Finite Group Databasebeta

← #20243553

Subgroups — #20243553

Order 6016.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13093957C211yesmaximal, characteristic
3C2×#13093955C211yesmaximal, characteristic
4C2×#13093934C211yesmaximal, characteristic
5#15688992C211yesmaximal, characteristic
6#15688988C211yesmaximal, characteristic
7C2×#106×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—22no—
12C2×C4×Dic47C2211yescharacteristic
13#13093958—22no—
14#13093957—22no—
15#13093955—22no—
16#13093934C414yescomplemented
17C47⋊#95—22no—
18C22×C8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21#106×C47—22no—
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47—21no—
27C22×Dic47D412yes—
28C2×C8×C47C2×C412yes—
29C2×C8×C47D412yes—
30C2×C8×C47Q812yes—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊Dic47—21no—
36C4⋊Dic47—21no—
37C4⋊Dic47—21no—
38C4⋊Dic47—21no—
39Dic47⋊C4—44no—
40C4×Dic47C2×C412yes—
41C4×Dic47Q812yes—
42C2×C47⋊C8C2×C412yes—
43C2×C47⋊C8D412yes—
44C2×C47⋊C8Q812yes—
45C23×C47C2×D411yescharacteristic
46C2×C4×C47—41no—
47C2×C4×C47—41no—
48C2×C4×C47—42no—
49C2×C4×C47—42no—
50C2×C4×C47C22×C411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×Q811yescharacteristic
54C2×C4×C47C2×Q811yescharacteristic
55C2×C4×C47C2×Q811yescharacteristic
56C2×Dic47—22no—
57C2×Dic47—22no—
58C2×Dic47—41no—
59C2×Dic47—41no—
60C2×Dic47—42no—
61C2×Dic47—42no—
62C2×Dic47C4⋊C414yes—
63C8×C47C4⋊C414yescomplemented
64C47⋊C8C4⋊C414yescomplemented
65C22×C47C2×C4⋊C411yescharacteristic
66C22×C47#12711yescharacteristic
67C22×C47C4⋊Q811yescharacteristic
68C22×C47AGL(1,ℤ/8)12yes—
69C22×C47#13712yes—
70C4×C47—81no—
71C4×C47—81no—
72C4×C47C2×C4⋊C411yescharacteristic
73C4×C47C2×C4⋊C411yescharacteristic
74C4×C47C4⋊Q811yescharacteristic
75C4×C47C4⋊Q811yescharacteristic
76Dic47—24no—
77Dic47—81no—
78Dic47—81no—
79#1847—471nomaximal, Sylow
80C2×C47#38411yescharacteristic
81C2×C47#42812yes—
82C2×C47#49611yescharacteristic
83C2×C47#49711yescharacteristic
84C2×C47#50112yes—
85C2×#107—471no—
86C2×#107—471no—
87C2×#106—471no—
88C2×#106D4711yescharacteristic
89C2×#97—471no—
90#384—471no—
91#382—471no—
92C47#184711yescharacteristic, complemented, Sylow
93C22×C8—471no—
94C22×C8C2×D4711yescharacteristic
95C2×C4⋊C4—471no—
96C2×C4⋊C4—471no—
97C2×C4⋊C4—942no—
98C2×C4⋊C4C2×D4711yescharacteristic
99C2×C4⋊C4C2×D4711yescharacteristic
100C2×C42—471no—
101#107—942no—
102#107—942no—
103#106—22no—
104#106—942no—
105#97—474no—
106#95—942no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—472no—
110C22×C4—941no—
111C22×C4—941no—
112C22×C4C22×D4711yescharacteristic
113C2×C8—472no—
114C2×C8—472no—
115C2×C8—472no—
116C2×C8Dic9412yes—
117C2×C8C4×D4712yes—
118C2×C8C22⋊D4712yes—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—941no—
124C4⋊C4—941no—
125C4⋊C4—941no—
126C4⋊C4—941no—
127C4⋊C4—1884no—
128C42—472no—
129C42—472no—
130C23D4×D4711yescharacteristic
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4—474no—
136C2×C4—942no—
137C2×C4—942no—
138C2×C4—1881no—
139C2×C4—1881no—
140C2×C4—1882no—
141C2×C4—1882no—
142C2×C4C2×Dic9411yescharacteristic
143C2×C4C2×C4×D4711yescharacteristic
144C2×C4D4×D4711yescharacteristic
145C2×C4Q8×D4711yescharacteristic
146C2×C4Q8×D4711yescharacteristic
147C2×C4C2×C22⋊D4711yescharacteristic
148C8—474no—
149C8Dic47⋊C414yescomplemented
150C22C4⋊C4×D4711yescharacteristic
151C22#1309402011yescharacteristic
152C22#1309402311yescharacteristic
153C22#1309405112yes—
154C22#1309405312yes—
155C4—81no—
156C4—81no—
157C4—944no—
158C4—3761no—
159C4—3761no—
160C4C4⋊C4×D4711yescharacteristic
161C4C2×Dic47⋊C411yescharacteristic
162C4#1309402211yescharacteristic
163C4#1309402311yescharacteristic
164C2#1568899211yescharacteristic
165C2#1568916212yes—
166C2#1568950911yescharacteristic
167C2#1568951411yescharacteristic
168C2#1568953012yes—
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#106×C47C2
socleC23×C47C2×D4
hypercenterC2×#106D47
hypocenterC47#1847
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
16. #13093934C4semidirect
63. C8×C47C4⋊C4semidirect
64. C47⋊C8C4⋊C4semidirect
92. C47#1847semidirect
149. C8Dic47⋊C4semidirect