Finite Group Databasebeta

← #20247671

Subgroups — #20247671

Order 6016.

512 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 153 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×Dic47⋊C4C211yesmaximal, characteristic
2#15689061C212yesmaximal, complemented
3#15689054C212yesmaximal, complemented
4#15689007C214yesmaximal, complemented
5#15688995C212yesmaximal
6#15688986C211yesmaximal, characteristic
7#15688984C212yesmaximal
8C2×#117×C47C211yesmaximal, characteristic
9C23×Dic47C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11C2×Dic47⋊C4—24no—
12C2×Dic47⋊C4C2214yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×C22⋊Dic47C2212yes—
16C47⋊#95C2214yes—
17C47⋊#95C2214yes—
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2214yes—
21C23×C4×C47C2211yescharacteristic
22#117×C47—24no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C22⋊C4×C47C2212yes—
26C2×C42×C47C2212yes—
27C24×C47C2311yescharacteristic
28C22×C4×C47—24no—
29C22×C4×C47D414yes—
30C22×C4×C47C2312yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—22no—
35C22×Dic47—24no—
36C22×Dic47—22no—
37C22×Dic47—24no—
38C22×Dic47C2314yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C4⋊C4×C47—22no—
42C4⋊C4×C47—22no—
43C22⋊C4×C47—24no—
44C42×C47—24no—
45C22⋊Dic47—24no—
46Dic47⋊C4—24no—
47Dic47⋊C4—24no—
48Dic47⋊C4—28no—
49C23×C47—22no—
50C23×C47—22no—
51C23×C47C2×D412yes—
52C23×C47#4114yes—
53C23×C47C2411yescharacteristic
54C2×C4×C47—28no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—24no—
60C2×C4×C47—24no—
61C2×C4×C47C2×D412yes—
62C2×C4×C47C2×D412yes—
63C2×Dic47—28no—
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—22no—
67C2×Dic47—24no—
68C2×Dic47—24no—
69C2×Dic47—24no—
70C2×Dic47—24no—
71C2×Dic47—44no—
72C2×Dic47#4114yes—
73C22×C47—22no—
74C22×C47—22no—
75C22×C47—28no—
76C22×C47#12314yes—
77C22×C47C22×D411yescharacteristic
78C22×C47C2×#4112yes—
79C22×C47C2×#4112yes—
80C22×C472−1+412yes—
81C4×C47—22no—
82C4×C47—22no—
83C4×C47—42no—
84C4×C47—42no—
85Dic47—24no—
86Dic47—42no—
87Dic47—44no—
88#2484—471nomaximal, Sylow
89C2×C47—24no—
90C2×C47C2×#12311yescharacteristic
91C2×C47#52511yescharacteristic
92C2×C47#53611yescharacteristic
93C2×C47#55214yes—
94C2×#117D4711yescharacteristic
95C22×C4⋊C4—471no—
96#400—472no—
97#398—472no—
98#387—474no—
99#385—472no—
100#381—471no—
101#381—472no—
102C47#248411yescharacteristic, complemented, Sylow
103C23×C4—471no—
104C23×C4—471no—
105C23×C4C2×D4711yescharacteristic
106#117—24no—
107C2×C4⋊C4—472no—
108C2×C4⋊C4—472no—
109C2×C4⋊C4—474no—
110C2×C4⋊C4—944no—
111C2×C4⋊C4C2×D4711yescharacteristic
112C2×C4⋊C4C2×D4711yescharacteristic
113C2×C22⋊C4—472no—
114C2×C22⋊C4C2×D4712yes—
115C2×C42C2×D4712yes—
116#95—472no—
117#95—474no—
118#95—474no—
119#95—472no—
120#95—474no—
121C24C22×D4711yescharacteristic
122C22×C4—24no—
123C22×C4—472no—
124C22×C4—474no—
125C22×C4—472no—
126C22×C4—944no—
127C22×C4—942no—
128C22×C4—944no—
129C22×C4—942no—
130C22×C4C22⋊D4714yes—
131C22×C4C22×D4712yes—
132C22×C4C22×D4712yes—
133C22×C4C22×D4711yescharacteristic
134C22×C4C22×D4711yescharacteristic
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4—948no—
138C4⋊C4—944no—
139C4⋊C4—944no—
140C22⋊C4—24no—
141C22⋊C4—944no—
142C42—24no—
143C23—22no—
144C23—22no—
145C23#1062535014yes—
146C23C2×C22⋊D4712yes—
147C23C23×D4711yescharacteristic
148C2×C4—28no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—474no—
156C2×C4—948no—
157C2×C4—942no—
158C2×C4—942no—
159C2×C4—942no—
160C2×C4—944no—
161C2×C4—944no—
162C2×C4—944no—
163C2×C4—944no—
164C2×C4—1884no—
165C2×C4C2×C22⋊D4712yes—
166C2×C4C2×C22⋊D4712yes—
167C22—28no—
168C22—22no—
169C22—22no—
170C22#1309400714yes—
171C22C22×C22⋊D4711yescharacteristic
172C22#41×D4712yes—
173C22C2×#1062535012yes—
174C22#1309407112yes—
175C4—22no—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—944no—
180C4—1884no—
181C4—1882no—
182C2—24no—
183C2C2×#1309400711yescharacteristic
184C2#1568963011yescharacteristic
185C2#1568969411yescharacteristic
186C2#1568980614yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#117×C47C2
hypercenterC2×#117D47
hypocenterC47#2484
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
3. #15689054C2semidirect
4. #15689007C2semidirect
102. C47#2484semidirect