Finite Group Databasebeta

← #14730642

Subgroups — #14730642

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079810C211yesmaximal, characteristic, complemented
2#13079330C211yesmaximal, characteristic, complemented
3#13078624C211yesmaximal, characteristic, complemented
4#13067851C212yesmaximal, complemented
5#13067795C212yesmaximal, complemented
6#13067767C212yesmaximal, complemented
7#13067732C212yesmaximal, complemented
8#13067321C211yesmaximal, characteristic, complemented
9#13067059C211yesmaximal, characteristic, complemented
10#13067033C211yesmaximal, characteristic, complemented
11C11×#3496C211yesmaximal, characteristic
12C2×C11×H(5,𝔽2)—21no—
13C11×#547—21no—
14C11×#547C2212yes—
15C11×#546—22no—
16C11×#546—22no—
17D42×C11—21no—
18D42×C11C2212yes—
19C11×#537—21no—
20C11×#534—22no—
21C11×#532C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C2×C11×#121—22no—
24C2×C4×D4×C11C2211yescharacteristic
25#10623001C2211yescharacteristic, complemented
26#10622831—21no—
27#10622706C2211yescharacteristic, complemented
28#10622693—21no—
29#10622691C2211yescharacteristic, complemented
30#10622689C2211yescharacteristic, complemented
31#10622684—21no—
32#10622683C2211yescharacteristic, complemented
33#10622655—22no—
34#10622648—22no—
35#10622632C2212yescomplemented
36#10622631—22no—
37C4×#4324—22no—
38#10622621C2212yescomplemented
39#10622621C2212yescomplemented
40#10622620C2212yescomplemented
41#10622584—21no—
42#10622539C2211yescharacteristic, complemented
43#10622538C2211yescharacteristic, complemented
44C4×#4318C2211yescharacteristic, complemented
45#10622185C2212yescomplemented
46#10622182C2212yescomplemented
47D4⋊(C11⋊C8)C2212yescomplemented
48D4⋊(C11⋊C8)C2212yescomplemented
49D4⋊(C11⋊C8)C2212yescomplemented
50D4⋊(C11⋊C8)C2212yescomplemented
51C11×H(5,𝔽2)—48no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41—21no—
55C2×C11×#41—21no—
56C22×D4×C11—24no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11D411yescharacteristic
61C23×C4×C11—21no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127D411yescharacteristic
65C11×#127C2311yescharacteristic
66C11×#124—21no—
67C11×#124—21no—
68C11×#123—24no—
69C11×#123—24no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×#121—24no—
73C11×#121—24no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—21no—
77C11×#121—21no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121D412yes—
81C11×#121D412yes—
82C11×#120—24no—
83C11×#120—24no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11D412yes—
89C4×D4×C11D412yes—
90C4×D4×C11C2312yes—
91C4×D4×C11C2312yes—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—21no—
96C2×C42×C11C2311yescharacteristic
97C2×#4324—22no—
98C2×#4324—22no—
99#66979—21no—
100#66977—21no—
101#66977—21no—
102C2×#4318—21no—
103#66923—21no—
104#66922C2311yescharacteristic
105#66922C2311yescharacteristic
106C4×Dic22—21no—
107C4×Dic22—21no—
108#66896—22no—
109#66896—22no—
110#66896—22no—
111#66896—22no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114#66874—22no—
115#66874—22no—
116#66872—22no—
117#66872—22no—
118#66871—22no—
119#66871—22no—
120C4⋊(C11⋊C8)C2312yes—
121C4⋊(C11⋊C8)C2312yes—
122#66867—21no—
123#66867—21no—
124C4×C11⋊C8—21no—
125C4×C11⋊C8C2311yescharacteristic
126C4×C11⋊C8C2311yescharacteristic
127#18599—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11—24no—
130C11×#41—44no—
131C11×#41—44no—
132C11×#41—48no—
133C11×#41—44no—
134C11×#41—44no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—48no—
149C2×D4×C11—44no—
150C2×D4×C11—416no—
151C2×D4×C11—44no—
152C2×D4×C11—84no—
153C2×D4×C11C2×D412yes—
154C2×D4×C11C2×D412yes—
155C2×D4×C11C2×D412yes—
156C22×C4×C11—24no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—82no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C2×Dic22—21no—
167C2×Dic22—21no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—41no—
188#4324—44no—
189#4324—44no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196C4×Dic11—41no—
197#4318—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—22no—
202#3496D1111yescharacteristic
203#3235—111no—
204#3182—111no—
205#3101—111no—
206#1647—112no—
207#1639—112no—
208#1635—112no—
209#1629—112no—
210#1553—111no—
211#1490—111no—
212#1484—111no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—48no—
218C23×C11—81no—
219C23×C11—81no—
220C23×C11—84no—
221C23×C11—84no—
222C23×C11#12011yescharacteristic
223Q8×C11—42no—
224Q8×C11—42no—
225D4×C11—24no—
226D4×C11—22no—
227D4×C11—24no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—44no—
231D4×C11—44no—
232D4×C11—48no—
233D4×C11—48no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—81no—
237D4×C11—84no—
238D4×C11AGL(1,ℤ/8)14yes—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11—44no—
246C2×C4×C11—48no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11—82no—
251C2×C4×C11—81no—
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×Dic11—41no—
259C2×Dic11—41no—
260Dic22—42no—
261Dic22—42no—
262C11⋊C8—22no—
263C11⋊C8—41no—
264C11⋊C8—42no—
265C11⋊C8—42no—
266C2×H(5,𝔽2)—21no—
267#547—21no—
268#547C2×D1112yes—
269#546—22no—
270#546—22no—
271D42—21no—
272D42C2×D1112yes—
273#537—21no—
274#534—22no—
275#533—111no—
276#532C2×D1111yescharacteristic
277#532C2×D1111yescharacteristic
278C2×#121—22no—
279C2×C4×D4C2×D1111yescharacteristic
280#501—221no—
281#500—111no—
282#492—111no—
283#490—221no—
284#487—111no—
285#486—111no—
286#483—221no—
287#482—222no—
288#476—112no—
289#476—112no—
290#474—112no—
291#468—222no—
292#461—112no—
293#450—221no—
294#440—222no—
295C4×SD16—222no—
296#432—111no—
297#431—111no—
298C4×M16—111no—
299#332—112no—
300#331—112no—
301D4⋊C8—112no—
302D4⋊C8—112no—
303D4⋊C8—112no—
304D4⋊C8—112no—
305C22×C11—21no—
306C22×C11—24no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—84no—
318C22×C11—168no—
319C22×C11C2×#12011yescharacteristic
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11C2×AGL(1,ℤ/8)12yes—
328C4×C11#57712yes—
329Dic11—81no—
330Dic11—81no—
331H(5,𝔽2)—48no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—21no—
335C2×#41—21no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4C22⋊D1111yescharacteristic
341C23×C4—21no—
342C2×SD16—222no—
343C2×SD16—222no—
344C2×M16—221no—
345C4⋊Q8—111no—
346C4⋊Q8—111no—
347C4⋊Q8C22⋊D1111yescharacteristic
348C4⋊Q8C22×D1111yescharacteristic
349#127C22⋊D1111yescharacteristic
350#127C22×D1111yescharacteristic
351#125—221no—
352#124—21no—
353#124—21no—
354#123—24no—
355#123—24no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360#121—24no—
361#121—24no—
362#121—22no—
363#121—22no—
364#121—21no—
365#121—21no—
366#121—22no—
367#121—22no—
368#121C22⋊D1112yes—
369#121C22⋊D1112yes—
370#120—24no—
371#120—24no—
372C4×Q8—221no—
373C4×Q8—221no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C22⋊D1112yes—
379C4×D4C22⋊D1112yes—
380C4×D4C22×D1112yes—
381C4×D4C22×D1112yes—
382#117—221no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4C22⋊D1111yescharacteristic
385C2×C22⋊C4—24no—
386C2×C22⋊C4—21no—
387C2×C42C22×D1111yescharacteristic
388#107—222no—
389#107—222no—
390#106—222no—
391#106—222no—
392C4⋊C8—112no—
393C4⋊C8—112no—
394#103—222no—
395#103—222no—
396#102—222no—
397#102—222no—
398#102—222no—
399#102—222no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402#97—221no—
403#97—221no—
404C4×C8—111no—
405C4×C8—111no—
406C4×C8—221no—
407C2×C11—41no—
408C2×C11—44no—
409C2×C11—82no—
410C2×C11—82no—
411C2×C11#300311yescharacteristic
412C2×C11#300911yescharacteristic
413C2×C11#301811yescharacteristic
414C24—21no—
415C24—24no—
416#41—44no—
417#41—44no—
418#41—48no—
419#41—44no—
420#41—44no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—24no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—48no—
437C2×D4—44no—
438C2×D4—416no—
439C2×D4—44no—
440C2×D4—84no—
441C2×D4C2×C22⋊D1112yes—
442C2×D4C2×C22⋊D1112yes—
443C2×D4C2×C22⋊D1112yes—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—82no—
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454SD16—444no—
455SD16—444no—
456M16—442no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—222no—
460C2×C8—222no—
461C4⋊C4—24no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C4⋊C4C2×C22⋊D1112yes—
472C4⋊C4C2×C22⋊D1112yes—
473C4⋊C4C2×C22⋊D1112yes—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—441no—
483C42—441no—
484C42C2×C22⋊D1111yescharacteristic
485C42C2×C22⋊D1111yescharacteristic
486C42C2×C22⋊D1111yescharacteristic
487C42C23×D1111yescharacteristic
488C11#1859911yescharacteristic, complemented, Sylow
489C23—24no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—48no—
494C23—81no—
495C23—81no—
496C23—84no—
497C23—84no—
498C23#6700611yescharacteristic
499Q8—42no—
500Q8—42no—
501Q8—442no—
502Q8—442no—
503D4—24no—
504D4—22no—
505D4—24no—
506D4—42no—
507D4—42no—
508D4—44no—
509D4—44no—
510D4—48no—
511D4—48no—
512D4—42no—
513D4—42no—
514D4—81no—
515D4—84no—
516D4#6698514yes—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—44no—
528C2×C4—82no—
529C2×C4—81no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4#6700611yescharacteristic
533C2×C4#6700611yescharacteristic
534C2×C4#6700611yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C2×C4C22×C22⋊D1111yescharacteristic
538C8—222no—
539C8—441no—
540C8—442no—
541C8—442no—
542C22—21no—
543C22—24no—
544C22—21no—
545C22—21no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—84no—
555C22—168no—
556C22C2×#6700611yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—881no—
565C4—881no—
566C4C2×#6698512yes—
567C4#1062336712yes—
568C2—41no—
569C2—44no—
570C2—82no—
571C2—82no—
572C2#1307784311yescharacteristic
573C2#1307789311yescharacteristic
574C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18599
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13079810C2semidirect
2. #13079330C2semidirect
3. #13078624C2semidirect
4. #13067851C2semidirect
5. #13067795C2semidirect
6. #13067767C2semidirect
7. #13067732C2semidirect
8. #13067321C2semidirect
9. #13067059C2semidirect
10. #13067033C2semidirect
25. #10623001C22semidirect
27. #10622706C22semidirect
29. #10622691C22semidirect
30. #10622689C22semidirect
32. #10622683C22semidirect
35. #10622632C22semidirect
38. #10622621C22semidirect
39. #10622621C22semidirect
40. #10622620C22semidirect
42. #10622539C22semidirect
43. #10622538C22semidirect
44. C4×#4318C22semidirect
45. #10622185C22semidirect
46. #10622182C22semidirect
47. D4⋊(C11⋊C8)C22semidirect
48. D4⋊(C11⋊C8)C22semidirect
49. D4⋊(C11⋊C8)C22semidirect
50. D4⋊(C11⋊C8)C22semidirect
488. C11#18599semidirect

Maximal subgroups

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

subgroupindex
#130798102
#130793302
#130786242
#130678512
#130677952
#130677672
#130677322
#130673212
#130670592
#130670332
C11×#34962
#1859911