Finite Group Databasebeta

← #20244793

Subgroups — #20244793

Order 6016.

274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13093946C212yesmaximal
2#15689025C211yesmaximal, characteristic
3#15688993C211yesmaximal, characteristic, complemented
4#15688886C212yesmaximal, complemented
5C47×#336C211yesmaximal, characteristic, complemented
6C22×D188C2211yescharacteristic
7C2×C4⋊Dic47—21no—
8C2×C4⋊Dic47—21no—
9C2×C4⋊Dic47C2212yes—
10C2×C4⋊Dic47C2211yescharacteristic
11C2×(C2×D47)⋊C4—21no—
12C2×(C2×D47)⋊C4—21no—
13#13093946—24no—
14C22×C8×C47C2212yes—
15C2×C42×C47C2211yescharacteristic
16C23×D47—21no—
17C22×C4×C47D411yescharacteristic
18C22×C4×C47D411yescharacteristic
19C22×C4×C47C2311yescharacteristic
20C22×Dic47—21no—
21C22×Dic47—22no—
22C2×D188—22no—
23C2×D188—22no—
24C2×D188—21no—
25C2×D188D412yes—
26C2×C8×C47—22no—
27C2×C8×C47—22no—
28C2×C8×C47—22no—
29C42×C47—22no—
30(C2×D47)⋊C4—42no—
31(C2×D47)⋊C4—42no—
32C4⋊Dic47—22no—
33C4⋊Dic47—22no—
34C4⋊Dic47—22no—
35C4⋊Dic47—42no—
36C4⋊Dic47—42no—
37C23×C47C2×D411yescharacteristic
38C22×D47—22no—
39C22×D47—41no—
40C22×D47—41no—
41C22×D47—41no—
42C22×D47—41no—
43C22×D47—41no—
44C22×D47—41no—
45C2×C4×C47—21no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47D812yes—
50C2×C4×C47SD1612yes—
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47#4112yes—
53C2×C4×C47#4112yes—
54C2×C4×C47#4111yescharacteristic
55C2×Dic47—42no—
56C2×Dic47—41no—
57C2×Dic47—42no—
58C2×Dic47—41no—
59C2×Dic47—41no—
60C2×Dic47—42no—
61D188—24no—
62D188—42no—
63C8×C47—42no—
64C22×C47#12111yescharacteristic
65C22×C47#12311yescharacteristic
66C22×C47#12411yescharacteristic
67C22×C47C2×D811yescharacteristic
68C22×C47C2×SD1611yescharacteristic
69C22×C47AGL(1,ℤ/8)11yescharacteristic
70C22×C47#13711yescharacteristic
71C2×D47—42no—
72C2×D47—42no—
73C2×D47—42no—
74C2×D47—81no—
75C2×D47—81no—
76C2×D47—81no—
77C2×D47—81no—
78C4×C47—22no—
79C4×C47—22no—
80C4×C47#12312yes—
81C4×C47#12612yes—
82Dic47—82no—
83Dic47—81no—
84#2071—471nomaximal, Sylow
85C2×C47#39711yescharacteristic
86C2×C47#45911yescharacteristic
87C2×C47#46111yescharacteristic
88C2×C47#48011yescharacteristic
89C2×C47#48111yescharacteristic
90C2×C47#48611yescharacteristic
91C2×C47#48911yescharacteristic
92D47—82no—
93C2×#102—472no—
94#390—471no—
95#384—471no—
96#340—472no—
97#336D4711yescharacteristic, complemented
98C47#207111yescharacteristic, complemented, Sylow
99C22×D4—471no—
100C22×C8C2×D4712yes—
101C2×C4⋊C4—471no—
102C2×C4⋊C4—472no—
103C2×C4⋊C4—941no—
104C2×C4⋊C4—941no—
105C2×C22⋊C4—941no—
106C2×C22⋊C4—941no—
107C2×C42C2×D4711yescharacteristic
108#102—944no—
109C24—941no—
110C2×D4—472no—
111C2×D4—942no—
112C2×D4—942no—
113C2×D4—941no—
114C22×C4—941no—
115C22×C4—942no—
116C22×C4D18811yescharacteristic
117C22×C4D18811yescharacteristic
118C22×C4C22×D4711yescharacteristic
119C2×C8—22no—
120C2×C8—22no—
121C2×C8—22no—
122C4⋊C4—942no—
123C4⋊C4—942no—
124C4⋊C4—942no—
125C4⋊C4—1882no—
126C4⋊C4—1882no—
127C22⋊C4—1882no—
128C22⋊C4—1882no—
129C42—22no—
130C23—942no—
131C23—1881no—
132C23—1881no—
133C23—1881no—
134C23—1881no—
135C23—1881no—
136C23—1881no—
137C23C2×D18811yescharacteristic
138D4—944no—
139D4—1882no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—1882no—
145C2×C4—1881no—
146C2×C4—1881no—
147C2×C4—1882no—
148C2×C4—1881no—
149C2×C4—1882no—
150C2×C4#1062532512yes—
151C2×C4D37612yes—
152C2×C4#1062535012yes—
153C2×C4D4×D4711yescharacteristic
154C2×C4#1062535212yes—
155C2×C4#1062535411yescharacteristic
156C8—42no—
157C22—3761no—
158C22—3761no—
159C22—3761no—
160C22—3761no—
161C22—1882no—
162C22—1882no—
163C22—1882no—
164C22#1309399911yescharacteristic
165C22#1309400811yescharacteristic
166C22#1309401211yescharacteristic
167C22C2×D37611yescharacteristic
168C22C2×#1062532511yescharacteristic
169C22#1309405211yescharacteristic
170C22#1309405711yescharacteristic
171C4—22no—
172C4—22no—
173C4—3762no—
174C4—3761no—
175C4#1309400612yes—
176C4#1309401912yes—
177C2—3762no—
178C2#1568905011yescharacteristic
179C2#1568931911yescharacteristic
180C2#1568932911yescharacteristic
181C2#1568943711yescharacteristic
182C2#1568944211yescharacteristic
183C2#1568947011yescharacteristic
184C2#1568948311yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#336C2
socleC23×C47C2×D4
hypercenter#336D47
hypocenterC47#2071
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
3. #15688993C2semidirect
4. #15688886C2semidirect
5. C47×#336C2semidirect
97. #336D47semidirect
98. C47#2071semidirect