Finite Group Databasebeta

← #20241716

Subgroups — #20241716

Order 6016.

312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4⋊C4×D47C211yesmaximal, characteristic
2#15689085C212yesmaximal
3#15688849C211yesmaximal, characteristic, complemented
4#15688848C212yesmaximal, complemented
5C47×#324C211yesmaximal, characteristic, complemented
6C22×C4×D47C411yescharacteristic
7C22×C4×D47C411yescharacteristic
8C22×C4×D47C2211yescharacteristic
9C2×#10625324—22no—
10C2×C4⋊Dic47C411yescharacteristic
11C2×Dic47⋊C4C411yescharacteristic
12C2×Dic47⋊C4C2211yescharacteristic
13C4⋊C4×D47—22no—
14C4⋊C4×D47—22no—
15C22⋊(C47⋊C8)C2212yes—
16(C2×D47)⋊C8—22no—
17C2×C4⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C23×D47C2×C411yescharacteristic
20C22×C4×C47C2×C411yescharacteristic
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47C2311yescharacteristic
23C22×Dic47C2×C411yescharacteristic
24C22×Dic47C2×C411yescharacteristic
25C22×Dic47C2×C411yescharacteristic
26C2×C4×D47—21no—
27C2×C4×D47—21no—
28C2×C4×D47—22no—
29C2×C4×D47—22no—
30C2×C4×D47—21no—
31C2×C4×D47—21no—
32C2×C4×D47—42no—
33C2×C4×D47—42no—
34C2×C4×D47D412yes—
35C2×C4×D47D412yes—
36C2×C8×C47—22no—
37C4⋊C4×C47—22no—
38C4⋊Dic47—22no—
39Dic47⋊C4—22no—
40Dic47⋊C4—22no—
41C2×C47⋊C8—22no—
42#10625324—44no—
43C23×C47C22×C411yescharacteristic
44C22×D47—21no—
45C22×D47—21no—
46C22×D47—22no—
47C22×D47—22no—
48C22×D47C22⋊C411yescharacteristic
49C22×D47C22⋊C411yescharacteristic
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47M1612yescomplemented
56C2×C4×C47C2×D412yes—
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—21no—
60C2×Dic47—41no—
61C2×Dic47—41no—
62C2×Dic47C22⋊C412yes—
63C2×Dic47M1612yescomplemented
64C4×D47—24no—
65C4×D47—24no—
66C4×D47—24no—
67C4×D47—42no—
68C4×D47—42no—
69C4×D47—42no—
70C8×C47—42no—
71C47⋊C8—42no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47C2×C22⋊C411yescharacteristic
75C22×C47C2×M1611yescharacteristic
76C22×C47C2×M1611yescharacteristic
77C2×D47—24no—
78C2×D47—24no—
79C2×D47—21no—
80C2×D47—21no—
81C2×D47—21no—
82C2×D47—21no—
83C2×D47#9912yes—
84C2×D47#10112yes—
85C4×C47—22no—
86C4×C47—22no—
87C4×C47—41no—
88Dic47—22no—
89Dic47—22no—
90Dic47—41no—
91#1463—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—21no—
94C2×C47#40711yescharacteristic
95C2×C47C2×#9911yescharacteristic
96C2×C47C2×#10111yescharacteristic
97D47—22no—
98D47—22no—
99C22×C4⋊C4—471no—
100#407—472no—
101#324—471no—
102#324—472no—
103#324D4711yescharacteristic, complemented
104C47#146311yescharacteristic, complemented, Sylow
105C23×C4—471no—
106C23×C4—471no—
107C23×C4—471no—
108C2×M16—942no—
109C2×C4⋊C4—471no—
110C2×C4⋊C4—471no—
111C2×C4⋊C4—471no—
112C2×C4⋊C4—942no—
113C2×C4⋊C4—942no—
114C2×C4⋊C4C2×D4711yescharacteristic
115C22⋊C8—472no—
116C22⋊C8—942no—
117C22⋊C8C2×D4712yes—
118C24—471no—
119C22×C4—471no—
120C22×C4—471no—
121C22×C4—472no—
122C22×C4—472no—
123C22×C4—471no—
124C22×C4—942no—
125C22×C4—941no—
126C22×C4—941no—
127C22×C4—941no—
128C22×C4—941no—
129C22×C4—942no—
130C22×C4—1882no—
131C22×C4—1882no—
132C22×C4C4×D4711yescharacteristic
133C22×C4C4×D4711yescharacteristic
134C22×C4C22×D4711yescharacteristic
135M16—1884no—
136C2×C8—22no—
137C2×C8—942no—
138C4⋊C4—22no—
139C4⋊C4—942no—
140C4⋊C4—942no—
141C4⋊C4—942no—
142C23—471no—
143C23—471no—
144C23—942no—
145C23—942no—
146C23—941no—
147C23—941no—
148C23C2×C4×D4711yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—472no—
155C2×C4—472no—
156C2×C4—944no—
157C2×C4—944no—
158C2×C4—944no—
159C2×C4—941no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—1882no—
163C2×C4—1882no—
164C2×C4—1882no—
165C2×C4—1881no—
166C2×C4—1881no—
167C2×C4#1062532412yescomplemented
168C2×C4D4×D4712yes—
169C8—42no—
170C8—1882no—
171C22—21no—
172C22—21no—
173C22—472no—
174C22—472no—
175C22—944no—
176C22—944no—
177C22—941no—
178C22—941no—
179C22—941no—
180C22—941no—
181C22C22⋊C4×D4711yescharacteristic
182C22M16×D4711yescharacteristic
183C22C2×#1062532411yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—942no—
188C4—942no—
189C4—1881no—
190C2—21no—
191C2—21no—
192C2—942no—
193C2—942no—
194C2#1568908511yescharacteristic
195C2#99×D4711yescharacteristic
196C2#101×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47C2×C22⋊C4
hypercenter#324D47
hypocenterC47#1463
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. #15688849C2semidirect
4. #15688848C2semidirect
5. C47×#324C2semidirect
55. C2×C4×C47M16semidirect
63. C2×Dic47M16semidirect
103. #324D47semidirect
104. C47#1463semidirect
167. C2×C4#10625324semidirect