Finite Group Databasebeta

← #471×D43 #19144290

Subgroups — #471×D43 #19144290

Order 5504.

468 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×D43C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D43C211yesmaximal, characteristic
3C2×SD16×D43C211yesmaximal, characteristic, complemented
4#131×D43C211yesmaximal, characteristic, complemented
5#14583165C211yesmaximal, characteristic, complemented
6#14583164C211yesmaximal, characteristic, complemented
7#14583163C211yesmaximal, characteristic, complemented
8#14583162C211yesmaximal, characteristic, complemented
9#14583161C211yesmaximal, characteristic, complemented
10#14583160C211yesmaximal, characteristic, complemented
11#14583159C211yesmaximal, characteristic, complemented
12#108×D43C211yesmaximal, characteristic, complemented
13#101×D43C211yesmaximal, characteristic, complemented
14#100×D43C211yesmaximal, characteristic, complemented
15C43×#471C211yesmaximal, characteristic, complemented
16#41×D43C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19#13063358C2211yescharacteristic, complemented
20#13063357—21no—
21#13063356C2211yescharacteristic, complemented
22#13063355C2211yescharacteristic, complemented
23#13063354—21no—
24#13063353C2211yescharacteristic
25#13063352—21no—
26#13063351C2211yescharacteristic
27#13063350C2211yescharacteristic
28#13063349—21no—
29Q16×D43—21no—
30C2×#10621873C2211yescharacteristic, complemented
31C2×#10621883C2211yescharacteristic, complemented
32C2×#10621884C2211yescharacteristic, complemented
33SD16×D43—21no—
34SD16×D43—21no—
35SD16×D43—21no—
36SD16×D43—21no—
37SD16×D43—21no—
38SD16×D43—21no—
39D8×D43—21no—
40#13063333—21no—
41#13063333C2211yescharacteristic, complemented
42#13063332C2211yescharacteristic, complemented
43#13063331—21no—
44#13063331C2211yescharacteristic, complemented
45M16×D43—21no—
46M16×D43C2211yescharacteristic
47M16×D43C2211yescharacteristic
48M16×D43C2211yescharacteristic
49C2×C8×D43—21no—
50C2×C8×D43C2211yescharacteristic
51#13063261C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063260C2211yescharacteristic, complemented
54#13063244C2211yescharacteristic, complemented
55#13063243C2211yescharacteristic, complemented
56#13063243C2211yescharacteristic, complemented
57#13063242C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59#13063241C2211yescharacteristic, complemented
60#137×C43C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C43C2211yescharacteristic
62C2×SD16×C43C2211yescharacteristic, complemented
63#131×C43C2211yescharacteristic, complemented
64#108×C43C2211yescharacteristic, complemented
65#101×C43C2211yescharacteristic, complemented
66#100×C43C2211yescharacteristic, complemented
67C23×D43—21no—
68#41×C43C2311yescharacteristic
69C2×Q8×C43C2311yescharacteristic
70C2×D4×C43C2311yescharacteristic
71C2×C22⋊D43—21no—
72#10621902D411yescharacteristic
73Q8×D43—21no—
74Q8×D43—21no—
75Q8×D43—21no—
76Q8×D43—21no—
77Q8×D43D411yescharacteristic
78#10621900—21no—
79#10621900D411yescharacteristic
80D4×D43—21no—
81D4×D43—21no—
82D4×D43—21no—
83D4×D43—21no—
84D4×D43—21no—
85D4×D43D411yescharacteristic
86#10621898—21no—
87#10621898C2311yescharacteristic
88C2×D172C2311yescharacteristic
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43C2311yescharacteristic
92C2×Dic86—21no—
93C2×Dic86C2311yescharacteristic
94Q16×C43—21no—
95SD16×C43—21no—
96SD16×C43—21no—
97SD16×C43—21no—
98SD16×C43—21no—
99D8×C43—21no—
100M16×C43—21no—
101M16×C43C2311yescharacteristic
102M16×C43C2311yescharacteristic
103M16×C43C2311yescharacteristic
104C2×C8×C43—21no—
105C2×C8×C43C2311yescharacteristic
106#10621885—21no—
107#10621885—21no—
108#10621884—21no—
109#10621884—21no—
110#10621884—21no—
111#10621884—21no—
112#10621883—21no—
113#10621883—21no—
114#10621883—21no—
115#10621883—21no—
116#10621882—21no—
117#10621882—21no—
118#10621877—21no—
119#10621877C2311yescharacteristic
120#10621877C2311yescharacteristic
121#10621877C2311yescharacteristic
122C2×C43⋊C8—21no—
123C2×C43⋊C8C2311yescharacteristic
124Dic172—21no—
125D344—21no—
126#10621873—21no—
127#10621873—21no—
128#10621873—21no—
129#10621873—21no—
130#10621872—21no—
131#10621872—21no—
132#10621872—21no—
133#10621872—21no—
134#10621872—21no—
135C8×D43—21no—
136C8×D43—21no—
137C8×D43—21no—
138C8×D43—21no—
139C8×D43—21no—
140C8×D43D411yescharacteristic
141C8×D43D411yescharacteristic
142C8×D43D411yescharacteristic
143C8×D43D411yescharacteristic
144C23×C43—21no—
145C22×D43—21no—
146C22×D43—21no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—82no—
150C22×D43#4111yescharacteristic
151Q8×C43—21no—
152Q8×C43—21no—
153Q8×C43C2×D411yescharacteristic
154D4×C43—21no—
155D4×C43—21no—
156D4×C43—21no—
157D4×C43C2×D411yescharacteristic
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43C2411yescharacteristic
161C22⋊D43—21no—
162C22⋊D43—21no—
163C22⋊D43—21no—
164C22⋊D43—41no—
165C22⋊D43—41no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43#4111yescharacteristic
169D172—21no—
170D172—21no—
171D172—21no—
172D172C2×D411yescharacteristic
173C4×D43—21no—
174C4×D43—21no—
175C4×D43—21no—
176C4×D43—41no—
177C4×D43—41no—
178C4×D43C2×D411yescharacteristic
179C4×D43C2×D411yescharacteristic
180C4×D43C2×D411yescharacteristic
181C4×D43C2×D411yescharacteristic
182Dic86—21no—
183Dic86—21no—
184Dic86—21no—
185Dic86—41no—
186Dic86—41no—
187Dic86C2×D411yescharacteristic
188C8×C43—21no—
189C8×C43—21no—
190C8×C43—21no—
191C8×C43C2×D411yescharacteristic
192C8×C43C2×D411yescharacteristic
193C43⋊C8—21no—
194C43⋊C8—21no—
195C43⋊C8—21no—
196C43⋊C8C2×D411yescharacteristic
197C43⋊C8C2×D411yescharacteristic
198C22×C43—21no—
199C22×C43—41no—
200C22×C43—81no—
201C22×C43C2×#4111yescharacteristic
202C2×D43—22no—
203C2×D43—21no—
204C2×D43—42no—
205C2×D43—41no—
206C2×D43—82no—
207C2×D43—82no—
208C2×D43—81no—
209C2×D43#12111yescharacteristic
210C2×D43#12111yescharacteristic
211C4×C43—21no—
212C4×C43—41no—
213C4×C43C22×D411yescharacteristic
214C4×C43C22×D411yescharacteristic
215Dic43—21no—
216Dic43—41no—
217Dic43#12111yescharacteristic
218Dic43#12111yescharacteristic
219C2×#471—431nomaximal, Sylow
220C2×C43—21no—
221C2×C43—41no—
222C2×C43—81no—
223C2×C43C2×#12111yescharacteristic
224D43—21no—
225D43—41no—
226D43—81no—
227D43#47112yesdirect product factor
228C2×#137—431no—
229C2×AGL(1,ℤ/8)—431no—
230C22×SD16—431no—
231C2×#131—431no—
232#471—431no—
233#471—431no—
234#471—431no—
235#471—431no—
236#471—431no—
237#471—431no—
238#471—431no—
239#471D4311yescharacteristic, direct product factor
240C2×#108—431no—
241C2×#101—431no—
242C2×#100—431no—
243C43C2×#47111yescharacteristic, complemented, Sylow
244C2×#41—431no—
245C22×Q8—431no—
246C22×D4—431no—
247#137—431no—
248#137—431no—
249#137—431no—
250#137—861no—
251#137—861no—
252#137C2×D4311yescharacteristic, complemented
253AGL(1,ℤ/8)—431no—
254AGL(1,ℤ/8)—431no—
255AGL(1,ℤ/8)—431no—
256AGL(1,ℤ/8)—861no—
257AGL(1,ℤ/8)—861no—
258AGL(1,ℤ/8)C2×D4311yescharacteristic
259C2×Q16—861no—
260C2×SD16—431no—
261C2×SD16—431no—
262C2×SD16—431no—
263C2×SD16—861no—
264C2×SD16—861no—
265C2×SD16—861no—
266C2×SD16—861no—
267C2×SD16—861no—
268C2×SD16—861no—
269C2×SD16C2×D4311yescharacteristic, complemented
270C2×D8—861no—
271#131—431no—
272#131—431no—
273#131—431no—
274#131—861no—
275#131—861no—
276#131C2×D4311yescharacteristic, complemented
277C2×M16—431no—
278C2×M16—431no—
279C2×M16—431no—
280C2×M16—861no—
281C22×C8—431no—
282C22×C8—861no—
283#108—431no—
284#108—431no—
285#108—431no—
286#108C2×D4311yescharacteristic, complemented
287#101—431no—
288#101—431no—
289#101—431no—
290#101C2×D4311yescharacteristic, complemented
291#100—431no—
292#100—431no—
293#100—431no—
294#100C2×D4311yescharacteristic, complemented
295C24—861no—
296#41—431no—
297#41—431no—
298#41—431no—
299#41—861no—
300#41—861no—
301#41C22×D4311yescharacteristic
302C2×Q8—431no—
303C2×Q8—431no—
304C2×Q8—861no—
305C2×Q8—861no—
306C2×Q8—861no—
307C2×Q8—861no—
308C2×Q8—861no—
309C2×Q8C22×D4311yescharacteristic
310C2×D4—431no—
311C2×D4—431no—
312C2×D4—861no—
313C2×D4—861no—
314C2×D4—861no—
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4C22×D4311yescharacteristic
319C22×C4—431no—
320C22×C4—861no—
321C22×C4—861no—
322Q16—21no—
323Q16—861no—
324Q16—861no—
325Q16—861no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—861no—
331SD16—861no—
332SD16—861no—
333SD16—861no—
334SD16—861no—
335SD16—861no—
336SD16—861no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342D8—21no—
343D8—861no—
344D8—861no—
345D8—861no—
346M16—21no—
347M16—431no—
348M16—431no—
349M16—431no—
350M16—861no—
351M16—861no—
352M16—861no—
353M16—861no—
354M16—861no—
355M16—861no—
356M16C22×D4311yescharacteristic
357M16C22×D4311yescharacteristic
358M16C22×D4311yescharacteristic
359C2×C8—21no—
360C2×C8—431no—
361C2×C8—431no—
362C2×C8—431no—
363C2×C8—431no—
364C2×C8—431no—
365C2×C8—861no—
366C2×C8—861no—
367C2×C8—861no—
368C2×C8—861no—
369C2×C8—861no—
370C2×C8—861no—
371C2×C8C22×D4311yescharacteristic
372C23—21no—
373C23—431no—
374C23—861no—
375C23—861no—
376C23—3442no—
377C23—1721no—
378C23—1721no—
379Q8—21no—
380Q8—21no—
381Q8—431no—
382Q8—861no—
383Q8—861no—
384Q8—861no—
385Q8—1721no—
386Q8—1721no—
387Q8D4×D4311yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—431no—
392D4—861no—
393D4—861no—
394D4—861no—
395D4—861no—
396D4—861no—
397D4—861no—
398D4—1721no—
399D4—1721no—
400D4D4×D4311yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—431no—
404C2×C4—431no—
405C2×C4—431no—
406C2×C4—431no—
407C2×C4—431no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4C23×D4311yescharacteristic
416C8—21no—
417C8—21no—
418C8—21no—
419C8—431no—
420C8—431no—
421C8—861no—
422C8—861no—
423C8—861no—
424C8D4×D4311yescharacteristic
425C8D4×D4311yescharacteristic
426C22—21no—
427C22—41no—
428C22—81no—
429C22—431no—
430C22—431no—
431C22—862no—
432C22—861no—
433C22—3441no—
434C22—3442no—
435C22—3442no—
436C22—1722no—
437C22—1721no—
438C22#41×D4311yescharacteristic
439C4—21no—
440C4—41no—
441C4—431no—
442C4—431no—
443C4—861no—
444C4—1721no—
445C4C2×D4×D4311yescharacteristic
446C4C2×D4×D4311yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—432no—
451C2—861no—
452C2—3441no—
453C2—1721no—
454C2#121×D4311yescharacteristic
subgroupG/H
centerC2#121×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#471C2
socleC2×C43C2×#121
hypercenter#471D43
hypocenterC43C2×#471
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #137×D43C2semidirect
3. C2×SD16×D43C2semidirect
4. #131×D43C2semidirect
5. #14583165C2semidirect
6. #14583164C2semidirect
7. #14583163C2semidirect
8. #14583162C2semidirect
9. #14583161C2semidirect
10. #14583160C2semidirect
11. #14583159C2semidirect
12. #108×D43C2semidirect
13. #101×D43C2semidirect
14. #100×D43C2semidirect
15. C43×#471C2semidirect
19. #13063358C22semidirect
21. #13063356C22semidirect
22. #13063355C22semidirect
30. C2×#10621873C22semidirect
31. C2×#10621883C22semidirect
32. C2×#10621884C22semidirect
41. #13063333C22semidirect
42. #13063332C22semidirect
44. #13063331C22semidirect
51. #13063261C22semidirect
52. #13063260C22semidirect
53. #13063260C22semidirect
54. #13063244C22semidirect
55. #13063243C22semidirect
56. #13063243C22semidirect
57. #13063242C22semidirect
58. #13063241C22semidirect
59. #13063241C22semidirect
60. #137×C43C22semidirect
62. C2×SD16×C43C22semidirect
63. #131×C43C22semidirect
64. #108×C43C22semidirect
65. #101×C43C22semidirect
66. #100×C43C22semidirect
227. D43#471direct (N × H)
239. #471D43direct (N × H)
243. C43C2×#471semidirect
252. #137C2×D43semidirect
269. C2×SD16C2×D43semidirect
276. #131C2×D43semidirect
286. #108C2×D43semidirect
290. #101C2×D43semidirect
294. #100C2×D43semidirect