Finite Group Databasebeta

← #19146357

Subgroups — #19146357

Order 5504.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583707C211yesmaximal, characteristic, complemented
2#14583702C211yesmaximal, characteristic, complemented
3#14583701C211yesmaximal, characteristic, complemented
4#14583285C211yesmaximal, characteristic, complemented
5#14583169C211yesmaximal, characteristic, complemented
6#14583167C211yesmaximal, characteristic, complemented
7#14583164C211yesmaximal, characteristic, complemented
8#14583159C211yesmaximal, characteristic, complemented
9#14583075C211yesmaximal, characteristic, complemented
10#14583072C211yesmaximal, characteristic, complemented
11#14583067C211yesmaximal, characteristic, complemented
12#14583065C211yesmaximal, characteristic, complemented
13#14583021C211yesmaximal, characteristic, complemented
14#14583019C211yesmaximal, characteristic, complemented
15C43×#577C211yesmaximal, characteristic, complemented
16#13063371C2211yescharacteristic
17#13063371C2211yescharacteristic, complemented
18#13063356—21no—
19#13063356C2211yescharacteristic, complemented
20#13063352—21no—
21#13063352—21no—
22#13063351—21no—
23#13063351C2211yescharacteristic
24#13063350—21no—
25#13063350—21no—
26#13063350C2211yescharacteristic
27#13063350C2211yescharacteristic, complemented
28#13063350C2211yescharacteristic, complemented
29#13063350C2211yescharacteristic, complemented
30#13063348—21no—
31#13063345—21no—
32#13063345—21no—
33#13063345C2211yescharacteristic
34C2×#10621884—21no—
35C2×#10621884C2211yescharacteristic, complemented
36C2×D344C2211yescharacteristic, complemented
37C2×#10621882—21no—
38C2×#10621882C2211yescharacteristic, complemented
39D8×D43—21no—
40#13063332C2211yescharacteristic, complemented
41#13063332C2211yescharacteristic, complemented
42#13063331C2211yescharacteristic, complemented
43#13063321C2211yescharacteristic, complemented
44#13063314C2211yescharacteristic, complemented
45#13063261C2211yescharacteristic, complemented
46#13063260C2211yescharacteristic, complemented
47#13063252C2211yescharacteristic, complemented
48#13063252C2211yescharacteristic, complemented
49#13063252C2211yescharacteristic, complemented
50#13063251C2211yescharacteristic, complemented
51#13063244C2211yescharacteristic, complemented
52#13063242C2211yescharacteristic, complemented
53#13063241C2211yescharacteristic, complemented
54#13063241C2211yescharacteristic, complemented
55#13063235C2211yescharacteristic, complemented
562−1+4×C43C2211yescharacteristic, complemented
57H(5,𝔽2)×C43C2211yescharacteristic, complemented
58#137×C43—21no—
59#137×C43C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C43—21no—
61AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
62#135×C43—21no—
63#135×C43C2211yescharacteristic
64C2×SD16×C43—21no—
65C2×SD16×C43C2211yescharacteristic, complemented
66#131×C43C2211yescharacteristic, complemented
67#41×C43—21no—
68#41×C43—21no—
69#41×C43—21no—
70#41×C43—21no—
71#41×C43—41no—
72#41×C43C2311yescharacteristic
73#41×C43C2311yescharacteristic
74#41×C43C2311yescharacteristic
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43C2311yescharacteristic
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—41no—
81C2×D4×C43C2311yescharacteristic
82C2×C22⋊D43—41no—
83#10621902—21no—
84#10621902—21no—
85D4×D43—21no—
86D4×D43—21no—
87D4×D43—41no—
88D4×D43—41no—
89#10621898—21no—
90#10621898—21no—
91#10621898C2311yescharacteristic
92C2×D172—21no—
93C2×D172—21no—
94C2×D172C2311yescharacteristic
95C2×D172C2311yescharacteristic
96Q16×C43—21no—
97Q16×C43D411yescharacteristic, complemented
98SD16×C43—21no—
99SD16×C43—21no—
100SD16×C43—21no—
101SD16×C43—21no—
102SD16×C43D411yescharacteristic, complemented
103SD16×C43D411yescharacteristic, complemented
104D8×C43—21no—
105D8×C43D411yescharacteristic, complemented
106M16×C43—21no—
107M16×C43C2311yescharacteristic
108C2×C8×C43—21no—
109C2×C8×C43C2311yescharacteristic
110#10621885—21no—
111#10621885D411yescharacteristic, complemented
112#10621884—21no—
113#10621884—21no—
114#10621884—21no—
115#10621884—21no—
116#10621884—21no—
117#10621884—21no—
118#10621884—21no—
119#10621884D411yescharacteristic, complemented
120#10621883—21no—
121#10621883D411yescharacteristic, complemented
122#10621882—21no—
123#10621882—21no—
124#10621882—21no—
125#10621882—21no—
126#10621882—21no—
127#10621882—21no—
128#10621882—21no—
129#10621882D411yescharacteristic, complemented
130(C2×D43)⋊C4—41no—
131C4×Dic43C2311yescharacteristic
132#10621877—21no—
133#10621877—21no—
134#10621877C2311yescharacteristic
135#10621877C2311yescharacteristic
136#10621877C2311yescharacteristic
137C2×C43⋊C8—21no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8C2311yescharacteristic
140D344—21no—
141D344—21no—
142#10621872—21no—
143C8×D43—21no—
144C23×C43—21no—
145C23×C43—41no—
146C22×D43—21no—
147C22×D43—21no—
148C22×D43—41no—
149C22×D43—41no—
150Q8×C43—21no—
151Q8×C43—21no—
152Q8×C43—41no—
153Q8×C43C2×D411yescharacteristic
154Q8×C43C2×D411yescharacteristic
155Q8×C43C2×D411yescharacteristic
156D4×C43—21no—
157D4×C43—21no—
158D4×C43—21no—
159D4×C43—21no—
160D4×C43—21no—
161D4×C43—41no—
162D4×C43—41no—
163D4×C43—41no—
164D4×C43C2×D411yescharacteristic
165D4×C43C2×D411yescharacteristic
166D4×C43C2×D411yescharacteristic
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43C2411yescharacteristic
175C22⋊D43—21no—
176C22⋊D43—41no—
177C22⋊D43—41no—
178C22⋊D43—82no—
179C2×Dic43—21no—
180D172—21no—
181D172—21no—
182D172—21no—
183D172—21no—
184D172—41no—
185D172—41no—
186D172C2×D411yescharacteristic
187C4×D43—21no—
188C4×D43—41no—
189C4×D43—41no—
190Dic86C2×D411yescharacteristic
191C8×C43—21no—
192C8×C43C2×D411yescharacteristic
193C8×C43C2×D411yescharacteristic
194C43⋊C8—21no—
195C43⋊C8—21no—
196C43⋊C8—21no—
197C43⋊C8C2×D411yescharacteristic
198C43⋊C8C2×D411yescharacteristic
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—41no—
203C22×C43—81no—
204C22×C43—161no—
205C22×C43H(5,𝔽2)11yescharacteristic
206C2×D43—21no—
207C2×D43—41no—
208C2×D43—41no—
209C2×D43—81no—
210C2×D43—81no—
211C2×D43—161no—
212C2×D43—161no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—41no—
217C4×C43C22×D411yescharacteristic
218C4×C43C22×D411yescharacteristic
219Dic43—21no—
220Dic43—41no—
221#3288—431nomaximal, Sylow
222C2×C43—21no—
223C2×C43—41no—
224C2×C43—41no—
225C2×C43—41no—
226C2×C43—81no—
227C2×C43D4211yescharacteristic
228D43—41no—
229D43—81no—
230D43—81no—
231#577—431no—
232#577D4311yescharacteristic, complemented
233#576—431no—
234#576—431no—
235#496—431no—
236#472—431no—
237#472—431no—
238#471—431no—
239#471—431no—
240#455—431no—
241#454—431no—
242#453—431no—
243#453—431no—
244#444—431no—
245#444—431no—
246C43#328811yescharacteristic, complemented, Sylow
2472−1+4C2×D4311yescharacteristic, complemented
248H(5,𝔽2)—431no—
249H(5,𝔽2)—431no—
250H(5,𝔽2)C2×D4311yescharacteristic, complemented
251#137—21no—
252#137—431no—
253#137—861no—
254#137C2×D4311yescharacteristic, complemented
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—431no—
258AGL(1,ℤ/8)—431no—
259AGL(1,ℤ/8)—431no—
260AGL(1,ℤ/8)—431no—
261AGL(1,ℤ/8)—861no—
262AGL(1,ℤ/8)—861no—
263AGL(1,ℤ/8)—861no—
264AGL(1,ℤ/8)—861no—
265AGL(1,ℤ/8)—861no—
266AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
267#135—21no—
268#135—431no—
269#135—861no—
270#135—861no—
271#135—861no—
272#135C2×D4311yescharacteristic
273C2×SD16—21no—
274C2×SD16—431no—
275C2×SD16—861no—
276C2×SD16C2×D4311yescharacteristic, complemented
277C2×D8—431no—
278C2×D8—431no—
279C2×D8—861no—
280C2×D8—861no—
281#131—431no—
282#131—431no—
283#131—431no—
284#131C2×D4311yescharacteristic, complemented
285#127—431no—
286#124—431no—
287#108—431no—
288#108—431no—
289#104—431no—
290#104—431no—
291#104—431no—
292#104—431no—
293#101—431no—
294#100—431no—
295#100—431no—
296#100—431no—
297#97—431no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—41no—
303#41—431no—
304#41—861no—
305#41—861no—
306#41—861no—
307#41—861no—
308#41C22×D4311yescharacteristic
309#41C22×D4311yescharacteristic
310#41C22×D4311yescharacteristic
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8C22×D4311yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—431no—
318C2×D4—431no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—861no—
322C2×D4—861no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C2×D4C22×D4311yescharacteristic
327Q16—21no—
328Q16—431no—
329Q16—861no—
330Q16C22⋊D4311yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—431no—
336SD16—431no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16C22⋊D4311yescharacteristic, complemented
346SD16C22⋊D4311yescharacteristic, complemented
347D8—21no—
348D8—431no—
349D8—861no—
350D8—861no—
351D8—861no—
352D8—861no—
353D8—861no—
354D8—861no—
355D8—861no—
356D8—861no—
357D8—861no—
358D8C22⋊D4311yescharacteristic, complemented
359M16—21no—
360M16—431no—
361M16—431no—
362M16—431no—
363M16—861no—
364M16—861no—
365M16—861no—
366M16C22×D4311yescharacteristic
367C2×C8—21no—
368C2×C8—431no—
369C2×C8—861no—
370C2×C8—861no—
371C2×C8—861no—
372C2×C8C22×D4311yescharacteristic
373C22⋊C4—1721no—
374C42—431no—
375C23—21no—
376C23—41no—
377C23—861no—
378C23—861no—
379C23—1721no—
380C23—1721no—
381Q8—21no—
382Q8—21no—
383Q8—41no—
384Q8—431no—
385Q8D4×D4311yescharacteristic
386Q8C2×C22⋊D4311yescharacteristic
387Q8C2×C22⋊D4311yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—431no—
397D4—861no—
398D4—861no—
399D4—861no—
400D4—861no—
401D4—861no—
402D4—3442no—
403D4—1721no—
404D4—1721no—
405D4—1721no—
406D4—1721no—
407D4D4×D4311yescharacteristic
408D4C2×C22⋊D4311yescharacteristic
409D4C2×C22⋊D4311yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—861no—
418C2×C4—861no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4C23×D4311yescharacteristic
422C8—21no—
423C8—431no—
424C8—431no—
425C8—861no—
426C8—861no—
427C8—861no—
428C8C2×C22⋊D4311yescharacteristic
429C8C2×C22⋊D4311yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—81no—
435C22—161no—
436C22—861no—
437C22—3441no—
438C22—3441no—
439C22—1721no—
440C22—1721no—
441C22—6881no—
442C22—6881no—
443C22#1306337011yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—861no—
449C4—1721no—
450C4C2×D4×D4311yescharacteristic
451C4C22×C22⋊D4311yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—3441no—
458C2—3441no—
459C2—1721no—
460C2D4×C22⋊D4311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#577C2
socleC2×C43D42
hypercenter#577D43
hypocenterC43#3288
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #14583707C2semidirect
2. #14583702C2semidirect
3. #14583701C2semidirect
4. #14583285C2semidirect
5. #14583169C2semidirect
6. #14583167C2semidirect
7. #14583164C2semidirect
8. #14583159C2semidirect
9. #14583075C2semidirect
10. #14583072C2semidirect
11. #14583067C2semidirect
12. #14583065C2semidirect
13. #14583021C2semidirect
14. #14583019C2semidirect
15. C43×#577C2semidirect
17. #13063371C22semidirect
19. #13063356C22semidirect
27. #13063350C22semidirect
28. #13063350C22semidirect
29. #13063350C22semidirect
35. C2×#10621884C22semidirect
36. C2×D344C22semidirect
38. C2×#10621882C22semidirect
40. #13063332C22semidirect
41. #13063332C22semidirect
42. #13063331C22semidirect
43. #13063321C22semidirect
44. #13063314C22semidirect
45. #13063261C22semidirect
46. #13063260C22semidirect
47. #13063252C22semidirect
48. #13063252C22semidirect
49. #13063252C22semidirect
50. #13063251C22semidirect
51. #13063244C22semidirect
52. #13063242C22semidirect
53. #13063241C22semidirect
54. #13063241C22semidirect
55. #13063235C22semidirect
56. 2−1+4×C43C22semidirect
57. H(5,𝔽2)×C43C22semidirect
59. #137×C43C22semidirect
61. AGL(1,ℤ/8)×C43C22semidirect
65. C2×SD16×C43C22semidirect
66. #131×C43C22semidirect
97. Q16×C43D4semidirect
102. SD16×C43D4semidirect
103. SD16×C43D4semidirect
105. D8×C43D4semidirect
111. #10621885D4semidirect
119. #10621884D4semidirect
121. #10621883D4semidirect
129. #10621882D4semidirect
232. #577D43semidirect
246. C43#3288semidirect
247. 2−1+4C2×D43semidirect
250. H(5,𝔽2)C2×D43semidirect
254. #137C2×D43semidirect
266. AGL(1,ℤ/8)C2×D43semidirect
276. C2×SD16C2×D43semidirect
284. #131C2×D43semidirect
330. Q16C22⋊D43semidirect
345. SD16C22⋊D43semidirect
346. SD16C22⋊D43semidirect
358. D8C22⋊D43semidirect