Finite Group Databasebeta

← #20252245

Subgroups — #20252245

Order 6016.

492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C22×#10625335C211yesmaximal, characteristic
2#15689600C211yesmaximal, characteristic, complemented
3#15689223C214yesmaximal, complemented
4C4×#10625335C214yesmaximal, complemented
5#15689159C211yesmaximal, characteristic, complemented
6#15689131C211yesmaximal, characteristic, complemented
7#15689128C211yesmaximal, characteristic
8#15689079C211yesmaximal, characteristic, complemented
9C47×#518C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C2×#10625335C418yescomplemented
12C2×#10625335C2212yes—
13C2×#10625335C2212yes—
14C2×#10625329C2211yescharacteristic
15C22×C47⋊C8C2211yescharacteristic
16C4×Dic94C2214yescomplemented
17#13093989—22no—
18#13093983C2211yescharacteristic
19#13093980—22no—
20#13093957C2212yescomplemented
21#13093955C2212yescomplemented
22#13093947C2214yescomplemented
23#13093945C2214yes—
24#13093935C2212yescomplemented
25C4×C47⋊C8C2212yescomplemented
26C22×D4×C47C2211yescharacteristic
27C4×D4×C47—22no—
28C4×D4×C47C2214yes—
29#117×C47C2211yescharacteristic
30#117×C47C2211yescharacteristic
31C2×C22⋊C4×C47—22no—
32C24×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—22no—
35C2×D4×C47C2×C414yes—
36C2×D4×C47C2312yes—
37C22×C4×C47—24no—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—21no—
40C2×Dic94—21no—
41C2×Dic94—22no—
42C2×Dic94C2×C414yescomplemented
43C2×Dic94C2312yes—
44C4⋊C4×C47D412yes—
45C4⋊C4×C47C2312yes—
46C22⋊C4×C47—21no—
47C22⋊C4×C47—24no—
48C22⋊C4×C47D412yes—
49C42×C47—21no—
50C42×C47C2312yes—
51C22⋊Dic47—21no—
52#10625335C2×C418yescomplemented
53#10625335C2×C418yescomplemented
54C4⋊Dic47C2312yes—
55Dic47⋊C4—24no—
56C4×Dic47—24no—
57C4×Dic47—21no—
58#10625329—22no—
59C2×C47⋊C8C2×C414yescomplemented
60C2×C47⋊C8C2312yes—
61C2×C47⋊C8C2311yescharacteristic
62C2×C47⋊C8C2311yescharacteristic
63C23×C47—22no—
64C23×C47—24no—
65C23×C47—82no—
66C23×C47C2×D411yescharacteristic
67D4×C47—24no—
68D4×C47—22no—
69D4×C47C22×C414yes—
70C2×C4×C47—22no—
71C2×C4×C47—84no—
72C2×C4×C47C22×C412yes—
73C2×C4×C47C2×D414yes—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47#4112yes—
76C2×C4×C47C2411yescharacteristic
77C2×Dic47—24no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80Dic94—24no—
81Dic94—22no—
82Dic94C22×C414yes—
83C47⋊C8—22no—
84C47⋊C8C22×C412yes—
85C47⋊C8C22×C412yes—
86C22×C47—22no—
87C22×C47—24no—
88C22×C47—44no—
89C22×C47—84no—
90C22×C47C4×D412yes—
91C22×C47C22×D411yescharacteristic
92C4×C47—24no—
93C4×C47—42no—
94C4×C47C4×D412yes—
95C4×C47C23×C411yescharacteristic
96C4×C47C2×#4111yescharacteristic
97Dic47—24no—
98Dic47—42no—
99#2949—471nomaximal, Sylow
100C2×C47—22no—
101C2×C47—44no—
102C2×C47C2×C4×D411yescharacteristic
103C2×C47#57712yes—
104C22×SD16—471no—
105#519—471no—
106#518D4711yescharacteristic
107#440—474no—
108C4×SD16—474no—
109#427—471no—
110#419—471no—
111#418—471no—
112#405—471no—
113C47#294911yescharacteristic, complemented, Sylow
114C22×Q8—471no—
115C22×D4C2×D4711yescharacteristic
116C2×SD16—478no—
117C2×SD16—472no—
118C2×SD16—472no—
119C2×M16—471no—
120C22×C8—471no—
121C4×Q8—474no—
122C4×Q8—942no—
123C4×D4—22no—
124C4×D4C2×D4714yes—
125#117—471no—
126#117—942no—
127#117C2×D4711yescharacteristic
128#117C2×D4711yescharacteristic
129C2×C22⋊C4—22no—
130#107—472no—
131#106—472no—
132#103—474no—
133#102—474no—
134#97—472no—
135C4×C8—472no—
136C24—21no—
137C2×Q8—474no—
138C2×Q8—472no—
139C2×Q8—942no—
140C2×Q8—941no—
141C2×D4—22no—
142C2×D4—21no—
143C2×D4C4×D4714yes—
144C2×D4C22×D4712yes—
145C22×C4—24no—
146C22×C4—941no—
147C22×C4C22×D4711yescharacteristic
148SD16—478no—
149SD16—478no—
150M16—942no—
151C2×C8—474no—
152C2×C8—471no—
153C2×C8—471no—
154C2×C8—472no—
155C4⋊C4—472no—
156C4⋊C4—944no—
157C4⋊C4C22⋊D4712yes—
158C4⋊C4C22×D4712yes—
159C22⋊C4—21no—
160C22⋊C4—24no—
161C22⋊C4—941no—
162C22⋊C4C22⋊D4712yes—
163C42—21no—
164C42—941no—
165C42—944no—
166C42C22×D4712yes—
167C23—22no—
168C23—24no—
169C23—82no—
170C23C2×C22⋊D4711yescharacteristic
171Q8—474no—
172Q8—944no—
173Q8—942no—
174D4—24no—
175D4—22no—
176D4C2×C4×D4714yes—
177C2×C4—22no—
178C2×C4—84no—
179C2×C4—944no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4C2×C4×D4712yes—
183C2×C4#1062535012yes—
184C2×C4C2×C22⋊D4714yes—
185C2×C4C2×C22⋊D4711yescharacteristic
186C2×C4C23×D4711yescharacteristic
187C8—472no—
188C8—472no—
189C8—942no—
190C22—22no—
191C22—24no—
192C22—44no—
193C22—84no—
194C22C4×C22⋊D4712yes—
195C22C22×C22⋊D4711yescharacteristic
196C4—24no—
197C4—42no—
198C4—944no—
199C4—1882no—
200C4C4×C22⋊D4712yes—
201C4C22×C4×D4711yescharacteristic
202C4C2×#1062535011yescharacteristic
203C2—22no—
204C2—44no—
205C2C2×C4×C22⋊D4711yescharacteristic
206C2#1568993412yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#518C2
socleC22×C47C22×D4
hypercenter#518D47
hypocenterC47#2949
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #15689600C2semidirect
3. #15689223C2semidirect
4. C4×#10625335C2semidirect
5. #15689159C2semidirect
6. #15689131C2semidirect
8. #15689079C2semidirect
11. C2×#10625335C4semidirect
16. C4×Dic94C22semidirect
20. #13093957C22semidirect
21. #13093955C22semidirect
22. #13093947C22semidirect
24. #13093935C22semidirect
25. C4×C47⋊C8C22semidirect
42. C2×Dic94C2×C4semidirect
52. #10625335C2×C4semidirect
53. #10625335C2×C4semidirect
59. C2×C47⋊C8C2×C4semidirect
113. C47#2949semidirect