Finite Group Databasebeta

← #14737251

Subgroups — #14737251

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic, complemented
2#13079534C211yesmaximal, characteristic, complemented
3#13077362C211yesmaximal, characteristic, complemented
4#13068092C212yesmaximal, complemented
5#13068078C212yesmaximal, complemented
6#13067968C212yesmaximal, complemented
7#13067954C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067265C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3151C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×AGL(1,ℤ/8)—21no—
14C11×#532C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16C2×#66960—21no—
17#10623008C2211yescharacteristic
18C11×#496—22no—
19C11×#493C2212yes—
20C11×#492C2212yes—
21C4×C11×M16C2211yescharacteristic
22#10622830—22no—
23#10622742—21no—
24#10622700C2212yescomplemented
25#10622686—21no—
26#10622685C2212yes—
27#10622685C2212yes—
28#10622685C2212yescomplemented
29#10622683—21no—
30#10622651—22no—
31#10622628—21no—
32#10622620—21no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622319—22no—
37#10622301C2212yescomplemented
38C8×D44C2212yescomplemented
39#10622185C2211yescharacteristic, complemented
40#10622185C2211yescharacteristic, complemented
41#10622182C2212yes—
42#10622182C2212yes—
43#10622182C2211yescharacteristic, complemented
44#10622182C2211yescharacteristic, complemented
45#10622096C2212yescomplemented
46#10622095C2212yescomplemented
47C2×C11×#41—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C2×#4339—21no—
52C11×AGL(1,ℤ/8)—44no—
53C11×AGL(1,ℤ/8)—44no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C2×C11×D8—22no—
57C2×C11×D8—22no—
58C2×C11×M16D411yescharacteristic
59C2×C11×M16D411yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×#127—21no—
62C11×#127—21no—
63C11×#127—21no—
64C11×#127C2312yes—
65C11×#127C2311yescharacteristic
66C11×#124—21no—
67C11×#121—21no—
68C11×#121—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4323—22no—
73C2×#4323—22no—
74C2×#4323—22no—
75#66983—21no—
76#66983D412yes—
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79#66960—44no—
80C2×#4313—22no—
81C2×C8×D11—22no—
82#66928—21no—
83#66927D411yescharacteristic
84C4×D44—21no—
85C4×D44C2312yes—
86#66922D411yescharacteristic
87C11×#97D412yes—
88C4×C8×C11C2312yes—
89#66896—22no—
90#66896—22no—
91#66896—22no—
92C22⋊(C11⋊C8)—21no—
93(C2×D11)⋊C8—22no—
94(C2×D11)⋊C8—22no—
95#66873—22no—
96#66871—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4×C11⋊C8—21no—
105#19230—111nomaximal, Sylow
106C24×C11—41no—
107C11×#41—42no—
108C11×#41—42no—
109C2×Q8×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—81no—
123C2×D4×C11—81no—
124C2×D4×C11—82no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C2×C22⋊D11—22no—
130#4339—42no—
131#4339—42no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44C2×D412yes—
135C2×C4×D11—22no—
136C2×Dic22—21no—
137C11×SD16—44no—
138C11×SD16—44no—
139C11×D8—44no—
140C11×D8—44no—
141C11×M16—22no—
142C11×M16D814yescomplemented
143C2×C8×C11C2×D412yes—
144C2×C8×C11C2×D412yes—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11#4111yescharacteristic
152C42×C11C2411yescharacteristic
153#4323—82no—
154#4323—82no—
155#4323—82no—
156(C2×D11)⋊C4—22no—
157(C2×D11)⋊C4—22no—
158C4⋊Dic11—21no—
159C4⋊Dic11C2×D412yes—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—42no—
166C2×C11⋊C8—81no—
167#4313—44no—
168C8×D11—44no—
169#3245—111no—
170#3205—111no—
171#3151D1111yescharacteristic, complemented
172#2935—111no—
173#1687—112no—
174#1685—112no—
175#1667—112no—
176#1665—112no—
177#1565—111no—
178#1540—111no—
179C2×#331—111no—
180C23×C11—41no—
181C23×C11—42no—
182C23×C11—82no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11#12111yescharacteristic
186C22×D11—22no—
187Q8×C11—41no—
188Q8×C11—41no—
189D4×C11—41no—
190D4×C11—42no—
191D4×C11—41no—
192D4×C11—42no—
193D4×C11—41no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—41no—
197D4×C11—81no—
198D4×C11—82no—
199D4×C11—82no—
200D4×C11—82no—
201D4×C11—82no—
202D4×C11—82no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—82no—
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11C2×D812yes—
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C22⋊D11—44no—
217C2×Dic11—22no—
218D44—22no—
219D44—22no—
220D44—42no—
221D44—81no—
222C4×D11—42no—
223C4×D11—42no—
224Dic22—42no—
225C8×C11—22no—
226C8×C11C2×D814yes—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C11⋊C8—42no—
230C11⋊C8—41no—
231C11⋊C8—41no—
232C2×AGL(1,ℤ/8)—21no—
233C2×AGL(1,ℤ/8)—21no—
234C2×#131—221no—
235#532—111no—
236#532C2×D1111yescharacteristic
237C2×#127C2×D1111yescharacteristic
238#496—22no—
239#493—221no—
240#493C2×D1112yes—
241#492C2×D1112yes—
242#486—221no—
243#474—112no—
244#474—221no—
245#466—222no—
246#459—112no—
247#459—112no—
248#459—112no—
249#459—221no—
250#447—222no—
251#436—112no—
252#435—222no—
253C8×D4—112no—
254#431—111no—
255C2×C4⋊C8—111no—
256C2×C4⋊C8—111no—
257#408—221no—
258C4×M16C2×D1111yescharacteristic
259#335—112no—
260#334—112no—
261#332—111no—
262#332—111no—
263#331—112no—
264#331—112no—
265#331—111no—
266#331—111no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—81no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—81no—
273C22×C11—82no—
274C22×C11—81no—
275C22×C11—164no—
276C22×C11#45912yes—
277C22×C11C2×#12111yescharacteristic
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—42no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—81no—
285C4×C11#45912yes—
286C4×C11C22×D811yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11#57611yescharacteristic
289C4×C11#57711yescharacteristic
290Dic11—42no—
291C2×#41—21no—
292C2×#41—221no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296AGL(1,ℤ/8)—44no—
297AGL(1,ℤ/8)—44no—
298C2×SD16—22no—
299C2×SD16—22no—
300C2×D8—22no—
301C2×D8—22no—
302C2×D8—222no—
303C2×D8—222no—
304C2×D8—222no—
305#131—444no—
306C2×M16—222no—
307C2×M16C22⋊D1111yescharacteristic
308C2×M16C22⋊D1111yescharacteristic
309C22×C8—221no—
310C22×C8—221no—
311C22×C8—222no—
312C4⋊Q8—111no—
313C4⋊Q8C22×D1111yescharacteristic
314#127—21no—
315#127—21no—
316#127—21no—
317#127—111no—
318#127C22×D1112yes—
319#127C22×D1111yescharacteristic
320#124—21no—
321#124—221no—
322#121—21no—
323#121—21no—
324#121—112no—
325#121—221no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—112no—
329C4×D4—221no—
330C2×C42C22×D1111yescharacteristic
331#107—222no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—112no—
335C4⋊C8—111no—
336C4⋊C8—111no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339#102—222no—
340#102—222no—
341#102—222no—
342#102—222no—
343C22⋊C8—221no—
344C22⋊C8—222no—
345C22⋊C8—222no—
346#97C22⋊D1112yes—
347C4×C8—221no—
348C4×C8C22×D1112yes—
349C2×C11—22no—
350C2×C11—161no—
351C2×C11—162no—
352C2×C11C2×#45911yescharacteristic
353C2×C11#306211yescharacteristic
354C2×C11#306811yescharacteristic
355D11—82no—
356C24—41no—
357#41—42no—
358#41—42no—
359#41—442no—
360#41—442no—
361C2×Q8—21no—
362C2×Q8—221no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—41no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—81no—
376C2×D4—81no—
377C2×D4—82no—
378C2×D4—112no—
379C2×D4—222no—
380C2×D4—221no—
381C2×D4—221no—
382C22×C4—41no—
383C22×C4—222no—
384C22×C4D4×D1111yescharacteristic
385C22×C4#434111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387SD16—44no—
388SD16—44no—
389D8—44no—
390D8—44no—
391D8—882no—
392D8—882no—
393D8—882no—
394M16—22no—
395M16—444no—
396M16#432314yescomplemented
397C2×C8—221no—
398C2×C8—221no—
399C2×C8—222no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—442no—
403C2×C8—444no—
404C2×C8—881no—
405C2×C8C2×C22⋊D1112yes—
406C2×C8C2×C22⋊D1112yes—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—112no—
410C4⋊C4—221no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—222no—
414C22⋊C4—222no—
415C42D4×D1111yescharacteristic
416C42#434111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C42C23×D1111yescharacteristic
419C11#1923011yescharacteristic, complemented, Sylow
420C23—41no—
421C23—42no—
422C23—82no—
423C23—82no—
424C23—82no—
425C23—222no—
426C23#6699111yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—442no—
430D4—41no—
431D4—42no—
432D4—42no—
433D4—41no—
434D4—41no—
435D4—42no—
436D4—41no—
437D4—42no—
438D4—81no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4—82no—
443D4—82no—
444D4—222no—
445D4—222no—
446D4—444no—
447D4—442no—
448D4—881no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—82no—
454C2×C4—222no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4C2×#432312yes—
458C2×C4#6698512yes—
459C2×C4#6699111yescharacteristic
460C2×C4#6699111yescharacteristic
461C2×C4#6699111yescharacteristic
462C2×C4C2×D4×D1111yescharacteristic
463C2×C4C2×#434111yescharacteristic
464C2×C4C22×C22⋊D1111yescharacteristic
465C8—22no—
466C8—442no—
467C8—441no—
468C8—441no—
469C8—441no—
470C8—441no—
471C8C2×#432314yes—
472C22—21no—
473C22—21no—
474C22—81no—
475C22—82no—
476C22—82no—
477C22—81no—
478C22—82no—
479C22—81no—
480C22—164no—
481C22—442no—
482C22—442no—
483C22—442no—
484C22#1062268512yes—
485C22C2×#6699111yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—81no—
490C4—442no—
491C4#1062268512yes—
492C4#1062330511yescharacteristic
493C4#1062330611yescharacteristic
494C4C22×#432311yescharacteristic
495C4C2×#6698511yescharacteristic
496C2—22no—
497C2—162no—
498C2—161no—
499C2—882no—
500C2C2×#1062268511yescharacteristic
501C2#1307829011yescharacteristic
502C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3151C2
socleC22×C11C2×#121
hypercenter#3151D11
hypocenterC11#19230
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. #13079923C2semidirect
2. #13079534C2semidirect
3. #13077362C2semidirect
4. #13068092C2semidirect
5. #13068078C2semidirect
6. #13067968C2semidirect
7. #13067954C2semidirect
8. #13067368C2semidirect
9. #13067265C2semidirect
10. C2×#10622182C2semidirect
11. C11×#3151C2semidirect
24. #10622700C22semidirect
28. #10622685C22semidirect
37. #10622301C22semidirect
38. C8×D44C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
43. #10622182C22semidirect
44. #10622182C22semidirect
45. #10622096C22semidirect
46. #10622095C22semidirect
142. C11×M16D8semidirect
171. #3151D11semidirect
396. M16#4323semidirect
419. C11#19230semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130795342
#130773622
#130680922
#130680782
#130679682
#130679542
#130673682
#130672652
C2×#106221822
C11×#31512
#1923011