Finite Group Databasebeta

← #15618647

Subgroups — #15618647

Order 2816.

2090 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
1#13081949C211yesmaximal, characteristic
2#13077677C214yesmaximal, complemented
3#13077671C214yesmaximal, complemented
4#13077662C218yesmaximal, complemented
5#13077359C214yesmaximal, complemented
6#13077335C212yesmaximal, complemented
7#13077329C212yesmaximal, complemented
8#13077254C211yesmaximal, characteristic, complemented
9#13077062C214yesmaximal, complemented
10C2×C11×#433C211yesmaximal, characteristic, complemented
11C22×#4339C2212yes—
12C2×C11×#117C2211yescharacteristic
13C2×#66954C2214yescomplemented
14C2×#66954C2214yescomplemented
15#10623057C414yes—
16#10623056C414yes—
17#10623055C2214yes—
18#10623055C2214yes—
19#10623041C414yes—
20#10623024C414yes—
21#10623008C2212yes—
22#10623008C2212yes—
23C11×#433C2214yescomplemented
24C11×#433C2212yescomplemented
25C11×#433C2212yescomplemented
26C2×C11×C4⋊C8C2212yescomplemented
27C2×C11×C22⋊C8C2212yes—
28C2×C11×#97C2211yescharacteristic, complemented
29C2×C4×C8×C11C2211yescharacteristic, complemented
30#10622820C2212yes—
31#10622723C2214yescomplemented
32#10622723C2214yescomplemented
33#10622613C2214yescomplemented
34#10622613C2214yescomplemented
35#10622537C2212yescomplemented
36C4×#4318C2212yescomplemented
37#10622451C2218yescomplemented
38#10622449C2218yescomplemented
39#10622449C2218yescomplemented
40#10622447C2218yescomplemented
41#10622340C2218yes—
42#10622340C2218yes—
43#10622339C2218yescomplemented
44D11×C22⋊C8C2218yescomplemented
45#10622319C2218yescomplemented
46#10622319C2218yescomplemented
47#10622301C2214yescomplemented
48#10622301C2214yescomplemented
49C8×D44C2214yescomplemented
50C8×D44C2214yescomplemented
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11C2×C414yes—
53C2×#4339—48no—
54C2×#4339C2×C414yes—
55C2×#4339C2×C414yes—
56C2×#4339C2314yes—
57C2×#4339C2314yes—
58C22×D44C2×C412yes—
59C22×C4×D11C2314yes—
60C22×Dic22C2×C412yes—
61C22×C8×C11C2312yes—
62C22×C8×C11C2312yes—
63C11×#117C2×C414yes—
64C11×#117C2312yes—
65C11×#117C2312yes—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2×C412yes—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70#66983C2×C414yes—
71#66983C2×C414yes—
72#66983C2×C418yes—
73C2×#4318C2314yes—
74#66954—48no—
75#66954—48no—
76C2×#4313C2318yes—
77C2×#4313C2318yes—
78C2×C8×D11C2318yes—
79C2×C8×D11C2318yes—
80#66950C2×C418yes—
81#66950C2×C418yes—
82#66948C2×C418yes—
83#66948C2×C418yes—
84#66939C2×C418yes—
85#66939C2×C418yes—
86#66935C2×C418yes—
87#66935C2×C418yes—
88#66928C2×C414yes—
89#66928C2×C414yes—
90#66927C2×C412yes—
91#66927C2×C412yes—
92C4×D44C2314yes—
93C4×D44C2314yes—
94C4×D44C2318yes—
95#66922C2×C412yes—
96#66922C2×C412yes—
97C11×C4⋊C8C2314yes—
98C11×C4⋊C8C2314yes—
99C11×C22⋊C8C2314yes—
100C11×C22⋊C8C2314yes—
101C11×#97C2312yes—
102C11×#97C2312yes—
103C4×C8×C11C2311yescharacteristic
104C4×C8×C11C2312yes—
105C4×C8×C11C2311yescharacteristic
106C22⋊(C11⋊C8)C2318yes—
107(C2×D11)⋊C8C2318yes—
108(C2×D11)⋊C8C2318yes—
109(C2×D11)⋊C8C2318yes—
110(C2×D11)⋊C8C2318yes—
111C4⋊(C11⋊C8)C2314yes—
112C4⋊(C11⋊C8)C2314yes—
113#66867C2314yes—
114C4×C11⋊C8C2314yes—
115#60238—111nomaximal, Sylow
116C24×C11C22×C411yescharacteristic
117C23×D11C22×C414yes—
118C22×C4×C11—24no—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2412yes—
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—48no—
126C2×C22⋊D11C22×C418yes—
127C2×C22⋊D11C22×C418yes—
128C22×Dic11C22×C414yes—
129#4339—28no—
130#4339—28no—
131#4339—48no—
132#4339—48no—
133#4339—48no—
134C2×D44—44no—
135C2×D44C22×C414yes—
136C2×D44C22×C414yes—
137C2×D44C22×C414yes—
138C2×D44C22×C418yes—
139C2×D44C22×C414yes—
140C2×C4×D11—48no—
141C2×C4×D11C22×C418yes—
142C2×C4×D11C2418yes—
143C2×Dic22—44no—
144C2×Dic22C22×C414yes—
145C2×Dic22C22×C414yes—
146C2×C8×C11—24no—
147C2×C8×C11—24no—
148C2×C8×C11C2412yes—
149C2×C8×C11C2412yes—
150C2×C8×C11C2414yes—
151C11×C4⋊C4C22×C414yes—
152C11×C4⋊C4C22×C414yes—
153C11×C22⋊C4C22×C414yes—
154C11×C22⋊C4C22×C414yes—
155C42×C11C22×C412yes—
156C42×C11C22×C412yes—
157C42×C11C2412yes—
158C42×C11C2411yescharacteristic
159C42×C11C2411yescharacteristic
160(C2×D11)⋊C4C22×C418yes—
161(C2×D11)⋊C4C22×C418yes—
162(C2×D11)⋊C4C22×C418yes—
163(C2×D11)⋊C4C22×C418yes—
164C4⋊Dic11C22×C414yes—
165C4⋊Dic11C22×C414yes—
166C4⋊Dic11C22×C418yes—
167#4318—28no—
168C2×C11⋊C8C2418yes—
169#4313—48no—
170#4313—48no—
171C8×D11—48no—
172C8×D11—48no—
173#3449—111no—
174#2978—114no—
175#2977—114no—
176#2976—118no—
177#2935—114no—
178#2932—112no—
179#2931—112no—
180#2921—111no—
181C2×#433D1111yescharacteristic, complemented
182#2880—114no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11C23×C412yes—
186C23×C11C23×C411yescharacteristic
187C22×D11—44no—
188C22×D11—48no—
189C22×D11C23×C418yes—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11C23×C414yes—
196C2×C4×C11C23×C412yes—
197C2×C4×C11C23×C412yes—
198C2×C4×C11C23×C412yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11H(5,𝔽2)14yes—
201C2×C4×C11C2511yescharacteristic
202C22⋊D11—216no—
203C22⋊D11—48no—
204C2×Dic11—44no—
205C2×Dic11C23×C418yes—
206D44—28no—
207D44—44no—
208D44—44no—
209D44—44no—
210D44—48no—
211C4×D11—28no—
212C4×D11—28no—
213C4×D11—48no—
214Dic22—28no—
215Dic22—44no—
216C8×C11—22no—
217C8×C11—24no—
218C8×C11—22no—
219C11⋊C8—28no—
220C22×#41—112no—
221C2×#131—114no—
222C2×#131—114no—
223#537—114no—
224#536—114no—
225#535—114no—
226#534—114no—
227#532—112no—
228#532—112no—
229#525—114no—
230#525—114no—
231C2×#117C2×D1111yescharacteristic
232#436—118no—
233#436—114no—
234#436—114no—
235#435—118no—
236#435—118no—
237#435—118no—
238#435—118no—
239C8×D4—118no—
240C8×D4—114no—
241C8×D4—114no—
242#433—114no—
243#433—114no—
244#433C2×D1114yescomplemented
245#433C2×D1112yescomplemented
246#433C2×D1112yescomplemented
247#423—112no—
248C2×C4⋊C8C2×D1112yescomplemented
249#408—114no—
250#408—114no—
251#408—118no—
252#408—118no—
253#407—112no—
254#407—118no—
255C2×C22⋊C8—118no—
256C2×C22⋊C8C2×D1112yes—
257C4×M16—112no—
258C2×#97C2×D1111yescharacteristic, complemented
259C2×C4×C8C2×D1111yescharacteristic, complemented
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—24no—
263C22×C11—82no—
264C22×C11#51812yes—
265C22×C11C24×C411yescharacteristic
266C2×D11—28no—
267C2×D11—28no—
268C2×D11—28no—
269C2×D11—88no—
270C4×C11—22no—
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11#51812yes—
275C4×C11C2×H(5,𝔽2)12yes—
276Dic11—28no—
277C2×#41—114no—
278C2×#41—114no—
279C2×#41—114no—
280C2×#41—114no—
281C2×#41—448no—
282C22×Q8—112no—
283C22×D4—114no—
284C22×D4—112no—
285C23×C4—114no—
286C23×C4C22×D1111yescharacteristic
287#131—448no—
288#131—448no—
289C2×M16—114no—
290C2×M16—118no—
291C2×M16—118no—
292C22×C8—118no—
293C22×C8—118no—
294C22×C8C22×D1112yes—
295C22×C8C22×D1112yes—
296C4⋊Q8—112no—
297C4⋊Q8—112no—
298#127—112no—
299#127—112no—
300#124—114no—
301#124—114no—
302#123—118no—
303#123—118no—
304C22⋊Q8—118no—
305C22⋊Q8—118no—
306#121—114no—
307#121—114no—
308#121—118no—
309#121—118no—
310#121—118no—
311#120—118no—
312#120—118no—
313C4×D4—118no—
314C4×D4—114no—
315C4×D4—114no—
316#117C4×D1114yes—
317#117C22×D1112yes—
318#117C22×D1112yes—
319C2×C4⋊C4C4×D1112yes—
320C2×C22⋊C4C4×D1112yes—
321C2×C42C22×D1111yescharacteristic
322C2×C42C22×D1111yescharacteristic
323C4⋊C8—114no—
324C4⋊C8—114no—
325C4⋊C8C22×D1114yes—
326C4⋊C8C22×D1114yes—
327C22⋊C8—118no—
328C22⋊C8—118no—
329C22⋊C8—118no—
330C22⋊C8—118no—
331C22⋊C8—118no—
332C22⋊C8C22×D1114yes—
333C22⋊C8C22×D1114yes—
334#97—114no—
335#97C22×D1112yes—
336#97C22×D1112yes—
337C4×C8—114no—
338C4×C8C22×D1111yescharacteristic
339C4×C8C22×D1112yes—
340C4×C8C22×D1111yescharacteristic
341C2×C11—22no—
342C2×C11—42no—
343C2×C11C2×#51811yescharacteristic
344C2×C11#357312yes—
345D11—48no—
346C24—114no—
347C24C2×C4×D1111yescharacteristic
348#41—228no—
349#41—228no—
350#41—448no—
351#41—448no—
352#41—448no—
353C2×Q8—114no—
354C2×Q8—114no—
355C2×Q8—444no—
356C2×D4—118no—
357C2×D4—118no—
358C2×D4—114no—
359C2×D4—118no—
360C2×D4—114no—
361C2×D4—114no—
362C2×D4—114no—
363C2×D4—444no—
364C2×D4—448no—
365C22×C4—24no—
366C22×C4—114no—
367C22×C4—118no—
368C22×C4—118no—
369C22×C4—448no—
370C22×C4C2×C4×D1111yescharacteristic
371C22×C4C2×C4×D1112yes—
372C22×C4C2×C4×D1112yes—
373C22×C4C2×C4×D1112yes—
374C22×C4C23×D1112yes—
375C22×C4C23×D1111yescharacteristic
376M16—228no—
377M16—448no—
378M16—448no—
379C2×C8—24no—
380C2×C8—24no—
381C2×C8—118no—
382C2×C8—448no—
383C2×C8—448no—
384C2×C8C23×D1112yes—
385C2×C8C23×D1112yes—
386C2×C8C23×D1114yes—
387C4⋊C4—118no—
388C4⋊C4—114no—
389C4⋊C4—114no—
390C4⋊C4C2×C4×D1114yes—
391C4⋊C4C2×C4×D1114yes—
392C22⋊C4—118no—
393C22⋊C4—118no—
394C22⋊C4—118no—
395C22⋊C4—118no—
396C22⋊C4C2×C4×D1114yes—
397C22⋊C4C2×C4×D1114yes—
398C42C2×C4×D1112yes—
399C42C2×C4×D1112yes—
400C42C23×D1112yes—
401C42C23×D1111yescharacteristic
402C42C23×D1111yescharacteristic
403C11#6023811yescharacteristic, complemented, Sylow
404C23—22no—
405C23—42no—
406C23—118no—
407C23—444no—
408C23—448no—
409C23C22×C4×D1112yes—
410C23C22×C4×D1111yescharacteristic
411Q8—228no—
412Q8—444no—
413D4—2216no—
414D4—228no—
415D4—444no—
416D4—448no—
417D4—444no—
418D4—444no—
419D4—448no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—118no—
426C2×C4—228no—
427C2×C4—228no—
428C2×C4—448no—
429C2×C4—444no—
430C2×C4C22×C4×D1114yes—
431C2×C4C22×C4×D1112yes—
432C2×C4C22×C4×D1112yes—
433C2×C4C22×C4×D1112yes—
434C2×C4C22×C4×D1111yescharacteristic
435C2×C4#6704214yes—
436C2×C4C24×D1111yescharacteristic
437C8—22no—
438C8—24no—
439C8—22no—
440C8—228no—
441C22—22no—
442C22—24no—
443C22—22no—
444C22—82no—
445C22—228no—
446C22—228no—
447C22—228no—
448C22—888no—
449C22#1062305212yes—
450C22C23×C4×D1111yescharacteristic
451C4—24no—
452C4—22no—
453C4—22no—
454C4—22no—
455C4—228no—
456C4#1062305212yes—
457C4C2×#6704212yes—
458C2—22no—
459C2—42no—
460C2—448no—
461C2C2×#1062305211yescharacteristic
462C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#433C2
prime radical#13081949C2
cosocleC2×C4×C11C25
hypercenterC2×#433D11
hypocenterC11#60238
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13077677C2semidirect
3. #13077671C2semidirect
4. #13077662C2semidirect
5. #13077359C2semidirect
6. #13077335C2semidirect
7. #13077329C2semidirect
8. #13077254C2semidirect
9. #13077062C2semidirect
10. C2×C11×#433C2semidirect
13. C2×#66954C22semidirect
14. C2×#66954C22semidirect
23. C11×#433C22semidirect
24. C11×#433C22semidirect
25. C11×#433C22semidirect
26. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#97C22semidirect
29. C2×C4×C8×C11C22semidirect
31. #10622723C22semidirect
32. #10622723C22semidirect
33. #10622613C22semidirect
34. #10622613C22semidirect
35. #10622537C22semidirect
36. C4×#4318C22semidirect
37. #10622451C22semidirect
38. #10622449C22semidirect
39. #10622449C22semidirect
40. #10622447C22semidirect
43. #10622339C22semidirect
44. D11×C22⋊C8C22semidirect
45. #10622319C22semidirect
46. #10622319C22semidirect
47. #10622301C22semidirect
48. #10622301C22semidirect
49. C8×D44C22semidirect
50. C8×D44C22semidirect
181. C2×#433D11semidirect
244. #433C2×D11semidirect
245. #433C2×D11semidirect
246. #433C2×D11semidirect
248. C2×C4⋊C8C2×D11semidirect
258. C2×#97C2×D11semidirect
259. C2×C4×C8C2×D11semidirect
403. C11#60238semidirect

Maximal subgroups

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

subgroupindex
#130819492
#130776772
#130776712
#130776622
#130773592
#130773352
#130773292
#130772542
#130770622
C2×C11×#4332
#6023811