Finite Group Databasebeta

← #15638460

Subgroups — #15638460

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic, complemented
2#13080429C218yesmaximal, complemented
3D4×#4323C218yesmaximal, complemented
4#13079534C212yesmaximal, complemented
5#13079364C214yesmaximal, complemented
6#13078616C212yesmaximal, complemented
7C2×#10622830C214yesmaximal, complemented
8#13077640C211yesmaximal, characteristic, complemented
9C2×D42×C11C211yesmaximal, characteristic, complemented
10C23×D4×C11—21no—
11C23×D4×C11C2212yescomplemented
12C2×#67037—21no—
13D42×C11—24no—
14D42×C11C2218yescomplemented
15C2×C11×#127C2211yescharacteristic, complemented
16C2×C11×#121—21no—
17C2×C11×#121C2212yescomplemented
18C2×C11×#120—22no—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic, complemented
21C22×#4323C2218yescomplemented
22C2×#66983C2214yescomplemented
23#10623086C2214yescomplemented
24#10623085—24no—
25D4×D44C2214yescomplemented
26#10623041—21no—
27#10623024—22no—
28#10623008C2212yescomplemented
29#10622830C2214yescomplemented
30#10622830C2218yescomplemented
31#10622830C22116yescomplemented
32C2×#66896C2218yescomplemented
33C2×C22⋊(C11⋊C8)C2214yescomplemented
34#10622686C2214yescomplemented
35#10622685C2218yescomplemented
36#10622683C2214yescomplemented
37#10622651C22116yescomplemented
38#10622649C2218yescomplemented
39#10622646C2218yescomplemented
40#10622628C2214yescomplemented
41C4×#4323C2218yescomplemented
42D4×C11⋊C8C2218yescomplemented
43#10622620C2214yescomplemented
44#10622580C2214yescomplemented
45#10622538C2212yescomplemented
46C25×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—28no—
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—24no—
52C22×D4×C11—21no—
53C22×D4×C11—48no—
54C22×D4×C11—48no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2318yes—
58C22×D4×C11C2312yes—
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C22×C22⋊D11—24no—
62#67037—48no—
63C2×#4341—24no—
64C2×D4×D11—24no—
65C2×#4339—22no—
66C22×D44C2314yescomplemented
67C11×#127—22no—
68C11×#127C2314yes—
69C11×#121—24no—
70C11×#121—28no—
71C11×#121C2318yes—
72C11×#120—216no—
73C4×D4×C11—22no—
74C4×D4×C11D414yes—
75C4×D4×C11C2314yes—
76C4×D4×C11C2314yes—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4D412yes—
82C2×C42×C11C2311yescharacteristic
83C2×#4323—416no—
84C2×#4323C2318yes—
85C2×#4323C23116yescomplemented
86#66983—22no—
87#66983—24no—
88#66983—24no—
89#66983C2314yes—
90#66983C2318yescomplemented
91C2×(C2×D11)⋊C4—24no—
92C2×C4⋊Dic11C2314yescomplemented
93C22×C11⋊C8C2318yescomplemented
94#66950—24no—
95#66948—24no—
96#66939—28no—
97#66935—28no—
98#66928—22no—
99#66927C2312yescomplemented
100C4×D44—22no—
101C4×D44C2314yescomplemented
102#66922C2312yescomplemented
103#66896C2318yes—
104#66896C23116yescomplemented
105C22⋊(C11⋊C8)C2314yes—
106C22⋊(C11⋊C8)C2318yescomplemented
107#66873C2318yescomplemented
108#66871C2318yescomplemented
109C4⋊(C11⋊C8)C2314yescomplemented
110C4×C11⋊C8C2314yescomplemented
111#61559—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11—22no—
114C24×C11—28no—
115C24×C11—48no—
116C24×C11—48no—
117C24×C11—84no—
118C24×C11C2×D412yes—
119C23×D11—24no—
120C2×D4×C11—24no—
121C2×D4×C11—216no—
122C2×D4×C11—28no—
123C2×D4×C11—21no—
124C2×D4×C11—28no—
125C2×D4×C11—22no—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—48no—
129C2×D4×C11—44no—
130C2×D4×C11—416no—
131C2×D4×C11—48no—
132C2×D4×C11—48no—
133C2×D4×C11—432no—
134C2×D4×C11—44no—
135C2×D4×C11—82no—
136C2×D4×C11D818yescomplemented
137C2×D4×C11C2×D414yes—
138C2×D4×C11C2414yes—
139C2×D4×C11C2412yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2414yes—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—24no—
152C2×C22⋊D11—416no—
153C22×Dic11—24no—
154#4341—416no—
155D4×D11—416no—
156#4339—48no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—24no—
160C2×D44—48no—
161C2×D44C2414yes—
162C2×C4×D11—24no—
163C2×Dic22—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C2×D414yes—
166C11×C4⋊C4C2412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4C2×D418yes—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172#4323—216no—
173#4323—416no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—28no—
177C4⋊Dic11—22no—
178C4⋊Dic11—24no—
179C4⋊Dic11C2414yes—
180C2×C11⋊C8—48no—
181C2×C11⋊C8C2418yes—
182#3496—111no—
183C2×D42D1111yescharacteristic, complemented
184#3294—118no—
185D4×D8—118no—
186#3205—112no—
187#3186—114no—
188#3100—112no—
189C2×#447—114no—
190#2972—111no—
191C23×C11—24no—
192C23×C11—22no—
193C23×C11—24no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—416no—
197C23×C11—42no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—42no—
201C23×C11—416no—
202C23×C11—44no—
203C23×C11—88no—
204C23×C11—832no—
205C23×C11C2×D818yescomplemented
206C23×C11C22×D414yes—
207C23×C11C22×D411yescharacteristic
208C22×D11—24no—
209C22×D11—48no—
210C22×D11—84no—
211C22×D11—84no—
212D4×C11—24no—
213D4×C11—22no—
214D4×C11—28no—
215D4×C11—416no—
216D4×C11—44no—
217D4×C11—416no—
218D4×C11—48no—
219D4×C11—84no—
220D4×C11C2×D8116yescomplemented
221D4×C11H(5,𝔽2)14yescomplemented
222C2×C4×C11—28no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—48no—
230C2×C4×C11C2×D814yescomplemented
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2511yescharacteristic
236C22⋊D11—48no—
237C22⋊D11—416no—
238C2×Dic11—24no—
239C2×Dic11—48no—
240D44—28no—
241D44—44no—
242D44—82no—
243D44—84no—
244C4×D11—48no—
245Dic22—44no—
246C11⋊C8—28no—
247C2×H(5,𝔽2)—221no—
248C23×D4—21no—
249C23×D4C2×D1112yescomplemented
250C22×D8—118no—
251#547—114no—
252#546—224no—
253D42—24no—
254D42—114no—
255D42C2×D1118yescomplemented
256#537—221no—
257#534—222no—
258#532—112no—
259C2×#127C2×D1111yescharacteristic, complemented
260C2×#121—21no—
261C2×#121—114no—
262C2×#121C2×D1112yescomplemented
263C2×#120—22no—
264C2×C4×D4C2×D1111yescharacteristic
265C2×C4×D4C2×D1111yescharacteristic, complemented
266#493—114no—
267#486—114no—
268#480—118no—
269#480—114no—
270#474—114no—
271#466—1116no—
272#459—118no—
273#459—114no—
274#447—114no—
275#447—118no—
276#447—1116no—
277#447—118no—
278C4×D8—118no—
279C8×D4—118no—
280#431—112no—
281C2×#102—118no—
282C2×C22⋊C8—114no—
283C22×C11—21no—
284C22×C11—24no—
285C22×C11—21no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—48no—
289C22×C11—48no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—832no—
296C22×C11—88no—
297C22×C11C22×D812yes—
298C22×C11C22×D818yes—
299C22×C11C23×D411yescharacteristic
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—44no—
303C2×D11—168no—
304C4×C11—22no—
305C4×C11—21no—
306C4×C11—24no—
307C4×C11—42no—
308C4×C11C22×D814yes—
309C4×C11C2×H(5,𝔽2)12yes—
310Dic11—44no—
311C25—22no—
312H(5,𝔽2)—448no—
313C2×#41—224no—
314C2×#41—222no—
315C22×D4—22no—
316C22×D4—28no—
317C22×D4—22no—
318C22×D4—21no—
319C22×D4—24no—
320C22×D4—21no—
321C22×D4—48no—
322C22×D4—48no—
323C22×D4—114no—
324C22×D4—224no—
325C22×D4—224no—
326C22×D4C22⋊D1111yescharacteristic
327C22×D4C22×D1111yescharacteristic
328C22×D4C22×D1118yes—
329C22×D4C22×D1112yes—
330C23×C4—21no—
331C23×C4C22×D1112yes—
332C2×D8—118no—
333C2×D8—1116no—
334C2×D8—4416no—
335C22×C8—118no—
336C4⋊Q8—112no—
337#127—22no—
338#127—112no—
339#127C22×D1114yes—
340#124—222no—
341#123—228no—
342C22⋊Q8—224no—
343#121—24no—
344#121—28no—
345#121—114no—
346#121—118no—
347#121—224no—
348#121—224no—
349#121—222no—
350#121—224no—
351#121C22×D1118yes—
352#120—216no—
353#120—228no—
354C4×D4—22no—
355C4×D4—114no—
356C4×D4—222no—
357C4×D4C22⋊D1114yes—
358C4×D4C22×D1114yes—
359C4×D4C22×D1114yes—
360C2×C4⋊C4—114no—
361C2×C4⋊C4C22⋊D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4C22⋊D1112yes—
367C2×C42C22×D1111yescharacteristic
368#107—118no—
369C4⋊C8—114no—
370#102—118no—
371#102—1116no—
372#102—118no—
373C22⋊C8—114no—
374C22⋊C8—118no—
375C4×C8—114no—
376C2×C11—28no—
377C2×C11—22no—
378C2×C11—44no—
379C2×C11—84no—
380C2×C11#348411yescharacteristic
381C2×C11C23×D811yescharacteristic
382C2×C11#358511yescharacteristic
383D11—84no—
384C24—21no—
385C24—22no—
386C24—28no—
387C24—48no—
388C24—48no—
389C24—84no—
390C24—224no—
391C24C2×C22⋊D1112yes—
392#41—4416no—
393#41—448no—
394C2×Q8—222no—
395C2×D4—24no—
396C2×D4—216no—
397C2×D4—28no—
398C2×D4—21no—
399C2×D4—28no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—48no—
404C2×D4—44no—
405C2×D4—416no—
406C2×D4—48no—
407C2×D4—48no—
408C2×D4—432no—
409C2×D4—44no—
410C2×D4—82no—
411C2×D4—114no—
412C2×D4—228no—
413C2×D4—224no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—224no—
417C2×D4—448no—
418C2×D4—4416no—
419C2×D4—4416no—
420C2×D4#432318yescomplemented
421C2×D4C2×C22⋊D1114yes—
422C2×D4C23×D1114yes—
423C2×D4C23×D1112yes—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1114yes—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C22×C4C23×D1114yes—
436D8—2216no—
437D8—4416no—
438C2×C8—118no—
439C2×C8—448no—
440C4⋊C4—21no—
441C4⋊C4—114no—
442C4⋊C4—224no—
443C4⋊C4—222no—
444C4⋊C4C2×C22⋊D1114yes—
445C4⋊C4C23×D1112yes—
446C22⋊C4—24no—
447C22⋊C4—28no—
448C22⋊C4—224no—
449C22⋊C4—228no—
450C22⋊C4—224no—
451C22⋊C4C2×C22⋊D1118yes—
452C42C2×C22⋊D1112yes—
453C42C23×D1112yes—
454C11#6155911yescharacteristic, complemented, Sylow
455C23—24no—
456C23—22no—
457C23—24no—
458C23—42no—
459C23—42no—
460C23—416no—
461C23—42no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—416no—
466C23—44no—
467C23—88no—
468C23—832no—
469C23—224no—
470C23—448no—
471C23—884no—
472C23—884no—
473C23C2×#432318yescomplemented
474C23C22×C22⋊D1114yes—
475C23C22×C22⋊D1111yescharacteristic
476Q8—444no—
477D4—24no—
478D4—22no—
479D4—28no—
480D4—416no—
481D4—44no—
482D4—416no—
483D4—48no—
484D4—84no—
485D4—228no—
486D4—448no—
487D4—4416no—
488D4—444no—
489D4—884no—
490D4—882no—
491D4C2×#4323116yescomplemented
492D4#6703714yescomplemented
493C2×C4—28no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—48no—
501C2×C4—224no—
502C2×C4—448no—
503C2×C4—448no—
504C2×C4C2×#432314yescomplemented
505C2×C4C22×C22⋊D1111yescharacteristic
506C2×C4C22×C22⋊D1112yes—
507C2×C4C22×C22⋊D1114yes—
508C2×C4C22×C22⋊D1112yes—
509C2×C4C24×D1111yescharacteristic
510C8—228no—
511C22—21no—
512C22—24no—
513C22—21no—
514C22—24no—
515C22—24no—
516C22—48no—
517C22—48no—
518C22—42no—
519C22—42no—
520C22—44no—
521C22—44no—
522C22—44no—
523C22—832no—
524C22—88no—
525C22—444no—
526C22—444no—
527C22—444no—
528C22—1768no—
529C22C22×#432312yes—
530C22C22×#432318yes—
531C22C23×C22⋊D1111yescharacteristic
532C4—22no—
533C4—21no—
534C4—24no—
535C4—42no—
536C4—444no—
537C4C22×#432314yes—
538C4C2×#6703712yes—
539C2—22no—
540C2—28no—
541C2—44no—
542C2—84no—
543C2—884no—
544C2#1308225111yescharacteristic
545C2C23×#432311yescharacteristic
546C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D42×C11C2
socleC22×C11C23×D4
hypercenterC2×D42D11
hypocenterC11#61559
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. #13082380C2semidirect
2. #13080429C2semidirect
3. D4×#4323C2semidirect
4. #13079534C2semidirect
5. #13079364C2semidirect
6. #13078616C2semidirect
7. C2×#10622830C2semidirect
8. #13077640C2semidirect
9. C2×D42×C11C2semidirect
11. C23×D4×C11C22semidirect
14. D42×C11C22semidirect
15. C2×C11×#127C22semidirect
17. C2×C11×#121C22semidirect
20. C2×C4×D4×C11C22semidirect
21. C22×#4323C22semidirect
22. C2×#66983C22semidirect
23. #10623086C22semidirect
25. D4×D44C22semidirect
28. #10623008C22semidirect
29. #10622830C22semidirect
30. #10622830C22semidirect
31. #10622830C22semidirect
32. C2×#66896C22semidirect
33. C2×C22⋊(C11⋊C8)C22semidirect
34. #10622686C22semidirect
35. #10622685C22semidirect
36. #10622683C22semidirect
37. #10622651C22semidirect
38. #10622649C22semidirect
39. #10622646C22semidirect
40. #10622628C22semidirect
41. C4×#4323C22semidirect
42. D4×C11⋊C8C22semidirect
43. #10622620C22semidirect
44. #10622580C22semidirect
45. #10622538C22semidirect
66. C22×D44C23semidirect
85. C2×#4323C23semidirect
90. #66983C23semidirect
92. C2×C4⋊Dic11C23semidirect
93. C22×C11⋊C8C23semidirect
99. #66927C23semidirect
101. C4×D44C23semidirect
102. #66922C23semidirect
104. #66896C23semidirect
106. C22⋊(C11⋊C8)C23semidirect
107. #66873C23semidirect
108. #66871C23semidirect
109. C4⋊(C11⋊C8)C23semidirect
110. C4×C11⋊C8C23semidirect
136. C2×D4×C11D8semidirect
183. C2×D42D11semidirect
205. C23×C11C2×D8semidirect
220. D4×C11C2×D8semidirect
221. D4×C11H(5,𝔽2)semidirect
230. C2×C4×C11C2×D8semidirect
249. C23×D4C2×D11semidirect
255. D42C2×D11semidirect
259. C2×#127C2×D11semidirect
262. C2×#121C2×D11semidirect
265. C2×C4×D4C2×D11semidirect
420. C2×D4#4323semidirect
454. C11#61559semidirect
473. C23C2×#4323semidirect
491. D4C2×#4323semidirect
492. D4#67037semidirect
504. C2×C4C2×#4323semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130804292
D4×#43232
#130795342
#130793642
#130786162
C2×#106228302
#130776402
C2×D42×C112
#6155911