Finite Group Databasebeta

← #20251457

Subgroups — #20251457

Order 6016.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13094015C211yesmaximal, characteristic
2C2×#13094014C211yesmaximal, characteristic
3#15689064C212yesmaximal
4#15689061C211yesmaximal, characteristic
5#15689057C212yesmaximal
6#15689057C212yesmaximal
7#15689055C212yesmaximal
8#15689055C211yesmaximal, characteristic
9#15689053C211yesmaximal, characteristic
10#15688987C211yesmaximal, characteristic
11C47×#400C211yesmaximal, characteristic
12#13094015—24no—
13#13094014—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2212yes—
17C2×C4⋊Dic47C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2212yes—
24C2×Dic47⋊C4C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2212yes—
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C4⋊C4×C47—22no—
49C4⋊C4×C47—22no—
50C4⋊Dic47—22no—
51C4⋊Dic47—22no—
52C4⋊Dic47—24no—
53C4⋊Dic47—42no—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—24no—
59Dic47⋊C4—42no—
60Dic47⋊C4—42no—
61C4×Dic47D414yes—
62C23×C47C2411yescharacteristic
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—24no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47C2×D412yes—
75C2×Dic47—21no—
76C2×Dic47—22no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D412yes—
91C22×C47C22×D411yescharacteristic
92C22×C47H(5,𝔽2)11yescharacteristic
93C22×C472−1+412yes—
94C22×C472−1+412yes—
95C22×C472−1+411yescharacteristic
96C4×C47—22no—
97C4×C47—42no—
98C4×C47—41no—
99C4×C47—41no—
100C4×C47—42no—
101Dic47—22no—
102Dic47—22no—
103Dic47—41no—
104Dic47—41no—
105Dic47—42no—
106Dic47—42no—
107#2822—471nomaximal, Sylow
108C2×C47#53611yescharacteristic
109C2×C47#53611yescharacteristic
110C2×C47#53711yescharacteristic
111C2×C47#56312yes—
112C2×C47#56412yes—
113C2×#125—471no—
114C2×#125—471no—
115#400—471no—
116#400—472no—
117#400D4711yescharacteristic
118#398—471no—
119#398—471no—
120#398—472no—
121#398—472no—
122#398—472no—
123#382—471no—
124C47#282211yescharacteristic, complemented, Sylow
125#125—944no—
126#125—944no—
127C2×C4⋊C4—471no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4—471no—
131C2×C4⋊C4—471no—
132C2×C4⋊C4—471no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—471no—
135C2×C4⋊C4—472no—
136C2×C4⋊C4—472no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C4⋊C4C2×D4711yescharacteristic
140C2×C42—471no—
141#95—472no—
142#95—471no—
143#95—472no—
144#95—472no—
145#95—472no—
146#95—472no—
147#95C2×D4711yescharacteristic
148#95C2×D4712yes—
149#95C2×D4712yes—
150C22×C4—471no—
151C22×C4—471no—
152C22×C4—472no—
153C22×C4—471no—
154C22×C4—471no—
155C22×C4—472no—
156C22×C4C22×D4712yes—
157C22×C4C22×D4711yescharacteristic
158C22×C4C22×D4712yes—
159C22×C4C22×D4711yescharacteristic
160C22×C4C22×D4711yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—942no—
166C4⋊C4—944no—
167C4⋊C4—942no—
168C4⋊C4—944no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C4⋊C4—1882no—
172C4⋊C4—1882no—
173C4⋊C4—1882no—
174C42—474no—
175C23C23×D4711yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—472no—
188C2×C4—472no—
189C2×C4—941no—
190C2×C4—942no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—941no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—941no—
202C2×C4—942no—
203C2×C4D4×D4712yes—
204C22C2×D4×D4711yescharacteristic
205C22#1309407011yescharacteristic
206C22#1309407112yes—
207C22#1309407112yes—
208C22#1309407211yescharacteristic
209C4—22no—
210C4—42no—
211C4—42no—
212C4—41no—
213C4—41no—
214C4—942no—
215C4—942no—
216C4—1882no—
217C4—1881no—
218C4—1881no—
219C4—1882no—
220C2#1568969311yescharacteristic
221C2#1568969511yescharacteristic
222C2#1568970311yescharacteristic
223C2#1568987512yes—
224C2C47⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2822
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
124. C47#2822semidirect