Finite Group Databasebeta

← #20241720

Subgroups — #20241720

Order 6016.

252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13093981C211yesmaximal, characteristic
2#15689180C211yesmaximal, characteristic, complemented
3#15688848C212yesmaximal, complemented
4#15688846C212yesmaximal
5C47×#432C211yesmaximal, characteristic, complemented
6C22×C4×D47C411yescharacteristic
7#13093981—21no—
8#13093981—21no—
9#13093981—21no—
10#13093981—21no—
11C2×Dic47⋊C4C411yescharacteristic
12C2×Dic47⋊C4C2211yescharacteristic
13C2×(C2×D47)⋊C4C411yescharacteristic
14C2×(C2×D47)⋊C4C2211yescharacteristic
15C2×C4×Dic47C411yescharacteristic
16C4⋊(C47⋊C8)—21no—
17C22⋊(C47⋊C8)C2212yes—
18#13093935—21no—
19C2×C42×C47C2211yescharacteristic
20C4⋊C8×C47—21no—
21C22⋊C8×C47C2212yes—
22#97×C47—21no—
23C23×D47C2×C411yescharacteristic
24C22×C4×C47C2×C411yescharacteristic
25C22×C4×C47C2×C411yescharacteristic
26C22×C4×C47C2311yescharacteristic
27C22×Dic47C2×C411yescharacteristic
28C22×Dic47C2×C411yescharacteristic
29C22×Dic47C2×C411yescharacteristic
30C2×C4×D47—22no—
31C2×C4×D47—21no—
32C2×C4×D47—21no—
33C2×C4×D47—22no—
34C2×C8×C47—22no—
35C42×C47D411yescharacteristic
36C42×C47D411yescharacteristic
37C42×C47D411yescharacteristic
38C42×C47D411yescharacteristic
39(C2×D47)⋊C4—21no—
40(C2×D47)⋊C4—21no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C2×C47⋊C8—22no—
50C23×C47C22×C411yescharacteristic
51C22×D47—21no—
52C22×D47—21no—
53C22×D47—41no—
54C22×D47—41no—
55C22×D47M1612yes—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47C22⋊C411yescharacteristic
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47C22⋊C411yescharacteristic
63C2×C4×C47C22⋊C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47M1612yes—
73C4×D47—24no—
74C4×D47—24no—
75C8×C47—42no—
76C47⋊C8—42no—
77C22×C47—21no—
78C22×C47—21no—
79C22×C47C2×C22⋊C411yescharacteristic
80C22×C47C2×M1611yescharacteristic
81C22×C47C2×M1611yescharacteristic
82C2×D47—22no—
83C2×D47—42no—
84C2×D47—41no—
85C2×D47—41no—
86C2×D47—42no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—21no—
90C4×C47—21no—
91C4×C47—21no—
92C4×C47—21no—
93Dic47—22no—
94Dic47—41no—
95Dic47—41no—
96#1464—471nomaximal, Sylow
97C2×C47—21no—
98C2×C47—21no—
99C2×C47#40711yescharacteristic
100C2×C47#41011yescharacteristic
101C2×C47#41311yescharacteristic
102D47—42no—
103C2×#117—471no—
104#432—471no—
105#432D4711yescharacteristic, complemented
106#324—472no—
107#323—472no—
108C47#146411yescharacteristic, complemented, Sylow
109C23×C4—471no—
110#117—941no—
111#117—941no—
112#117—941no—
113#117—941no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4—471no—
116C2×C22⋊C4—471no—
117C2×C22⋊C4—471no—
118C2×C42—471no—
119C2×C42C2×D4711yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—941no—
122C22⋊C8—472no—
123C22⋊C8C2×D4712yes—
124#97—21no—
125#97—941no—
126C24—471no—
127C22×C4—471no—
128C22×C4—471no—
129C22×C4—471no—
130C22×C4—942no—
131C22×C4—942no—
132C22×C4—941no—
133C22×C4—941no—
134C22×C4C4×D4711yescharacteristic
135C22×C4C4×D4711yescharacteristic
136C22×C4C22×D4711yescharacteristic
137C2×C8—22no—
138C2×C8—942no—
139C4⋊C4—941no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C22⋊C4—941no—
144C22⋊C4—941no—
145C22⋊C4—941no—
146C22⋊C4—941no—
147C42—941no—
148C42—941no—
149C42D18811yescharacteristic
150C42D18811yescharacteristic
151C42C22⋊D4711yescharacteristic
152C42C22⋊D4711yescharacteristic
153C23—472no—
154C23—941no—
155C23—941no—
156C23—1881no—
157C23—1881no—
158C23C2×C4×D4711yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—472no—
164C2×C4—944no—
165C2×C4—944no—
166C2×C4—941no—
167C2×C4—941no—
168C2×C4—941no—
169C2×C4—941no—
170C2×C4—1881no—
171C2×C4—1881no—
172C2×C4(C2×D47)⋊C411yescharacteristic
173C2×C4(C2×D47)⋊C411yescharacteristic
174C2×C4(C2×D47)⋊C411yescharacteristic
175C2×C4(C2×D47)⋊C411yescharacteristic
176C2×C4C2×D18811yescharacteristic
177C2×C4C2×C22⋊D4711yescharacteristic
178C8—42no—
179C8—1882no—
180C22—21no—
181C22—21no—
182C22—942no—
183C22—1882no—
184C22—1882no—
185C22—1881no—
186C22—1881no—
187C22C2×(C2×D47)⋊C411yescharacteristic
188C22M16×D4711yescharacteristic
189C22M16×D4711yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—942no—
197C4—1881no—
198C4—1881no—
199C2—21no—
200C2—21no—
201C2—1882no—
202C2#1568908611yescharacteristic
203C2#1568909611yescharacteristic
204C2#1568910511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#432C2
socleC22×C47C2×C22⋊C4
hypercenter#432D47
hypocenterC47#1464
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #15689180C2semidirect
3. #15688848C2semidirect
5. C47×#432C2semidirect
105. #432D47semidirect
108. C47#1464semidirect