Finite Group Databasebeta

← #20249203

Subgroups — #20249203

Order 6016.

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

normal subgroups only

This group has 508 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
1C22×Dic47⋊C4C211yesmaximal, characteristic
2#15689061C212yesmaximal, complemented
3#15689056C214yesmaximal, complemented
4#15689042C212yesmaximal, complemented
5#15688995C212yesmaximal
6#15688984C212yesmaximal
7#15688983C211yesmaximal, characteristic
8C2×C22⋊Q8×C47C211yesmaximal, characteristic
9C23×Dic47C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2212yes—
12C2×Dic47⋊C4—24no—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2214yes—
16C2×C22⋊Dic47C2212yes—
17C47⋊#95C2212yes—
18C47⋊#95C2214yes—
19C47⋊#95C2214yes—
20C47⋊#95C2214yes—
21C22×Q8×C47C2211yescharacteristic
22C23×C4×C47C2211yescharacteristic
23C22⋊Q8×C47—24no—
24C2×C4⋊C4×C47C2212yes—
25C2×C4⋊C4×C47C2211yescharacteristic
26C2×C22⋊C4×C47C2212yes—
27C24×C47C2311yescharacteristic
28C2×Q8×C47—22no—
29C2×Q8×C47—42no—
30C22×C4×C47—42no—
31C22×C4×C47D414yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—22no—
37C22×Dic47—22no—
38C22×Dic47—22no—
39C22×Dic47—42no—
40C22×Dic47Q814yescomplemented
41C22×Dic47C2314yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C4⋊C4×C47—22no—
45C4⋊C4×C47—24no—
46C22⋊C4×C47—24no—
47C22⋊Dic47—24no—
48C4⋊Dic47—42no—
49Dic47⋊C4—24no—
50Dic47⋊C4—24no—
51Dic47⋊C4—44no—
52C23×C47—22no—
53C23×C47—22no—
54C23×C47C2×D412yes—
55C23×C47C2×Q812yes—
56C23×C47#4112yes—
57C23×C47C2411yescharacteristic
58Q8×C47—44no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—24no—
64C2×C4×C47—24no—
65C2×C4×C47—44no—
66C2×C4×C47C2×D412yes—
67C2×C4×C47C2×D412yes—
68C2×Dic47—28no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—24no—
73C2×Dic47—24no—
74C2×Dic47—24no—
75C2×Dic47—24no—
76C2×Dic47—44no—
77C2×Dic47C2×Q814yes—
78C22×C47—22no—
79C22×C47—22no—
80C22×C47—24no—
81C22×C47—24no—
82C22×C47C22⋊Q814yes—
83C22×C47C22×D411yescharacteristic
84C22×C47C22×Q811yescharacteristic
85C22×C47C2×#4111yescharacteristic
86C22×C47H(5,𝔽2)12yes—
87C22×C472−1+412yes—
88C4×C47—22no—
89C4×C47—22no—
90C4×C47—42no—
91C4×C47—42no—
92Dic47—24no—
93Dic47—42no—
94Dic47—44no—
95#2627—471nomaximal, Sylow
96C2×C47—24no—
97C2×C47C2×C22⋊Q811yescharacteristic
98C2×C47#53411yescharacteristic
99C2×C47#53611yescharacteristic
100C2×C47#53912yes—
101C2×C47#54412yes—
102C2×C22⋊Q8D4711yescharacteristic
103C22×C4⋊C4—471no—
104#400—472no—
105#398—474no—
106#395—472no—
107#385—472no—
108#381—472no—
109#380—471no—
110C47#262711yescharacteristic, complemented, Sylow
111C22×Q8C2×D4711yescharacteristic
112C23×C4—471no—
113C23×C4—471no—
114C23×C4C2×D4711yescharacteristic
115C22⋊Q8—24no—
116C2×C4⋊C4—472no—
117C2×C4⋊C4—472no—
118C2×C4⋊C4—474no—
119C2×C4⋊C4—472no—
120C2×C4⋊C4—944no—
121C2×C4⋊C4C2×D4712yes—
122C2×C4⋊C4C2×D4711yescharacteristic
123C2×C22⋊C4—472no—
124C2×C22⋊C4C2×D4712yes—
125#95—472no—
126#95—474no—
127#95—474no—
128#95—474no—
129C24C22×D4711yescharacteristic
130C2×Q8—22no—
131C2×Q8—42no—
132C22×C4—42no—
133C22×C4—474no—
134C22×C4—472no—
135C22×C4—474no—
136C22×C4—472no—
137C22×C4—942no—
138C22×C4—942no—
139C22×C4—942no—
140C22×C4—1882no—
141C22×C4C22⋊D4714yes—
142C22×C4C22×D4712yes—
143C22×C4C22×D4712yes—
144C22×C4C22×D4711yescharacteristic
145C22×C4C22×D4711yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—24no—
148C4⋊C4—944no—
149C4⋊C4—944no—
150C4⋊C4—1884no—
151C4⋊C4—1882no—
152C22⋊C4—24no—
153C22⋊C4—944no—
154C23—22no—
155C23—22no—
156C23Q8×D4712yes—
157C23#1062535412yes—
158C23C2×C22⋊D4712yes—
159C23C23×D4711yescharacteristic
160Q8—44no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—44no—
168C2×C4—474no—
169C2×C4—948no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—944no—
174C2×C4—944no—
175C2×C4—944no—
176C2×C4—944no—
177C2×C4—1884no—
178C2×C4C2×C22⋊D4712yes—
179C2×C4C2×C22⋊D4712yes—
180C22—24no—
181C22—22no—
182C22—22no—
183C22—24no—
184C22#1309400014yes—
185C22C22×C22⋊D4711yescharacteristic
186C22C2×Q8×D4711yescharacteristic
187C22C2×#1062535411yescharacteristic
188C22#1309406912yes—
189C22#1309407112yes—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—944no—
195C4—1882no—
196C4—1884no—
197C2—24no—
198C2C2×#1309400011yescharacteristic
199C2#1568968211yescharacteristic
200C2#1568969411yescharacteristic
201C2#1568972212yes—
202C2#1568975212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2627
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
3. #15689056C2semidirect
4. #15689042C2semidirect
40. C22×Dic47Q8semidirect
110. C47#2627semidirect