Finite Group Databasebeta

← #19144321

Subgroups — #19144321

Order 5504.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583695C211yesmaximal, characteristic, complemented
2C2×#13063349C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D43C211yesmaximal, characteristic, complemented
4#14583664C211yesmaximal, characteristic, complemented
5#14583168C211yesmaximal, characteristic, complemented
6#14583167C211yesmaximal, characteristic, complemented
7#14583166C211yesmaximal, characteristic, complemented
8#14583163C211yesmaximal, characteristic, complemented
9#14583162C211yesmaximal, characteristic, complemented
10#14583161C211yesmaximal, characteristic, complemented
11#14583160C211yesmaximal, characteristic, complemented
12#14582946C211yesmaximal, characteristic, complemented
13#14582880C211yesmaximal, characteristic, complemented
14#100×D43C211yesmaximal, characteristic, complemented
15C43×#472C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17#41×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19#13063358C2211yescharacteristic, complemented
20#13063355C2211yescharacteristic, complemented
21#13063354—21no—
22#13063353C2211yescharacteristic
23#13063352—21no—
24#13063351C2211yescharacteristic
25#13063351C2211yescharacteristic, complemented
26#13063350C2211yescharacteristic
27#13063349—21no—
28#13063349—21no—
29#13063349—21no—
30#13063349—21no—
31#13063349—21no—
32#13063349—21no—
33#13063346—21no—
34#13063344—21no—
35C2×#10621873C2211yescharacteristic, complemented
36C2×#10621883C2211yescharacteristic, complemented
37SD16×D43—21no—
38C2×#10621882C2211yescharacteristic, complemented
39D8×D43—21no—
40#13063333—21no—
41#13063333C2211yescharacteristic, complemented
42#13063332C2211yescharacteristic, complemented
43#13063331—21no—
44#13063331C2211yescharacteristic, complemented
45C2×#10621872—21no—
46C2×#10621872C2211yescharacteristic
47M16×D43—21no—
48M16×D43C2211yescharacteristic
49M16×D43C2211yescharacteristic
50M16×D43C2211yescharacteristic
51#13063261C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063260C2211yescharacteristic, complemented
54#13063243C2211yescharacteristic, complemented
55#13063243C2211yescharacteristic, complemented
56#13063242C2211yescharacteristic, complemented
57#13063242C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59#13063241C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C43C2211yescharacteristic
61AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
62C2×D8×C43C2211yescharacteristic, complemented
63#131×C43C2211yescharacteristic, complemented
64#108×C43C2211yescharacteristic, complemented
65#100×C43C2211yescharacteristic, complemented
66#100×C43C2211yescharacteristic, complemented
67C23×D43—21no—
68#41×C43C2311yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×D4×C43C2311yescharacteristic
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C22×Dic43—21no—
74#10621902D411yescharacteristic
75Q8×D43D411yescharacteristic
76#10621900—21no—
77#10621900—21no—
78#10621900—21no—
79#10621900—21no—
80#10621900—21no—
81#10621900D411yescharacteristic
82D4×D43—21no—
83D4×D43—21no—
84D4×D43—21no—
85D4×D43—21no—
86D4×D43—21no—
87D4×D43D411yescharacteristic
88#10621898—21no—
89#10621898C2311yescharacteristic
90C2×D172C2311yescharacteristic
91C2×C4×D43—21no—
92C2×C4×D43C2311yescharacteristic
93C2×Dic86C2311yescharacteristic
94SD16×C43—21no—
95SD16×C43—21no—
96D8×C43—21no—
97D8×C43—21no—
98D8×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#10621884—21no—
108#10621883—21no—
109#10621883—21no—
110#10621883—21no—
111#10621883—21no—
112#10621883—21no—
113#10621882—21no—
114#10621882—21no—
115#10621882—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—
135#10621872D411yescharacteristic
136#10621872D411yescharacteristic
137#10621872D411yescharacteristic
138#10621872D411yescharacteristic
139C8×D43—21no—
140C8×D43—21no—
141C8×D43—21no—
142C8×D43—21no—
143C8×D43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C22×D43—21no—
147C22×D43—21no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—82no—
151C22×D43#4111yescharacteristic
152Q8×C43C2×D411yescharacteristic
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—21no—
156D4×C43—21no—
157D4×C43—21no—
158D4×C43C2×D411yescharacteristic
159C2×C4×C43—21no—
160C2×C4×C43C2411yescharacteristic
161C22⋊D43—21no—
162C22⋊D43—21no—
163C22⋊D43—21no—
164C22⋊D43—41no—
165C22⋊D43—41no—
166C22⋊D43—41no—
167C22⋊D43—41no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43#4111yescharacteristic
173D172—21no—
174D172—21no—
175D172—21no—
176D172C2×D411yescharacteristic
177C4×D43—21no—
178C4×D43—21no—
179C4×D43—21no—
180C4×D43C2×D411yescharacteristic
181C4×D43C2×D411yescharacteristic
182C4×D43C2×D411yescharacteristic
183C4×D43C2×D411yescharacteristic
184Dic86—21no—
185Dic86—21no—
186Dic86—21no—
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—41no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43C2×#4111yescharacteristic
204C2×D43—21no—
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—81no—
208C2×D43—82no—
209C2×D43—82no—
210C2×D43—81no—
211C2×D43#12111yescharacteristic
212C2×D43#12111yescharacteristic
213C4×C43—21no—
214C4×C43C22×D411yescharacteristic
215C4×C43C22×D411yescharacteristic
216Dic43—21no—
217Dic43—41no—
218Dic43#12111yescharacteristic
219Dic43#12111yescharacteristic
220#3068—431nomaximal, Sylow
221C2×C43—21no—
222C2×C43—41no—
223C2×C43—81no—
224C2×C43—81no—
225C2×C43C2×#12111yescharacteristic
226D43—21no—
227D43—21no—
228D43—41no—
229D43—81no—
230#575—431no—
231C2×AGL(1,ℤ/8)—431no—
232C2×AGL(1,ℤ/8)—431no—
233#568—431no—
234#472—431no—
235#472—431no—
236#472—431no—
237#472D4311yescharacteristic, complemented
238#471—431no—
239#471—431no—
240#471—431no—
241#471—431no—
242#430—431no—
243#413—431no—
244C2×#100—431no—
245C43#306811yescharacteristic, complemented, Sylow
246C2×#41—431no—
247C2×#41—431no—
248C22×D4—431no—
249#137—431no—
250#137—431no—
251#137—861no—
252AGL(1,ℤ/8)—431no—
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)—861no—
259AGL(1,ℤ/8)—861no—
260AGL(1,ℤ/8)—861no—
261AGL(1,ℤ/8)—861no—
262AGL(1,ℤ/8)—861no—
263AGL(1,ℤ/8)C2×D4311yescharacteristic
264AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
265#135—861no—
266#135—861no—
267C2×SD16—431no—
268C2×SD16—431no—
269C2×SD16—861no—
270C2×D8—431no—
271C2×D8—861no—
272C2×D8C2×D4311yescharacteristic, complemented
273#131—431no—
274#131—431no—
275#131—431no—
276#131—861no—
277#131—861no—
278#131C2×D4311yescharacteristic, complemented
279C2×M16—431no—
280C2×M16—431no—
281C2×M16—431no—
282C2×M16—431no—
283C2×M16—861no—
284C2×M16—861no—
285#108—431no—
286#108—431no—
287#108—431no—
288#108C2×D4311yescharacteristic, complemented
289#101—431no—
290#101—431no—
291#100—431no—
292#100—431no—
293#100—431no—
294#100—431no—
295#100C2×D4311yescharacteristic, complemented
296#100C2×D4311yescharacteristic, complemented
297C24—861no—
298#41—431no—
299#41—431no—
300#41—431no—
301#41—861no—
302#41—861no—
303#41—861no—
304#41—861no—
305#41—861no—
306#41—861no—
307#41C22×D4311yescharacteristic
308C2×Q8—431no—
309C2×Q8—431no—
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×D4—861no—
319C2×D4C22×D4311yescharacteristic
320C2×D4C22×D4311yescharacteristic
321C22×C4—431no—
322C22×C4—861no—
323C22×C4—861no—
324Q16—861no—
325Q16—861no—
326SD16—21no—
327SD16—21no—
328SD16—861no—
329SD16—861no—
330SD16—861no—
331SD16—861no—
332SD16—861no—
333SD16—861no—
334SD16—861no—
335SD16—861no—
336SD16—861no—
337SD16—861no—
338D8—21no—
339D8—21no—
340D8—21no—
341D8—21no—
342D8—861no—
343D8—861no—
344D8—861no—
345D8—861no—
346D8—861no—
347D8—861no—
348M16—21no—
349M16—431no—
350M16—431no—
351M16—431no—
352M16—431no—
353M16—431no—
354M16—431no—
355M16—431no—
356M16—861no—
357M16—861no—
358M16—861no—
359M16—861no—
360M16—861no—
361M16—861no—
362M16C22×D4311yescharacteristic
363M16C22×D4311yescharacteristic
364M16C22×D4311yescharacteristic
365C2×C8—21no—
366C2×C8—431no—
367C2×C8—861no—
368C2×C8—861no—
369C2×C8—861no—
370C2×C8—861no—
371C2×C8—861no—
372C2×C8—861no—
373C2×C8C22×D4311yescharacteristic
374C23—21no—
375C23—21no—
376C23—431no—
377C23—861no—
378C23—861no—
379C23—3442no—
380C23—1721no—
381C23—1721no—
382Q8—431no—
383Q8—861no—
384Q8—861no—
385Q8—861no—
386Q8D4×D4311yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—431no—
393D4—861no—
394D4—861no—
395D4—861no—
396D4—861no—
397D4—861no—
398D4—861no—
399D4—1721no—
400D4—1721no—
401D4—1721no—
402D4—1721no—
403D4D4×D4311yescharacteristic
404C2×C4—21no—
405C2×C4—431no—
406C2×C4—431no—
407C2×C4—431no—
408C2×C4—431no—
409C2×C4—431no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—861no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4C23×D4311yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—431no—
422C8—431no—
423C8—861no—
424C8—861no—
425C8—861no—
426C8D4×D4311yescharacteristic
427C8D4×D4311yescharacteristic
428C22—21no—
429C22—41no—
430C22—41no—
431C22—81no—
432C22—81no—
433C22—431no—
434C22—431no—
435C22—861no—
436C22—3441no—
437C22—3441no—
438C22—3442no—
439C22—3442no—
440C22—1721no—
441C22—1721no—
442C22#41×D4311yescharacteristic
443C4—21no—
444C4—431no—
445C4—431no—
446C4—861no—
447C4—1721no—
448C4C2×D4×D4311yescharacteristic
449C4C2×D4×D4311yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—81no—
454C2—861no—
455C2—861no—
456C2—3441no—
457C2—1721no—
458C2#121×D4311yescharacteristic
subgroupG/H
centerC2#121×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#472C2
socleC2×C43C2×#121
hypercenter#472D43
hypocenterC43#3068
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #14583695C2semidirect
2. C2×#13063349C2semidirect
3. AGL(1,ℤ/8)×D43C2semidirect
4. #14583664C2semidirect
5. #14583168C2semidirect
6. #14583167C2semidirect
7. #14583166C2semidirect
8. #14583163C2semidirect
9. #14583162C2semidirect
10. #14583161C2semidirect
11. #14583160C2semidirect
12. #14582946C2semidirect
13. #14582880C2semidirect
14. #100×D43C2semidirect
15. C43×#472C2semidirect
19. #13063358C22semidirect
20. #13063355C22semidirect
25. #13063351C22semidirect
35. C2×#10621873C22semidirect
36. C2×#10621883C22semidirect
38. C2×#10621882C22semidirect
41. #13063333C22semidirect
42. #13063332C22semidirect
44. #13063331C22semidirect
51. #13063261C22semidirect
52. #13063260C22semidirect
53. #13063260C22semidirect
54. #13063243C22semidirect
55. #13063243C22semidirect
56. #13063242C22semidirect
57. #13063242C22semidirect
58. #13063241C22semidirect
59. #13063241C22semidirect
61. AGL(1,ℤ/8)×C43C22semidirect
62. C2×D8×C43C22semidirect
63. #131×C43C22semidirect
64. #108×C43C22semidirect
65. #100×C43C22semidirect
66. #100×C43C22semidirect
237. #472D43semidirect
245. C43#3068semidirect
264. AGL(1,ℤ/8)C2×D43semidirect
272. C2×D8C2×D43semidirect
278. #131C2×D43semidirect
288. #108C2×D43semidirect
295. #100C2×D43semidirect
296. #100C2×D43semidirect