Finite Group Databasebeta

← #20253508

Subgroups — #20253508

Order 6016.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689670C211yesmaximal, characteristic
2C4×Q8×D47C211yesmaximal, characteristic, complemented
3#15689438C211yesmaximal, characteristic, complemented
4#15689435C211yesmaximal, characteristic, complemented
5#15689417C211yesmaximal, characteristic, complemented
6#15689416C211yesmaximal, characteristic, complemented
7#15689322C211yesmaximal, characteristic, complemented
8#15689321C211yesmaximal, characteristic, complemented
9#15689263C211yesmaximal, characteristic, complemented
10#15689260C211yesmaximal, characteristic, complemented
11#15689225C211yesmaximal, characteristic, complemented
12#15689223C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14#15689178C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×Q8×D47C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094020C2211yescharacteristic
23#13094010—21no—
24#13093999C2211yescharacteristic
25#13093997—21no—
26#13093995C2211yescharacteristic
27Q8×Dic47C2211yescharacteristic
28C4×Dic94—21no—
29C4×Dic94C2211yescharacteristic
30#13093989—21no—
31#13093989C2211yescharacteristic
32C4×D188C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4⋊C4×D47—21no—
35C4⋊C4×D47C2211yescharacteristic
36C42×D47—21no—
37C42×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093935C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65Q8×D47—22no—
66Q8×D47—22no—
67#10625350—44no—
68C2×D188—21no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47D411yescharacteristic
74C2×C4×D47D411yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×Dic94—21no—
77C2×Dic94—21no—
78C2×Dic94C2311yescharacteristic
79SD16×C47—22no—
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C42×C47—21no—
87C42×C47C2311yescharacteristic
88C22⋊Dic47—21no—
89#10625336—22no—
90#10625335—22no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47D411yescharacteristic
104C4×Dic47D411yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108#10625325—22no—
109C23×C47—21no—
110C22×D47—21no—
111C22×D47C2×D411yescharacteristic
112Q8×C47—21no—
113Q8×C47#4112yescomplemented
114D4×C47—21no—
115D4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—42no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2411yescharacteristic
123C22⋊D47—42no—
124C22⋊D47—42no—
125C22⋊D47—42no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132D188—21no—
133D188—21no—
134D188—42no—
135C4×D47—24no—
136C4×D47—22no—
137C4×D47—21no—
138C4×D47—21no—
139C4×D47—22no—
140C4×D47—42no—
141C4×D47—42no—
142Dic94—24no—
143Dic94—21no—
144Dic94—42no—
145Dic94#4112yescomplemented
146C8×C47—21no—
147C8×C47—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47C22×D411yescharacteristic
154C2×D47—21no—
155C2×D47—21no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47AGL(1,ℤ/8)12yes—
160C4×C47—22no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47C2×#4111yescharacteristic
166C4×C47C2×#4111yescharacteristic
167Dic47—21no—
168Dic47—22no—
169Dic47—21no—
170Dic47—41no—
171Dic47—41no—
172Dic47#13712yes—
173#3112—471nomaximal, Sylow
174C2×C47—81no—
175C2×C47#52511yescharacteristic
176C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C47C2×#13711yescharacteristic
178D47—22no—
179D47—81no—
180#532—471no—
181C2×C4×Q8—471no—
182#480—471no—
183#480—471no—
184#477—471no—
185#477—471no—
186#460—471no—
187#460—471no—
188#448—471no—
189#448—471no—
190#440—471no—
191#440—471no—
192#440—471no—
193#440D4711yescharacteristic, complemented
194#432—471no—
195C47#311211yescharacteristic, complemented, Sylow
196C2×#41—941no—
197C22×Q8—471no—
198C2×SD16—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×SD16C2×D4711yescharacteristic
202C4⋊Q8—471no—
203#127—471no—
204#124—941no—
205#121—471no—
206#121—471no—
207#121—941no—
208C4×Q8—471no—
209C4×Q8—471no—
210C4×Q8—471no—
211C4×Q8—941no—
212C4×Q8—941no—
213C4×Q8C2×D4711yescharacteristic
214C4×D4—471no—
215C4×D4—941no—
216C4×D4C2×D4711yescharacteristic
217C2×C4⋊C4—471no—
218C2×C4⋊C4—941no—
219C2×C42—471no—
220C2×C42—941no—
221#107—471no—
222#107—471no—
223#107—471no—
224#107C2×D4711yescharacteristic
225C4⋊C8—471no—
226C4⋊C8—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103C2×D4711yescharacteristic
231#102—471no—
232#102—471no—
233#102—471no—
234#102C2×D4711yescharacteristic
235C22⋊C8—471no—
236C22⋊C8—471no—
237#97—471no—
238#97C2×D4711yescharacteristic
239#41—1884no—
240C2×Q8—471no—
241C2×Q8—941no—
242C2×Q8—941no—
243C2×Q8—942no—
244C2×Q8—942no—
245C2×Q8C22×D4711yescharacteristic
246C2×D4—471no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4—941no—
251C2×D4C22×D4711yescharacteristic
252C22×C4—21no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—941no—
259SD16—22no—
260SD16—942no—
261SD16—942no—
262SD16—942no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8C22×D4711yescharacteristic
266C2×C8C22×D4711yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C42—21no—
282C42—471no—
283C42—471no—
284C42—471no—
285C42—941no—
286C42—941no—
287C42—941no—
288C42C22×D4711yescharacteristic
289C23—21no—
290C23—471no—
291C23—941no—
292Q8—21no—
293Q8—472no—
294Q8—944no—
295Q8—941no—
296Q8—1882no—
297Q8#1062535012yescomplemented
298D4—21no—
299D4—21no—
300D4—941no—
301D4—941no—
302D4—1882no—
303D4—1882no—
304D4—1882no—
305D4—1882no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—471no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—944no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4D4×D4711yescharacteristic
324C2×C4D4×D4711yescharacteristic
325C2×C4C23×D4711yescharacteristic
326C8—21no—
327C8—21no—
328C8—941no—
329C8—941no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—472no—
334C22—941no—
335C22—941no—
336C22—1881no—
337C22—1881no—
338C22—1881no—
339C22C2×D4×D4711yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—472no—
346C4—941no—
347C4—942no—
348C4—941no—
349C4—1881no—
350C4—1881no—
351C4#41×D4711yescharacteristic
352C4C2×#1062535011yescharacteristic
353C2—81no—
354C2—942no—
355C2—3761no—
356C2#1568963211yescharacteristic
357C2AGL(1,ℤ/8)×D4711yescharacteristic
358C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3112
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D47C2semidirect
3. #15689438C2semidirect
4. #15689435C2semidirect
5. #15689417C2semidirect
6. #15689416C2semidirect
7. #15689322C2semidirect
8. #15689321C2semidirect
9. #15689263C2semidirect
10. #15689260C2semidirect
11. #15689225C2semidirect
12. #15689223C2semidirect
13. #15689221C2semidirect
14. #15689178C2semidirect
15. C47×#440C2semidirect
113. Q8×C47#41semidirect
145. Dic94#41semidirect
193. #440D47semidirect
195. C47#3112semidirect
297. Q8#10625350semidirect