Finite Group Databasebeta

← #15640554

Subgroups — #15640554

Order 2816.

2136 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083021C211yesmaximal, characteristic, complemented
2#13082396C211yesmaximal, characteristic, complemented
3#13080911C214yesmaximal, complemented
4#13080545C214yesmaximal, complemented
5D4×#4314C214yesmaximal, complemented
6#13080218C214yesmaximal, complemented
7#13079543C212yesmaximal, complemented
8#13079489C214yesmaximal, complemented
9#13078677C212yesmaximal, complemented
10#13077904C214yesmaximal, complemented
11C11×#2979C211yesmaximal, characteristic, complemented
12C2×#67043C2212yescomplemented
13C11×#532C2211yescharacteristic
14#10623361C2214yes—
15#10623356C2212yescomplemented
16C2×#66961C2214yescomplemented
17C22×#4314C2214yescomplemented
18#10623265—21no—
19D11×C4⋊Q8—21no—
20#10623248—21no—
21#10623247—21no—
22#10623214—22no—
23#10623206—22no—
24#10623142—24no—
25#10623138—24no—
26#10623094C2214yes—
27#10623082C2214yescomplemented
28D4×D44C2214yes—
29D4×Dic22C2214yescomplemented
30#10623008C2212yes—
31C4×#4339C2211yescharacteristic, complemented
32C2×#66922C2211yescharacteristic, complemented
33C11×#436C2214yescomplemented
34C8×D4×C11C2214yescomplemented
35C11×#431C2212yescomplemented
36C11×#408C2214yescomplemented
37#10622747C2218yescomplemented
38#10622733C2214yescomplemented
39#10622727C2218yescomplemented
40#10622726C2214yescomplemented
41#10622463C2212yescomplemented
42#10622461C2212yes—
43#10622456C2212yes—
44#10622455C2212yescomplemented
45#10622454C2214yescomplemented
46#10622454C2214yescomplemented
47#10622351C2218yescomplemented
48#10622351C2218yescomplemented
49#10622350C2214yescomplemented
50#10622347C2214yescomplemented
51#10622347C2218yescomplemented
52#10622344C2218yescomplemented
53#10622336C2218yescomplemented
54#10622306C2214yes—
55C4×D88C2214yescomplemented
56C4×#4314C2214yescomplemented
57#10622294C2214yescomplemented
58C2×C11×#41C2312yes—
59#67043—44no—
60#67043—44no—
61C2×Q8×D11—22no—
62C2×#4341—22no—
63C2×#4341—24no—
64C2×D4×D11—24no—
65C2×#4339—22no—
66C2×#4339C2311yescharacteristic
67C2×#4339C2314yes—
68C22×D44C2314yes—
69C22×Dic22C2314yes—
70C22×Dic22C2312yes—
71C2×C11×M16C2314yes—
72C22×C8×C11C2314yes—
73C11×C4⋊Q8D411yescharacteristic
74C11×#127D411yescharacteristic
75C11×#124D412yes—
76C11×#121D414yes—
77C4×D4×C11C2314yes—
78C2×C42×C11C2311yescharacteristic
79#67000—24no—
80#66997—22no—
81#66993—24no—
82#66991—24no—
83#66991—24no—
84#66990—24no—
85#66990—24no—
86#66989—22no—
87#66988—24no—
88D4×Dic11—24no—
89#66983—22no—
90#66983C2318yes—
91#66983C2314yes—
92C4×C22⋊D11—22no—
93#66979C2314yes—
94#66979C2311yescharacteristic
95C2×C4⋊Dic11—22no—
96#66977C2318yes—
97#66961—48no—
98C2×D88C2314yes—
99C2×#4314—48no—
100C2×#4314C2314yes—
101C2×#4314C2318yes—
102C2×#4314C2318yes—
103#66948—24no—
104#66945—24no—
105C4⋊C4×D11—24no—
106#66941—24no—
107#66938—28no—
108#66936—28no—
109#66935—28no—
110#66931—28no—
111#66928—22no—
112#66927C2312yes—
113C4×D44—22no—
114C4×D44C2312yes—
115C4×D44C2314yes—
116#66925—21no—
117C42×D11—21no—
118#66922—21no—
119#66922—21no—
120#66922C2314yes—
121#66922C2312yes—
122C4×Dic22C2312yes—
123C11×C4⋊C8C2312yes—
124C11×C4⋊C8C2312yes—
125C11×C22⋊C8C2318yes—
126C11×C22⋊C8C2314yes—
127C4×C8×C11C2314yes—
128#66885C2314yes—
129#66885C2314yes—
130#66885C2314yes—
131#66882C2314yes—
132#66881C2314yes—
133#66880C2318yes—
134#66880C2314yes—
135#66880C2318yes—
136#61664—111nomaximal, Sylow
137C23×D11—24no—
138C11×#41—42no—
139C11×#41—42no—
140C2×Q8×C11C2×D412yes—
141C2×D4×C11C2×D414yes—
142C2×D4×C11C2×D414yes—
143C2×D4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2414yes—
147C2×C22⋊D11—21no—
148C2×C22⋊D11—24no—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—24no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153Q8×D11—48no—
154#4341—48no—
155#4341—416no—
156D4×D11—88no—
157#4339—22no—
158#4339—28no—
159#4339—22no—
160#4339—44no—
161#4339—84no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—24no—
165C2×D44—44no—
166C2×D44—44no—
167C2×D44C2414yes—
168C2×D44C2411yescharacteristic
169C2×C4×D11—21no—
170C2×C4×D11—22no—
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×Dic22—28no—
174C2×Dic22—22no—
175C2×Dic22—24no—
176C2×Dic22—22no—
177C2×Dic22—44no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C2×Dic22C2414yes—
181C2×Dic22C2411yescharacteristic
182C11×M16—44no—
183C2×C8×C11—44no—
184C2×C8×C11C2414yes—
185C2×C8×C11C2414yes—
186C11×C4⋊C4C2×D414yes—
187C11×C22⋊C4C2×D418yes—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2412yes—
191C22⋊Dic11—28no—
192C22⋊Dic11—24no—
193C22⋊Dic11—21no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—28no—
198C4⋊Dic11—24no—
199C4⋊Dic11—24no—
200C4⋊Dic11—22no—
201C4⋊Dic11C2414yes—
202C4⋊Dic11C2412yes—
203Dic11⋊C4—22no—
204Dic11⋊C4—28no—
205C4×Dic11—22no—
206C4×Dic11—21no—
207C4×Dic11—24no—
208D88—28no—
209#4314—28no—
210#4314—48no—
211#4314—48no—
212#3549—111no—
213#3499—111no—
214#3329—114no—
215#3303—114no—
216D4×SD16—114no—
217#3272—114no—
218#3206—112no—
219#3200—114no—
220#3106—112no—
221#3010—114no—
222#2979D1111yescharacteristic, complemented
223C23×C11C22×D414yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—21no—
226C22×D11—24no—
227C22×D11—84no—
228C22×D11—88no—
229Q8×C11—42no—
230D4×C11—28no—
231D4×C11—42no—
232D4×C11—44no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C2511yescharacteristic
243C22⋊D11—24no—
244C22⋊D11—48no—
245C22⋊D11—84no—
246C22⋊D11—88no—
247C2×Dic11—21no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—48no—
252C2×Dic11—44no—
253D44—21no—
254D44—24no—
255D44—24no—
256D44—44no—
257D44—84no—
258D44—82no—
259D44H(5,𝔽2)12yes—
260C4×D11—24no—
261C4×D11—48no—
262C4×D11—44no—
263C4×D11—48no—
264Dic22—21no—
265Dic22—24no—
266Dic22—24no—
267Dic22—48no—
268Dic22—44no—
269Dic22—82no—
270Dic22H(5,𝔽2)12yes—
271C8×C11—24no—
272C8×C11—24no—
273C2×2−1+4—112no—
274C2×AGL(1,ℤ/8)—114no—
275C22×SD16—114no—
276H(3,𝔽4)—222no—
277#555—114no—
278#555—221no—
279D4×Q8—114no—
280#547—114no—
281#547—224no—
282D42—114no—
283D42—221no—
284#536—112no—
285#536—222no—
286#535—114no—
287#535—224no—
288#532—112no—
289#532—221no—
290#532C2×D1111yescharacteristic
291C2×C4⋊Q8—111no—
292C2×C4⋊Q8—221no—
293C4×#41—111no—
294#492—114no—
295#487—114no—
296#485—118no—
297#482—114no—
298#477—112no—
299#476—112no—
300#468—118no—
301#465—118no—
302#461—114no—
303#461—114no—
304#460—112no—
305#459—112no—
306#450—118no—
307#449—114no—
308#449—118no—
309#448—118no—
310#448—118no—
311C4×SD16—114no—
312C4×D8—114no—
313#436C2×D1114yescomplemented
314C8×D4C2×D1114yescomplemented
315#431C2×D1112yescomplemented
316#419—114no—
317#416—114no—
318#408C2×D1114yescomplemented
319C22×C11—21no—
320C22×C11—24no—
321C22×C11—22no—
322C22×C11—28no—
323C22×C11C23×D411yescharacteristic
324C2×D11—22no—
325C2×D11—42no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—168no—
330C4×C11—21no—
331C4×C11—24no—
332C4×C11—22no—
333C4×C11#57714yes—
334C4×C11C2×H(5,𝔽2)11yescharacteristic
335C4×C11C2×H(5,𝔽2)11yescharacteristic
336Dic11—22no—
337Dic11—44no—
338Dic11—44no—
339Dic11—42no—
3402−1+4—444no—
3412−1+4—444no—
342C2×#41—111no—
343C2×#41—114no—
344C2×#41—222no—
345C2×#41—224no—
346C2×#41—222no—
347C2×#41C22×D1112yes—
348C22×Q8—114no—
349C22×Q8—112no—
350C22×Q8—222no—
351C22×D4—114no—
352C22×D4—224no—
353AGL(1,ℤ/8)—448no—
354C2×SD16—114no—
355C2×SD16—118no—
356C2×SD16—118no—
357C2×SD16—448no—
358C2×D8—114no—
359C2×M16C22×D1114yes—
360C22×C8C22×D1114yes—
361C4⋊Q8—112no—
362C4⋊Q8—114no—
363C4⋊Q8—222no—
364C4⋊Q8—224no—
365C4⋊Q8—221no—
366C4⋊Q8—221no—
367C4⋊Q8D4411yescharacteristic
368#127—112no—
369#127—224no—
370#127D4411yescharacteristic
371#124—224no—
372#124—222no—
373#124—228no—
374#124—222no—
375#124D4412yes—
376#123—224no—
377#123—228no—
378C22⋊Q8—118no—
379C22⋊Q8—228no—
380#121—114no—
381#121—118no—
382#121—224no—
383#121—224no—
384#121—222no—
385#121—224no—
386#121D4414yes—
387#120—224no—
388#120—224no—
389#120—228no—
390C4×Q8—112no—
391C4×D4—112no—
392C4×D4—114no—
393C4×D4—224no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4C22×D1114yes—
397#117—111no—
398#117—114no—
399#117—224no—
400#117—221no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—224no—
403C2×C42—221no—
404C2×C42C22×D1111yescharacteristic
405#107—114no—
406#106—114no—
407C4⋊C8C22×D1112yes—
408C4⋊C8C22×D1112yes—
409#103—118no—
410#103—114no—
411#103—118no—
412#102—114no—
413#102—114no—
414#102—114no—
415C22⋊C8C22×D1114yes—
416C22⋊C8C22×D1118yes—
417C4×C8C22×D1114yes—
418C2×C11—44no—
419C2×C11—41no—
420C2×C11#348411yescharacteristic
421C2×C11C2×#57712yes—
422D11—42no—
423D11—84no—
424C24—224no—
425#41—42no—
426#41—42no—
427#41—222no—
428#41—222no—
429#41—228no—
430#41—444no—
431#41—448no—
432#41—4416no—
433#41—884no—
434C2×Q8—111no—
435C2×Q8—114no—
436C2×Q8—228no—
437C2×Q8—224no—
438C2×Q8—222no—
439C2×Q8—222no—
440C2×Q8—444no—
441C2×Q8—442no—
442C2×Q8—442no—
443C2×Q8—448no—
444C2×Q8C2×D4412yes—
445C2×D4—111no—
446C2×D4—114no—
447C2×D4—221no—
448C2×D4—224no—
449C2×D4—228no—
450C2×D4—224no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—224no—
454C2×D4—444no—
455C2×D4—444no—
456C2×D4—888no—
457C2×D4C2×D4414yes—
458C2×D4C2×D4412yes—
459C2×D4C2×D4414yes—
460C22×C4—221no—
461C22×C4—222no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4C2×D4412yes—
467C22×C4C23×D1111yescharacteristic
468C22×C4C23×D1114yes—
469SD16—228no—
470SD16—448no—
471SD16—448no—
472D8—228no—
473M16—44no—
474C2×C8—44no—
475C2×C8C23×D1114yes—
476C2×C8C23×D1114yes—
477C4⋊C4—112no—
478C4⋊C4—114no—
479C4⋊C4—224no—
480C4⋊C4—228no—
481C4⋊C4—224no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4C2×D4414yes—
485C22⋊C4—221no—
486C22⋊C4—224no—
487C22⋊C4—228no—
488C22⋊C4—222no—
489C22⋊C4—228no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4C2×D4418yes—
493C42—221no—
494C42—222no—
495C42—224no—
496C42C2×D4411yescharacteristic
497C42C2×D4411yescharacteristic
498C42C23×D1112yes—
499C11#6166411yescharacteristic, complemented, Sylow
500C23—221no—
501C23—224no—
502C23—884no—
503C23—888no—
504C23C22×D4414yes—
505C23C22×D4411yescharacteristic
506Q8—42no—
507Q8—112no—
508Q8—221no—
509Q8—224no—
510Q8—224no—
511Q8—448no—
512Q8—444no—
513Q8—882no—
514D4—28no—
515D4—42no—
516D4—44no—
517D4—112no—
518D4—224no—
519D4—221no—
520D4—224no—
521D4—224no—
522D4—448no—
523D4—444no—
524D4—884no—
525D4—882no—
526D4—888no—
527D4—884no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—224no—
534C2×C4—221no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—448no—
539C2×C4—448no—
540C2×C4—444no—
541C2×C4—448no—
542C2×C4—444no—
543C2×C4C22×D4411yescharacteristic
544C2×C4C22×D4414yes—
545C2×C4C22×D4412yes—
546C2×C4C22×D4412yes—
547C2×C4C24×D1111yescharacteristic
548C8—24no—
549C8—24no—
550C22—21no—
551C22—24no—
552C22—22no—
553C22—28no—
554C22—222no—
555C22—442no—
556C22—444no—
557C22—444no—
558C22—444no—
559C22—1768no—
560C22C23×D4411yescharacteristic
561C4—21no—
562C4—24no—
563C4—22no—
564C4—222no—
565C4—444no—
566C4—444no—
567C4—442no—
568C4#1062328214yes—
569C4D11×H(5,𝔽2)11yescharacteristic
570C4D11×H(5,𝔽2)11yescharacteristic
571C2—44no—
572C2—41no—
573C2—442no—
574C2—884no—
575C2#1308225211yescharacteristic
576C2C2×#1062328212yes—
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2979C2
socleC22×C11C23×D4
hypercenter#2979D11
hypocenterC11#61664
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #532 ◁ #2979

Complements

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

NH ≅ G/Ntype
1. #13083021C2semidirect
2. #13082396C2semidirect
3. #13080911C2semidirect
4. #13080545C2semidirect
5. D4×#4314C2semidirect
6. #13080218C2semidirect
7. #13079543C2semidirect
8. #13079489C2semidirect
9. #13078677C2semidirect
10. #13077904C2semidirect
11. C11×#2979C2semidirect
12. C2×#67043C22semidirect
15. #10623356C22semidirect
16. C2×#66961C22semidirect
17. C22×#4314C22semidirect
27. #10623082C22semidirect
29. D4×Dic22C22semidirect
31. C4×#4339C22semidirect
32. C2×#66922C22semidirect
33. C11×#436C22semidirect
34. C8×D4×C11C22semidirect
35. C11×#431C22semidirect
36. C11×#408C22semidirect
37. #10622747C22semidirect
38. #10622733C22semidirect
39. #10622727C22semidirect
40. #10622726C22semidirect
41. #10622463C22semidirect
44. #10622455C22semidirect
45. #10622454C22semidirect
46. #10622454C22semidirect
47. #10622351C22semidirect
48. #10622351C22semidirect
49. #10622350C22semidirect
50. #10622347C22semidirect
51. #10622347C22semidirect
52. #10622344C22semidirect
53. #10622336C22semidirect
55. C4×D88C22semidirect
56. C4×#4314C22semidirect
57. #10622294C22semidirect
222. #2979D11semidirect
313. #436C2×D11semidirect
314. C8×D4C2×D11semidirect
315. #431C2×D11semidirect
318. #408C2×D11semidirect
499. C11#61664semidirect

Maximal subgroups

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

subgroupindex
#130830212
#130823962
#130809112
#130805452
D4×#43142
#130802182
#130795432
#130794892
#130786772
#130779042
C11×#29792
#6166411