Finite Group Databasebeta

← #20244649

Subgroups — #20244649

Order 6016.

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

normal subgroups only

This group has 276 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×#10625335C211yesmaximal, characteristic
2#15689151C211yesmaximal, characteristic, complemented
3#15689133C211yesmaximal, characteristic, complemented
4#15689128C211yesmaximal, characteristic
5C2×#13093942C211yesmaximal, characteristic, complemented
6#15688887C211yesmaximal, characteristic, complemented
7C2×#100×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625335—22no—
10C2×#10625335—22no—
11C2×#10625335—22no—
12C2×#10625329C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14#13093983C2211yescharacteristic
15Dic47⋊C8—22no—
16#13093949—22no—
17#13093945—22no—
18#13093942—22no—
19C22×D4×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22#100×C47—22no—
23C24×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47D412yes—
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#10625335—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—22no—
55C23×C47—41no—
56C23×C47—41no—
57C23×C47—82no—
58C23×C47#4111yescharacteristic
59D4×C47—22no—
60D4×C47—22no—
61D4×C47—41no—
62D4×C47—41no—
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73Dic94—22no—
74Dic94—22no—
75Dic94—41no—
76Dic94—41no—
77C8×C47—41no—
78C8×C47—41no—
79C47⋊C8—22no—
80C47⋊C8—41no—
81C22×C47—22no—
82C22×C47—42no—
83C22×C47—82no—
84C22×C47—82no—
85C22×C47—82no—
86C22×C47#12111yescharacteristic
87C22×C47#12311yescharacteristic
88C22×C47#12311yescharacteristic
89C4×C47#12011yescharacteristic
90C4×C47#12111yescharacteristic
91C4×C47#12111yescharacteristic
92C4×C47#12411yescharacteristic
93Dic47—42no—
94Dic47—42no—
95#2046—471nomaximal, Sylow
96C2×C47—21no—
97C2×C47—21no—
98C2×C47—82no—
99C2×C47#39411yescharacteristic
100C2×C47#47112yes—
101C22×SD16—471no—
102#424—471no—
103#419—471no—
104#418—471no—
105C2×#101—471no—
106C2×#100D4711yescharacteristic
107#341—471no—
108C47#204611yescharacteristic, complemented, Sylow
109C22×Q8—471no—
110C22×D4C2×D4711yescharacteristic
111C2×SD16—942no—
112C2×SD16—942no—
113C2×SD16—942no—
114C2×M16—471no—
115C2×M16C2×D4711yescharacteristic
116C2×M16C2×D4711yescharacteristic
117C22×C8—471no—
118#117—471no—
119C4⋊C8—942no—
120#103—942no—
121#102—942no—
122#101—942no—
123#100—22no—
124C24—21no—
125C2×Q8—472no—
126C2×Q8—941no—
127C2×Q8—941no—
128C2×Q8—941no—
129C2×Q8—941no—
130C2×Q8—941no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4C22⋊D4712yes—
137C22×C4—941no—
138C22×C4C22×D4711yescharacteristic
139SD16—948no—
140M16—21no—
141M16—21no—
142M16—21no—
143M16—21no—
144M16—941no—
145M16—941no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—472no—
149C2×C8—941no—
150C2×C8—941no—
151C2×C8—941no—
152C4⋊C4—472no—
153C22⋊C4—941no—
154C42—941no—
155C23—22no—
156C23—41no—
157C23—41no—
158C23—82no—
159C23#1062535011yescharacteristic
160Q8—942no—
161Q8—942no—
162Q8—1881no—
163Q8—1881no—
164D4—22no—
165D4—22no—
166D4—41no—
167D4—41no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—1881no—
171C2×C4—1881no—
172C2×C4#1062535011yescharacteristic
173C2×C4D4×D4711yescharacteristic
174C2×C4D4×D4711yescharacteristic
175C2×C4D4×D4711yescharacteristic
176C2×C4#1062535211yescharacteristic
177C2×C4C2×C22⋊D4711yescharacteristic
178C8—41no—
179C8—41no—
180C8—942no—
181C8—1881no—
182C22—22no—
183C22—42no—
184C22—82no—
185C22—82no—
186C22—82no—
187C22#1309399711yescharacteristic
188C22#1309400611yescharacteristic
189C22#1309400711yescharacteristic
190C4—1882no—
191C4—1882no—
192C4#1309399211yescharacteristic
193C4#1309399611yescharacteristic
194C4#1309399711yescharacteristic
195C4#1309401011yescharacteristic
196C2—21no—
197C2—21no—
198C2—82no—
199C2#1568903811yescharacteristic
200C2#1568938512yes—
subgroupG/H
centerC22#13093997
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#100×C47C2
socleC22×C47#121
hypercenterC2×#100D47
hypocenterC47#2046
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #15689151C2semidirect
3. #15689133C2semidirect
5. C2×#13093942C2semidirect
6. #15688887C2semidirect
108. C47#2046semidirect