Finite Group Databasebeta

← #20250340

Subgroups — #20250340

Order 6016.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094014C212yesmaximal
2#15689055C212yesmaximal
3#15689053C212yesmaximal
4#15689053C212yesmaximal
5#15689022C212yesmaximal
6#15689021C211yesmaximal, characteristic
7#15689021C211yesmaximal, characteristic
8#15689008C212yesmaximal
9C47×#389C211yesmaximal, characteristic
10#13094014—28no—
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×C4×Dic47C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C42×C47C2211yescharacteristic
31#95×C47C2212yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C4⋊C4×C47—24no—
42C4⋊C4×C47—41no—
43C4⋊C4×C47D414yes—
44C42×C47—41no—
45C4⋊Dic47—24no—
46C4⋊Dic47—22no—
47C4⋊Dic47—41no—
48C4⋊Dic47—41no—
49C4⋊Dic47—42no—
50C4⋊Dic47Q814yes—
51Dic47⋊C4—24no—
52Dic47⋊C4—24no—
53Dic47⋊C4—24no—
54Dic47⋊C4—24no—
55C4×Dic47—24no—
56C23×C47C2411yescharacteristic
57C2×C4×C47—22no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47C2×D414yes—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×Q812yes—
71C2×C4×C47#4112yes—
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—22no—
82C2×Dic47—22no—
83C2×Dic47C2×Q814yes—
84C22×C47C22×D411yescharacteristic
85C22×C47C22×Q811yescharacteristic
86C22×C47C2×#4111yescharacteristic
87C22×C47H(5,𝔽2)11yescharacteristic
88C22×C472−1+411yescharacteristic
89C22×C472−1+411yescharacteristic
90C22×C472−1+411yescharacteristic
91C4×C47—22no—
92C4×C47—22no—
93C4×C47—22no—
94C4×C47—24no—
95C4×C47—42no—
96Dic47—24no—
97Dic47—42no—
98Dic47—42no—
99Dic47—42no—
100#2726—471nomaximal, Sylow
101C2×C47#53711yescharacteristic
102C2×C47#53911yescharacteristic
103C2×C47#54411yescharacteristic
104C2×C47#54711yescharacteristic
105C2×C47D4×Q811yescharacteristic
106C2×C47#55711yescharacteristic
107C2×C47#56411yescharacteristic
108C2×#125—472no—
109#398—472no—
110#398—472no—
111#398—472no—
112#389—472no—
113#389—471no—
114#389—471no—
115#389D4711yescharacteristic
116#387—472no—
117C47#272611yescharacteristic, complemented, Sylow
118#125—948no—
119C2×C4⋊C4—471no—
120C2×C4⋊C4—472no—
121C2×C4⋊C4—472no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—471no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4—472no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4C2×D4712yes—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C42—472no—
133C2×C42C2×D4711yescharacteristic
134#95—472no—
135#95—472no—
136#95—472no—
137#95—472no—
138#95—472no—
139#95C2×D4712yes—
140C22×C4—472no—
141C22×C4—472no—
142C22×C4—472no—
143C22×C4—472no—
144C22×C4C22×D4712yes—
145C22×C4C22×D4712yes—
146C22×C4C22×D4711yescharacteristic
147C22×C4C22×D4711yescharacteristic
148C22×C4C22×D4711yescharacteristic
149C4⋊C4—24no—
150C4⋊C4—41no—
151C4⋊C4—474no—
152C4⋊C4—944no—
153C4⋊C4—944no—
154C4⋊C4—944no—
155C4⋊C4—944no—
156C4⋊C4—944no—
157C4⋊C4—942no—
158C4⋊C4—1881no—
159C4⋊C4—1881no—
160C4⋊C4—1882no—
161C4⋊C4D18814yes—
162C42—41no—
163C42—944no—
164C23C23×D4711yescharacteristic
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—474no—
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×C4C2×D18814yes—
189C2×C4C2×D18812yes—
190C2×C4#1062535212yes—
191C2×C4Q8×D4712yes—
192C22C22×D18811yescharacteristic
193C22C2×Q8×D4711yescharacteristic
194C22C2×#1062535211yescharacteristic
195C22#1309406911yescharacteristic
196C22#1309407111yescharacteristic
197C22#1309407111yescharacteristic
198C22#1309407211yescharacteristic
199C4—22no—
200C4—24no—
201C4—22no—
202C4—22no—
203C4—42no—
204C4—944no—
205C4—1882no—
206C4—1882no—
207C4—1882no—
208C2#1568970411yescharacteristic
209C2#1568971811yescharacteristic
210C2#1568975211yescharacteristic
211C2#1568977711yescharacteristic
212C2Q8×D18811yescharacteristic
213C2#1568984811yescharacteristic
214C2C47⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2726
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
117. C47#2726semidirect