Finite Group Databasebeta

← #20246527

Subgroups — #20246527

Order 6016.

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

normal subgroups only

This group has 688 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×#13093993C211yesmaximal, characteristic
2#15689023C213yesmaximal, complemented
3#15689017C213yesmaximal, complemented
4#15689011C213yesmaximal, complemented
5#15688999C213yesmaximal, complemented
6#15688979C211yesmaximal, characteristic, complemented
7C47×#379C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2213yes—
9C22×C4×D47C2211yescharacteristic, complemented
10#13093993C418yescomplemented
11C2×Dic47⋊C4C2213yescomplemented
12C2×C22⋊Dic47C2213yes—
13C2×C22⋊Dic47C2213yes—
14C2×C22⋊Dic47C2213yes—
15C2×(C2×D47)⋊C4C2213yescomplemented
16C2×C4×Dic47C2213yescomplemented
17C47⋊#95C2213yescomplemented
18C47⋊#95C2213yescomplemented
19C25×C47C2211yescharacteristic
20C2×C22⋊C4×C47C2213yes—
21C2×C22⋊C4×C47C2213yes—
22C24×C47—43no—
23C24×C47—43no—
24C24×C47C2×C414yescomplemented
25C24×C47C2313yes—
26C23×D47C2311yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C22×C4×C47C2313yes—
29C2×C22⋊D47—43no—
30C2×C22⋊D47—43no—
31C2×C22⋊D47C2×C4112yes—
32C22×Dic47C2311yescharacteristic
33C22×Dic47C2313yes—
34C22×Dic47C2313yes—
35C2×C4×D47—43no—
36C22⋊C4×C47—43no—
37C22⋊C4×C47—43no—
38C22⋊Dic47—43no—
39C22⋊Dic47—43no—
40C22⋊Dic47C2×C4112yescomplemented
41(C2×D47)⋊C4—43no—
42Dic47⋊C4—43no—
43C4×Dic47—43no—
44C23×C47—23no—
45C23×C47—23no—
46C23×C47—23no—
47C23×C47—23no—
48C23×C47—23no—
49C23×C47—23no—
50C23×C47—412no—
51C23×C47—412no—
52C23×C47—44no—
53C23×C47C22×C416yes—
54C23×C47C2411yescharacteristic
55C22×D47—23no—
56C22×D47—23no—
57C22×D47C22×C412yes—
58C2×C4×C47—23no—
59C2×C4×C47—23no—
60C2×C4×C47—23no—
61C2×C4×C47—23no—
62C22⋊D47—412no—
63C2×Dic47—23no—
64C2×Dic47—23no—
65C2×Dic47—23no—
66C2×Dic47—23no—
67C2×Dic47—23no—
68C2×Dic47—23no—
69C2×Dic47C22×C416yes—
70C4×D47—44no—
71C22×C47—26no—
72C22×C47—26no—
73C22×C47—26no—
74C22×C47—416no—
75C22×C47—43no—
76C22×C47—43no—
77C22×C47—43no—
78C22×C47—43no—
79C22×C47C23×C411yescharacteristic
80C22×C47H(5,𝔽2)13yes—
81C22×C47H(5,𝔽2)13yes—
82C2×D47—26no—
83C2×D47—43no—
84C2×D47—41no—
85C4×C47—43no—
86C4×C47—41no—
87Dic47—26no—
88Dic47—43no—
89Dic47—41no—
90#2375—471nomaximal, Sylow
91C2×C47—46no—
92C2×C47#51813yes—
93C2×C47#56013yes—
94C2×C47H(3,𝔽4)11yescharacteristic
95D47—42no—
96C2×#120—471no—
97#390—473no—
98#388—473no—
99#388—473no—
100#386—473no—
101#379—471no—
102#379D4711yescharacteristic, complemented
103C47#237511yescharacteristic, complemented, Sylow
104C25C2×D4711yescharacteristic
105C22×D4—473no—
106C23×C4—471no—
107#120—478no—
108C2×C4⋊C4—473no—
109C2×C22⋊C4—473no—
110C2×C22⋊C4—473no—
111C2×C22⋊C4—473no—
112C2×C22⋊C4—473no—
113C2×C22⋊C4C2×D4713yes—
114C2×C22⋊C4C2×D4713yes—
115C2×C42—473no—
116#95—473no—
117#95—473no—
118C24—43no—
119C24—43no—
120C24—471no—
121C24C4×D4714yescomplemented
122C24C22×D4713yes—
123C2×D4—4712no—
124C2×D4—1883no—
125C2×D4—1883no—
126C22×C4—473no—
127C22×C4—471no—
128C22×C4—473no—
129C22×C4—1883no—
130C22×C4C22×D4711yescharacteristic
131C22×C4C22×D4713yes—
132C4⋊C4—1883no—
133C22⋊C4—43no—
134C22⋊C4—43no—
135C22⋊C4—4712no—
136C22⋊C4—1883no—
137C22⋊C4—1883no—
138C22⋊C4—1883no—
139C42—1883no—
140C23—23no—
141C23—23no—
142C23—23no—
143C23—23no—
144C23—23no—
145C23—23no—
146C23—412no—
147C23—412no—
148C23—44no—
149C23—472no—
150C23—943no—
151C23—943no—
152C23C2×C4×D4716yes—
153C23C23×D4711yescharacteristic
154D4—18812no—
155C2×C4—23no—
156C2×C4—23no—
157C2×C4—23no—
158C2×C4—23no—
159C2×C4—476no—
160C2×C4—943no—
161C2×C4—943no—
162C2×C4—943no—
163C2×C4—943no—
164C2×C4—943no—
165C2×C4—943no—
166C2×C4—1884no—
167C22—26no—
168C22—26no—
169C22—26no—
170C22—416no—
171C22—43no—
172C22—43no—
173C22—43no—
174C22—43no—
175C22—946no—
176C22—1883no—
177C22—1881no—
178C22C22×C4×D4711yescharacteristic
179C22#1309406913yes—
180C22#1309406913yes—
181C4—43no—
182C4—41no—
183C4—946no—
184C4—1883no—
185C4—1881no—
186C2—46no—
187C2—1882no—
188C2#1568959613yes—
189C2#1568986213yes—
190C2#1568986611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#379C2
socleC23×C47C24
hypercenter#379D47
hypocenterC47#2375
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #15689023C2semidirect
3. #15689017C2semidirect
4. #15689011C2semidirect
5. #15688999C2semidirect
6. #15688979C2semidirect
7. C47×#379C2semidirect
9. C22×C4×D47C22semidirect
10. #13093993C4semidirect
11. C2×Dic47⋊C4C22semidirect
15. C2×(C2×D47)⋊C4C22semidirect
16. C2×C4×Dic47C22semidirect
17. C47⋊#95C22semidirect
18. C47⋊#95C22semidirect
24. C24×C47C2×C4semidirect
40. C22⋊Dic47C2×C4semidirect
102. #379D47semidirect
103. C47#2375semidirect
121. C24C4×D47semidirect