Finite Group Databasebeta

← #20243461

Subgroups — #20243461

Order 6016.

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

normal subgroups only

This group has 504 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
1C2×C22⋊C4×D47C211yesmaximal, characteristic
2#15688978C212yesmaximal
3#15688890C211yesmaximal, characteristic, complemented
4#15688889C212yesmaximal, complemented
5C47×#342C211yesmaximal, characteristic, complemented
6C24×D47C2211yescharacteristic
7C22×C4×D47C412yescomplemented
8C2×C22⋊Dic47C2212yes—
9C2×C22⋊Dic47C2211yescharacteristic
10C2×(C2×D47)⋊C4—24no—
11C2×(C2×D47)⋊C4C412yescomplemented
12C22⋊C4×D47—24no—
13C2×C22⋊C4×C47C2212yes—
14C2×C22⋊C4×C47C2211yescharacteristic
15C24×C47C2311yescharacteristic
16C23×D47—22no—
17C23×D47—21no—
18C23×D47—21no—
19C23×D47—44no—
20C23×D47C2×C411yescharacteristic
21C23×D47C2×C411yescharacteristic
22C23×D47D414yes—
23C22×C4×C47—22no—
24C22×C4×C47C2×C412yes—
25C22×Dic47—22no—
26C22×Dic47C2×C412yes—
27C2×C4×D47—22no—
28C2×C4×D47—22no—
29C2×C4×D47—44no—
30C22⋊C4×C47—22no—
31C22⋊C4×C47—22no—
32C22⋊C4×C47—22no—
33C22⋊Dic47—22no—
34C22⋊Dic47—22no—
35C22⋊Dic47—22no—
36(C2×D47)⋊C4—24no—
37(C2×D47)⋊C4—48no—
38C23×C47—42no—
39C23×C47C22×C411yescharacteristic
40C23×C47C2×D412yes—
41C23×C47#4112yes—
42C23×C47#4111yescharacteristic
43C23×C47#4111yescharacteristic
44C22×D47—21no—
45C22×D47—21no—
46C22×D47—24no—
47C22×D47—21no—
48C22×D47—21no—
49C22×D47—24no—
50C22×D47—24no—
51C22×D47—28no—
52C22×D47—42no—
53C22×D47—44no—
54C22×D47—48no—
55C22×D47—44no—
56C22×D47—44no—
57C22×D47C22⋊C412yes—
58C22×D47C22⋊C412yes—
59C2×C4×C47—22no—
60C2×C4×C47—42no—
61C2×C4×C47—44no—
62C2×C4×C47—42no—
63C2×Dic47—22no—
64C2×Dic47—42no—
65C2×Dic47—44no—
66C2×Dic47—42no—
67C4×D47—44no—
68C4×D47—44no—
69C22×C47—22no—
70C22×C47—24no—
71C22×C47—42no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47C2×C22⋊C411yescharacteristic
75C22×C47#11711yescharacteristic
76C22×C47#11711yescharacteristic
77C22×C47#12312yes—
78C22×C47#12312yes—
79C2×D47—24no—
80C2×D47—24no—
81C2×D47—22no—
82C2×D47—22no—
83C2×D47—22no—
84C2×D47—24no—
85C2×D47—48no—
86C2×D47—48no—
87C2×D47—42no—
88C2×D47—42no—
89C2×D47#9914yes—
90C4×C47—42no—
91C4×C47—82no—
92Dic47—42no—
93Dic47—82no—
94#1819—471nomaximal, Sylow
95C2×C47—22no—
96C2×C47—22no—
97C2×C47—21no—
98C2×C47—21no—
99C2×C47#38111yescharacteristic
100C2×C47C2×#9912yes—
101D47—24no—
102D47—42no—
103C22×C22⋊C4—471no—
104#379—472no—
105#342—472no—
106#342—471no—
107#342D4711yescharacteristic, complemented
108C47#181911yescharacteristic, complemented, Sylow
109C25—471no—
110C23×C4—472no—
111C2×C22⋊C4—471no—
112C2×C22⋊C4—472no—
113C2×C22⋊C4—472no—
114C2×C22⋊C4—944no—
115C2×C22⋊C4—944no—
116C2×C22⋊C4C2×D4712yes—
117C2×C22⋊C4C2×D4711yescharacteristic
118C24—471no—
119C24—474no—
120C24—471no—
121C24—942no—
122C24—941no—
123C24—941no—
124C24—1884no—
125C24C22×D4711yescharacteristic
126C22×C4—22no—
127C22×C4—472no—
128C22×C4—942no—
129C22×C4—942no—
130C22×C4—942no—
131C22×C4—1884no—
132C22×C4C4×D4712yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—944no—
137C22⋊C4—942no—
138C22⋊C4—942no—
139C22⋊C4—942no—
140C22⋊C4—1888no—
141C23—42no—
142C23—472no—
143C23—472no—
144C23—944no—
145C23—948no—
146C23—941no—
147C23—941no—
148C23—941no—
149C23—941no—
150C23—944no—
151C23—944no—
152C23—1882no—
153C23—1884no—
154C23—1888no—
155C23—1884no—
156C23—1884no—
157C23C2×C4×D4711yescharacteristic
158C23#1062535012yes—
159C23D4×D4712yes—
160C23#1062535211yescharacteristic
161C23#1062535411yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—942no—
167C2×C4—1884no—
168C2×C4—1884no—
169C2×C4—1884no—
170C2×C4—1882no—
171C2×C4—1882no—
172C22—22no—
173C22—24no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—474no—
178C22—944no—
179C22—944no—
180C22—942no—
181C22—942no—
182C22—942no—
183C22—944no—
184C22—1888no—
185C22—1888no—
186C22—1882no—
187C22—1882no—
188C22C22⋊C4×D4711yescharacteristic
189C22#1309398111yescharacteristic
190C22#1309398211yescharacteristic
191C22#1309400612yes—
192C22#1309400912yes—
193C4—42no—
194C4—82no—
195C4—3762no—
196C4—1882no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—944no—
202C2—1882no—
203C2#1568898511yescharacteristic
204C2#99×D4712yes—
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC47×#342C2
socleC22×C47C2×C22⋊C4
hypercenter#342D47
hypocenterC47#1819
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #15688890C2semidirect
4. #15688889C2semidirect
5. C47×#342C2semidirect
7. C22×C4×D47C4semidirect
11. C2×(C2×D47)⋊C4C4semidirect
107. #342D47semidirect
108. C47#1819semidirect