Finite Group Databasebeta

← #20253760

Subgroups — #20253760

Order 6016.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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#15689676C211yesmaximal, characteristic, complemented
2C2×#13094020C211yesmaximal, characteristic
3#15689486C214yesmaximal, complemented
4#15689468C214yesmaximal, complemented
5#15689129C211yesmaximal, characteristic, complemented
6#15689128C211yesmaximal, characteristic, complemented
7#15689127C211yesmaximal, characteristic, complemented
8M16×Dic47C211yesmaximal, characteristic, complemented
9C47×#418C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C22×C22⋊D47—22no—
12C2×#10625329C2211yescharacteristic
13#13094023C2212yescomplemented
14#13094020—22no—
15#13094020C2212yes—
16#13094020C2212yes—
17#13094015C2212yescomplemented
18#13094001—22no—
19C4×Dic94—22no—
20#13093983C2211yescharacteristic
21C2×C4×Dic47C2211yescharacteristic
22#13093946C2214yescomplemented
23#13093945C2214yescomplemented
24#13093944C2214yescomplemented
25#13093934C2212yescomplemented
26C8×Dic47C2212yescomplemented
27C22×D4×C47C2211yescharacteristic
28C2×M16×C47C2211yescharacteristic
29#117×C47C2211yescharacteristic
30#102×C47C2214yescomplemented
31C24×C47—21no—
32C23×D47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—22no—
35C2×D4×C47—22no—
36C2×D4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—24no—
39C2×C22⋊D47—24no—
40C2×C22⋊D47—48no—
41C22×Dic47D412yes—
42C2×D188—22no—
43C2×D188—22no—
44C2×D188—21no—
45C2×D188C2312yes—
46C2×Dic94—22no—
47M16×C47—22no—
48C2×C8×C47C2312yes—
49C4⋊C4×C47C2312yes—
50C22⋊C4×C47—21no—
51C42×C47—21no—
52C22⋊Dic47—21no—
53C4⋊Dic47—22no—
54C4⋊Dic47C2312yes—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57C4×Dic47—21no—
58C4×Dic47D412yes—
59C4×Dic47C2311yescharacteristic
60C4×Dic47C2311yescharacteristic
61#10625329—22no—
62C2×C47⋊C8C2312yes—
63C23×C47—22no—
64C23×C47—44no—
65C23×C47—42no—
66C23×C47C2×D411yescharacteristic
67C22×D47—22no—
68C22×D47—44no—
69C22×D47—42no—
70D4×C47—22no—
71D4×C47—22no—
72D4×C47—42no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47#4112yes—
76C2×C4×C47#4112yes—
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—48no—
79C22⋊D47—48no—
80C2×Dic47—24no—
81C2×Dic47—22no—
82C2×Dic47C2×D412yes—
83C2×Dic47C2×D412yes—
84D188—22no—
85D188—22no—
86D188—42no—
87Dic94—44no—
88C8×C47—22no—
89C47⋊C8—22no—
90C22×C47—22no—
91C22×C47—42no—
92C22×C47—44no—
93C22×C47—84no—
94C22×C47#12412yes—
95C22×C47C22×D411yescharacteristic
96C2×D47—42no—
97C2×D47—44no—
98C2×D47—84no—
99C4×C47—42no—
100C4×C47#12412yes—
101C4×C47C2×#4111yescharacteristic
102C4×C47C2×#4111yescharacteristic
103Dic47—22no—
104Dic47—42no—
105Dic47AGL(1,ℤ/8)14yes—
106#3138—471nomaximal, Sylow
107C2×C47—22no—
108C2×C47—82no—
109C2×C47C2×#12411yescharacteristic
110C2×C47C2×AGL(1,ℤ/8)12yes—
111D47—82no—
112#533—471no—
113C2×#127—471no—
114#490—474no—
115#486—474no—
116#418—471no—
117#418—471no—
118#418—471no—
119#418D4711yescharacteristic, complemented
120C4×M16—471no—
121C47#313811yescharacteristic, complemented, Sylow
122C22×D4—471no—
123C22×D4—942no—
124C22×D4C2×D4711yescharacteristic
125C2×M16—471no—
126C2×M16C2×D4711yescharacteristic
127C4⋊Q8—472no—
128#127—472no—
129#127—472no—
130#127—942no—
131#125—472no—
132C22⋊Q8—942no—
133C4×Q8—942no—
134#117—471no—
135#117C2×D4711yescharacteristic
136C2×C42—471no—
137#102—474no—
138#102—474no—
139#102—474no—
140#102C2×D4714yescomplemented
141#97—472no—
142C4×C8—472no—
143C24—21no—
144C24—941no—
145C2×Q8—942no—
146C2×D4—22no—
147C2×D4—21no—
148C2×D4—22no—
149C2×D4—472no—
150C2×D4—944no—
151C2×D4—944no—
152C2×D4—942no—
153C2×D4—941no—
154C2×D4—942no—
155C2×D4—1888no—
156C2×D4C22×D4712yes—
157C22×C4—472no—
158C22×C4C22×D4711yescharacteristic
159M16—22no—
160M16—942no—
161C2×C8—472no—
162C2×C8C22×D4712yes—
163C4⋊C4—472no—
164C4⋊C4—942no—
165C4⋊C4—942no—
166C4⋊C4—942no—
167C4⋊C4C22×D4712yes—
168C22⋊C4—21no—
169C22⋊C4—941no—
170C42—21no—
171C42—472no—
172C42—471no—
173C42—471no—
174C42—941no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—942no—
179C23—1884no—
180C23—1882no—
181C23D4×D4711yescharacteristic
182Q8—1884no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—942no—
187D4—942no—
188D4—1888no—
189D4—1888no—
190D4—1882no—
191C2×C4—22no—
192C2×C4—472no—
193C2×C4—472no—
194C2×C4—944no—
195C2×C4—942no—
196C2×C4#1062535012yes—
197C2×C4D4×D4711yescharacteristic
198C2×C4#1062535212yes—
199C2×C4C23×D4711yescharacteristic
200C8—22no—
201C8—942no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—3764no—
207C22—1882no—
208C22—1884no—
209C22#1309401012yes—
210C22C2×D4×D4711yescharacteristic
211C4—42no—
212C4—474no—
213C4—942no—
214C4—1882no—
215C4#1309401012yes—
216C4C2×#1062535211yescharacteristic
217C4C2×#1062535011yescharacteristic
218C2—22no—
219C2—82no—
220C2—3762no—
221C2C2×#1309401011yescharacteristic
222C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#418C2
socleC22×C47C22×D4
hypercenter#418D47
hypocenterC47#3138
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #15689676C2semidirect
3. #15689486C2semidirect
4. #15689468C2semidirect
5. #15689129C2semidirect
6. #15689128C2semidirect
7. #15689127C2semidirect
8. M16×Dic47C2semidirect
9. C47×#418C2semidirect
13. #13094023C22semidirect
17. #13094015C22semidirect
22. #13093946C22semidirect
23. #13093945C22semidirect
24. #13093944C22semidirect
25. #13093934C22semidirect
26. C8×Dic47C22semidirect
30. #102×C47C22semidirect
119. #418D47semidirect
121. C47#3138semidirect
140. #102C2×D47semidirect