Finite Group Databasebeta

← C11×#60566 #14637759

Subgroups — C11×#60566 #14637759

Order 2816.

2002 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3455C211yesmaximal, characteristic
2C2×C11×#519C211yesmaximal, characteristic, complemented
3C11×#3127C214yesmaximal, complemented
4C11×#3126C214yesmaximal, complemented
5C11×#3121C218yesmaximal, complemented
6C11×#3093C212yesmaximal, complemented
7C11×#3078C212yesmaximal, complemented
8C11×#3037C212yesmaximal, complemented
9C11×#3004C212yesmaximal, complemented
10C4×C11×#137C214yesmaximal, complemented
11C11×#2921C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C2×C11×#137C2214yes—
14C11×#542C2214yes—
15C11×#541C2212yes—
16C11×#540C2212yes—
17C11×#539—22no—
18C11×#538—22no—
19C11×#533C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C11×#529—24no—
22C11×#525C2212yes—
23C11×#519—24no—
24C11×#519C2214yes—
25C11×#519C2214yes—
26C4×C11×#41C2212yes—
27C2×C4×Q8×C11—22no—
28C2×C4×Q8×C11C2212yes—
29C2×C4×Q8×C11C2212yes—
30C2×C11×#117—22no—
31C2×C11×#117C2211yescharacteristic
32C2×C11×#117C2211yescharacteristic
33C11×#485C2218yes—
34C11×#482C2218yes—
35C11×#479C2218yescomplemented
36C11×#477C2214yescomplemented
37C11×#475C2214yescomplemented
38C11×#464C2218yescomplemented
39C11×#462C2214yescomplemented
40C11×#460C2214yescomplemented
41C11×#451C2218yes—
42C11×#448C2218yes—
43C11×#441C2218yescomplemented
44C11×#440C2218yescomplemented
45C4×C11×Q16C2218yescomplemented
46C4×C11×SD16C2218yescomplemented
47C11×#433C2214yes—
48C11×#433C2214yes—
49C11×#428C2214yes—
50C11×#423C2212yes—
51C11×#419C2214yes—
52C11×#417C2214yes—
53C11×#407C2212yes—
54C4×C11×M16C2212yes—
55C2×C11×#41C2312yes—
56C22×Q8×C11—28no—
57C22×Q8×C11—21no—
58C22×Q8×C11—22no—
59C22×Q8×C11C2314yes—
60C22×Q8×C11C2312yes—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C11×#137—216no—
64C2×C11×Q16C2318yes—
65C2×C11×SD16C2318yes—
66C2×C11×M16C2314yes—
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2312yes—
69C11×#127C2311yescharacteristic
70C11×#126—24no—
71C11×#126—24no—
72C11×#125—24no—
73C11×#125C2312yes—
74C11×#124—24no—
75C11×#124C2312yes—
76C11×#123—22no—
77C11×#123—24no—
78C11×#123—24no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8C2314yes—
82C11×#121—22no—
83C11×#121—24no—
84C11×#121C2314yes—
85C11×#120—22no—
86C4×Q8×C11—28no—
87C4×Q8×C11—28no—
88C4×Q8×C11—24no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11C2318yes—
93C4×Q8×C11C2314yes—
94C4×Q8×C11C2314yes—
95C4×Q8×C11C2314yes—
96C4×D4×C11—24no—
97C4×D4×C11—24no—
98C4×D4×C11—22no—
99C4×D4×C11C2314yes—
100C11×#117—22no—
101C11×#117—28no—
102C11×#117—28no—
103C11×#117—22no—
104C11×#117D414yes—
105C11×#117C2314yes—
106C11×#117C2312yes—
107C11×#117C2312yes—
108C11×#117C2312yes—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4D412yes—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4D412yes—
115C2×C42×C11—22no—
116C2×C42×C11—22no—
117C2×C42×C11—21no—
118C2×C42×C11—22no—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C11×#107C2318yes—
122C11×#106C2318yes—
123C11×C4⋊C8C2314yes—
124C11×C4⋊C8C2314yes—
125C11×#103C2318yes—
126C11×#103C2318yes—
127C11×#103C2318yes—
128C11×#102C2318yes—
129C11×C22⋊C8C2318yes—
130C11×#97C2314yes—
131C4×C8×C11C2314yes—
132#60566C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11C2×D411yescharacteristic
134C11×#41—28no—
135C2×Q8×C11—216no—
136C2×Q8×C11—28no—
137C2×Q8×C11—216no—
138C2×Q8×C11—24no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—24no—
142C2×Q8×C11#4118yes—
143C2×Q8×C11C2412yes—
144C2×Q8×C11C2414yes—
145C2×D4×C11—22no—
146C2×D4×C11—24no—
147C2×D4×C11—22no—
148C2×D4×C11C2412yes—
149C22×C4×C11—28no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—24no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2411yescharacteristic
162C11×Q16—216no—
163C11×SD16—216no—
164C11×M16—28no—
165C2×C8×C11C2418yes—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4C2×D414yes—
176C11×C4⋊C4C2×D414yes—
177C11×C4⋊C4C2414yes—
178C11×C4⋊C4C2414yes—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4C2×D414yes—
186C11×C22⋊C4C2×D414yes—
187C42×C11—28no—
188C42×C11—24no—
189C42×C11—24no—
190C42×C11—22no—
191C42×C11—24no—
192C42×C11—24no—
193C42×C11C2×D412yes—
194C42×C11C2×D412yes—
195C42×C11C2412yes—
196C42×C11C2411yescharacteristic
197C42×C11C2411yescharacteristic
198#3455C2×C1111yescharacteristic
199C2×#519C2×C1111yescharacteristic, complemented
200#3127C2×C1114yescomplemented
201#3126C2×C1114yescomplemented
202#3121C2×C1118yescomplemented
203#3093C2×C1112yescomplemented
204#3078C2×C1112yescomplemented
205#3037C2×C1112yescomplemented
206#3004C2×C1112yescomplemented
207C4×#137C2×C1114yescomplemented
208#2921C2×C1111yescharacteristic, complemented
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—42no—
212C23×C11C22×D412yes—
213C23×C11C22×D411yescharacteristic
214Q8×C11—216no—
215Q8×C11—28no—
216Q8×C11—24no—
217Q8×C11—24no—
218Q8×C11—82no—
219Q8×C11C2×#4118yes—
220D4×C11—24no—
221D4×C11—44no—
222D4×C11—82no—
223D4×C11—84no—
224C2×C4×C11—216no—
225C2×C4×C11—28no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—44no—
237C2×C4×C11—84no—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4114yes—
244C2×C4×C11C2511yescharacteristic
245C8×C11—28no—
246C23×Q8C22×C1111yescharacteristic
247C2×#137C22×C1114yes—
248#542C22×C1114yes—
249#541C22×C1112yes—
250#540C22×C1112yes—
251#539—22no—
252#538—22no—
253#533C22×C1111yescharacteristic
254#532C22×C1111yescharacteristic
255#529—24no—
256#525C22×C1112yes—
257#519—24no—
258#519C22×C1114yes—
259#519C22×C1114yes—
260C4×#41C22×C1112yes—
261C2×C4×Q8—22no—
262C2×C4×Q8C22×C1112yes—
263C2×C4×Q8C22×C1112yes—
264C2×#117—22no—
265C2×#117C22×C1111yescharacteristic
266C2×#117C22×C1111yescharacteristic
267#485C22×C1118yes—
268#482C22×C1118yes—
269#479C22×C1118yescomplemented
270#477C22×C1114yescomplemented
271#475C22×C1114yescomplemented
272#464C22×C1118yescomplemented
273#462C22×C1114yescomplemented
274#460C22×C1114yescomplemented
275#451C22×C1118yes—
276#448C22×C1118yes—
277#441C22×C1118yescomplemented
278#440C22×C1118yescomplemented
279C4×Q16C22×C1118yescomplemented
280C4×SD16C22×C1118yescomplemented
281#433C22×C1114yes—
282#433C22×C1114yes—
283#428C22×C1114yes—
284#423C22×C1112yes—
285#419C22×C1114yes—
286#417C22×C1114yes—
287#407C22×C1112yes—
288C4×M16C22×C1112yes—
289C22×C11—22no—
290C22×C11—24no—
291C22×C11—22no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—42no—
295C22×C11#52512yes—
296C22×C11C23×D411yescharacteristic
297C4×C11—24no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—28no—
301C4×C11—22no—
302C4×C11—44no—
303C4×C11—44no—
304C4×C11—42no—
305C4×C11#52512yes—
306C4×C11C22×#4112yes—
307C2×#41C23×C1112yes—
308C22×Q8—28no—
309C22×Q8—21no—
310C22×Q8—22no—
311C22×Q8C23×C1114yes—
312C22×Q8C23×C1112yes—
313C23×C4—21no—
314C23×C4C23×C1111yescharacteristic
315#137—216no—
316C2×Q16C23×C1118yes—
317C2×SD16C23×C1118yes—
318C2×M16C23×C1114yes—
319C4⋊Q8C23×C1111yescharacteristic
320C4⋊Q8C23×C1112yes—
321#127C23×C1111yescharacteristic
322#126—24no—
323#126—24no—
324#125—24no—
325#125C23×C1112yes—
326#124—24no—
327#124C23×C1112yes—
328#123—22no—
329#123—24no—
330#123—24no—
331C22⋊Q8—22no—
332C22⋊Q8—24no—
333C22⋊Q8C23×C1114yes—
334#121—22no—
335#121—24no—
336#121C23×C1114yes—
337#120—22no—
338C4×Q8—28no—
339C4×Q8—28no—
340C4×Q8—24no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8C23×C1118yes—
345C4×Q8C23×C1114yes—
346C4×Q8C23×C1114yes—
347C4×Q8C23×C1114yes—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—22no—
351C4×D4C23×C1114yes—
352#117—22no—
353#117—28no—
354#117—28no—
355#117—22no—
356#117D4×C1114yes—
357#117C23×C1114yes—
358#117C23×C1112yes—
359#117C23×C1112yes—
360#117C23×C1112yes—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4D4×C1112yes—
364C2×C4⋊C4C23×C1112yes—
365C2×C22⋊C4—21no—
366C2×C22⋊C4D4×C1112yes—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—21no—
370C2×C42—22no—
371C2×C42C23×C1111yescharacteristic
372C2×C42C23×C1111yescharacteristic
373#107C23×C1118yes—
374#106C23×C1118yes—
375C4⋊C8C23×C1114yes—
376C4⋊C8C23×C1114yes—
377#103C23×C1118yes—
378#103C23×C1118yes—
379#103C23×C1118yes—
380#102C23×C1118yes—
381C22⋊C8C23×C1118yes—
382#97C23×C1114yes—
383C4×C8C23×C1114yes—
384C2×C11—22no—
385C2×C11—42no—
386C2×C11—82no—
387C2×C11C2×#52511yescharacteristic
388C2×C11#358612yes—
389C24C2×D4×C1111yescharacteristic
390#41—28no—
391C2×Q8—216no—
392C2×Q8—28no—
393C2×Q8—216no—
394C2×Q8—24no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—24no—
398C2×Q8C11×#4118yes—
399C2×Q8C24×C1112yes—
400C2×Q8C24×C1114yes—
401C2×D4—22no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4C24×C1112yes—
405C22×C4—28no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1112yes—
414C22×C4C2×D4×C1112yes—
415C22×C4C2×D4×C1112yes—
416C22×C4C24×C1112yes—
417C22×C4C24×C1111yescharacteristic
418Q16—216no—
419SD16—216no—
420M16—28no—
421C2×C8C24×C1118yes—
422C4⋊C4—28no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—24no—
427C4⋊C4—22no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4C2×D4×C1114yes—
432C4⋊C4C2×D4×C1114yes—
433C4⋊C4C24×C1114yes—
434C4⋊C4C24×C1114yes—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4C2×D4×C1114yes—
442C22⋊C4C2×D4×C1114yes—
443C42—28no—
444C42—24no—
445C42—24no—
446C42—22no—
447C42—24no—
448C42—24no—
449C42C2×D4×C1112yes—
450C42C2×D4×C1112yes—
451C42C24×C1112yes—
452C42C24×C1111yescharacteristic
453C42C24×C1111yescharacteristic
454C11#6056611yescharacteristic, direct product factor, Sylow
455C23—22no—
456C23—22no—
457C23—42no—
458C23C22×D4×C1112yes—
459C23C22×D4×C1111yescharacteristic
460Q8—216no—
461Q8—28no—
462Q8—24no—
463Q8—24no—
464Q8—82no—
465Q8C2×C11×#4118yes—
466D4—24no—
467D4—44no—
468D4—82no—
469D4—84no—
470C2×C4—216no—
471C2×C4—28no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—84no—
484C2×C4C22×D4×C1114yes—
485C2×C4C22×D4×C1112yes—
486C2×C4C22×D4×C1112yes—
487C2×C4C22×D4×C1112yes—
488C2×C4C22×D4×C1111yescharacteristic
489C2×C4C2×C11×#4114yes—
490C2×C4C25×C1111yescharacteristic
491C8—28no—
492C22—22no—
493C22—22no—
494C22—24no—
495C22—44no—
496C22—42no—
497C22—44no—
498C22C11×#52512yes—
499C22C23×D4×C1111yescharacteristic
500C4—28no—
501C4—22no—
502C4—24no—
503C4—22no—
504C4—22no—
505C4—42no—
506C4—44no—
507C4—44no—
508C4C11×#52512yes—
509C4C22×C11×#4112yes—
510C2—22no—
511C2—42no—
512C2—82no—
513C2C2×C11×#52511yescharacteristic
514C2C11×#358612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3455C2
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
2. C2×C11×#519C2semidirect
3. C11×#3127C2semidirect
4. C11×#3126C2semidirect
5. C11×#3121C2semidirect
6. C11×#3093C2semidirect
7. C11×#3078C2semidirect
8. C11×#3037C2semidirect
9. C11×#3004C2semidirect
10. C4×C11×#137C2semidirect
11. C11×#2921C2semidirect
35. C11×#479C22semidirect
36. C11×#477C22semidirect
37. C11×#475C22semidirect
38. C11×#464C22semidirect
39. C11×#462C22semidirect
40. C11×#460C22semidirect
43. C11×#441C22semidirect
44. C11×#440C22semidirect
45. C4×C11×Q16C22semidirect
46. C4×C11×SD16C22semidirect
132. #60566C11direct (N × H)
199. C2×#519C2×C11semidirect
200. #3127C2×C11semidirect
201. #3126C2×C11semidirect
202. #3121C2×C11semidirect
203. #3093C2×C11semidirect
204. #3078C2×C11semidirect
205. #3037C2×C11semidirect
206. #3004C2×C11semidirect
207. C4×#137C2×C11semidirect
208. #2921C2×C11semidirect
269. #479C22×C11semidirect
270. #477C22×C11semidirect
271. #475C22×C11semidirect
272. #464C22×C11semidirect
273. #462C22×C11semidirect
274. #460C22×C11semidirect
277. #441C22×C11semidirect
278. #440C22×C11semidirect
279. C4×Q16C22×C11semidirect
280. C4×SD16C22×C11semidirect
454. C11#60566direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34552
C2×C11×#5192
C11×#31272
C11×#31262
C11×#31212
C11×#30932
C11×#30782
C11×#30372
C11×#30042
C4×C11×#1372
C11×#29212
#6056611