Finite Group Databasebeta

← #20241924

Subgroups — #20241924

Order 6016.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#15689657C211yesmaximal, characteristic
2#15689180C211yesmaximal, characteristic, complemented
3#15688859C212yesmaximal, complemented
4#15688856C212yesmaximal
5C47×#382C211yesmaximal, characteristic, complemented
6#13094018—21no—
7#13094016C411yescharacteristic, complemented
8#13094012C411yescharacteristic, complemented
9#13094007—21no—
10#13094003C2211yescharacteristic
11#13093998C2211yescharacteristic
12C4×Dic94C411yescharacteristic, complemented
13C4×D188C411yescharacteristic, complemented
14C4×C22⋊D47—21no—
15#13093981—21no—
16C4⋊(C47⋊C8)—21no—
17C22⋊(C47⋊C8)C2212yes—
18#13093935—21no—
19C2×C4⋊C4×C47—21no—
20C2×C42×C47C2211yescharacteristic
21#95×C47—21no—
22#95×C47C2212yes—
23C22×C4×C47—22no—
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47—21no—
28C2×D188C2×C411yescharacteristic
29C2×C4×D47—21no—
30C2×Dic94C2×C411yescharacteristic
31C4⋊C4×C47—42no—
32C42×C47C2×C411yescharacteristic
33C42×C47C2×C411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47D411yescharacteristic
36C22⋊Dic47—21no—
37(C2×D47)⋊C4—21no—
38(C2×D47)⋊C4—21no—
39(C2×D47)⋊C4—21no—
40(C2×D47)⋊C4—21no—
41C4⋊Dic47C2×C411yescharacteristic
42C4⋊Dic47C2×C411yescharacteristic
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C2×C47⋊C8—22no—
49C23×C47C2×D411yescharacteristic
50C22×D47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—42no—
56C2×C4×C47—42no—
57C2×C4×C47—42no—
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47C22⋊C411yescharacteristic
60C2×C4×C47C22⋊C411yescharacteristic
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47C22×C411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C22⋊D47—41no—
65C22⋊D47—41no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69D188—41no—
70C4×D47—42no—
71Dic94—41no—
72C47⋊C8—42no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47C2×C22⋊C411yescharacteristic
76C22×C47AGL(1,ℤ/8)11yescharacteristic
77C22×C47#13711yescharacteristic
78C2×D47—41no—
79C2×D47—41no—
80C2×D47—41no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—21no—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47—82no—
88Dic47—41no—
89Dic47—41no—
90Dic47—41no—
91#1512—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—21no—
94C2×C47#41011yescharacteristic
95C2×C47#41711yescharacteristic
96C2×C47#42111yescharacteristic
97D47—81no—
98#529—471no—
99#432—471no—
100#382D4711yescharacteristic, complemented
101#328—472no—
102#327—472no—
103C47#151211yescharacteristic, complemented, Sylow
104#126—941no—
105#125—471no—
106#124—471no—
107#123—941no—
108C22⋊Q8—471no—
109#121—471no—
110C4×Q8—471no—
111C4×D4—471no—
112C4×D4—941no—
113#117—941no—
114C2×C4⋊C4—21no—
115C2×C42C2×D4711yescharacteristic
116C4⋊C8—941no—
117C22⋊C8—472no—
118#97—941no—
119#95—21no—
120#95C2×D4712yes—
121C2×Q8—471no—
122C2×D4—471no—
123C2×D4—941no—
124C22×C4—22no—
125C22×C4—941no—
126C22×C4C22⋊D4711yescharacteristic
127C22×C4C22⋊D4711yescharacteristic
128C22×C4C22×D4711yescharacteristic
129C2×C8—942no—
130C4⋊C4—42no—
131C4⋊C4—471no—
132C4⋊C4—471no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C22⋊C4—941no—
138C22⋊C4—941no—
139C22⋊C4—941no—
140C22⋊C4—941no—
141C22⋊C4—941no—
142C42—941no—
143C42C4×D4711yescharacteristic
144C42C4×D4711yescharacteristic
145C42D18811yescharacteristic
146C42D18811yescharacteristic
147C23—941no—
148C23C2×C22⋊D4711yescharacteristic
149Q8—1881no—
150D4—1881no—
151D4—1881no—
152D4—1881no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—941no—
163C2×C4—1882no—
164C2×C4(C2×D47)⋊C411yescharacteristic
165C2×C4(C2×D47)⋊C411yescharacteristic
166C2×C4(C2×D47)⋊C411yescharacteristic
167C2×C4(C2×D47)⋊C411yescharacteristic
168C2×C4C2×C4×D4711yescharacteristic
169C2×C4C2×D18811yescharacteristic
170C8—1882no—
171C22—21no—
172C22—21no—
173C22—1881no—
174C22—1881no—
175C22—1881no—
176C22C2×(C2×D47)⋊C411yescharacteristic
177C22#1309405011yescharacteristic
178C22#1309405511yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—1881no—
187C4—1881no—
188C4—1881no—
189C2—21no—
190C2—21no—
191C2—3761no—
192C2#1568909611yescharacteristic
193C2#1568912211yescharacteristic
194C2#1568914111yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#382C2
socleC22×C47C2×C22⋊C4
hypercenter#382D47
hypocenterC47#1512
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #15689180C2semidirect
3. #15688859C2semidirect
5. C47×#382C2semidirect
7. #13094016C4semidirect
8. #13094012C4semidirect
12. C4×Dic94C4semidirect
13. C4×D188C4semidirect
100. #382D47semidirect
103. C47#1512semidirect