Finite Group Databasebeta

← #19146387

Subgroups — #19146387

Order 5504.

460 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#14583711C211yesmaximal, characteristic, complemented
2#14583709C211yesmaximal, characteristic, complemented
3#14583708C211yesmaximal, characteristic, complemented
4#14583705C211yesmaximal, characteristic, complemented
5#14583270C211yesmaximal, characteristic, complemented
6#14583165C211yesmaximal, characteristic, complemented
7#14583163C211yesmaximal, characteristic, complemented
8#14583161C211yesmaximal, characteristic, complemented
9#14583084C211yesmaximal, characteristic, complemented
10#14583080C211yesmaximal, characteristic, complemented
11#14583069C211yesmaximal, characteristic, complemented
12#14583065C211yesmaximal, characteristic, complemented
13#14583015C211yesmaximal, characteristic, complemented
14#14583014C211yesmaximal, characteristic, complemented
15C43×#471C211yesmaximal, characteristic, complemented
16#13063373C2211yescharacteristic
17#13063372C2211yescharacteristic
18#13063371C2211yescharacteristic, complemented
19#13063370C2211yescharacteristic, complemented
20#13063358—21no—
21#13063358C2211yescharacteristic, complemented
22#13063358C2211yescharacteristic, complemented
23#13063357—21no—
24#13063356C2211yescharacteristic, complemented
25#13063354—21no—
26#13063354—21no—
27#13063353—21no—
28#13063353C2211yescharacteristic
29#13063353C2211yescharacteristic
30#13063352—21no—
31#13063352—21no—
32#13063351C2211yescharacteristic
33#13063349—21no—
34#13063348—21no—
35#13063347—21no—
36#13063347C2211yescharacteristic
37#13063346—21no—
38#13063345C2211yescharacteristic
39#13063344—21no—
40C2×#10621873—21no—
41C2×#10621873C2211yescharacteristic, complemented
42C2×#10621883C2211yescharacteristic, complemented
43C2×#10621884C2211yescharacteristic, complemented
44SD16×D43—21no—
45SD16×D43—21no—
46SD16×D43—21no—
47#13063333C2211yescharacteristic, complemented
48#13063333C2211yescharacteristic, complemented
49#13063331C2211yescharacteristic, complemented
50#13063323C2211yescharacteristic, complemented
51#13063321C2211yescharacteristic
52#13063260C2211yescharacteristic, complemented
53#13063252C2211yescharacteristic, complemented
54#13063251C2211yescharacteristic, complemented
55#13063251C2211yescharacteristic, complemented
56#13063251C2211yescharacteristic, complemented
57#13063243C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59C8×Dic43C2211yescharacteristic, 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
67#41×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×C22⋊D43—41no—
71C2×C22⋊D43—41no—
72#10621902—21no—
73#10621902—21no—
74#10621902—21no—
75Q8×D43—21no—
76Q8×D43—21no—
77Q8×D43—21no—
78#10621900—21no—
79#10621900—21no—
80#10621900—21no—
81#10621900—41no—
82D4×D43—21no—
83D4×D43—21no—
84D4×D43—21no—
85D4×D43—41no—
86#10621898—21no—
87#10621898—21no—
88#10621898—41no—
89#10621898C2311yescharacteristic
90#10621898C2311yescharacteristic
91#10621898C2311yescharacteristic
92C2×D172—21no—
93C2×D172C2311yescharacteristic
94C2×Dic86—21no—
95C2×Dic86C2311yescharacteristic
96Q16×C43—21no—
97SD16×C43—21no—
98SD16×C43—21no—
99SD16×C43—21no—
100SD16×C43—21no—
101D8×C43—21no—
102M16×C43—21no—
103M16×C43C2311yescharacteristic
104M16×C43C2311yescharacteristic
105M16×C43C2311yescharacteristic
106C2×C8×C43—21no—
107C2×C8×C43C2311yescharacteristic
108#10621885—21no—
109#10621885D411yescharacteristic, complemented
110#10621884—21no—
111#10621884—21no—
112#10621884—21no—
113#10621884D411yescharacteristic, complemented
114#10621883—21no—
115#10621883—21no—
116#10621883—21no—
117#10621883D411yescharacteristic, complemented
118#10621882—21no—
119#10621882D411yescharacteristic, complemented
120Dic43⋊C4—41no—
121C4×Dic43C2311yescharacteristic
122#10621877C2311yescharacteristic
123C2×C43⋊C8C2311yescharacteristic
124Dic172—21no—
125Dic172—21no—
126Dic172D411yescharacteristic, complemented
127D344—21no—
128D344—21no—
129D344D411yescharacteristic, complemented
130#10621873—21no—
131#10621873—21no—
132#10621873—21no—
133#10621873—21no—
134#10621873—21no—
135#10621873—21no—
136#10621873D411yescharacteristic, complemented
137#10621873D411yescharacteristic, complemented
138#10621872—21no—
139#10621872—21no—
140#10621872—21no—
141C8×D43—21no—
142C8×D43—21no—
143C8×D43—21no—
144C23×C43—21no—
145C22×D43—21no—
146C22×D43—41no—
147C22×D43—41no—
148Q8×C43—21no—
149Q8×C43—21no—
150Q8×C43C2×D411yescharacteristic
151D4×C43—21no—
152D4×C43—21no—
153D4×C43—21no—
154D4×C43C2×D411yescharacteristic
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43C2411yescharacteristic
158C22⋊D43—21no—
159C22⋊D43—21no—
160C22⋊D43—21no—
161C22⋊D43—41no—
162C22⋊D43—41no—
163C22⋊D43—41no—
164C22⋊D43—41no—
165C22⋊D43—82no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170D172—21no—
171D172—21no—
172D172—41no—
173D172—41no—
174D172C2×D411yescharacteristic
175D172C2×D411yescharacteristic
176D172C2×D411yescharacteristic
177C4×D43—21no—
178C4×D43—21no—
179C4×D43—21no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—41no—
183C4×D43—41no—
184Dic86—21no—
185Dic86—21no—
186Dic86—41no—
187Dic86—41no—
188Dic86C2×D411yescharacteristic
189Dic86C2×D411yescharacteristic
190Dic86C2×D411yescharacteristic
191C8×C43—21no—
192C8×C43—21no—
193C8×C43—21no—
194C8×C43C2×D411yescharacteristic
195C8×C43C2×D411yescharacteristic
196C43⋊C8—21no—
197C43⋊C8C2×D411yescharacteristic
198C43⋊C8C2×D411yescharacteristic
199C22×C43—21no—
200C22×C43—41no—
201C22×C43—81no—
202C22×C43H(5,𝔽2)11yescharacteristic
203C2×D43—21no—
204C2×D43—21no—
205C2×D43—21no—
206C2×D43—41no—
207C2×D43—81no—
208C2×D43—161no—
209C2×D43—161no—
210C4×C43—21no—
211C4×C43—41no—
212C4×C43C22×D411yescharacteristic
213C4×C43C22×D411yescharacteristic
214Dic43—22no—
215Dic43—21no—
216Dic43—21no—
217Dic43—21no—
218Dic43—41no—
219#3291—431nomaximal, Sylow
220C2×C43—21no—
221C2×C43—41no—
222C2×C43—81no—
223C2×C43D4211yescharacteristic
224D43—41no—
225D43—41no—
226D43—41no—
227D43—81no—
228#577—431no—
229#577—431no—
230#577—431no—
231#577—431no—
232#492—431no—
233#471—431no—
234#471—431no—
235#471—431no—
236#471D4311yescharacteristic, complemented
237#456—431no—
238#456—431no—
239#453—431no—
240#453—431no—
241#443—431no—
242#443—431no—
243C43#329111yescharacteristic, complemented, Sylow
2442−1+4—431no—
2452−1+4—431no—
246H(5,𝔽2)—431no—
247H(5,𝔽2)—431no—
248#137—431no—
249#137—431no—
250#137—431no—
251#137—861no—
252#137—861no—
253#137—861no—
254#137—861no—
255#137C2×D4311yescharacteristic, complemented
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—431no—
258AGL(1,ℤ/8)—431no—
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
264#135—431no—
265#135—431no—
266#135—861no—
267#135—861no—
268#135—861no—
269#135—861no—
270C2×SD16—431no—
271C2×SD16—431no—
272C2×SD16—431no—
273C2×SD16—861no—
274C2×SD16—861no—
275C2×SD16—861no—
276C2×SD16—861no—
277C2×SD16C2×D4311yescharacteristic, complemented
278#131—431no—
279#131—431no—
280#131—431no—
281#131C2×D4311yescharacteristic, complemented
282C4⋊Q8—431no—
283#127—431no—
284#108—431no—
285#108C2×D4311yescharacteristic, complemented
286#104—431no—
287#104—431no—
288#104—431no—
289#104—431no—
290#101—431no—
291#101C2×D4311yescharacteristic, complemented
292#100—431no—
293#100C2×D4311yescharacteristic, complemented
294C4×C8—431no—
295#41—431no—
296#41—431no—
297#41—431no—
298#41—861no—
299#41—861no—
300#41—861no—
301#41—861no—
302#41—861no—
303#41—861no—
304#41—861no—
305#41—861no—
306#41—1721no—
307#41—1721no—
308#41C22×D4311yescharacteristic
309C2×Q8—431no—
310C2×Q8—861no—
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8C22×D4311yescharacteristic
315C2×D4—431no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—1721no—
321C2×D4—1721no—
322C2×D4—1721no—
323C2×D4C22×D4311yescharacteristic
324Q16—21no—
325Q16—431no—
326Q16—431no—
327Q16—861no—
328Q16—861no—
329Q16—861no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—431no—
335SD16—431no—
336SD16—431no—
337SD16—431no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346SD16—861no—
347SD16—861no—
348SD16—861no—
349SD16—861no—
350D8—21no—
351D8—431no—
352D8—431no—
353D8—861no—
354D8—861no—
355D8—861no—
356M16—21no—
357M16—431no—
358M16—861no—
359M16—861no—
360M16—861no—
361M16C22×D4311yescharacteristic
362M16C22×D4311yescharacteristic
363M16C22×D4311yescharacteristic
364C2×C8—21no—
365C2×C8—431no—
366C2×C8—861no—
367C2×C8—861no—
368C2×C8—861no—
369C2×C8C22×D4311yescharacteristic
370C4⋊C4—1721no—
371C42—431no—
372C23—21no—
373C23—861no—
374C23—1721no—
375C23—1721no—
376Q8—21no—
377Q8—21no—
378Q8—431no—
379Q8—431no—
380Q8—431no—
381Q8—861no—
382Q8—861no—
383Q8—1721no—
384Q8—1721no—
385Q8D4×D4311yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—431no—
390D4—431no—
391D4—431no—
392D4—861no—
393D4—861no—
394D4—861no—
395D4—861no—
396D4—861no—
397D4—3442no—
398D4—1721no—
399D4—1721no—
400D4—1721no—
401D4—1721no—
402D4—1721no—
403D4—1721no—
404D4D4×D4311yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4C23×D4311yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—431no—
423C8—431no—
424C8—861no—
425C8D4×D4311yescharacteristic
426C8D4×D4311yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—861no—
431C22—861no—
432C22—861no—
433C22—3441no—
434C22—1721no—
435C22—6881no—
436C22—6881no—
437C22#1306337111yescharacteristic
438C4—21no—
439C4—41no—
440C4—862no—
441C4—861no—
442C4—861no—
443C4—861no—
444C4—1721no—
445C4C2×D4×D4311yescharacteristic
446C4C2×D4×D4311yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—3441no—
451C2—1721no—
452C2—1721no—
453C2—1721no—
454C2#1458353311yescharacteristic
subgroupG/H
centerC2#14583533
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#471C2
socleC2×C43D42
hypercenter#471D43
hypocenterC43#3291
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. #14583711C2semidirect
2. #14583709C2semidirect
3. #14583708C2semidirect
4. #14583705C2semidirect
5. #14583270C2semidirect
6. #14583165C2semidirect
7. #14583163C2semidirect
8. #14583161C2semidirect
9. #14583084C2semidirect
10. #14583080C2semidirect
11. #14583069C2semidirect
12. #14583065C2semidirect
13. #14583015C2semidirect
14. #14583014C2semidirect
15. C43×#471C2semidirect
18. #13063371C22semidirect
19. #13063370C22semidirect
21. #13063358C22semidirect
22. #13063358C22semidirect
24. #13063356C22semidirect
41. C2×#10621873C22semidirect
42. C2×#10621883C22semidirect
43. C2×#10621884C22semidirect
47. #13063333C22semidirect
48. #13063333C22semidirect
49. #13063331C22semidirect
50. #13063323C22semidirect
52. #13063260C22semidirect
53. #13063252C22semidirect
54. #13063251C22semidirect
55. #13063251C22semidirect
56. #13063251C22semidirect
57. #13063243C22semidirect
58. #13063241C22semidirect
59. C8×Dic43C22semidirect
60. #137×C43C22semidirect
62. C2×SD16×C43C22semidirect
63. #131×C43C22semidirect
64. #108×C43C22semidirect
65. #101×C43C22semidirect
66. #100×C43C22semidirect
109. #10621885D4semidirect
113. #10621884D4semidirect
117. #10621883D4semidirect
119. #10621882D4semidirect
126. Dic172D4semidirect
129. D344D4semidirect
136. #10621873D4semidirect
137. #10621873D4semidirect
236. #471D43semidirect
243. C43#3291semidirect
255. #137C2×D43semidirect
277. C2×SD16C2×D43semidirect
281. #131C2×D43semidirect
285. #108C2×D43semidirect
291. #101C2×D43semidirect
293. #100C2×D43semidirect