Finite Group Databasebeta

← #100×Dic47 #20243182

Subgroups — #100×Dic47 #20243182

Order 6016.

360 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×D4×Dic47C211yesmaximal, characteristic
2C2×#13093941C211yesmaximal, characteristic
3M16×Dic47C212yesmaximal, complemented
4#15688891C212yesmaximal, complemented
5C2×#100×C47C211yesmaximal, characteristic
6C23×Dic47C412yes—
7C2×#10625329C2212yes—
8D4×Dic47—22no—
9D4×Dic47—22no—
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C22⋊Dic47C412yes—
12C2×C4×Dic47C2211yescharacteristic
13#13093941C414yescomplemented
14#13093934—22no—
15C8×Dic47—22no—
16C22×D4×C47C2211yescharacteristic
17C2×M16×C47C2212yes—
18#100×C47C414yescomplemented
19C24×C47C2×C412yes—
20C2×D4×C47—22no—
21C2×D4×C47—22no—
22C2×D4×C47C2×C412yes—
23C2×D4×C47C2×C412yes—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—22no—
26C22×Dic47—22no—
27C22×Dic47—44no—
28C22×Dic47C2×C411yescharacteristic
29C22×Dic47C2×C412yes—
30C22×Dic47C2×C411yescharacteristic
31M16×C47—22no—
32M16×C47C2×C414yescomplemented
33C2×C8×C47—22no—
34C22⋊Dic47—24no—
35C4⋊Dic47—22no—
36C4×Dic47D412yes—
37C4×Dic47D412yes—
38#10625329—22no—
39#10625329C2×C414yescomplemented
40C2×C47⋊C8—22no—
41C23×C47—22no—
42C23×C47—22no—
43C23×C47—42no—
44C23×C47—42no—
45C23×C47C4214yes—
46C23×C47C22×C411yescharacteristic
47D4×C47—24no—
48D4×C47—24no—
49C2×C4×C47C22×C411yescharacteristic
50C2×C4×C47C22×C411yescharacteristic
51C2×C4×C47C2×D412yes—
52C2×C4×C47#4112yes—
53C2×Dic47—22no—
54C2×Dic47—22no—
55C2×Dic47—41no—
56C2×Dic47—44no—
57C2×Dic47—44no—
58C2×Dic47—42no—
59C2×Dic47C22⋊C412yes—
60C2×Dic47C22⋊C411yescharacteristic
61C2×Dic47C22⋊C411yescharacteristic
62C8×C47—24no—
63C47⋊C8—24no—
64C22×C47—21no—
65C22×C47—21no—
66C22×C47—24no—
67C22×C47—44no—
68C22×C47—44no—
69C22×C47—42no—
70C22×C47—42no—
71C22×C47C2×C4211yescharacteristic
72C22×C47C2×C22⋊C411yescharacteristic
73C22×C47#11711yescharacteristic
74C4×C47C4×D412yes—
75C4×C47C4×D412yes—
76Dic47—21no—
77Dic47—22no—
78Dic47—42no—
79Dic47#10012yesdirect product factor
80C4×#100—471nomaximal, Sylow
81C2×C47—21no—
82C2×C47—21no—
83C2×C47—44no—
84C2×C47C4×C22⋊C411yescharacteristic
85C2×C47C2×#10011yescharacteristic
86C2×C47#41311yescharacteristic
87C2×C4×D4—471no—
88C2×#100—471no—
89C2×#100D4711yescharacteristic
90C4×M16—472no—
91#343—472no—
92C47C4×#10011yescharacteristic, complemented, Sylow
93C22×D4C2×D4711yescharacteristic
94C23×C4—472no—
95C2×M16—472no—
96C2×M16C2×D4712yes—
97C4×D4—942no—
98C4×D4—942no—
99C2×C4⋊C4—471no—
100C2×C22⋊C4—472no—
101C2×C42—471no—
102#100—474no—
103#100Dic4714yesdirect product factor
104#97—942no—
105C4×C8—942no—
106C24C4×D4712yes—
107C2×D4—22no—
108C2×D4—22no—
109C2×D4C4×D4712yes—
110C2×D4C2×Dic4712yes—
111C22×C4—471no—
112C22×C4—471no—
113C22×C4—472no—
114C22×C4—942no—
115C22×C4—942no—
116C22×C4—1884no—
117C22×C4C22×D4711yescharacteristic
118M16—22no—
119M16—474no—
120M16—942no—
121M16C2×Dic4714yescomplemented
122C2×C8—22no—
123C2×C8—942no—
124C4⋊C4—942no—
125C22⋊C4—944no—
126C42—472no—
127C42—472no—
128C23—22no—
129C23—22no—
130C23—42no—
131C23—42no—
132C23C4×Dic4714yes—
133C23C2×C4×D4711yescharacteristic
134D4—24no—
135D4—24no—
136C2×C4—471no—
137C2×C4—472no—
138C2×C4—471no—
139C2×C4—942no—
140C2×C4—942no—
141C2×C4—1884no—
142C2×C4—1881no—
143C2×C4—1884no—
144C2×C4—1882no—
145C2×C4C2×C4×D4711yescharacteristic
146C2×C4D4×D4712yes—
147C2×C4#1062535212yes—
148C2×C4C22×Dic4711yescharacteristic
149C8—24no—
150C8—944no—
151C22—21no—
152C22—21no—
153C22—24no—
154C22—44no—
155C22—44no—
156C22—42no—
157C22—42no—
158C22C2×C4×Dic4711yescharacteristic
159C22C22⋊C4×D4711yescharacteristic
160C22#1309398011yescharacteristic
161C4—472no—
162C4—941no—
163C4—942no—
164C4—1882no—
165C4(C22⋊D47)⋊C412yes—
166C4D4×Dic4712yes—
167C2—21no—
168C2—21no—
169C2—44no—
170C2C22⋊C4×Dic4711yescharacteristic
171C2#100×D4711yescharacteristic
172C2#1568910411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC22×C47C2×C42
FrattiniC22×C4C22×D47
FittingC2×#100×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#100D47
hypocenterC47C4×#100
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
3. M16×Dic47C2semidirect
4. #15688891C2semidirect
13. #13093941C4semidirect
18. #100×C47C4semidirect
32. M16×C47C2×C4semidirect
39. #10625329C2×C4semidirect
79. Dic47#100direct (N × H)
92. C47C4×#100semidirect
103. #100Dic47direct (N × H)
121. M16C2×Dic47semidirect