Finite Group Databasebeta

← #20254046

Subgroups — #20254046

Order 6016.

338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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#15689736C211yesmaximal, characteristic
2#15689734C211yesmaximal, characteristic
3#15689522C211yesmaximal, characteristic, complemented
4#15689502C211yesmaximal, characteristic, complemented
5#15689492C211yesmaximal, characteristic, complemented
6#15689380C212yesmaximal
7#15689363C212yesmaximal
8#15689227C212yesmaximal, complemented
9#15689215C212yesmaximal, complemented
10#15689080C211yesmaximal, characteristic
11C47×#491C211yesmaximal, characteristic, complemented
12C2×#10625337C2212yes—
13C2×#10625337C2212yes—
14C2×#10625324C2211yescharacteristic
15C2×C8×D47C2211yescharacteristic
16#13094024C2211yescharacteristic
17#13094019—22no—
18#13094019—22no—
19#13094016C2211yescharacteristic
20#13094015—22no—
21#13094014—22no—
22#13094004C2212yes—
23#13094000C2212yes—
24Q8×Dic47C2212yes—
25#13093989C2212yes—
26#13093981C2211yescharacteristic
27#13093957C2212yes—
28#13093955C2212yes—
29#13093949C2212yes—
30#13093949C2212yes—
31#13093934C2211yescharacteristic
32C4×C47⋊C8C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C4⋊Q8×C47C2211yescharacteristic
35#125×C47C2211yescharacteristic
36#103×C47C2212yes—
37#103×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×Q8×C47C2312yes—
40C2×C4×D47C2311yescharacteristic
41C2×Dic94C2312yes—
42C2×C8×C47C2311yescharacteristic
43C2×C8×C47C2311yescharacteristic
44C4⋊C4×C47—22no—
45C4⋊C4×C47—22no—
46C4⋊C4×C47C2312yes—
47C42×C47C2311yescharacteristic
48#10625337—24no—
49#10625337—24no—
50(C2×D47)⋊C4—22no—
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4D412yes—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47—22no—
56C4⋊Dic47C2312yes—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4D412yes—
61C4×Dic47—22no—
62C4×Dic47—22no—
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66#10625324—22no—
67C8×D47—22no—
68C22×D47C2×D411yescharacteristic
69Q8×C47—22no—
70Q8×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47C2×D412yes—
78C2×Dic47C2×D411yescharacteristic
79C4×D47—21no—
80C4×D47—21no—
81Dic94—22no—
82Dic94—22no—
83C8×C47—21no—
84C8×C47—21no—
85C47⋊C8#4112yes—
86C47⋊C8#4112yes—
87C22×C47C22×D411yescharacteristic
88C2×D47—21no—
89C2×D47—22no—
90C4×C47—22no—
91C4×C47—42no—
92C4×C47—42no—
93C4×C47C2×#4111yescharacteristic
94C4×C47C2×#4111yescharacteristic
95Dic47—21no—
96Dic47—22no—
97Dic47—42no—
98Dic47—42no—
99#3177—471nomaximal, Sylow
100C2×C47#53211yescharacteristic
101C2×C47#57812yes—
102D47—41no—
103#541—471no—
104#541—471no—
105#499—471no—
106#494—471no—
107#491—471no—
108#491D4711yescharacteristic, complemented
109#470—472no—
110#467—472no—
111#441—472no—
112C4×Q16—472no—
113#405—471no—
114C47#317711yescharacteristic, complemented, Sylow
115C2×Q16—472no—
116C2×Q16—472no—
117C2×M16—471no—
118C22×C8—471no—
119C4⋊Q8—471no—
120C4⋊Q8C2×D4711yescharacteristic
121#126—942no—
122#126—942no—
123#125—471no—
124#125—942no—
125#125—942no—
126#125C2×D4711yescharacteristic
127C22⋊Q8—472no—
128C22⋊Q8—472no—
129C4×Q8—472no—
130C4×Q8—472no—
131#117—471no—
132#107—472no—
133#106—472no—
134#103—472no—
135#103—472no—
136#103C2×D4712yes—
137#103C2×D4712yes—
138#97—471no—
139#97C2×D4711yescharacteristic
140C4×C8—471no—
141C4×C8—471no—
142C2×Q8—472no—
143C2×Q8C22×D4712yes—
144C22×C4—471no—
145Q16—944no—
146Q16—944no—
147M16—942no—
148C2×C8—471no—
149C2×C8—471no—
150C2×C8—942no—
151C2×C8C22×D4711yescharacteristic
152C2×C8C22×D4711yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—472no—
156C4⋊C4—472no—
157C4⋊C4—942no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4—942no—
161C4⋊C4—942no—
162C4⋊C4—942no—
163C4⋊C4C22×D4712yes—
164C22⋊C4—472no—
165C22⋊C4—942no—
166C22⋊C4—942no—
167C42—471no—
168C42—942no—
169C42—942no—
170C42C22×D4711yescharacteristic
171C23—471no—
172Q8—22no—
173Q8—22no—
174Q8—942no—
175Q8—942no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—472no—
179C2×C4—471no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4D4×D4712yes—
185C2×C4C23×D4711yescharacteristic
186C8—21no—
187C8—21no—
188C8—472no—
189C8—472no—
190C22—941no—
191C22—942no—
192C22C2×D4×D4711yescharacteristic
193C4—22no—
194C4—42no—
195C4—42no—
196C4—941no—
197C4—942no—
198C4—1882no—
199C4—1882no—
200C4#41×D4711yescharacteristic
201C4#41×D4711yescharacteristic
202C2—1881no—
203C2#1568967211yescharacteristic
204C2#1568993912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#491C2
socleC22×C47C22×D4
hypercenter#491D47
hypocenterC47#3177
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
3. #15689522C2semidirect
4. #15689502C2semidirect
5. #15689492C2semidirect
8. #15689227C2semidirect
9. #15689215C2semidirect
11. C47×#491C2semidirect
108. #491D47semidirect
114. C47#3177semidirect