Finite Group Databasebeta

← #20248554

Subgroups — #20248554

Order 6016.

532 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13094016C211yesmaximal, characteristic, complemented
2#15689061C212yesmaximal, complemented
3#15689037C212yesmaximal
4#15689017C214yesmaximal, complemented
5#15688983C212yesmaximal, complemented
6#15688983C212yesmaximal, complemented
7C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
8C2×C4×D4×C47C211yesmaximal, characteristic
9#13094016—24no—
10C2×C4⋊Dic47C2212yes—
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×C22⋊Dic47C2214yes—
16C2×C22⋊Dic47C2214yes—
17C2×C4×Dic47C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2214yes—
20C47⋊#95C2214yes—
21C22×D4×C47C2211yescharacteristic
22C23×C4×C47C2212yes—
23C4×D4×C47—24no—
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C22⋊C4×C47C2212yes—
26C2×C42×C47C2211yescharacteristic
27C24×C47C2312yes—
28C2×D4×C47—24no—
29C2×D4×C47—22no—
30C22×C4×C47—24no—
31C22×C4×C47—24no—
32C22×C4×C47—24no—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×Dic47C2314yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C4⋊C4×C47—22no—
41C22⋊C4×C47—24no—
42C42×C47D414yes—
43C22⋊Dic47—28no—
44C22⋊Dic47—44no—
45C4⋊Dic47—22no—
46C4⋊Dic47—22no—
47C4⋊Dic47—24no—
48Dic47⋊C4—24no—
49Dic47⋊C4—24no—
50C4×Dic47—42no—
51C23×C47—22no—
52C23×C47—22no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—22no—
56C23×C47—22no—
57C23×C47#4114yes—
58C23×C47C2411yescharacteristic
59D4×C47—28no—
60C2×C4×C47—22no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—48no—
67C2×C4×C47C2×D412yes—
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×D412yes—
70C2×C4×C47#4114yes—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—24no—
74C2×Dic47—24no—
75C2×Dic47—24no—
76C2×Dic47—24no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C22×C47—24no—
80C22×C47—24no—
81C22×C47—24no—
82C22×C47—42no—
83C22×C47—42no—
84C22×C47—42no—
85C22×C47—42no—
86C22×C47C22×D411yescharacteristic
87C22×C47C2×#4112yes—
88C22×C47C2×#4112yes—
89C22×C47H(5,𝔽2)11yescharacteristic
90C22×C472−1+411yescharacteristic
91C4×C47—22no—
92C4×C47—22no—
93C4×C47—42no—
94C4×C47#12414yes—
95Dic47—42no—
96Dic47—42no—
97Dic47—44no—
98#2562—471nomaximal, Sylow
99C2×C47—44no—
100C2×C47#52511yescharacteristic
101C2×C47C2×#12411yescharacteristic
102C2×C47#53711yescharacteristic
103C2×C47#55212yes—
104C2×C47#55312yes—
105C2×#125—471no—
106C2×C4×D4D4711yescharacteristic
107#400—472no—
108#394—472no—
109#388—474no—
110#380—472no—
111#380—472no—
112C4×C4⋊C4—471no—
113C47#256211yescharacteristic, complemented, Sylow
114C22×D4C2×D4711yescharacteristic
115C23×C4C2×D4712yes—
116#125—944no—
117C4×D4—24no—
118C2×C4⋊C4—472no—
119C2×C4⋊C4—472no—
120C2×C4⋊C4—471no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4C2×D4711yescharacteristic
124C2×C22⋊C4—474no—
125C2×C22⋊C4—474no—
126C2×C22⋊C4C2×D4712yes—
127C2×C42—472no—
128C2×C42C2×D4711yescharacteristic
129#95—472no—
130#95—474no—
131#95—474no—
132C24C22×D4712yes—
133C2×D4—24no—
134C2×D4—22no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—474no—
139C22×C4—472no—
140C22×C4—472no—
141C22×C4C22×D4712yes—
142C22×C4C22×D4711yescharacteristic
143C22×C4C22×D4711yescharacteristic
144C22×C4C22×D4711yescharacteristic
145C4⋊C4—22no—
146C4⋊C4—944no—
147C4⋊C4—944no—
148C4⋊C4—944no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C22⋊C4—24no—
152C22⋊C4—948no—
153C22⋊C4—1884no—
154C42—1882no—
155C42C22⋊D4714yes—
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23#1062535014yes—
163C23C23×D4711yescharacteristic
164D4—28no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—48no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—944no—
175C2×C4—944no—
176C2×C4—944no—
177C2×C4—944no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4#1062535214yes—
181C2×C4C2×C22⋊D4712yes—
182C2×C4C2×C22⋊D4712yes—
183C2×C4C2×C22⋊D4712yes—
184C22—24no—
185C22—24no—
186C22—24no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D4711yescharacteristic
192C22C2×#1062535212yes—
193C22C2×#1062535012yes—
194C22#1309407011yescharacteristic
195C22#1309407111yescharacteristic
196C4—22no—
197C4—22no—
198C4—42no—
199C4—1884no—
200C4—1882no—
201C4—1882no—
202C4#1309401114yes—
203C2—44no—
204C2#1568963411yescharacteristic
205C2C2×#1309401111yescharacteristic
206C2#1568970111yescharacteristic
207C2#1568981312yes—
208C2#1568981912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×D4×C47C2
hypercenterC2×C4×D4D47
hypocenterC47#2562
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13094016C2semidirect
2. #15689061C2semidirect
4. #15689017C2semidirect
5. #15688983C2semidirect
6. #15688983C2semidirect
7. C4×C4⋊Dic47C2semidirect
113. C47#2562semidirect