Finite Group Databasebeta

← #20252199

Subgroups — #20252199

Order 6016.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic
2C4×#10625352C211yesmaximal, characteristic, complemented
3C4×D4×D47C211yesmaximal, characteristic, complemented
4#15689233C211yesmaximal, characteristic, complemented
5#15689225C211yesmaximal, characteristic, complemented
6#15689223C211yesmaximal, characteristic, complemented
7#15689214C211yesmaximal, characteristic, complemented
8#15689210C211yesmaximal, characteristic, complemented
9D8×Dic47C211yesmaximal, characteristic, complemented
10#15689203C211yesmaximal, characteristic, complemented
11#15689162C211yesmaximal, characteristic, complemented
12#15689126C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic, complemented
14#15689075C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C22×C4×D47—21no—
19#13094048C418yescomplemented
20C2×#10625325C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23C2×#10625324C2211yescharacteristic
24C2×#10625324C2211yescharacteristic
25C4×Dic94C2211yescharacteristic, complemented
26#13093989C2211yescharacteristic, complemented
27C4×D188C2211yescharacteristic
28D4×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic, complemented
30#13093986C2211yescharacteristic
31C4×C22⋊D47—21no—
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34(C22⋊D47)⋊C4—21no—
35#13093982C2211yescharacteristic
36#13093980—21no—
37C4⋊C4×D47C2211yescharacteristic
38C22⋊C4×D47—21no—
39C2×C4×Dic47—21no—
40C42×D47C2211yescharacteristic
41#13093958C2211yescharacteristic, complemented
42#13093957C2211yescharacteristic, complemented
43#13093955C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic
50#13093935C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C8×Dic47C2211yescharacteristic, complemented
53C2×D8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic, complemented
56#106×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic, complemented
59#97×C47C2211yescharacteristic, complemented
60C23×D47—21no—
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70#10625352—22no—
71#10625352C2×C414yescomplemented
72D4×D47—22no—
73D4×D47C2×C414yescomplemented
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—44no—
79C2×C4×D47D411yescharacteristic
80C2×C4×D47D411yescharacteristic
81C2×C4×D47C2311yescharacteristic
82C2×Dic94C2311yescharacteristic
83D8×C47C2×C414yescomplemented
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93#10625335C2×C414yescomplemented
94#10625334C2×C414yescomplemented
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47D411yescharacteristic
107C4×Dic47D411yescharacteristic
108C4×Dic47C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625325C2×C414yescomplemented
112#10625324—22no—
113#10625324C2×C414yescomplemented
114C23×C47—21no—
115C23×C47—21no—
116C22×D47—21no—
117C22×D47—24no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47C2×D411yescharacteristic
121D4×C47—21no—
122D4×C47—21no—
123D4×C47C22×C412yes—
124D4×C47C22×C412yescomplemented
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—24no—
133C22⋊D47—24no—
134C2×Dic47—21no—
135C2×Dic47—24no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—42no—
139C2×Dic47—42no—
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143D188—21no—
144D188C22×C412yes—
145C4×D47—22no—
146C4×D47—41no—
147C4×D47—42no—
148C4×D47—42no—
149C4×D47—42no—
150C4×D47C22×C412yes—
151C4×D47#4112yes—
152Dic94—21no—
153Dic94C22×C412yescomplemented
154C8×C47—21no—
155C8×C47C22×C412yescomplemented
156C47⋊C8—21no—
157C47⋊C8C22×C412yescomplemented
158C22×C47—22no—
159C22×C47—22no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—22no—
168C2×D47—48no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47C4×D412yes—
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47C23×C411yescharacteristic
177C4×C47C2×#4111yescharacteristic
178Dic47—22no—
179Dic47—21no—
180Dic47—41no—
181Dic47—41no—
182Dic47C4×D412yes—
183Dic47AGL(1,ℤ/8)12yescomplemented
184C4×AGL(1,ℤ/8)—471nomaximal, Sylow
185C2×C47—42no—
186C2×C47—42no—
187C2×C47C2×C4×D411yescharacteristic
188C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C47#57511yescharacteristic
190D47—22no—
191D47—42no—
192C2×AGL(1,ℤ/8)—471no—
193C4×#41—471no—
194C2×C4×D4—471no—
195#442—471no—
196#442D4711yescharacteristic, complemented
197#440—471no—
198#440—471no—
199C4×SD16—471no—
200C4×SD16—471no—
201C4×D8—471no—
202C4×D8—471no—
203#428—471no—
204#418—471no—
205#417—471no—
206C4×M16—471no—
207C47C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
208C2×#41—471no—
209C22×D4—471no—
210C23×C4—941no—
211AGL(1,ℤ/8)—478no—
212C2×SD16—471no—
213C2×SD16—471no—
214C2×D8—471no—
215C2×D8C2×D4711yescharacteristic
216C2×M16—471no—
217C2×M16—471no—
218C4×Q8—471no—
219C4×Q8—471no—
220C4×D4—471no—
221C4×D4—471no—
222C4×D4—471no—
223C4×D4—471no—
224C4×D4—941no—
225C4×D4—941no—
226C4×D4—941no—
227C4×D4—941no—
228C4×D4C2×D4711yescharacteristic
229C4×D4C2×D4711yescharacteristic, complemented
230#117—471no—
231#117—941no—
232C2×C4⋊C4—471no—
233C2×C22⋊C4—941no—
234C2×C42—471no—
235C2×C42—941no—
236#107—471no—
237#107—471no—
238#106—471no—
239#106C2×D4711yescharacteristic, complemented
240#103—471no—
241#103—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102C2×D4711yescharacteristic
247#102C2×D4711yescharacteristic, complemented
248#97—471no—
249#97C2×D4711yescharacteristic, complemented
250C4×C8—471no—
251C4×C8—471no—
252C24—941no—
253#41—474no—
254#41—942no—
255C2×Q8—471no—
256C2×D4—474no—
257C2×D4—471no—
258C2×D4—942no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4C22×D4711yescharacteristic
262C2×D4C22×D4711yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4—941no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—1884no—
275SD16—474no—
276SD16—474no—
277D8—474no—
278D8C4×D4714yescomplemented
279M16—474no—
280M16—942no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8C22×D4711yescharacteristic
284C2×C8C22×D4711yescharacteristic
285C4⋊C4—471no—
286C4⋊C4—471no—
287C4⋊C4—941no—
288C4⋊C4—941no—
289C4⋊C4—941no—
290C4⋊C4C22×D4711yescharacteristic
291C4⋊C4C22×D4711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C42—471no—
300C42—471no—
301C42—471no—
302C42—941no—
303C42—941no—
304C42—941no—
305C42C22×D4711yescharacteristic
306C23—21no—
307C23—21no—
308C23—471no—
309C23—944no—
310C23—941no—
311C23—1882no—
312C23—1882no—
313Q8—472no—
314Q8—941no—
315D4—21no—
316D4—21no—
317D4—472no—
318D4—944no—
319D4—944no—
320D4—941no—
321D4C2×C4×D4712yes—
322D4C2×C4×D4712yescomplemented
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—471no—
328C2×C4—471no—
329C2×C4—472no—
330C2×C4—472no—
331C2×C4—471no—
332C2×C4—942no—
333C2×C4—944no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—1881no—
338C2×C4—1882no—
339C2×C4—1882no—
340C2×C4—1882no—
341C2×C4—1882no—
342C2×C4—1882no—
343C2×C4D4×D4711yescharacteristic
344C2×C4D4×D4711yescharacteristic
345C2×C4C23×D4711yescharacteristic
346C8—21no—
347C8—472no—
348C8—941no—
349C8C2×C4×D4712yescomplemented
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—472no—
357C22—941no—
358C22—941no—
359C22—942no—
360C22—1888no—
361C22—1881no—
362C22—1881no—
363C22C2×D4×D4711yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—472no—
369C4—472no—
370C4—942no—
371C4—941no—
372C4—1881no—
373C4—1881no—
374C4C22×C4×D4711yescharacteristic
375C4#41×D4711yescharacteristic
376C2—42no—
377C2—42no—
378C2—942no—
379C2—1882no—
380C2C4×D4×D4711yescharacteristic
381C2AGL(1,ℤ/8)×D4711yescharacteristic
382C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47C4×AGL(1,ℤ/8)
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×#10625352C2semidirect
3. C4×D4×D47C2semidirect
4. #15689233C2semidirect
5. #15689225C2semidirect
6. #15689223C2semidirect
7. #15689214C2semidirect
8. #15689210C2semidirect
9. D8×Dic47C2semidirect
10. #15689203C2semidirect
11. #15689162C2semidirect
12. #15689126C2semidirect
13. #15689121C2semidirect
14. #15689075C2semidirect
15. C47×#442C2semidirect
19. #13094048C4semidirect
25. C4×Dic94C22semidirect
26. #13093989C22semidirect
29. D4×Dic47C22semidirect
41. #13093958C22semidirect
42. #13093957C22semidirect
43. #13093955C22semidirect
44. #13093949C22semidirect
45. #13093947C22semidirect
48. #13093945C22semidirect
50. #13093935C22semidirect
51. C8×Dic47C22semidirect
52. C8×Dic47C22semidirect
55. C4×D4×C47C22semidirect
56. #106×C47C22semidirect
58. #102×C47C22semidirect
59. #97×C47C22semidirect
71. #10625352C2×C4semidirect
73. D4×D47C2×C4semidirect
83. D8×C47C2×C4semidirect
93. #10625335C2×C4semidirect
94. #10625334C2×C4semidirect
111. #10625325C2×C4semidirect
113. #10625324C2×C4semidirect
124. D4×C47C22×C4semidirect
153. Dic94C22×C4semidirect
155. C8×C47C22×C4semidirect
157. C47⋊C8C22×C4semidirect
183. Dic47AGL(1,ℤ/8)semidirect
196. #442D47semidirect
207. C47C4×AGL(1,ℤ/8)semidirect
229. C4×D4C2×D47semidirect
239. #106C2×D47semidirect
247. #102C2×D47semidirect
249. #97C2×D47semidirect
278. D8C4×D47semidirect
322. D4C2×C4×D47semidirect
349. C8C2×C4×D47semidirect