Finite Group Databasebeta

← #14960998

Subgroups — #14960998

Order 2816.

1770 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076903C212yesmaximal
2#13075770C214yesmaximal, complemented
3#13075701C214yesmaximal, complemented
4#13075190C214yesmaximal, complemented
5#13075067C214yesmaximal, complemented
6#13074730C211yesmaximal, characteristic, complemented
7#13074586C211yesmaximal, characteristic, complemented
8#13073117C214yesmaximal, complemented
9#13072856C214yesmaximal
10#13071349C212yesmaximal, complemented
11C2×C11×#381C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C2×#66977C2212yes—
15C2×#66977C2212yes—
16C2×#66977C2212yes—
17C2×#66932C2214yes—
18C11×#381C2214yes—
19C11×#381C2214yes—
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23#10622860C2214yes—
24#10622825C2214yes—
25#10622825C2212yes—
26#10622825C2212yes—
27#10622825C2212yes—
28#10622823C2214yes—
29#10622823C2214yes—
30#10622823C2214yes—
31#10622823C2214yes—
32#10622823C2214yes—
33C4×C22⋊Dic11C2214yes—
34#10622566C2214yes—
35#10622565C2214yes—
36#10622565C2214yes—
37#10622564C2214yes—
38#10622561C2214yes—
39#10622558C2214yes—
40#10622557C2214yes—
41#10622274C2214yescomplemented
42#10622273C2214yescomplemented
43#10622272C2214yescomplemented
44#10622271C2214yescomplemented
45#10622271C2214yescomplemented
46#10622270C2214yescomplemented
47#10622270C2214yescomplemented
48#10622269C2214yescomplemented
49#10622268C2214yescomplemented
50#10622267C2214yescomplemented
51#10622266C2214yescomplemented
52#10622265C2214yescomplemented
53#10622263C2214yescomplemented
54#10622260C2214yescomplemented
55#10622260C2214yescomplemented
56#10622259C2214yescomplemented
57C25×C11C2311yescharacteristic
58C23×C4×C11—24no—
59C23×C4×C11—44no—
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C22×Dic22C2312yes—
67C2×C11×C22⋊C4—44no—
68C2×C11×C22⋊C4C2314yes—
69C2×C11×C22⋊C4C2314yes—
70C2×C22⋊Dic11C2314yes—
71C2×C22⋊Dic11C2314yes—
72C2×C22⋊Dic11C2314yes—
73C2×C22⋊Dic11C2314yes—
74C2×C22⋊Dic11C2314yes—
75C2×C22⋊Dic11C2314yes—
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2314yes—
78C2×C4⋊Dic11C2312yes—
79C2×C4⋊Dic11C2314yes—
80C2×C4⋊Dic11C2312yes—
81#66977—28no—
82#66977—44no—
83#66977—44no—
84C2×Dic11⋊C4C2314yes—
85C2×Dic11⋊C4C2314yes—
86C2×Dic11⋊C4C2314yes—
87C2×Dic11⋊C4C2314yes—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×Dic11⋊C4C2314yes—
91C2×C4×Dic11C2314yes—
92C2×C4×Dic11C2314yes—
93#66932—48no—
94C11×#95C2314yes—
95C11×#95C2314yes—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C11⋊#95C2314yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109#36732—111nomaximal, Sylow
110C24×C11—22no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—41no—
114C24×C11—41no—
115C24×C11C2412yes—
116C24×C11C2411yescharacteristic
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—416no—
133C22×C4×C11#4114yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×Dic11C2414yes—
140C22×Dic11C2414yes—
141C22×Dic11C2414yes—
142C22×Dic11C2414yes—
143C2×Dic22—24no—
144C2×Dic22—42no—
145C2×Dic22—42no—
146C11×C22⋊C4—28no—
147C11×C22⋊C4—44no—
148C22⋊Dic11—28no—
149C22⋊Dic11—28no—
150C22⋊Dic11—28no—
151C22⋊Dic11—28no—
152C22⋊Dic11—44no—
153C22⋊Dic11—44no—
154C4⋊Dic11—24no—
155C4⋊Dic11—44no—
156C4⋊Dic11—42no—
157C4⋊Dic11—42no—
158C4⋊Dic11—44no—
159Dic11⋊C4—28no—
160Dic11⋊C4—44no—
161Dic11⋊C4—44no—
162Dic11⋊C4—44no—
163Dic11⋊C4—44no—
164Dic11⋊C4—44no—
165Dic11⋊C4—44no—
166C4×Dic11—44no—
167C4×Dic11—44no—
168#2848—112no—
169#2744—114no—
170#2739—114no—
171#2698—114no—
172#2689—114no—
173#2659—111no—
174#2646—111no—
175#2505—114no—
176#2480—114no—
177#2329—112no—
178C2×#381D1111yescharacteristic
179C23×C11—22no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—28no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—48no—
190C23×C11—48no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11C2×#4112yes—
194C23×C11H(5,𝔽2)14yes—
195C23×C112−1+414yes—
196C23×C11C2511yescharacteristic
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—44no—
210C2×C4×C11—48no—
211C2×C4×C11—48no—
212C2×C4×C11—44no—
213C2×C4×C11—84no—
214C2×C4×C11—84no—
215C2×C4×C11C2×#4114yes—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228Dic22—84no—
229C24×C4C2×D1111yescharacteristic
230C2×#126—114no—
231C2×C22⋊Q8—112no—
232C2×C22⋊Q8—112no—
233C2×C22⋊Q8—112no—
234C22×C22⋊C4C2×D1112yes—
235#400—114no—
236#400—114no—
237#400—114no—
238#400—114no—
239#398—114no—
240#398—114no—
241#398—114no—
242#397—114no—
243#397—114no—
244#397—114no—
245#396—114no—
246#395—114no—
247#391—114no—
248#389—114no—
249#389—114no—
250#388—114no—
251#388—114no—
252#388—114no—
253#387—114no—
254#387—114no—
255#387—114no—
256#387—114no—
257#385—114no—
258#385—114no—
259#385—114no—
260#385—114no—
261#385—114no—
262#382—114no—
263#381C2×D1114yes—
264#381C2×D1114yes—
265#380—112no—
266#380—112no—
267#380—112no—
268#380—114no—
269#379—114no—
270C4×C22⋊C4—114no—
271C2×#95C2×D1111yescharacteristic
272C2×#95C2×D1111yescharacteristic
273C2×#95C2×D1112yes—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11—416no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11#54114yes—
287C22×C11C22×#4111yescharacteristic
288C22×C11C2×H(5,𝔽2)12yes—
289C22×C11C2×2−1+412yes—
290C22×C11#58511yescharacteristic
291C22×C11#58511yescharacteristic
292C4×C11—24no—
293C4×C11—41no—
294C4×C11—41no—
295C4×C11—44no—
296C4×C11—44no—
297Dic11—44no—
298Dic11—44no—
299Dic11—44no—
300Dic11—44no—
301C25C22×D1111yescharacteristic
302C22×Q8—112no—
303C23×C4—24no—
304C23×C4—44no—
305C23×C4C22×D1112yes—
306C23×C4C22×D1112yes—
307C23×C4C22×D1112yes—
308C23×C4C22×D1112yes—
309C23×C4C22×D1111yescharacteristic
310C23×C4C22×D1111yescharacteristic
311#126—448no—
312C22⋊Q8—228no—
313C22⋊Q8—444no—
314C22⋊Q8—444no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—114no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—114no—
320C2×C4⋊C4—114no—
321C2×C4⋊C4—114no—
322C2×C4⋊C4—114no—
323C2×C4⋊C4—114no—
324C2×C4⋊C4—114no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—114no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—114no—
329C2×C22⋊C4—114no—
330C2×C22⋊C4—114no—
331C2×C22⋊C4—114no—
332C2×C22⋊C4—114no—
333C2×C22⋊C4—114no—
334C2×C22⋊C4C22×D1114yes—
335C2×C22⋊C4C22×D1114yes—
336C2×C42—114no—
337C2×C42—114no—
338#95—114no—
339#95—114no—
340#95—114no—
341#95—114no—
342#95—114no—
343#95—114no—
344#95—114no—
345#95—114no—
346#95—114no—
347#95—114no—
348#95—114no—
349#95C22×D1114yes—
350#95C22×D1114yes—
351#95C22×D1114yes—
352#95C22×D1114yes—
353C2×C11—24no—
354C2×C11—44no—
355C2×C11C2×#54111yescharacteristic
356C2×C11#349011yescharacteristic
357C2×C11#349311yescharacteristic
358C2×C11#353512yes—
359C2×C11#353512yes—
360C24—22no—
361C24—24no—
362C24—24no—
363C24—41no—
364C24—41no—
365C24C23×D1112yes—
366C24C23×D1111yescharacteristic
367C2×Q8—224no—
368C2×Q8—442no—
369C2×Q8—442no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—416no—
386C22×C4—114no—
387C22×C4—114no—
388C22×C4—114no—
389C22×C4—114no—
390C22×C4#433914yes—
391C22×C4C23×D1114yes—
392C22×C4C23×D1114yes—
393C22×C4C23×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395C22×C4C23×D1112yes—
396C4⋊C4—228no—
397C4⋊C4—224no—
398C4⋊C4—444no—
399C4⋊C4—444no—
400C4⋊C4—442no—
401C4⋊C4—442no—
402C4⋊C4—444no—
403C4⋊C4—444no—
404C4⋊C4—444no—
405C4⋊C4—444no—
406C4⋊C4—444no—
407C4⋊C4—444no—
408C22⋊C4—28no—
409C22⋊C4—44no—
410C22⋊C4—228no—
411C22⋊C4—228no—
412C22⋊C4—228no—
413C22⋊C4—228no—
414C22⋊C4—444no—
415C22⋊C4—444no—
416C42—444no—
417C42—444no—
418C11#3673211yescharacteristic, complemented, Sylow
419C23—22no—
420C23—21no—
421C23—21no—
422C23—28no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—48no—
430C23—48no—
431C23—44no—
432C23—44no—
433C23C2×#433912yes—
434C23#6703714yes—
435C23#6704314yes—
436C23C24×D1111yescharacteristic
437Q8—884no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—44no—
451C2×C4—48no—
452C2×C4—48no—
453C2×C4—44no—
454C2×C4—84no—
455C2×C4—84no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4C2×#433914yes—
469C22—22no—
470C22—24no—
471C22—24no—
472C22—22no—
473C22—24no—
474C22—24no—
475C22—24no—
476C22—416no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22#1062304914yes—
482C22C22×#433911yescharacteristic
483C22C2×#6703712yes—
484C22C2×#6704312yes—
485C22#1062345311yescharacteristic
486C22#1062345311yescharacteristic
487C4—24no—
488C4—41no—
489C4—41no—
490C4—44no—
491C4—44no—
492C4—444no—
493C4—444no—
494C4—444no—
495C4—444no—
496C2—24no—
497C2—44no—
498C2C2×#1062304911yescharacteristic
499C2#1308230511yescharacteristic
500C2#1308233611yescharacteristic
501C2#1308282912yes—
502C2#1308282912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#381C2
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11#36732
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. #13075770C2semidirect
3. #13075701C2semidirect
4. #13075190C2semidirect
5. #13075067C2semidirect
6. #13074730C2semidirect
7. #13074586C2semidirect
8. #13073117C2semidirect
10. #13071349C2semidirect
41. #10622274C22semidirect
42. #10622273C22semidirect
43. #10622272C22semidirect
44. #10622271C22semidirect
45. #10622271C22semidirect
46. #10622270C22semidirect
47. #10622270C22semidirect
48. #10622269C22semidirect
49. #10622268C22semidirect
50. #10622267C22semidirect
51. #10622266C22semidirect
52. #10622265C22semidirect
53. #10622263C22semidirect
54. #10622260C22semidirect
55. #10622260C22semidirect
56. #10622259C22semidirect
418. C11#36732semidirect

Maximal subgroups

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

subgroupindex
#130769032
#130757702
#130757012
#130751902
#130750672
#130747302
#130745862
#130731172
#130728562
#130713492
C2×C11×#3812
#3673211