Finite Group Databasebeta

← #20253782

Subgroups — #20253782

Order 6016.

424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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#15689673C211yesmaximal, characteristic
2C2×#13094024C211yesmaximal, characteristic, complemented
3#15689483C214yesmaximal, complemented
4#15689474C212yesmaximal, complemented
5#15689470C212yesmaximal, complemented
6#15689125C214yesmaximal, complemented
7C4×M16×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2212yes—
9C22×Dic94—21no—
10#13094024—21no—
11#13094024—21no—
12#13094024C2211yescharacteristic
13#13094024C2212yes—
14#13094024C2212yes—
15#13094021C2211yescharacteristic
16#13094012C2212yes—
17#13093998—21no—
18#13093998—21no—
19C4×D188—21no—
20C4×D188—21no—
21C2×C4⋊Dic47—21no—
22C2×C4⋊Dic47C2212yes—
23#13093949C2218yes—
24#13093946C2218yes—
25C2×M16×C47C2212yes—
26C2×C42×C47C2211yescharacteristic
27#97×C47C2212yes—
28C4×C8×C47C2212yes—
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—22no—
33C22×Dic47—22no—
34#10625350—28no—
35C2×D188—21no—
36C2×D188—21no—
37C2×D188C2312yes—
38C2×C4×D47—22no—
39C2×Dic94—22no—
40C2×Dic94—22no—
41C2×Dic94—44no—
42C2×Dic94C2312yes—
43M16×C47—24no—
44C2×C8×C47C2314yes—
45C42×C47D411yescharacteristic
46C42×C47D411yescharacteristic
47C42×C47C2311yescharacteristic
48C42×C47C2311yescharacteristic
49(C2×D47)⋊C4—22no—
50(C2×D47)⋊C4—22no—
51C4⋊Dic47—22no—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47C2314yes—
57C23×C47C2×D411yescharacteristic
58C22×D47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47#4114yes—
67C2×C4×C47C2411yescharacteristic
68C22⋊D47—44no—
69C2×Dic47—24no—
70C2×Dic47—22no—
71C2×Dic47—44no—
72D188—24no—
73D188—42no—
74D188—42no—
75C4×D47—44no—
76Dic94—24no—
77Dic94—44no—
78Dic94—44no—
79C8×C47—24no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47#12412yes—
83C22×C47C22×D411yescharacteristic
84C2×D47—42no—
85C2×D47—42no—
86C2×D47—42no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47#12412yes—
90C4×C47AGL(1,ℤ/8)12yes—
91C4×C47#13712yes—
92C4×C47C2×#4112yes—
93Dic47—42no—
94Dic47—44no—
95#3141—471nomaximal, Sylow
96C2×C47—22no—
97C2×C47C2×#12411yescharacteristic
98C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
99C2×C47C2×#13711yescharacteristic
100D47—82no—
101#532—471no—
102C2×C4⋊Q8—471no—
103#489—474no—
104#487—472no—
105#486—472no—
106#417—474no—
107C4×M16D4711yescharacteristic, complemented
108C47#314111yescharacteristic, complemented, Sylow
109C2×#41—472no—
110C22×Q8—941no—
111C2×M16C2×D4712yes—
112C4⋊Q8—472no—
113C4⋊Q8—472no—
114C4⋊Q8—471no—
115C4⋊Q8—941no—
116C4⋊Q8—941no—
117#127—471no—
118#124—472no—
119#121—941no—
120#121—941no—
121C4×D4—941no—
122C4×D4—941no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—941no—
125C2×C42C2×D4711yescharacteristic
126#103—478no—
127#102—478no—
128#97C2×D4712yes—
129C4×C8C2×D4712yes—
130#41—948no—
131C2×Q8—472no—
132C2×Q8—942no—
133C2×Q8—942no—
134C2×Q8—1884no—
135C2×D4—472no—
136C2×D4—942no—
137C2×D4—941no—
138C2×D4—941no—
139C22×C4—942no—
140C22×C4—942no—
141C22×C4D18811yescharacteristic
142C22×C4D18811yescharacteristic
143C22×C4C22×D4711yescharacteristic
144M16—24no—
145C2×C8C22×D4714yes—
146C4⋊C4—474no—
147C4⋊C4—942no—
148C4⋊C4—942no—
149C4⋊C4—942no—
150C4⋊C4—941no—
151C4⋊C4—941no—
152C22⋊C4—942no—
153C22⋊C4—942no—
154C42D18811yescharacteristic
155C42D18811yescharacteristic
156C42C22×D4711yescharacteristic
157C42C22×D4711yescharacteristic
158C23—942no—
159C23C2×D18811yescharacteristic
160Q8—944no—
161Q8—1884no—
162Q8—1884no—
163D4—944no—
164D4—1884no—
165D4—1882no—
166D4—1882no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—942no—
170C2×C4—944no—
171C2×C4—1884no—
172C2×C4—1884no—
173C2×C4C2×D18811yescharacteristic
174C2×C4C2×D18811yescharacteristic
175C2×C4C2×D18811yescharacteristic
176C2×C4C2×D18811yescharacteristic
177C2×C4C2×D18811yescharacteristic
178C2×C4#1062535014yes—
179C2×C4C23×D4711yescharacteristic
180C8—24no—
181C22—21no—
182C22—21no—
183C22—1882no—
184C22—1882no—
185C22—1882no—
186C22#1309401212yes—
187C22C22×D18811yescharacteristic
188C4—21no—
189C4—21no—
190C4—1882no—
191C4—1884no—
192C4#1309401212yes—
193C4#1309405212yes—
194C4#1309405712yes—
195C4C2×#1062535012yes—
196C2—22no—
197C2—3762no—
198C2C2×#1309401211yescharacteristic
199C2C2×#1309405211yescharacteristic
200C2C2×#1309405711yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×M16×C47C2
socleC22×C47C22×D4
hypercenterC4×M16D47
hypocenterC47#3141
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×#13094024C2semidirect
3. #15689483C2semidirect
4. #15689474C2semidirect
5. #15689470C2semidirect
6. #15689125C2semidirect
7. C4×M16×C47C2semidirect
107. C4×M16D47semidirect
108. C47#3141semidirect