Finite Group Databasebeta

← #20251573

Subgroups — #20251573

Order 6016.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C47⋊#401C212yesmaximal, complemented
2#15689059C211yesmaximal, characteristic
3#15689057C212yesmaximal, complemented
4#15689055C212yesmaximal, complemented
5#15689053C212yesmaximal, complemented
6#15689051C212yesmaximal
7#15688998C212yesmaximal
8#15688995C211yesmaximal, characteristic
9C47×#397C211yesmaximal, characteristic
10C23×Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C22⋊Dic47C2211yescharacteristic
18C2×C22⋊Dic47C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2212yes—
28C2×C22⋊C4×C47C2211yescharacteristic
29#95×C47C2212yes—
30#95×C47C2211yescharacteristic
31C24×C47C2311yescharacteristic
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×Dic47—42no—
37C22×Dic47—41no—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C4⋊C4×C47—41no—
43C22⋊C4×C47—24no—
44C22⋊C4×C47—41no—
45C22⋊Dic47—22no—
46C22⋊Dic47—42no—
47C4⋊Dic47—42no—
48C4⋊Dic47—41no—
49C4⋊Dic47—42no—
50Dic47⋊C4—42no—
51Dic47⋊C4—42no—
52Dic47⋊C4—42no—
53C23×C47—22no—
54C23×C47—21no—
55C23×C47—22no—
56C23×C47—21no—
57C23×C47#4112yes—
58C23×C47C2411yescharacteristic
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—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×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—44no—
82C22×C47—24no—
83C22×C47—22no—
84C22×C47—41no—
85C22×C47—41no—
86C22×C47—42no—
87C22×C47C2×#4111yescharacteristic
88C22×C47H(5,𝔽2)11yescharacteristic
89C22×C47H(5,𝔽2)12yes—
90C22×C472−1+412yes—
91C22×C472−1+411yescharacteristic
92C4×C47—42no—
93C4×C47—42no—
94C4×C47—41no—
95C4×C47—41no—
96Dic47—42no—
97Dic47—42no—
98Dic47—42no—
99Dic47—42no—
100#2834—471nomaximal, Sylow
101C2×C47—42no—
102C2×C47#53912yes—
103C2×C47#53911yescharacteristic
104C2×C47#56011yescharacteristic
105C2×C47#56311yescharacteristic
106C2×C47#56312yes—
107#401—472no—
108#399—471no—
109#398—472no—
110#398—472no—
111#398—472no—
112#397—472no—
113#397D4711yescharacteristic
114#385—471no—
115#385—472no—
116C47#283411yescharacteristic, complemented, Sylow
117C23×C4—471no—
118C2×C4⋊C4—472no—
119C2×C4⋊C4—472no—
120C2×C4⋊C4—472no—
121C2×C4⋊C4—472no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—471no—
124C2×C4⋊C4C2×D4711yescharacteristic
125C2×C22⋊C4—471no—
126C2×C22⋊C4—472no—
127C2×C22⋊C4C2×D4712yes—
128C2×C22⋊C4C2×D4711yescharacteristic
129#95—472no—
130#95—472no—
131#95—472no—
132#95—472no—
133#95—472no—
134#95—472no—
135#95—471no—
136#95C2×D4711yescharacteristic
137#95C2×D4712yes—
138C24C22×D4711yescharacteristic
139C22×C4—472no—
140C22×C4—472no—
141C22×C4—472no—
142C22×C4—472no—
143C22×C4—1881no—
144C22×C4—1882no—
145C22×C4C22×D4711yescharacteristic
146C22×C4C22×D4712yes—
147C22×C4C22×D4712yes—
148C22×C4C22×D4711yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—1882no—
151C4⋊C4—1882no—
152C4⋊C4—1882no—
153C4⋊C4—1881no—
154C4⋊C4—1882no—
155C4⋊C4—1882no—
156C22⋊C4—24no—
157C22⋊C4—41no—
158C22⋊C4—942no—
159C22⋊C4—1882no—
160C23—21no—
161C23—22no—
162C23—22no—
163C23—21no—
164C23#1062535212yes—
165C23C23×D4711yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—942no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—1884no—
189C22—24no—
190C22—22no—
191C22—41no—
192C22—41no—
193C22—42no—
194C22C2×#1062535211yescharacteristic
195C22#1309406911yescharacteristic
196C22#1309407012yes—
197C22#1309407112yes—
198C22#1309407111yescharacteristic
199C4—41no—
200C4—41no—
201C4—42no—
202C4—42no—
203C4—1882no—
204C4—1882no—
205C4—1882no—
206C4—1882no—
207C2—42no—
208C2#1568971712yes—
209C2#1568971811yescharacteristic
210C2#1568986311yescharacteristic
211C2#1568987311yescharacteristic
212C2#1568987512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2834
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C47⋊#401C2semidirect
3. #15689057C2semidirect
4. #15689055C2semidirect
5. #15689053C2semidirect
116. C47#2834semidirect