Finite Group Databasebeta

← #20246189

Subgroups — #20246189

Order 6016.

428 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 177 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#15689010C212yesmaximal
4#15689008C212yesmaximal
5#15689006C212yesmaximal
6#15689005C212yesmaximal
7C4×C4⋊Dic47C211yesmaximal, characteristic
8#15688974C212yesmaximal
9C47×#383C211yesmaximal, characteristic
10#13094016C418yescomplemented
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C4×Dic47C2212yes—
19C2×C4×Dic47C2211yescharacteristic
20C2×C4×Dic47C2212yes—
21C2×C4×Dic47C2211yescharacteristic
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C2×C42×C47C2211yescharacteristic
28#95×C47C2212yes—
29#95×C47C2212yes—
30#95×C47C2211yescharacteristic
31#95×C47C2211yescharacteristic
32C22×C4×C47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C42×C47C2×C414yes—
42C4⋊Dic47—24no—
43C4⋊Dic47C2×C414yes—
44C4⋊Dic47C2×C414yes—
45Dic47⋊C4—24no—
46Dic47⋊C4—42no—
47Dic47⋊C4C2×C418yes—
48Dic47⋊C4C2×C418yes—
49C4×Dic47—24no—
50C4×Dic47—41no—
51C4×Dic47—42no—
52C4×Dic47—41no—
53C23×C47C2411yescharacteristic
54C2×C4×C47—22no—
55C2×C4×C47—21no—
56C2×C4×C47—22no—
57C2×C4×C47—21no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47C22×C412yes—
65C2×C4×C47C22×C412yes—
66C2×C4×C47C22×C412yes—
67C2×Dic47—22no—
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×Dic47C22×C414yes—
77C2×Dic47C22×C414yes—
78C2×Dic47#4114yes—
79C22×C47C23×C411yescharacteristic
80C22×C47C2×#4112yes—
81C22×C47H(5,𝔽2)11yescharacteristic
82C22×C472−1+412yes—
83C22×C472−1+411yescharacteristic
84C4×C47—22no—
85C4×C47—22no—
86C4×C47—22no—
87C4×C47—42no—
88C4×C47—42no—
89Dic47—24no—
90Dic47—24no—
91Dic47—24no—
92Dic47—42no—
93#2336—471nomaximal, Sylow
94C2×C47C4×#4111yescharacteristic
95C2×C47#51911yescharacteristic
96C2×C47#52011yescharacteristic
97C2×C47#53912yes—
98C2×C47#54112yes—
99C2×#125—471no—
100#389—472no—
101#387—472no—
102#387—472no—
103#387—472no—
104#387—472no—
105#383D4711yescharacteristic
106C4×C4⋊C4—471no—
107C4×C4⋊C4—472no—
108C47#233611yescharacteristic, complemented, Sylow
109#125—478no—
110C2×C4⋊C4—472no—
111C2×C4⋊C4—472no—
112C2×C4⋊C4—471no—
113C2×C4⋊C4—471no—
114C2×C4⋊C4—472no—
115C2×C4⋊C4—472no—
116C2×C4⋊C4—472no—
117C2×C42—472no—
118C2×C42—471no—
119C2×C42—471no—
120C2×C42—472no—
121C2×C42C2×D4711yescharacteristic
122#95—472no—
123#95—472no—
124#95—472no—
125#95—472no—
126#95—472no—
127#95C2×D4712yes—
128#95C2×D4711yescharacteristic
129#95C2×D4712yes—
130#95C2×D4711yescharacteristic
131C22×C4—472no—
132C22×C4—472no—
133C22×C4—472no—
134C22×C4—472no—
135C22×C4C22×D4712yes—
136C22×C4C22×D4712yes—
137C22×C4C22×D4711yescharacteristic
138C22×C4C22×D4711yescharacteristic
139C22×C4C22×D4711yescharacteristic
140C4⋊C4—478no—
141C4⋊C4—478no—
142C4⋊C4—474no—
143C4⋊C4—474no—
144C4⋊C4—944no—
145C4⋊C4—944no—
146C4⋊C4—1882no—
147C42—944no—
148C42—1881no—
149C42—1881no—
150C42—1882no—
151C42C4×D4714yes—
152C23C23×D4711yescharacteristic
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—474no—
164C2×C4—474no—
165C2×C4—474no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4C2×C4×D4712yes—
176C2×C4C2×C4×D4712yes—
177C2×C4C2×C4×D4712yes—
178C22C22×C4×D4711yescharacteristic
179C22#41×D4712yes—
180C22#1309407011yescharacteristic
181C22#1309407111yescharacteristic
182C22#1309407112yes—
183C4—22no—
184C4—22no—
185C4—22no—
186C4—42no—
187C4—42no—
188C4—944no—
189C4—944no—
190C4—944no—
191C4—1882no—
192C2#1568959111yescharacteristic
193C2#1568960011yescharacteristic
194C2#1568960311yescharacteristic
195C2#1568971412yes—
196C2#1568973012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#383C2
socleC23×C47C24
hypercenter#383D47
hypocenterC47#2336
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
10. #13094016C4semidirect
108. C47#2336semidirect