Finite Group Databasebeta

← #20251189

Subgroups — #20251189

Order 6016.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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
1#15689056C212yesmaximal
2#15689053C211yesmaximal, characteristic
3#15689042C212yesmaximal
4#15689020C212yesmaximal
5#15689019C212yesmaximal
6#15689008C212yesmaximal
7#15689006C212yesmaximal
8#15688992C211yesmaximal, characteristic
9C47×#395C211yesmaximal, characteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C4×Dic47C2211yescharacteristic
19C2×C4×Dic47C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C22×Q8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2212yes—
29#95×C47C2211yescharacteristic
30#95×C47C2212yes—
31C2×Q8×C47—41no—
32C2×Q8×C47—42no—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×C4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C4⋊C4×C47—42no—
43C4⋊C4×C47—41no—
44C4⋊Dic47—41no—
45C4⋊Dic47—41no—
46C4⋊Dic47Q818yescomplemented
47Dic47⋊C4—24no—
48Dic47⋊C4—42no—
49Dic47⋊C4—42no—
50Dic47⋊C4—42no—
51Dic47⋊C4—42no—
52C4×Dic47—22no—
53C4×Dic47—42no—
54C23×C47C2411yescharacteristic
55Q8×C47—44no—
56C2×C4×C47—22no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47C2×Q814yes—
68C2×C4×C47#4112yes—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47C2×Q814yes—
80C2×Dic47C2×Q814yes—
81C22×C47C22×Q812yes—
82C22×C47C2×#4111yescharacteristic
83C22×C47H(5,𝔽2)11yescharacteristic
84C22×C47H(5,𝔽2)12yes—
85C22×C472−1+411yescharacteristic
86C4×C47—22no—
87C4×C47—24no—
88C4×C47—41no—
89C4×C47—42no—
90C4×C47—41no—
91Dic47—24no—
92Dic47—24no—
93Dic47—42no—
94Dic47—42no—
95#2792—471nomaximal, Sylow
96C2×C47#53911yescharacteristic
97C2×C47#54412yes—
98C2×C47#55412yes—
99C2×C47Q8211yescharacteristic
100C2×C47#56011yescharacteristic
101#398—471no—
102#398—472no—
103#395—472no—
104#395D4711yescharacteristic
105#389—472no—
106#389—472no—
107#387—472no—
108#387—472no—
109#384—471no—
110C47#279211yescharacteristic, complemented, Sylow
111C22×Q8C2×D4711yescharacteristic
112C2×C4⋊C4—472no—
113C2×C4⋊C4—472no—
114C2×C4⋊C4—472no—
115C2×C4⋊C4—472no—
116C2×C4⋊C4—472no—
117C2×C4⋊C4—472no—
118C2×C4⋊C4—471no—
119C2×C4⋊C4—471no—
120C2×C4⋊C4C2×D4711yescharacteristic
121C2×C4⋊C4C2×D4712yes—
122C2×C42—471no—
123C2×C42—472no—
124#95—472no—
125#95—472no—
126#95—472no—
127#95—472no—
128#95—472no—
129#95—471no—
130#95C2×D4711yescharacteristic
131#95C2×D4712yes—
132C2×Q8—42no—
133C2×Q8—41no—
134C22×C4—472no—
135C22×C4—472no—
136C22×C4—472no—
137C22×C4—472no—
138C22×C4C22×D4712yes—
139C22×C4C22×D4711yescharacteristic
140C22×C4C22×D4711yescharacteristic
141C22×C4C22×D4712yes—
142C22×C4C22×D4711yescharacteristic
143C4⋊C4—42no—
144C4⋊C4—41no—
145C4⋊C4—478no—
146C4⋊C4—944no—
147C4⋊C4—1882no—
148C4⋊C4—1882no—
149C4⋊C4—1882no—
150C4⋊C4—1882no—
151C4⋊C4—1881no—
152C4⋊C4—1881no—
153C42—942no—
154C42—1882no—
155C23C23×D4711yescharacteristic
156Q8—44no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—474no—
169C2×C4—474no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4Q8×D4714yes—
181C2×C4#1062535412yes—
182C22C2×Q8×D4712yes—
183C22C2×#1062535411yescharacteristic
184C22#1309406912yes—
185C22#1309406911yescharacteristic
186C22#1309407111yescharacteristic
187C4—24no—
188C4—22no—
189C4—42no—
190C4—41no—
191C4—41no—
192C4—944no—
193C4—944no—
194C4—1882no—
195C4—1882no—
196C2#1568972211yescharacteristic
197C2#1568975212yes—
198C2#1568983412yes—
199C2#1568985311yescharacteristic
200C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2792
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
46. C4⋊Dic47Q8semidirect
110. C47#2792semidirect