Finite Group Databasebeta

← #20244132

Subgroups — #20244132

Order 6016.

240 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#13093958C211yesmaximal, characteristic
2C2×#13093934C211yesmaximal, characteristic
3#15689022C212yesmaximal
4#15688885C212yesmaximal
5C2×#106×C47C211yesmaximal, characteristic
6C22×C47⋊C8C2211yescharacteristic
7C2×C4⋊Dic47—22no—
8C2×C4⋊Dic47C2212yes—
9C2×C4×Dic47C2211yescharacteristic
10#13093958—22no—
11#13093934—22no—
12C47⋊#95—22no—
13C22×C8×C47C2211yescharacteristic
14C2×C4⋊C4×C47C2212yes—
15#106×C47C414yescomplemented
16C22×C4×C47—22no—
17C22×C4×C47C2311yescharacteristic
18C22×Dic47—22no—
19C22×Dic47D411yescharacteristic
20C22×Dic47D411yescharacteristic
21C2×C8×C47C2×C412yes—
22C2×C8×C47D412yes—
23C2×C8×C47Q812yes—
24C4⋊C4×C47—22no—
25C4⋊C4×C47C2×C414yes—
26C4⋊Dic47—22no—
27C4⋊Dic47—22no—
28C4⋊Dic47—44no—
29C4×Dic47—21no—
30C4×Dic47—21no—
31C2×C47⋊C8—21no—
32C2×C47⋊C8—21no—
33C2×C47⋊C8Q812yes—
34C23×C47C2×D411yescharacteristic
35C2×C4×C47—24no—
36C2×C4×C47—42no—
37C2×C4×C47—42no—
38C2×C4×C47C22×C411yescharacteristic
39C2×C4×C47C2×D411yescharacteristic
40C2×C4×C47C2×Q811yescharacteristic
41C2×C4×C47C2×Q811yescharacteristic
42C2×C4×C47#4111yescharacteristic
43C2×C4×C47#4111yescharacteristic
44C2×Dic47—21no—
45C2×Dic47—21no—
46C2×Dic47—22no—
47C2×Dic47—22no—
48C2×Dic47—42no—
49C2×Dic47—42no—
50C2×Dic47—42no—
51C8×C47C4⋊C414yescomplemented
52C47⋊C8—22no—
53C22×C47C4×D411yescharacteristic
54C22×C47#12111yescharacteristic
55C22×C47C4⋊Q811yescharacteristic
56C22×C47AGL(1,ℤ/8)12yes—
57C22×C47#13712yes—
58C4×C47—44no—
59C4×C47C2×C4⋊C411yescharacteristic
60C4×C47C4×Q811yescharacteristic
61C4×C47C22⋊Q811yescharacteristic
62C4×C47#12511yescharacteristic
63Dic47—41no—
64Dic47—41no—
65Dic47—82no—
66#1944—471nomaximal, Sylow
67C2×C47#38911yescharacteristic
68C2×C47#44012yes—
69C2×C47#46911yescharacteristic
70C2×C47#47011yescharacteristic
71C2×C47#50112yes—
72C2×#107—471no—
73C2×#106D4711yescharacteristic
74C2×#97—471no—
75#389—472no—
76#340—472no—
77C47#194411yescharacteristic, complemented, Sylow
78C22×C8—471no—
79C22×C8C2×D4711yescharacteristic
80C2×C4⋊C4—472no—
81C2×C4⋊C4—942no—
82C2×C4⋊C4C2×D4712yes—
83C2×C42—471no—
84#107—942no—
85#106Dic4714yescomplemented
86#97—942no—
87#95—942no—
88C22×C4—22no—
89C22×C4—471no—
90C22×C4—471no—
91C22×C4—942no—
92C22×C4C22×D4711yescharacteristic
93C2×C8—472no—
94C2×C8—941no—
95C2×C8—941no—
96C2×C8Dic9412yes—
97C2×C8D18812yes—
98C2×C8C2×Dic4712yes—
99C4⋊C4—22no—
100C4⋊C4—942no—
101C4⋊C4—942no—
102C4⋊C4—1884no—
103C4⋊C4C2×Dic4714yes—
104C42—941no—
105C42—941no—
106C23D4×D4711yescharacteristic
107C2×C4—24no—
108C2×C4—42no—
109C2×C4—42no—
110C2×C4—941no—
111C2×C4—941no—
112C2×C4—942no—
113C2×C4—942no—
114C2×C4—1882no—
115C2×C4—1882no—
116C2×C4—1882no—
117C2×C4C2×Dic9411yescharacteristic
118C2×C4C2×D18811yescharacteristic
119C2×C4#1062535211yescharacteristic
120C2×C4Q8×D4711yescharacteristic
121C2×C4#1062535411yescharacteristic
122C2×C4C22×Dic4711yescharacteristic
123C8—942no—
124C8C4⋊Dic4714yescomplemented
125C22D4×Dic4711yescharacteristic
126C22#1309399911yescharacteristic
127C22#1309402311yescharacteristic
128C22#1309405112yes—
129C22#1309405312yes—
130C4—44no—
131C4—3762no—
132C4—1881no—
133C4—1881no—
134C4C2×C4⋊Dic4711yescharacteristic
135C4Q8×Dic4711yescharacteristic
136C4#1309400411yescharacteristic
137C4#1309401511yescharacteristic
138C2#1568902211yescharacteristic
139C2#1568922412yes—
140C2#1568937711yescharacteristic
141C2#1568938211yescharacteristic
142C2#1568953012yes—
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#106×C47C2
socleC23×C47C2×D4
hypercenterC2×#106D47
hypocenterC47#1944
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
15. #106×C47C4semidirect
51. C8×C47C4⋊C4semidirect
77. C47#1944semidirect
85. #106Dic47semidirect
124. C8C4⋊Dic47semidirect