Finite Group Databasebeta

← #20241757

Subgroups — #20241757

Order 6016.

214 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 77 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#15689180C211yesmaximal, characteristic, complemented
2#15689176C211yesmaximal, characteristic, complemented
3#15688849C212yesmaximal, complemented
4#15688847C212yesmaximal
5C2×#126×C47C211yesmaximal, characteristic
6C4⋊(C47⋊C8)—21no—
7C4⋊(C47⋊C8)—21no—
8C22⋊(C47⋊C8)C2212yes—
9C22⋊(C47⋊C8)C2212yes—
10#13093935—21no—
11C4×C47⋊C8—21no—
12#126×C47—21no—
13#126×C47—21no—
14#126×C47—21no—
15#126×C47—21no—
16C2×C4⋊C4×C47C411yescharacteristic
17C2×C4⋊C4×C47C411yescharacteristic
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×C22⋊C4×C47C411yescharacteristic
20C2×C22⋊C4×C47C411yescharacteristic
21C2×C22⋊C4×C47C2211yescharacteristic
22C2×C42×C47C2211yescharacteristic
23C24×C47C2×C411yescharacteristic
24C22×C4×C47C2×C411yescharacteristic
25C22×C4×C47C2×C411yescharacteristic
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47C2×C411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C4⋊C4×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C22⋊C4×C47—21no—
37C22⋊C4×C47—21no—
38C22⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C22⋊C4×C47—21no—
42C42×C47D411yescharacteristic
43C42×C47D411yescharacteristic
44C42×C47D411yescharacteristic
45C42×C47D411yescharacteristic
46C2×C47⋊C8—22no—
47C2×C47⋊C8—22no—
48C23×C47—21no—
49C23×C47—22no—
50C23×C47—41no—
51C23×C47—41no—
52C23×C47C22×C411yescharacteristic
53C2×C4×C47—22no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—22no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47C22⋊C411yescharacteristic
63C2×C4×C47C22⋊C411yescharacteristic
64C2×C4×C47C22⋊C411yescharacteristic
65C2×C4×C47C22⋊C411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C47⋊C8—42no—
69C47⋊C8—42no—
70C22×C47—21no—
71C22×C47—21no—
72C22×C47—41no—
73C22×C47—41no—
74C22×C47—41no—
75C22×C47—82no—
76C22×C47C2×C22⋊C411yescharacteristic
77C22×C47#13112yes—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—21no—
84C4×C47—41no—
85C4×C47—41no—
86C4×C47—41no—
87#1473—471nomaximal, Sylow
88C2×C47—22no—
89C2×C47—81no—
90C2×C47#40811yescharacteristic
91C2×C47#41011yescharacteristic
92C2×C47#41311yescharacteristic
93C2×#126D4711yescharacteristic
94#432—471no—
95#431—471no—
96#324—472no—
97#323—472no—
98C47#147311yescharacteristic, complemented, Sylow
99#126—21no—
100#126—21no—
101#126—21no—
102#126—21no—
103C2×C4⋊C4Dic4711yescharacteristic
104C2×C4⋊C4Dic4711yescharacteristic
105C2×C4⋊C4C2×D4711yescharacteristic
106C2×C22⋊C4Dic4711yescharacteristic
107C2×C22⋊C4Dic4711yescharacteristic
108C2×C22⋊C4C2×D4711yescharacteristic
109C2×C42C2×D4711yescharacteristic
110C4⋊C8—941no—
111C4⋊C8—941no—
112C22⋊C8—472no—
113C22⋊C8—472no—
114#97—941no—
115C4×C8—941no—
116C24C2×Dic4711yescharacteristic
117C22×C4C2×Dic4711yescharacteristic
118C22×C4C2×Dic4711yescharacteristic
119C22×C4C2×Dic4711yescharacteristic
120C22×C4C2×Dic4711yescharacteristic
121C22×C4C2×Dic4711yescharacteristic
122C22×C4C22×D4711yescharacteristic
123C2×C8—942no—
124C2×C8—942no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C42C22⋊D4711yescharacteristic
138C42C22⋊D4711yescharacteristic
139C42C22⋊D4711yescharacteristic
140C42C22⋊D4711yescharacteristic
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×Dic4711yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4C22⋊Dic4711yescharacteristic
156C2×C4C22⋊Dic4711yescharacteristic
157C2×C4C22⋊Dic4711yescharacteristic
158C2×C4C22⋊Dic4711yescharacteristic
159C2×C4C2×C22⋊D4711yescharacteristic
160C2×C4C2×C22⋊D4711yescharacteristic
161C8—1882no—
162C8—1882no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22C2×C22⋊Dic4711yescharacteristic
170C22#1309403112yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—41no—
178C4—41no—
179C4—41no—
180C2—22no—
181C2—81no—
182C2#1568909011yescharacteristic
183C2#1568909711yescharacteristic
184C2#1568910711yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#126×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×#126D47
hypocenterC47#1473
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #15689180C2semidirect
2. #15689176C2semidirect
3. #15688849C2semidirect
98. C47#1473semidirect