Finite Group Databasebeta

← #20242071

Subgroups — #20242071

Order 6016.

240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4⋊Q8×D47C211yesmaximal, characteristic
2#15689175C211yesmaximal, characteristic
3#15689145C211yesmaximal, characteristic
4#15688870C211yesmaximal, characteristic, complemented
5#15688869C211yesmaximal, characteristic, complemented
6#15688868C211yesmaximal, characteristic, complemented
7C47×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D47—21no—
9C2×#10625324—21no—
10#13094024C2211yescharacteristic
11#13094023—21no—
12#13094023C412yes—
13#13094022—21no—
14C4⋊C4×D47—21no—
15C4⋊C4×D47C412yes—
16C42×D47C2211yescharacteristic
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21C8×Dic47—21no—
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26Q8×D47—42no—
27Q8×D47—42no—
28C2×C4×D47—22no—
29C2×C4×D47C2×C411yescharacteristic
30C2×C4×D47D411yescharacteristic
31C2×C4×D47D411yescharacteristic
32C2×Dic94—21no—
33C2×Dic94—22no—
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47C2×C412yes—
38C42×C47C2311yescharacteristic
39C4⋊Dic47—21no—
40C4⋊Dic47C2×C412yes—
41Dic47⋊C4—22no—
42Dic47⋊C4—22no—
43C4×Dic47C2×C411yescharacteristic
44C4×Dic47D411yescharacteristic
45C4×Dic47D411yescharacteristic
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48#10625324—42no—
49C22×D47C22⋊C411yescharacteristic
50Q8×C47—41no—
51Q8×C47—41no—
52C2×C4×C47—22no—
53C2×C4×C47C22×C411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×Dic47—22no—
57C2×Dic47C22⋊C411yescharacteristic
58C2×Dic47C22⋊C411yescharacteristic
59C2×Dic47C22⋊C411yescharacteristic
60C4×D47—21no—
61C4×D47—21no—
62C4×D47—22no—
63C4×D47—44no—
64C4×D47SD1612yes—
65C4×D47Q1612yes—
66Dic94—44no—
67Dic94—41no—
68Dic94—41no—
69C8×C47—41no—
70C8×C47—41no—
71C47⋊C8—41no—
72C47⋊C8—41no—
73C22×C47C2×C22⋊C411yescharacteristic
74C2×D47—21no—
75C2×D47—21no—
76C2×D47#10312yes—
77C4×C47—21no—
78C4×C47—42no—
79C4×C47C2×SD1611yescharacteristic
80C4×C47C2×Q1611yescharacteristic
81C4×C47AGL(1,ℤ/8)11yescharacteristic
82C4×C47AGL(1,ℤ/8)11yescharacteristic
83Dic47—21no—
84Dic47—42no—
85Dic47#10112yes—
86Dic47#10312yes—
87#1549—471nomaximal, Sylow
88C2×C47C2×#10111yescharacteristic
89C2×C47C2×#10311yescharacteristic
90C2×C47#41811yescharacteristic
91D47—22no—
92C2×C4⋊Q8—471no—
93#431—471no—
94#423—471no—
95#332—471no—
96#332—471no—
97#332—471no—
98#332D4711yescharacteristic, complemented
99C47#154911yescharacteristic, complemented, Sylow
100C22×Q8—941no—
101C2×M16—941no—
102C4⋊Q8—472no—
103C4⋊Q8—471no—
104C4⋊Q8—941no—
105C4⋊Q8—941no—
106C4⋊Q8C2×D4711yescharacteristic
107C2×C4⋊C4—472no—
108C2×C4⋊C4—941no—
109C2×C42—471no—
110C4⋊C8—471no—
111C4⋊C8—471no—
112C4⋊C8—941no—
113C4⋊C8C2×D4711yescharacteristic
114C4⋊C8C2×D4711yescharacteristic
115C22⋊C8—941no—
116C4×C8—941no—
117C2×Q8—21no—
118C2×Q8—942no—
119C2×Q8—941no—
120C2×Q8—1882no—
121C2×Q8—1882no—
122C22×C4—471no—
123C22×C4—471no—
124C22×C4—471no—
125C22×C4—942no—
126M16—1882no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—941no—
130C2×C8—941no—
131C4⋊C4—21no—
132C4⋊C4—472no—
133C4⋊C4—942no—
134C4⋊C4—942no—
135C4⋊C4—941no—
136C4⋊C4C4×D4712yes—
137C42—471no—
138C42—471no—
139C42—471no—
140C42C22×D4711yescharacteristic
141C23—471no—
142Q8—41no—
143Q8—41no—
144Q8—1884no—
145Q8—1881no—
146Q8—1881no—
147C2×C4—22no—
148C2×C4—471no—
149C2×C4—471no—
150C2×C4—472no—
151C2×C4—472no—
152C2×C4—471no—
153C2×C4—942no—
154C2×C4—941no—
155C2×C4—941no—
156C2×C4—942no—
157C2×C4—1884no—
158C2×C4C2×C4×D4711yescharacteristic
159C2×C4D4×D4711yescharacteristic
160C2×C4D4×D4711yescharacteristic
161C8—41no—
162C8—41no—
163C8—1881no—
164C8—1881no—
165C22—472no—
166C22—941no—
167C22—941no—
168C22C22⋊C4×D4711yescharacteristic
169C4—21no—
170C4—42no—
171C4—472no—
172C4—472no—
173C4—941no—
174C4—1882no—
175C4SD16×D4711yescharacteristic
176C4Q16×D4711yescharacteristic
177C4#1309404811yescharacteristic
178C4#1309405111yescharacteristic
179C2—942no—
180C2#101×D4711yescharacteristic
181C2#103×D4711yescharacteristic
182C2#1568912611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#332C2
socleC22×C47C2×C22⋊C4
hypercenter#332D47
hypocenterC47#1549
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #15688870C2semidirect
5. #15688869C2semidirect
6. #15688868C2semidirect
7. C47×#332C2semidirect
98. #332D47semidirect
99. C47#1549semidirect