Finite Group Databasebeta

← #20251188

Subgroups — #20251188

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#15689053C212yesmaximal
2#15689044C212yesmaximal
3#15689043C211yesmaximal, characteristic
4#15689022C212yesmaximal
5#15689020C212yesmaximal
6#15689005C212yesmaximal
7#15689004C212yesmaximal
8#15688992C211yesmaximal, characteristic
9C47×#398C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2212yes—
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⋊#95C2211yescharacteristic
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29#95×C47C2212yes—
30#95×C47C2211yescharacteristic
31C22×C4×C47C2312yes—
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C2×Dic94—42no—
41C2×Dic94—41no—
42C4⋊C4×C47—24no—
43C4⋊C4×C47—41no—
44C4⋊C4×C47—41no—
45C4⋊Dic47—42no—
46C4⋊Dic47—41no—
47C4⋊Dic47—42no—
48Dic47⋊C4—42no—
49Dic47⋊C4—42no—
50Dic47⋊C4—42no—
51Dic47⋊C4Q818yescomplemented
52C4×Dic47—22no—
53C4×Dic47—42no—
54C23×C47C2411yescharacteristic
55C2×C4×C47—22no—
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—21no—
64C2×C4×C47—21no—
65C2×C4×C47—22no—
66C2×C4×C47C2×Q814yes—
67C2×C4×C47#4112yes—
68C2×Dic47—22no—
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×Dic47C2×Q814yes—
79C2×Dic47C2×Q814yes—
80Dic94—44no—
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—42no—
89C4×C47—41no—
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—472no—
102#398D4711yescharacteristic
103#395—471no—
104#395—472no—
105#389—472no—
106#389—472no—
107#387—472no—
108#387—472no—
109#384—471no—
110C47#279211yescharacteristic, complemented, Sylow
111C22×Q8—471no—
112C2×C4⋊C4—472no—
113C2×C4⋊C4—472no—
114C2×C4⋊C4—472no—
115C2×C4⋊C4—472no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4—472no—
118C2×C4⋊C4—472no—
119C2×C4⋊C4C2×D4712yes—
120C2×C4⋊C4C2×D4711yescharacteristic
121C2×C4⋊C4C2×D4711yescharacteristic
122C2×C42—471no—
123C2×C42—472no—
124#95—471no—
125#95—472no—
126#95—472no—
127#95—472no—
128#95—472no—
129#95—472no—
130#95C2×D4712yes—
131#95C2×D4711yescharacteristic
132C2×Q8—1881no—
133C2×Q8—1882no—
134C22×C4—472no—
135C22×C4—472no—
136C22×C4—472no—
137C22×C4—472no—
138C22×C4C22×D4712yes—
139C22×C4C22×D4711yescharacteristic
140C22×C4C22×D4711yescharacteristic
141C22×C4C22×D4711yescharacteristic
142C22×C4C22×D4712yes—
143C4⋊C4—24no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—478no—
147C4⋊C4—1882no—
148C4⋊C4—1882no—
149C4⋊C4—1882no—
150C4⋊C4—1881no—
151C4⋊C4—1882no—
152C4⋊C4—1882no—
153C42—942no—
154C42—1882no—
155C23C23×D4711yescharacteristic
156Q8—1884no—
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×C4#1062535212yes—
181C2×C4Q8×D4714yes—
182C22C2×Q8×D4712yes—
183C22C2×#1062535211yescharacteristic
184C22#1309406911yescharacteristic
185C22#1309407012yes—
186C22#1309407111yescharacteristic
187C4—24no—
188C4—22no—
189C4—41no—
190C4—41no—
191C4—42no—
192C4—944no—
193C4—944no—
194C4—1882no—
195C4—1882no—
196C2#1568971811yescharacteristic
197C2#1568975312yes—
198C2#1568983112yes—
199C2#1568985311yescharacteristic
200C2#1568986311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2792
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
51. Dic47⋊C4Q8semidirect
110. C47#2792semidirect