Finite Group Databasebeta

← #20248584

Subgroups — #20248584

Order 6016.

548 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 169 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#15689046C214yesmaximal, complemented
3#15689026C211yesmaximal, characteristic
4#15689026C211yesmaximal, characteristic
5#15688996C214yesmaximal, complemented
6#15688992C211yesmaximal, characteristic, complemented
7#15688988C211yesmaximal, characteristic, complemented
8C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
9C2×C4×D4×C47C211yesmaximal, characteristic
10#13094016—24no—
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2214yes—
17C2×C22⋊Dic47C2214yes—
18C2×C22⋊Dic47C2214yes—
19C2×C4×Dic47C2211yescharacteristic
20C2×C4×Dic47C2211yescharacteristic
21C47⋊#95C2212yes—
22C47⋊#95C2214yes—
23C22×D4×C47C2211yescharacteristic
24C23×C4×C47C2212yes—
25C4×D4×C47—24no—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2212yes—
28C2×C42×C47C2211yescharacteristic
29C24×C47C2312yes—
30C2×D4×C47—22no—
31C2×D4×C47—22no—
32C2×D4×C47Q814yes—
33C22×C4×C47—24no—
34C22×C4×C47—44no—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C4⋊C4×C47—22no—
44C22⋊C4×C47—24no—
45C42×C47D414yes—
46C22⋊Dic47—28no—
47C22⋊Dic47—44no—
48C4⋊Dic47—22no—
49C4⋊Dic47—22no—
50C4⋊Dic47—24no—
51Dic47⋊C4—24no—
52Dic47⋊C4—24no—
53Dic47⋊C4—44no—
54C4×Dic47—22no—
55C4×Dic47—22no—
56C23×C47—22no—
57C23×C47—24no—
58C23×C47—22no—
59C23×C47—24no—
60C23×C47C2×Q814yes—
61C23×C47C2411yescharacteristic
62D4×C47—28no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—24no—
67C2×C4×C47—48no—
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×Q812yes—
72C2×C4×C47#4112yes—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—24no—
80C2×Dic47—24no—
81C2×Dic47—22no—
82C2×Dic47#4114yes—
83C22×C47—24no—
84C22×C47—28no—
85C22×C47—42no—
86C22×C47—42no—
87C22×C47—44no—
88C22×C47C22×D411yescharacteristic
89C22×C47C22×Q811yescharacteristic
90C22×C47C2×#4112yes—
91C22×C47C2×#4111yescharacteristic
92C22×C47H(5,𝔽2)12yes—
93C4×C47—22no—
94C4×C47—22no—
95C4×C47—42no—
96C4×C47C22⋊Q814yes—
97Dic47—24no—
98Dic47—42no—
99Dic47—42no—
100Dic47—42no—
101#2566—471nomaximal, Sylow
102C2×C47—44no—
103C2×C47C2×C22⋊Q811yescharacteristic
104C2×C47#53211yescharacteristic
105C2×C47#53511yescharacteristic
106C2×C47#55312yes—
107C2×C47#55412yes—
108C2×#125—471no—
109C2×C4×D4D4711yescharacteristic
110#396—474no—
111#390—471no—
112#390—471no—
113#385—474no—
114#384—471no—
115#382—471no—
116C4×C4⋊C4—471no—
117C47#256611yescharacteristic, complemented, Sylow
118C22×D4C2×D4711yescharacteristic
119C23×C4C2×D4712yes—
120#125—944no—
121C4×D4—24no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4—471no—
126C2×C4⋊C4—472no—
127C2×C4⋊C4—474no—
128C2×C4⋊C4C2×D4711yescharacteristic
129C2×C22⋊C4—474no—
130C2×C22⋊C4—474no—
131C2×C22⋊C4C2×D4712yes—
132C2×C42—471no—
133C2×C42—471no—
134C2×C42C2×D4711yescharacteristic
135#95—472no—
136#95—474no—
137C24C22×D4712yes—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4Dic9414yes—
141C22×C4—24no—
142C22×C4—44no—
143C22×C4—472no—
144C22×C4—472no—
145C22×C4—472no—
146C22×C4—472no—
147C22×C4C22×D4712yes—
148C22×C4C22×D4711yescharacteristic
149C22×C4C22×D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—944no—
153C4⋊C4—944no—
154C4⋊C4—944no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4—1884no—
158C22⋊C4—24no—
159C22⋊C4—948no—
160C22⋊C4—1884no—
161C42—942no—
162C42—942no—
163C42C22⋊D4714yes—
164C23—22no—
165C23—24no—
166C23—22no—
167C23—24no—
168C23C2×Dic9414yes—
169C23C23×D4711yescharacteristic
170D4—28no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—48no—
176C2×C4—474no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—944no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—944no—
186C2×C4C2×Dic9412yes—
187C2×C4#1062535012yes—
188C2×C4C2×C22⋊D4712yes—
189C2×C4C2×C22⋊D4712yes—
190C2×C4C2×C22⋊D4712yes—
191C22—28no—
192C22—24no—
193C22—44no—
194C22—42no—
195C22—42no—
196C22C22×C22⋊D4711yescharacteristic
197C22C22×Dic9411yescharacteristic
198C22#41×D4712yes—
199C22C2×#1062535011yescharacteristic
200C22#1309406912yes—
201C4—22no—
202C4—22no—
203C4—42no—
204C4—944no—
205C4—1882no—
206C4—1882no—
207C4—1882no—
208C4#1309400314yes—
209C2—44no—
210C2C2×#1309400311yescharacteristic
211C2#1568966911yescharacteristic
212C2#1568969011yescharacteristic
213C2#1568982312yes—
214C2#1568983212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×D4×C47C2
hypercenterC2×C4×D4D47
hypocenterC47#2566
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. #15689046C2semidirect
5. #15688996C2semidirect
6. #15688992C2semidirect
7. #15688988C2semidirect
8. C4×C4⋊Dic47C2semidirect
117. C47#2566semidirect