Finite Group Databasebeta

← #19146386

Subgroups — #19146386

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#14583710C211yesmaximal, characteristic, complemented
2#14583707C211yesmaximal, characteristic, complemented
3#14583706C211yesmaximal, characteristic, complemented
4#14583270C211yesmaximal, characteristic, complemented
5#14583164C211yesmaximal, characteristic, complemented
6#14583162C211yesmaximal, characteristic, complemented
7#14583160C211yesmaximal, characteristic, complemented
8#14583159C211yesmaximal, characteristic, complemented
9#14583082C211yesmaximal, characteristic, complemented
10#14583080C211yesmaximal, characteristic, complemented
11#14583067C211yesmaximal, characteristic, complemented
12#14583065C211yesmaximal, characteristic, complemented
13#14583016C211yesmaximal, characteristic, complemented
14#14583014C211yesmaximal, characteristic, complemented
15C43×#577C211yesmaximal, characteristic, complemented
16#13063372C2211yescharacteristic
17#13063371C2211yescharacteristic, complemented
18#13063357—21no—
19#13063356—21no—
20#13063356C2211yescharacteristic, complemented
21#13063355—21no—
22#13063355C2211yescharacteristic, complemented
23#13063355C2211yescharacteristic, complemented
24#13063351—21no—
25#13063351C2211yescharacteristic
26#13063350—21no—
27#13063350C2211yescharacteristic
28#13063350C2211yescharacteristic
29#13063349—21no—
30#13063346—21no—
31#13063345—21no—
32#13063345—21no—
33#13063345C2211yescharacteristic
34C2×#10621873C2211yescharacteristic, complemented
35C2×#10621883—21no—
36C2×#10621883C2211yescharacteristic, complemented
37C2×#10621884—21no—
38C2×#10621884C2211yescharacteristic, complemented
39SD16×D43—21no—
40#13063332C2211yescharacteristic, complemented
41#13063332C2211yescharacteristic, complemented
42#13063331C2211yescharacteristic, complemented
43#13063323C2211yescharacteristic, complemented
44#13063321C2211yescharacteristic
45#13063261C2211yescharacteristic, complemented
46#13063260C2211yescharacteristic, complemented
47#13063252C2211yescharacteristic, complemented
48#13063252C2211yescharacteristic, complemented
49#13063252C2211yescharacteristic, complemented
50#13063251C2211yescharacteristic, complemented
51#13063244C2211yescharacteristic, complemented
52#13063243C2211yescharacteristic, complemented
53#13063242C2211yescharacteristic, complemented
54#13063241C2211yescharacteristic, complemented
55C8×Dic43C2211yescharacteristic, complemented
562−1+4×C43C2211yescharacteristic
57H(5,𝔽2)×C43C2211yescharacteristic, complemented
58#137×C43—21no—
59#137×C43C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C43—21no—
61AGL(1,ℤ/8)×C43C2211yescharacteristic
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—
84Q8×D43—21no—
85#10621900—21no—
86#10621900—41no—
87D4×D43—21no—
88D4×D43—41no—
89#10621898—21no—
90#10621898—21no—
91#10621898C2311yescharacteristic
92C2×D172—21no—
93C2×D172C2311yescharacteristic
94C2×Dic86—21no—
95C2×Dic86C2311yescharacteristic
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#10621885—21no—
112#10621885—21no—
113#10621885D411yescharacteristic, complemented
114#10621884—21no—
115#10621884—21no—
116#10621884—21no—
117#10621884—21no—
118#10621884—21no—
119#10621884D411yescharacteristic, complemented
120#10621883—21no—
121#10621883—21no—
122#10621883—21no—
123#10621883—21no—
124#10621883—21no—
125#10621883D411yescharacteristic, complemented
126#10621882—21no—
127#10621882—21no—
128#10621882—21no—
129#10621882D411yescharacteristic, complemented
130Dic43⋊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
140#10621873—21no—
141#10621873—21no—
142#10621872—21no—
143C8×D43—21no—
144C23×C43—21no—
145C23×C43—41no—
146C22×D43—21no—
147C22×D43—41no—
148Q8×C43—21no—
149Q8×C43—21no—
150Q8×C43—41no—
151Q8×C43C2×D411yescharacteristic
152Q8×C43C2×D411yescharacteristic
153Q8×C43C2×D411yescharacteristic
154D4×C43—21no—
155D4×C43—21no—
156D4×C43—21no—
157D4×C43—21no—
158D4×C43—21no—
159D4×C43—41no—
160D4×C43—41no—
161D4×C43—41no—
162D4×C43C2×D411yescharacteristic
163D4×C43C2×D411yescharacteristic
164D4×C43C2×D411yescharacteristic
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43C2411yescharacteristic
173C22⋊D43—21no—
174C22⋊D43—41no—
175C22⋊D43—41no—
176C22⋊D43—82no—
177C2×Dic43—21no—
178C2×Dic43—21no—
179C2×Dic43—41no—
180D172—21no—
181D172—21no—
182D172—41no—
183D172C2×D411yescharacteristic
184C4×D43—21no—
185C4×D43—41no—
186C4×D43—41no—
187Dic86—21no—
188Dic86—21no—
189Dic86—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—81no—
209C2×D43—161no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—41no—
214C4×C43C22×D411yescharacteristic
215C4×C43C22×D411yescharacteristic
216Dic43—22no—
217Dic43—21no—
218Dic43—41no—
219#3291—431nomaximal, Sylow
220C2×C43—21no—
221C2×C43—41no—
222C2×C43—41no—
223C2×C43—41no—
224C2×C43—81no—
225C2×C43D4211yescharacteristic
226D43—41no—
227D43—81no—
228#577—431no—
229#577—431no—
230#577—431no—
231#577D4311yescharacteristic, complemented
232#492—431no—
233#471—431no—
234#471—431no—
235#471—431no—
236#471—431no—
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+4C2×D4311yescharacteristic
246H(5,𝔽2)—431no—
247H(5,𝔽2)C2×D4311yescharacteristic, complemented
248#137—21no—
249#137—431no—
250#137—431no—
251#137—431no—
252#137—861no—
253#137—861no—
254#137—861no—
255#137C2×D4311yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
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)C2×D4311yescharacteristic
264#135—21no—
265#135—431no—
266#135—861no—
267#135—861no—
268#135—861no—
269#135C2×D4311yescharacteristic
270C2×SD16—21no—
271C2×SD16—431no—
272C2×SD16—431no—
273C2×SD16—431no—
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#108—431no—
286#104—431no—
287#104—431no—
288#104—431no—
289#104—431no—
290#101—431no—
291#101—431no—
292#100—431no—
293#100—431no—
294C4×C8—431no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—431no—
301#41—861no—
302#41—861no—
303#41—861no—
304#41—861no—
305#41—1721no—
306#41C22×D4311yescharacteristic
307#41C22×D4311yescharacteristic
308#41C22×D4311yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—431no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8C22×D4311yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—431no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—1721no—
322C2×D4—1721no—
323C2×D4C22×D4311yescharacteristic
324Q16—21no—
325Q16—431no—
326Q16—861no—
327Q16—861no—
328Q16—861no—
329Q16C22⋊D4311yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—431no—
335SD16—431no—
336SD16—861no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346SD16—861no—
347SD16—861no—
348SD16C22⋊D4311yescharacteristic, complemented
349SD16C22⋊D4311yescharacteristic, complemented
350D8—21no—
351D8—431no—
352D8—861no—
353D8—861no—
354D8—861no—
355D8C22⋊D4311yescharacteristic, complemented
356M16—21no—
357M16—431no—
358M16—431no—
359M16—431no—
360M16—861no—
361M16—861no—
362M16—861no—
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—41no—
374C23—861no—
375C23—1721no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—431no—
380Q8—861no—
381Q8—861no—
382Q8—1721no—
383Q8D4×D4311yescharacteristic
384Q8C2×C22⋊D4311yescharacteristic
385Q8C2×C22⋊D4311yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—431no—
395D4—861no—
396D4—861no—
397D4—861no—
398D4—3442no—
399D4—1721no—
400D4—1721no—
401D4—1721no—
402D4D4×D4311yescharacteristic
403D4C2×C22⋊D4311yescharacteristic
404D4C2×C22⋊D4311yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—861no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4C23×D4311yescharacteristic
419C8—21no—
420C8—431no—
421C8—431no—
422C8—861no—
423C8—861no—
424C8—861no—
425C8C2×C22⋊D4311yescharacteristic
426C8C2×C22⋊D4311yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—861no—
434C22—3441no—
435C22—1721no—
436C22—6881no—
437C22#1306337011yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—862no—
443C4—861no—
444C4—1721no—
445C4C2×D4×D4311yescharacteristic
446C4C22×C22⋊D4311yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—3441no—
453C2—1721no—
454C2D4×C22⋊D4311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#577C2
socleC2×C43D42
hypercenter#577D43
hypocenterC43#3291
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. #14583710C2semidirect
2. #14583707C2semidirect
3. #14583706C2semidirect
4. #14583270C2semidirect
5. #14583164C2semidirect
6. #14583162C2semidirect
7. #14583160C2semidirect
8. #14583159C2semidirect
9. #14583082C2semidirect
10. #14583080C2semidirect
11. #14583067C2semidirect
12. #14583065C2semidirect
13. #14583016C2semidirect
14. #14583014C2semidirect
15. C43×#577C2semidirect
17. #13063371C22semidirect
20. #13063356C22semidirect
22. #13063355C22semidirect
23. #13063355C22semidirect
34. C2×#10621873C22semidirect
36. C2×#10621883C22semidirect
38. C2×#10621884C22semidirect
40. #13063332C22semidirect
41. #13063332C22semidirect
42. #13063331C22semidirect
43. #13063323C22semidirect
45. #13063261C22semidirect
46. #13063260C22semidirect
47. #13063252C22semidirect
48. #13063252C22semidirect
49. #13063252C22semidirect
50. #13063251C22semidirect
51. #13063244C22semidirect
52. #13063243C22semidirect
53. #13063242C22semidirect
54. #13063241C22semidirect
55. C8×Dic43C22semidirect
57. H(5,𝔽2)×C43C22semidirect
59. #137×C43C22semidirect
65. C2×SD16×C43C22semidirect
66. #131×C43C22semidirect
97. Q16×C43D4semidirect
102. SD16×C43D4semidirect
103. SD16×C43D4semidirect
105. D8×C43D4semidirect
113. #10621885D4semidirect
119. #10621884D4semidirect
125. #10621883D4semidirect
129. #10621882D4semidirect
231. #577D43semidirect
243. C43#3291semidirect
247. H(5,𝔽2)C2×D43semidirect
255. #137C2×D43semidirect
277. C2×SD16C2×D43semidirect
281. #131C2×D43semidirect
329. Q16C22⋊D43semidirect
348. SD16C22⋊D43semidirect
349. SD16C22⋊D43semidirect
355. D8C22⋊D43semidirect