Finite Group Databasebeta

← #20244654

Subgroups — #20244654

Order 6016.

256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C22×#10625337C211yesmaximal, characteristic
2#15689151C211yesmaximal, characteristic
3#15689133C211yesmaximal, characteristic
4#15689132C211yesmaximal, characteristic
5C2×#13093942C211yesmaximal, characteristic
6#15688887C211yesmaximal, characteristic
7C2×#101×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625337—22no—
10C2×#10625337—22no—
11C2×#10625337—22no—
12C2×#10625329C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14#13093983C2211yescharacteristic
15Dic47⋊C8—22no—
16#13093949—22no—
17#13093948—22no—
18#13093942—22no—
19C22×Q8×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22#101×C47—22no—
23C2×Q8×C47—21no—
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47D412yes—
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C22×Dic47—21no—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94—21no—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94D412yes—
38M16×C47—21no—
39M16×C47—21no—
40M16×C47—21no—
41M16×C47—21no—
42C2×C8×C47—21no—
43C2×C8×C47—21no—
44C22⋊Dic47—21no—
45#10625337—28no—
46C4⋊Dic47D412yes—
47C4×Dic47—21no—
48#10625329—21no—
49#10625329—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8D412yes—
54C23×C47#4111yescharacteristic
55Q8×C47—22no—
56Q8×C47—22no—
57Q8×C47—41no—
58Q8×C47—41no—
59C2×C4×C47—22no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72Dic94—22no—
73Dic94—22no—
74Dic94—41no—
75Dic94—41no—
76C8×C47—41no—
77C8×C47—41no—
78C47⋊C8—22no—
79C47⋊C8—41no—
80C22×C47—22no—
81C22×C47#12111yescharacteristic
82C22×C47#12311yescharacteristic
83C22×C47#12311yescharacteristic
84C4×C47—42no—
85C4×C47#12011yescharacteristic
86C4×C47#12111yescharacteristic
87C4×C47#12111yescharacteristic
88C4×C47#12411yescharacteristic
89Dic47—42no—
90Dic47—42no—
91#2047—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—21no—
94C2×C47#39411yescharacteristic
95C2×C47#47312yes—
96C22×Q16—471no—
97#424—471no—
98#419—471no—
99#419—471no—
100C2×#101—471no—
101C2×#101D4711yescharacteristic
102#341—471no—
103C47#204711yescharacteristic, complemented, Sylow
104C22×Q8—471no—
105C22×Q8C2×D4711yescharacteristic
106C2×Q16—942no—
107C2×Q16—942no—
108C2×Q16—942no—
109C2×M16—471no—
110C2×M16C2×D4711yescharacteristic
111C2×M16C2×D4711yescharacteristic
112C22×C8—471no—
113#117—471no—
114C4⋊C8—942no—
115#103—942no—
116#103—942no—
117#101—22no—
118#101—942no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—21no—
122C2×Q8—21no—
123C2×Q8—21no—
124C2×Q8—472no—
125C2×Q8—941no—
126C2×Q8—941no—
127C2×Q8—941no—
128C2×Q8—941no—
129C2×Q8—941no—
130C2×Q8C22⋊D4712yes—
131C22×C4—21no—
132C22×C4—941no—
133C22×C4C22×D4711yescharacteristic
134Q16—948no—
135M16—21no—
136M16—21no—
137M16—21no—
138M16—21no—
139M16—941no—
140M16—941no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—472no—
144C2×C8—941no—
145C2×C8—941no—
146C2×C8—941no—
147C4⋊C4—472no—
148C22⋊C4—941no—
149C42—941no—
150C23#1062535011yescharacteristic
151Q8—22no—
152Q8—22no—
153Q8—41no—
154Q8—41no—
155Q8—942no—
156Q8—942no—
157Q8—1881no—
158Q8—1881no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—942no—
163C2×C4—942no—
164C2×C4—1881no—
165C2×C4—1881no—
166C2×C4#1062535011yescharacteristic
167C2×C4D4×D4711yescharacteristic
168C2×C4D4×D4711yescharacteristic
169C2×C4D4×D4711yescharacteristic
170C2×C4#1062535211yescharacteristic
171C2×C4C2×C22⋊D4711yescharacteristic
172C8—41no—
173C8—41no—
174C8—942no—
175C8—1881no—
176C22—22no—
177C22#1309399711yescharacteristic
178C22#1309400611yescharacteristic
179C22#1309400711yescharacteristic
180C4—42no—
181C4—1882no—
182C4—1882no—
183C4#1309399211yescharacteristic
184C4#1309399611yescharacteristic
185C4#1309399711yescharacteristic
186C4#1309401011yescharacteristic
187C2—21no—
188C2—21no—
189C2#1568903811yescharacteristic
190C2#1568939712yes—
subgroupG/H
centerC22#13093997
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#101×C47C2
socleC22×C47#121
hypercenterC2×#101D47
hypocenterC47#2047
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
103. C47#2047semidirect