Finite Group Databasebeta

← #20242000

Subgroups — #20242000

Order 6016.

256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#15689673C211yesmaximal, characteristic
2C2×#13093935C211yesmaximal, characteristic, complemented
3#15688862C214yesmaximal, complemented
4C47×#432C211yesmaximal, characteristic, complemented
5C2×#10625350C412yes—
6C22×C47⋊C8—21no—
7#13094024C411yescharacteristic
8#13094021C411yescharacteristic
9#13094012C2212yes—
10#13093998—21no—
11#13093998—21no—
12C4×D188—21no—
13C4×D188—21no—
14#13093935—21no—
15#13093935C2212yes—
16C2×C42×C47C2211yescharacteristic
17C4⋊C8×C47—21no—
18C22⋊C8×C47—21no—
19#97×C47C2212yes—
20C22×C4×C47C2×C411yescharacteristic
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C2×C22⋊D47—22no—
24#10625350—44no—
25C2×D188—21no—
26C2×D188—21no—
27C2×D188C2×C412yes—
28C2×C4×D47—22no—
29C2×Dic94C2×C412yes—
30C2×C8×C47—22no—
31C42×C47C2×C411yescharacteristic
32C42×C47D411yescharacteristic
33C42×C47D411yescharacteristic
34C42×C47C2311yescharacteristic
35(C2×D47)⋊C4—22no—
36(C2×D47)⋊C4—22no—
37C4⋊Dic47—21no—
38C4⋊Dic47—21no—
39C2×C47⋊C8—24no—
40C2×C47⋊C8—22no—
41C23×C47C22⋊C411yescharacteristic
42C22×D47—22no—
43C2×C4×C47—22no—
44C2×C4×C47—22no—
45C2×C4×C47—41no—
46C2×C4×C47C22⋊C411yescharacteristic
47C2×C4×C47C22⋊C411yescharacteristic
48C2×C4×C47C22⋊C411yescharacteristic
49C2×C4×C47C22×C411yescharacteristic
50C2×C4×C47C2×D411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C22⋊D47—44no—
53C2×Dic47—22no—
54D188—42no—
55D188—42no—
56D188—42no—
57C4×D47—44no—
58Dic94—42no—
59C8×C47—42no—
60C47⋊C8—24no—
61C22×C47—21no—
62C22×C47—21no—
63C22×C47#10012yes—
64C22×C47C2×C22⋊C411yescharacteristic
65C2×D47—42no—
66C2×D47—42no—
67C2×D47—42no—
68C4×C47—21no—
69C4×C47—21no—
70C4×C47—21no—
71C4×C47—21no—
72C4×C47—21no—
73C4×C47#10412yes—
74Dic47—42no—
75#1530—471nomaximal, Sylow
76C2×C47—22no—
77C2×C47C2×#10011yescharacteristic
78C2×C47C2×#10411yescharacteristic
79C2×C47#42111yescharacteristic
80D47—82no—
81#532—471no—
82#432D4711yescharacteristic, complemented
83C2×#97—471no—
84#329—474no—
85C47#153011yescharacteristic, complemented, Sylow
86C2×#41—472no—
87C22×C8—941no—
88C4⋊Q8—471no—
89#127—471no—
90#124—472no—
91#121—941no—
92#121—941no—
93C4×D4—941no—
94C4×D4—941no—
95C2×C42C2×D4711yescharacteristic
96C4⋊C8—21no—
97C22⋊C8—21no—
98#97—472no—
99#97—941no—
100#97C2×D4712yes—
101#41—1884no—
102C2×Q8—472no—
103C2×D4—472no—
104C2×D4—942no—
105C2×D4—941no—
106C2×D4—941no—
107C22×C4—942no—
108C22×C4C4×D4711yescharacteristic
109C22×C4D18811yescharacteristic
110C22×C4C22⋊D4711yescharacteristic
111C2×C8—22no—
112C2×C8—944no—
113C2×C8—942no—
114C4⋊C4—941no—
115C4⋊C4—941no—
116C22⋊C4—942no—
117C22⋊C4—942no—
118C42C4×D4711yescharacteristic
119C42D18811yescharacteristic
120C42C22⋊D4711yescharacteristic
121C42C22×D4711yescharacteristic
122C23—942no—
123C23(C2×D47)⋊C411yescharacteristic
124Q8—1882no—
125D4—1882no—
126D4—1882no—
127D4—1884no—
128D4—1882no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—942no—
133C2×C4—1884no—
134C2×C4(C2×D47)⋊C411yescharacteristic
135C2×C4(C2×D47)⋊C411yescharacteristic
136C2×C4(C2×D47)⋊C411yescharacteristic
137C2×C4C2×C4×D4711yescharacteristic
138C2×C4C2×D18811yescharacteristic
139C2×C4C2×C22⋊D4711yescharacteristic
140C8—42no—
141C8—944no—
142C22—21no—
143C22—21no—
144C22—1882no—
145C22—1882no—
146C22—1882no—
147C22#1309394012yes—
148C22C2×(C2×D47)⋊C411yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—21no—
153C4—21no—
154C4—1882no—
155C4#1309395012yes—
156C2—22no—
157C2—3762no—
158C2C2×#1309394011yescharacteristic
159C2C2×#1309395011yescharacteristic
160C2#1568914111yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#432C2
socleC22×C47C2×C22⋊C4
hypercenter#432D47
hypocenterC47#1530
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×#13093935C2semidirect
3. #15688862C2semidirect
4. C47×#432C2semidirect
82. #432D47semidirect
85. C47#1530semidirect