Finite Group Databasebeta

← #15638469

Subgroups — #15638469

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082419C211yesmaximal, characteristic, complemented
2#13080440C218yesmaximal, complemented
3D4×#4324C218yesmaximal, complemented
4#13079557C212yesmaximal, complemented
5#13079373C214yesmaximal, complemented
6#13078624C212yesmaximal, complemented
7C2×#10622831C214yesmaximal, complemented
8#13077640C211yesmaximal, characteristic, complemented
9C2×D42×C11C211yesmaximal, characteristic
10C23×D4×C11—21no—
11C23×D4×C11C2212yes—
12D42×C11—24no—
13D42×C11C2218yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#121—21no—
16C2×C11×#121C2212yes—
17C2×C11×#120—22no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20#10623329—21no—
21C22×#4324C2218yescomplemented
22C2×#66977C2214yescomplemented
23#10623074C2214yescomplemented
24#10623070—24no—
25D4×Dic22C2214yescomplemented
26#10623031—21no—
27#10623014—22no—
28#10623001C2212yescomplemented
29#10622831C2214yes—
30#10622831C2218yescomplemented
31#10622831C22116yescomplemented
32C2×#66896C2218yescomplemented
33C2×C22⋊(C11⋊C8)C2214yescomplemented
34#10622689C2214yescomplemented
35#10622688C2218yescomplemented
36#10622683C2214yescomplemented
37#10622654C22116yescomplemented
38#10622653C2218yescomplemented
39#10622647C2218yescomplemented
40#10622632C2214yescomplemented
41C4×#4324C2218yescomplemented
42D4×C11⋊C8C2218yescomplemented
43#10622621C2214yescomplemented
44#10622584C2214yescomplemented
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×Dic22C2314yescomplemented
62C11×#127—22no—
63C11×#127C2314yes—
64C11×#121—24no—
65C11×#121—28no—
66C11×#121C2318yes—
67C11×#120—216no—
68C4×D4×C11—22no—
69C4×D4×C11D414yes—
70C4×D4×C11C2314yes—
71C4×D4×C11C2314yes—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—24no—
79D4×Dic11—24no—
80D4×Dic11—24no—
81C2×#4324—416no—
82C2×#4324C2318yes—
83C2×#4324C23116yescomplemented
84#66979—22no—
85C2×C4⋊Dic11C2314yescomplemented
86#66977—22no—
87#66977—24no—
88#66977—24no—
89#66977C2314yes—
90#66977C2318yescomplemented
91C2×Dic11⋊C4—24no—
92C22×C11⋊C8C2318yescomplemented
93#66943—24no—
94#66941—24no—
95#66931—28no—
96#66931—28no—
97#66923—22no—
98#66922C2312yescomplemented
99#66922C2312yescomplemented
100C4×Dic22—22no—
101C4×Dic22C2314yescomplemented
102#66896C2318yes—
103#66896C23116yescomplemented
104C22⋊(C11⋊C8)C2314yes—
105C22⋊(C11⋊C8)C2318yescomplemented
106#66874C2318yescomplemented
107#66872C2318yescomplemented
108C4⋊(C11⋊C8)C2314yescomplemented
109C4×C11⋊C8C2314yescomplemented
110#61560—111nomaximal, Sylow
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—28no—
114C24×C11—48no—
115C24×C11—48no—
116C24×C11—84no—
117C24×C11C2×D412yes—
118C2×D4×C11—24no—
119C2×D4×C11—216no—
120C2×D4×C11—28no—
121C2×D4×C11—21no—
122C2×D4×C11—28no—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—48no—
127C2×D4×C11—44no—
128C2×D4×C11—416no—
129C2×D4×C11—48no—
130C2×D4×C11—48no—
131C2×D4×C11—432no—
132C2×D4×C11—44no—
133C2×D4×C11—82no—
134C2×D4×C11SD1618yescomplemented
135C2×D4×C11C2×D414yes—
136C2×D4×C11C2414yes—
137C2×D4×C11C2412yes—
138C22×C4×C11—21no—
139C22×C4×C11—24no—
140C22×C4×C11—44no—
141C22×C4×C11—44no—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×C4×C11C2414yes—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C2×Dic22—22no—
151C2×Dic22—24no—
152C2×Dic22—48no—
153C2×Dic22C2414yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C2×D414yes—
156C11×C4⋊C4C2412yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—28no—
159C11×C22⋊C4C2×D418yes—
160C42×C11C2×D412yes—
161C42×C11C2412yes—
162C22⋊Dic11—28no—
163C22⋊Dic11—24no—
164#4324—216no—
165#4324—416no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—24no—
170C4⋊Dic11C2414yes—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173Dic11⋊C4—28no—
174C4×Dic11—24no—
175C2×C11⋊C8—48no—
176C2×C11⋊C8C2418yes—
177#3501—111no—
178C2×D42D1111yescharacteristic
179#3295—118no—
180D4×SD16—118no—
181#3208—112no—
182#3187—114no—
183#3101—112no—
184C2×#450—114no—
185#2972—111no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—416no—
192C23×C11—42no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—42no—
196C23×C11—416no—
197C23×C11—44no—
198C23×C11—88no—
199C23×C11—832no—
200C23×C11C2×SD1618yescomplemented
201C23×C11C22×D411yescharacteristic
202C23×C11C22×D414yes—
203D4×C11—24no—
204D4×C11—22no—
205D4×C11—28no—
206D4×C11—416no—
207D4×C11—44no—
208D4×C11—416no—
209D4×C11—48no—
210D4×C11—84no—
211D4×C11C2×SD16116yescomplemented
212D4×C11H(5,𝔽2)14yes—
213C2×C4×C11—28no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—48no—
221C2×C4×C11C2×SD1614yescomplemented
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D414yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2511yescharacteristic
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—84no—
230C2×Dic11—84no—
231Dic22—28no—
232Dic22—82no—
233Dic22—84no—
234C11⋊C8—28no—
235C23×D4—21no—
236C23×D4C2×D1112yes—
237C22×SD16—118no—
238#554—114no—
239#554—224no—
240D4×Q8—114no—
241D42—24no—
242D42C2×D1118yes—
243#544—221no—
244#543—222no—
245#533—112no—
246C2×#127C2×D1111yescharacteristic
247C2×C22⋊Q8—114no—
248C2×#121—21no—
249C2×#121C2×D1112yes—
250C2×#120—22no—
251#518—221no—
252C2×C4×D4C2×D1111yescharacteristic
253C2×C4×D4C2×D1111yescharacteristic
254#492—114no—
255#486—114no—
256#483—114no—
257#481—118no—
258#476—114no—
259#465—1116no—
260#461—114no—
261#460—118no—
262#450—114no—
263#450—118no—
264#450—1116no—
265#448—118no—
266C4×SD16—118no—
267C8×D4—118no—
268#431—112no—
269C2×#102—118no—
270C2×C22⋊C8—114no—
271C22×C11—21no—
272C22×C11—24no—
273C22×C11—21no—
274C22×C11—24no—
275C22×C11—24no—
276C22×C11—48no—
277C22×C11—48no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—44no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11—832no—
284C22×C11—88no—
285C22×C11C22×SD1612yes—
286C22×C11C22×SD1618yes—
287C22×C11C23×D411yescharacteristic
288C4×C11—22no—
289C4×C11—21no—
290C4×C11—24no—
291C4×C11—42no—
292C4×C11C22×SD1614yes—
293C4×C11C2×H(5,𝔽2)12yes—
294Dic11—44no—
295Dic11—44no—
296C25—22no—
297C22×Q8—114no—
298C22×D4—22no—
299C22×D4—28no—
300C22×D4—22no—
301C22×D4—21no—
302C22×D4—24no—
303C22×D4—21no—
304C22×D4—48no—
305C22×D4—48no—
306C22×D4C22⋊D1111yescharacteristic
307C22×D4C22×D1111yescharacteristic
308C22×D4C22×D1118yes—
309C22×D4C22×D1112yes—
310C23×C4—21no—
311C23×C4C22×D1112yes—
312C2×SD16—118no—
313C2×SD16—1116no—
314C2×SD16—4416no—
315C22×C8—118no—
316C4⋊Q8—112no—
317C4⋊Q8—112no—
318C4⋊Q8—224no—
319#127—22no—
320#127C22×D1114yes—
321#125—224no—
322#125—222no—
323C22⋊Q8—114no—
324C22⋊Q8—118no—
325C22⋊Q8—224no—
326C22⋊Q8—224no—
327C22⋊Q8—222no—
328C22⋊Q8—228no—
329C22⋊Q8—228no—
330#121—24no—
331#121—28no—
332#121C22×D1118yes—
333#120—216no—
334C4×Q8—114no—
335C4×Q8—222no—
336C4×D4—22no—
337C4×D4—224no—
338C4×D4—224no—
339C4×D4C22⋊D1114yes—
340C4×D4C22×D1114yes—
341C4×D4C22×D1114yes—
342#117—222no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4C22⋊D1111yescharacteristic
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—224no—
350C2×C22⋊C4C22⋊D1112yes—
351C2×C42C22×D1111yescharacteristic
352#106—118no—
353C4⋊C8—114no—
354#103—118no—
355#102—118no—
356#102—1116no—
357C22⋊C8—114no—
358C22⋊C8—118no—
359C4×C8—114no—
360C2×C11—22no—
361C2×C11—28no—
362C2×C11—44no—
363C2×C11—84no—
364C2×C11#348411yescharacteristic
365C2×C11C23×SD1611yescharacteristic
366C2×C11#358511yescharacteristic
367C24—21no—
368C24—22no—
369C24—28no—
370C24—48no—
371C24—48no—
372C24—84no—
373C24C2×C22⋊D1112yes—
374C2×Q8—114no—
375C2×Q8—222no—
376C2×Q8—224no—
377C2×Q8—448no—
378C2×D4—24no—
379C2×D4—216no—
380C2×D4—28no—
381C2×D4—21no—
382C2×D4—28no—
383C2×D4—22no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—48no—
387C2×D4—44no—
388C2×D4—416no—
389C2×D4—48no—
390C2×D4—48no—
391C2×D4—432no—
392C2×D4—44no—
393C2×D4—82no—
394C2×D4#432418yescomplemented
395C2×D4C2×C22⋊D1114yes—
396C2×D4C23×D1114yes—
397C2×D4C23×D1112yes—
398C22×C4—21no—
399C22×C4—24no—
400C22×C4—44no—
401C22×C4—44no—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1114yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409C22×C4C23×D1114yes—
410SD16—2216no—
411SD16—4416no—
412C2×C8—118no—
413C2×C8—448no—
414C4⋊C4—21no—
415C4⋊C4—114no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—228no—
419C4⋊C4—222no—
420C4⋊C4—222no—
421C4⋊C4—224no—
422C4⋊C4—222no—
423C4⋊C4C2×C22⋊D1114yes—
424C4⋊C4C23×D1112yes—
425C22⋊C4—24no—
426C22⋊C4—28no—
427C22⋊C4—224no—
428C22⋊C4—228no—
429C22⋊C4C2×C22⋊D1118yes—
430C42—224no—
431C42C2×C22⋊D1112yes—
432C42C23×D1112yes—
433C11#6156011yescharacteristic, complemented, Sylow
434C23—24no—
435C23—22no—
436C23—24no—
437C23—42no—
438C23—42no—
439C23—416no—
440C23—42no—
441C23—44no—
442C23—44no—
443C23—42no—
444C23—416no—
445C23—44no—
446C23—88no—
447C23—832no—
448C23C2×#432418yescomplemented
449C23C22×C22⋊D1111yescharacteristic
450C23C22×C22⋊D1114yes—
451Q8—228no—
452Q8—884no—
453Q8—882no—
454D4—24no—
455D4—22no—
456D4—28no—
457D4—416no—
458D4—44no—
459D4—416no—
460D4—48no—
461D4—84no—
462D4C2×#4324116yescomplemented
463D4#6703714yes—
464C2×C4—28no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—48no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—884no—
475C2×C4—884no—
476C2×C4C2×#432414yescomplemented
477C2×C4C22×C22⋊D1111yescharacteristic
478C2×C4C22×C22⋊D1112yes—
479C2×C4C22×C22⋊D1114yes—
480C2×C4C22×C22⋊D1112yes—
481C2×C4C24×D1111yescharacteristic
482C8—228no—
483C22—21no—
484C22—24no—
485C22—21no—
486C22—24no—
487C22—24no—
488C22—48no—
489C22—48no—
490C22—42no—
491C22—42no—
492C22—44no—
493C22—44no—
494C22—44no—
495C22—832no—
496C22—88no—
497C22C22×#432412yes—
498C22C22×#432418yes—
499C22C23×C22⋊D1111yescharacteristic
500C4—22no—
501C4—21no—
502C4—24no—
503C4—42no—
504C4—444no—
505C4—444no—
506C4C22×#432414yes—
507C4C2×#6703712yes—
508C2—22no—
509C2—28no—
510C2—44no—
511C2—84no—
512C2#1308225111yescharacteristic
513C2C23×#432411yescharacteristic
514C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×D42×C11C2
socleC22×C11C23×D4
hypercenterC2×D42D11
hypocenterC11#61560
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. #13082419C2semidirect
2. #13080440C2semidirect
3. D4×#4324C2semidirect
4. #13079557C2semidirect
5. #13079373C2semidirect
6. #13078624C2semidirect
7. C2×#10622831C2semidirect
8. #13077640C2semidirect
21. C22×#4324C22semidirect
22. C2×#66977C22semidirect
23. #10623074C22semidirect
25. D4×Dic22C22semidirect
28. #10623001C22semidirect
30. #10622831C22semidirect
31. #10622831C22semidirect
32. C2×#66896C22semidirect
33. C2×C22⋊(C11⋊C8)C22semidirect
34. #10622689C22semidirect
35. #10622688C22semidirect
36. #10622683C22semidirect
37. #10622654C22semidirect
38. #10622653C22semidirect
39. #10622647C22semidirect
40. #10622632C22semidirect
41. C4×#4324C22semidirect
42. D4×C11⋊C8C22semidirect
43. #10622621C22semidirect
44. #10622584C22semidirect
45. #10622538C22semidirect
61. C22×Dic22C23semidirect
83. C2×#4324C23semidirect
85. C2×C4⋊Dic11C23semidirect
90. #66977C23semidirect
92. C22×C11⋊C8C23semidirect
98. #66922C23semidirect
99. #66922C23semidirect
101. C4×Dic22C23semidirect
103. #66896C23semidirect
105. C22⋊(C11⋊C8)C23semidirect
106. #66874C23semidirect
107. #66872C23semidirect
108. C4⋊(C11⋊C8)C23semidirect
109. C4×C11⋊C8C23semidirect
134. C2×D4×C11SD16semidirect
200. C23×C11C2×SD16semidirect
211. D4×C11C2×SD16semidirect
221. C2×C4×C11C2×SD16semidirect
394. C2×D4#4324semidirect
433. C11#61560semidirect
448. C23C2×#4324semidirect
462. D4C2×#4324semidirect
476. C2×C4C2×#4324semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130804402
D4×#43242
#130795572
#130793732
#130786242
C2×#106228312
#130776402
C2×D42×C112
#6156011