Finite Group Databasebeta

← #20244307

Subgroups — #20244307

Order 6016.

336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13093950C214yesmaximal, complemented
3C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
4C4×M16×C47C211yesmaximal, characteristic, complemented
5C2×#10625350C2212yes—
6#13094024C411yescharacteristic, complemented
7#13094021C411yescharacteristic, complemented
8#13094012C412yescomplemented
9#13093998—21no—
10#13093998—21no—
11C4×D188—21no—
12C4×D188—21no—
13C2×C4⋊Dic47—21no—
14C2×C4×Dic47C2212yes—
15#13093950—28no—
16C47⋊#95—21no—
17C2×M16×C47C2212yes—
18C2×C42×C47C2211yescharacteristic
19#97×C47—21no—
20C4×C8×C47—21no—
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C2×C22⋊D47—22no—
25C22×Dic47—22no—
26#10625350—24no—
27#10625350—24no—
28C2×D188—21no—
29C2×D188—21no—
30C2×D188C2×C412yes—
31C2×C4×D47—22no—
32C2×Dic94C2×C412yes—
33M16×C47—22no—
34M16×C47D414yescomplemented
35C2×C8×C47—22no—
36C42×C47C2×C411yescharacteristic
37C42×C47C2×C411yescharacteristic
38C42×C47D411yescharacteristic
39C42×C47D411yescharacteristic
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—22no—
42C4⋊Dic47—24no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4×Dic47—24no—
46C23×C47C2×D411yescharacteristic
47C22×D47—22no—
48C2×C4×C47—22no—
49C2×C4×C47—41no—
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C22⋊C411yescharacteristic
54C2×C4×C47C22×C411yescharacteristic
55C2×C4×C47C2×D412yes—
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47#4112yes—
58C22⋊D47—42no—
59C22⋊D47—42no—
60C2×Dic47—24no—
61C2×Dic47—22no—
62C2×Dic47—42no—
63C2×Dic47—42no—
64D188—24no—
65D188—42no—
66D188—42no—
67C4×D47—44no—
68Dic94—24no—
69C8×C47—24no—
70C22×C47—21no—
71C22×C47—21no—
72C22×C47C2×C22⋊C411yescharacteristic
73C22×C47#12411yescharacteristic
74C22×C47#12711yescharacteristic
75C2×D47—42no—
76C2×D47—42no—
77C2×D47—42no—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47#10412yescomplemented
82C4×C47C4×D412yes—
83C4×C47#12112yes—
84Dic47—44no—
85Dic47—42no—
86#1980—471nomaximal, Sylow
87C2×C47—21no—
88C2×C47—21no—
89C2×C47#39011yescharacteristic
90C2×C47C2×#10411yescharacteristic
91C2×C47#42111yescharacteristic
92D47—82no—
93#532—471no—
94C2×#104—474no—
95C4×M16D4711yescharacteristic, complemented
96C4×C4⋊C4—471no—
97C47#198011yescharacteristic, complemented, Sylow
98C2×#41—472no—
99C2×M16C2×D4712yes—
100C4⋊Q8—471no—
101#127—471no—
102#124—472no—
103#121—941no—
104#121—941no—
105C4×D4—941no—
106C4×D4—941no—
107C2×C4⋊C4—941no—
108C2×C42—472no—
109C2×C42C2×D4711yescharacteristic
110#104—948no—
111#97—21no—
112C4×C8—21no—
113#95—941no—
114#41—944no—
115#41—944no—
116C2×Q8—472no—
117C2×D4—472no—
118C2×D4—942no—
119C2×D4—941no—
120C2×D4—941no—
121C22×C4—942no—
122C22×C4—942no—
123C22×C4D18811yescharacteristic
124C22×C4D18811yescharacteristic
125C22×C4C22×D4711yescharacteristic
126M16—22no—
127M16D18814yescomplemented
128C2×C8—22no—
129C4⋊C4—944no—
130C4⋊C4—941no—
131C4⋊C4—941no—
132C22⋊C4—942no—
133C22⋊C4—942no—
134C42—944no—
135C42C4×D4711yescharacteristic
136C42C4×D4711yescharacteristic
137C42C22⋊D4711yescharacteristic
138C42C22⋊D4711yescharacteristic
139C23—942no—
140C23C2×D18811yescharacteristic
141Q8—944no—
142D4—944no—
143D4—1882no—
144D4—1882no—
145D4—1882no—
146D4—1882no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—944no—
150C2×C4—942no—
151C2×C4—1882no—
152C2×C4—1882no—
153C2×C4—1884no—
154C2×C4(C2×D47)⋊C411yescharacteristic
155C2×C4(C2×D47)⋊C411yescharacteristic
156C2×C4(C2×D47)⋊C411yescharacteristic
157C2×C4(C2×D47)⋊C411yescharacteristic
158C2×C4C2×C4×D4711yescharacteristic
159C2×C4C2×D18812yes—
160C2×C4#1062535012yes—
161C2×C4C2×C22⋊D4711yescharacteristic
162C8—24no—
163C22—21no—
164C22—21no—
165C22—1882no—
166C22—1882no—
167C22—1882no—
168C22C2×(C2×D47)⋊C411yescharacteristic
169C22#1309401211yescharacteristic
170C22#1309402111yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—1884no—
175C4—1882no—
176C4#1309395012yescomplemented
177C4C4×D18812yes—
178C4#1309399812yes—
179C2—21no—
180C2—21no—
181C2—3762no—
182C2#1568902511yescharacteristic
183C2C2×#1309395011yescharacteristic
184C2#1568913911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC4×M16×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC4×M16D47
hypocenterC47#1980
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. C2×#13093950C2semidirect
3. C4×C4⋊Dic47C2semidirect
4. C4×M16×C47C2semidirect
6. #13094024C4semidirect
7. #13094021C4semidirect
8. #13094012C4semidirect
34. M16×C47D4semidirect
81. C4×C47#104semidirect
95. C4×M16D47semidirect
97. C47#1980semidirect
127. M16D188semidirect
176. C4#13093950semidirect