Finite Group Databasebeta

← #20249257

Subgroups — #20249257

Order 6016.

512 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×D188C211yesmaximal, characteristic
2#15689058C212yesmaximal, complemented
3#15689053C212yesmaximal, complemented
4#15689049C212yesmaximal, complemented
5#15689040C212yesmaximal
6#15688994C214yesmaximal, complemented
7#15688991C211yesmaximal, characteristic, complemented
8C2×#125×C47C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C4×D47C2212yes—
11C4×D188—24no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2214yes—
14C2×(C2×D47)⋊C4C2214yes—
15C2×(C2×D47)⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2214yes—
17C47⋊#95C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2214yes—
21#125×C47—24no—
22C2×C4⋊C4×C47C2212yes—
23C2×C4⋊C4×C47C2212yes—
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27C23×D47C2312yes—
28C22×C4×C47C2312yes—
29C22×C4×C47C2312yes—
30C22×C4×C47C2311yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×Dic47C2314yes—
34C22×Dic47C2312yes—
35C2×D188—24no—
36C2×D188—22no—
37C2×C4×D47—24no—
38C2×C4×D47—44no—
39C4⋊C4×C47—24no—
40C4⋊C4×C47—22no—
41C4⋊C4×C47—22no—
42C4⋊C4×C47—24no—
43C42×C47D414yes—
44(C2×D47)⋊C4—28no—
45(C2×D47)⋊C4—24no—
46(C2×D47)⋊C4—44no—
47C4⋊Dic47—22no—
48Dic47⋊C4—44no—
49C23×C47C2411yescharacteristic
50C22×D47—22no—
51C22×D47—22no—
52C22×D47—24no—
53C22×D47—24no—
54C22×D47#4114yes—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—24no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47C2×D412yes—
64C2×C4×C47C2×D412yes—
65C2×C4×C47C2×D412yes—
66C2×Dic47—22no—
67C2×Dic47—24no—
68C2×Dic47—24no—
69C2×Dic47—24no—
70C2×Dic47—24no—
71D188—28no—
72C4×D47—48no—
73C22×C47C22×D411yescharacteristic
74C22×C47C2×#4112yes—
75C22×C47H(5,𝔽2)12yes—
76C22×C472−1+412yes—
77C2×D47—24no—
78C2×D47—28no—
79C2×D47—42no—
80C2×D47—42no—
81C2×D47—44no—
82C4×C47—22no—
83C4×C47—22no—
84C4×C47—22no—
85C4×C47—42no—
86C4×C47—42no—
87Dic47—42no—
88Dic47—44no—
89#2633—471nomaximal, Sylow
90C2×C47#52511yescharacteristic
91C2×C47#53511yescharacteristic
92C2×C47#53611yescharacteristic
93C2×C47#53914yes—
94D47—44no—
95C2×#125D4711yescharacteristic, complemented
96C2×C4×D4—471no—
97#399—472no—
98#398—472no—
99#397—472no—
100#394—472no—
101#385—474no—
102#383—471no—
103C47#263311yescharacteristic, complemented, Sylow
104C22×D4—471no—
105C23×C4—472no—
106#125—24no—
107C4×D4—944no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4—474no—
110C2×C4⋊C4C2×D4712yes—
111C2×C4⋊C4C2×D4712yes—
112C2×C4⋊C4C2×D4711yescharacteristic
113C2×C4⋊C4C2×D4711yescharacteristic
114C2×C22⋊C4—472no—
115C2×C22⋊C4—474no—
116C2×C22⋊C4—474no—
117C2×C42C2×D4711yescharacteristic
118#95—472no—
119#95—472no—
120#95—472no—
121#95—474no—
122C24—472no—
123C2×D4—944no—
124C2×D4—942no—
125C22×C4—474no—
126C22×C4—472no—
127C22×C4—944no—
128C22×C4—1884no—
129C22×C4C22×D4712yes—
130C22×C4C22×D4712yes—
131C22×C4C22×D4711yescharacteristic
132C22×C4C22×D4711yescharacteristic
133C22×C4C22×D4711yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—24no—
137C4⋊C4—24no—
138C4⋊C4—942no—
139C4⋊C4—1884no—
140C22⋊C4—948no—
141C22⋊C4—944no—
142C22⋊C4—1884no—
143C42C22⋊D4714yes—
144C23—474no—
145C23—942no—
146C23—942no—
147C23—944no—
148C23—944no—
149C23C23×D4711yescharacteristic
150D4—948no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—942no—
160C2×C4—944no—
161C2×C4—944no—
162C2×C4—944no—
163C2×C4—944no—
164C2×C4—1888no—
165C2×C4C2×C22⋊D4712yes—
166C2×C4C2×C22⋊D4712yes—
167C2×C4C2×C22⋊D4712yes—
168C22—944no—
169C22—948no—
170C22—1882no—
171C22—1882no—
172C22—1884no—
173C22C22×C22⋊D4711yescharacteristic
174C22#41×D4712yes—
175C22#1309407012yes—
176C22#1309407212yes—
177C4—22no—
178C4—22no—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—1882no—
183C4—1884no—
184C2—1884no—
185C2#1568963011yescharacteristic
186C2#1568968711yescharacteristic
187C2#1568969711yescharacteristic
188C2#1568972114yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#125×C47C2
hypercenterC2×#125D47
hypocenterC47#2633
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #15689058C2semidirect
3. #15689053C2semidirect
4. #15689049C2semidirect
6. #15688994C2semidirect
7. #15688991C2semidirect
8. C2×#125×C47C2semidirect
95. C2×#125D47semidirect
103. C47#2633semidirect