Finite Group Databasebeta

← #14737260

Subgroups — #14737260

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#13079536C211yesmaximal, characteristic, complemented
3#13079069C211yesmaximal, characteristic, complemented
4#13077359C211yesmaximal, characteristic, complemented
5#13068094C212yesmaximal, complemented
6#13068084C212yesmaximal, complemented
7#13067970C212yesmaximal, complemented
8#13067960C212yesmaximal, complemented
9#13067369C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#1540C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×#67002—21no—
14C2×#67002—21no—
15C2×#66954—21no—
16#10623008C2211yescharacteristic
17C2×#66927C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20#10622723—21no—
21#10622700C2212yescomplemented
22#10622698C2212yes—
23#10622686C2212yes—
24#10622685C2212yescomplemented
25#10622671—22no—
26#10622651—22no—
27#10622628—21no—
28#10622620—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31#10622456C2212yes—
32#10622456C2212yes—
33#10622451C2212yescomplemented
34#10622449—22no—
35#10622447C2212yescomplemented
36#10622345—22no—
37#10622308—21no—
38#10622307—21no—
39C11×#332C2211yescharacteristic, complemented
40C11×#332C2211yescharacteristic, complemented
41C11×#331C2211yescharacteristic, complemented
42C11×#331C2211yescharacteristic, complemented
43#10622123C2212yes—
44#10622123C2212yes—
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C2×C11×#41—21no—
48C2×#4339—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C22×C8×C11—21no—
53C11×C4⋊Q8C2311yescharacteristic
54C11×#127C2311yescharacteristic
55C11×#124—21no—
56C11×#121—21no—
57C11×#121—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C2×C42×C11C2311yescharacteristic
61#67002—44no—
62#67002—44no—
63C2×#4325—22no—
64C2×#4325—22no—
65C2×#4323—22no—
66C2×#4323—22no—
67C2×#4323—22no—
68#66983—21no—
69#66983D412yes—
70C2×#4318D411yescharacteristic
71C2×#4318D411yescharacteristic
72C22×C11⋊C8—21no—
73C2×D88—22no—
74C2×D88—22no—
75#66954—44no—
76C2×#4313—22no—
77C2×C8×D11—22no—
78#66928—21no—
79#66927—21no—
80#66927—21no—
81#66927—21no—
82#66927D411yescharacteristic
83#66927C2312yes—
84C4×D44—21no—
85C4×D44C2312yes—
86#66922D411yescharacteristic
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2311yescharacteristic
89C11×C4⋊C8C2311yescharacteristic
90C11×C4⋊C8C2311yescharacteristic
91C11×C4⋊C8C2311yescharacteristic
92C11×C22⋊C8—21no—
93C4×C8×C11—21no—
94#66896—22no—
95#66885—22no—
96#66885—22no—
97(C2×D11)⋊C8—22no—
98(C2×D11)⋊C8—22no—
99#66873—22no—
100#66871—22no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)C2312yes—
103#66867D412yes—
104C4×C11⋊C8C2312yes—
105#19230—111nomaximal, Sylow
106C23×D11—41no—
107C11×#41—42no—
108C11×#41—42no—
109C2×Q8×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×C22⋊D11—22no—
119#4339—42no—
120#4339—42no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—41no—
127C2×D44—41no—
128C2×D44—41no—
129C2×D44—42no—
130C2×D44—42no—
131C2×D44—81no—
132C2×D44—81no—
133C2×D44—82no—
134C2×D44C2×D412yes—
135C2×C4×D11—22no—
136C2×Dic22—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—42no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150#4325—44no—
151#4325—44no—
152#4323—44no—
153#4323—44no—
154#4323—82no—
155(C2×D11)⋊C4—22no—
156(C2×D11)⋊C4—22no—
157C4⋊Dic11—21no—
158C4⋊Dic11C2×D412yes—
159#4318—22no—
160#4318D814yescomplemented
161C2×C11⋊C8—22no—
162C2×C11⋊C8—81no—
163C2×C11⋊C8C2×D412yes—
164C2×C11⋊C8C2×D412yes—
165D88—82no—
166D88—82no—
167#4313—44no—
168C8×D11—44no—
169#3245—111no—
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#1540D1111yescharacteristic, complemented
179C2×#331—111no—
180C23×C11—41no—
181C23×C11#12111yescharacteristic
182C22×D11—22no—
183C22×D11—42no—
184C22×D11—82no—
185C22×D11—82no—
186C22×D11—82no—
187Q8×C11—41no—
188Q8×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—81no—
194D4×C11—82no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—82no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11C2×D812yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C22⋊D11—44no—
209C2×Dic11—22no—
210D44—22no—
211D44—22no—
212D44—42no—
213D44—42no—
214D44—42no—
215D44—42no—
216D44—42no—
217D44—81no—
218D44—82no—
219D44—82no—
220D44—82no—
221D44—82no—
222C4×D11—42no—
223C4×D11—42no—
224Dic22—42no—
225C8×C11—41no—
226C8×C11—41no—
227C8×C11—41no—
228C8×C11—41no—
229C11⋊C8—22no—
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×#127—111no—
238#496—222no—
239#493—112no—
240#493—221no—
241#492—112no—
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#431C2×D1111yescharacteristic
255C2×C4⋊C8—111no—
256C2×C4⋊C8C2×D1111yescharacteristic
257#408—221no—
258C4×M16—111no—
259#335—112no—
260#334—112no—
261#332C2×D1111yescharacteristic, complemented
262#332C2×D1111yescharacteristic, complemented
263#331—112no—
264#331—112no—
265#331C2×D1111yescharacteristic, complemented
266#331C2×D1111yescharacteristic, complemented
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11#45912yes—
273C22×C11C2×#12111yescharacteristic
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—82no—
278C2×D11—82no—
279C2×D11—82no—
280C2×D11—164no—
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—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—222no—
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⋊Q8—111no—
313C4⋊Q8C22×D1111yescharacteristic
314#127—111no—
315#127—112no—
316#127—221no—
317#127—221no—
318#127—221no—
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—21no—
333C4⋊C8—112no—
334C4⋊C8—221no—
335C4⋊C8C22×D1111yescharacteristic
336C4⋊C8C22×D1111yescharacteristic
337C4⋊C8C22×D1111yescharacteristic
338C4⋊C8C22×D1111yescharacteristic
339#102—222no—
340#102—222no—
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—161no—
351C2×C11C2×#45911yescharacteristic
352C2×C11#306211yescharacteristic
353C2×C11#306811yescharacteristic
354D11—82no—
355D11—162no—
356C24—441no—
357#41—42no—
358#41—42no—
359#41—442no—
360#41—442no—
361C2×Q8—21no—
362C2×Q8—221no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—41no—
367C2×D4—112no—
368C2×D4—222no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—222no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—442no—
378C2×D4—442no—
379C2×D4—881no—
380C2×D4—881no—
381C2×D4—882no—
382C22×C4—41no—
383C22×C4—222no—
384C22×C4#433911yescharacteristic
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387SD16—444no—
388SD16—444no—
389D8—444no—
390D8—444no—
391D8—882no—
392D8—882no—
393D8—882no—
394M16—114no—
395M16—222no—
396M16—444no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—42no—
402C2×C8—112no—
403C2×C8—112no—
404C2×C8—222no—
405C2×C8—444no—
406C2×C8—881no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—112no—
410C4⋊C4—221no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—222no—
414C22⋊C4—222no—
415C42#433911yescharacteristic
416C42D4×D1111yescharacteristic
417C42D4×D1111yescharacteristic
418C42C23×D1111yescharacteristic
419C11#1923011yescharacteristic, complemented, Sylow
420C23—41no—
421C23—222no—
422C23—442no—
423C23—882no—
424C23—882no—
425C23—882no—
426C23#6693711yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—442no—
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—81no—
435D4—82no—
436D4—222no—
437D4—222no—
438D4—444no—
439D4—442no—
440D4—442no—
441D4—442no—
442D4—442no—
443D4—442no—
444D4—881no—
445D4—882no—
446D4—882no—
447D4—882no—
448D4—882no—
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×C4#6693711yescharacteristic
458C2×C4#6693711yescharacteristic
459C2×C4#6693711yescharacteristic
460C2×C4D8×D1112yes—
461C2×C4#6696712yes—
462C2×C4C2×#433911yescharacteristic
463C2×C4C2×D4×D1111yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C8—41no—
466C8—41no—
467C8—41no—
468C8—41no—
469C8—114no—
470C8—222no—
471C8—442no—
472C22—21no—
473C22—21no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—442no—
478C22—442no—
479C22—442no—
480C22—882no—
481C22—882no—
482C22—882no—
483C22—1764no—
484C22#1062239912yes—
485C22C2×#6693711yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—81no—
490C4—442no—
491C4#1062239912yes—
492C4C2×D8×D1111yescharacteristic
493C4C2×#6696711yescharacteristic
494C4#1062330011yescharacteristic
495C4#1062330111yescharacteristic
496C2—22no—
497C2—161no—
498C2—882no—
499C2—1762no—
500C2C2×#1062239911yescharacteristic
501C2#1307829911yescharacteristic
502C2#1307834711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C2×#121
hypercenter#1540D11
hypocenterC11#19230
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #13079923C2semidirect
2. #13079536C2semidirect
3. #13079069C2semidirect
4. #13077359C2semidirect
5. #13068094C2semidirect
6. #13068084C2semidirect
7. #13067970C2semidirect
8. #13067960C2semidirect
9. #13067369C2semidirect
10. C2×#10622123C2semidirect
11. C11×#1540C2semidirect
21. #10622700C22semidirect
24. #10622685C22semidirect
33. #10622451C22semidirect
35. #10622447C22semidirect
39. C11×#332C22semidirect
40. C11×#332C22semidirect
41. C11×#331C22semidirect
42. C11×#331C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
160. #4318D8semidirect
178. #1540D11semidirect
261. #332C2×D11semidirect
262. #332C2×D11semidirect
265. #331C2×D11semidirect
266. #331C2×D11semidirect
419. C11#19230semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130795362
#130790692
#130773592
#130680942
#130680842
#130679702
#130679602
#130673692
C2×#106221232
C11×#15402
#1923011