Finite Group Databasebeta

← #20245102

Subgroups — #20245102

Order 6016.

260 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 69 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×D8×D47C211yesmaximal, characteristic
2C2×#13093963C211yesmaximal, characteristic, complemented
3#15689160C211yesmaximal, characteristic, complemented
4#15688925C211yesmaximal, characteristic, complemented
5#15688924C211yesmaximal, characteristic, complemented
6#15688923C211yesmaximal, characteristic, complemented
7C47×#357C211yesmaximal, characteristic, complemented
8C2×D4×D47—21no—
9C2×D376C2211yescharacteristic
10C2×#10625334—21no—
11D8×D47—22no—
12D8×D47C414yescomplemented
13C2×C8×D47C2211yescharacteristic
14#13093982—21no—
15#13093963—22no—
16C2×C47⋊C16C2211yescharacteristic, complemented
17#13093958C2211yescharacteristic, complemented
18#13093955—21no—
19C2×D8×C47C2211yescharacteristic
20C2×C16×C47C2211yescharacteristic, complemented
21#107×C47C2211yescharacteristic, complemented
22C23×D47—41no—
23C2×D4×C47—21no—
24C2×C22⋊D47—41no—
25D4×D47—24no—
26D4×D47—42no—
27C2×D188—21no—
28C2×C4×D47D411yescharacteristic
29D8×C47—21no—
30D8×C47C2×C412yes—
31C2×C8×C47C2311yescharacteristic
32C4⋊C4×C47—21no—
33#10625334—24no—
34(C2×D47)⋊C4—41no—
35C4⋊Dic47—21no—
36C4×Dic47—41no—
37C2×C47⋊C8D411yescharacteristic
38D376—21no—
39D376C2×C412yes—
40C8×D47C2×C412yes—
41C8×D47D412yes—
42C16×C47—21no—
43C47⋊C16—21no—
44C23×C47—41no—
45C22×D47—41no—
46C22×D47—44no—
47C22×D47—82no—
48C22×D47—82no—
49C22×D47D811yescharacteristic
50D4×C47—22no—
51D4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47C2×D411yescharacteristic
54C22⋊D47—44no—
55C2×Dic47—41no—
56C2×Dic47D811yescharacteristic
57D188—22no—
58D188—41no—
59C4×D47C22⋊C412yes—
60C4×D47SD1612yes—
61C8×C47C22×C411yescharacteristic
62C8×C47C2×D411yescharacteristic
63C47⋊C8C22⋊C412yes—
64C22×C47—42no—
65C22×C47—81no—
66C22×C47—81no—
67C22×C47C2×D811yescharacteristic
68C2×D47—21no—
69C2×D47—21no—
70C2×D47—42no—
71C2×D47—88no—
72C2×D47—81no—
73C2×D47—81no—
74C2×D47#10212yes—
75C4×C47—81no—
76C4×C47C2×C22⋊C411yescharacteristic
77C4×C47C2×SD1611yescharacteristic
78Dic47—81no—
79Dic47#10212yes—
80#2140—471nomaximal, Sylow
81C2×C47—82no—
82C2×C47C2×#10211yescharacteristic
83C2×C47#50911yescharacteristic
84C2×C47#50911yescharacteristic
85D47—22no—
86D47—82no—
87C22×D8—471no—
88C2×M32—471no—
89#427—471no—
90#357—471no—
91#357—471no—
92#357—471no—
93#357D4711yescharacteristic, complemented
94C47#214011yescharacteristic, complemented, Sylow
95C22×D4—941no—
96C2×D8—474no—
97C2×D8—471no—
98C2×D8—942no—
99C2×D8—941no—
100C2×D8C2×D4711yescharacteristic
101C22×C8—471no—
102#117—941no—
103M32—942no—
104C2×C16—471no—
105C2×C16C2×D4711yescharacteristic, complemented
106#107—471no—
107#107C2×D4711yescharacteristic, complemented
108#106—941no—
109C24—1881no—
110C2×D4—21no—
111C2×D4—944no—
112C2×D4—941no—
113C2×D4—1882no—
114C2×D4—1881no—
115C22×C4—471no—
116D8—21no—
117D8—472no—
118D8—944no—
119D8—941no—
120D8C4×D4712yes—
121C2×C8—471no—
122C2×C8—472no—
123C2×C8—472no—
124C2×C8C22×D4711yescharacteristic
125C4⋊C4—21no—
126C4⋊C4—941no—
127C22⋊C4—1881no—
128C42—1881no—
129C16—21no—
130C16—941no—
131C23—41no—
132C23—471no—
133C23—3762no—
134C23—3762no—
135C23—1884no—
136C23—1881no—
137D4—22no—
138D4—41no—
139D4—942no—
140D4—1884no—
141D4—1881no—
142C2×C4—41no—
143C2×C4—471no—
144C2×C4—472no—
145C2×C4—472no—
146C2×C4—1881no—
147C2×C4D4×D4711yescharacteristic
148C8—472no—
149C8C2×C4×D4711yescharacteristic
150C8D4×D4711yescharacteristic
151C22—42no—
152C22—81no—
153C22—81no—
154C22—472no—
155C22—941no—
156C22—941no—
157C22—3768no—
158C22—3761no—
159C22—3761no—
160C22—1882no—
161C22D8×D4711yescharacteristic
162C4—81no—
163C4—472no—
164C4—3761no—
165C4C22⋊C4×D4711yescharacteristic
166C4SD16×D4711yescharacteristic
167C2—82no—
168C2—942no—
169C2—3762no—
170C2#102×D4711yescharacteristic
171C2#1568955711yescharacteristic
172C2#1568956011yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC47×#357C2
socleC22×C47C2×D8
hypercenter#357D47
hypocenterC47#2140
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×#13093963C2semidirect
3. #15689160C2semidirect
4. #15688925C2semidirect
5. #15688924C2semidirect
6. #15688923C2semidirect
7. C47×#357C2semidirect
12. D8×D47C4semidirect
16. C2×C47⋊C16C22semidirect
17. #13093958C22semidirect
20. C2×C16×C47C22semidirect
21. #107×C47C22semidirect
93. #357D47semidirect
94. C47#2140semidirect
105. C2×C16C2×D47semidirect
107. #107C2×D47semidirect