Finite Group Databasebeta

← #20242121

Subgroups — #20242121

Order 6016.

254 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 77 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#15689147C211yesmaximal, characteristic, complemented
3#15688871C212yesmaximal, complemented
4#15688866C212yesmaximal, complemented
5C47×#423C211yesmaximal, characteristic, complemented
6C2×#10625350C412yes—
7C2×#10625329—21no—
8#13094024C2211yescharacteristic
9#13094021C2211yescharacteristic
10#13094012C412yes—
11#13093998—21no—
12#13093998—21no—
13C4×D188—21no—
14C4×D188—21no—
15C4⋊(C47⋊C8)—21no—
16C4⋊(C47⋊C8)C2212yes—
17C2×M16×C47—21no—
18C2×C42×C47C2211yescharacteristic
19C4⋊C8×C47—21no—
20C4⋊C8×C47C2212yes—
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C2×C22⋊D47—22no—
25#10625350—44no—
26C2×D188—21no—
27C2×D188—21no—
28C2×D188C2×C412yes—
29C2×C4×D47—22no—
30C2×Dic94C2×C412yes—
31M16×C47—42no—
32C2×C8×C47—22no—
33C42×C47C2×C411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47D411yescharacteristic
36C42×C47C2311yescharacteristic
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41#10625329—42no—
42C2×C47⋊C8—22no—
43C23×C47C22⋊C411yescharacteristic
44C22×D47—22no—
45C2×C4×C47—22no—
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—21no—
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C22×C411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C22⋊D47—44no—
57C2×Dic47—22no—
58D188—42no—
59D188—41no—
60D188—41no—
61D188—41no—
62D188—41no—
63C4×D47—44no—
64Dic94—42no—
65C8×C47—42no—
66C47⋊C8—42no—
67C22×C47—21no—
68C22×C47—21no—
69C22×C47—21no—
70C22×C47C2×C22⋊C411yescharacteristic
71C2×D47—42no—
72C2×D47—42no—
73C2×D47—42no—
74C4×C47—21no—
75C4×C47—21no—
76C4×C47—21no—
77C4×C47#10012yes—
78C4×C47AGL(1,ℤ/8)11yescharacteristic
79C4×C47AGL(1,ℤ/8)11yescharacteristic
80C4×C47#13711yescharacteristic
81C4×C47#13711yescharacteristic
82Dic47—42no—
83#1560—471nomaximal, Sylow
84C2×C47—41no—
85C2×C47C2×#10011yescharacteristic
86C2×C47#41711yescharacteristic
87C2×C47#41711yescharacteristic
88D47—82no—
89#532—471no—
90#423—471no—
91#423D4711yescharacteristic, complemented
92#333—472no—
93#331—472no—
94C47#156011yescharacteristic, complemented, Sylow
95C2×#41—472no—
96C2×M16—21no—
97C2×M16—941no—
98C4⋊Q8—471no—
99#127—471no—
100#124—472no—
101#121—941no—
102#121—941no—
103C4×D4—941no—
104C4×D4—941no—
105C2×C42C2×D4711yescharacteristic
106C4⋊C8—21no—
107C4⋊C8—472no—
108C4⋊C8—941no—
109C4⋊C8C2×D4712yes—
110#41—1884no—
111C2×Q8—472no—
112C2×D4—472no—
113C2×D4—942no—
114C2×D4—941no—
115C2×D4—941no—
116C22×C4—942no—
117C22×C4C4×D4711yescharacteristic
118C22×C4D18811yescharacteristic
119C22×C4C22⋊D4711yescharacteristic
120M16—42no—
121M16—1882no—
122C2×C8—22no—
123C2×C8—942no—
124C4⋊C4—941no—
125C4⋊C4—941no—
126C22⋊C4—942no—
127C22⋊C4—942no—
128C42C4×D4711yescharacteristic
129C42D18811yescharacteristic
130C42C22⋊D4711yescharacteristic
131C42C22×D4711yescharacteristic
132C23—942no—
133C23(C2×D47)⋊C411yescharacteristic
134Q8—1882no—
135D4—1882no—
136D4—1884no—
137D4—1881no—
138D4—1881no—
139D4—1881no—
140D4—1881no—
141C2×C4—22no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—942no—
147C2×C4—1884no—
148C2×C4(C2×D47)⋊C411yescharacteristic
149C2×C4(C2×D47)⋊C411yescharacteristic
150C2×C4(C2×D47)⋊C411yescharacteristic
151C2×C4C2×C4×D4711yescharacteristic
152C2×C4C2×D18811yescharacteristic
153C2×C4C2×C22⋊D4711yescharacteristic
154C8—42no—
155C8—1882no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—1882no—
160C22—1882no—
161C22—1882no—
162C22C2×(C2×D47)⋊C411yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—1882no—
167C4#1309394012yes—
168C4#1309405011yescharacteristic
169C4#1309405211yescharacteristic
170C4#1309405511yescharacteristic
171C4#1309405711yescharacteristic
172C2—41no—
173C2—3762no—
174C2C2×#1309394011yescharacteristic
175C2#1568912211yescharacteristic
176C2#1568912511yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#423C2
socleC22×C47C2×C22⋊C4
hypercenter#423D47
hypocenterC47#1560
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #15689147C2semidirect
3. #15688871C2semidirect
4. #15688866C2semidirect
5. C47×#423C2semidirect
91. #423D47semidirect
94. C47#1560semidirect