Finite Group Databasebeta

← #14810408

Subgroups — #14810408

Order 2816.

1104 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic, complemented
2C2×#10622669C211yesmaximal, characteristic, complemented
3#13076912C211yesmaximal, characteristic
4#13069755C212yesmaximal, complemented
5#13069750C212yesmaximal, complemented
6#13069582C211yesmaximal, characteristic, complemented
7#13069581C211yesmaximal, characteristic, complemented
8#13068935C212yesmaximal
9#13068925C212yesmaximal, complemented
10C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
11C2×C11×#488C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C2×C11×#124C2211yescharacteristic
14C2×#66999C2211yescharacteristic
15C2×#66991C2211yescharacteristic
16#10623219—24no—
17#10623219—24no—
18C2×#66949—22no—
19C2×#66945C2212yes—
20C2×#66941C2212yes—
21C2×#66940—22no—
22C2×C42×D11C2211yescharacteristic
23C2×#66923C2211yescharacteristic
24C11×#488—24no—
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2212yes—
30#10622834C2211yescharacteristic
31C2×#66896C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33#10622669—24no—
34#10622569—22no—
35#10622557—22no—
36#10622549C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C22×C22⋊D11—21no—
46C22×C4×D11D412yes—
47C22×C4×D11C2311yescharacteristic
48C22×Dic22—22no—
49C22×C8×C11C2312yes—
50C11×#125—22no—
51C11×#125D414yescomplemented
52C11×#124—22no—
53C11×#124—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—22no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—22no—
60#66999—24no—
61#66991—24no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11D412yes—
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74#66949—216no—
75#66945—24no—
76#66945—24no—
77#66941—24no—
78#66941—24no—
79#66940—216no—
80C42×D11—22no—
81C42×D11—22no—
82#66923—22no—
83#66923D414yescomplemented
84C11×#103—24no—
85C11×#102—24no—
86C4×C8×C11—22no—
87#66899—24no—
88#66896—24no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91(C2×D11)⋊C8—24no—
92C4×C11⋊C8—22no—
93#25906—111nomaximal, Sylow
94C24×C11—21no—
95C23×D11C2×D411yescharacteristic
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2411yescharacteristic
108C2×C22⋊D11—44no—
109C2×C22⋊D11—42no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11C2×D411yescharacteristic
114C22×Dic11C2×D412yes—
115C2×C4×D11—24no—
116C2×C4×D11—24no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—22no—
120C2×C4×D11—42no—
121C2×C4×D11#4114yes—
122C2×Dic22—28no—
123C2×Dic22—44no—
124C2×Dic22—44no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C11×C4⋊C4—28no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4C2×D414yes—
131C11×C22⋊C4—44no—
132C42×C11C2×D412yes—
133C42×C11C2×D412yes—
134C22⋊Dic11—42no—
135C22⋊Dic11—44no—
136(C2×D11)⋊C4—28no—
137(C2×D11)⋊C4—42no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11C2×D414yes—
142Dic11⋊C4—28no—
143Dic11⋊C4—28no—
144Dic11⋊C4—42no—
145C4×Dic11—28no—
146C4×Dic11—24no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×#533—111no—
153C2×#488—111no—
154C2×#488D1111yescharacteristic, complemented
155#2850—111no—
156#2024—112no—
157#2023—112no—
158#1991—111no—
159#1991—111no—
160#1875—112no—
161#1873—112no—
162C4×C22⋊C8—111no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11C22×D411yescharacteristic
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11#12412yes—
174Q8×C11—42no—
175Q8×C11—42no—
176D4×C11—42no—
177D4×C11—42no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11#12014yes—
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C2×#4112yes—
190C2×C4×C112−1+412yes—
191C22⋊D11—84no—
192C2×Dic11—21no—
193C2×Dic11—22no—
194C2×Dic11—21no—
195C2×Dic11—22no—
196C2×Dic11—24no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11#12412yes—
204C2×Dic11#13514yes—
205C4×D11—24no—
206C4×D11—24no—
207C4×D11—48no—
208Dic22—416no—
209C8×C11—42no—
210C11⋊C8—42no—
211#533—224no—
212#533—224no—
213C2×C4⋊Q8—112no—
214C2×#125—111no—
215C2×#125C2×D1111yescharacteristic
216C2×#124C2×D1111yescharacteristic
217C2×C22⋊Q8—111no—
218C2×C22⋊Q8—222no—
219C2×#121—111no—
220C2×C4×Q8—222no—
221C2×#117—112no—
222C22×C42—111no—
223#488—24no—
224#488—224no—
225C2×#103—112no—
226C2×#103C2×D1112yes—
227C2×#102—112no—
228C2×#102C2×D1112yes—
229C2×C22⋊C8—112no—
230C2×C4×C8—111no—
231C2×C4×C8C2×D1111yescharacteristic
232#391—111no—
233#390—111no—
234#388—222no—
235#386—222no—
236#382—111no—
237#340—112no—
238#340—112no—
239#340—112no—
240#340—112no—
241#336—112no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11C2×#12011yescharacteristic
248C22×C11C2×#12411yescharacteristic
249C22×C11#53611yescharacteristic
250C22×C11C2×#13512yes—
251C22×C11#57512yes—
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—42no—
256C2×D11—42no—
257C4×C11—24no—
258C4×C11—44no—
259C4×C11—81no—
260C4×C11#54812yes—
261C4×C11#54812yes—
262Dic11—22no—
263Dic11—24no—
264Dic11—44no—
265Dic11—81no—
266Dic11—81no—
267C22×Q8—222no—
268C22×Q8C22×D1111yescharacteristic
269C22×D4—221no—
270C22×D4C22×D1111yescharacteristic
271C23×C4—111no—
272C23×C4—112no—
273C22×C8—112no—
274C22×C8C22×D1112yes—
275C4⋊Q8—224no—
276C4⋊Q8—224no—
277#125—22no—
278#125—114no—
279#125—222no—
280#125C22⋊D1114yescomplemented
281#124—22no—
282#124—22no—
283C22⋊Q8—2216no—
284C22⋊Q8—224no—
285#121—224no—
286C4×Q8—2216no—
287#117—224no—
288#117—224no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4C22×D1112yes—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C42—112no—
303C2×C42—111no—
304C2×C42—222no—
305C2×C42—222no—
306C2×C42—222no—
307C2×C42C22×D1111yescharacteristic
308#103—24no—
309#103—224no—
310#102—24no—
311#102—224no—
312C22⋊C8—224no—
313C4×C8—22no—
314C4×C8—222no—
315#95—222no—
316#95—222no—
317C2×C11—161no—
318C2×C11#243611yescharacteristic
319C2×C11#300212yes—
320C2×C11#313111yescharacteristic
321C2×C11#314011yescharacteristic
322C2×C11#323312yes—
323D11—42no—
324C24—21no—
325C24—111no—
326C2×Q8—21no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8—21no—
330C2×Q8—228no—
331C2×Q8—444no—
332C2×Q8—444no—
333C2×D4—21no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—21no—
337C2×D4—442no—
338C2×D4—444no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—112no—
342C22×C4—111no—
343C22×C4—114no—
344C22×C4—224no—
345C22×C4—221no—
346C22×C4—222no—
347C22×C4—221no—
348C22×C4—222no—
349C22×C4—224no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—442no—
353C22×C4D4×D1112yes—
354C22×C4C23×D1111yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C4⋊C4—28no—
362C4⋊C4—22no—
363C4⋊C4—114no—
364C4⋊C4—228no—
365C4⋊C4—228no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—442no—
370C4⋊C4C2×C22⋊D1114yes—
371C22⋊C4—44no—
372C22⋊C4—228no—
373C22⋊C4—442no—
374C22⋊C4—442no—
375C22⋊C4—444no—
376C42—228no—
377C42—224no—
378C42—221no—
379C42—221no—
380C42D4×D1112yes—
381C42C2×C22⋊D1112yes—
382C11#2590611yescharacteristic, complemented, Sylow
383C23—42no—
384C23—42no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—112no—
389C23—222no—
390C23—222no—
391C23—221no—
392C23—221no—
393C23C2×D4×D1111yescharacteristic
394Q8—42no—
395Q8—42no—
396Q8—4416no—
397D4—42no—
398D4—42no—
399D4—884no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—114no—
409C2×C4—112no—
410C2×C4—222no—
411C2×C4—221no—
412C2×C4—222no—
413C2×C4—221no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—224no—
417C2×C4—448no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4#6699014yes—
425C2×C4C2×D4×D1111yescharacteristic
426C2×C4#41×D1112yes—
427C2×C4#6704312yes—
428C2×C4C22×C22⋊D1111yescharacteristic
429C8—42no—
430C8—442no—
431C22—82no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—82no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22—442no—
440C22—442no—
441C22D11×#12411yescharacteristic
442C22#1062320611yescharacteristic
443C22D11×#13512yes—
444C22#1062329912yes—
445C22C2×#6699011yescharacteristic
446C4—24no—
447C4—44no—
448C4—81no—
449C4—224no—
450C4—222no—
451C4—444no—
452C4—881no—
453C4—881no—
454C4#1062320812yes—
455C4#1062336212yes—
456C2—161no—
457C2—442no—
458C2#1307227111yescharacteristic
459C2#1307783012yes—
460C2#1307893711yescharacteristic
461C2#1307899911yescharacteristic
462C2#1307979012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#488C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#488D11
hypocenterC11#25906
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#10623219C2semidirect
2. C2×#10622669C2semidirect
4. #13069755C2semidirect
5. #13069750C2semidirect
6. #13069582C2semidirect
7. #13069581C2semidirect
9. #13068925C2semidirect
10. C4×(C2×D11)⋊C8C2semidirect
11. C2×C11×#488C2semidirect
51. C11×#125D4semidirect
83. #66923D4semidirect
154. C2×#488D11semidirect
280. #125C22⋊D11semidirect
382. C11#25906semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106226692
#130769122
#130697552
#130697502
#130695822
#130695812
#130689352
#130689252
C4×(C2×D11)⋊C82
C2×C11×#4882
#2590611