Finite Group Databasebeta

← #20242597

Subgroups — #20242597

Order 6016.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689830C211yesmaximal, characteristic
2#15689474C211yesmaximal, characteristic, complemented
3#15689409C211yesmaximal, characteristic, complemented
4#15689328C211yesmaximal, characteristic
5#15688871C211yesmaximal, characteristic, complemented
6#15688855C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic
8C2×#10625335—21no—
9#13094024C2211yescharacteristic
10#13094024C2211yescharacteristic
11#13094015—21no—
12#13094003—21no—
13#13094001—22no—
14C4×Dic94C2211yescharacteristic
15D4×Dic47—21no—
16C2×C4⋊Dic47—21no—
17#13093956—21no—
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093949—22no—
20#13093949—21no—
21#13093947—21no—
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4×C8×C47C2211yescharacteristic
25C2×D4×C47D411yescharacteristic
26C22×C4×C47—21no—
27C22×Dic47—22no—
28C2×Dic94—21no—
29C2×Dic94D411yescharacteristic
30C2×Dic94D412yes—
31C2×C8×C47—21no—
32C2×C8×C47—21no—
33C4⋊C4×C47D411yescharacteristic
34C22⋊C4×C47—21no—
35C42×C47C2311yescharacteristic
36C22⋊Dic47—22no—
37#10625335—42no—
38C4⋊Dic47—22no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D411yescharacteristic
44Dic47⋊C4—22no—
45Dic47⋊C4—21no—
46C4×Dic47—21no—
47C2×C47⋊C8—21no—
48C23×C47—21no—
49D4×C47—21no—
50D4×C47SD1612yes—
51C2×C4×C47—21no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—22no—
60C2×Dic47—41no—
61C2×Dic47—82no—
62Dic94—21no—
63Dic94—21no—
64Dic94—42no—
65Dic94—41no—
66Dic94—41no—
67C8×C47—41no—
68C8×C47—41no—
69C47⋊C8—41no—
70C22×C47—22no—
71C22×C47—41no—
72C22×C47—41no—
73C22×C47#12011yescharacteristic
74C4×C47—21no—
75C4×C47—41no—
76C4×C47C2×SD1611yescharacteristic
77C4×C47#13511yescharacteristic
78C4×C47#13711yescharacteristic
79C4×C47#13711yescharacteristic
80Dic47—41no—
81Dic47—42no—
82Dic47—41no—
83Dic47—81no—
84#1643—471nomaximal, Sylow
85C2×C47—42no—
86C2×C47#44811yescharacteristic
87C2×C47#45211yescharacteristic
88C2×C47#45511yescharacteristic
89#554—471no—
90#487—471no—
91#475—471no—
92#461—471no—
93#333—471no—
94Q8⋊C8—471no—
95D4⋊C8D4711yescharacteristic
96C47#164311yescharacteristic, complemented, Sylow
97C2×SD16—941no—
98C4⋊Q8—471no—
99C4⋊Q8—471no—
100#125—941no—
101C22⋊Q8—942no—
102C22⋊Q8—941no—
103C4×Q8—471no—
104C4×D4—941no—
105C4×D4C2×D4711yescharacteristic
106C2×C4⋊C4—941no—
107#106—941no—
108C4⋊C8—471no—
109C4⋊C8C2×D4711yescharacteristic
110#103—941no—
111#103—942no—
112#103—941no—
113C4×C8C2×D4711yescharacteristic
114C2×Q8—471no—
115C2×Q8—472no—
116C2×Q8—941no—
117C2×D4D18811yescharacteristic
118C22×C4—21no—
119C22×C4—942no—
120SD16—1882no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—941no—
124C4⋊C4—471no—
125C4⋊C4—942no—
126C4⋊C4—942no—
127C4⋊C4—941no—
128C4⋊C4—941no—
129C4⋊C4—941no—
130C4⋊C4—941no—
131C4⋊C4—941no—
132C4⋊C4D18811yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—942no—
135C42—941no—
136C42C22×D4711yescharacteristic
137C23—21no—
138Q8—941no—
139Q8—941no—
140Q8—1882no—
141Q8—1881no—
142Q8—1881no—
143D4—21no—
144D4#1062532512yes—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—941no—
149C2×C4—941no—
150C2×C4—942no—
151C2×C4—3762no—
152C2×C4—1881no—
153C2×C4C2×D18811yescharacteristic
154C2×C4D4×D4711yescharacteristic
155C2×C4D4×D4711yescharacteristic
156C8—41no—
157C8—41no—
158C8—1881no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1309399411yescharacteristic
163C4—21no—
164C4—41no—
165C4—3761no—
166C4—1881no—
167C4—1881no—
168C4—1882no—
169C4C2×#1062532511yescharacteristic
170C4#1309404311yescharacteristic
171C4#1309405311yescharacteristic
172C4#1309405711yescharacteristic
173C2—42no—
174C2#1568926411yescharacteristic
175C2#1568928611yescharacteristic
176C2#1568930211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47#120
hypercenterD4⋊C8D47
hypocenterC47#1643
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #15689474C2semidirect
3. #15689409C2semidirect
5. #15688871C2semidirect
6. #15688855C2semidirect
96. C47#1643semidirect