Finite Group Databasebeta

← #20246573

Subgroups — #20246573

Order 6016.

408 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13094016C211yesmaximal, characteristic
2#15689020C212yesmaximal
3#15689018C212yesmaximal
4#15689010C212yesmaximal
5#15689008C212yesmaximal
6#15689006C212yesmaximal
7#15689004C212yesmaximal
8#15688989C211yesmaximal, characteristic
9C47×#382C211yesmaximal, characteristic
10#13094016C418yescomplemented
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×C4×Dic47C2212yes—
20C2×C4×Dic47C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C42×C47C2211yescharacteristic
30#95×C47C2212yes—
31#95×C47C2212yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C4⋊C4×C47—41no—
42C4⋊C4×C47—41no—
43C42×C47C2×C414yes—
44C4⋊Dic47—41no—
45C4⋊Dic47—41no—
46C4⋊Dic47C2×C414yes—
47C4⋊Dic47C2×C414yes—
48Dic47⋊C4—42no—
49Dic47⋊C4—42no—
50Dic47⋊C4C2×C418yes—
51Dic47⋊C4C2×C418yes—
52C4×Dic47—42no—
53C4×Dic47—42no—
54C23×C47C2411yescharacteristic
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47C22×C412yes—
68C2×C4×C47C22×C412yes—
69C2×C4×C47C22×C412yes—
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×Dic47C22×C414yes—
81C2×Dic47C22×C414yes—
82C22×C47C23×C411yescharacteristic
83C22×C47H(5,𝔽2)11yescharacteristic
84C22×C47H(5,𝔽2)11yescharacteristic
85C22×C472−1+411yescharacteristic
86C22×C472−1+411yescharacteristic
87C22×C472−1+411yescharacteristic
88C22×C472−1+411yescharacteristic
89C4×C47—22no—
90C4×C47—22no—
91C4×C47—22no—
92C4×C47—42no—
93C4×C47—42no—
94Dic47—24no—
95Dic47—24no—
96Dic47—42no—
97Dic47—42no—
98#2382—471nomaximal, Sylow
99C2×C47#51911yescharacteristic
100C2×C47#52011yescharacteristic
101C2×C47#52011yescharacteristic
102C2×C47#56211yescharacteristic
103C2×C47#56311yescharacteristic
104C2×C47#56311yescharacteristic
105C2×C47#56411yescharacteristic
106C2×#125—471no—
107#389—472no—
108#389—472no—
109#387—472no—
110#387—472no—
111#387—472no—
112#387—472no—
113#382—471no—
114#382D4711yescharacteristic
115C47#238211yescharacteristic, complemented, Sylow
116#125—478no—
117C2×C4⋊C4—472no—
118C2×C4⋊C4—472no—
119C2×C4⋊C4—471no—
120C2×C4⋊C4—471no—
121C2×C4⋊C4—472no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—471no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4C2×D4711yescharacteristic
126C2×C4⋊C4C2×D4711yescharacteristic
127C2×C42—472no—
128C2×C42—472no—
129C2×C42C2×D4711yescharacteristic
130#95—472no—
131#95—472no—
132#95—472no—
133#95—472no—
134#95—472no—
135#95—472no—
136#95C2×D4712yes—
137#95C2×D4712yes—
138C22×C4—472no—
139C22×C4—472no—
140C22×C4—472no—
141C22×C4—472no—
142C22×C4C22×D4712yes—
143C22×C4C22×D4712yes—
144C22×C4C22×D4711yescharacteristic
145C22×C4C22×D4711yescharacteristic
146C22×C4C22×D4711yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—478no—
150C4⋊C4—478no—
151C4⋊C4—474no—
152C4⋊C4—474no—
153C4⋊C4—1882no—
154C4⋊C4—1882no—
155C4⋊C4—1881no—
156C4⋊C4—1881no—
157C42—1882no—
158C42—1882no—
159C42C4×D4714yes—
160C23C23×D4711yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—474no—
174C2×C4—474no—
175C2×C4—942no—
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×C4C2×C4×D4712yes—
186C2×C4C2×C4×D4712yes—
187C2×C4C2×C4×D4712yes—
188C22C22×C4×D4711yescharacteristic
189C22#1309406911yescharacteristic
190C22#1309407011yescharacteristic
191C22#1309407111yescharacteristic
192C22#1309407111yescharacteristic
193C22#1309407111yescharacteristic
194C22#1309407211yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—944no—
201C4—944no—
202C4—1882no—
203C4—1882no—
204C2#1568960011yescharacteristic
205C2#1568960311yescharacteristic
206C2#1568960411yescharacteristic
207C2#1568986711yescharacteristic
208C2#1568987311yescharacteristic
209C2#1568987711yescharacteristic
210C2C47⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#382C2
socleC23×C47C24
hypercenter#382D47
hypocenterC47#2382
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #13094016C4semidirect
115. C47#2382semidirect