Finite Group Databasebeta

← #20252898

Subgroups — #20252898

Order 6016.

494 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic
2C2×SD16×D47C211yesmaximal, characteristic, complemented
3#15689693C211yesmaximal, characteristic, complemented
4#15689595C211yesmaximal, characteristic, complemented
5#15689337C211yesmaximal, characteristic, complemented
6#15689336C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689329C211yesmaximal, characteristic, complemented
9#15689328C211yesmaximal, characteristic, complemented
10#15689327C211yesmaximal, characteristic, complemented
11#15689326C211yesmaximal, characteristic, complemented
12#15689148C211yesmaximal, characteristic, complemented
13#15689130C211yesmaximal, characteristic, complemented
14#15689116C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094048—24no—
20C2×#10625325C2211yescharacteristic
21C2×#10625325C2211yescharacteristic
22C2×#10625335C2211yescharacteristic
23C2×#10625335C2211yescharacteristic
24C2×#10625336C2211yescharacteristic
25SD16×D47—24no—
26C2×#10625334C2211yescharacteristic
27C2×#10625324C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic
29#13094024C2211yescharacteristic, complemented
30#13094022C2211yescharacteristic, complemented
31#13094011C2211yescharacteristic, complemented
32#13094006—21no—
33#13094006—21no—
34#13094001—21no—
35#13094001—21no—
36C4×D188C2211yescharacteristic
37D4×Dic47C2211yescharacteristic
38#13093986C2211yescharacteristic
39C4×C22⋊D47—21no—
40(C22⋊D47)⋊C4—21no—
41#13093982C2211yescharacteristic
42#13093981C2211yescharacteristic
43C2×(C2×D47)⋊C4—21no—
44C22⋊C4×D47—21no—
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46Dic47⋊C8C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093949C2211yescharacteristic, complemented
50#13093948C2211yescharacteristic, complemented
51#13093947C2211yescharacteristic, complemented
52#13093947C2211yescharacteristic, complemented
53#13093945C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70Q8×D47—22no—
71Q8×D47—22no—
72#10625352—22no—
73#10625352—22no—
74D4×D47—22no—
75D4×D47D414yes—
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—21no—
82C2×Dic94C2311yescharacteristic
83C2×Dic94C2311yescharacteristic
84SD16×C47—22no—
85D8×C47—22no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C42×C47C2311yescharacteristic
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96#10625336—22no—
97#10625335—22no—
98#10625335—22no—
99#10625334—22no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4D411yescharacteristic
104(C2×D47)⋊C4D411yescharacteristic
105C4⋊Dic47—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47C2311yescharacteristic
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110Dic47⋊C4D411yescharacteristic
111Dic47⋊C4D411yescharacteristic
112C4×Dic47—21no—
113C4×Dic47C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116#10625325—22no—
117#10625325—22no—
118#10625324—22no—
119C8×D47—22no—
120C23×C47—21no—
121C23×C47—21no—
122C22×D47—21no—
123C22×D47—24no—
124C22×D47—81no—
125C22×D47—81no—
126C22×D47C2×D411yescharacteristic
127Q8×C47—21no—
128Q8×C47—21no—
129D4×C47—21no—
130D4×C47—21no—
131D4×C47—21no—
132D4×C47C2×D412yes—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—81no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2411yescharacteristic
139C22⋊D47—24no—
140C22⋊D47—42no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—42no—
145C2×Dic47—81no—
146C2×Dic47C2×D411yescharacteristic
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149D188—21no—
150D188C2×D412yes—
151C4×D47—42no—
152C4×D47—81no—
153C4×D47—81no—
154C4×D47C2×D412yes—
155C4×D47#4112yes—
156Dic94—21no—
157Dic94—21no—
158Dic94—21no—
159Dic94—21no—
160Dic94—42no—
161C8×C47—21no—
162C8×C47—21no—
163C47⋊C8—21no—
164C47⋊C8—21no—
165C22×C47—22no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47C22×D411yescharacteristic
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—22no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—84no—
178C2×D47#12112yes—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47C22×D411yescharacteristic
184C4×C47C2×#4111yescharacteristic
185Dic47—21no—
186Dic47—21no—
187Dic47—41no—
188Dic47—41no—
189Dic47—41no—
190Dic47#12112yes—
191#3042—471nomaximal, Sylow
192C2×C47—42no—
193C2×C47—81no—
194C2×C47C2×#12111yescharacteristic
195C2×C47#57711yescharacteristic
196C2×C47#57711yescharacteristic
197D47—22no—
198D47—42no—
199C2×AGL(1,ℤ/8)—471no—
200C22×SD16—471no—
201#536—471no—
202#518—471no—
203#463—471no—
204#463—471no—
205#463—471no—
206#463D4711yescharacteristic, complemented
207#461—471no—
208#461—471no—
209#461—471no—
210#461—471no—
211#424—471no—
212#419—471no—
213#416—471no—
214C47#304211yescharacteristic, complemented, Sylow
215C2×#41—471no—
216C22×Q8—471no—
217C22×D4—471no—
218AGL(1,ℤ/8)—944no—
219C2×SD16—471no—
220C2×SD16—471no—
221C2×SD16—471no—
222C2×SD16—471no—
223C2×SD16—471no—
224C2×SD16—944no—
225C2×SD16C2×D4711yescharacteristic
226C2×D8—471no—
227C2×D8C2×D4711yescharacteristic
228C2×M16—471no—
229C22×C8—471no—
230C4⋊Q8—471no—
231C4⋊Q8—471no—
232#124—471no—
233#124C2×D4711yescharacteristic, complemented
234#123—941no—
235#123—941no—
236C22⋊Q8—941no—
237C22⋊Q8—941no—
238C4×D4—471no—
239C4×D4—471no—
240C4×D4—471no—
241C4×D4—941no—
242C4×D4—941no—
243C4×D4C2×D4711yescharacteristic
244#117—471no—
245#117—471no—
246C2×C22⋊C4—941no—
247C2×C22⋊C4—941no—
248C4⋊C8—471no—
249C4⋊C8—471no—
250C4⋊C8—471no—
251C4⋊C8C2×D4711yescharacteristic, complemented
252#103—471no—
253#103—471no—
254#103—471no—
255#103—471no—
256#103—471no—
257#103C2×D4711yescharacteristic, complemented
258#102—471no—
259#102C2×D4711yescharacteristic, complemented
260C24—941no—
261#41—942no—
262#41—942no—
263C2×Q8—471no—
264C2×Q8—471no—
265C2×Q8—941no—
266C2×Q8—942no—
267C2×Q8—942no—
268C2×Q8C22×D4711yescharacteristic
269C2×D4—474no—
270C2×D4—471no—
271C2×D4—942no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4C22×D4711yescharacteristic
275C2×D4C22×D4711yescharacteristic
276C22×C4—21no—
277C22×C4—471no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283SD16—22no—
284SD16—942no—
285SD16—942no—
286SD16—942no—
287SD16—942no—
288SD16—942no—
289D8—22no—
290D8—942no—
291M16—942no—
292C2×C8—471no—
293C2×C8—471no—
294C2×C8—942no—
295C2×C8C22×D4711yescharacteristic
296C2×C8C22×D4711yescharacteristic
297C4⋊C4—471no—
298C4⋊C4—471no—
299C4⋊C4—471no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C4⋊C4—941no—
303C4⋊C4—941no—
304C4⋊C4C22×D4711yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—471no—
309C22⋊C4—471no—
310C22⋊C4—941no—
311C22⋊C4—941no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C42—471no—
317C42—941no—
318C42C22×D4711yescharacteristic
319C23—21no—
320C23—21no—
321C23—471no—
322C23—944no—
323C23—941no—
324C23—3761no—
325C23—3761no—
326Q8—21no—
327Q8—21no—
328Q8—941no—
329Q8—941no—
330Q8—941no—
331Q8—941no—
332Q8—1882no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—472no—
337D4—944no—
338D4—941no—
339D4—1882no—
340D4D4×D4712yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—81no—
344C2×C4—471no—
345C2×C4—472no—
346C2×C4—472no—
347C2×C4—471no—
348C2×C4—471no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—3761no—
353C2×C4—3761no—
354C2×C4—3761no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4D4×D4711yescharacteristic
358C2×C4D4×D4711yescharacteristic
359C2×C4C23×D4711yescharacteristic
360C8—21no—
361C8—21no—
362C8—941no—
363C8—941no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—472no—
371C22—941no—
372C22—941no—
373C22—942no—
374C22—3764no—
375C22—1881no—
376C22—1881no—
377C22C2×D4×D4711yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—472no—
383C4—941no—
384C4—941no—
385C4—1881no—
386C4—1881no—
387C4—1881no—
388C4C2×D4×D4711yescharacteristic
389C4#41×D4711yescharacteristic
390C2—42no—
391C2—81no—
392C2—942no—
393C2—1882no—
394C2#121×D4711yescharacteristic
395C2#1568993011yescharacteristic
396C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3042
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
2. C2×SD16×D47C2semidirect
3. #15689693C2semidirect
4. #15689595C2semidirect
5. #15689337C2semidirect
6. #15689336C2semidirect
7. #15689335C2semidirect
8. #15689329C2semidirect
9. #15689328C2semidirect
10. #15689327C2semidirect
11. #15689326C2semidirect
12. #15689148C2semidirect
13. #15689130C2semidirect
14. #15689116C2semidirect
15. C47×#463C2semidirect
29. #13094024C22semidirect
30. #13094022C22semidirect
31. #13094011C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. Dic47⋊C8C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093949C22semidirect
50. #13093948C22semidirect
51. #13093947C22semidirect
52. #13093947C22semidirect
53. #13093945C22semidirect
56. #124×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
60. #102×C47C22semidirect
206. #463D47semidirect
214. C47#3042semidirect
233. #124C2×D47semidirect
251. C4⋊C8C2×D47semidirect
257. #103C2×D47semidirect
259. #102C2×D47semidirect