Finite Group Databasebeta

← C11×#61932 #14639125

Subgroups — C11×#61932 #14639125

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic, complemented
2C11×#3508C211yesmaximal, characteristic, complemented
3C11×#3399C214yesmaximal, complemented
4C11×#3391C214yesmaximal, complemented
5C11×#3366C214yesmaximal, complemented
6C11×#3361C214yesmaximal, complemented
7C11×#3220C214yesmaximal, complemented
8C11×#3205C212yesmaximal, complemented
9C11×#3122C214yesmaximal, complemented
10C11×#3106C212yesmaximal, complemented
11C11×#2986C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#559C2214yes—
14C11×#554C2214yescomplemented
15C11×#550C2214yes—
16C11×#550C2214yescomplemented
17C11×#547—22no—
18C11×#546—24no—
19C11×#540—22no—
20C11×#540C2214yes—
21C11×#537—24no—
22C11×#535C2212yes—
23C11×#533C2211yescharacteristic
24C11×#532—22no—
25C11×#532C2212yes—
26C2×C11×#127C2211yescharacteristic
27C11×#518C2212yes—
28C4×C11×#41C2211yescharacteristic
29C11×#496C2214yescomplemented
30C11×#493C2214yes—
31C11×#493C2214yescomplemented
32C11×#490C2214yescomplemented
33C11×#488C2214yescomplemented
34C11×#486C2214yes—
35C11×#482C2214yes—
36C11×#478C2218yescomplemented
37C11×#477C2212yescomplemented
38C11×#476C2212yescomplemented
39C11×#463C2218yescomplemented
40C11×#460C2212yescomplemented
41C11×#459C2214yes—
42C11×#459C2214yes—
43C11×#459C2218yescomplemented
44C11×#459C2212yescomplemented
45C11×#459C2218yescomplemented
46C11×#449C2214yes—
47C11×#447C2218yes—
48C11×#446C2214yescomplemented
49C8×Q8×C11C2214yescomplemented
50C11×#442C2218yescomplemented
51C4×C11×SD16C2214yescomplemented
52C4×C11×D8C2218yescomplemented
53C4×C11×D8C2214yescomplemented
54C11×#433C2214yes—
55C11×#431C2212yes—
56C2×C11×#41—24no—
57C2×C11×#41—24no—
58C2×C11×#41—22no—
59C2×C11×#41C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11C2312yes—
62C2×C11×SD16C2314yes—
63C2×C11×D8C2318yes—
64C2×C11×D8C2318yes—
65C2×C11×D8C2314yes—
66C11×C4⋊Q8D412yes—
67C11×C4⋊Q8C2312yes—
68C11×#127—21no—
69C11×#127—21no—
70C11×#127C2314yes—
71C11×#127C2312yes—
72C11×#127C2314yes—
73C11×#127C2314yes—
74C11×#125D412yes—
75C11×#125C2314yes—
76C11×#124—24no—
77C11×#124—22no—
78C11×#124C2314yes—
79C11×#123—28no—
80C11×#123—28no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—28no—
83C11×C22⋊Q8D414yes—
84C11×#121—22no—
85C11×#121—24no—
86C11×#121—24no—
87C11×#121—24no—
88C11×#121—28no—
89C11×#121—28no—
90C11×#121—28no—
91C11×#121C2314yes—
92C11×#120—24no—
93C4×Q8×C11C2312yes—
94C4×Q8×C11C2314yes—
95C4×D4×C11—22no—
96C4×D4×C11—24no—
97C4×D4×C11—24no—
98C4×D4×C11—22no—
99C4×D4×C11C2312yes—
100C4×D4×C11C2318yes—
101C4×D4×C11C2314yes—
102C4×D4×C11C2318yes—
103C11×#117—21no—
104C11×#117C2311yescharacteristic
105C11×#117C2312yes—
106C2×C11×C4⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C11×#107C2314yes—
111C11×#106C2314yes—
112C11×C4⋊C8C2312yes—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2318yes—
115C11×#103C2314yes—
116C11×#102C2314yes—
117C11×#102C2318yes—
118C11×#102C2314yes—
119C11×#102C2314yes—
120C11×#102C2318yes—
121C11×C22⋊C8C2314yes—
122C11×#97C2314yes—
123C4×C8×C11C2314yes—
124C4×C8×C11C2314yes—
125#61932C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11—22no—
127C11×#41—42no—
128C11×#41—84no—
129C11×#41—88no—
130C11×#41—88no—
131C2×Q8×C11—22no—
132C2×Q8×C11C2×D414yes—
133C2×Q8×C11C2411yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—24no—
139C2×D4×C11—28no—
140C2×D4×C11—28no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—44no—
144C2×D4×C11—84no—
145C2×D4×C11C2414yes—
146C2×D4×C11C2411yescharacteristic
147C2×D4×C11C2414yes—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—28no—
152C22×C4×C11—28no—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2411yescharacteristic
155C11×SD16—44no—
156C11×D8—48no—
157C11×D8—44no—
158C11×D8—48no—
159C2×C8×C11C2414yes—
160C2×C8×C11C2414yes—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C2×D414yes—
165C11×C4⋊C4C2×D414yes—
166C11×C4⋊C4C2×D418yes—
167C11×C4⋊C4C2414yes—
168C11×C4⋊C4C2412yes—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4C2×D414yes—
177C42×C11—21no—
178C42×C11—22no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2412yes—
182C42×C11C2414yes—
183#3548C2×C1111yescharacteristic, complemented
184#3508C2×C1111yescharacteristic, complemented
185#3399C2×C1114yescomplemented
186#3391C2×C1114yescomplemented
187#3366C2×C1114yescomplemented
188#3361C2×C1114yescomplemented
189#3220C2×C1114yescomplemented
190#3205C2×C1112yescomplemented
191#3122C2×C1114yescomplemented
192#3106C2×C1112yescomplemented
193#2986C2×C1111yescharacteristic, complemented
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—21no—
197C23×C11—44no—
198C23×C11—84no—
199C23×C11C22×D411yescharacteristic
200Q8×C11—28no—
201Q8×C11—22no—
202Q8×C11—82no—
203D4×C11—24no—
204D4×C11—24no—
205D4×C11—28no—
206D4×C11—22no—
207D4×C11—44no—
208D4×C11—42no—
209D4×C11—48no—
210D4×C11—44no—
211D4×C11—84no—
212D4×C11—82no—
213D4×C11—88no—
214D4×C11—88no—
215D4×C11—84no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—42no—
222C2×C4×C11—44no—
223C2×C4×C11—48no—
224C2×C4×C11—88no—
225C2×C4×C11—88no—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D412yes—
228C2×C4×C11C22×D418yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C2511yescharacteristic
231C8×C11—24no—
232C8×C11—24no—
233#562—22no—
234#559C22×C1114yes—
235#554C22×C1114yescomplemented
236#550C22×C1114yes—
237#550C22×C1114yescomplemented
238#547—22no—
239#546—24no—
240#540—22no—
241#540C22×C1114yes—
242#537—24no—
243#535C22×C1112yes—
244#533C22×C1111yescharacteristic
245#532—22no—
246#532C22×C1112yes—
247C2×#127C22×C1111yescharacteristic
248#518C22×C1112yes—
249C4×#41C22×C1111yescharacteristic
250#496C22×C1114yescomplemented
251#493C22×C1114yes—
252#493C22×C1114yescomplemented
253#490C22×C1114yescomplemented
254#488C22×C1114yescomplemented
255#486C22×C1114yes—
256#482C22×C1114yes—
257#478C22×C1118yescomplemented
258#477C22×C1112yescomplemented
259#476C22×C1112yescomplemented
260#463C22×C1118yescomplemented
261#460C22×C1112yescomplemented
262#459C22×C1114yes—
263#459C22×C1114yes—
264#459C22×C1112yescomplemented
265#459C22×C1118yescomplemented
266#459C22×C1118yescomplemented
267#449C22×C1114yes—
268#447C22×C1118yes—
269#446C22×C1114yescomplemented
270C8×Q8C22×C1114yescomplemented
271#442C22×C1118yescomplemented
272C4×SD16C22×C1114yescomplemented
273C4×D8C22×C1118yescomplemented
274C4×D8C22×C1114yescomplemented
275#433C22×C1114yes—
276#431C22×C1112yes—
277C22×C11—21no—
278C22×C11—22no—
279C22×C11—41no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—42no—
283C22×C11—44no—
284C22×C11—44no—
285C22×C11—48no—
286C22×C11—164no—
287C22×C11C23×D411yescharacteristic
288C4×C11—21no—
289C4×C11—22no—
290C4×C11—28no—
291C4×C11—41no—
292C4×C11—42no—
293C4×C11—44no—
294C4×C11#57614yes—
295C4×C11#58512yes—
296C2×#41—24no—
297C2×#41—24no—
298C2×#41—22no—
299C2×#41C23×C1111yescharacteristic
300C22×D4—22no—
301C22×D4C23×C1112yes—
302C2×SD16C23×C1114yes—
303C2×D8C23×C1118yes—
304C2×D8C23×C1114yes—
305C2×D8C23×C1118yes—
306C4⋊Q8D4×C1112yes—
307C4⋊Q8C23×C1112yes—
308#127—21no—
309#127—21no—
310#127C23×C1114yes—
311#127C23×C1112yes—
312#127C23×C1114yes—
313#127C23×C1114yes—
314#125D4×C1112yes—
315#125C23×C1114yes—
316#124—24no—
317#124—22no—
318#124C23×C1114yes—
319#123—28no—
320#123—28no—
321C22⋊Q8—24no—
322C22⋊Q8—28no—
323C22⋊Q8D4×C1114yes—
324#121—22no—
325#121—24no—
326#121—24no—
327#121—24no—
328#121—28no—
329#121—28no—
330#121—28no—
331#121C23×C1114yes—
332#120—24no—
333C4×Q8C23×C1112yes—
334C4×Q8C23×C1114yes—
335C4×D4—22no—
336C4×D4—24no—
337C4×D4—24no—
338C4×D4—22no—
339C4×D4C23×C1112yes—
340C4×D4C23×C1118yes—
341C4×D4C23×C1114yes—
342C4×D4C23×C1118yes—
343#117—21no—
344#117C23×C1111yescharacteristic
345#117C23×C1112yes—
346C2×C4⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C42—21no—
349C2×C42C23×C1111yescharacteristic
350#107C23×C1114yes—
351#106C23×C1114yes—
352C4⋊C8C23×C1112yes—
353C4⋊C8C23×C1112yes—
354C4⋊C8C23×C1118yes—
355#103C23×C1114yes—
356#102C23×C1114yes—
357#102C23×C1114yes—
358#102C23×C1118yes—
359#102C23×C1114yes—
360#102C23×C1118yes—
361C22⋊C8C23×C1114yes—
362#97C23×C1114yes—
363C4×C8C23×C1114yes—
364C4×C8C23×C1114yes—
365C2×C11—41no—
366C2×C11—81no—
367C2×C11—84no—
368C2×C11—84no—
369C2×C11#348711yescharacteristic
370C2×C11C2×#57612yes—
371C24—22no—
372#41—42no—
373#41—84no—
374#41—88no—
375#41—88no—
376C2×Q8—22no—
377C2×Q8C2×D4×C1114yes—
378C2×Q8C24×C1111yescharacteristic
379C2×D4—21no—
380C2×D4—24no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—24no—
384C2×D4—28no—
385C2×D4—28no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—44no—
389C2×D4—84no—
390C2×D4C24×C1114yes—
391C2×D4C24×C1111yescharacteristic
392C2×D4C24×C1114yes—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—28no—
397C22×C4—28no—
398C22×C4C2×D4×C1112yes—
399C22×C4C24×C1111yescharacteristic
400SD16—44no—
401D8—44no—
402D8—48no—
403D8—48no—
404C2×C8C24×C1114yes—
405C2×C8C24×C1114yes—
406C4⋊C4—22no—
407C4⋊C4—28no—
408C4⋊C4—22no—
409C4⋊C4C2×D4×C1114yes—
410C4⋊C4C2×D4×C1114yes—
411C4⋊C4C2×D4×C1118yes—
412C4⋊C4C24×C1114yes—
413C4⋊C4C24×C1112yes—
414C22⋊C4—21no—
415C22⋊C4—28no—
416C22⋊C4—22no—
417C22⋊C4—28no—
418C22⋊C4—24no—
419C22⋊C4—28no—
420C22⋊C4—24no—
421C22⋊C4C2×D4×C1114yes—
422C42—21no—
423C42—22no—
424C42C2×D4×C1111yescharacteristic
425C42C2×D4×C1111yescharacteristic
426C42C24×C1112yes—
427C42C24×C1114yes—
428C11#6193211yescharacteristic, direct product factor, Sylow
429C23—24no—
430C23—24no—
431C23—21no—
432C23—44no—
433C23—84no—
434C23C22×D4×C1111yescharacteristic
435Q8—28no—
436Q8—22no—
437Q8—82no—
438D4—24no—
439D4—24no—
440D4—28no—
441D4—22no—
442D4—44no—
443D4—42no—
444D4—48no—
445D4—44no—
446D4—84no—
447D4—82no—
448D4—88no—
449D4—88no—
450D4—84no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—48no—
459C2×C4—88no—
460C2×C4—88no—
461C2×C4C22×D4×C1111yescharacteristic
462C2×C4C22×D4×C1112yes—
463C2×C4C22×D4×C1118yes—
464C2×C4C22×D4×C1112yes—
465C2×C4C25×C1111yescharacteristic
466C8—24no—
467C8—24no—
468C22—21no—
469C22—22no—
470C22—41no—
471C22—44no—
472C22—44no—
473C22—42no—
474C22—44no—
475C22—44no—
476C22—48no—
477C22—164no—
478C22C23×D4×C1111yescharacteristic
479C4—21no—
480C4—22no—
481C4—28no—
482C4—41no—
483C4—42no—
484C4—44no—
485C4C11×#57614yes—
486C4C11×#58512yes—
487C2—41no—
488C2—84no—
489C2—81no—
490C2—84no—
491C2C11×#348711yescharacteristic
492C2C2×C11×#57612yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3548C2semidirect
2. C11×#3508C2semidirect
3. C11×#3399C2semidirect
4. C11×#3391C2semidirect
5. C11×#3366C2semidirect
6. C11×#3361C2semidirect
7. C11×#3220C2semidirect
8. C11×#3205C2semidirect
9. C11×#3122C2semidirect
10. C11×#3106C2semidirect
11. C11×#2986C2semidirect
14. C11×#554C22semidirect
16. C11×#550C22semidirect
29. C11×#496C22semidirect
31. C11×#493C22semidirect
32. C11×#490C22semidirect
33. C11×#488C22semidirect
36. C11×#478C22semidirect
37. C11×#477C22semidirect
38. C11×#476C22semidirect
39. C11×#463C22semidirect
40. C11×#460C22semidirect
43. C11×#459C22semidirect
44. C11×#459C22semidirect
45. C11×#459C22semidirect
48. C11×#446C22semidirect
49. C8×Q8×C11C22semidirect
50. C11×#442C22semidirect
51. C4×C11×SD16C22semidirect
52. C4×C11×D8C22semidirect
53. C4×C11×D8C22semidirect
125. #61932C11direct (N × H)
183. #3548C2×C11semidirect
184. #3508C2×C11semidirect
185. #3399C2×C11semidirect
186. #3391C2×C11semidirect
187. #3366C2×C11semidirect
188. #3361C2×C11semidirect
189. #3220C2×C11semidirect
190. #3205C2×C11semidirect
191. #3122C2×C11semidirect
192. #3106C2×C11semidirect
193. #2986C2×C11semidirect
235. #554C22×C11semidirect
237. #550C22×C11semidirect
250. #496C22×C11semidirect
252. #493C22×C11semidirect
253. #490C22×C11semidirect
254. #488C22×C11semidirect
257. #478C22×C11semidirect
258. #477C22×C11semidirect
259. #476C22×C11semidirect
260. #463C22×C11semidirect
261. #460C22×C11semidirect
264. #459C22×C11semidirect
265. #459C22×C11semidirect
266. #459C22×C11semidirect
269. #446C22×C11semidirect
270. C8×Q8C22×C11semidirect
271. #442C22×C11semidirect
272. C4×SD16C22×C11semidirect
273. C4×D8C22×C11semidirect
274. C4×D8C22×C11semidirect
428. C11#61932direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#35082
C11×#33992
C11×#33912
C11×#33662
C11×#33612
C11×#32202
C11×#32052
C11×#31222
C11×#31062
C11×#29862
#6193211