Finite Group Databasebeta

← #20252886

Subgroups — #20252886

Order 6016.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic, complemented
2C2×D8×D47C211yesmaximal, characteristic, complemented
3#15689686C211yesmaximal, characteristic, complemented
4#15689595C211yesmaximal, characteristic, complemented
5#15689339C211yesmaximal, characteristic, complemented
6#15689338C211yesmaximal, characteristic, complemented
7#15689337C211yesmaximal, characteristic, complemented
8#15689336C211yesmaximal, characteristic, complemented
9#15689317C211yesmaximal, characteristic, complemented
10#15689316C211yesmaximal, characteristic, complemented
11#15689315C211yesmaximal, characteristic, complemented
12#15689148C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14#15689116C211yesmaximal, characteristic, complemented
15C47×#459C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094048—24no—
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×D376C2211yescharacteristic
23C2×#10625334C2211yescharacteristic
24C2×#10625334C2211yescharacteristic
25C2×#10625334C2211yescharacteristic, complemented
26D8×D47—24no—
27C2×#10625324C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic
29#13094020C2211yescharacteristic, complemented
30#13094012C2211yescharacteristic, complemented
31#13094011C2211yescharacteristic, complemented
32#13093996—21no—
33#13093996—21no—
34#13093992—21no—
35#13093992—21no—
36C4×D188C2211yescharacteristic, complemented
37D4×Dic47C2211yescharacteristic, complemented
38#13093986C2211yescharacteristic, complemented
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#13093947C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52#13093945C2211yescharacteristic, complemented
53#13093944C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic
55C2×D8×C47C2211yescharacteristic, complemented
56#127×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C22×C4×C47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76#10625352—22no—
77#10625352—22no—
78D4×D47—22no—
79D4×D47—22no—
80D4×D47—22no—
81D4×D47D414yescomplemented
82C2×D188C2311yescharacteristic
83C2×D188C2311yescharacteristic
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88D8×C47—22no—
89D8×C47—22no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C22⋊C4×C47—21no—
94C42×C47C2311yescharacteristic
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98#10625335—22no—
99#10625334—22no—
100#10625334—22no—
101#10625334—22no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4D411yescharacteristic
108(C2×D47)⋊C4D411yescharacteristic
109C4⋊Dic47C2311yescharacteristic
110Dic47⋊C4D411yescharacteristic
111Dic47⋊C4D411yescharacteristic
112C4×Dic47—21no—
113C4×Dic47C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116D376—22no—
117#10625325—22no—
118#10625324—22no—
119C8×D47—22no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C22×D47—21no—
124C22×D47—24no—
125C22×D47—21no—
126C22×D47—42no—
127C22×D47—81no—
128C22×D47—81no—
129C22×D47—81no—
130C22×D47—81no—
131C22×D47C2×D411yescharacteristic
132D4×C47—21no—
133D4×C47—21no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—21no—
137D4×C47—81no—
138D4×C47—81no—
139D4×C47C2×D412yes—
140C2×C4×C47—21no—
141C2×C4×C47—81no—
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2411yescharacteristic
145C22⋊D47—24no—
146C22⋊D47—42no—
147C22⋊D47—42no—
148C22⋊D47—81no—
149C22⋊D47—81no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—42no—
153C2×Dic47—81no—
154C2×Dic47C2×D411yescharacteristic
155C2×Dic47C2×D411yescharacteristic
156C2×Dic47C2×D411yescharacteristic
157D188—21no—
158D188—21no—
159D188—21no—
160D188C2×D412yes—
161C4×D47—81no—
162C4×D47—81no—
163C4×D47C2×D412yes—
164C4×D47#4112yes—
165Dic94—21no—
166Dic94—21no—
167C8×C47—21no—
168C8×C47—21no—
169C47⋊C8—21no—
170C47⋊C8—21no—
171C22×C47—22no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47C22×D411yescharacteristic
181C2×D47—21no—
182C2×D47—21no—
183C2×D47—22no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—84no—
190C2×D47—84no—
191C2×D47#12112yes—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—41no—
195C4×C47C22×D411yescharacteristic
196C4×C47C2×#4111yescharacteristic
197Dic47—21no—
198Dic47—21no—
199Dic47—41no—
200Dic47—41no—
201Dic47#12112yes—
202#3041—471nomaximal, Sylow
203C2×C47—42no—
204C2×C47—81no—
205C2×C47—81no—
206C2×C47C2×#12111yescharacteristic
207C2×C47#57611yescharacteristic
208C2×C47#57611yescharacteristic
209D47—22no—
210D47—42no—
211D47—81no—
212C2×AGL(1,ℤ/8)—471no—
213C22×D8—471no—
214#535—471no—
215#518—471no—
216#463—471no—
217#463—471no—
218#463—471no—
219#463—471no—
220#459—471no—
221#459—471no—
222#459—471no—
223#459D4711yescharacteristic, complemented
224#424—471no—
225#418—471no—
226#416—471no—
227C47#304111yescharacteristic, complemented, Sylow
228C2×#41—471no—
229C22×D4—471no—
230C22×D4—471no—
231AGL(1,ℤ/8)—944no—
232C2×SD16—471no—
233C2×SD16—471no—
234C2×D8—471no—
235C2×D8—471no—
236C2×D8—471no—
237C2×D8—471no—
238C2×D8—944no—
239C2×D8C2×D4711yescharacteristic
240C2×D8C2×D4711yescharacteristic, complemented
241C2×M16—471no—
242C22×C8—471no—
243#127—471no—
244#127C2×D4711yescharacteristic, complemented
245#124—471no—
246#124—471no—
247#121—941no—
248#121—941no—
249#120—941no—
250#120—941no—
251C4×D4—471no—
252C4×D4—471no—
253C4×D4—471no—
254C4×D4—941no—
255C4×D4—941no—
256C4×D4C2×D4711yescharacteristic, complemented
257#117—471no—
258#117—471no—
259C2×C22⋊C4—941no—
260C2×C22⋊C4—941no—
261C4⋊C8—471no—
262C4⋊C8—471no—
263C4⋊C8—471no—
264C4⋊C8C2×D4711yescharacteristic, complemented
265#103—471no—
266#103—471no—
267#102—471no—
268#102—471no—
269#102—471no—
270#102—471no—
271#102C2×D4711yescharacteristic, complemented
272#102C2×D4711yescharacteristic, complemented
273C24—941no—
274C24—941no—
275#41—942no—
276#41—942no—
277C2×Q8—471no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—474no—
281C2×D4—471no—
282C2×D4—471no—
283C2×D4—942no—
284C2×D4—942no—
285C2×D4—942no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4C22×D4711yescharacteristic
292C2×D4C22×D4711yescharacteristic
293C2×D4C22×D4711yescharacteristic
294C22×C4—21no—
295C22×C4—471no—
296C22×C4—941no—
297C22×C4—941no—
298C22×C4—941no—
299C22×C4—941no—
300SD16—942no—
301SD16—942no—
302D8—22no—
303D8—22no—
304D8—942no—
305D8—942no—
306D8—942no—
307D8—942no—
308M16—942no—
309C2×C8—471no—
310C2×C8—471no—
311C2×C8—942no—
312C2×C8C22×D4711yescharacteristic
313C2×C8C22×D4711yescharacteristic
314C4⋊C4—471no—
315C4⋊C4—471no—
316C4⋊C4—471no—
317C4⋊C4C22×D4711yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—471no—
320C22⋊C4—471no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C42—471no—
330C42—941no—
331C42C22×D4711yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—471no—
336C23—944no—
337C23—941no—
338C23—941no—
339C23—3761no—
340C23—3761no—
341C23—3761no—
342C23—3761no—
343C23—1882no—
344Q8—941no—
345Q8—941no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—472no—
354D4—944no—
355D4—941no—
356D4—941no—
357D4—941no—
358D4—3761no—
359D4—3761no—
360D4—1882no—
361D4—1882no—
362D4D4×D4712yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—471no—
366C2×C4—472no—
367C2×C4—472no—
368C2×C4—471no—
369C2×C4—471no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—3761no—
373C2×C4—3761no—
374C2×C4—3761no—
375C2×C4—1882no—
376C2×C4D4×D4711yescharacteristic
377C2×C4D4×D4711yescharacteristic
378C2×C4C23×D4711yescharacteristic
379C8—21no—
380C8—21no—
381C8—941no—
382C8—941no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—472no—
393C22—941no—
394C22—941no—
395C22—942no—
396C22—3764no—
397C22—3764no—
398C22—1881no—
399C22—1881no—
400C22—1881no—
401C22—1881no—
402C22—1881no—
403C22C2×D4×D4711yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—472no—
408C4—941no—
409C4—941no—
410C4—1881no—
411C4—1881no—
412C4C2×D4×D4711yescharacteristic
413C4#41×D4711yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—942no—
418C2—3761no—
419C2—1882no—
420C2#121×D4711yescharacteristic
421C2#1568992411yescharacteristic
422C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3041
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×D8×D47C2semidirect
3. #15689686C2semidirect
4. #15689595C2semidirect
5. #15689339C2semidirect
6. #15689338C2semidirect
7. #15689337C2semidirect
8. #15689336C2semidirect
9. #15689317C2semidirect
10. #15689316C2semidirect
11. #15689315C2semidirect
12. #15689148C2semidirect
13. #15689126C2semidirect
14. #15689116C2semidirect
15. C47×#459C2semidirect
20. C2×#10625325C22semidirect
21. C2×#10625335C22semidirect
25. C2×#10625334C22semidirect
29. #13094020C22semidirect
30. #13094012C22semidirect
31. #13094011C22semidirect
36. C4×D188C22semidirect
37. D4×Dic47C22semidirect
38. #13093986C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. Dic47⋊C8C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093947C22semidirect
50. #13093946C22semidirect
51. #13093945C22semidirect
52. #13093945C22semidirect
53. #13093944C22semidirect
55. C2×D8×C47C22semidirect
56. #127×C47C22semidirect
57. C4×D4×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #102×C47C22semidirect
60. #102×C47C22semidirect
81. D4×D47D4semidirect
223. #459D47semidirect
227. C47#3041semidirect
240. C2×D8C2×D47semidirect
244. #127C2×D47semidirect
256. C4×D4C2×D47semidirect
264. C4⋊C8C2×D47semidirect
271. #102C2×D47semidirect
272. #102C2×D47semidirect