Finite Group Databasebeta

← #20241707

Subgroups — #20241707

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
1C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2#15689173C212yesmaximal, complemented
3#15688847C211yesmaximal, characteristic, complemented
4#15688846C212yesmaximal, complemented
5C47×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C411yescharacteristic
7C23×Dic47C411yescharacteristic
8C22×C4×D47C411yescharacteristic
9(C22⋊D47)⋊C4—22no—
10(C22⋊D47)⋊C4—22no—
11C2×Dic47⋊C4C411yescharacteristic
12C2×(C2×D47)⋊C4C2211yescharacteristic
13C2×C4×Dic47C2211yescharacteristic
14Dic47⋊C8—22no—
15C22⋊(C47⋊C8)C2212yes—
16C8×Dic47—22no—
17C2×C22⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C24×C47C2×C411yescharacteristic
20C23×D47C2×C411yescharacteristic
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47C2311yescharacteristic
23C2×C22⋊D47—22no—
24C2×C22⋊D47—22no—
25C2×C22⋊D47C814yescomplemented
26C22×Dic47—21no—
27C22×Dic47—21no—
28C22×Dic47—42no—
29C22×Dic47C2×C411yescharacteristic
30C22×Dic47C2×C411yescharacteristic
31C22×Dic47C2×C411yescharacteristic
32C2×C4×D47—21no—
33C2×C4×D47—21no—
34C2×C4×D47—42no—
35C2×C8×C47—22no—
36C22⋊C4×C47—22no—
37(C2×D47)⋊C4—22no—
38Dic47⋊C4—22no—
39C4×Dic47D412yes—
40C4×Dic47D412yes—
41C2×C47⋊C8—22no—
42C23×C47—21no—
43C23×C47—21no—
44C23×C47—41no—
45C23×C47—41no—
46C23×C47C2×C812yes—
47C23×C47C22×C411yescharacteristic
48C22×D47—21no—
49C22×D47—21no—
50C22×D47—41no—
51C22×D47—41no—
52C22×D47C2×C812yes—
53C2×C4×C47—21no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47C2×D412yes—
57C22⋊D47—28no—
58C2×Dic47—22no—
59C2×Dic47—21no—
60C2×Dic47—42no—
61C2×Dic47—42no—
62C2×Dic47—41no—
63C2×Dic47C22⋊C411yescharacteristic
64C2×Dic47C22⋊C412yes—
65C2×Dic47C22⋊C411yescharacteristic
66C2×Dic47C2×C812yes—
67C2×Dic47M1612yes—
68C4×D47—42no—
69C4×D47—42no—
70C8×C47—42no—
71C47⋊C8—42no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—22no—
75C22×C47—42no—
76C22×C47—42no—
77C22×C47—41no—
78C22×C47—41no—
79C22×C47C2×C22⋊C411yescharacteristic
80C22×C47C22×C811yescharacteristic
81C22×C47C2×M1611yescharacteristic
82C2×D47—22no—
83C2×D47—42no—
84C2×D47—41no—
85C2×D47—41no—
86C2×D47—42no—
87C4×C47—22no—
88C4×C47—41no—
89Dic47—21no—
90Dic47—41no—
91Dic47C22⋊C814yes—
92Dic47#10012yes—
93#1460—471nomaximal, Sylow
94C2×C47—21no—
95C2×C47—21no—
96C2×C47—42no—
97C2×C47C2×C22⋊C811yescharacteristic
98C2×C47#41011yescharacteristic
99C2×C47C2×#10011yescharacteristic
100D47—42no—
101C2×C4×D4—471no—
102#431—472no—
103#323—471no—
104#323—472no—
105#323D4711yescharacteristic, complemented
106C47#146011yescharacteristic, complemented, Sylow
107C22×D4—471no—
108C23×C4—471no—
109C23×C4—471no—
110C4×D4—942no—
111C4×D4—942no—
112C2×C4⋊C4—471no—
113C2×C22⋊C4—471no—
114C2×C22⋊C4C2×D4711yescharacteristic
115C2×C42—471no—
116C4⋊C8—942no—
117C22⋊C8—472no—
118C22⋊C8C2×D4712yes—
119C4×C8—942no—
120C24—471no—
121C24C4×D4711yescharacteristic
122C2×D4—474no—
123C2×D4—942no—
124C2×D4—942no—
125C22×C4—471no—
126C22×C4—471no—
127C22×C4—471no—
128C22×C4—941no—
129C22×C4—941no—
130C22×C4—941no—
131C22×C4—941no—
132C22×C4—1882no—
133C22×C4—1882no—
134C22×C4C4×D4711yescharacteristic
135C22×C4C22×D4711yescharacteristic
136C2×C8—22no—
137C2×C8—942no—
138C4⋊C4—942no—
139C22⋊C4—22no—
140C22⋊C4—942no—
141C42—472no—
142C42—472no—
143C23—21no—
144C23—21no—
145C23—41no—
146C23—41no—
147C23—472no—
148C23—941no—
149C23—941no—
150C23—1881no—
151C23—1881no—
152C23C8×D4712yes—
153C23C2×C4×D4711yescharacteristic
154D4—948no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—472no—
159C2×C4—471no—
160C2×C4—472no—
161C2×C4—472no—
162C2×C4—471no—
163C2×C4—942no—
164C2×C4—941no—
165C2×C4—1882no—
166C2×C4—1882no—
167C2×C4—1882no—
168C2×C4—1882no—
169C2×C4—1881no—
170C2×C4D4×D4712yes—
171C8—42no—
172C8—1882no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—42no—
178C22—41no—
179C22—41no—
180C22—942no—
181C22—1882no—
182C22—1882no—
183C22—1881no—
184C22—1881no—
185C22C22⋊C4×D4711yescharacteristic
186C22C2×C8×D4711yescharacteristic
187C22M16×D4711yescharacteristic
188C4—22no—
189C4—41no—
190C4—474no—
191C4—472no—
192C4—941no—
193C4—1881no—
194C2—21no—
195C2—21no—
196C2—42no—
197C2—1882no—
198C2C22⋊C8×D4711yescharacteristic
199C2#1568909511yescharacteristic
200C2#100×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC22×C47C22×C8
FrattiniC22×C4C22×D47
FittingC47×#323C2
socleC22×C47C2×C22⋊C4
hypercenter#323D47
hypocenterC47#1460
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #15689173C2semidirect
3. #15688847C2semidirect
4. #15688846C2semidirect
5. C47×#323C2semidirect
25. C2×C22⋊D47C8semidirect
105. #323D47semidirect
106. C47#1460semidirect