Finite Group Databasebeta

← #14737659

Subgroups — #14737659

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×#10622306C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic
4#13067964C214yesmaximal, complemented
5#13067957C214yesmaximal, complemented
6#13067372C211yesmaximal, characteristic, complemented
7#13067300C211yesmaximal, characteristic, complemented
8#13067283C211yesmaximal, characteristic, complemented
9C8×C11×#41C211yesmaximal, characteristic, complemented
10C4×C11×#41C2211yescharacteristic
11C2×#67002—21no—
12C22×#4314—22no—
13C2×#66927C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C8×Q8×C11C2212yescomplemented
16C8×D4×C11—22no—
17C8×D4×C11C2212yescomplemented
18C11×#431—21no—
19C11×#431C2211yescharacteristic
20C2×C4×C8×C11—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622845—21no—
23#10622640—21no—
24#10622640C2212yes—
25#10622634—21no—
26#10622633C2212yescomplemented
27#10622628—21no—
28#10622628C2212yes—
29#10622621—21no—
30#10622620C2212yescomplemented
31#10622614—21no—
32#10622608—21no—
33#10622537C2211yescharacteristic
34#10622537C2211yescharacteristic
35#10622306—21no—
36#10622306—21no—
37#10622306C2214yes—
38#10622123C2214yes—
39#10622120C2214yescomplemented
40#10622095C2214yescomplemented
41C2×C11×#41D411yescharacteristic
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×Dic22—21no—
46C22×C8×C11—22no—
47C22×C8×C11D412yes—
48C4×Q8×C11D411yescharacteristic
49C4×Q8×C11C2311yescharacteristic
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11D411yescharacteristic
53C4×D4×C11C2311yescharacteristic
54C11×#117—21no—
55C11×#117D411yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58#67002—44no—
59C2×#4325—22no—
60C2×#4323—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×#4318—21no—
64C2×#4318—21no—
65C2×#4314—24no—
66C2×#4314—24no—
67C2×#4314—48no—
68#66927—21no—
69#66927—21no—
70#66927—21no—
71#66927C2312yes—
72#66922—21no—
73#66922—21no—
74#66922—21no—
75#66922C2312yes—
76C11×C4⋊C8—22no—
77C11×C4⋊C8C2312yes—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—22no—
80C4×C8×C11—22no—
81C4×C8×C11—21no—
82C4×C8×C11D411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11C2312yes—
85#66899—22no—
86#66896—22no—
87#66873—22no—
88#66873—22no—
89#66872—22no—
90#66871—22no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)—21no—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95#19266—111nomaximal, Sylow
96C23×D11—41no—
97C11×#41—22no—
98C11×#41SD1614yescomplemented
99C2×Q8×C11C2×D411yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11C2×D411yescharacteristic
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×Dic11—41no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—44no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—41no—
116C2×D44—42no—
117C2×D44—42no—
118C2×D44—82no—
119C2×Dic22—22no—
120C2×Dic22—44no—
121C2×Dic22—41no—
122C2×C8×C11—24no—
123C2×C8×C11—22no—
124C2×C8×C11—44no—
125C2×C8×C11C2×D412yes—
126C2×C8×C11C2×D412yes—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4C2×D411yescharacteristic
130C11×C4⋊C4C2×D411yescharacteristic
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C11×C22⋊C4—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11—21no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140C42×C11C2411yescharacteristic
141#4325—44no—
142#4323—44no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147#4318—42no—
148#4318—42no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151#4314—48no—
152#4314—48no—
153C2×#492—111no—
154#3079—111no—
155#3038—111no—
156C8×#41D1111yescharacteristic, complemented
157#1666—114no—
158#1665—114no—
159#1566—111no—
160#1549—111no—
161#1545—111no—
162C23×C11—21no—
163C23×C11#12111yescharacteristic
164C22×D11—42no—
165C22×D11—82no—
166C22×D11—82no—
167C22×D11—82no—
168Q8×C11—21no—
169Q8×C11C2×SD1612yescomplemented
170D4×C11—24no—
171D4×C11—21no—
172D4×C11C2×SD1612yescomplemented
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11C2×SD1612yes—
185C2×C4×C11#13512yes—
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×Dic11—42no—
190C2×Dic11—82no—
191D44—42no—
192D44—42no—
193D44—44no—
194D44—82no—
195D44—82no—
196D44—82no—
197D44—82no—
198Dic22—44no—
199Dic22—82no—
200C8×C11—22no—
201C8×C11—42no—
202C8×C11AGL(1,ℤ/8)14yescomplemented
203C11⋊C8—42no—
204C11⋊C8—42no—
205C2×AGL(1,ℤ/8)—221no—
206C22×SD16—222no—
207C2×C4⋊Q8—111no—
208C2×#127—111no—
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—112no—
218#460—221no—
219#459—112no—
220#459—221no—
221C8×Q8C2×D1112yescomplemented
222C8×D4—22no—
223C8×D4C2×D1112yescomplemented
224#431—21no—
225#431C2×D1111yescharacteristic
226#428—221no—
227#423—111no—
228#423—111no—
229#418—221no—
230#417—221no—
231C2×C4×C8—21no—
232C2×C4×C8C2×D1111yescharacteristic
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#46512yes—
242C22×C11C2×#12111yescharacteristic
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—82no—
246C2×D11—164no—
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×#41D4411yescharacteristic
259C22×Q8—221no—
260C22×D4—221no—
261C22×D4—221no—
262C22×D4—221no—
263AGL(1,ℤ/8)—444no—
264C2×SD16—222no—
265C2×SD16—224no—
266C2×SD16—224no—
267C2×SD16—448no—
268C2×D8—222no—
269C2×M16—221no—
270C2×M16—221no—
271C22×C8—22no—
272C22×C8C22⋊D1112yes—
273C4⋊Q8—112no—
274C4⋊Q8—221no—
275C4⋊Q8—221no—
276C4⋊Q8—221no—
277#127—112no—
278#127—221no—
279#127—221no—
280#127—221no—
281C4×Q8D4411yescharacteristic
282C4×Q8C22×D1111yescharacteristic
283C4×D4—21no—
284C4×D4—21no—
285C4×D4D4411yescharacteristic
286C4×D4C22×D1111yescharacteristic
287#117—21no—
288#117D4411yescharacteristic
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C42—21no—
292C2×C42C22×D1111yescharacteristic
293#107—222no—
294#106—222no—
295C4⋊C8—22no—
296C4⋊C8—112no—
297C4⋊C8—112no—
298C4⋊C8—221no—
299C4⋊C8—221no—
300C4⋊C8C22×D1112yes—
301#103—222no—
302#102—222no—
303#102—222no—
304#102—222no—
305C22⋊C8—21no—
306C22⋊C8—22no—
307C4×C8—22no—
308C4×C8—21no—
309C4×C8C22⋊D1111yescharacteristic
310C4×C8C22⋊D1111yescharacteristic
311C4×C8C22×D1112yes—
312C2×C11—22no—
313C2×C11—42no—
314C2×C11#303811yescharacteristic
315C2×C11C2×#46511yescharacteristic
316C2×C11C2×#47111yescharacteristic
317D11—162no—
318C24—441no—
319#41—22no—
320#41#431414yescomplemented
321C2×Q8—222no—
322C2×Q8—444no—
323C2×Q8—441no—
324C2×Q8C2×D4411yescharacteristic
325C2×D4—21no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—444no—
330C2×D4—442no—
331C2×D4—442no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—441no—
335C2×D4—882no—
336C2×D4C2×D4411yescharacteristic
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—441no—
341C22×C4C2×D4411yescharacteristic
342C22×C4#433911yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344SD16—448no—
345SD16—444no—
346SD16—448no—
347D8—444no—
348M16—442no—
349M16—442no—
350C2×C8—24no—
351C2×C8—22no—
352C2×C8—44no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8C2×C22⋊D1112yes—
356C2×C8C2×C22⋊D1112yes—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C4⋊C4C2×D4411yescharacteristic
364C4⋊C4C2×D4411yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42C2×D4411yescharacteristic
372C42#433911yescharacteristic
373C42C2×C22⋊D1111yescharacteristic
374C42C23×D1111yescharacteristic
375C11#1926611yescharacteristic, complemented, Sylow
376C23—21no—
377C23—442no—
378C23—882no—
379C23—882no—
380C23—882no—
381C23#6698311yescharacteristic
382Q8—21no—
383Q8—444no—
384Q8—882no—
385Q8C2×#431412yescomplemented
386D4—24no—
387D4—21no—
388D4—442no—
389D4—442no—
390D4—444no—
391D4—882no—
392D4—882no—
393D4—882no—
394D4—882no—
395D4C2×#431412yescomplemented
396C2×C4—21no—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—442no—
405C2×C4—882no—
406C2×C4C2×#431412yes—
407C2×C4#6695712yes—
408C2×C4#6698311yescharacteristic
409C2×C4#6698311yescharacteristic
410C2×C4#6698311yescharacteristic
411C2×C4C22×D4411yescharacteristic
412C2×C4C2×#433911yescharacteristic
413C2×C4C22×C22⋊D1111yescharacteristic
414C8—22no—
415C8—42no—
416C8—442no—
417C8—442no—
418C8#6700214yescomplemented
419C22—21no—
420C22—21no—
421C22—22no—
422C22—41no—
423C22—41no—
424C22—882no—
425C22—882no—
426C22—882no—
427C22—1764no—
428C22#1062272712yes—
429C22C2×#6698311yescharacteristic
430C4—21no—
431C4—21no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—882no—
436C4#1062272712yes—
437C4#1062275412yes—
438C4C22×#431411yescharacteristic
439C4C2×#6695711yescharacteristic
440C4C2×#6700212yes—
441C2—22no—
442C2—42no—
443C2—1762no—
444C2#1307809611yescharacteristic
445C2C2×#1062272711yescharacteristic
446C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C2×#121
prime radical#13078096C2
hypercenterC8×#41D11
hypocenterC11#19266
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10622306C2semidirect
2. #13078431C2semidirect
4. #13067964C2semidirect
5. #13067957C2semidirect
6. #13067372C2semidirect
7. #13067300C2semidirect
8. #13067283C2semidirect
9. C8×C11×#41C2semidirect
15. C8×Q8×C11C22semidirect
17. C8×D4×C11C22semidirect
26. #10622633C22semidirect
30. #10622620C22semidirect
39. #10622120C22semidirect
40. #10622095C22semidirect
98. C11×#41SD16semidirect
156. C8×#41D11semidirect
169. Q8×C11C2×SD16semidirect
172. D4×C11C2×SD16semidirect
202. C8×C11AGL(1,ℤ/8)semidirect
221. C8×Q8C2×D11semidirect
223. C8×D4C2×D11semidirect
320. #41#4314semidirect
375. C11#19266semidirect
385. Q8C2×#4314semidirect
395. D4C2×#4314semidirect
418. C8#67002semidirect

Maximal subgroups

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

subgroupindex
C2×#106223062
#130784312
#130780962
#130679642
#130679572
#130673722
#130673002
#130672832
C8×C11×#412
#1926611