Finite Group Databasebeta

← #14737259

Subgroups — #14737259

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#13079531C211yesmaximal, characteristic, complemented
2#13079069C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic, complemented
4#13068093C212yesmaximal, complemented
5#13068083C212yesmaximal, complemented
6#13067969C212yesmaximal, complemented
7#13067959C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067265C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#3245C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67002—21no—
15C2×#67002—21no—
16C2×#67001—21no—
17C2×#66927C2211yescharacteristic
18C11×#474—21no—
19C11×#474C2212yescomplemented
20C11×#466—22no—
21C11×#459—21no—
22C11×#459C2212yescomplemented
23C2×C11×C4⋊C8C2211yescharacteristic
24#10622847—21no—
25#10622701—21no—
26#10622698C2212yes—
27#10622686—21no—
28#10622686C2212yes—
29#10622671—22no—
30#10622649—22no—
31#10622628C2212yes—
32#10622628C2212yes—
33#10622625C2212yescomplemented
34#10622624—22no—
35D4×C11⋊C8C2212yescomplemented
36#10622538C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×#4318C2211yescharacteristic
39#10622185C2211yescharacteristic, complemented
40#10622185C2211yescharacteristic, complemented
41#10622182C2211yescharacteristic, complemented
42#10622182C2211yescharacteristic, complemented
43#10622123C2212yes—
44#10622123C2212yes—
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C2×C11×D8—22no—
53C22×C8×C11—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127D411yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#124—21no—
60C11×#121—21no—
61C11×#121—21no—
62C11×#121—21no—
63C11×#121D412yes—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11C2312yes—
68C2×C42×C11C2311yescharacteristic
69#67002—44no—
70#67002—44no—
71#67001—44no—
72C2×#4325—22no—
73C2×#4325—22no—
74C2×#4323—22no—
75C2×#4323—22no—
76C2×#4323—22no—
77C2×#4323—22no—
78C2×#4318—22no—
79C2×#4318D411yescharacteristic
80C2×#4318D411yescharacteristic
81C22×C11⋊C8—21no—
82C22×C11⋊C8—22no—
83#66927—21no—
84#66927—21no—
85#66927—21no—
86#66927C2312yes—
87C11×#107—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2312yes—
90C11×#102—22no—
91C11×#102—22no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)—22no—
94C22⋊(C11⋊C8)—22no—
95#66873—22no—
96#66873—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2311yescharacteristic
102#66867D412yes—
103C4×C11⋊C8—21no—
104C4×C11⋊C8C2312yes—
105#19230—111nomaximal, Sylow
106C23×D11—41no—
107C11×#41—42no—
108C11×#41—42no—
109C11×#41—42no—
110C11×#41—42no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C2×D4×C11C2×D412yes—
121C22×C4×C11—22no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—41no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—81no—
135C2×D44—81no—
136C2×D44—82no—
137C11×D8—82no—
138C2×C8×C11—22no—
139C2×C8×C11—81no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4C2×D412yes—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11#4111yescharacteristic
151C42×C11C2411yescharacteristic
152#4325—44no—
153#4325—44no—
154#4323—44no—
155#4323—44no—
156#4323—82no—
157#4323—82no—
158#4318—22no—
159#4318—44no—
160#4318D814yescomplemented
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—44no—
166C2×C11⋊C8—42no—
167C2×C11⋊C8C2×D412yes—
168C2×C11⋊C8C2×D412yes—
169#3245D1111yescharacteristic, complemented
170#3205—111no—
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—41no—
182C23×C11#12111yescharacteristic
183C22×D11—42no—
184C22×D11—82no—
185C22×D11—82no—
186C22×D11—82no—
187Q8×C11—42no—
188Q8×C11—41no—
189Q8×C11—41no—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—44no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—42no—
198D4×C11—81no—
199D4×C11—81no—
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—41no—
208C2×C4×C11—82no—
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11C2×D812yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217D44—42no—
218D44—42no—
219D44—42no—
220D44—42no—
221D44—82no—
222D44—82no—
223D44—82no—
224D44—82no—
225C8×C11—42no—
226C11⋊C8—22no—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—41no—
231C11⋊C8C2×D814yes—
232C2×AGL(1,ℤ/8)—221no—
233C2×AGL(1,ℤ/8)—221no—
234C2×#131—221no—
235#532C2×D1111yescharacteristic
236#532C2×D1111yescharacteristic
237C2×#127—111no—
238#496—222no—
239#493—112no—
240#493—221no—
241#492—112no—
242#486—221no—
243#474—21no—
244#474C2×D1112yescomplemented
245#466—22no—
246#459—21no—
247#459—112no—
248#459—112no—
249#459C2×D1112yescomplemented
250#447—222no—
251#436—112no—
252#435—222no—
253C8×D4—112no—
254#431—111no—
255C2×C4⋊C8—111no—
256C2×C4⋊C8C2×D1111yescharacteristic
257#408—221no—
258C4×M16—111no—
259#335—112no—
260#334—112no—
261#332—111no—
262#332—111no—
263#331—111no—
264#331—111no—
265#331—112no—
266#331—112no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11#45912yes—
276C22×C11C2×#12111yescharacteristic
277C2×D11—82no—
278C2×D11—82no—
279C2×D11—82no—
280C2×D11—164no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—42no—
285C4×C11—81no—
286C4×C11#45912yes—
287C4×C11C22×D811yescharacteristic
288C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C11#57611yescharacteristic
290C4×C11#57711yescharacteristic
291C2×#41—21no—
292C2×#41—21no—
293C22×D4—221no—
294C22×D4—221no—
295C22×D4—221no—
296AGL(1,ℤ/8)—444no—
297AGL(1,ℤ/8)—444no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×D8—22no—
301C2×D8—222no—
302C2×D8—222no—
303C2×D8—222no—
304C2×D8—222no—
305#131—444no—
306C2×M16—111no—
307C2×M16—111no—
308C2×M16—222no—
309C22×C8—21no—
310C22×C8—222no—
311C22×C8—221no—
312C4⋊Q8C22⋊D1111yescharacteristic
313C4⋊Q8C22×D1111yescharacteristic
314#127—112no—
315#127—221no—
316#127—221no—
317#127—221no—
318#127C22⋊D1111yescharacteristic
319#127C22×D1111yescharacteristic
320#124—21no—
321#124—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121C22⋊D1112yes—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4C22×D1112yes—
330C2×C42C22×D1111yescharacteristic
331#107—22no—
332C4⋊C8—21no—
333C4⋊C8—111no—
334C4⋊C8—111no—
335C4⋊C8—111no—
336C4⋊C8—111no—
337C4⋊C8—221no—
338C4⋊C8C22×D1112yes—
339#102—22no—
340#102—22no—
341#102—222no—
342#102—222no—
343C22⋊C8—222no—
344C22⋊C8—222no—
345C22⋊C8—221no—
346#97—112no—
347C4×C8—112no—
348C4×C8—221no—
349C2×C11—22no—
350C2×C11—82no—
351C2×C11—161no—
352C2×C11C2×#45911yescharacteristic
353C2×C11#306211yescharacteristic
354C2×C11#306811yescharacteristic
355D11—162no—
356C24—441no—
357#41—42no—
358#41—42no—
359#41—42no—
360#41—42no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—41no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—222no—
373C2×D4—442no—
374C2×D4—442no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—441no—
378C2×D4—881no—
379C2×D4—881no—
380C2×D4—882no—
381C2×D4C2×C22⋊D1112yes—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4D4×D1111yescharacteristic
385C22×C4#434111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387SD16—444no—
388SD16—444no—
389D8—82no—
390D8—444no—
391D8—444no—
392D8—882no—
393D8—882no—
394M16—114no—
395M16—222no—
396M16—444no—
397C2×C8—22no—
398C2×C8—81no—
399C2×C8—112no—
400C2×C8—112no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—444no—
406C2×C8—442no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4C2×C22⋊D1112yes—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C42D4×D1111yescharacteristic
416C42#434111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C42C23×D1111yescharacteristic
419C11#1923011yescharacteristic, complemented, Sylow
420C23—22no—
421C23—41no—
422C23—442no—
423C23—882no—
424C23—882no—
425C23—882no—
426C23#6699211yescharacteristic
427Q8—42no—
428Q8—41no—
429Q8—41no—
430D4—22no—
431D4—22no—
432D4—44no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—81no—
439D4—81no—
440D4—82no—
441D4—442no—
442D4—442no—
443D4—442no—
444D4—442no—
445D4—882no—
446D4—882no—
447D4—882no—
448D4—882no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—82no—
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—42no—
466C8—114no—
467C8—222no—
468C8—441no—
469C8—441no—
470C8—441no—
471C8—441no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—882no—
481C22—882no—
482C22—882no—
483C22—1764no—
484C22#1062276312yes—
485C22C2×#6699211yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—81no—
491C4#1062276312yes—
492C4C2×D8×D1111yescharacteristic
493C4C2×#6696411yescharacteristic
494C4#1062336611yescharacteristic
495C4#1062336811yescharacteristic
496C2—22no—
497C2—82no—
498C2—161no—
499C2—1762no—
500C2C2×#1062276311yescharacteristic
501C2#1307829811yescharacteristic
502C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3245C2
socleC22×C11C2×#121
hypercenter#3245D11
hypocenterC11#19230
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. #13079069C2semidirect
3. #13077360C2semidirect
4. #13068093C2semidirect
5. #13068083C2semidirect
6. #13067969C2semidirect
7. #13067959C2semidirect
8. #13067366C2semidirect
9. #13067265C2semidirect
10. C2×#10622123C2semidirect
11. C11×#3245C2semidirect
19. C11×#474C22semidirect
22. C11×#459C22semidirect
33. #10622625C22semidirect
35. D4×C11⋊C8C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
41. #10622182C22semidirect
42. #10622182C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
160. #4318D8semidirect
169. #3245D11semidirect
244. #474C2×D11semidirect
249. #459C2×D11semidirect
419. C11#19230semidirect

Maximal subgroups

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

subgroupindex
#130795312
#130790692
#130773602
#130680932
#130680832
#130679692
#130679592
#130673662
#130672652
C2×#106221232
C11×#32452
#1923011