Finite Group Databasebeta

← #20254702

Subgroups — #20254702

Order 6016.

392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689677C211yesmaximal, characteristic, complemented
2#15689671C211yesmaximal, characteristic
3#15689411C212yesmaximal, complemented
4#15689409C211yesmaximal, characteristic, complemented
5#15689408C211yesmaximal, characteristic, complemented
6#15689351C212yesmaximal, complemented
7#15689349C212yesmaximal, complemented
8#15689326C212yesmaximal, complemented
9#15689320C211yesmaximal, characteristic, complemented
10C4⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#460C211yesmaximal, characteristic, complemented
12C2×#10625352—21no—
13C2×#10625335C2212yes—
14C2×C8×D47C2212yes—
15#13094024C2211yescharacteristic
16#13094023C2211yescharacteristic
17#13094022C2211yescharacteristic
18#13094014—21no—
19#13094011—21no—
20#13094004C2211yescharacteristic
21#13094002—21no—
22#13094000C2211yescharacteristic
23#13093995—21no—
24#13093995C2212yes—
25C4×Dic94—21no—
26C4×Dic94C2211yescharacteristic
27D4×Dic47—21no—
28D4×Dic47C2212yes—
29#13093981—21no—
30C42×D47C2211yescharacteristic
31#13093956C2212yes—
32#13093955C2212yes—
33C4⋊(C47⋊C8)C2211yescharacteristic
34Dic47⋊C8C2212yes—
35#13093949C2212yes—
36#13093948C2212yes—
37#13093945C2212yes—
38C2×SD16×C47C2212yes—
39#127×C47C2211yescharacteristic
40C4×Q8×C47C2211yescharacteristic
41C4⋊C8×C47C2211yescharacteristic
42#102×C47C2212yes—
43C2×Q8×C47C2311yescharacteristic
44C2×D4×C47—21no—
45C2×D4×C47—21no—
46C2×D4×C47C2312yes—
47C2×C22⋊D47—22no—
48C22×Dic47—22no—
49#10625352—44no—
50C2×C4×D47D411yescharacteristic
51C2×C4×D47D411yescharacteristic
52C2×C4×D47C2311yescharacteristic
53C2×Dic94—21no—
54C2×Dic94—21no—
55C2×Dic94C2311yescharacteristic
56SD16×C47—42no—
57C2×C8×C47C2312yes—
58C4⋊C4×C47—21no—
59C4⋊C4×C47C2311yescharacteristic
60C42×C47—21no—
61C42×C47C2311yescharacteristic
62C22⋊Dic47—22no—
63C22⋊Dic47—22no—
64#10625335—42no—
65(C2×D47)⋊C4—21no—
66(C2×D47)⋊C4—21no—
67C4⋊Dic47—21no—
68C4⋊Dic47—21no—
69C4⋊Dic47C2311yescharacteristic
70C4⋊Dic47C2312yes—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75Dic47⋊C4—21no—
76C4×Dic47—21no—
77C4×Dic47D411yescharacteristic
78C4×Dic47D411yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81C8×D47—42no—
82C23×C47—22no—
83C22×D47C2×D411yescharacteristic
84Q8×C47—21no—
85Q8×C47—21no—
86D4×C47—22no—
87D4×C47—22no—
88D4×C47—42no—
89D4×C47—42no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2411yescharacteristic
95C22⋊D47—44no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—44no—
100C2×Dic47C2×D411yescharacteristic
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103C4×D47—21no—
104C4×D47—21no—
105C4×D47—41no—
106C4×D47SD1614yescomplemented
107Dic94—21no—
108Dic94—21no—
109Dic94—42no—
110Dic94—42no—
111C8×C47—22no—
112C47⋊C8—22no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47C22×D411yescharacteristic
117C2×D47—21no—
118C2×D47—21no—
119C2×D47C2×SD1612yes—
120C4×C47—21no—
121C4×C47—41no—
122C4×C47—41no—
123C4×C47C2×SD1612yes—
124C4×C47H(5,𝔽2)11yescharacteristic
125C4×C472−1+411yescharacteristic
126Dic47—21no—
127Dic47—21no—
128Dic47—41no—
129Dic47—42no—
130Dic47—41no—
131Dic47C2×SD1612yes—
132#3246—471nomaximal, Sylow
133C2×C47—82no—
134C2×C47#53711yescharacteristic
135C2×C47C22×SD1611yescharacteristic
136C2×C47#57511yescharacteristic
137D47—22no—
138#533—471no—
139#532—471no—
140#476—472no—
141#475—471no—
142#475—471no—
143#465—472no—
144#465—472no—
145#461—472no—
146#460—471no—
147#460D4711yescharacteristic, complemented
148C2×C4⋊C8—471no—
149C47#324611yescharacteristic, complemented, Sylow
150C2×#41—941no—
151C2×SD16—472no—
152C2×SD16C2×D4712yes—
153C22×C8—472no—
154C4⋊Q8—471no—
155C4⋊Q8—471no—
156C4⋊Q8—471no—
157#127C2×D4711yescharacteristic
158#125—941no—
159#124—941no—
160C22⋊Q8—471no—
161C22⋊Q8—471no—
162C22⋊Q8—941no—
163#121—472no—
164#121—941no—
165C4×Q8—471no—
166C4×Q8—941no—
167C4×Q8C2×D4711yescharacteristic
168C4×D4—472no—
169C4×D4—941no—
170#117—941no—
171C2×C42—471no—
172#106—472no—
173#106—472no—
174C4⋊C8—472no—
175C4⋊C8—471no—
176C4⋊C8C2×D4711yescharacteristic
177#103—472no—
178#103—472no—
179#102—472no—
180#102C2×D4712yes—
181#41—1884no—
182C2×Q8—471no—
183C2×Q8—941no—
184C2×Q8—941no—
185C2×Q8C22×D4711yescharacteristic
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—942no—
189C2×D4C22×D4712yes—
190C22×C4—471no—
191C22×C4—471no—
192C22×C4—471no—
193C22×C4—942no—
194SD16—42no—
195SD16—1882no—
196C2×C8—472no—
197C2×C8—1882no—
198C2×C8C22×D4712yes—
199C4⋊C4—21no—
200C4⋊C4—471no—
201C4⋊C4—472no—
202C4⋊C4—941no—
203C4⋊C4—941no—
204C4⋊C4—941no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C4⋊C4—941no—
209C4⋊C4C22×D4711yescharacteristic
210C22⋊C4—941no—
211C22⋊C4—941no—
212C22⋊C4—942no—
213C22⋊C4—942no—
214C42—21no—
215C42—471no—
216C42—471no—
217C42—471no—
218C42—941no—
219C42C22×D4711yescharacteristic
220C23—22no—
221C23—471no—
222Q8—21no—
223Q8—21no—
224Q8—941no—
225Q8—941no—
226Q8—1882no—
227Q8—1882no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—42no—
232D4—1884no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—471no—
236C2×C4—474no—
237C2×C4—471no—
238C2×C4—471no—
239C2×C4—941no—
240C2×C4—941no—
241C2×C4—941no—
242C2×C4—941no—
243C2×C4—942no—
244C2×C4—1881no—
245C2×C4—1884no—
246C2×C4D4×D4711yescharacteristic
247C2×C4D4×D4711yescharacteristic
248C2×C4C23×D4711yescharacteristic
249C8—22no—
250C8—942no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—472no—
255C22—941no—
256C22—941no—
257C22C2×D4×D4711yescharacteristic
258C4—21no—
259C4—41no—
260C4—41no—
261C4—472no—
262C4—941no—
263C4—941no—
264C4—1882no—
265C4—1881no—
266C4—1881no—
267C4SD16×D4712yes—
268C4#1309406911yescharacteristic
269C4#1309407111yescharacteristic
270C2—82no—
271C2—942no—
272C2#1568970211yescharacteristic
273C2C2×SD16×D4711yescharacteristic
274C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3246
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689411C2semidirect
4. #15689409C2semidirect
5. #15689408C2semidirect
6. #15689351C2semidirect
7. #15689349C2semidirect
8. #15689326C2semidirect
9. #15689320C2semidirect
10. C4⋊C8×D47C2semidirect
11. C47×#460C2semidirect
106. C4×D47SD16semidirect
147. #460D47semidirect
149. C47#3246semidirect