Finite Group Databasebeta

← #20253640

Subgroups — #20253640

Order 6016.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689735C211yesmaximal, characteristic, complemented
2#15689464C212yesmaximal, complemented
3#15689423C212yesmaximal, complemented
4#15689328C212yesmaximal, complemented
5#15689274C212yesmaximal
6#15689223C212yesmaximal, complemented
7C4×#10625335C212yesmaximal, complemented
8#15689184C211yesmaximal, characteristic, complemented
9C47×#518C211yesmaximal, characteristic
10C2×#10625335C2212yes—
11C2×#10625335C2212yes—
12#13094024C2211yescharacteristic, complemented
13#13094017—22no—
14#13094016C2211yescharacteristic, complemented
15#13094014—22no—
16#13094003C2212yes—
17C4×Dic94C2212yescomplemented
18#13093957C2212yescomplemented
19#13093955C2212yescomplemented
20C4⋊(C47⋊C8)C2212yescomplemented
21#13093947C2212yescomplemented
22#13093947C2212yescomplemented
23#13093945C2212yes—
24#13093945C2212yes—
25C22⋊(C47⋊C8)C2212yes—
26#13093935C2211yescharacteristic, complemented
27C4×C47⋊C8C2211yescharacteristic, complemented
28C22×D4×C47C2211yescharacteristic
29C4×D4×C47—22no—
30C4×D4×C47C2212yes—
31C4×D4×C47C2212yes—
32#117×C47C2211yescharacteristic
33#117×C47C2211yescharacteristic
34C2×C22⋊C4×C47—22no—
35C24×C47—21no—
36C2×D4×C47—24no—
37C2×D4×C47—21no—
38C2×D4×C47C2312yes—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47C2311yescharacteristic
42C2×Dic94C2312yes—
43C4⋊C4×C47D412yes—
44C4⋊C4×C47C2312yes—
45C22⋊C4×C47—21no—
46C22⋊C4×C47—22no—
47C22⋊C4×C47—22no—
48C22⋊C4×C47D412yes—
49C42×C47—21no—
50C42×C47C2311yescharacteristic
51C42×C47C2311yescharacteristic
52C22⋊Dic47—22no—
53#10625335—24no—
54#10625335—24no—
55C4⋊Dic47—22no—
56C4⋊Dic47C2312yes—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60C4×Dic47—22no—
61C2×C47⋊C8C2312yes—
62C2×C47⋊C8C2312yes—
63C23×C47—24no—
64C23×C47—22no—
65C23×C47—82no—
66C23×C47C2×D411yescharacteristic
67D4×C47—24no—
68D4×C47—22no—
69D4×C47#4114yes—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—82no—
73C2×C4×C47—82no—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2411yescharacteristic
78C2×Dic47—22no—
79C2×Dic47—22no—
80Dic94—22no—
81Dic94—22no—
82C47⋊C8—22no—
83C47⋊C8—22no—
84C22×C47—21no—
85C22×C47—24no—
86C22×C47—22no—
87C22×C47—42no—
88C22×C47—42no—
89C22×C47—84no—
90C22×C47C22×D411yescharacteristic
91C4×C47—21no—
92C4×C47—22no—
93C4×C47—22no—
94C4×C47—42no—
95C4×C47C2×#4112yes—
96Dic47—42no—
97Dic47—42no—
98#3123—471nomaximal, Sylow
99C2×C47—41no—
100C2×C47—44no—
101C2×C47#52511yescharacteristic
102C2×C47#57712yes—
103#541—471no—
104#518D4711yescharacteristic
105#485—472no—
106#478—472no—
107#461—472no—
108#450—472no—
109#440—472no—
110C4×SD16—472no—
111#433—471no—
112C47#312311yescharacteristic, complemented, Sylow
113C22×D4C2×D4711yescharacteristic
114C2×SD16—472no—
115C2×SD16—472no—
116C4⋊Q8—471no—
117#126—942no—
118#125—471no—
119#125—942no—
120C22⋊Q8—472no—
121C4×Q8—472no—
122C4×D4—22no—
123C4×D4C2×D4712yes—
124C4×D4C2×D4712yes—
125#117C2×D4711yescharacteristic
126#117C2×D4711yescharacteristic
127C2×C22⋊C4—22no—
128#107—472no—
129#106—472no—
130C4⋊C8—472no—
131#103—472no—
132#103—472no—
133#102—472no—
134#102—472no—
135C22⋊C8—472no—
136#97—471no—
137C4×C8—471no—
138C24—21no—
139C2×Q8—472no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D4712yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D4711yescharacteristic
146SD16—944no—
147SD16—944no—
148C2×C8—472no—
149C2×C8—472no—
150C4⋊C4—472no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4C22⋊D4712yes—
156C4⋊C4C22×D4712yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—942no—
161C22⋊C4C22⋊D4712yes—
162C42—21no—
163C42—942no—
164C42C22×D4711yescharacteristic
165C42C22×D4711yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D4711yescharacteristic
170Q8—942no—
171Q8—942no—
172D4—24no—
173D4—22no—
174D4#1062535014yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4C2×C22⋊D4711yescharacteristic
182C2×C4C2×C22⋊D4712yes—
183C2×C4C2×C22⋊D4712yes—
184C2×C4C23×D4711yescharacteristic
185C8—942no—
186C8—942no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D4711yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—1882no—
199C4—1882no—
200C4C2×#1062535012yes—
201C2—41no—
202C2—44no—
203C2#1568963411yescharacteristic
204C2#1568993412yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#518C2
socleC22×C47C22×D4
hypercenter#518D47
hypocenterC47#3123
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #15689735C2semidirect
2. #15689464C2semidirect
3. #15689423C2semidirect
4. #15689328C2semidirect
6. #15689223C2semidirect
7. C4×#10625335C2semidirect
8. #15689184C2semidirect
12. #13094024C22semidirect
14. #13094016C22semidirect
17. C4×Dic94C22semidirect
18. #13093957C22semidirect
19. #13093955C22semidirect
20. C4⋊(C47⋊C8)C22semidirect
21. #13093947C22semidirect
22. #13093947C22semidirect
26. #13093935C22semidirect
27. C4×C47⋊C8C22semidirect
112. C47#3123semidirect