Finite Group Databasebeta

← #20253319

Subgroups — #20253319

Order 6016.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689634C211yesmaximal, characteristic
2#15689464C214yesmaximal, complemented
3#15689447C214yesmaximal, complemented
4#15689163C212yesmaximal, complemented
5#15689122C212yesmaximal, complemented
6#15689087C211yesmaximal, characteristic, complemented
7C2×#117×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625329C2212yes—
10#13094007—21no—
11#13094003C2212yes—
12#13093998C2212yes—
13#13093993—21no—
14C4×C22⋊D47—22no—
15#13093983C2211yescharacteristic
16#13093957C2214yescomplemented
17#13093955C2214yescomplemented
18#13093947C2214yescomplemented
19#13093944C2214yescomplemented
20C22⋊(C47⋊C8)C2214yes—
21C23×C4×C47C2211yescharacteristic
22#117×C47—22no—
23#117×C47C2214yes—
24C2×C4⋊C4×C47C2212yes—
25C2×C22⋊C4×C47—21no—
26C2×C42×C47—21no—
27C24×C47D411yescharacteristic
28C22×C4×C47—24no—
29C22×C4×C47—22no—
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D412yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47—22no—
35C2×C22⋊D47—21no—
36#10625350—24no—
37C2×D188C2311yescharacteristic
38C2×C4×D47—21no—
39C2×Dic94C2311yescharacteristic
40C4⋊C4×C47—22no—
41C4⋊C4×C47C2314yes—
42C22⋊C4×C47—24no—
43C42×C47—24no—
44C22⋊Dic47—21no—
45C22⋊Dic47—22no—
46(C2×D47)⋊C4—22no—
47C4⋊Dic47C2312yes—
48Dic47⋊C4—22no—
49C4×Dic47—21no—
50#10625329—24no—
51C2×C47⋊C8C2314yes—
52C23×C47—22no—
53C23×C47—42no—
54C23×C47C2×D412yes—
55C23×C47C2×D411yescharacteristic
56C22×D47—21no—
57C2×C4×C47—22no—
58C2×C4×C47—24no—
59C2×C4×C47—24no—
60C2×C4×C47—24no—
61C2×C4×C47—44no—
62C2×C4×C47C2×D412yes—
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47#4114yes—
65C2×C4×C47C2411yescharacteristic
66C22⋊D47—44no—
67C22⋊D47—42no—
68C2×Dic47—22no—
69C2×Dic47—21no—
70D188—22no—
71C4×D47—42no—
72Dic94—22no—
73C47⋊C8—24no—
74C22×C47—22no—
75C22×C47—22no—
76C22×C47—22no—
77C22×C47—22no—
78C22×C47—44no—
79C22×C47#12312yes—
80C22×C47C22×D411yescharacteristic
81C2×D47—41no—
82C2×D47—42no—
83C4×C47—22no—
84C4×C47—44no—
85C4×C47#12312yes—
86C4×C47C2×#4112yes—
87Dic47—41no—
88Dic47—42no—
89#3093—471nomaximal, Sylow
90C2×C47—22no—
91C2×C47—42no—
92C2×C47C2×#12311yescharacteristic
93C2×C47#57512yes—
94D47—81no—
95#525—471no—
96C2×#117D4711yescharacteristic, complemented
97#485—474no—
98#482—474no—
99#428—472no—
100#417—472no—
101#407—471no—
102C47#309311yescharacteristic, complemented, Sylow
103C2×#41—471no—
104C23×C4C2×D4711yescharacteristic
105C2×M16—472no—
106#123—941no—
107C22⋊Q8—472no—
108#121—472no—
109#120—941no—
110C4×D4—942no—
111#117—22no—
112#117—471no—
113#117C2×D4714yes—
114C2×C4⋊C4C2×D4712yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—474no—
118#106—474no—
119#103—474no—
120#102—474no—
121C22⋊C8—474no—
122C24C22⋊D4711yescharacteristic
123#41—944no—
124C2×Q8—471no—
125C2×D4—471no—
126C2×D4—942no—
127C2×D4—941no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—941no—
131C22×C4C22⋊D4711yescharacteristic
132C22×C4C22⋊D4712yes—
133C22×C4C22×D4712yes—
134C22×C4C22×D4711yescharacteristic
135M16—944no—
136C2×C8—474no—
137C4⋊C4—22no—
138C4⋊C4—472no—
139C4⋊C4—942no—
140C4⋊C4C22×D4714yes—
141C22⋊C4—24no—
142C22⋊C4—941no—
143C22⋊C4—942no—
144C22⋊C4—942no—
145C42—24no—
146C42—941no—
147C23—22no—
148C23—42no—
149C23—941no—
150C23C2×C22⋊D4712yes—
151C23C2×C22⋊D4711yescharacteristic
152Q8—942no—
153D4—942no—
154D4—1884no—
155D4—1882no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—942no—
162C2×C4—941no—
163C2×C4—1882no—
164C2×C4#1062535014yes—
165C2×C4C2×C22⋊D4712yes—
166C2×C4C2×C22⋊D4711yescharacteristic
167C2×C4C23×D4711yescharacteristic
168C8—944no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—1881no—
175C22—1882no—
176C22#1309400712yes—
177C22C22×C22⋊D4711yescharacteristic
178C4—22no—
179C4—44no—
180C4—1881no—
181C4—1882no—
182C4#1309400712yes—
183C4C2×#1062535012yes—
184C2—22no—
185C2—42no—
186C2—3761no—
187C2C2×#1309400711yescharacteristic
188C2#1568992112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#117×C47C2
socleC22×C47C22×D4
hypercenterC2×#117D47
hypocenterC47#3093
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #15689464C2semidirect
3. #15689447C2semidirect
4. #15689163C2semidirect
5. #15689122C2semidirect
6. #15689087C2semidirect
7. C2×#117×C47C2semidirect
16. #13093957C22semidirect
17. #13093955C22semidirect
18. #13093947C22semidirect
19. #13093944C22semidirect
96. C2×#117D47semidirect
102. C47#3093semidirect