8C23semidirect
154. C2×C11×M16C23semidirect
155. C22×C8×C11C23semidirect
156. C11×C4⋊Q8C23semidirect
161. C11×#127C23semidirect
167. C11×#125C23semidirect
168. C11×#125C23semidirect
187. C11×C22⋊Q8C23semidirect
207. C11×#121C23semidirect
219. C4×Q8×C11C23semidirect
230. C4×D4×C11C23semidirect
236. C2×C11×C4⋊C4C23semidirect
240. C11×#107C23semidirect
241. C11×#107C23semidirect
242. C11×#106C23semidirect
243. C11×#106C23semidirect
244. C11×C4⋊C8C23semidirect
245. C11×C4⋊C8C23semidirect
246. C11×#103C23semidirect
247. C11×#103C23semidirect
248. C11×#103C23semidirect
249. C11×#103C23semidirect
258. C11×#102C23semidirect
259. C11×#102C23semidirect
260. C11×#102C23semidirect
261. C11×#102C23semidirect
266. C11×C22⋊C8C23semidirect
267. C11×C22⋊C8C23semidirect
268. C11×#97C23semidirect
269. C11×#97C23semidirect
270. C4×C8×C11C23semidirect
271. C4×C8×C11C23semidirect
272. #61643C11direct (N × H)
410. #3539C2×C11semidirect
411. #3484C2×C11semidirect
412. #3323C2×C11semidirect
413. #3322C2×C11semidirect
414. #3318C2×C11semidirect
415. #3310C2×C11semidirect
416. #3274C2×C11semidirect
417. #3272C2×C11semidirect
418. #3268C2×C11semidirect
419. #3267C2×C11semidirect
420. #3222C2×C11semidirect
421. #3220C2×C11semidirect
422. #3198C2×C11semidirect
423. #3197C2×C11semidirect
424. #3123C2×C11semidirect
425. #3122C2×C11semidirect
426. #3012C2×C11semidirect
427. #3003C2×C11semidirect
428. #2978C2×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
524. #553C22×C11semidirect
525. #552C22×C11semidirect
526. #550C22×C11semidirect
527. #547C22×C11semidirect
534. #541C22×C11semidirect
536. #540C22×C11semidirect
538. #537C22×C11semidirect
544. #525C22×C11semidirect
547. #497C22×C11semidirect
548. #496C22×C11semidirect
549. #493C22×C11semidirect
550. #492C22×C11semidirect
551. #490C22×C11semidirect
552. #490C22×C11semidirect
553. #488C22×C11semidirect
554. #488C22×C11semidirect
555. #485C22×C11semidirect
556. #485C22×C11semidirect
557. #482C22×C11semidirect
558. #482C22×C11semidirect
559. #481C22×C11semidirect
560. #480C22×C11semidirect
561. #478C22×C11semidirect
562. #478C22×C11semidirect
563. #470C22×C11semidirect
564. #469C22×C11semidirect
565. #469C22×C11semidirect
566. #468C22×C11semidirect
567. #468C22×C11semidirect
568. #468C22×C11semidirect
569. #466C22×C11semidirect
570. #465C22×C11semidirect
571. #464C22×C11semidirect
572. #463C22×C11semidirect
573. #461C22×C11semidirect
574. #460C22×C11semidirect
575. #459C22×C11semidirect
576. #459C22×C11semidirect
577. #452C22×C11semidirect
578. #452C22×C11semidirect
579. #452C22×C11semidirect
581. #450C22×C11semidirect
582. #450C22×C11semidirect
583. #450C22×C11semidirect
584. #450C22×C11semidirect
585. #449C22×C11semidirect
586. #449C22×C11semidirect
587. #449C22×C11semidirect
588. #449C22×C11semidirect
589. #449C22×C11semidirect
591. #447C22×C11semidirect
592. #447C22×C11semidirect
593. #447C22×C11semidirect
594. #447C22×C11semidirect
595. #442C22×C11semidirect
596. #440C22×C11semidirect
597. C4×SD16C22×C11semidirect
598. C4×D8C22×C11semidirect
599. #436C22×C11semidirect
600. #436C22×C11semidirect
601. #435C22×C11semidirect
602. #435C22×C11semidirect
603. #433C22×C11semidirect
604. #433C22×C11semidirect
605. #418C22×C11semidirect
606. #418C22×C11semidirect
607. #417C22×C11semidirect
608. C2×#102C22×C11semidirect
609. #408C22×C11semidirect
610. #407C22×C11semidirect
656. C2×#41C23×C11semidirect
674. C2×Q16C23×C11semidirect
679. C2×SD16C23×C11semidirect
680. C2×SD16C23×C11semidirect
685. C2×D8C23×C11semidirect
688. C2×M16C23×C11semidirect
689. C22×C8C23×C11semidirect
690. C4⋊Q8C23×C11semidirect
695. #127C23×C11semidirect
701. #125C23×C11semidirect
702. #125C23×C11semidirect
721. C22⋊Q8C23×C11semidirect
741. #121C23×C11semidirect
753. C4×Q8C23×C11semidirect
764. C4×D4C23×C11semidirect
770. C2×C4⋊C4C23×C11semidirect
774. #107C23×C11semidirect
775. #107C23×C11semidirect
776. #106C23×C11semidirect
777. #106C23×C11semidirect
778. C4⋊C8C23×C11semidirect
779. C4⋊C8C23×C11semidirect
780. #103C23×C11semidirect
781. #103C23×C11semidirect
782. #103C23×C11semidirect
783. #103C23×C11semidirect
792. #102C23×C11semidirect
793. #102C23×C11semidirect
794. #102C23×C11semidirect
795. #102C23×C11semidirect
800. C22⋊C8C23×C11semidirect
801. C22⋊C8C23×C11semidirect
802. #97C23×C11semidirect
803. #97C23×C11semidirect
804. C4×C8C23×C11semidirect
805. C4×C8C23×C11semidirect
953. C11#61643direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35392
C11×#34842
C11×#33232
C11×#33222
C11×#33182
C11×#33102
C11×#32742
C11×#32722
C11×#32682
C11×#32672
C11×#32222
C11×#32202
C11×#31982
C11×#31972
C11×#31232
C11×#31222
C11×#30122
C11×#30032
C11×#29782
#6164311