Finite Group Databasebeta

← #20241708

Subgroups — #20241708

Order 6016.

312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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×C4×D188C211yesmaximal, characteristic
2#15689176C211yesmaximal, characteristic, complemented
3#15688846C214yesmaximal, complemented
4C47×#431C211yesmaximal, characteristic, complemented
5C22×D188C411yescharacteristic
6C22×C4×D47C412yes—
7C4×D188—21no—
8C4×D188—21no—
9C4×D188—21no—
10C4×D188—21no—
11C2×C4⋊Dic47C411yescharacteristic
12C2×(C2×D47)⋊C4C2212yes—
13C4⋊(C47⋊C8)—21no—
14C22⋊(C47⋊C8)C2212yes—
15C4×C47⋊C8—21no—
16C2×C42×C47C2211yescharacteristic
17C4⋊C8×C47—21no—
18C22⋊C8×C47C2212yes—
19C4×C8×C47—21no—
20C23×D47C2×C412yes—
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C22×Dic47C2×C412yes—
25C2×D188—21no—
26C2×D188—21no—
27C2×D188—22no—
28C2×D188C814yescomplemented
29C2×C4×D47—22no—
30C2×C4×D47—22no—
31C2×C4×D47—44no—
32C2×C8×C47—22no—
33C42×C47D411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47D411yescharacteristic
36C42×C47D411yescharacteristic
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C2×C47⋊C8—22no—
42C23×C47C22×C411yescharacteristic
43C22×D47—22no—
44C22×D47—22no—
45C22×D47—42no—
46C22×D47—42no—
47C22×D47C2×C814yes—
48C2×C4×C47—22no—
49C2×C4×C47—41no—
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C22⋊C411yescharacteristic
54C2×C4×C47C2×C812yes—
55C2×C4×C47M1612yes—
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×Dic47—22no—
59C2×Dic47—42no—
60D188—24no—
61D188—24no—
62C4×D47—44no—
63C4×D47—44no—
64C8×C47—42no—
65C47⋊C8—42no—
66C22×C47—21no—
67C22×C47—21no—
68C22×C47C2×C22⋊C411yescharacteristic
69C22×C47C22×C811yescharacteristic
70C22×C47C2×M1611yescharacteristic
71C2×D47—24no—
72C2×D47—44no—
73C2×D47—42no—
74C2×D47—42no—
75C2×D47—44no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79C4×C47C22⋊C812yes—
80C4×C47C22⋊C812yes—
81C4×C47#10012yes—
82Dic47—42no—
83#1460—471nomaximal, Sylow
84C2×C47—21no—
85C2×C47—21no—
86C2×C47C2×C22⋊C811yescharacteristic
87C2×C47#41011yescharacteristic
88C2×C47C2×#10011yescharacteristic
89D47—44no—
90C2×C4×D4—471no—
91#431—471no—
92#431D4711yescharacteristic, complemented
93#323—474no—
94C47#146011yescharacteristic, complemented, Sylow
95C22×D4—471no—
96C23×C4—472no—
97C4×D4—941no—
98C4×D4—941no—
99C4×D4—941no—
100C4×D4—941no—
101C2×C4⋊C4—471no—
102C2×C22⋊C4—472no—
103C2×C42C2×D4711yescharacteristic
104C4⋊C8—21no—
105C4⋊C8—941no—
106C22⋊C8—472no—
107C22⋊C8C2×D4712yes—
108C4×C8—21no—
109C4×C8—941no—
110C24—472no—
111C2×D4—474no—
112C2×D4—942no—
113C2×D4—941no—
114C2×D4—941no—
115C22×C4—472no—
116C22×C4—942no—
117C22×C4—942no—
118C22×C4—1884no—
119C22×C4C4×D4711yescharacteristic
120C22×C4C4×D4711yescharacteristic
121C22×C4C22×D4711yescharacteristic
122C2×C8—22no—
123C2×C8—942no—
124C4⋊C4—941no—
125C4⋊C4—941no—
126C22⋊C4—942no—
127C22⋊C4—942no—
128C42D18811yescharacteristic
129C42D18811yescharacteristic
130C42C22⋊D4711yescharacteristic
131C42C22⋊D4711yescharacteristic
132C23—474no—
133C23—942no—
134C23—942no—
135C23—1882no—
136C23—1882no—
137C23C2×C4×D4711yescharacteristic
138D4—944no—
139D4—944no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—942no—
143C2×C4—1884no—
144C2×C4—1884no—
145C2×C4—1882no—
146C2×C4C8×D4712yes—
147C2×C4#1062532412yes—
148C2×C4(C2×D47)⋊C411yescharacteristic
149C2×C4(C2×D47)⋊C411yescharacteristic
150C2×C4(C2×D47)⋊C411yescharacteristic
151C2×C4(C2×D47)⋊C411yescharacteristic
152C2×C4C2×D18811yescharacteristic
153C2×C4C2×C22⋊D4711yescharacteristic
154C8—42no—
155C8—1882no—
156C22—21no—
157C22—21no—
158C22—944no—
159C22—1884no—
160C22—1884no—
161C22—1882no—
162C22—1882no—
163C22C2×(C2×D47)⋊C411yescharacteristic
164C22C2×C8×D4711yescharacteristic
165C22C2×#1062532411yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—1882no—
170C4(C2×D47)⋊C812yes—
171C4(C2×D47)⋊C812yes—
172C4#1309394012yes—
173C2—21no—
174C2—21no—
175C2—1884no—
176C2C2×(C2×D47)⋊C811yescharacteristic
177C2#1568909611yescharacteristic
178C2C2×#1309394011yescharacteristic
subgroupG/H
centerC2×C4(C2×D47)⋊C4
commutatorC22×C47C22×C8
FrattiniC22×C4C22×D47
FittingC47×#431C2
socleC22×C47C2×C22⋊C4
hypercenter#431D47
hypocenterC47#1460
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #15689176C2semidirect
3. #15688846C2semidirect
4. C47×#431C2semidirect
28. C2×D188C8semidirect
92. #431D47semidirect
94. C47#1460semidirect