Finite Group Databasebeta

← #19144780

Subgroups — #19144780

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#14583522C211yesmaximal, characteristic, complemented
2#14583374C211yesmaximal, characteristic, complemented
3#14583237C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583187C211yesmaximal, characteristic, complemented
6#14583177C211yesmaximal, characteristic, complemented
7#14583116C211yesmaximal, characteristic, complemented
8#14583116C211yesmaximal, characteristic, complemented
9#14583033C211yesmaximal, characteristic
10#14583008C211yesmaximal, characteristic, complemented
11#14583000C211yesmaximal, characteristic, complemented
12SD16×Dic43C211yesmaximal, characteristic, complemented
13#14582979C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#450C211yesmaximal, characteristic, complemented
16C2×#10621882C2211yescharacteristic
17C2×#10621882C2211yescharacteristic
18#13063324C2211yescharacteristic, complemented
19#13063320—21no—
20#13063314C2211yescharacteristic, complemented
21#13063311—21no—
22#13063307—21no—
23#13063305—21no—
24#13063299C2211yescharacteristic
25Q8×Dic43C2211yescharacteristic, complemented
26D4×Dic43—21no—
27D4×Dic43—21no—
28D4×Dic43C2211yescharacteristic
29D4×Dic43C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31D4×Dic43C2211yescharacteristic
32#13063287C2211yescharacteristic, complemented
33#13063284C2211yescharacteristic
34#13063284C2211yescharacteristic
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063249C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C24×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—22no—
62C2×D4×C43—22no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×Dic86—21no—
75SD16×C43—22no—
76SD16×C43—22no—
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43C2311yescharacteristic
81C22⋊C4×C43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43D411yescharacteristic
88C22⋊Dic43D411yescharacteristic
89#10621882—22no—
90#10621882—22no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43D411yescharacteristic
97C4⋊Dic43D411yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C4×Dic43C2311yescharacteristic
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—
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—24no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43#4112yes—
121D4×C43#4112yes—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—81no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140D172—21no—
141D172—21no—
142C4×D43—81no—
143Dic86—81no—
144C8×C43—21no—
145C8×C43—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—41no—
164C4×C43—41no—
165C4×C43C2×#4111yescharacteristic
166C4×C43C2×#4111yescharacteristic
167Dic43—21no—
168Dic43—21no—
169Dic43—21no—
170Dic43—21no—
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#518—431no—
184#485—431no—
185#482—431no—
186#476—431no—
187#474—431no—
188#463—431no—
189#463—431no—
190#450D4311yescharacteristic, complemented
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×SD16C2×D4311yescharacteristic
200C2×SD16C2×D4311yescharacteristic
201C2×D8—431no—
202C2×D8—431no—
203C4⋊Q8—431no—
204#126—861no—
205#124—431no—
206#124—861no—
207#123—861no—
208C22⋊Q8—861no—
209C22⋊Q8C2×D4311yescharacteristic
210#121—431no—
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—431no—
217C4×D4—861no—
218C4×D4—861no—
219#117—431no—
220#117—431no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
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#102C2×D4311yescharacteristic
236#102C2×D4311yescharacteristic
237C22⋊C8—431no—
238C22⋊C8C2×D4311yescharacteristic
239#97—431no—
240C4×C8—431no—
241C24—21no—
242C2×Q8—861no—
243C2×Q8C22×D4311yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—431no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C2×D4C22×D4311yescharacteristic
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4C22×D4311yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—862no—
260D8—862no—
261C2×C8—431no—
262C2×C8—431no—
263C2×C8C22×D4311yescharacteristic
264C2×C8C22×D4311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—431no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4C22×D4311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—431no—
276C22⋊C4—431no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—431no—
287C42—431no—
288C42—861no—
289C42—861no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—861no—
296C23D4×D4311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—3441no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—861no—
304D4—861no—
305D4—3441no—
306D4#1062190012yes—
307D4#1062190012yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—431no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4D4×D4311yescharacteristic
325C2×C4C23×D4311yescharacteristic
326C8—21no—
327C8—21no—
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—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—861no—
348C4—861no—
349C4—861no—
350C4—861no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4C2×#1062190011yescharacteristic
355C4C2×#1062190011yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—3441no—
360C2#1458340511yescharacteristic
361C2#1458370311yescharacteristic
362C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3118
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. #14583522C2semidirect
2. #14583374C2semidirect
3. #14583237C2semidirect
4. #14583224C2semidirect
5. #14583187C2semidirect
6. #14583177C2semidirect
7. #14583116C2semidirect
8. #14583116C2semidirect
10. #14583008C2semidirect
11. #14583000C2semidirect
12. SD16×Dic43C2semidirect
13. #14582979C2semidirect
14. #14582957C2semidirect
15. C43×#450C2semidirect
18. #13063324C22semidirect
20. #13063314C22semidirect
25. Q8×Dic43C22semidirect
32. #13063287C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063249C22semidirect
44. #13063249C22semidirect
45. #13063247C22semidirect
46. #13063247C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
190. #450D43semidirect
197. C43#3118semidirect