Finite Group Databasebeta

← #19146412

Subgroups — #19146412

Order 5504.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583607C211yesmaximal, characteristic, complemented
2D4×C22⋊D43C211yesmaximal, characteristic
3#14583244C211yesmaximal, characteristic, complemented
4#14583218C211yesmaximal, characteristic, complemented
5#14583216C211yesmaximal, characteristic, complemented
6#14583187C211yesmaximal, characteristic, complemented
7#14583130C211yesmaximal, characteristic, complemented
8#14583125C211yesmaximal, characteristic, complemented
9#14583097C211yesmaximal, characteristic, complemented
10#14583048C211yesmaximal, characteristic, complemented
11SD16×Dic43C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
13C2×#13063246C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#450C211yesmaximal, characteristic, complemented
16C22×C22⋊D43—21no—
17C2×D4×D43C2211yescharacteristic
18C2×#10621884C2211yescharacteristic, complemented
19C22×C43⋊C8C2211yescharacteristic, complemented
20C2×C8×D43C2211yescharacteristic, complemented
21#13063324C2211yescharacteristic, complemented
22#13063321C2211yescharacteristic
23#13063315—21no—
24#13063305—21no—
25#13063302—21no—
26#13063301C2211yescharacteristic, complemented
27#13063299C2211yescharacteristic
28#13063297—21no—
29#13063296C2211yescharacteristic
30#13063294—21no—
31#13063293—21no—
32Q8×Dic43C2211yescharacteristic, complemented
33D4×Dic43C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36C2×C4⋊Dic43C2211yescharacteristic, complemented
37C4⋊C4×D43C2211yescharacteristic, complemented
38#13063257C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic, complemented
48#13063246C2211yescharacteristic, complemented
49#13063245C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic, complemented
55C22⋊Q8×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic, complemented
59C24×C43—21no—
60C23×D43—21no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43—22no—
64C2×D4×C43—41no—
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—44no—
74C2×C22⋊D43D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77D4×D43—22no—
78D4×D43—41no—
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43C2311yescharacteristic
82C2×Dic86—21no—
83SD16×C43—22no—
84SD16×C43—41no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43D411yescharacteristic
93#10621884—41no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4D411yescharacteristic
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8—41no—
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C8×D43—41no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—42no—
115C23×C43—42no—
116C23×C43—81no—
117C23×C43C2×D411yescharacteristic
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—42no—
121C22×D43—81no—
122C22×D43C2×D411yescharacteristic
123Q8×C43—21no—
124Q8×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—42no—
129D4×C43#4112yes—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2411yescharacteristic
136C22⋊D43—42no—
137C22⋊D43—42no—
138C22⋊D43—42no—
139C22⋊D43—42no—
140C22⋊D43—81no—
141C22⋊D43SD1614yescomplemented
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—42no—
146C2×Dic43—81no—
147C2×Dic43C2×D411yescharacteristic
148C2×Dic43C2×D411yescharacteristic
149C2×Dic43C2×D411yescharacteristic
150D172—21no—
151D172—21no—
152C4×D43—21no—
153C4×D43—21no—
154C4×D43—81no—
155Dic86—81no—
156C8×C43—21no—
157C8×C43—21no—
158C43⋊C8—21no—
159C43⋊C8—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—22no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—84no—
169C22×C43C2×SD1612yes—
170C22×C43C22×D411yescharacteristic
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—84no—
177C2×D43C2×SD1612yes—
178C4×C43—21no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43C2×#4111yescharacteristic
182C4×C43H(5,𝔽2)11yescharacteristic
183Dic43—21no—
184Dic43—21no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188Dic43C2×SD1612yes—
189#3295—431nomaximal, Sylow
190C2×C43—22no—
191C2×C43—42no—
192C2×C43—81no—
193C2×C43#54611yescharacteristic
194C2×C43C22×SD1611yescharacteristic
195C2×C43#57611yescharacteristic
196D43—22no—
197D43—81no—
198#554—431no—
199D42—431no—
200#486—431no—
201#481—431no—
202#481—431no—
203#476—431no—
204#465—431no—
205#465—431no—
206#460—431no—
207#450—431no—
208#450D4311yescharacteristic, complemented
209C4×SD16—431no—
210C8×D4—431no—
211C2×#102—431no—
212C2×#102—431no—
213C43#329511yescharacteristic, complemented, Sylow
214C22×D4—431no—
215C22×D4—861no—
216C22×D4C2×D4311yescharacteristic
217C2×SD16—431no—
218C2×SD16C2×D4311yescharacteristic
219C2×SD16C2×D4311yescharacteristic, complemented
220C22×C8—431no—
221C22×C8—431no—
222C4⋊Q8—431no—
223#127—431no—
224#125—861no—
225C22⋊Q8—431no—
226C22⋊Q8—861no—
227C22⋊Q8—861no—
228C22⋊Q8C2×D4311yescharacteristic, complemented
229#121—431no—
230#121—431no—
231#121—861no—
232#120—861no—
233#120—861no—
234C4×Q8—431no—
235C4×D4—431no—
236C4×D4—431no—
237C4×D4—861no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240#106—431no—
241#106—431no—
242#106—431no—
243C4⋊C8—431no—
244#103—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252#102C2×D4311yescharacteristic
253#102C2×D4311yescharacteristic, complemented
254C22⋊C8—431no—
255C22⋊C8C2×D4311yescharacteristic, complemented
256C4×C8—431no—
257C24—21no—
258C24—861no—
259C2×Q8—861no—
260C2×Q8C22×D4311yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—431no—
265C2×D4—431no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—862no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—1721no—
273C2×D4—1724no—
274C2×D4C22×D4311yescharacteristic
275C2×D4C22×D4311yescharacteristic
276C22×C4—431no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4C22×D4311yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—1721no—
284C2×C8—431no—
285C2×C8—431no—
286C2×C8—1721no—
287C2×C8—1721no—
288C2×C8C22×D4311yescharacteristic
289C2×C8C22×D4311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—431no—
292C4⋊C4—431no—
293C4⋊C4—431no—
294C4⋊C4—431no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4C22×D4311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—431no—
303C22⋊C4—431no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C42—431no—
309C42—861no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—431no—
316C23—861no—
317C23—3441no—
318C23—1722no—
319C23—1722no—
320C23D4×D4311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—3441no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—434no—
329D4—861no—
330D4—861no—
331D4—3441no—
332D4—1722no—
333D4—1722no—
334D4—1722no—
335D4—1722no—
336D4#1062190012yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—431no—
342C2×C4—431no—
343C2×C4—431no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—1722no—
352C2×C4D4×D4311yescharacteristic
353C2×C4C23×D4311yescharacteristic
354C8—21no—
355C8—21no—
356C8—861no—
357C8—861no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—432no—
368C22—861no—
369C22—861no—
370C22—3444no—
371C22—1721no—
372C22—1721no—
373C22—1721no—
374C22SD16×D4312yes—
375C22C2×D4×D4311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—432no—
380C4—861no—
381C4—861no—
382C4—1721no—
383C4—1721no—
384C4—1721no—
385C4C2×#1062190011yescharacteristic
386C4#1306337011yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—862no—
391C2—3441no—
392C2#1458353611yescharacteristic
393C2C2×SD16×D4311yescharacteristic
394C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3295
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583607C2semidirect
3. #14583244C2semidirect
4. #14583218C2semidirect
5. #14583216C2semidirect
6. #14583187C2semidirect
7. #14583130C2semidirect
8. #14583125C2semidirect
9. #14583097C2semidirect
10. #14583048C2semidirect
11. SD16×Dic43C2semidirect
12. (C22⋊D43)⋊C8C2semidirect
13. C2×#13063246C2semidirect
14. #102×D43C2semidirect
15. C43×#450C2semidirect
18. C2×#10621884C22semidirect
19. C22×C43⋊C8C22semidirect
20. C2×C8×D43C22semidirect
21. #13063324C22semidirect
26. #13063301C22semidirect
32. Q8×Dic43C22semidirect
36. C2×C4⋊Dic43C22semidirect
37. C4⋊C4×D43C22semidirect
38. #13063257C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063249C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
47. #13063246C22semidirect
48. #13063246C22semidirect
49. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
54. C2×SD16×C43C22semidirect
55. C22⋊Q8×C43C22semidirect
57. #102×C43C22semidirect
58. C22⋊C8×C43C22semidirect
141. C22⋊D43SD16semidirect
208. #450D43semidirect
213. C43#3295semidirect
219. C2×SD16C2×D43semidirect
228. C22⋊Q8C2×D43semidirect
253. #102C2×D43semidirect
255. C22⋊C8C2×D43semidirect