Finite Group Databasebeta

← #20242022

Subgroups — #20242022

Order 6016.

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

normal subgroups only

This group has 238 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
1#15689673C211yesmaximal, characteristic
2#15689180C211yesmaximal, characteristic, complemented
3#15688862C214yesmaximal, complemented
4C47×#432C211yesmaximal, characteristic, complemented
5C2×#10625350C412yes—
6#13094024C411yescharacteristic
7#13094021C411yescharacteristic
8#13094012C2212yes—
9#13093998—21no—
10#13093998—21no—
11C4×D188—21no—
12C4×D188—21no—
13C4⋊(C47⋊C8)—21no—
14C22⋊(C47⋊C8)—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—22no—
40C23×C47C22⋊C411yescharacteristic
41C22×D47—22no—
42C2×C4×C47—22no—
43C2×C4×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47C22⋊C411yescharacteristic
46C2×C4×C47C22⋊C411yescharacteristic
47C2×C4×C47C22⋊C411yescharacteristic
48C2×C4×C47C22×C411yescharacteristic
49C2×C4×C47C2×D411yescharacteristic
50C2×C4×C47C2×D411yescharacteristic
51C22⋊D47—44no—
52C2×Dic47—22no—
53D188—42no—
54D188—42no—
55D188—42no—
56C4×D47—44no—
57Dic94—42no—
58C8×C47—42no—
59C47⋊C8—42no—
60C22×C47—21no—
61C22×C47—21no—
62C22×C47—21no—
63C22×C47C2×C22⋊C411yescharacteristic
64C2×D47—42no—
65C2×D47—42no—
66C2×D47—42no—
67C4×C47—21no—
68C4×C47—21no—
69C4×C47—21no—
70C4×C47—21no—
71C4×C47—21no—
72C4×C47#10012yes—
73Dic47—42no—
74#1536—471nomaximal, Sylow
75C2×C47—41no—
76C2×C47C2×#10011yescharacteristic
77C2×C47#42111yescharacteristic
78C2×C47#42111yescharacteristic
79D47—82no—
80#532—471no—
81#432—471no—
82#432D4711yescharacteristic, complemented
83#329—474no—
84C47#153611yescharacteristic, complemented, Sylow
85C2×#41—472no—
86C4⋊Q8—471no—
87#127—471no—
88#124—472no—
89#121—941no—
90#121—941no—
91C4×D4—941no—
92C4×D4—941no—
93C2×C42C2×D4711yescharacteristic
94C4⋊C8—21no—
95C4⋊C8—941no—
96C22⋊C8—21no—
97C22⋊C8—941no—
98#97—472no—
99#97C2×D4712yes—
100#41—1884no—
101C2×Q8—472no—
102C2×D4—472no—
103C2×D4—942no—
104C2×D4—941no—
105C2×D4—941no—
106C22×C4—942no—
107C22×C4C4×D4711yescharacteristic
108C22×C4D18811yescharacteristic
109C22×C4C22⋊D4711yescharacteristic
110C2×C8—22no—
111C2×C8—942no—
112C4⋊C4—941no—
113C4⋊C4—941no—
114C22⋊C4—942no—
115C22⋊C4—942no—
116C42C4×D4711yescharacteristic
117C42D18811yescharacteristic
118C42C22⋊D4711yescharacteristic
119C42C22×D4711yescharacteristic
120C23—942no—
121C23(C2×D47)⋊C411yescharacteristic
122Q8—1882no—
123D4—1882no—
124D4—1882no—
125D4—1882no—
126D4—1884no—
127C2×C4—22no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—942no—
131C2×C4—1884no—
132C2×C4(C2×D47)⋊C411yescharacteristic
133C2×C4(C2×D47)⋊C411yescharacteristic
134C2×C4(C2×D47)⋊C411yescharacteristic
135C2×C4C2×C4×D4711yescharacteristic
136C2×C4C2×D18811yescharacteristic
137C2×C4C2×C22⋊D4711yescharacteristic
138C8—42no—
139C8—1882no—
140C22—21no—
141C22—21no—
142C22—21no—
143C22—1882no—
144C22—1882no—
145C22—1882no—
146C22C2×(C2×D47)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—21no—
151C4—21no—
152C4—1882no—
153C4#1309394012yes—
154C2—41no—
155C2—3762no—
156C2C2×#1309394011yescharacteristic
157C2#1568913911yescharacteristic
158C2#1568914111yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#432C2
socleC22×C47C2×C22⋊C4
hypercenter#432D47
hypocenterC47#1536
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. #15689180C2semidirect
3. #15688862C2semidirect
4. C47×#432C2semidirect
82. #432D47semidirect
84. C47#1536semidirect