Finite Group Databasebeta

← #19144781

Subgroups — #19144781

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#14583373C211yesmaximal, characteristic, complemented
3#14583241C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583190C211yesmaximal, characteristic, complemented
6#14583180C211yesmaximal, characteristic, complemented
7#14583115C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583052C211yesmaximal, characteristic, complemented
10#14583035C211yesmaximal, characteristic
11#14583012C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13C4×#10621873C211yesmaximal, characteristic, complemented
14C4×D344C211yesmaximal, characteristic, complemented
15C43×#433C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×D344C2211yescharacteristic
20C2×D344C2211yescharacteristic
21#13063325C2211yescharacteristic, complemented
22#13063320—21no—
23#13063313C2211yescharacteristic, complemented
24#13063311—21no—
25#13063307—21no—
26#13063304C2211yescharacteristic
27#13063303—21no—
28#13063299C2211yescharacteristic
29C4×Dic86C2211yescharacteristic, complemented
30C4×D172C2211yescharacteristic
31C4×D172C2211yescharacteristic
32C4×D172C2211yescharacteristic
33C4×D172C2211yescharacteristic
34C4×D172C2211yescharacteristic, complemented
35#13063287—21no—
36#13063287—21no—
37#13063284C2211yescharacteristic
38C22⋊C4×D43—21no—
39C22⋊C4×D43—21no—
40#13063259C2211yescharacteristic, complemented
41#13063259C2211yescharacteristic, complemented
42#13063257C2211yescharacteristic, complemented
43#13063257C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063250C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic, complemented
51#13063247C2211yescharacteristic, complemented
52#117×C43C2211yescharacteristic
53C4⋊C8×C43C2211yescharacteristic, complemented
54C4⋊C8×C43C2211yescharacteristic, complemented
55C22⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57#97×C43C2211yescharacteristic, complemented
58C4×C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—21no—
62C2×D172—21no—
63C2×D172—22no—
64C2×D172—22no—
65C2×D172C2311yescharacteristic
66C2×D172C2311yescharacteristic
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×Dic86—21no—
74C2×Dic86C2311yescharacteristic
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43D411yescharacteristic
80C4⋊C4×C43D411yescharacteristic
81C22⋊C4×C43D411yescharacteristic
82C22⋊C4×C43D411yescharacteristic
83C42×C43C2311yescharacteristic
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104D344—22no—
105D344—22no—
106#10621873—22no—
107#10621873—22no—
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—24no—
112C22×D43—21no—
113C22×D43—81no—
114C22×D43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2411yescharacteristic
123C22⋊D43—81no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129D172—24no—
130D172—21no—
131D172—21no—
132D172—21no—
133D172—21no—
134D172#4112yes—
135D172#4112yes—
136C4×D43—81no—
137C4×D43—81no—
138C4×D43—81no—
139C4×D43—81no—
140C4×D43—81no—
141Dic86—21no—
142Dic86—21no—
143Dic86—81no—
144C8×C43—21no—
145C8×C43—21no—
146C8×C43—21no—
147C8×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43C22×D411yescharacteristic
152C2×D43—22no—
153C2×D43—22no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—84no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43C2×#4111yescharacteristic
168C4×C43C2×#4111yescharacteristic
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3118—431nomaximal, Sylow
175C2×C43—41no—
176C2×C43#52511yescharacteristic
177C2×C43#57611yescharacteristic
178C2×C43#57711yescharacteristic
179D43—42no—
180D43—42no—
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#450—431no—
191#447—431no—
192#442—431no—
193#440—431no—
194C4×SD16—431no—
195C4×D8—431no—
196#433D4311yescharacteristic, complemented
197C43#311811yescharacteristic, complemented, Sylow
198C22×D4—431no—
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—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—431no—
217C4×D4—861no—
218C4×D4—861no—
219#117—431no—
220#117C2×D4311yescharacteristic
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223#107—431no—
224#107—431no—
225#106—431no—
226#106—431no—
227C4⋊C8C2×D4311yescharacteristic, complemented
228C4⋊C8C2×D4311yescharacteristic, complemented
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⋊C8C2×D4311yescharacteristic
238C22⋊C8C2×D4311yescharacteristic
239#97C2×D4311yescharacteristic, complemented
240C4×C8C2×D4311yescharacteristic, complemented
241C24—861no—
242C2×Q8—431no—
243C2×Q8—861no—
244C2×D4—431no—
245C2×D4—431no—
246C2×D4—431no—
247C2×D4—862no—
248C2×D4—862no—
249C2×D4—861no—
250C2×D4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4C22×D4311yescharacteristic
257SD16—862no—
258SD16—862no—
259D8—862no—
260D8—862no—
261C2×C8C22×D4311yescharacteristic
262C2×C8C22×D4311yescharacteristic
263C2×C8C22×D4311yescharacteristic
264C2×C8C22×D4311yescharacteristic
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4D17211yescharacteristic
273C4⋊C4D17211yescharacteristic
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4D17211yescharacteristic
285C22⋊C4D17211yescharacteristic
286C42—861no—
287C42—861no—
288C42C22×D4311yescharacteristic
289C42C22×D4311yescharacteristic
290C23—864no—
291C23—861no—
292C23—861no—
293C23—861no—
294C23—3441no—
295C23—3441no—
296C23C2×D17211yescharacteristic
297Q8—861no—
298Q8—861no—
299Q8—3441no—
300D4—432no—
301D4—432no—
302D4—864no—
303D4—861no—
304D4—861no—
305D4—861no—
306D4—861no—
307D4—3441no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—3441no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4C2×D17211yescharacteristic
321C2×C4C2×D17211yescharacteristic
322C2×C4C2×D17211yescharacteristic
323C2×C4C2×D17211yescharacteristic
324C2×C4C2×D17211yescharacteristic
325C2×C4C23×D4311yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—862no—
334C22—862no—
335C22—3444no—
336C22—1721no—
337C22—1721no—
338C22—1721no—
339C22—1721no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22C22×D17211yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—1721no—
350C4—1721no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4#41×D4311yescharacteristic
355C4#41×D4311yescharacteristic
356C2—41no—
357C2—3441no—
358C2—1722no—
359C2—1722no—
360C2#1458341111yescharacteristic
361C2#1458370411yescharacteristic
362C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#433C2
socleC22×C43C22×D4
hypercenter#433D43
hypocenterC43#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14583520C2semidirect
2. #14583373C2semidirect
3. #14583241C2semidirect
4. #14583224C2semidirect
5. #14583190C2semidirect
6. #14583180C2semidirect
7. #14583115C2semidirect
8. #14583115C2semidirect
9. #14583052C2semidirect
11. #14583012C2semidirect
12. #14583001C2semidirect
13. C4×#10621873C2semidirect
14. C4×D344C2semidirect
15. C43×#433C2semidirect
21. #13063325C22semidirect
23. #13063313C22semidirect
29. C4×Dic86C22semidirect
34. C4×D172C22semidirect
40. #13063259C22semidirect
41. #13063259C22semidirect
42. #13063257C22semidirect
43. #13063257C22semidirect
44. #13063250C22semidirect
45. #13063250C22semidirect
50. #13063247C22semidirect
51. #13063247C22semidirect
53. C4⋊C8×C43C22semidirect
54. C4⋊C8×C43C22semidirect
57. #97×C43C22semidirect
58. C4×C8×C43C22semidirect
196. #433D43semidirect
197. C43#3118semidirect
227. C4⋊C8C2×D43semidirect
228. C4⋊C8C2×D43semidirect
239. #97C2×D43semidirect
240. C4×C8C2×D43semidirect