Finite Group Databasebeta

← #20256284

Subgroups — #20256284

Order 6016.

374 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689829C211yesmaximal, characteristic, complemented
2#15689788C211yesmaximal, characteristic, complemented
3#15689531C211yesmaximal, characteristic, complemented
4#15689520C211yesmaximal, characteristic, complemented
5#15689426C211yesmaximal, characteristic, complemented
6#15689420C211yesmaximal, characteristic, complemented
7#15689412C211yesmaximal, characteristic, complemented
8#15689412C211yesmaximal, characteristic, complemented
9#15689410C211yesmaximal, characteristic, complemented
10#15689402C211yesmaximal, characteristic, complemented
11#15689251C211yesmaximal, characteristic, complemented
12#15689236C211yesmaximal, characteristic
13#15689234C211yesmaximal, characteristic
14#15689205C211yesmaximal, characteristic
15C47×#501C211yesmaximal, characteristic, complemented
16C2×Q8×D47—21no—
17C2×D376C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094004—21no—
23#13094002—21no—
24#13094002—21no—
25#13094002—21no—
26#13094002—21no—
27#13094000—21no—
28C4×Dic94C2211yescharacteristic
29C4×D188C2211yescharacteristic
30C4×D188C2211yescharacteristic
31#13093986C2211yescharacteristic
32#13093986C2211yescharacteristic
33#13093986C2211yescharacteristic
34#13093986C2211yescharacteristic
35C4⋊C4×D47—21no—
36#13093957C2211yescharacteristic
37#13093956C2211yescharacteristic
38#13093955C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60Q8×D47—44no—
61C2×D188C2311yescharacteristic
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×Dic94—21no—
70C2×Dic94—21no—
71C2×Dic94—21no—
72C2×Dic94D411yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C42×C47C2311yescharacteristic
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47D411yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98Dic47⋊C4D411yescharacteristic
99C4×Dic47C2311yescharacteristic
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103D376Q814yescomplemented
104C22×D47—21no—
105C22×D47—21no—
106Q8×C47—42no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2411yescharacteristic
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47C2×D411yescharacteristic
117C2×Dic47C2×D411yescharacteristic
118C2×Dic47C2×D411yescharacteristic
119C2×Dic47C2×D411yescharacteristic
120D188—21no—
121D188—21no—
122D188C2×Q812yes—
123D188C2×Q812yescomplemented
124C4×D47—42no—
125C4×D47—42no—
126C4×D47—42no—
127C4×D47—42no—
128C4×D47—81no—
129C4×D47—81no—
130Dic94—22no—
131Dic94—42no—
132Dic94—42no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47C2×Q812yescomplemented
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47C22×D411yescharacteristic
139C2×D47—22no—
140C2×D47—22no—
141C2×D47—41no—
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47C22×Q811yescharacteristic
152C4×C472−1+411yescharacteristic
153Dic47—21no—
154Dic47—21no—
155Dic47—21no—
156Dic47—41no—
157Dic47—41no—
158Dic47AGL(1,ℤ/8)12yes—
159#3384—471nomaximal, Sylow
160C2×C47D4×Q811yescharacteristic
161C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
162C2×C47#57711yescharacteristic
163D47—42no—
164D47—42no—
165#554—471no—
166D4×Q8—471no—
167#501—471no—
168#501D4711yescharacteristic, complemented
169#498—471no—
170#478—471no—
171#478—471no—
172#476—471no—
173#476—471no—
174#476—471no—
175#474—471no—
176#446—471no—
177#442—471no—
178#442—471no—
179C4×D8—471no—
180C47#338411yescharacteristic, complemented, Sylow
181C22×Q8—941no—
182C2×D8—471no—
183C4⋊Q8—471no—
184C4⋊Q8—471no—
185C4⋊Q8—471no—
186C4⋊Q8C2×D4711yescharacteristic
187#125—471no—
188#125C2×D4711yescharacteristic
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191C22⋊Q8—941no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195C4×Q8—471no—
196C4×D4—471no—
197C4×D4—471no—
198C4×D4—471no—
199C4×D4—471no—
200C4×D4—471no—
201C4×D4—471no—
202C2×C4⋊C4—941no—
203#107—471no—
204#107C2×D4711yescharacteristic
205#107C2×D4711yescharacteristic
206#106—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106C2×D4711yescharacteristic
211#106C2×D4711yescharacteristic
212C4⋊C8—471no—
213C4⋊C8—471no—
214C4⋊C8—471no—
215#102—471no—
216#102—471no—
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221#97—471no—
222#97C2×D4711yescharacteristic
223C4×C8—471no—
224C2×Q8—21no—
225C2×Q8—471no—
226C2×Q8—941no—
227C2×Q8—941no—
228C2×Q8—941no—
229C2×Q8—1884no—
230C2×D4—471no—
231C2×D4—471no—
232C22×C4—941no—
233C22×C4—941no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238D8—474no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8C22×D4711yescharacteristic
242C2×C8C22×D4711yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C4⋊C4C22×D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C42—471no—
267C42—471no—
268C42C22×D4711yescharacteristic
269C23—941no—
270C23—941no—
271Q8—42no—
272Q8—942no—
273Q8—3761no—
274Q8—1882no—
275Q8—1882no—
276D4—472no—
277D4—472no—
278D4—941no—
279D4—941no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—471no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—3761no—
291C2×C4—3761no—
292C2×C4—1882no—
293C2×C4—1882no—
294C2×C4—1882no—
295C2×C4—1882no—
296C2×C4D4×D4711yescharacteristic
297C2×C4D4×D4711yescharacteristic
298C2×C4C23×D4711yescharacteristic
299C8—21no—
300C8—941no—
301C8—941no—
302C8Q8×D4712yescomplemented
303C22—942no—
304C22—942no—
305C22—1881no—
306C22—1881no—
307C22—1881no—
308C22—1881no—
309C22C2×D4×D4711yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—472no—
317C4—941no—
318C4—941no—
319C4—941no—
320C4—1881no—
321C4—1881no—
322C4C2×Q8×D4711yescharacteristic
323C4#1309407211yescharacteristic
324C2—1882no—
325C2—1882no—
326C2#1568978811yescharacteristic
327C2AGL(1,ℤ/8)×D4711yescharacteristic
328C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3384
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #15689829C2semidirect
2. #15689788C2semidirect
3. #15689531C2semidirect
4. #15689520C2semidirect
5. #15689426C2semidirect
6. #15689420C2semidirect
7. #15689412C2semidirect
8. #15689412C2semidirect
9. #15689410C2semidirect
10. #15689402C2semidirect
11. #15689251C2semidirect
15. C47×#501C2semidirect
103. D376Q8semidirect
123. D188C2×Q8semidirect
135. C8×C47C2×Q8semidirect
168. #501D47semidirect
180. C47#3384semidirect
302. C8Q8×D47semidirect