Finite Group Databasebeta

← #14737657

Subgroups — #14737657

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622689C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13067962C214yesmaximal, complemented
5#13067955C214yesmaximal, complemented
6#13067371C211yesmaximal, characteristic, complemented
7#13067302C211yesmaximal, characteristic, complemented
8#13067284C211yesmaximal, characteristic, complemented
9C11×#3038C211yesmaximal, characteristic
10C2×C11×AGL(1,ℤ/8)—21no—
11C2×C11×#127C2211yescharacteristic
12C4×C11×#41C2211yescharacteristic
13C22×#4324—22no—
14C2×#66922C2211yescharacteristic
15C11×#460—21no—
16C11×#460C2212yes—
17C11×#459—21no—
18C11×#459C2212yes—
19C11×#423C2211yescharacteristic
20C11×#418—21no—
21#10622845—21no—
22#10622689—21no—
23#10622689—21no—
24#10622689C2214yes—
25Q8×C11⋊C8C2212yescomplemented
26#10622634—21no—
27#10622633C2212yescomplemented
28D4×C11⋊C8—22no—
29D4×C11⋊C8C2212yescomplemented
30#10622621—21no—
31#10622620C2212yescomplemented
32#10622608—21no—
33#10622538—21no—
34#10622538C2211yescharacteristic
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8—21no—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622182C2214yes—
39#10622124C2214yescomplemented
40#10622118C2214yescomplemented
41C2×C11×#41D411yescharacteristic
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×Dic22—21no—
46C11×AGL(1,ℤ/8)—44no—
47C2×C11×SD16—22no—
48C2×C11×D8—22no—
49C2×C11×M16—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127C2312yes—
54C4×Q8×C11D411yescharacteristic
55C4×Q8×C11C2311yescharacteristic
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D411yescharacteristic
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C11×#117D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4324—24no—
65C2×#4324—24no—
66C2×#4324—48no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×#4318—21no—
70C22×C11⋊C8—22no—
71C22×C11⋊C8D412yes—
72#66922—21no—
73#66922—21no—
74#66922—21no—
75#66922C2312yes—
76C11×C4⋊C8—21no—
77C11×C4⋊C8C2312yes—
78C11×#102—22no—
79C11×#102—22no—
80#66899—22no—
81#66896—22no—
82C22⋊(C11⋊C8)—21no—
83C22⋊(C11⋊C8)—22no—
84#66872—22no—
85#66871—22no—
86C4⋊(C11⋊C8)—21no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)C2312yes—
89C4⋊(C11⋊C8)C2312yes—
90C4×C11⋊C8—21no—
91C4×C11⋊C8—22no—
92C4×C11⋊C8D411yescharacteristic
93C4×C11⋊C8D411yescharacteristic
94C4×C11⋊C8C2312yes—
95#19266—111nomaximal, Sylow
96C24×C11—41no—
97C11×#41—22no—
98C11×#41SD1614yescomplemented
99C2×Q8×C11C2×D411yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—44no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—82no—
111C2×D4×C11C2×D411yescharacteristic
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×Dic11—41no—
119C2×Dic22—22no—
120C2×Dic22—44no—
121C2×Dic22—41no—
122C11×SD16—44no—
123C11×D8—44no—
124C11×M16—42no—
125C2×C8×C11—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4C2×D411yescharacteristic
129C11×C4⋊C4C2×D411yescharacteristic
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140#4324—48no—
141#4324—48no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146#4318—42no—
147C2×C11⋊C8—24no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—44no—
151C2×C11⋊C8C2×D412yes—
152C2×C11⋊C8C2×D412yes—
153C2×#492—111no—
154#3079—111no—
155#3038D1111yescharacteristic
156C8×#41—111no—
157#1666—114no—
158#1665—114no—
159#1566—111no—
160#1549—111no—
161#1545—111no—
162C23×C11—21no—
163C23×C11—42no—
164C23×C11—82no—
165C23×C11—82no—
166C23×C11—82no—
167C23×C11#12111yescharacteristic
168Q8×C11—21no—
169Q8×C11C2×SD1612yescomplemented
170D4×C11—24no—
171D4×C11—21no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—44no—
175D4×C11—82no—
176D4×C11—82no—
177D4×C11—82no—
178D4×C11—82no—
179D4×C11C2×SD1612yescomplemented
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11C2×SD1612yes—
192C2×C4×C11#13512yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×Dic11—42no—
197C2×Dic11—82no—
198Dic22—44no—
199Dic22—82no—
200C8×C11—42no—
201C11⋊C8—22no—
202C11⋊C8—42no—
203C11⋊C8—42no—
204C11⋊C8AGL(1,ℤ/8)14yescomplemented
205C2×AGL(1,ℤ/8)—21no—
206C22×SD16—222no—
207C2×C4⋊Q8—111no—
208C2×#127C2×D1111yescharacteristic
209C4×#41C2×D1111yescharacteristic
210#492—114no—
211#492—221no—
212#492—221no—
213#477—221no—
214#476—221no—
215#475—112no—
216#474—112no—
217#460—21no—
218#460C2×D1112yes—
219#459—21no—
220#459C2×D1112yes—
221C8×Q8—112no—
222C8×D4—112no—
223C8×D4—222no—
224#431—111no—
225#431—221no—
226#428—221no—
227#423—111no—
228#423C2×D1111yescharacteristic
229#418—21no—
230#417—221no—
231C2×C4×C8—111no—
232C2×C4×C8—221no—
233#334—114no—
234#332—114no—
235#331—114no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—22no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—164no—
245C22×C11#46512yes—
246C22×C11C2×#12111yescharacteristic
247C4×C11—21no—
248C4×C11—22no—
249C4×C11—21no—
250C4×C11—41no—
251C4×C11—41no—
252C4×C11#46512yes—
253C4×C11#47112yes—
254C4×C11C22×SD1611yescharacteristic
255C4×C11C2×#13511yescharacteristic
256C4×C11C2×AGL(1,ℤ/8)12yes—
257Dic11—82no—
258C2×#41C22⋊D1111yescharacteristic
259C22×Q8—221no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263AGL(1,ℤ/8)—44no—
264C2×SD16—22no—
265C2×SD16—224no—
266C2×SD16—224no—
267C2×SD16—448no—
268C2×D8—22no—
269C2×M16—21no—
270C2×M16—221no—
271C22×C8—112no—
272C22×C8—222no—
273C4⋊Q8—112no—
274C4⋊Q8—221no—
275C4⋊Q8—221no—
276C4⋊Q8—221no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127C22×D1112yes—
281C4×Q8C22⋊D1111yescharacteristic
282C4×Q8C22×D1111yescharacteristic
283C4×D4—21no—
284C4×D4—21no—
285C4×D4C22⋊D1111yescharacteristic
286C4×D4C22×D1111yescharacteristic
287#117—21no—
288#117C22⋊D1111yescharacteristic
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C42—21no—
292C2×C42C22×D1111yescharacteristic
293#107—222no—
294#106—222no—
295C4⋊C8—21no—
296C4⋊C8—112no—
297C4⋊C8—112no—
298C4⋊C8—222no—
299C4⋊C8—221no—
300C4⋊C8C22×D1112yes—
301#103—222no—
302#102—22no—
303#102—22no—
304#102—222no—
305C22⋊C8—222no—
306C22⋊C8—221no—
307C4×C8—111no—
308C4×C8—111no—
309C4×C8—112no—
310C4×C8—222no—
311C4×C8—221no—
312C2×C11—22no—
313C2×C11—42no—
314C2×C11—162no—
315C2×C11#303811yescharacteristic
316C2×C11C2×#46511yescharacteristic
317C2×C11C2×#47111yescharacteristic
318C24—41no—
319#41—22no—
320#41#432414yescomplemented
321C2×Q8—222no—
322C2×Q8—444no—
323C2×Q8—441no—
324C2×Q8C2×C22⋊D1111yescharacteristic
325C2×D4—21no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—44no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—42no—
335C2×D4—82no—
336C2×D4C2×C22⋊D1111yescharacteristic
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—441no—
341C22×C4D4×D1111yescharacteristic
342C22×C4#434111yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344SD16—44no—
345SD16—448no—
346SD16—448no—
347D8—44no—
348M16—42no—
349M16—442no—
350C2×C8—22no—
351C2×C8—112no—
352C2×C8—112no—
353C2×C8—224no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—444no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C4⋊C4C2×C22⋊D1111yescharacteristic
364C4⋊C4C2×C22⋊D1111yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42D4×D1111yescharacteristic
372C42#434111yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C42C23×D1111yescharacteristic
375C11#1926611yescharacteristic, complemented, Sylow
376C23—21no—
377C23—42no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23#6699211yescharacteristic
382Q8—21no—
383Q8—444no—
384Q8—882no—
385Q8C2×#432412yescomplemented
386D4—24no—
387D4—21no—
388D4—44no—
389D4—42no—
390D4—42no—
391D4—82no—
392D4—82no—
393D4—82no—
394D4—82no—
395D4C2×#432412yescomplemented
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—442no—
405C2×C4—882no—
406C2×C4C2×#432412yes—
407C2×C4#6699211yescharacteristic
408C2×C4#6699211yescharacteristic
409C2×C4#6699211yescharacteristic
410C2×C4#6700312yes—
411C2×C4C2×D4×D1111yescharacteristic
412C2×C4C2×#434111yescharacteristic
413C2×C4C22×C22⋊D1111yescharacteristic
414C8—42no—
415C8—114no—
416C8—222no—
417C8—442no—
418C8—442no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—41no—
423C22—41no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—164no—
428C22#1062265412yes—
429C22C2×#6699211yescharacteristic
430C4—21no—
431C4—21no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—882no—
436C4#1062265412yes—
437C4#1062281312yes—
438C4D11×AGL(1,ℤ/8)12yes—
439C4C22×#432411yescharacteristic
440C4C2×#6700311yescharacteristic
441C2—22no—
442C2—42no—
443C2—162no—
444C2#1307809411yescharacteristic
445C2C2×#1062265411yescharacteristic
446C2C2×#1062281311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3038C2
socleC22×C11C2×#121
hypercenter#3038D11
hypocenterC11#19266
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. C2×#10622689C2semidirect
2. #13078431C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13067962C2semidirect
5. #13067955C2semidirect
6. #13067371C2semidirect
7. #13067302C2semidirect
8. #13067284C2semidirect
25. Q8×C11⋊C8C22semidirect
27. #10622633C22semidirect
29. D4×C11⋊C8C22semidirect
31. #10622620C22semidirect
39. #10622124C22semidirect
40. #10622118C22semidirect
98. C11×#41SD16semidirect
169. Q8×C11C2×SD16semidirect
179. D4×C11C2×SD16semidirect
204. C11⋊C8AGL(1,ℤ/8)semidirect
320. #41#4324semidirect
375. C11#19266semidirect
385. Q8C2×#4324semidirect
395. D4C2×#4324semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
#130784312
#41×C11⋊C82
#130679622
#130679552
#130673712
#130673022
#130672842
C11×#30382
#1926611