Finite Group Databasebeta

← C11×#60568 #14637761

Subgroups — C11×#60568 #14637761

Order 2816.

2138 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#540C211yesmaximal, characteristic, complemented
2C11×#3428C211yesmaximal, characteristic, complemented
3C11×#3126C214yesmaximal, complemented
4C11×#3122C214yesmaximal, complemented
5C11×#3119C218yesmaximal, complemented
6C11×#3094C212yesmaximal, complemented
7C11×#3080C212yesmaximal, complemented
8C11×#3038C212yesmaximal, complemented
9C11×#3006C212yesmaximal, complemented
10C4×C11×AGL(1,ℤ/8)C214yesmaximal, complemented
11C11×#2921C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2214yes—
14C11×#540—22no—
15C11×#540—22no—
16C11×#540C2214yes—
17C11×#540C2214yescomplemented
18C2×C11×#127C2211yescharacteristic, complemented
19C2×C11×#125C2211yescharacteristic, complemented
20C2×C11×#123—22no—
21C2×C11×#121—22no—
22C2×C11×#121C2212yes—
23C11×#520—22no—
24C11×#520C2214yescomplemented
25C11×#519C2212yescomplemented
26C11×#518—22no—
27C11×#518C2212yescomplemented
28C4×C11×#41—22no—
29C4×C11×#41C2212yes—
30C4×C11×#41C2212yes—
31C2×C4×D4×C11C2212yescomplemented
32C2×C11×#117—22no—
33C2×C11×#117C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C11×#482C2218yescomplemented
36C11×#481C2214yescomplemented
37C11×#480C2214yescomplemented
38C11×#479C2218yescomplemented
39C11×#478C2218yescomplemented
40C11×#460C2218yescomplemented
41C11×#459C2218yescomplemented
42C11×#449C2218yescomplemented
43C11×#448C2214yescomplemented
44C11×#447C2214yescomplemented
45C11×#442C2218yescomplemented
46C11×#440C2218yescomplemented
47C4×C11×SD16C2218yescomplemented
48C4×C11×D8C2218yescomplemented
49C11×#433C2214yescomplemented
50C11×#433C2214yescomplemented
51C11×#428C2214yescomplemented
52C11×#423C2212yescomplemented
53C11×#418C2214yescomplemented
54C11×#417C2214yes—
55C11×#407C2212yes—
56C4×C11×M16C2212yescomplemented
57C2×C11×#41—28no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41C2312yes—
61C2×C11×#41C2312yes—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11C2312yes—
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11—22no—
70C23×C4×C11C2311yescharacteristic
71C11×AGL(1,ℤ/8)—216no—
72C2×C11×SD16C2318yes—
73C2×C11×D8C2318yes—
74C2×C11×M16C2314yes—
75C11×#127—22no—
76C11×#127C2314yes—
77C11×#125—22no—
78C11×#125C2314yes—
79C11×#123—28no—
80C11×#123—28no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—28no—
84C11×#121—28no—
85C11×#121C2314yes—
86C11×#121C2314yes—
87C4×Q8×C11—24no—
88C4×Q8×C11C2314yes—
89C4×Q8×C11C2314yes—
90C4×D4×C11—24no—
91C4×D4×C11—24no—
92C4×D4×C11—24no—
93C4×D4×C11—24no—
94C4×D4×C11—24no—
95C4×D4×C11—24no—
96C4×D4×C11C2318yes—
97C4×D4×C11C2314yes—
98C4×D4×C11C2314yes—
99C11×#117—21no—
100C11×#117—21no—
101C11×#117—24no—
102C11×#117—24no—
103C11×#117—22no—
104C11×#117—22no—
105C11×#117D412yes—
106C11×#117D412yes—
107C11×#117C2312yes—
108C11×#117C2312yes—
109C11×#117C2312yes—
110C11×#117C2312yes—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4D412yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4D412yes—
121C2×C42×C11—21no—
122C2×C42×C11—22no—
123C2×C42×C11—22no—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C11×#107C2318yes—
127C11×#106C2318yes—
128C11×C4⋊C8C2318yes—
129C11×#103C2318yes—
130C11×#102C2318yes—
131C11×#102C2318yes—
132C11×#102C2318yes—
133C11×C22⋊C8C2314yes—
134C11×C22⋊C8C2314yes—
135C11×#97C2314yes—
136C4×C8×C11C2314yes—
137#60568C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11—22no—
140C24×C11C2×D411yescharacteristic
141C11×#41—28no—
142C11×#41—28no—
143C11×#41—24no—
144C11×#41—24no—
145C11×#41—24no—
146C11×#41#4118yes—
147C2×Q8×C11—24no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2412yes—
150C2×D4×C11—28no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11—28no—
159C2×D4×C11—28no—
160C2×D4×C11—84no—
161C2×D4×C11—84no—
162C2×D4×C11C2414yes—
163C2×D4×C11C2412yes—
164C22×C4×C11—28no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—24no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—24no—
172C22×C4×C11—24no—
173C22×C4×C11—28no—
174C22×C4×C11—84no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C11×SD16—216no—
184C11×D8—216no—
185C11×M16—28no—
186C2×C8×C11C2418yes—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—28no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4C2×D414yes—
193C11×C4⋊C4C2×D414yes—
194C11×C4⋊C4C2414yes—
195C11×C4⋊C4C2414yes—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—28no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4C2×D414yes—
204C11×C22⋊C4C2×D414yes—
205C42×C11—22no—
206C42×C11—24no—
207C42×C11—24no—
208C42×C11—22no—
209C42×C11C2×D412yes—
210C42×C11C2×D412yes—
211C42×C11C2412yes—
212C42×C11C2412yes—
213C2×#540C2×C1111yescharacteristic, complemented
214#3428C2×C1111yescharacteristic, complemented
215#3126C2×C1114yescomplemented
216#3122C2×C1114yescomplemented
217#3119C2×C1118yescomplemented
218#3094C2×C1112yescomplemented
219#3080C2×C1112yescomplemented
220#3038C2×C1112yescomplemented
221#3006C2×C1112yescomplemented
222C4×AGL(1,ℤ/8)C2×C1114yescomplemented
223#2921C2×C1111yescharacteristic, complemented
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—24no—
228C23×C11—42no—
229C23×C11—44no—
230C23×C11—44no—
231C23×C11—44no—
232C23×C11—82no—
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C22×D411yescharacteristic
236Q8×C11—24no—
237Q8×C11—22no—
238Q8×C11C2×#4114yes—
239D4×C11—28no—
240D4×C11—24no—
241D4×C11—28no—
242D4×C11—22no—
243D4×C11—28no—
244D4×C11—44no—
245D4×C11—88no—
246D4×C11—84no—
247D4×C11—84no—
248D4×C11C2×#4114yes—
249C2×C4×C11—24no—
250C2×C4×C11—28no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—28no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—44no—
263C2×C4×C11—84no—
264C2×C4×C11—84no—
265C2×C4×C11—88no—
266C2×C4×C11—82no—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D414yes—
269C2×C4×C11C22×D414yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4114yes—
273C2×C4×C11C2511yescharacteristic
274C8×C11—28no—
275C22×#41C22×C1111yescharacteristic
276C2×AGL(1,ℤ/8)C22×C1114yes—
277#540—22no—
278#540—22no—
279#540C22×C1114yes—
280#540C22×C1114yescomplemented
281C2×#127C22×C1111yescharacteristic, complemented
282C2×#125C22×C1111yescharacteristic, complemented
283C2×#123—22no—
284C2×#121—22no—
285C2×#121C22×C1112yes—
286#520—22no—
287#520C22×C1114yescomplemented
288#519C22×C1112yescomplemented
289#518—22no—
290#518C22×C1112yescomplemented
291C4×#41—22no—
292C4×#41C22×C1112yes—
293C4×#41C22×C1112yes—
294C2×C4×D4C22×C1112yescomplemented
295C2×#117—22no—
296C2×#117C22×C1111yescharacteristic
297C2×#117C22×C1111yescharacteristic
298#482C22×C1118yescomplemented
299#481C22×C1114yescomplemented
300#480C22×C1114yescomplemented
301#479C22×C1118yescomplemented
302#478C22×C1118yescomplemented
303#460C22×C1118yescomplemented
304#459C22×C1118yescomplemented
305#449C22×C1118yescomplemented
306#448C22×C1114yescomplemented
307#447C22×C1114yescomplemented
308#442C22×C1118yescomplemented
309#440C22×C1118yescomplemented
310C4×SD16C22×C1118yescomplemented
311C4×D8C22×C1118yescomplemented
312#433C22×C1114yescomplemented
313#433C22×C1114yescomplemented
314#428C22×C1114yescomplemented
315#423C22×C1112yescomplemented
316#418C22×C1114yescomplemented
317#417C22×C1114yes—
318#407C22×C1112yes—
319C4×M16C22×C1112yescomplemented
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—24no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—82no—
331C22×C11—88no—
332C22×C11—84no—
333C22×C11#52512yes—
334C22×C11C23×D411yescharacteristic
335C4×C11—24no—
336C4×C11—24no—
337C4×C11—21no—
338C4×C11—24no—
339C4×C11—21no—
340C4×C11—44no—
341C4×C11—44no—
342C4×C11#52512yes—
343C4×C11C22×#4112yes—
344C2×#41—28no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41C23×C1112yes—
348C2×#41C23×C1112yes—
349C22×Q8C23×C1111yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4C23×C1112yes—
354C22×D4C23×C1111yescharacteristic
355C23×C4—21no—
356C23×C4—22no—
357C23×C4C23×C1111yescharacteristic
358AGL(1,ℤ/8)—216no—
359C2×SD16C23×C1118yes—
360C2×D8C23×C1118yes—
361C2×M16C23×C1114yes—
362#127—22no—
363#127C23×C1114yes—
364#125—22no—
365#125C23×C1114yes—
366#123—28no—
367#123—28no—
368#121—22no—
369#121—22no—
370#121—28no—
371#121—28no—
372#121C23×C1114yes—
373#121C23×C1114yes—
374C4×Q8—24no—
375C4×Q8C23×C1114yes—
376C4×Q8C23×C1114yes—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4C23×C1118yes—
384C4×D4C23×C1114yes—
385C4×D4C23×C1114yes—
386#117—21no—
387#117—21no—
388#117—24no—
389#117—24no—
390#117—22no—
391#117—22no—
392#117D4×C1112yes—
393#117D4×C1112yes—
394#117C23×C1112yes—
395#117C23×C1112yes—
396#117C23×C1112yes—
397#117C23×C1112yes—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4D4×C1112yes—
401C2×C4⋊C4C23×C1112yes—
402C2×C4⋊C4C23×C1112yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4D4×C1112yes—
408C2×C42—21no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42C23×C1111yescharacteristic
412C2×C42C23×C1111yescharacteristic
413#107C23×C1118yes—
414#106C23×C1118yes—
415C4⋊C8C23×C1118yes—
416#103C23×C1118yes—
417#102C23×C1118yes—
418#102C23×C1118yes—
419#102C23×C1118yes—
420C22⋊C8C23×C1114yes—
421C22⋊C8C23×C1114yes—
422#97C23×C1114yes—
423C4×C8C23×C1114yes—
424C2×C11—22no—
425C2×C11—41no—
426C2×C11—41no—
427C2×C11—44no—
428C2×C11—84no—
429C2×C11C2×#52511yescharacteristic
430C2×C11#358512yes—
431C24—21no—
432C24—22no—
433C24C2×D4×C1111yescharacteristic
434#41—28no—
435#41—28no—
436#41—24no—
437#41—24no—
438#41—24no—
439#41C11×#4118yes—
440C2×Q8—24no—
441C2×Q8—21no—
442C2×Q8C24×C1112yes—
443C2×D4—28no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—84no—
454C2×D4—84no—
455C2×D4C24×C1114yes—
456C2×D4C24×C1112yes—
457C22×C4—28no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—28no—
467C22×C4—84no—
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1112yes—
472C22×C4C2×D4×C1112yes—
473C22×C4C24×C1111yescharacteristic
474C22×C4C24×C1111yescharacteristic
475C22×C4C24×C1111yescharacteristic
476SD16—216no—
477D8—216no—
478M16—28no—
479C2×C8C24×C1118yes—
480C4⋊C4—22no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—28no—
484C4⋊C4—22no—
485C4⋊C4C2×D4×C1114yes—
486C4⋊C4C2×D4×C1114yes—
487C4⋊C4C24×C1114yes—
488C4⋊C4C24×C1114yes—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—28no—
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4C2×D4×C1114yes—
497C22⋊C4C2×D4×C1114yes—
498C42—22no—
499C42—24no—
500C42—24no—
501C42—22no—
502C42C2×D4×C1112yes—
503C42C2×D4×C1112yes—
504C42C24×C1112yes—
505C42C24×C1112yes—
506C11#6056811yescharacteristic, direct product factor, Sylow
507C23—24no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—42no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—82no—
516C23C22×D4×C1111yescharacteristic
517C23C22×D4×C1111yescharacteristic
518C23C22×D4×C1111yescharacteristic
519Q8—24no—
520Q8—22no—
521Q8C2×C11×#4114yes—
522D4—28no—
523D4—24no—
524D4—28no—
525D4—22no—
526D4—28no—
527D4—44no—
528D4—88no—
529D4—84no—
530D4—84no—
531D4C2×C11×#4114yes—
532C2×C4—24no—
533C2×C4—28no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—28no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—84no—
547C2×C4—84no—
548C2×C4—88no—
549C2×C4—82no—
550C2×C4C22×D4×C1111yescharacteristic
551C2×C4C22×D4×C1114yes—
552C2×C4C22×D4×C1114yes—
553C2×C4C22×D4×C1111yescharacteristic
554C2×C4C22×D4×C1111yescharacteristic
555C2×C4C2×C11×#4114yes—
556C2×C4C25×C1111yescharacteristic
557C8—28no—
558C22—22no—
559C22—21no—
560C22—21no—
561C22—24no—
562C22—22no—
563C22—22no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—44no—
568C22—82no—
569C22—88no—
570C22—84no—
571C22C11×#52512yes—
572C22C23×D4×C1111yescharacteristic
573C4—21no—
574C4—24no—
575C4—21no—
576C4—24no—
577C4—24no—
578C4—44no—
579C4—44no—
580C4C11×#52512yes—
581C4C22×C11×#4112yes—
582C2—22no—
583C2—41no—
584C2—41no—
585C2—44no—
586C2—84no—
587C2C2×C11×#52511yescharacteristic
588C2C11×#358512yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#540C2semidirect
2. C11×#3428C2semidirect
3. C11×#3126C2semidirect
4. C11×#3122C2semidirect
5. C11×#3119C2semidirect
6. C11×#3094C2semidirect
7. C11×#3080C2semidirect
8. C11×#3038C2semidirect
9. C11×#3006C2semidirect
10. C4×C11×AGL(1,ℤ/8)C2semidirect
11. C11×#2921C2semidirect
17. C11×#540C22semidirect
18. C2×C11×#127C22semidirect
19. C2×C11×#125C22semidirect
24. C11×#520C22semidirect
25. C11×#519C22semidirect
27. C11×#518C22semidirect
31. C2×C4×D4×C11C22semidirect
35. C11×#482C22semidirect
36. C11×#481C22semidirect
37. C11×#480C22semidirect
38. C11×#479C22semidirect
39. C11×#478C22semidirect
40. C11×#460C22semidirect
41. C11×#459C22semidirect
42. C11×#449C22semidirect
43. C11×#448C22semidirect
44. C11×#447C22semidirect
45. C11×#442C22semidirect
46. C11×#440C22semidirect
47. C4×C11×SD16C22semidirect
48. C4×C11×D8C22semidirect
49. C11×#433C22semidirect
50. C11×#433C22semidirect
51. C11×#428C22semidirect
52. C11×#423C22semidirect
53. C11×#418C22semidirect
56. C4×C11×M16C22semidirect
137. #60568C11direct (N × H)
213. C2×#540C2×C11semidirect
214. #3428C2×C11semidirect
215. #3126C2×C11semidirect
216. #3122C2×C11semidirect
217. #3119C2×C11semidirect
218. #3094C2×C11semidirect
219. #3080C2×C11semidirect
220. #3038C2×C11semidirect
221. #3006C2×C11semidirect
222. C4×AGL(1,ℤ/8)C2×C11semidirect
223. #2921C2×C11semidirect
280. #540C22×C11semidirect
281. C2×#127C22×C11semidirect
282. C2×#125C22×C11semidirect
287. #520C22×C11semidirect
288. #519C22×C11semidirect
290. #518C22×C11semidirect
294. C2×C4×D4C22×C11semidirect
298. #482C22×C11semidirect
299. #481C22×C11semidirect
300. #480C22×C11semidirect
301. #479C22×C11semidirect
302. #478C22×C11semidirect
303. #460C22×C11semidirect
304. #459C22×C11semidirect
305. #449C22×C11semidirect
306. #448C22×C11semidirect
307. #447C22×C11semidirect
308. #442C22×C11semidirect
309. #440C22×C11semidirect
310. C4×SD16C22×C11semidirect
311. C4×D8C22×C11semidirect
312. #433C22×C11semidirect
313. #433C22×C11semidirect
314. #428C22×C11semidirect
315. #423C22×C11semidirect
316. #418C22×C11semidirect
319. C4×M16C22×C11semidirect
506. C11#60568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5402
C11×#34282
C11×#31262
C11×#31222
C11×#31192
C11×#30942
C11×#30802
C11×#30382
C11×#30062
C4×C11×AGL(1,ℤ/8)2
C11×#29212
#6056811