Finite Group Databasebeta

← #20252213

Subgroups — #20252213

Order 6016.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic
2#15689602C211yesmaximal, characteristic, complemented
3#15689595C211yesmaximal, characteristic, complemented
4#15689235C211yesmaximal, characteristic, complemented
5#15689233C211yesmaximal, characteristic, complemented
6#15689223C211yesmaximal, characteristic, complemented
7#15689222C211yesmaximal, characteristic, complemented
8#15689214C211yesmaximal, characteristic, complemented
9C4×#10625325C211yesmaximal, characteristic, complemented
10#15689203C211yesmaximal, characteristic, complemented
11#15689164C211yesmaximal, characteristic, complemented
12#15689116C211yesmaximal, characteristic, complemented
13#102×D47C211yesmaximal, characteristic, complemented
14#15689077C211yesmaximal, characteristic, complemented
15C4×D8×C47C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18#13094048C418yescomplemented
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×#10625324C2211yescharacteristic
23C2×C8×D47C2211yescharacteristic
24C4×Dic94C2211yescharacteristic, complemented
25#13093989C2211yescharacteristic, complemented
26C4×D188C2211yescharacteristic
27D4×Dic47C2211yescharacteristic
28D4×Dic47C2211yescharacteristic, complemented
29#13093986C2211yescharacteristic
30C4×C22⋊D47—21no—
31C4×C22⋊D47—21no—
32(C22⋊D47)⋊C4—21no—
33(C22⋊D47)⋊C4—21no—
34#13093982C2211yescharacteristic
35#13093981C2211yescharacteristic
36#13093980—21no—
37C2×Dic47⋊C4—21no—
38C4⋊C4×D47C2211yescharacteristic
39C2×(C2×D47)⋊C4—21no—
40C22⋊C4×D47—21no—
41#13093957C2211yescharacteristic, complemented
42#13093956C2211yescharacteristic, complemented
43#13093955C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic
50#13093935C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C8×Dic47C2211yescharacteristic, complemented
53C2×D8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic, complemented
56#107×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic, complemented
59C4×C8×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×D47C2311yescharacteristic
79C2×Dic94C2311yescharacteristic
80D8×C47C2×C414yescomplemented
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C42×C47C2311yescharacteristic
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90#10625335C2×C414yescomplemented
91#10625334C2×C414yescomplemented
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4D411yescharacteristic
96(C2×D47)⋊C4D411yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4D411yescharacteristic
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625325C2×C414yescomplemented
111#10625324C2×C414yescomplemented
112C8×D47—22no—
113C23×C47—21no—
114C23×C47—21no—
115C22×D47—21no—
116C22×D47—24no—
117C22×D47—81no—
118C22×D47—81no—
119C22×D47C2×D411yescharacteristic
120D4×C47—21no—
121D4×C47—21no—
122D4×C47C22×C412yes—
123D4×C47C22×C412yes—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—24no—
132C22⋊D47—24no—
133C2×Dic47—21no—
134C2×Dic47—24no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—81no—
138C2×Dic47—81no—
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142D188—21no—
143D188C22×C412yes—
144C4×D47—81no—
145C4×D47—81no—
146C4×D47—81no—
147C4×D47C22×C412yes—
148C4×D47#4112yes—
149Dic94—21no—
150Dic94C22×C412yes—
151C8×C47—21no—
152C8×C47C22×C412yes—
153C47⋊C8—21no—
154C47⋊C8C22×C412yes—
155C22×C47—22no—
156C22×C47—22no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47C22×D411yescharacteristic
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—22no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—84no—
168C2×D47C4×D412yes—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47C23×C411yescharacteristic
174C4×C47C2×#4111yescharacteristic
175Dic47—22no—
176Dic47—21no—
177Dic47—21no—
178Dic47—41no—
179Dic47—41no—
180Dic47C4×D412yes—
181#2946—471nomaximal, Sylow
182C2×C47—42no—
183C2×C47—42no—
184C2×C47C2×C4×D411yescharacteristic
185C2×C47#57611yescharacteristic
186C2×C47#57711yescharacteristic
187D47—22no—
188D47—42no—
189C2×AGL(1,ℤ/8)—471no—
190#520—471no—
191#518—471no—
192#442—471no—
193#442—471no—
194#440—471no—
195#440—471no—
196C4×SD16—471no—
197C4×SD16—471no—
198C4×D8—471no—
199C4×D8D4711yescharacteristic, complemented
200#428—471no—
201#416—471no—
202C2×#102—471no—
203#405—471no—
204C47#294611yescharacteristic, complemented, Sylow
205C2×#41—471no—
206C22×D4—471no—
207AGL(1,ℤ/8)—478no—
208C2×SD16—471no—
209C2×SD16—471no—
210C2×D8—471no—
211C2×D8C2×D4711yescharacteristic
212C2×M16—471no—
213C22×C8—471no—
214C4×Q8—471no—
215C4×Q8—471no—
216C4×D4—471no—
217C4×D4—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—941no—
221C4×D4—941no—
222C4×D4—941no—
223C4×D4—941no—
224C4×D4C2×D4711yescharacteristic
225C4×D4C2×D4711yescharacteristic, complemented
226#117—471no—
227#117—471no—
228#117—941no—
229C2×C4⋊C4—471no—
230C2×C4⋊C4—941no—
231C2×C22⋊C4—941no—
232C2×C22⋊C4—941no—
233#107—471no—
234#107C2×D4711yescharacteristic, complemented
235#106—471no—
236#106—471no—
237#103—471no—
238#103—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102C2×D4711yescharacteristic
244#102C2×D4711yescharacteristic, complemented
245#97—471no—
246#97—471no—
247C4×C8—471no—
248C4×C8C2×D4711yescharacteristic, complemented
249C24—941no—
250#41—474no—
251#41—942no—
252C2×Q8—471no—
253C2×D4—474no—
254C2×D4—471no—
255C2×D4—942no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4C22×D4711yescharacteristic
259C2×D4C22×D4711yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—471no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269SD16—474no—
270SD16—474no—
271D8—474no—
272D8C4×D4714yescomplemented
273M16—474no—
274C2×C8—471no—
275C2×C8—471no—
276C2×C8—942no—
277C2×C8C22×D4711yescharacteristic
278C2×C8C22×D4711yescharacteristic
279C4⋊C4—471no—
280C4⋊C4—471no—
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4C22×D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—471no—
291C22⋊C4—471no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C42—471no—
298C42—941no—
299C42—941no—
300C42—941no—
301C42C22×D4711yescharacteristic
302C23—21no—
303C23—21no—
304C23—471no—
305C23—944no—
306C23—941no—
307C23—3761no—
308C23—3761no—
309Q8—472no—
310Q8—941no—
311D4—21no—
312D4—21no—
313D4—472no—
314D4—944no—
315D4—944no—
316D4—941no—
317D4C2×C4×D4712yes—
318D4C2×C4×D4712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—471no—
324C2×C4—472no—
325C2×C4—472no—
326C2×C4—471no—
327C2×C4—471no—
328C2×C4—944no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—3761no—
333C2×C4—3761no—
334C2×C4—3761no—
335C2×C4—3761no—
336C2×C4—3761no—
337C2×C4D4×D4711yescharacteristic
338C2×C4D4×D4711yescharacteristic
339C2×C4C23×D4711yescharacteristic
340C8—21no—
341C8—472no—
342C8—941no—
343C8C2×C4×D4712yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—472no—
351C22—941no—
352C22—941no—
353C22—942no—
354C22—3764no—
355C22—1881no—
356C22—1881no—
357C22C2×D4×D4711yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—472no—
363C4—942no—
364C4—941no—
365C4—941no—
366C4—1881no—
367C4—1881no—
368C4C22×C4×D4711yescharacteristic
369C4#41×D4711yescharacteristic
370C2—42no—
371C2—42no—
372C2—942no—
373C2—1882no—
374C2C4×D4×D4711yescharacteristic
375C2#1568992411yescharacteristic
376C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC4×D8×C47C2
socleC22×C47C22×D4
hypercenterC4×D8D47
hypocenterC47#2946
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. #15689602C2semidirect
3. #15689595C2semidirect
4. #15689235C2semidirect
5. #15689233C2semidirect
6. #15689223C2semidirect
7. #15689222C2semidirect
8. #15689214C2semidirect
9. C4×#10625325C2semidirect
10. #15689203C2semidirect
11. #15689164C2semidirect
12. #15689116C2semidirect
13. #102×D47C2semidirect
14. #15689077C2semidirect
15. C4×D8×C47C2semidirect
18. #13094048C4semidirect
24. C4×Dic94C22semidirect
25. #13093989C22semidirect
28. D4×Dic47C22semidirect
41. #13093957C22semidirect
42. #13093956C22semidirect
43. #13093955C22semidirect
44. #13093949C22semidirect
45. #13093947C22semidirect
48. #13093945C22semidirect
50. #13093935C22semidirect
51. #13093934C22semidirect
52. C8×Dic47C22semidirect
55. C4×D4×C47C22semidirect
56. #107×C47C22semidirect
58. #102×C47C22semidirect
59. C4×C8×C47C22semidirect
71. #10625352C2×C4semidirect
73. D4×D47C2×C4semidirect
80. D8×C47C2×C4semidirect
90. #10625335C2×C4semidirect
91. #10625334C2×C4semidirect
110. #10625325C2×C4semidirect
111. #10625324C2×C4semidirect
199. C4×D8D47semidirect
204. C47#2946semidirect
225. C4×D4C2×D47semidirect
234. #107C2×D47semidirect
244. #102C2×D47semidirect
248. C4×C8C2×D47semidirect
272. D8C4×D47semidirect