Finite Group Databasebeta

← #14737253

Subgroups — #14737253

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#13079066C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068093C212yesmaximal, complemented
5#13068079C212yesmaximal, complemented
6#13067969C212yesmaximal, complemented
7#13067955C212yesmaximal, complemented
8#13067369C211yesmaximal, characteristic, complemented
9#13067263C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3205C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×#67001—21no—
15C2×#66985—21no—
16C2×#66985—21no—
17#10623008C2211yescharacteristic
18C11×#493—21no—
19C11×#486—21no—
20C11×#459C2212yes—
21C11×#459C2212yes—
22C11×#447—22no—
23C11×#431C2211yescharacteristic
24#10622847—21no—
25#10622700—21no—
26#10622689C2212yes—
27#10622687—22no—
28#10622686C2212yes—
29#10622685—21no—
30#10622651—22no—
31#10622628C2212yescomplemented
32#10622625C2212yescomplemented
33#10622624—22no—
34D4×C11⋊C8C2212yescomplemented
35#10622620C2212yescomplemented
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622182C2212yes—
40#10622182C2212yes—
41#10622124C2211yescharacteristic, complemented
42#10622124C2211yescharacteristic, complemented
43#10622123C2211yescharacteristic, complemented
44#10622123C2211yescharacteristic, complemented
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C2×C11×#41—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C2×#4339—21no—
52C2×C11×D8—22no—
53C2×C11×D8—22no—
54C11×C4⋊Q8D411yescharacteristic
55C11×#127—21no—
56C11×#127—21no—
57C11×#127—21no—
58C11×#127D411yescharacteristic
59C11×#127C2312yes—
60C11×#124—21no—
61C11×#121—21no—
62C11×#121D412yes—
63C4×D4×C11—21no—
64C4×D4×C11C2312yes—
65C2×C42×C11C2311yescharacteristic
66#67001—44no—
67C2×#4324—22no—
68C2×#4324—22no—
69#66985—44no—
70#66985—44no—
71C2×#4323—22no—
72C2×#4323—22no—
73C2×#4323—22no—
74#66983—21no—
75#66983—21no—
76C2×#4318—22no—
77C2×#4318D411yescharacteristic
78C2×#4318D411yescharacteristic
79C22×C11⋊C8—21no—
80C22×C11⋊C8—21no—
81C22×C11⋊C8—22no—
82#66928—21no—
83#66927C2311yescharacteristic
84C4×D44—21no—
85C4×D44—21no—
86#66922C2311yescharacteristic
87C11×C4⋊C8C2311yescharacteristic
88C11×C4⋊C8C2311yescharacteristic
89C11×#102—22no—
90C11×#102—22no—
91C11×C22⋊C8—21no—
92C4×C8×C11—21no—
93#66896—22no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)—22no—
96#66873—22no—
97#66871—22no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103#66867D412yes—
104C4×C11⋊C8C2312yes—
105#19230—111nomaximal, Sylow
106C24×C11—41no—
107C11×#41—42no—
108C11×#41—42no—
109C2×Q8×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—81no—
122C2×D4×C11—81no—
123C2×D4×C11—82no—
124C2×D4×C11C2×D412yes—
125C22×C4×C11—22no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C2×C22⋊D11—41no—
130#4339—42no—
131#4339—42no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×Dic22—21no—
137C11×D8—82no—
138C11×D8—82no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C2×D412yes—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11#4111yescharacteristic
148C42×C11C2411yescharacteristic
149#4324—44no—
150#4324—44no—
151#4323—44no—
152#4323—44no—
153#4323—82no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158#4318—22no—
159#4318—44no—
160#4318D814yescomplemented
161C2×C11⋊C8—22no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—44no—
165C2×C11⋊C8—42no—
166C2×C11⋊C8—81no—
167C2×C11⋊C8C2×D412yes—
168C2×C11⋊C8C2×D412yes—
169#3245—111no—
170#3205D1111yescharacteristic, complemented
171#3151—111no—
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—22no—
181C23×C11—42no—
182C23×C11—82no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11#12111yescharacteristic
186C22×D11—41no—
187Q8×C11—42no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—44no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—81no—
197D4×C11—82no—
198D4×C11—82no—
199D4×C11—82no—
200D4×C11—82no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11C2×D812yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C22⋊D11—82no—
216C2×Dic11—41no—
217D44—41no—
218D44—41no—
219D44—41no—
220D44—41no—
221D44—81no—
222C4×D11—82no—
223Dic22—41no—
224Dic22—41no—
225C8×C11—41no—
226C8×C11—41no—
227C11⋊C8—22no—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—42no—
231C11⋊C8C2×D814yes—
232C2×AGL(1,ℤ/8)—221no—
233C2×AGL(1,ℤ/8)—221no—
234C2×#131—221no—
235#532—111no—
236#532C2×D1111yescharacteristic
237C2×#127C2×D1111yescharacteristic
238#496—222no—
239#493—21no—
240#493—112no—
241#492—112no—
242#486—21no—
243#474—112no—
244#474—221no—
245#466—222no—
246#459—112no—
247#459—221no—
248#459C2×D1112yes—
249#459C2×D1112yes—
250#447—22no—
251#436—112no—
252#435—222no—
253C8×D4—112no—
254#431C2×D1111yescharacteristic
255C2×C4⋊C8—111no—
256C2×C4⋊C8—111no—
257#408—221no—
258C4×M16—111no—
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—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—164no—
276C22×C11#45912yes—
277C22×C11C2×#12111yescharacteristic
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—42no—
285C4×C11#45912yes—
286C4×C11C22×D811yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11#57611yescharacteristic
289C4×C11#57711yescharacteristic
290Dic11—81no—
291C2×#41—21no—
292C2×#41—221no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296AGL(1,ℤ/8)—444no—
297AGL(1,ℤ/8)—444no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×D8—22no—
301C2×D8—22no—
302C2×D8—222no—
303C2×D8—222no—
304C2×D8—222no—
305#131—444no—
306C2×M16—111no—
307C2×M16—111no—
308C2×M16—222no—
309C22×C8—222no—
310C22×C8—221no—
311C22×C8—221no—
312C4⋊Q8—111no—
313C4⋊Q8C22⋊D1111yescharacteristic
314#127—21no—
315#127—21no—
316#127—21no—
317#127—111no—
318#127C22⋊D1111yescharacteristic
319#127C22×D1112yes—
320#124—21no—
321#124—221no—
322#121—21no—
323#121—221no—
324#121—221no—
325#121C22⋊D1112yes—
326C4×D4—21no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4C22×D1112yes—
330C2×C42C22×D1111yescharacteristic
331#107—222no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—112no—
335C4⋊C8—221no—
336C4⋊C8—221no—
337C4⋊C8C22×D1111yescharacteristic
338C4⋊C8C22×D1111yescharacteristic
339#102—22no—
340#102—22no—
341#102—222no—
342#102—222no—
343C22⋊C8—21no—
344C22⋊C8—222no—
345C22⋊C8—222no—
346#97—112no—
347C4×C8—21no—
348C4×C8—112no—
349C2×C11—22no—
350C2×C11—82no—
351C2×C11—162no—
352C2×C11C2×#45911yescharacteristic
353C2×C11#306211yescharacteristic
354C2×C11#306811yescharacteristic
355D11—161no—
356C24—41no—
357#41—42no—
358#41—42no—
359#41—442no—
360#41—442no—
361C2×Q8—21no—
362C2×Q8—221no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—81no—
375C2×D4—81no—
376C2×D4—82no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—441no—
381C2×D4C2×C22⋊D1112yes—
382C22×C4—22no—
383C22×C4—441no—
384C22×C4D4×D1111yescharacteristic
385C22×C4#434111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387SD16—444no—
388SD16—444no—
389D8—82no—
390D8—82no—
391D8—444no—
392D8—444no—
393D8—882no—
394M16—114no—
395M16—222no—
396M16—444no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—112no—
400C2×C8—112no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—222no—
404C2×C8—444no—
405C2×C8—442no—
406C2×C8—881no—
407C4⋊C4—21no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4C2×C22⋊D1112yes—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42D4×D1111yescharacteristic
416C42#434111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C42C23×D1111yescharacteristic
419C11#1923011yescharacteristic, complemented, Sylow
420C23—22no—
421C23—42no—
422C23—82no—
423C23—82no—
424C23—82no—
425C23—441no—
426C23#6699211yescharacteristic
427Q8—42no—
428Q8—441no—
429Q8—441no—
430D4—22no—
431D4—22no—
432D4—44no—
433D4—42no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—81no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4—82no—
443D4—441no—
444D4—441no—
445D4—441no—
446D4—441no—
447D4—881no—
448D4—882no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—441no—
456C2×C4—882no—
457C2×C4D8×D1112yes—
458C2×C4#6696412yes—
459C2×C4#6699211yescharacteristic
460C2×C4#6699211yescharacteristic
461C2×C4#6699211yescharacteristic
462C2×C4C2×D4×D1111yescharacteristic
463C2×C4C2×#434111yescharacteristic
464C2×C4C22×C22⋊D1111yescharacteristic
465C8—41no—
466C8—41no—
467C8—114no—
468C8—222no—
469C8—441no—
470C8—441no—
471C8—442no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—82no—
478C22—82no—
479C22—82no—
480C22—164no—
481C22—881no—
482C22—881no—
483C22—881no—
484C22#1062276312yes—
485C22C2×#6699211yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—881no—
491C4#1062276312yes—
492C4C2×D8×D1111yescharacteristic
493C4C2×#6696411yescharacteristic
494C4#1062336611yescharacteristic
495C4#1062336711yescharacteristic
496C2—22no—
497C2—82no—
498C2—162no—
499C2—1761no—
500C2C2×#1062276311yescharacteristic
501C2#1307829211yescharacteristic
502C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3205C2
socleC22×C11C2×#121
hypercenter#3205D11
hypocenterC11#19230
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13079923C2semidirect
2. #13079066C2semidirect
3. #13077360C2semidirect
4. #13068093C2semidirect
5. #13068079C2semidirect
6. #13067969C2semidirect
7. #13067955C2semidirect
8. #13067369C2semidirect
9. #13067263C2semidirect
10. C2×#10622182C2semidirect
11. C11×#3205C2semidirect
31. #10622628C22semidirect
32. #10622625C22semidirect
34. D4×C11⋊C8C22semidirect
35. #10622620C22semidirect
41. #10622124C22semidirect
42. #10622124C22semidirect
43. #10622123C22semidirect
44. #10622123C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
160. #4318D8semidirect
170. #3205D11semidirect
419. C11#19230semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130790662
#130773602
#130680932
#130680792
#130679692
#130679552
#130673692
#130672632
C2×#106221822
C11×#32052
#1923011