Finite Group Databasebeta

← C2×D11×#487 #15622960

Subgroups — C2×D11×#487 #15622960

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3C2×#10622706C211yesmaximal, characteristic, complemented
4C2×#10622294C211yesmaximal, characteristic, complemented
5C2×#10622694C211yesmaximal, characteristic, complemented
6C2×#10622405C214yesmaximal, complemented
7D11×#487C2116yesmaximal, direct product factor
8C2×D11×#103C214yesmaximal
9C2×C4×C8×D11C211yesmaximal, characteristic
10C2×C11×#487C211yesmaximal, characteristic, complemented
11C22×Q8×D11—21no—
12C22×Q8×D11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#66997—21no—
16C2×#66997C2212yes—
17C22×C8×D11C2212yes—
18D11×C4⋊Q8—24no—
19D11×C4⋊Q8—24no—
20D11×C4⋊Q8C2218yes—
21D11×C4⋊Q8C2218yes—
22C2×C4⋊C4×D11—21no—
23C2×C4⋊C4×D11—21no—
24C2×C4⋊C4×D11—21no—
25C2×C4⋊C4×D11C2212yes—
26C2×#66941—21no—
27C2×#66941—21no—
28C2×#66941—21no—
29C2×#66941C2212yes—
30C2×C42×D11C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C11×#487C2218yescomplemented
34C2×C11×#103C2214yes—
35C2×C4×C8×C11C2211yescharacteristic
36C2×#66899C2214yes—
37C2×#66880C2214yes—
38C2×C8×Dic11C2212yes—
39#10622706C2218yescomplemented
40#10622694C2218yescomplemented
41C2×#66874C2214yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43D11×#103C22132yes—
44#10622405C22132yescomplemented
45C4×C8×D11C2218yes—
46#10622294C2218yescomplemented
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C2×Q8×D11—24no—
50C2×Q8×D11—28no—
51C2×Q8×D11—216no—
52C2×Q8×D11—48no—
53C2×Q8×D11C2318yes—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×Dic22—21no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22C2312yes—
63C22×C8×C11C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C11×C4⋊Q8C2314yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2312yes—
72C2×C42×C11C2311yescharacteristic
73#66997—24no—
74#66997—28no—
75#66997C2318yes—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2312yes—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C2×C8×D11—28no—
89C2×C8×D11C2318yes—
90C4⋊C4×D11—24no—
91C4⋊C4×D11—28no—
92C4⋊C4×D11—28no—
93C4⋊C4×D11—28no—
94C4⋊C4×D11C2318yes—
95#66941—24no—
96#66941—28no—
97#66941—28no—
98#66941—28no—
99#66941C2318yes—
100C42×D11D414yes—
101C42×D11C2314yes—
102#66922—22no—
103#66922—22no—
104#66922C2314yes—
105#66922C2314yes—
106C11×#103C23116yes—
107C4×C8×C11C2314yes—
108#66899C23116yes—
109#66880C23116yes—
110C8×Dic11C2318yes—
111#66874C23116yes—
112C4×C11⋊C8C2314yes—
113C22×#487—111nomaximal, Sylow
114C23×D11C2×D411yescharacteristic
115C2×Q8×C11—22no—
116C2×Q8×C11—24no—
117C2×Q8×C11—28no—
118C2×Q8×C11—44no—
119C2×Q8×C11C2414yes—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130Q8×D11—232no—
131Q8×D11—416no—
132Q8×D11—432no—
133C2×C4×D11—28no—
134C2×C4×D11—28no—
135C2×C4×D11—48no—
136C2×C4×D11—48no—
137C2×C4×D11SD1618yes—
138C2×C4×D11Q1618yes—
139C2×C4×D11C2×D412yes—
140C2×C4×D11C2×D414yes—
141C2×C4×D11C2×D414yes—
142C2×C4×D11#4118yes—
143C2×C4×D11C2412yes—
144C2×Dic22—28no—
145C2×Dic22—28no—
146C2×Dic22—22no—
147C2×Dic22—24no—
148C2×Dic22—28no—
149C2×Dic22—48no—
150C2×Dic22—48no—
151C2×Dic22—44no—
152C2×Dic22C2414yes—
153C2×C8×C11—24no—
154C2×C8×C11C2414yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2414yes—
160C42×C11C2×D412yes—
161C42×C11C2412yes—
162C4⋊Dic11—22no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11—24no—
166C4⋊Dic11C2414yes—
167Dic11⋊C4—28no—
168Dic11⋊C4—28no—
169Dic11⋊C4—28no—
170Dic11⋊C4—28no—
171C4×Dic11C2×D412yes—
172C4×Dic11C2×D414yes—
173C4×Dic11C2×D414yes—
174C4×Dic11C2412yes—
175C2×C11⋊C8—24no—
176C2×C11⋊C8C2414yes—
177C8×D11—216no—
178C22×C4⋊Q8—111no—
179C22×C4⋊Q8—111no—
180C2×#487—1116no—
181C2×#487—114no—
182C2×#487—111no—
183C2×#487—111no—
184C2×#487—111no—
185C2×#487D1111yescharacteristic, direct product factor
186C22×#103—114no—
187C22×C4×C8—111no—
188C23×C11C22×D411yescharacteristic
189C22×D11#12414yes—
190C22×D11C2×SD1614yes—
191C22×D11C2×Q1614yes—
192C22×D11C22×D412yes—
193Q8×C11—28no—
194Q8×C11—44no—
195Q8×C11—48no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—44no—
199C2×C4×C11—44no—
200C2×C4×C11C2×SD1614yes—
201C2×C4×C11C2×Q1614yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D412yes—
204C2×C4×C11C22×D412yes—
205C2×C4×C11C2×#4114yes—
206C2×C4×C11C2511yescharacteristic
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—44no—
210C2×Dic11—44no—
211C2×Dic11#12414yes—
212C2×Dic11C2×SD1614yes—
213C2×Dic11C2×Q1614yes—
214C2×Dic11C22×D412yes—
215C2×Dic11C22×D412yes—
216C2×Dic11C22×D412yes—
217C4×D11—416no—
218C4×D11—416no—
219C4×D11#12418yes—
220C4×D11C2×SD16116yes—
221C4×D11C2×Q16116yes—
222C4×D11C2×#4118yes—
223Dic22—28no—
224Dic22—44no—
225Dic22—48no—
226Dic22—416no—
227Dic22—416no—
228C8×C11—24no—
229C11⋊C8—24no—
230C23×Q8—112no—
231C23×Q8—221no—
232C23×C8—112no—
233C2×C4⋊Q8—118no—
234C2×C4⋊Q8—112no—
235C2×C4⋊Q8—112no—
236C2×C4⋊Q8—118no—
237C2×C4⋊Q8—111no—
238C2×C4⋊Q8—111no—
239C2×C4⋊Q8—221no—
240C2×C4⋊Q8—221no—
241C2×C4⋊Q8—221no—
242C2×C4⋊Q8—224no—
243C2×C4⋊Q8—224no—
244C2×C4⋊Q8—221no—
245C2×C4⋊Q8C2×D1111yescharacteristic
246C2×C4⋊Q8C2×D1111yescharacteristic
247C22×C4⋊C4—112no—
248C22×C4⋊C4—221no—
249C22×C4⋊C4—221no—
250C22×C4⋊C4—221no—
251C22×C42—111no—
252#487—118no—
253#487—118no—
254#487—1132no—
255#487—118no—
256#487C2×D1118yesdirect product factor
257C2×#103—114no—
258C2×#103—114no—
259C2×#103—114no—
260C2×#103—1132no—
261C2×#103C2×D1114yes—
262C2×C4×C8—112no—
263C2×C4×C8—111no—
264C2×C4×C8—118no—
265C2×C4×C8C2×D1111yescharacteristic
266C22×C11C2×#12412yes—
267C22×C11C22×SD1612yes—
268C22×C11C22×Q1612yes—
269C22×C11C23×D411yescharacteristic
270C2×D11#487116yesdirect product factor
271C2×D11C2×#12414yes—
272C2×D11C22×SD1614yes—
273C2×D11C22×Q1614yes—
274C4×C11—44no—
275C4×C11—44no—
276C4×C11C2×#12412yes—
277C4×C11C22×SD1614yes—
278C4×C11C22×Q1614yes—
279C4×C11C22×#4112yes—
280Dic11—44no—
281Dic11—44no—
282Dic11C2×#12414yes—
283Dic11C22×SD1614yes—
284Dic11C22×Q1614yes—
285C22×Q8—21no—
286C22×Q8—118no—
287C22×Q8—112no—
288C22×Q8—222no—
289C22×Q8—222no—
290C22×Q8—228no—
291C22×Q8—224no—
292C22×Q8—2216no—
293C22×Q8—221no—
294C22×Q8—448no—
295C22×Q8C22×D1112yes—
296C23×C4—111no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—222no—
300C23×C4—222no—
301C22×C8—112no—
302C22×C8—118no—
303C22×C8—228no—
304C22×C8C22×D1112yes—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—118no—
308C4⋊Q8—118no—
309C4⋊Q8—114no—
310C4⋊Q8—114no—
311C4⋊Q8—228no—
312C4⋊Q8—228no—
313C4⋊Q8—228no—
314C4⋊Q8—224no—
315C4⋊Q8—228no—
316C4⋊Q8—224no—
317C4⋊Q8—222no—
318C4⋊Q8—222no—
319C4⋊Q8C22×D1114yes—
320C4⋊Q8C22×D1114yes—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—118no—
326C2×C4⋊C4—224no—
327C2×C4⋊C4—228no—
328C2×C4⋊C4—228no—
329C2×C4⋊C4—228no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4C22×D1112yes—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—114no—
342C2×C42—114no—
343C2×C42C22×D1111yescharacteristic
344#103—1116no—
345#103—1116no—
346#103—1116no—
347#103C22×D11116yes—
348C4×C8—118no—
349C4×C8—114no—
350C4×C8C22×D1114yes—
351C2×C11C2×#48714yescomplemented
352C2×C11C22×#12411yescharacteristic
353C2×C11C23×SD1611yescharacteristic
354C2×C11C23×Q1611yescharacteristic
355D11C2×#48718yesdirect product factor
356C24—111no—
357C2×Q8—22no—
358C2×Q8—24no—
359C2×Q8—28no—
360C2×Q8—44no—
361C2×Q8—114no—
362C2×Q8—228no—
363C2×Q8—228no—
364C2×Q8—2232no—
365C2×Q8—224no—
366C2×Q8—222no—
367C2×Q8—228no—
368C2×Q8—448no—
369C2×Q8—448no—
370C2×Q8—4416no—
371C2×Q8—4432no—
372C2×Q8—444no—
373C2×Q8C23×D1114yes—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—111no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—118no—
380C22×C4—118no—
381C22×C4—114no—
382C22×C4—114no—
383C22×C4—112no—
384C22×C4—118no—
385C22×C4—112no—
386C22×C4—228no—
387C22×C4—228no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—448no—
391C22×C4—448no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395C2×C8—24no—
396C2×C8—114no—
397C2×C8—2216no—
398C2×C8—224no—
399C2×C8C23×D1114yes—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—114no—
405C4⋊C4—228no—
406C4⋊C4—228no—
407C4⋊C4—228no—
408C4⋊C4—228no—
409C4⋊C4—222no—
410C4⋊C4—224no—
411C4⋊C4—224no—
412C4⋊C4—224no—
413C4⋊C4C23×D1114yes—
414C42—114no—
415C42—112no—
416C42—114no—
417C42—112no—
418C42D4×D1112yes—
419C42C23×D1112yes—
420C11C22×#48711yescharacteristic, complemented, Sylow
421C23—114no—
422C23—114no—
423C23—112no—
424C23—114no—
425C23C2×D4×D1111yescharacteristic
426Q8—28no—
427Q8—48no—
428Q8—44no—
429Q8—228no—
430Q8—4416no—
431Q8—4416no—
432Q8—448no—
433Q8—444no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—114no—
439C2×C4—114no—
440C2×C4—112no—
441C2×C4—112no—
442C2×C4—112no—
443C2×C4—114no—
444C2×C4—1116no—
445C2×C4—1116no—
446C2×C4—118no—
447C2×C4—118no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—4416no—
451C2×C4—4416no—
452C2×C4—444no—
453C2×C4—444no—
454C2×C4SD16×D1114yes—
455C2×C4Q16×D1114yes—
456C2×C4C2×D4×D1112yes—
457C2×C4C2×D4×D1112yes—
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4#41×D1114yes—
460C2×C4C24×D1111yescharacteristic
461C8—24no—
462C8—224no—
463C22—114no—
464C22—1116no—
465C22—114no—
466C22—114no—
467C22D11×#12412yes—
468C22C2×SD16×D1112yes—
469C22C2×Q16×D1112yes—
470C22C22×D4×D1111yescharacteristic
471C4—44no—
472C4—44no—
473C4—114no—
474C4—114no—
475C4—114no—
476C4—444no—
477C4—444no—
478C4D11×#12412yes—
479C4C2×SD16×D1114yes—
480C4C2×Q16×D1114yes—
481C4C2×#41×D1112yes—
482C2—118no—
483C2D11×#48714yesdirect product factor
484C2C2×D11×#12411yescharacteristic
485C2C22×SD16×D1111yescharacteristic
486C2C22×Q16×D1111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#487D11
hypocenterC11C22×#487
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. C2×#10622706C2semidirect
4. C2×#10622294C2semidirect
5. C2×#10622694C2semidirect
6. C2×#10622405C2semidirect
7. D11×#487C2direct (N × H)
10. C2×C11×#487C2semidirect
33. C11×#487C22semidirect
39. #10622706C22semidirect
40. #10622694C22semidirect
44. #10622405C22semidirect
46. #10622294C22semidirect
185. C2×#487D11direct (N × H)
256. #487C2×D11direct (N × H)
270. C2×D11#487direct (N × H)
351. C2×C11C2×#487semidirect
355. D11C2×#487direct (N × H)
420. C11C22×#487semidirect
483. C2D11×#487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106227062
C2×#106222942
C2×#106226942
C2×#106224052
D11×#4872
C2×D11×#1032
C2×C4×C8×D112
C2×C11×#4872
C22×#48711