Finite Group Databasebeta

← #20241828

Subgroups — #20241828

Order 6016.

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

normal subgroups only

This group has 266 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
1C4×#10625350C211yesmaximal, characteristic
2#15689147C211yesmaximal, characteristic, complemented
3#15688855C212yesmaximal, complemented
4#15688852C212yesmaximal, complemented
5C4×M16×C47C211yesmaximal, characteristic, complemented
6C2×#10625350C411yescharacteristic
7C2×#10625329—21no—
8C4×Dic94C411yescharacteristic
9C4×Dic94C2211yescharacteristic
10C4×D188C411yescharacteristic
11C4×D188C2211yescharacteristic
12C4×C22⋊D47—21no—
13C4×C22⋊D47—21no—
14#13093983C411yescharacteristic
15#13093981—21no—
16C42×D47—21no—
17C4⋊(C47⋊C8)—21no—
18C4⋊(C47⋊C8)C2212yes—
19C2×M16×C47—21no—
20C2×C42×C47C2211yescharacteristic
21#97×C47—21no—
22C4×C8×C47C2212yes—
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C2×C22⋊D47—21no—
27#10625350—22no—
28#10625350—22no—
29C2×D188C2×C411yescharacteristic
30C2×C4×D47—21no—
31C2×C4×D47—21no—
32C2×C4×D47—21no—
33C2×Dic94C2×C411yescharacteristic
34M16×C47—24no—
35C2×C8×C47—22no—
36C42×C47C2×C411yescharacteristic
37C42×C47D411yescharacteristic
38C42×C47D411yescharacteristic
39C42×C47C2311yescharacteristic
40C22⋊Dic47—21no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47C2×C411yescharacteristic
44C4⋊Dic47C2×C411yescharacteristic
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50#10625329—42no—
51C2×C47⋊C8—22no—
52C23×C47C22⋊C411yescharacteristic
53C22×D47—21no—
54C2×C4×C47—22no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47C22⋊C411yescharacteristic
60C2×C4×C47C22⋊C411yescharacteristic
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47C22×C411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C22⋊D47—24no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69D188—21no—
70D188M1612yescomplemented
71C4×D47—24no—
72C4×D47—42no—
73C4×D47—41no—
74C4×D47—41no—
75Dic94—21no—
76Dic94M1612yescomplemented
77C8×C47—24no—
78C47⋊C8—42no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47C2×C22⋊C411yescharacteristic
83C2×D47—22no—
84C2×D47—41no—
85C2×D47—41no—
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47#10412yes—
90C4×C47C2×M1611yescharacteristic
91C4×C47C2×M1611yescharacteristic
92C4×C47AGL(1,ℤ/8)11yescharacteristic
93C4×C47#13711yescharacteristic
94Dic47—22no—
95Dic47—41no—
96Dic47—41no—
97#1489—471nomaximal, Sylow
98C2×C47—41no—
99C2×C47#40711yescharacteristic
100C2×C47#41711yescharacteristic
101C2×C47C2×#10411yescharacteristic
102D47—42no—
103C4×#41—471no—
104#423—471no—
105C4×M16D4711yescharacteristic, complemented
106Q8⋊C8—472no—
107D4⋊C8—472no—
108C47#148911yescharacteristic, complemented, Sylow
109C2×#41—471no—
110C2×M16—21no—
111C2×M16—941no—
112C4×Q8—471no—
113C4×Q8—471no—
114C4×D4—471no—
115C4×D4—471no—
116C4×D4—941no—
117C4×D4—941no—
118#117—471no—
119#117—941no—
120C2×C42—941no—
121C2×C42C2×D4711yescharacteristic
122C4⋊C8—472no—
123C4⋊C8—941no—
124#97—21no—
125C4×C8C2×D4712yes—
126#41—942no—
127#41—942no—
128C2×Q8—471no—
129C2×D4—471no—
130C2×D4—941no—
131C22×C4—941no—
132C22×C4—941no—
133C22×C4—941no—
134C22×C4C4×D4711yescharacteristic
135C22×C4D18811yescharacteristic
136C22×C4C22⋊D4711yescharacteristic
137M16—24no—
138M16—1882no—
139C2×C8—22no—
140C2×C8—942no—
141C4⋊C4—471no—
142C4⋊C4—471no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C22⋊C4—941no—
146C22⋊C4—941no—
147C22⋊C4—941no—
148C42—941no—
149C42—941no—
150C42—941no—
151C42C4×D4711yescharacteristic
152C42D18811yescharacteristic
153C42C22⋊D4711yescharacteristic
154C42C22×D4711yescharacteristic
155C23—941no—
156C23(C2×D47)⋊C411yescharacteristic
157Q8—472no—
158Q8—941no—
159D4—472no—
160D4—944no—
161D4—941no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—944no—
168C2×C4—941no—
169C2×C4—941no—
170C2×C4—941no—
171C2×C4—1882no—
172C2×C4—1881no—
173C2×C4—1881no—
174C2×C4(C2×D47)⋊C411yescharacteristic
175C2×C4(C2×D47)⋊C411yescharacteristic
176C2×C4(C2×D47)⋊C411yescharacteristic
177C2×C4C2×C4×D4711yescharacteristic
178C2×C4C2×D18811yescharacteristic
179C2×C4C2×C22⋊D4711yescharacteristic
180C8—24no—
181C8—1882no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—942no—
186C22—1881no—
187C22—1881no—
188C22C2×(C2×D47)⋊C411yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—942no—
193C4—1881no—
194C4—1881no—
195C4#1309395212yes—
196C4M16×D4711yescharacteristic
197C4M16×D4711yescharacteristic
198C4#1309405211yescharacteristic
199C4#1309405711yescharacteristic
200C2—41no—
201C2—1882no—
202C2#1568908611yescharacteristic
203C2#1568912511yescharacteristic
204C2C2×#1309395211yescharacteristic
subgroupG/H
centerC2×C4C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC4×M16×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC4×M16D47
hypocenterC47#1489
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #15689147C2semidirect
3. #15688855C2semidirect
4. #15688852C2semidirect
5. C4×M16×C47C2semidirect
70. D188M16semidirect
76. Dic94M16semidirect
105. C4×M16D47semidirect
108. C47#1489semidirect