Finite Group Databasebeta

← #20241717

Subgroups — #20241717

Order 6016.

312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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#15689087C211yesmaximal, characteristic
3#15688848C214yesmaximal, complemented
4C47×#407C211yesmaximal, characteristic
5C23×Dic47C411yescharacteristic
6C23×Dic47C411yescharacteristic
7C2×#10625329—21no—
8C2×Dic47⋊C4—21no—
9C2×Dic47⋊C4—21no—
10C2×Dic47⋊C4—21no—
11C2×Dic47⋊C4—21no—
12C2×Dic47⋊C4C412yes—
13C2×Dic47⋊C4C2212yes—
14C22⋊(C47⋊C8)—21no—
15C22⋊(C47⋊C8)C2212yes—
16C23×C4×C47C2211yescharacteristic
17C2×M16×C47—21no—
18C22⋊C8×C47—21no—
19C22⋊C8×C47C2212yes—
20C24×C47C2×C411yescharacteristic
21C22×C4×C47—42no—
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—21no—
29C22×Dic47—21no—
30C22×Dic47—24no—
31C22×Dic47—21no—
32C22×Dic47—21no—
33C22×Dic47—42no—
34C22×Dic47C2×C412yes—
35C22×Dic47C2×C412yes—
36M16×C47—42no—
37C2×C8×C47—22no—
38Dic47⋊C4—22no—
39Dic47⋊C4—22no—
40Dic47⋊C4—22no—
41Dic47⋊C4—22no—
42#10625329—42no—
43C2×C47⋊C8—22no—
44C23×C47—22no—
45C23×C47—22no—
46C23×C47—22no—
47C23×C47C22⋊C411yescharacteristic
48C23×C47C22⋊C411yescharacteristic
49C23×C47C22×C411yescharacteristic
50C2×C4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×Dic47—24no—
61C2×Dic47—24no—
62C2×Dic47—22no—
63C2×Dic47—22no—
64C2×Dic47—22no—
65C2×Dic47—42no—
66C2×Dic47—42no—
67C2×Dic47—42no—
68C2×Dic47M1614yescomplemented
69C8×C47—42no—
70C47⋊C8—42no—
71C22×C47—28no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47#9912yes—
79C22×C47#10112yes—
80C22×C47C2×C22⋊C411yescharacteristic
81C22×C47C2×M1612yes—
82C4×C47—21no—
83C4×C47—21no—
84C4×C47—21no—
85C4×C47—21no—
86Dic47—24no—
87Dic47—42no—
88#1463—471nomaximal, Sylow
89C2×C47—22no—
90C2×C47—22no—
91C2×C47—22no—
92C2×C47#40711yescharacteristic
93C2×C47C2×#9911yescharacteristic
94C2×C47C2×#10111yescharacteristic
95C22×C4⋊C4—471no—
96#407—471no—
97#407D4711yescharacteristic
98#324—474no—
99C47#146311yescharacteristic, complemented, Sylow
100C23×C4—471no—
101C23×C4—471no—
102C23×C4C2×D4711yescharacteristic
103C2×M16—21no—
104C2×M16—941no—
105C2×C4⋊C4—472no—
106C2×C4⋊C4—472no—
107C2×C4⋊C4—941no—
108C2×C4⋊C4—941no—
109C2×C4⋊C4—941no—
110C2×C4⋊C4—941no—
111C22⋊C8—21no—
112C22⋊C8—472no—
113C22⋊C8—941no—
114C22⋊C8C2×D4712yes—
115C24C4×D4711yescharacteristic
116C22×C4—42no—
117C22×C4—472no—
118C22×C4—472no—
119C22×C4—944no—
120C22×C4—941no—
121C22×C4—941no—
122C22×C4—941no—
123C22×C4—941no—
124C22×C4—1882no—
125C22×C4C4×D4711yescharacteristic
126C22×C4D18811yescharacteristic
127C22×C4D18811yescharacteristic
128C22×C4C22⋊D4711yescharacteristic
129C22×C4C22⋊D4711yescharacteristic
130C22×C4C22×D4711yescharacteristic
131M16—42no—
132M16—1882no—
133C2×C8—22no—
134C2×C8—942no—
135C4⋊C4—942no—
136C4⋊C4—942no—
137C4⋊C4—942no—
138C4⋊C4—942no—
139C23—22no—
140C23—22no—
141C23—22no—
142C23(C2×D47)⋊C411yescharacteristic
143C23(C2×D47)⋊C411yescharacteristic
144C23C2×C4×D4711yescharacteristic
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—474no—
152C2×C4—944no—
153C2×C4—944no—
154C2×C4—942no—
155C2×C4—942no—
156C2×C4—942no—
157C2×C4—1882no—
158C2×C4—1882no—
159C2×C4—1882no—
160C2×C4(C2×D47)⋊C411yescharacteristic
161C2×C4(C2×D47)⋊C411yescharacteristic
162C2×C4C2×D18811yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—42no—
165C8—1882no—
166C22—28no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22#1309393812yes—
174C22#1309394212yes—
175C22C2×(C2×D47)⋊C411yescharacteristic
176C22M16×D4712yes—
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—944no—
182C4—1882no—
183C2—22no—
184C2—22no—
185C2—22no—
186C2#1568908611yescharacteristic
187C2C2×#1309393811yescharacteristic
188C2C2×#1309394211yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC22×C47C2×C22⋊C4
hypercenter#407D47
hypocenterC47#1463
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #15688848C2semidirect
68. C2×Dic47M16semidirect
99. C47#1463semidirect