Finite Group Databasebeta

← #20244265

Subgroups — #20244265

Order 6016.

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

normal subgroups only

This group has 376 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×#13093956C211yesmaximal, characteristic, complemented
2C2×#13093945C212yesmaximal, complemented
3C2×#13093934C211yesmaximal, characteristic, complemented
4#15689026C212yesmaximal, complemented
5C22×D8×C47C211yesmaximal, characteristic
6C22×C47⋊C8C2211yescharacteristic
7C2×C4⋊Dic47C2212yes—
8C2×C22⋊Dic47—24no—
9C2×C4×Dic47C2211yescharacteristic
10#13093956—22no—
11#13093945—24no—
12#13093934—22no—
13C22×D4×C47C2212yes—
14C2×D8×C47—22no—
15C2×D8×C47—22no—
16C2×D8×C47C414yescomplemented
17C22×C8×C47C2211yescharacteristic
18C24×C47—22no—
19C2×D4×C47—22no—
20C2×D4×C47—22no—
21C2×D4×C47—22no—
22C2×D4×C47—22no—
23C2×D4×C47—22no—
24C2×D4×C47C2×C414yes—
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—22no—
27C22×Dic47D412yes—
28D8×C47—28no—
29C2×C8×C47C2×C412yes—
30C2×C8×C47D412yes—
31C2×C8×C47D412yes—
32C22⋊Dic47—48no—
33C4⋊Dic47—22no—
34C4⋊Dic47—22no—
35C4×Dic47—21no—
36C4×Dic47—21no—
37C2×C47⋊C8—21no—
38C2×C47⋊C8—21no—
39C2×C47⋊C8D412yes—
40C23×C47—24no—
41C23×C47—42no—
42C23×C47—42no—
43C23×C47—44no—
44C23×C47—44no—
45C23×C47C2×D411yescharacteristic
46D4×C47—24no—
47D4×C47—24no—
48D4×C47—42no—
49D4×C47—42no—
50C2×C4×C47C22×C411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47#4111yescharacteristic
55C2×C4×C47#4111yescharacteristic
56C2×Dic47—22no—
57C2×Dic47—24no—
58C2×Dic47—42no—
59C2×Dic47—44no—
60C8×C47C22⋊C414yescomplemented
61C47⋊C8—22no—
62C22×C47—44no—
63C22×C47—48no—
64C22×C47—84no—
65C22×C47—82no—
66C22×C47—82no—
67C22×C47C4×D411yescharacteristic
68C22×C47#12111yescharacteristic
69C22×C47#12711yescharacteristic
70C22×C47AGL(1,ℤ/8)14yes—
71C4×C47C2×C22⋊C411yescharacteristic
72C4×C47C4×D411yescharacteristic
73C4×C47#12111yescharacteristic
74C4×C47#12411yescharacteristic
75Dic47—42no—
76Dic47—82no—
77#1972—471nomaximal, Sylow
78C2×C47—84no—
79C2×C47#39011yescharacteristic
80C2×C47#44212yes—
81C2×C47#46912yes—
82C2×C47#49612yes—
83C22×D8D4711yescharacteristic
84C2×#106—471no—
85C2×#102—472no—
86C2×#97—471no—
87#390—472no—
88C47#197211yescharacteristic, complemented, Sylow
89C22×D4C2×D4712yes—
90C2×D8—22no—
91C2×D8—22no—
92C2×D8Dic4714yescomplemented
93C22×C8—471no—
94C22×C8C2×D4711yescharacteristic
95C2×C4⋊C4—472no—
96C2×C22⋊C4—944no—
97C2×C42—471no—
98#106—942no—
99#102—944no—
100#97—942no—
101C24—22no—
102C2×D4—22no—
103C2×D4—22no—
104C2×D4—22no—
105C2×D4—22no—
106C2×D4—22no—
107C2×D4C2×Dic4714yes—
108C22×C4—472no—
109C22×C4—942no—
110C22×C4C22×D4711yescharacteristic
111D8—28no—
112C2×C8—472no—
113C2×C8—941no—
114C2×C8—941no—
115C2×C8C2×Dic4712yes—
116C2×C8C22⋊D4712yes—
117C2×C8C22⋊D4712yes—
118C4⋊C4—942no—
119C4⋊C4—942no—
120C22⋊C4—1888no—
121C42—941no—
122C42—941no—
123C23—24no—
124C23—42no—
125C23—42no—
126C23—44no—
127C23—44no—
128C23D4×D4711yescharacteristic
129D4—24no—
130D4—24no—
131D4—42no—
132D4—42no—
133C2×C4—942no—
134C2×C4—944no—
135C2×C4—1882no—
136C2×C4—1884no—
137C2×C4D4×D4711yescharacteristic
138C2×C4#1062535211yescharacteristic
139C2×C4#1062535211yescharacteristic
140C2×C4C22×Dic4711yescharacteristic
141C2×C4C2×C22⋊D4711yescharacteristic
142C2×C4C2×C22⋊D4711yescharacteristic
143C8—942no—
144C8C22⋊Dic4714yescomplemented
145C22—48no—
146C22—44no—
147C22—82no—
148C22—82no—
149C22—84no—
150C22D4×Dic4711yescharacteristic
151C22#1309399511yescharacteristic
152C22#1309402011yescharacteristic
153C22#1309404814yes—
154C4—3762no—
155C4—1882no—
156C4C2×C22⋊Dic4711yescharacteristic
157C4D4×Dic4711yescharacteristic
158C4#1309399511yescharacteristic
159C4#1309401111yescharacteristic
160C2—84no—
161C2#1568902611yescharacteristic
162C2#1568923512yes—
163C2#1568937312yes—
164C2#1568951112yes—
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×D8×C47C2
socleC23×C47C2×D4
hypercenterC22×D8D47
hypocenterC47#1972
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#13093956C2semidirect
2. C2×#13093945C2semidirect
3. C2×#13093934C2semidirect
4. #15689026C2semidirect
16. C2×D8×C47C4semidirect
60. C8×C47C22⋊C4semidirect
88. C47#1972semidirect
92. C2×D8Dic47semidirect
144. C8C22⋊Dic47semidirect