Finite Group Databasebeta

← #15625322

Subgroups — #15625322

Order 2816.

2034 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081949C211yesmaximal, characteristic
2#13079693C218yesmaximal, complemented
3#13079682C218yesmaximal, complemented
4#13079073C212yesmaximal, complemented
5#13079019C212yesmaximal, complemented
6#13078088C214yesmaximal, complemented
7#13077874C214yesmaximal, complemented
8#13077254C211yesmaximal, characteristic, complemented
9C2×C11×#541C211yesmaximal, characteristic, complemented
10C22×#4339C2212yes—
11C11×#541—24no—
12C11×#541C2218yescomplemented
13C2×C11×C4⋊Q8C2211yescharacteristic, complemented
14C2×C11×#126—22no—
15C2×C11×#125—22no—
16C2×C11×#125C2211yescharacteristic, complemented
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11C2212yescomplemented
19C2×C11×#117C2211yescharacteristic
20C2×#66995C2218yescomplemented
21#10623057C2214yes—
22#10623056C2214yes—
23#10623055—24no—
24#10623041—22no—
25#10623024—22no—
26#10623008C2212yes—
27#10623008C2212yes—
28#10622820C2212yes—
29#10622705C2214yescomplemented
30#10622699C2218yescomplemented
31#10622698C2214yescomplemented
32#10622682C2214yescomplemented
33#10622681C2218yescomplemented
34#10622680C2214yescomplemented
35#10622663C2218yescomplemented
36#10622660C22116yes—
37#10622659C2218yescomplemented
38#10622644C2218yescomplemented
39#10622641C22116yescomplemented
40#10622640C2218yescomplemented
41#10622613C2218yescomplemented
42#10622579C2218yescomplemented
43#10622537C2212yescomplemented
44C4×#4318C2212yescomplemented
45C22×Q8×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—22no—
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—48no—
51C2×#4339C2314yes—
52C2×#4339C2314yes—
53C22×D44C2312yes—
54C22×C4×D11—22no—
55C22×Dic22C2312yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8C2314yes—
58C11×#126—216no—
59C11×#125—216no—
60C11×#125—22no—
61C11×#125C2314yes—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8C2318yes—
64C4×Q8×C11—24no—
65C4×Q8×C11C2318yes—
66C11×#117D414yes—
67C11×#117C2314yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D412yes—
76C2×C42×C11—22no—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×#4326C23116yes—
80#66995—416no—
81C2×#4325C23116yes—
82#66983—24no—
83#66983—24no—
84C2×#4318C2314yes—
85#66950—28no—
86#66948—28no—
87#66939—28no—
88#66935—28no—
89#66928C2314yes—
90#66928C2314yes—
91#66927C2312yes—
92#66927C2312yes—
93C4×D44—24no—
94C4×D44—24no—
95#66922C2312yes—
96#66922C2312yes—
97C22⋊(C11⋊C8)C2318yes—
98#66874C23116yes—
99#66873C23116yes—
100C4⋊(C11⋊C8)C2318yes—
101#66867C2314yes—
102C4×C11⋊C8C2314yes—
103#60809—111nomaximal, Sylow
104C24×C11C2×D411yescharacteristic
105C23×D11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—28no—
108C2×Q8×C11C2414yes—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2412yes—
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—24no—
119C2×C22⋊D11—24no—
120C2×C22⋊D11—48no—
121C22×Dic11—22no—
122#4339—216no—
123#4339—48no—
124#4339—48no—
125#4339—48no—
126C2×D44—22no—
127C2×D44—24no—
128C2×D44—24no—
129C2×D44—44no—
130C2×D44C2414yes—
131C2×C4×D11—24no—
132C2×C4×D11—24no—
133C2×C4×D11—48no—
134C2×Dic22—22no—
135C2×Dic22—44no—
136C2×Dic22C2414yes—
137C11×C4⋊C4—28no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C2×D418yes—
143C11×C4⋊C4C2414yes—
144C11×C22⋊C4—28no—
145C11×C22⋊C4C2×D418yes—
146C42×C11—28no—
147C42×C11C2×D412yes—
148C42×C11C2×D412yes—
149C42×C11C2412yes—
150C42×C11C2412yes—
151#4326—416no—
152#4325—416no—
153(C2×D11)⋊C4—28no—
154(C2×D11)⋊C4—28no—
155C4⋊Dic11—24no—
156C4⋊Dic11—24no—
157#4318—28no—
158C2×C11⋊C8C2418yes—
159C2×#541D1111yescharacteristic, complemented
160#3449—111no—
161#3223—118no—
162#3222—118no—
163#3152—112no—
164#3142—112no—
165#3037—114no—
166#3007—114no—
167#2921—111no—
168C23×C11—22no—
169C23×C11—42no—
170C23×C11C22×D412yes—
171C23×C11C22×D411yescharacteristic
172C22×D11—24no—
173C22×D11—44no—
174C22×D11—84no—
175Q8×C11—28no—
176Q8×C11—44no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—44no—
185C2×C4×C11—44no—
186C2×C4×C11C22×D414yes—
187C2×C4×C11C22×D414yes—
188C2×C4×C11C22×D412yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11H(5,𝔽2)14yes—
191C2×C4×C11C2511yescharacteristic
192C22⋊D11—48no—
193C22⋊D11—48no—
194C2×Dic11—24no—
195C2×Dic11—44no—
196D44—28no—
197D44—44no—
198D44—84no—
199D44—84no—
200C4×D11—48no—
201C4×D11—48no—
202Dic22—28no—
203Dic22—44no—
204C11⋊C8—28no—
205C22×#41—112no—
206C2×#137—118no—
207#541—24no—
208#541C2×D1118yescomplemented
209#537—222no—
210#536—114no—
211#535—114no—
212#534—222no—
213#532—112no—
214#532—112no—
215C2×C4⋊Q8C2×D1111yescharacteristic, complemented
216C2×#126—22no—
217C2×#125—22no—
218C2×#125C2×D1111yescharacteristic, complemented
219#525—224no—
220C2×C22⋊Q8C2×D1112yes—
221C2×C4×Q8C2×D1112yescomplemented
222C2×#117C2×D1111yescharacteristic
223#497—118no—
224#494—114no—
225#492—114no—
226#491—114no—
227#490—114no—
228#488—118no—
229#464—1116no—
230#462—118no—
231#460—118no—
232#452—1116no—
233#451—118no—
234#450—118no—
235#433—118no—
236#423—112no—
237#417—118no—
238#407—112no—
239C4×M16—112no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—22no—
243C22×C11—82no—
244C22×C11#53512yes—
245C22×C11C23×D411yescharacteristic
246C2×D11—48no—
247C2×D11—44no—
248C2×D11—88no—
249C4×C11—24no—
250C4×C11—24no—
251C4×C11—22no—
252C4×C11—44no—
253C4×C11—44no—
254C4×C11#53512yes—
255C4×C11C2×H(5,𝔽2)12yes—
256Dic11—44no—
257C2×#41—114no—
258C2×#41—114no—
259C2×#41—222no—
260C2×#41—222no—
261C2×#41—448no—
262C22×Q8—112no—
263C22×Q8C22×D1112yes—
264C22×D4—112no—
265C22×D4—222no—
266C23×C4—222no—
267C23×C4C22×D1111yescharacteristic
268#137—4416no—
269C2×Q16—1116no—
270C2×SD16—1116no—
271C2×M16—114no—
272C4⋊Q8—22no—
273C4⋊Q8—112no—
274C4⋊Q8—112no—
275C4⋊Q8C22×D1114yes—
276#127—112no—
277#127—112no—
278#126—216no—
279#125—216no—
280#125—22no—
281#125C22×D1114yes—
282#124—114no—
283#124—114no—
284#123—228no—
285C22⋊Q8—24no—
286C22⋊Q8—228no—
287C22⋊Q8C22×D1118yes—
288#121—224no—
289#121—224no—
290#121—228no—
291#120—228no—
292C4×Q8—24no—
293C4×Q8C22×D1118yes—
294C4×D4—224no—
295C4×D4—224no—
296#117C22⋊D1114yes—
297#117C22×D1114yes—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4C22⋊D1112yes—
303C2×C4⋊C4C22×D1112yes—
304C2×C22⋊C4—22no—
305C2×C22⋊C4C22⋊D1112yes—
306C2×C42—22no—
307C2×C42C22×D1111yescharacteristic
308C2×C42C22×D1111yescharacteristic
309C4⋊C8—118no—
310#103—1116no—
311#102—1116no—
312C22⋊C8—118no—
313#97—114no—
314C4×C8—114no—
315C2×C11—22no—
316C2×C11—42no—
317C2×C11C2×#53511yescharacteristic
318C2×C11#358612yes—
319D11—84no—
320C24—222no—
321C24C2×C22⋊D1111yescharacteristic
322#41—2216no—
323#41—448no—
324#41—448no—
325#41—448no—
326C2×Q8—22no—
327C2×Q8—28no—
328C2×Q8—114no—
329C2×Q8—222no—
330C2×Q8—444no—
331C2×Q8C23×D1114yes—
332C2×D4—114no—
333C2×D4—224no—
334C2×D4—224no—
335C2×D4—222no—
336C2×D4—224no—
337C2×D4—224no—
338C2×D4—444no—
339C2×D4—448no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—222no—
344C22×C4—224no—
345C22×C4—224no—
346C22×C4—448no—
347C22×C4C2×C22⋊D1111yescharacteristic
348C22×C4C2×C22⋊D1112yes—
349C22×C4C2×C22⋊D1112yes—
350C22×C4C2×C22⋊D1112yes—
351C22×C4C23×D1112yes—
352C22×C4C23×D1111yescharacteristic
353Q16—4416no—
354SD16—4416no—
355M16—228no—
356C2×C8—118no—
357C4⋊C4—28no—
358C4⋊C4—28no—
359C4⋊C4—28no—
360C4⋊C4—28no—
361C4⋊C4—22no—
362C4⋊C4—224no—
363C4⋊C4—224no—
364C4⋊C4C2×C22⋊D1118yes—
365C4⋊C4C23×D1114yes—
366C22⋊C4—28no—
367C22⋊C4—228no—
368C22⋊C4—228no—
369C22⋊C4C2×C22⋊D1118yes—
370C42—28no—
371C42C2×C22⋊D1112yes—
372C42C2×C22⋊D1112yes—
373C42C23×D1112yes—
374C42C23×D1112yes—
375C11#6080911yescharacteristic, complemented, Sylow
376C23—22no—
377C23—42no—
378C23—224no—
379C23—444no—
380C23—884no—
381C23C22×C22⋊D1112yes—
382C23C22×C22⋊D1111yescharacteristic
383Q8—28no—
384Q8—44no—
385Q8—228no—
386Q8—444no—
387D4—228no—
388D4—444no—
389D4—448no—
390D4—448no—
391D4—884no—
392D4—884no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—224no—
403C2×C4—448no—
404C2×C4—444no—
405C2×C4—448no—
406C2×C4#6704214yes—
407C2×C4C22×C22⋊D1114yes—
408C2×C4C22×C22⋊D1114yes—
409C2×C4C22×C22⋊D1112yes—
410C2×C4C22×C22⋊D1111yescharacteristic
411C2×C4C24×D1111yescharacteristic
412C8—228no—
413C22—22no—
414C22—24no—
415C22—22no—
416C22—82no—
417C22—448no—
418C22—444no—
419C22—888no—
420C22#1062336112yes—
421C22C23×C22⋊D1111yescharacteristic
422C4—24no—
423C4—24no—
424C4—22no—
425C4—44no—
426C4—44no—
427C4—444no—
428C4#1062336112yes—
429C4C2×#6704212yes—
430C2—22no—
431C2—42no—
432C2—884no—
433C2C2×#1062336111yescharacteristic
434C2#1308340312yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#541C2
socleC22×C11C23×D4
prime radical#13081949C2
hypercenterC2×#541D11
hypocenterC11#60809
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #13079693C2semidirect
3. #13079682C2semidirect
4. #13079073C2semidirect
5. #13079019C2semidirect
6. #13078088C2semidirect
7. #13077874C2semidirect
8. #13077254C2semidirect
9. C2×C11×#541C2semidirect
12. C11×#541C22semidirect
13. C2×C11×C4⋊Q8C22semidirect
16. C2×C11×#125C22semidirect
18. C2×C4×Q8×C11C22semidirect
20. C2×#66995C22semidirect
29. #10622705C22semidirect
30. #10622699C22semidirect
31. #10622698C22semidirect
32. #10622682C22semidirect
33. #10622681C22semidirect
34. #10622680C22semidirect
35. #10622663C22semidirect
37. #10622659C22semidirect
38. #10622644C22semidirect
39. #10622641C22semidirect
40. #10622640C22semidirect
41. #10622613C22semidirect
42. #10622579C22semidirect
43. #10622537C22semidirect
44. C4×#4318C22semidirect
159. C2×#541D11semidirect
208. #541C2×D11semidirect
215. C2×C4⋊Q8C2×D11semidirect
218. C2×#125C2×D11semidirect
221. C2×C4×Q8C2×D11semidirect
375. C11#60809semidirect

Maximal subgroups

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

subgroupindex
#130819492
#130796932
#130796822
#130790732
#130790192
#130780882
#130778742
#130772542
C2×C11×#5412
#6080911