Finite Group Databasebeta

← #19144779

Subgroups — #19144779

Order 5504.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583520C211yesmaximal, characteristic, complemented
2#14583240C211yesmaximal, characteristic, complemented
3#14583223C211yesmaximal, characteristic, complemented
4#14583189C211yesmaximal, characteristic, complemented
5#14583179C211yesmaximal, characteristic, complemented
6#14583114C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583050C211yesmaximal, characteristic, complemented
9#14583033C211yesmaximal, characteristic
10#14583009C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12C4×#10621883C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582960C211yesmaximal, characteristic, complemented
15C43×#518C211yesmaximal, characteristic, complemented
16C2×#10621883C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20#13063325C2211yescharacteristic, complemented
21#13063320—21no—
22#13063313C2211yescharacteristic, complemented
23#13063311—21no—
24#13063307—21no—
25#13063304C2211yescharacteristic
26#13063303—21no—
27#13063299C2211yescharacteristic
28C4×Dic86C2211yescharacteristic, complemented
29C4×D172C2211yescharacteristic, complemented
30#13063258C2211yescharacteristic, complemented
31#13063258C2211yescharacteristic, complemented
32#13063256C2211yescharacteristic, complemented
33#13063256C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35C4⋊(C43⋊C8)C2211yescharacteristic, complemented
36#13063248C2211yescharacteristic, complemented
37#13063248C2211yescharacteristic, complemented
38#13063246C2211yescharacteristic
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic, complemented
43#13063245C2211yescharacteristic, complemented
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46#13063236C2211yescharacteristic, complemented
47C4×C43⋊C8C2211yescharacteristic, complemented
48C22×D4×C43C2211yescharacteristic
49C4×D4×C43—21no—
50C4×D4×C43—21no—
51C4×D4×C43C2211yescharacteristic
52C4×D4×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#117×C43C2211yescharacteristic
56#117×C43C2211yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C24×C43—21no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×Dic86—21no—
74C2×Dic86C2311yescharacteristic
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43D411yescharacteristic
85C22⋊C4×C43D411yescharacteristic
86C42×C43—21no—
87C42×C43C2311yescharacteristic
88C42×C43C2311yescharacteristic
89C22⋊Dic43—21no—
90#10621883—22no—
91#10621883—22no—
92#10621882—22no—
93#10621882—22no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—24no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—81no—
112C23×C43—81no—
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115D4×C43—24no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43#4112yes—
119D4×C43#4112yes—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—81no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—81no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138D172—21no—
139D172—21no—
140C4×D43—81no—
141Dic86—21no—
142Dic86—21no—
143Dic86—81no—
144C43⋊C8—21no—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—21no—
149C22×C43—22no—
150C22×C43—22no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—84no—
158C22×C43C22×D411yescharacteristic
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43C2×#4111yescharacteristic
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3118—431nomaximal, Sylow
175C2×C43—41no—
176C2×C43—42no—
177C2×C43—42no—
178C2×C43#52511yescharacteristic
179C2×C43#57611yescharacteristic
180C2×C43#57711yescharacteristic
181D43—81no—
182#542—431no—
183#518D4311yescharacteristic, complemented
184#485—431no—
185#482—431no—
186#476—431no—
187#474—431no—
188#463—431no—
189#463—431no—
190#450—431no—
191#447—431no—
192#442—431no—
193#440—431no—
194C4×SD16—431no—
195C4×D8—431no—
196#433—431no—
197C43#311811yescharacteristic, complemented, Sylow
198C22×D4C2×D4311yescharacteristic
199C2×SD16—431no—
200C2×SD16—431no—
201C2×D8—431no—
202C2×D8—431no—
203C4⋊Q8—431no—
204#126—861no—
205#124—431no—
206#124—861no—
207#123—861no—
208C22⋊Q8—431no—
209C22⋊Q8—861no—
210#121—431no—
211C4×Q8—431no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—431no—
215C4×D4C2×D4311yescharacteristic
216C4×D4C2×D4311yescharacteristic
217C4×D4C2×D4311yescharacteristic
218C4×D4C2×D4311yescharacteristic
219#117C2×D4311yescharacteristic
220#117C2×D4311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—431no—
224#107—431no—
225#106—431no—
226#106—431no—
227C4⋊C8—431no—
228C4⋊C8—431no—
229#103—431no—
230#103—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102—431no—
236#102—431no—
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240C4×C8—431no—
241C24—21no—
242C2×Q8—431no—
243C2×Q8—861no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—431no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C2×D4C22×D4311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—861no—
256C22×C4C22×D4311yescharacteristic
257SD16—862no—
258SD16—862no—
259D8—862no—
260D8—862no—
261C2×C8—431no—
262C2×C8—431no—
263C2×C8—431no—
264C2×C8—431no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4C22⋊D4311yescharacteristic
271C4⋊C4C22⋊D4311yescharacteristic
272C4⋊C4C22×D4311yescharacteristic
273C4⋊C4C22×D4311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4C22⋊D4311yescharacteristic
285C22⋊C4C22⋊D4311yescharacteristic
286C42—21no—
287C42—861no—
288C42C22×D4311yescharacteristic
289C42C22×D4311yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—861no—
296C23C2×C22⋊D4311yescharacteristic
297Q8—861no—
298Q8—861no—
299Q8—3441no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—861no—
304D4—861no—
305D4—3441no—
306D4#1062189812yes—
307D4#1062189812yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—3441no—
320C2×C4C2×C22⋊D4311yescharacteristic
321C2×C4C2×C22⋊D4311yescharacteristic
322C2×C4C2×C22⋊D4311yescharacteristic
323C2×C4C2×C22⋊D4311yescharacteristic
324C2×C4C2×C22⋊D4311yescharacteristic
325C2×C4C23×D4311yescharacteristic
326C8—861no—
327C8—861no—
328C8—861no—
329C8—861no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22C22×C22⋊D4311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4C2×#1062189811yescharacteristic
355C4C2×#1062189811yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—3441no—
360C2#1458341011yescharacteristic
361C2#1458370211yescharacteristic
362C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#518C2
socleC22×C43C22×D4
hypercenter#518D43
hypocenterC43#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14583520C2semidirect
2. #14583240C2semidirect
3. #14583223C2semidirect
4. #14583189C2semidirect
5. #14583179C2semidirect
6. #14583114C2semidirect
7. #14583114C2semidirect
8. #14583050C2semidirect
10. #14583009C2semidirect
11. #14582999C2semidirect
12. C4×#10621883C2semidirect
13. C4×#10621882C2semidirect
14. #14582960C2semidirect
15. C43×#518C2semidirect
20. #13063325C22semidirect
22. #13063313C22semidirect
28. C4×Dic86C22semidirect
29. C4×D172C22semidirect
30. #13063258C22semidirect
31. #13063258C22semidirect
32. #13063256C22semidirect
33. #13063256C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. C4⋊(C43⋊C8)C22semidirect
36. #13063248C22semidirect
37. #13063248C22semidirect
42. #13063245C22semidirect
43. #13063245C22semidirect
46. #13063236C22semidirect
47. C4×C43⋊C8C22semidirect
183. #518D43semidirect
197. C43#3118semidirect