Finite Group Databasebeta

← #20248763

Subgroups — #20248763

Order 6016.

544 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 185 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×#13094003C211yesmaximal, characteristic
2C22×Dic47⋊C4C211yesmaximal, characteristic
3#15689055C212yesmaximal, complemented
4#15689044C212yesmaximal, complemented
5#15689021C214yesmaximal, complemented
6#15688998C212yesmaximal
7#15688998C212yesmaximal
8C4×C22⋊C4×C47C211yesmaximal, characteristic
9C22×Dic94C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12#13094003—24no—
13C2×C4⋊Dic47C2214yes—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2214yes—
16C2×Dic47⋊C4—24no—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×C22⋊Dic47C2212yes—
21C47⋊#95C2214yes—
22C47⋊#95C2214yes—
23C23×C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47C2212yes—
25C2×C42×C47C2212yes—
26#95×C47C2212yes—
27C24×C47C2311yescharacteristic
28C22×C4×C47—42no—
29C22×C4×C47D414yes—
30C22×C4×C47C2311yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C22×C4×C47C2314yes—
33C22×Dic47—22no—
34C22×Dic47—24no—
35C22×Dic47—22no—
36C22×Dic47—42no—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C2×Dic94—22no—
42C2×Dic94—42no—
43C22⋊C4×C47Q818yescomplemented
44C42×C47—42no—
45C22⋊Dic47—24no—
46C4⋊Dic47—22no—
47C4⋊Dic47—28no—
48C4⋊Dic47—44no—
49Dic47⋊C4—24no—
50Dic47⋊C4—24no—
51Dic47⋊C4—24no—
52C23×C47—22no—
53C23×C47—22no—
54C23×C47C2×D412yes—
55C23×C47C2×Q814yes—
56C23×C47C2411yescharacteristic
57C2×C4×C47—24no—
58C2×C4×C47—24no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—44no—
62C2×C4×C47C2×D412yes—
63C2×C4×C47C2×D412yes—
64C2×C4×C47C2×Q818yes—
65C2×Dic47—28no—
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—24no—
72C2×Dic47—24no—
73C2×Dic47—24no—
74C2×Dic47—44no—
75C2×Dic47#4114yes—
76Dic94—44no—
77C22×C47—22no—
78C22×C47—22no—
79C22×C47—28no—
80C22×C47C4⋊Q814yes—
81C22×C47C22×D411yescharacteristic
82C22×C47C22×Q812yes—
83C22×C47C2×#4112yes—
84C22×C47H(5,𝔽2)12yes—
85C4×C47—22no—
86C4×C47—22no—
87C4×C47—28no—
88Dic47—24no—
89Dic47—42no—
90Dic47—42no—
91Dic47—42no—
92#2583—471nomaximal, Sylow
93C2×C47—24no—
94C2×C47#52511yescharacteristic
95C2×C47C2×C4⋊Q811yescharacteristic
96C2×C47#53411yescharacteristic
97C2×C47#55414yes—
98C2×C22⋊Q8—471no—
99C22×C4⋊C4—471no—
100#398—472no—
101#395—472no—
102#389—474no—
103#385—472no—
104#385—472no—
105C4×C22⋊C4D4711yescharacteristic
106C47#258311yescharacteristic, complemented, Sylow
107C22×Q8—471no—
108C23×C4—471no—
109C23×C4—471no—
110C23×C4C2×D4711yescharacteristic
111C22⋊Q8—944no—
112C2×C4⋊C4—472no—
113C2×C4⋊C4—472no—
114C2×C4⋊C4—472no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4—474no—
117C2×C4⋊C4—474no—
118C2×C4⋊C4—944no—
119C2×C22⋊C4—472no—
120C2×C22⋊C4C2×D4712yes—
121C2×C42C2×D4712yes—
122#95—474no—
123#95—474no—
124#95C2×D4712yes—
125C24C22×D4711yescharacteristic
126C2×Q8—942no—
127C2×Q8—1882no—
128C22×C4—42no—
129C22×C4—472no—
130C22×C4—472no—
131C22×C4—472no—
132C22×C4—472no—
133C22×C4—944no—
134C22×C4—942no—
135C22×C4—942no—
136C22×C4—1882no—
137C22×C4D18814yes—
138C22×C4C22×D4714yes—
139C22×C4C22×D4711yescharacteristic
140C22×C4C22×D4711yescharacteristic
141C4⋊C4—948no—
142C4⋊C4—944no—
143C4⋊C4—944no—
144C4⋊C4—944no—
145C4⋊C4—942no—
146C4⋊C4—1884no—
147C22⋊C4—944no—
148C22⋊C4Dic9418yescomplemented
149C42—42no—
150C23—22no—
151C23—22no—
152C23C2×Dic9414yes—
153C23C2×D18812yes—
154C23C23×D4711yescharacteristic
155Q8—1884no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—474no—
162C2×C4—948no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4—944no—
169C2×C4—944no—
170C2×C4—944no—
171C2×C4—1884no—
172C2×C4C2×Dic9418yes—
173C2×C4C2×D18812yes—
174C2×C4C2×D18812yes—
175C22—28no—
176C22—22no—
177C22—22no—
178C22#1309402414yes—
179C22C22×D18811yescharacteristic
180C22C22×Dic9412yes—
181C22#41×D4712yes—
182C22#1309406912yes—
183C4—28no—
184C4—22no—
185C4—22no—
186C4—944no—
187C4—1882no—
188C4—1882no—
189C4—1882no—
190C2—24no—
191C2#1568963511yescharacteristic
192C2C2×#1309402411yescharacteristic
193C2#1568968511yescharacteristic
194C2#1568983214yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C22⋊C4×C47C2
hypercenterC4×C22⋊C4D47
hypocenterC47#2583
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #15689055C2semidirect
4. #15689044C2semidirect
5. #15689021C2semidirect
43. C22⋊C4×C47Q8semidirect
106. C47#2583semidirect
148. C22⋊C4Dic94semidirect