Finite Group Databasebeta

← #19143897

Subgroups — #19143897

Order 5504.

764 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063371C211yesmaximal, characteristic, complemented
2C2×#13063349C211yesmaximal, characteristic, complemented
3C2×#13063346C211yesmaximal, characteristic, complemented
4#14583478C211yesmaximal, characteristic, complemented
5#14583064C211yesmaximal, characteristic, complemented
6#14583061C211yesmaximal, characteristic, complemented
7#14583052C211yesmaximal, characteristic, complemented
8#14583051C211yesmaximal, characteristic, complemented
9#14583043C211yesmaximal, characteristic, complemented
10#14583032C211yesmaximal, characteristic, complemented
11#14583031C211yesmaximal, characteristic, complemented
12#14582899C211yesmaximal, characteristic, complemented
13#102×D43C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#449C211yesmaximal, characteristic, complemented
16#13063371—24no—
17#13063371—24no—
18C2×#10621902C2211yescharacteristic
19C2×#10621902C2211yescharacteristic
20C2×#10621898—21no—
21C2×#10621898C2211yescharacteristic
22C2×#10621900C2211yescharacteristic, complemented
23C22×D172—21no—
24C22×D172C2211yescharacteristic
25C2×D4×D43—21no—
26C2×D4×D43—21no—
27C2×D4×D43C2211yescharacteristic
28C2×D4×D43C2211yescharacteristic
29#13063349—24no—
30#13063346—24no—
31C2×#10621885C2211yescharacteristic, complemented
32C2×#10621873C2211yescharacteristic, complemented
33C2×#10621873C2211yescharacteristic, complemented
34C2×#10621883C2211yescharacteristic, complemented
35C2×#10621882C2211yescharacteristic, complemented
36C2×#10621882C2211yescharacteristic, complemented
37C2×#10621872C2211yescharacteristic, complemented
38C2×C8×D43C2211yescharacteristic, complemented
39#13063305C2211yescharacteristic, complemented
40#13063304C2211yescharacteristic, complemented
41#13063302—21no—
42#13063298—21no—
43#13063297—21no—
44#13063296—21no—
45#13063296C2211yescharacteristic, complemented
46C4⋊C4×D43C2211yescharacteristic, complemented
47#13063249C2211yescharacteristic, complemented
48#13063247C2211yescharacteristic, complemented
49#13063247C2211yescharacteristic, complemented
50#13063246C2211yescharacteristic, complemented
51#13063245C2211yescharacteristic, complemented
52#13063245C2211yescharacteristic, complemented
53C22⋊(C43⋊C8)C2211yescharacteristic, complemented
54(C2×D43)⋊C8C2211yescharacteristic, complemented
55(C2×D43)⋊C8C2211yescharacteristic, complemented
56C2×#41×C43C2211yescharacteristic
57C2×SD16×C43C2211yescharacteristic, complemented
58C2×D8×C43C2211yescharacteristic, complemented
59#121×C43C2211yescharacteristic, complemented
60#103×C43C2211yescharacteristic, complemented
61#102×C43C2211yescharacteristic, complemented
62C22⋊C8×C43C2211yescharacteristic, complemented
63C23×D43—21no—
64C23×D43—21no—
65C23×D43—21no—
66#41×C43—22no—
67#41×C43—22no—
68C2×Q8×C43C2311yescharacteristic
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43C2311yescharacteristic
72C2×D4×C43C2311yescharacteristic
73C22×C4×C43—21no—
74C22×C4×C43C2311yescharacteristic
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79C2×C22⋊D43D411yescharacteristic
80C2×C22⋊D43D411yescharacteristic
81C22×Dic43—21no—
82#10621902—22no—
83#10621902—22no—
84#10621902—22no—
85#10621902D414yescomplemented
86#10621900—22no—
87#10621900—22no—
88D4×D43—28no—
89D4×D43—28no—
90D4×D43—22no—
91D4×D43—22no—
92D4×D43—22no—
93D4×D43D414yescomplemented
94#10621898—28no—
95#10621898—22no—
96#10621898—22no—
97C2×D172—28no—
98C2×D172—21no—
99C2×D172—22no—
100C2×D172—22no—
101C2×D172—21no—
102C2×D172—21no—
103C2×D172D411yescharacteristic
104C2×D172C2311yescharacteristic
105C2×D172C2311yescharacteristic
106C2×C4×D43—21no—
107C2×C4×D43—21no—
108C2×C4×D43—21no—
109C2×C4×D43C2311yescharacteristic
110C2×C4×D43C2311yescharacteristic
111C2×Dic86D411yescharacteristic
112C2×Dic86C2311yescharacteristic
113SD16×C43—22no—
114D8×C43—22no—
115C2×C8×C43C2311yescharacteristic
116C2×C8×C43C2311yescharacteristic
117C4⋊C4×C43C2311yescharacteristic
118C22⋊C4×C43—21no—
119C22⋊Dic43—21no—
120C22⋊Dic43—21no—
121#10621885—22no—
122#10621883—22no—
123#10621882—22no—
124#10621882—22no—
125(C2×D43)⋊C4—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43C2311yescharacteristic
128Dic43⋊C4—21no—
129Dic43⋊C4—21no—
130C2×C43⋊C8C2311yescharacteristic
131C2×C43⋊C8C2311yescharacteristic
132#10621873—22no—
133#10621873—22no—
134#10621872—22no—
135C8×D43—22no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43C2×D411yescharacteristic
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—24no—
142C22×D43—24no—
143C22×D43—24no—
144C22×D43—81no—
145C22×D43—81no—
146C22×D43—81no—
147C22×D43—81no—
148C22×D43—81no—
149C22×D43—81no—
150C22×D43C2×D411yescharacteristic
151C22×D43C2×D411yescharacteristic
152Q8×C43—21no—
153Q8×C43C2×D412yes—
154D4×C43—24no—
155D4×C43—21no—
156D4×C43—21no—
157D4×C43—21no—
158D4×C43—81no—
159D4×C43C2×D412yes—
160C2×C4×C43—24no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43C2×D411yescharacteristic
166C2×C4×C43C2411yescharacteristic
167C22⋊D43—24no—
168C22⋊D43—22no—
169C22⋊D43—22no—
170C22⋊D43—24no—
171C22⋊D43—42no—
172C22⋊D43—81no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—42no—
176C2×Dic43C2×D411yescharacteristic
177C2×Dic43C2×D411yescharacteristic
178D172—24no—
179D172—24no—
180D172—22no—
181D172—24no—
182D172—21no—
183D172—21no—
184D172C2×D412yes—
185D172C2×D412yes—
186C4×D43—24no—
187C4×D43—21no—
188C4×D43—21no—
189C4×D43—24no—
190C4×D43—81no—
191C4×D43C2×D412yes—
192C4×D43C2×D412yes—
193Dic86—22no—
194Dic86—21no—
195Dic86—21no—
196C8×C43—21no—
197C8×C43—21no—
198C43⋊C8—21no—
199C43⋊C8—21no—
200C22×C43—22no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43C22×D411yescharacteristic
210C2×D43—21no—
211C2×D43—21no—
212C2×D43—22no—
213C2×D43—22no—
214C2×D43—21no—
215C2×D43—21no—
216C2×D43—21no—
217C2×D43—41no—
218C2×D43—41no—
219C2×D43—41no—
220C2×D43—41no—
221C2×D43—84no—
222C2×D43—84no—
223C2×D43—84no—
224C2×D43#12012yes—
225C4×C43—21no—
226C4×C43—22no—
227C4×C43—41no—
228C4×C43C22×D411yescharacteristic
229C4×C43C22×D411yescharacteristic
230Dic43—21no—
231Dic43—41no—
232Dic43—41no—
233Dic43#12012yes—
234#3012—431nomaximal, Sylow
235C2×C43—41no—
236C2×C43—42no—
237C2×C43—81no—
238C2×C43C2×#12011yescharacteristic
239C2×C43#57611yescharacteristic
240C2×C43#57711yescharacteristic
241D43—22no—
242D43—41no—
243D43—42no—
244D43—42no—
245C2×H(5,𝔽2)—431no—
246C2×AGL(1,ℤ/8)—431no—
247C2×#135—431no—
248#537—431no—
249#452—431no—
250#452—431no—
251#450—431no—
252#450—431no—
253#449—431no—
254#449D4311yescharacteristic, complemented
255#447—431no—
256#447—431no—
257#417—431no—
258C2×#102—431no—
259#408—431no—
260C43#301211yescharacteristic, complemented, Sylow
261H(5,𝔽2)—864no—
262H(5,𝔽2)—864no—
263C2×#41—431no—
264C2×#41—431no—
265C2×#41—431no—
266C2×#41—431no—
267C2×#41—861no—
268C2×#41C2×D4311yescharacteristic
269C22×D4—431no—
270C22×D4—431no—
271C22×D4—431no—
272C22×D4—861no—
273C22×D4—861no—
274C22×D4—861no—
275AGL(1,ℤ/8)—864no—
276#135—864no—
277C2×Q16—431no—
278C2×SD16—431no—
279C2×SD16—431no—
280C2×SD16—431no—
281C2×SD16C2×D4311yescharacteristic, complemented
282C2×D8—431no—
283C2×D8—431no—
284C2×D8C2×D4311yescharacteristic, complemented
285C2×M16—431no—
286C22×C8—431no—
287C22⋊Q8—431no—
288C22⋊Q8—431no—
289C22⋊Q8—861no—
290#121—431no—
291#121—861no—
292#121—861no—
293#121—861no—
294#121C2×D4311yescharacteristic, complemented
295C2×C4⋊C4—431no—
296#103—431no—
297#103C2×D4311yescharacteristic, complemented
298#102—431no—
299#102—431no—
300#102—431no—
301#102—431no—
302#102—431no—
303#102C2×D4311yescharacteristic, complemented
304C22⋊C8—431no—
305C22⋊C8—431no—
306C22⋊C8—431no—
307C22⋊C8C2×D4311yescharacteristic, complemented
308C24—861no—
309C24—861no—
310C24—861no—
311#41—22no—
312#41—22no—
313#41—434no—
314#41—862no—
315#41—862no—
316#41—868no—
317#41—862no—
318#41—862no—
319#41—862no—
320#41—862no—
321#41—862no—
322C2×Q8—431no—
323C2×Q8—431no—
324C2×Q8C22×D4311yescharacteristic
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—434no—
328C2×D4—431no—
329C2×D4—431no—
330C2×D4—431no—
331C2×D4—431no—
332C2×D4—431no—
333C2×D4—862no—
334C2×D4—862no—
335C2×D4—861no—
336C2×D4—861no—
337C2×D4—868no—
338C2×D4—862no—
339C2×D4—861no—
340C2×D4—861no—
341C2×D4—862no—
342C2×D4—868no—
343C2×D4—868no—
344C2×D4—862no—
345C2×D4—861no—
346C2×D4—861no—
347C2×D4—861no—
348C2×D4C22×D4311yescharacteristic
349C2×D4C22×D4311yescharacteristic
350C22×C4—21no—
351C22×C4—431no—
352C22×C4—431no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4C22×D4311yescharacteristic
358Q16—862no—
359SD16—22no—
360SD16—862no—
361SD16—862no—
362SD16—862no—
363D8—22no—
364D8—862no—
365D8—862no—
366M16—862no—
367C2×C8—431no—
368C2×C8—431no—
369C2×C8—862no—
370C2×C8C22×D4311yescharacteristic
371C2×C8C22×D4311yescharacteristic
372C4⋊C4—431no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—861no—
376C4⋊C4C22×D4311yescharacteristic
377C22⋊C4—21no—
378C22⋊C4—861no—
379C22⋊C4—861no—
380C22⋊C4—861no—
381C23—21no—
382C23—21no—
383C23—431no—
384C23—431no—
385C23—864no—
386C23—864no—
387C23—864no—
388C23—861no—
389C23—861no—
390C23—3441no—
391C23—3441no—
392C23—3441no—
393C23—3441no—
394C23—3441no—
395C23—3441no—
396C23D4×D4311yescharacteristic
397Q8—21no—
398Q8—862no—
399Q8—861no—
400Q8—861no—
401Q8D4×D4312yes—
402D4—24no—
403D4—21no—
404D4—21no—
405D4—21no—
406D4—81no—
407D4—432no—
408D4—432no—
409D4—862no—
410D4—864no—
411D4—864no—
412D4—864no—
413D4—862no—
414D4—864no—
415D4—862no—
416D4—864no—
417D4—861no—
418D4—861no—
419D4—3441no—
420D4—1722no—
421D4D4×D4312yes—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—431no—
428C2×C4—432no—
429C2×C4—432no—
430C2×C4—431no—
431C2×C4—864no—
432C2×C4—864no—
433C2×C4—861no—
434C2×C4—861no—
435C2×C4—861no—
436C2×C4—861no—
437C2×C4—3441no—
438C2×C4—1722no—
439C2×C4D4×D4311yescharacteristic
440C2×C4C23×D4311yescharacteristic
441C8—21no—
442C8—21no—
443C8—861no—
444C8—861no—
445C22—21no—
446C22—22no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—432no—
455C22—861no—
456C22—861no—
457C22—862no—
458C22—862no—
459C22—861no—
460C22—861no—
461C22—861no—
462C22—3444no—
463C22—3444no—
464C22—3444no—
465C22—1721no—
466C22—1721no—
467C22—1721no—
468C22—1721no—
469C22C2×D4×D4311yescharacteristic
470C4—21no—
471C4—22no—
472C4—41no—
473C4—432no—
474C4—861no—
475C4—1721no—
476C4—1721no—
477C4C2×D4×D4311yescharacteristic
478C4C2×D4×D4311yescharacteristic
479C2—41no—
480C2—42no—
481C2—81no—
482C2—862no—
483C2—1721no—
484C2—1722no—
485C2—1722no—
486C2#120×D4311yescharacteristic
487C2#1458370311yescharacteristic
488C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#449C2
socleC22×C43C22×D4
hypercenter#449D43
hypocenterC43#3012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#13063371C2semidirect
2. C2×#13063349C2semidirect
3. C2×#13063346C2semidirect
4. #14583478C2semidirect
5. #14583064C2semidirect
6. #14583061C2semidirect
7. #14583052C2semidirect
8. #14583051C2semidirect
9. #14583043C2semidirect
10. #14583032C2semidirect
11. #14583031C2semidirect
12. #14582899C2semidirect
13. #102×D43C2semidirect
14. #14582864C2semidirect
15. C43×#449C2semidirect
22. C2×#10621900C22semidirect
31. C2×#10621885C22semidirect
32. C2×#10621873C22semidirect
33. C2×#10621873C22semidirect
34. C2×#10621883C22semidirect
35. C2×#10621882C22semidirect
36. C2×#10621882C22semidirect
37. C2×#10621872C22semidirect
38. C2×C8×D43C22semidirect
39. #13063305C22semidirect
40. #13063304C22semidirect
45. #13063296C22semidirect
46. C4⋊C4×D43C22semidirect
47. #13063249C22semidirect
48. #13063247C22semidirect
49. #13063247C22semidirect
50. #13063246C22semidirect
51. #13063245C22semidirect
52. #13063245C22semidirect
53. C22⋊(C43⋊C8)C22semidirect
54. (C2×D43)⋊C8C22semidirect
55. (C2×D43)⋊C8C22semidirect
57. C2×SD16×C43C22semidirect
58. C2×D8×C43C22semidirect
59. #121×C43C22semidirect
60. #103×C43C22semidirect
61. #102×C43C22semidirect
62. C22⋊C8×C43C22semidirect
85. #10621902D4semidirect
93. D4×D43D4semidirect
254. #449D43semidirect
260. C43#3012semidirect
281. C2×SD16C2×D43semidirect
284. C2×D8C2×D43semidirect
294. #121C2×D43semidirect
297. #103C2×D43semidirect
303. #102C2×D43semidirect
307. C22⋊C8C2×D43semidirect