Finite Group Databasebeta

← #20253574

Subgroups — #20253574

Order 6016.

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#15689744C211yesmaximal, characteristic, complemented
2#15689597C211yesmaximal, characteristic, complemented
3#15689465C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689414C211yesmaximal, characteristic, complemented
6#15689404C211yesmaximal, characteristic, complemented
7#15689339C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689276C211yesmaximal, characteristic, complemented
10#15689259C211yesmaximal, characteristic
11#15689236C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13C4×#10625325C211yesmaximal, characteristic, complemented
14C4×D376C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic
21#13094024C2211yescharacteristic, complemented
22#13094019—21no—
23#13094012C2211yescharacteristic, complemented
24#13094010—21no—
25#13094006—21no—
26#13094003C2211yescharacteristic
27#13094002—21no—
28#13093998C2211yescharacteristic
29C4×Dic94C2211yescharacteristic, complemented
30C4×D188C2211yescharacteristic
31C4×D188C2211yescharacteristic
32C4×D188C2211yescharacteristic
33C4×D188C2211yescharacteristic
34C4×D188C2211yescharacteristic, complemented
35#13093986—21no—
36#13093986—21no—
37#13093983C2211yescharacteristic
38C22⋊C4×D47—21no—
39C22⋊C4×D47—21no—
40#13093958C2211yescharacteristic, complemented
41#13093958C2211yescharacteristic, complemented
42#13093956C2211yescharacteristic, complemented
43#13093956C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093949C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic, complemented
52#117×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic, complemented
54C4⋊C8×C47C2211yescharacteristic, complemented
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic, complemented
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47—21no—
62C2×D188—21no—
63C2×D188—22no—
64C2×D188—22no—
65C2×D188C2311yescharacteristic
66C2×D188C2311yescharacteristic
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×Dic94—21no—
74C2×Dic94C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47D411yescharacteristic
80C4⋊C4×C47D411yescharacteristic
81C22⋊C4×C47D411yescharacteristic
82C22⋊C4×C47D411yescharacteristic
83C42×C47C2311yescharacteristic
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104D376—22no—
105D376—22no—
106#10625325—22no—
107#10625325—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—24no—
112C22×D47—21no—
113C22×D47—81no—
114C22×D47—81no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2411yescharacteristic
123C22⋊D47—81no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129D188—24no—
130D188—21no—
131D188—21no—
132D188—21no—
133D188—21no—
134D188#4112yes—
135D188#4112yes—
136C4×D47—81no—
137C4×D47—81no—
138C4×D47—81no—
139C4×D47—81no—
140C4×D47—81no—
141Dic94—21no—
142Dic94—21no—
143Dic94—81no—
144C8×C47—21no—
145C8×C47—21no—
146C8×C47—21no—
147C8×C47—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47C22×D411yescharacteristic
152C2×D47—22no—
153C2×D47—22no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—84no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47C2×#4111yescharacteristic
168C4×C47C2×#4111yescharacteristic
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3118—471nomaximal, Sylow
175C2×C47—41no—
176C2×C47#52511yescharacteristic
177C2×C47#57611yescharacteristic
178C2×C47#57711yescharacteristic
179D47—42no—
180D47—42no—
181D47—81no—
182#542—471no—
183#518—471no—
184#485—471no—
185#482—471no—
186#476—471no—
187#474—471no—
188#463—471no—
189#463—471no—
190#450—471no—
191#447—471no—
192#442—471no—
193#440—471no—
194C4×SD16—471no—
195C4×D8—471no—
196#433D4711yescharacteristic, complemented
197C47#311811yescharacteristic, complemented, Sylow
198C22×D4—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×D8—471no—
202C2×D8—471no—
203C4⋊Q8—471no—
204#126—941no—
205#124—471no—
206#124—941no—
207#123—941no—
208C22⋊Q8—471no—
209C22⋊Q8—941no—
210#121—471no—
211C4×Q8—471no—
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—471no—
217C4×D4—941no—
218C4×D4—941no—
219#117—471no—
220#117C2×D4711yescharacteristic
221C2×C22⋊C4—941no—
222C2×C22⋊C4—941no—
223#107—471no—
224#107—471no—
225#106—471no—
226#106—471no—
227C4⋊C8C2×D4711yescharacteristic, complemented
228C4⋊C8C2×D4711yescharacteristic, complemented
229#103—471no—
230#103—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237C22⋊C8C2×D4711yescharacteristic
238C22⋊C8C2×D4711yescharacteristic
239#97C2×D4711yescharacteristic, complemented
240C4×C8C2×D4711yescharacteristic, complemented
241C24—941no—
242C2×Q8—471no—
243C2×Q8—941no—
244C2×D4—471no—
245C2×D4—471no—
246C2×D4—471no—
247C2×D4—942no—
248C2×D4—942no—
249C2×D4—941no—
250C2×D4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4C22×D4711yescharacteristic
257SD16—942no—
258SD16—942no—
259D8—942no—
260D8—942no—
261C2×C8C22×D4711yescharacteristic
262C2×C8C22×D4711yescharacteristic
263C2×C8C22×D4711yescharacteristic
264C2×C8C22×D4711yescharacteristic
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4D18811yescharacteristic
273C4⋊C4D18811yescharacteristic
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4D18811yescharacteristic
285C22⋊C4D18811yescharacteristic
286C42—941no—
287C42—941no—
288C42C22×D4711yescharacteristic
289C42C22×D4711yescharacteristic
290C23—944no—
291C23—941no—
292C23—941no—
293C23—941no—
294C23—3761no—
295C23—3761no—
296C23C2×D18811yescharacteristic
297Q8—941no—
298Q8—941no—
299Q8—3761no—
300D4—472no—
301D4—472no—
302D4—944no—
303D4—941no—
304D4—941no—
305D4—941no—
306D4—941no—
307D4—3761no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—3761no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4—3761no—
320C2×C4C2×D18811yescharacteristic
321C2×C4C2×D18811yescharacteristic
322C2×C4C2×D18811yescharacteristic
323C2×C4C2×D18811yescharacteristic
324C2×C4C2×D18811yescharacteristic
325C2×C4C23×D4711yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—942no—
334C22—942no—
335C22—3764no—
336C22—1881no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22—1881no—
341C22—1881no—
342C22—1881no—
343C22C22×D18811yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4—1881no—
354C4#41×D4711yescharacteristic
355C4#41×D4711yescharacteristic
356C2—41no—
357C2—3761no—
358C2—1882no—
359C2—1882no—
360C2#1568963511yescharacteristic
361C2#1568992811yescharacteristic
362C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3118
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689597C2semidirect
3. #15689465C2semidirect
4. #15689448C2semidirect
5. #15689414C2semidirect
6. #15689404C2semidirect
7. #15689339C2semidirect
8. #15689339C2semidirect
9. #15689276C2semidirect
11. #15689236C2semidirect
12. #15689225C2semidirect
13. C4×#10625325C2semidirect
14. C4×D376C2semidirect
15. C47×#433C2semidirect
21. #13094024C22semidirect
23. #13094012C22semidirect
29. C4×Dic94C22semidirect
34. C4×D188C22semidirect
40. #13093958C22semidirect
41. #13093958C22semidirect
42. #13093956C22semidirect
43. #13093956C22semidirect
44. #13093949C22semidirect
45. #13093949C22semidirect
50. #13093946C22semidirect
51. #13093946C22semidirect
53. C4⋊C8×C47C22semidirect
54. C4⋊C8×C47C22semidirect
57. #97×C47C22semidirect
58. C4×C8×C47C22semidirect
196. #433D47semidirect
197. C47#3118semidirect
227. C4⋊C8C2×D47semidirect
228. C4⋊C8C2×D47semidirect
239. #97C2×D47semidirect
240. C4×C8C2×D47semidirect