Finite Group Databasebeta

← #19146360

Subgroups — #19146360

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#14583708C211yesmaximal, characteristic, complemented
2#14583705C211yesmaximal, characteristic, complemented
3#14583704C211yesmaximal, characteristic, complemented
4#14583703C211yesmaximal, characteristic, complemented
5#14583285C211yesmaximal, characteristic, complemented
6#14583170C211yesmaximal, characteristic, complemented
7#14583168C211yesmaximal, characteristic, complemented
8#14583165C211yesmaximal, characteristic, complemented
9#14583075C211yesmaximal, characteristic, complemented
10#14583074C211yesmaximal, characteristic, complemented
11#14583069C211yesmaximal, characteristic, complemented
12#14583065C211yesmaximal, characteristic, complemented
13#14583020C211yesmaximal, characteristic, complemented
14#14583019C211yesmaximal, characteristic, complemented
15C43×#471C211yesmaximal, characteristic, complemented
16#13063373C2211yescharacteristic, complemented
17#13063371C2211yescharacteristic
18#13063371C2211yescharacteristic, complemented
19#13063370C2211yescharacteristic, complemented
20#13063357—21no—
21#13063356C2211yescharacteristic, complemented
22#13063354—21no—
23#13063353—21no—
24#13063353—21no—
25#13063353C2211yescharacteristic
26#13063353C2211yescharacteristic, complemented
27#13063353C2211yescharacteristic, complemented
28#13063353C2211yescharacteristic, complemented
29#13063352—21no—
30#13063352—21no—
31#13063352—21no—
32#13063351C2211yescharacteristic, complemented
33#13063349—21no—
34#13063348—21no—
35#13063347—21no—
36#13063347C2211yescharacteristic
37#13063346—21no—
38#13063346—21no—
39#13063345C2211yescharacteristic
40C2×#10621884C2211yescharacteristic, complemented
41SD16×D43—21no—
42SD16×D43—21no—
43C2×D344—21no—
44C2×D344C2211yescharacteristic, complemented
45C2×#10621882C2211yescharacteristic, complemented
46D8×D43—21no—
47#13063333C2211yescharacteristic, complemented
48#13063333C2211yescharacteristic, complemented
49#13063331C2211yescharacteristic, complemented
50#13063321C2211yescharacteristic, complemented
51#13063314C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063252C2211yescharacteristic, complemented
54#13063251C2211yescharacteristic, complemented
55#13063251C2211yescharacteristic, complemented
56#13063251C2211yescharacteristic, complemented
57#13063241C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59#13063235C2211yescharacteristic, 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—
75#10621902—21no—
76Q8×D43—21no—
77Q8×D43—21no—
78#10621900—21no—
79#10621900—21no—
80D4×D43—21no—
81D4×D43—21no—
82D4×D43—21no—
83D4×D43—21no—
84D4×D43—41no—
85D4×D43—41no—
86#10621898—21no—
87#10621898—21no—
88#10621898—41no—
89#10621898C2311yescharacteristic
90#10621898C2311yescharacteristic
91#10621898C2311yescharacteristic
92C2×D172—21no—
93C2×D172—21no—
94C2×D172C2311yescharacteristic
95C2×D172C2311yescharacteristic
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#10621883D411yescharacteristic, complemented
116#10621882—21no—
117#10621882—21no—
118#10621882—21no—
119#10621882D411yescharacteristic, complemented
120(C2×D43)⋊C4—41no—
121C4×Dic43C2311yescharacteristic
122#10621877C2311yescharacteristic
123C2×C43⋊C8C2311yescharacteristic
124Dic172D411yescharacteristic, complemented
125D344—21no—
126D344—21no—
127D344—21no—
128D344—21no—
129D344—21no—
130D344—21no—
131D344D411yescharacteristic, complemented
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—21no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150Q8×C43—21no—
151Q8×C43—21no—
152Q8×C43C2×D411yescharacteristic
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—21no—
156D4×C43C2×D411yescharacteristic
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43C2411yescharacteristic
160C22⋊D43—21no—
161C22⋊D43—21no—
162C22⋊D43—21no—
163C22⋊D43—41no—
164C22⋊D43—41no—
165C22⋊D43—41no—
166C22⋊D43—41no—
167C22⋊D43—82no—
168C2×Dic43—21no—
169C2×Dic43—41no—
170D172—21no—
171D172—21no—
172D172—21no—
173D172—21no—
174D172—41no—
175D172—41no—
176D172—41no—
177D172C2×D411yescharacteristic
178D172C2×D411yescharacteristic
179D172C2×D411yescharacteristic
180C4×D43—21no—
181C4×D43—21no—
182C4×D43—21no—
183C4×D43—41no—
184C4×D43—41no—
185C4×D43—41no—
186C4×D43—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—41no—
208C2×D43—81no—
209C2×D43—81no—
210C2×D43—161no—
211C2×D43—161no—
212C2×D43—161no—
213C4×C43—21no—
214C4×C43—41no—
215C4×C43C22×D411yescharacteristic
216C4×C43C22×D411yescharacteristic
217Dic43—21no—
218Dic43—21no—
219Dic43—21no—
220Dic43—41no—
221#3288—431nomaximal, Sylow
222C2×C43—21no—
223C2×C43—41no—
224C2×C43—81no—
225C2×C43D4211yescharacteristic
226D43—41no—
227D43—41no—
228D43—41no—
229D43—81no—
230D43—81no—
231#577—431no—
232#577—431no—
233#576—431no—
234#576—431no—
235#496—431no—
236#472—431no—
237#472—431no—
238#471—431no—
239#471D4311yescharacteristic, complemented
240#455—431no—
241#454—431no—
242#453—431no—
243#453—431no—
244#444—431no—
245#444—431no—
246C43#328811yescharacteristic, complemented, Sylow
2472−1+4—431no—
248H(5,𝔽2)—431no—
249H(5,𝔽2)—431no—
250H(5,𝔽2)—431no—
251#137—431no—
252#137—861no—
253#137—861no—
254#137C2×D4311yescharacteristic, complemented
255AGL(1,ℤ/8)—431no—
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—431no—
258AGL(1,ℤ/8)—431no—
259AGL(1,ℤ/8)—431no—
260AGL(1,ℤ/8)—861no—
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
267#135—431no—
268#135—431no—
269#135—861no—
270#135—861no—
271#135—861no—
272#135—861no—
273C2×SD16—431no—
274C2×SD16—861no—
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#108C2×D4311yescharacteristic, complemented
289#104—431no—
290#104—431no—
291#104—431no—
292#104—431no—
293#101C2×D4311yescharacteristic, complemented
294#100—431no—
295#100—431no—
296#100C2×D4311yescharacteristic, complemented
297#97—431no—
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#41—861no—
308#41—861no—
309#41—1721no—
310#41C22×D4311yescharacteristic
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8C22×D4311yescharacteristic
314C2×D4—431no—
315C2×D4—431no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—861no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C2×D4C22×D4311yescharacteristic
327Q16—21no—
328Q16—431no—
329Q16—431no—
330Q16—861no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—431no—
336SD16—431no—
337SD16—431no—
338SD16—431no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346SD16—861no—
347D8—21no—
348D8—431no—
349D8—431no—
350D8—861no—
351D8—861no—
352D8—861no—
353D8—861no—
354D8—861no—
355D8—861no—
356D8—861no—
357D8—861no—
358D8—861no—
359M16—21no—
360M16—431no—
361M16—861no—
362M16—861no—
363M16—861no—
364M16C22×D4311yescharacteristic
365M16C22×D4311yescharacteristic
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—861no—
377C23—861no—
378C23—1721no—
379C23—1721no—
380C23—1721no—
381Q8—21no—
382Q8—21no—
383Q8—431no—
384Q8—431no—
385Q8—431no—
386Q8—1721no—
387Q8D4×D4311yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—431no—
392D4—431no—
393D4—431no—
394D4—861no—
395D4—861no—
396D4—861no—
397D4—861no—
398D4—861no—
399D4—861no—
400D4—861no—
401D4—3442no—
402D4—1721no—
403D4—1721no—
404D4—1721no—
405D4—1721no—
406D4—1721no—
407D4—1721no—
408D4—1721no—
409D4D4×D4311yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—861no—
415C2×C4—861no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4C23×D4311yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—431no—
426C8—431no—
427C8—861no—
428C8D4×D4311yescharacteristic
429C8D4×D4311yescharacteristic
430C22—21no—
431C22—41no—
432C22—81no—
433C22—861no—
434C22—861no—
435C22—861no—
436C22—3441no—
437C22—3441no—
438C22—1721no—
439C22—1721no—
440C22—6881no—
441C22—6881no—
442C22—6881no—
443C22#1306337111yescharacteristic
444C4—21no—
445C4—41no—
446C4—861no—
447C4—861no—
448C4—861no—
449C4—1721no—
450C4C2×D4×D4311yescharacteristic
451C4C2×D4×D4311yescharacteristic
452C2—21no—
453C2—41no—
454C2—81no—
455C2—3441no—
456C2—3441no—
457C2—1721no—
458C2—1721no—
459C2—1721no—
460C2#1458353311yescharacteristic
subgroupG/H
centerC2#14583533
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#471C2
socleC2×C43D42
hypercenter#471D43
hypocenterC43#3288
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. #14583708C2semidirect
2. #14583705C2semidirect
3. #14583704C2semidirect
4. #14583703C2semidirect
5. #14583285C2semidirect
6. #14583170C2semidirect
7. #14583168C2semidirect
8. #14583165C2semidirect
9. #14583075C2semidirect
10. #14583074C2semidirect
11. #14583069C2semidirect
12. #14583065C2semidirect
13. #14583020C2semidirect
14. #14583019C2semidirect
15. C43×#471C2semidirect
16. #13063373C22semidirect
18. #13063371C22semidirect
19. #13063370C22semidirect
21. #13063356C22semidirect
26. #13063353C22semidirect
27. #13063353C22semidirect
28. #13063353C22semidirect
32. #13063351C22semidirect
40. C2×#10621884C22semidirect
44. C2×D344C22semidirect
45. C2×#10621882C22semidirect
47. #13063333C22semidirect
48. #13063333C22semidirect
49. #13063331C22semidirect
50. #13063321C22semidirect
51. #13063314C22semidirect
52. #13063260C22semidirect
53. #13063252C22semidirect
54. #13063251C22semidirect
55. #13063251C22semidirect
56. #13063251C22semidirect
57. #13063241C22semidirect
58. #13063241C22semidirect
59. #13063235C22semidirect
60. #137×C43C22semidirect
62. C2×SD16×C43C22semidirect
63. #131×C43C22semidirect
64. #108×C43C22semidirect
65. #101×C43C22semidirect
66. #100×C43C22semidirect
109. #10621885D4semidirect
113. #10621884D4semidirect
115. #10621883D4semidirect
119. #10621882D4semidirect
124. Dic172D4semidirect
131. D344D4semidirect
136. #10621873D4semidirect
137. #10621873D4semidirect
239. #471D43semidirect
246. C43#3288semidirect
254. #137C2×D43semidirect
276. C2×SD16C2×D43semidirect
284. #131C2×D43semidirect
288. #108C2×D43semidirect
293. #101C2×D43semidirect
296. #100C2×D43semidirect