Finite Group Databasebeta

← #20245968

Subgroups — #20245968

Order 6016.

1104 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 269 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
1C23×D188C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic, complemented
3#15689025C214yesmaximal, complemented
4#15689024C214yesmaximal, complemented
5#15688978C214yesmaximal, complemented
6C2×#117×C47C211yesmaximal, characteristic, complemented
7C24×D47C2212yes—
8C22×D188—24no—
9C22×D188—24no—
10C22×D188C418yescomplemented
11C22×D188C2212yes—
12C22×D188C2212yes—
13#13093983—24no—
14C2×C4⋊Dic47C2212yescomplemented
15C2×C22⋊Dic47C2212yes—
16C2×(C2×D47)⋊C4C22116yescomplemented
17C2×C4×Dic47C2212yescomplemented
18C23×C4×C47C2211yescharacteristic
19#117×C47—24no—
20C2×C4⋊C4×C47C2212yescomplemented
21C2×C22⋊C4×C47C2212yes—
22C2×C42×C47C2212yescomplemented
23C24×C47C2311yescharacteristic
24C23×D47—24no—
25C23×D47—24no—
26C23×D47—48no—
27C23×D47C2×C418yes—
28C23×D47C2314yes—
29C22×C4×C47C2×C414yes—
30C22×C4×C47D414yes—
31C22×C4×C47D414yes—
32C22×C4×C47C2314yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×Dic47C2314yes—
36C2×D188—232no—
37C2×D188—24no—
38C2×D188—24no—
39C2×D188—24no—
40C2×D188—24no—
41C2×D188C2×C418yes—
42C2×D188C2×C418yes—
43C4⋊C4×C47—24no—
44C22⋊C4×C47—24no—
45C42×C47—24no—
46C22⋊Dic47—24no—
47(C2×D47)⋊C4—416no—
48C4⋊Dic47—24no—
49C4×Dic47—24no—
50C23×C47—24no—
51C23×C47C22×C412yes—
52C23×C47C2×D412yes—
53C23×C47C2×D412yes—
54C23×C47C2411yescharacteristic
55C22×D47—216no—
56C22×D47—24no—
57C22×D47—24no—
58C22×D47—216no—
59C22×D47—416no—
60C22×D47—416no—
61C22×D47—416no—
62C22×D47C22×C418yes—
63C2×C4×C47—24no—
64C2×C4×C47—28no—
65C2×C4×C47C22⋊C4116yescomplemented
66C2×C4×C47C22×C412yes—
67C2×C4×C47C22×C412yes—
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D412yes—
72C2×Dic47—24no—
73C2×Dic47—28no—
74D188—216no—
75D188—216no—
76C22×C47—24no—
77C22×C47—24no—
78C22×C47—24no—
79C22×C47C2×C22⋊C414yes—
80C22×C47C23×C411yescharacteristic
81C22×C47C22×D411yescharacteristic
82C22×C47C22×D411yescharacteristic
83C22×C47H(5,𝔽2)14yes—
84C2×D47—28no—
85C2×D47—216no—
86C2×D47—432no—
87C2×D47—48no—
88C2×D47—48no—
89C4×C47—44no—
90C4×C47C2×C22⋊C414yes—
91C4×C47C2×C22⋊C414yes—
92Dic47—44no—
93#2309—471nomaximal, Sylow
94C2×C47—24no—
95C2×C47C22×C22⋊C411yescharacteristic
96C2×C47#51812yes—
97C2×C47#53512yes—
98C2×C47#53512yes—
99D47—48no—
100C23×D4—471no—
101C2×#117—471no—
102C2×#117D4711yescharacteristic, complemented
103#390—474no—
104#390—474no—
105#379—474no—
106C47#230911yescharacteristic, complemented, Sylow
107C25—472no—
108C22×D4—478no—
109C22×D4—472no—
110C22×D4—472no—
111C22×D4—944no—
112C22×D4—944no—
113C23×C4C2×D4711yescharacteristic
114#117—24no—
115#117—944no—
116C2×C4⋊C4—472no—
117C2×C4⋊C4C2×D4712yescomplemented
118C2×C22⋊C4—472no—
119C2×C22⋊C4—4716no—
120C2×C22⋊C4C2×D4712yes—
121C2×C42—472no—
122C2×C42C2×D4712yescomplemented
123C24—474no—
124C24—478no—
125C24—944no—
126C24—944no—
127C24—1888no—
128C24C22×D4711yescharacteristic
129C2×D4—478no—
130C2×D4—478no—
131C2×D4—9432no—
132C2×D4—944no—
133C2×D4—944no—
134C2×D4—944no—
135C2×D4—944no—
136C22×C4—474no—
137C22×C4C4×D4714yes—
138C22×C4D18814yes—
139C22×C4C22⋊D4714yes—
140C22×C4C22×D4714yes—
141C22×C4C22×D4711yescharacteristic
142C22×C4C22×D4711yescharacteristic
143C4⋊C4—24no—
144C4⋊C4—944no—
145C22⋊C4—24no—
146C22⋊C4—944no—
147C22⋊C4—18816no—
148C42—24no—
149C42—944no—
150C23—24no—
151C23—478no—
152C23—9416no—
153C23—944no—
154C23—944no—
155C23—9416no—
156C23—18816no—
157C23—18816no—
158C23—18816no—
159C23C2×C4×D4712yes—
160C23C2×D18812yes—
161C23C2×C22⋊D4712yes—
162C23C23×D4711yescharacteristic
163D4—9416no—
164D4—9416no—
165C2×C4—24no—
166C2×C4—28no—
167C2×C4—944no—
168C2×C4—948no—
169C2×C4(C2×D47)⋊C4116yescomplemented
170C2×C4C2×C4×D4712yes—
171C2×C4C2×C4×D4712yes—
172C2×C4C2×D18812yes—
173C2×C4C2×D18812yes—
174C2×C4C2×C22⋊D4712yes—
175C2×C4C2×C22⋊D4712yes—
176C22—24no—
177C22—24no—
178C22—24no—
179C22—948no—
180C22—9416no—
181C22—18832no—
182C22—1888no—
183C22—1888no—
184C22C2×(C2×D47)⋊C414yes—
185C22C22×C4×D4711yescharacteristic
186C22C22×C22⋊D4711yescharacteristic
187C22C22×D18811yescharacteristic
188C22#1309407014yes—
189C4—44no—
190C4—1884no—
191C4C2×(C2×D47)⋊C414yes—
192C4C2×(C2×D47)⋊C414yes—
193C2—24no—
194C2—1888no—
195C2C22×(C2×D47)⋊C411yescharacteristic
196C2#1568959712yes—
197C2#1568968712yes—
198C2#1568969212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC2×#117×C47C2
socleC23×C47C24
hypercenterC2×#117D47
hypocenterC47#2309
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#13093983C2semidirect
3. #15689025C2semidirect
4. #15689024C2semidirect
5. #15688978C2semidirect
6. C2×#117×C47C2semidirect
10. C22×D188C4semidirect
14. C2×C4⋊Dic47C22semidirect
16. C2×(C2×D47)⋊C4C22semidirect
17. C2×C4×Dic47C22semidirect
20. C2×C4⋊C4×C47C22semidirect
22. C2×C42×C47C22semidirect
65. C2×C4×C47C22⋊C4semidirect
102. C2×#117D47semidirect
106. C47#2309semidirect
117. C2×C4⋊C4C2×D47semidirect
122. C2×C42C2×D47semidirect
169. C2×C4(C2×D47)⋊C4semidirect