Finite Group Databasebeta

← #14960583

Subgroups — #14960583

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2#13076900C212yesmaximal
3#13075076C218yesmaximal, complemented
4#13074926C218yesmaximal, complemented
5#13074431C212yesmaximal, complemented
6#13073775C212yesmaximal
7#13072899C212yesmaximal, complemented
8#13072886C212yesmaximal
9#13072261C212yesmaximal, complemented
10#13071219C211yesmaximal, characteristic, complemented
11C2×C11×#544C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C11×#544—28no—
15C2×C11×C4⋊Q8C2214yescomplemented
16C2×C11×#125C2214yescomplemented
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#117C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66999C2214yes—
22C2×#66997C2214yescomplemented
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C2×#66949—28no—
28C2×#66949C2218yes—
29#10622844C2214yes—
30#10622842C2214yescomplemented
31#10622825C2212yes—
32#10622824C2212yes—
33C4×C22⋊Dic11C2212yes—
34#10622606C2214yes—
35#10622606C2214yes—
36#10622605C2214yes—
37#10622603C2218yes—
38#10622602C2218yes—
39#10622600C2214yes—
40#10622597C2218yescomplemented
41#10622595C2214yescomplemented
42#10622595C2214yescomplemented
43#10622594C2218yescomplemented
44#10622593C2214yescomplemented
45#10622592C2218yescomplemented
46#10622587C2214yescomplemented
47#10622568C2214yes—
48#10622559C2214yes—
49#10622559C2214yes—
50#10622556C2214yes—
51#10622553C2218yes—
52#10622546C2218yescomplemented
53C24×D11C2311yescharacteristic
54C22×Q8×C11C2312yes—
55C22×Q8×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—24no—
63C22×C4×D11—44no—
64C22×C4×D11C2314yes—
65C22×Dic22—24no—
66C22×Dic22—44no—
67C22×Dic22C2314yes—
68C11×C4⋊Q8—216no—
69C11×#125—216no—
70C11×C22⋊Q8—28no—
71C11×C22⋊Q8—28no—
72C11×#117—28no—
73C2×C11×C4⋊C4D418yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C42×C11C2314yes—
83C2×C22⋊Dic11C2314yes—
84#66999—48no—
85#66997—48no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11C2314yes—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2318yes—
98C2×Dic11⋊C4C2318yes—
99C2×C4×Dic11C2314yes—
100#66949—232no—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109#36708—111nomaximal, Sylow
110C24×C11C2411yescharacteristic
111C23×D11—22no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—42no—
115C23×D11C2412yes—
116C2×Q8×C11—24no—
117C2×Q8×C11—24no—
118C2×Q8×C11—44no—
119C2×Q8×C11—44no—
120C22×C4×C11—24no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D414yes—
124C22×C4×C11C2×D414yes—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2414yes—
127C22×C4×C11C2414yes—
128C22×C4×C11C2412yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2412yes—
131C22×Dic11—24no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11—42no—
137C22×Dic11C2418yes—
138C22×Dic11C2412yes—
139C22×Dic11C2412yes—
140C22×Dic11C2412yes—
141C2×C4×D11—28no—
142C2×C4×D11—28no—
143C2×C4×D11—44no—
144C2×C4×D11—416no—
145C2×Dic22—28no—
146C2×Dic22—28no—
147C2×Dic22—44no—
148C2×Dic22—416no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—28no—
155C11×C4⋊C4C2×D4116yes—
156C11×C22⋊C4—28no—
157C42×C11—28no—
158C22⋊Dic11—28no—
159(C2×D11)⋊C4—216no—
160(C2×D11)⋊C4—28no—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—48no—
163C4⋊Dic11—44no—
164Dic11⋊C4—216no—
165Dic11⋊C4—28no—
166Dic11⋊C4—28no—
167Dic11⋊C4—48no—
168C4×Dic11—44no—
169C2×#544D1111yescharacteristic, complemented
170C22×C22⋊Q8—111no—
171#2848—112no—
172#2690—118no—
173#2677—118no—
174#2627—112no—
175#2561—112no—
176#2484—112no—
177#2482—112no—
178#2434—112no—
179#2313—111no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11C22×D412yes—
183C23×C112−1+414yes—
184C23×C11C2511yescharacteristic
185C22×D11—28no—
186C22×D11—22no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—22no—
190C22×D11—416no—
191C22×D11—44no—
192C22×D11—44no—
193C22×D112−1+414yes—
194Q8×C11—84no—
195Q8×C11—84no—
196C2×C4×C11—28no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—28no—
203C2×C4×C11—28no—
204C2×C4×C11—44no—
205C2×C4×C11—44no—
206C2×C4×C11C22×D414yes—
207C2×C4×C11C22×D414yes—
208C2×C4×C11C22×D414yes—
209C2×Dic11—28no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—28no—
215C2×Dic11—24no—
216C2×Dic11—28no—
217C2×Dic11—28no—
218C2×Dic11—24no—
219C2×Dic11—44no—
220C2×Dic11—44no—
221C2×Dic11H(5,𝔽2)14yes—
222C4×D11—416no—
223Dic22—416no—
224C23×Q8—111no—
225C24×C4—111no—
226#544—28no—
227C2×C4⋊Q8—114no—
228C2×C4⋊Q8C2×D1114yescomplemented
229C2×#125C2×D1114yescomplemented
230C2×C22⋊Q8—114no—
231C2×C22⋊Q8—118no—
232C2×C22⋊Q8—228no—
233C2×C22⋊Q8C2×D1112yes—
234C2×C22⋊Q8C2×D1112yes—
235C2×#117C2×D1112yes—
236C22×C4⋊C4—111no—
237C22×C4⋊C4—111no—
238C22×C4⋊C4C2×D1111yescharacteristic
239C22×C22⋊C4—111no—
240C22×C22⋊C4—111no—
241#400—114no—
242#400—114no—
243#399—114no—
244#398—118no—
245#398—114no—
246#397—114no—
247#397—114no—
248#395—114no—
249#395—118no—
250#393—114no—
251#391—114no—
252#388—118no—
253#388—118no—
254#387—118no—
255#387—118no—
256#385—118no—
257#385—114no—
258#385—114no—
259#381—112no—
260#381—114no—
261#380—112no—
262#380—114no—
263#379—114no—
264C4×C22⋊C4—112no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—28no—
268C22×C11#53614yes—
269C22×C11C23×D411yescharacteristic
270C22×C11C2×H(5,𝔽2)12yes—
271C22×C11C2×2−1+412yes—
272C22×C11C2×2−1+412yes—
273C2×D11—24no—
274C2×D11—28no—
275C2×D11—416no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—44no—
279C4×C11—24no—
280C4×C11—24no—
281C4×C11—24no—
282C4×C11—44no—
283C4×C11—44no—
284Dic11—24no—
285Dic11—42no—
286Dic11—42no—
287Dic11—48no—
288C25—111no—
289C22×Q8—114no—
290C22×Q8—224no—
291C22×Q8—444no—
292C22×Q8C22×D1112yes—
293C22×Q8C22×D1112yes—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—111no—
297C23×C4—114no—
298C23×C4—224no—
299C23×C4—444no—
300C23×C4C22×D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302C23×C4C22×D1111yescharacteristic
303C4⋊Q8—216no—
304C4⋊Q8—448no—
305#125—216no—
306C22⋊Q8—28no—
307C22⋊Q8—28no—
308C22⋊Q8—2232no—
309C22⋊Q8—448no—
310#117—28no—
311C2×C4⋊C4—114no—
312C2×C4⋊C4—114no—
313C2×C4⋊C4—118no—
314C2×C4⋊C4—114no—
315C2×C4⋊C4—118no—
316C2×C4⋊C4—224no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4C22⋊D1118yes—
319C2×C4⋊C4C22×D1112yes—
320C2×C4⋊C4C22×D1112yes—
321C2×C4⋊C4C22×D1112yes—
322C2×C4⋊C4C22×D1112yes—
323C2×C4⋊C4C22×D1114yes—
324C2×C4⋊C4C22×D1114yes—
325C2×C4⋊C4C22×D1114yes—
326C2×C22⋊C4—114no—
327C2×C22⋊C4—114no—
328C2×C22⋊C4—114no—
329C2×C22⋊C4—118no—
330C2×C22⋊C4—118no—
331C2×C22⋊C4—224no—
332C2×C22⋊C4—224no—
333C2×C22⋊C4C22×D1114yes—
334C2×C42—114no—
335C2×C42C22×D1114yes—
336#95—114no—
337#95—114no—
338#95—118no—
339#95—114no—
340#95—114no—
341#95—118no—
342#95—118no—
343#95—118no—
344C2×C11—24no—
345C2×C11C2×#53611yescharacteristic
346C2×C11#348411yescharacteristic
347C2×C11#348611yescharacteristic
348C2×C11#353814yes—
349D11—44no—
350C24—112no—
351C24—224no—
352C24—222no—
353C24—224no—
354C24—442no—
355C24C23×D1111yescharacteristic
356C2×Q8—24no—
357C2×Q8—24no—
358C2×Q8—44no—
359C2×Q8—44no—
360C2×Q8—228no—
361C2×Q8—228no—
362C2×Q8—444no—
363C2×Q8—4416no—
364C22×C4—24no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—112no—
368C22×C4—118no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—228no—
372C22×C4—224no—
373C22×C4—222no—
374C22×C4—224no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—228no—
378C22×C4—444no—
379C22×C4—4416no—
380C22×C4—442no—
381C22×C4C2×C22⋊D1114yes—
382C22×C4C2×C22⋊D1114yes—
383C22×C4C2×C22⋊D1114yes—
384C22×C4C23×D1114yes—
385C22×C4C23×D1114yes—
386C22×C4C23×D1112yes—
387C22×C4C23×D1112yes—
388C22×C4C23×D1112yes—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—28no—
394C4⋊C4—28no—
395C4⋊C4—2216no—
396C4⋊C4—228no—
397C4⋊C4—228no—
398C4⋊C4—444no—
399C4⋊C4—448no—
400C4⋊C4C2×C22⋊D11116yes—
401C22⋊C4—28no—
402C22⋊C4—2216no—
403C22⋊C4—228no—
404C22⋊C4—228no—
405C22⋊C4—228no—
406C22⋊C4—448no—
407C42—28no—
408C42—444no—
409C11#3670811yescharacteristic, complemented, Sylow
410C23—22no—
411C23—22no—
412C23—114no—
413C23—228no—
414C23—224no—
415C23—224no—
416C23—222no—
417C23—222no—
418C23—4416no—
419C23—444no—
420C23—444no—
421C23#6704014yes—
422C23C22×C22⋊D1112yes—
423C23C24×D1111yescharacteristic
424Q8—84no—
425Q8—84no—
426Q8—4416no—
427C2×C4—28no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—28no—
432C2×C4—28no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—114no—
438C2×C4—228no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—228no—
442C2×C4—224no—
443C2×C4—228no—
444C2×C4—224no—
445C2×C4—228no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—4416no—
449C2×C4—444no—
450C2×C4—444no—
451C2×C4C22×C22⋊D1114yes—
452C2×C4C22×C22⋊D1114yes—
453C2×C4C22×C22⋊D1114yes—
454C22—22no—
455C22—22no—
456C22—28no—
457C22—224no—
458C22—228no—
459C22—4416no—
460C22—442no—
461C22—442no—
462C22—444no—
463C22#1062334714yes—
464C22C2×#6704012yes—
465C22D11×H(5,𝔽2)12yes—
466C22D11×2−1+412yes—
467C22C23×C22⋊D1111yescharacteristic
468C4—24no—
469C4—24no—
470C4—24no—
471C4—44no—
472C4—44no—
473C4—224no—
474C4—442no—
475C4—442no—
476C4—448no—
477C2—24no—
478C2—444no—
479C2C2×#1062334711yescharacteristic
480C2#1308224711yescharacteristic
481C2#1308226411yescharacteristic
482C2#1308285814yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#544C2
prime radicalC24×D11C23
hypercenterC2×#544D11
hypocenterC11#36708
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13075076C2semidirect
4. #13074926C2semidirect
5. #13074431C2semidirect
7. #13072899C2semidirect
9. #13072261C2semidirect
10. #13071219C2semidirect
11. C2×C11×#544C2semidirect
15. C2×C11×C4⋊Q8C22semidirect
16. C2×C11×#125C22semidirect
22. C2×#66997C22semidirect
30. #10622842C22semidirect
40. #10622597C22semidirect
41. #10622595C22semidirect
42. #10622595C22semidirect
43. #10622594C22semidirect
44. #10622593C22semidirect
45. #10622592C22semidirect
46. #10622587C22semidirect
52. #10622546C22semidirect
169. C2×#544D11semidirect
228. C2×C4⋊Q8C2×D11semidirect
229. C2×#125C2×D11semidirect
409. C11#36708semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
#130769002
#130750762
#130749262
#130744312
#130737752
#130728992
#130728862
#130722612
#130712192
C2×C11×#5442
#3670811