Finite Group Databasebeta

← #20244560

Subgroups — #20244560

Order 6016.

244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689680C211yesmaximal, characteristic, complemented
2#15689140C211yesmaximal, characteristic
3#15689097C211yesmaximal, characteristic
4#15688895C211yesmaximal, characteristic, complemented
5#15688883C211yesmaximal, characteristic, complemented
6#15688880C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9#13094024—21no—
10#13094016—21no—
11#13094003—22no—
12C4×Dic94—22no—
13#13093983C2211yescharacteristic
14#13093983C2211yescharacteristic
15#13093983C2211yescharacteristic
16#13093951—22no—
17#13093939—22no—
18C2×#41×C47C2211yescharacteristic
19C2×M16×C47C2211yescharacteristic
20C2×C42×C47C2211yescharacteristic
21#104×C47—21no—
22#104×C47—21no—
23#41×C47—21no—
24#41×C47—21no—
25#41×C47—21no—
26#41×C47—21no—
27C2×Q8×C47Q811yescharacteristic, complemented
28C2×D4×C47—21no—
29C2×D4×C47Q811yescharacteristic, complemented
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33C2×Dic94—22no—
34M16×C47—21no—
35M16×C47—21no—
36C2×C8×C47—21no—
37C42×C47—21no—
38C42×C47D411yescharacteristic
39C42×C47D411yescharacteristic
40C22⋊Dic47—21no—
41C22⋊Dic47—21no—
42C22⋊Dic47D412yes—
43C4⋊Dic47—22no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47Dic47⋊C4—24no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C4×Dic47D412yes—
51#10625329—21no—
52#10625329—21no—
53C2×C47⋊C8—21no—
54C23×C47—21no—
55C23×C47C2×D411yescharacteristic
56Q8×C47—21no—
57Q8×C47—21no—
58D4×C47—21no—
59D4×C47—21no—
60D4×C47—41no—
61D4×C47—41no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—42no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×Q811yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—41no—
77Dic94—44no—
78C8×C47—41no—
79C47⋊C8—41no—
80C22×C47—41no—
81C22×C47—41no—
82C22×C47—81no—
83C22×C47#12011yescharacteristic
84C22×C47C22⋊Q811yescharacteristic
85C22×C47#12411yescharacteristic
86C4×C47—22no—
87C4×C47—41no—
88C4×C47—41no—
89C4×C47C22⋊Q811yescharacteristic
90C4×C47C22⋊Q811yescharacteristic
91C4×C47#12411yescharacteristic
92C4×C47#12411yescharacteristic
93Dic47—42no—
94Dic47—42no—
95Dic47—81no—
96#2031—471nomaximal, Sylow
97C2×C47—21no—
98C2×C47—21no—
99C2×C47—21no—
100C2×C47—81no—
101C2×C47#39311yescharacteristic
102#533—471no—
103#421—471no—
104C2×#104D4711yescharacteristic
105#410—471no—
106#344—471no—
107#339—471no—
108H(3,ℤ/4)—471no—
109C47#203111yescharacteristic, complemented, Sylow
110C2×#41C2×D4711yescharacteristic
111C2×M16—471no—
112C2×M16C2×D4711yescharacteristic
113C4⋊Q8—941no—
114#125—941no—
115C22⋊Q8—942no—
116C4×Q8—942no—
117#117—471no—
118#117—471no—
119#117—471no—
120C2×C42C2×D4711yescharacteristic
121#104—21no—
122#104—21no—
123#104—942no—
124#99—942no—
125#41—21no—
126#41—21no—
127#41—21no—
128#41—21no—
129C2×Q8—942no—
130C2×Q8Dic9411yescharacteristic, complemented
131C2×D4—21no—
132C2×D4Dic9411yescharacteristic, complemented
133C22×C4—21no—
134C22×C4—21no—
135C22×C4C22×D4711yescharacteristic
136M16—21no—
137M16—21no—
138M16—941no—
139M16—941no—
140C2×C8—21no—
141C2×C8—941no—
142C4⋊C4—944no—
143C4⋊C4—942no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C22⋊C4—472no—
148C22⋊C4—941no—
149C22⋊C4—941no—
150C42—21no—
151C42—472no—
152C42—941no—
153C42—941no—
154C42C22⋊D4711yescharacteristic
155C42C22⋊D4711yescharacteristic
156C23—21no—
157C23D4×D4711yescharacteristic
158Q8—21no—
159Q8—21no—
160Q8—1884no—
161D4—21no—
162D4—21no—
163D4—41no—
164D4—41no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—942no—
172C2×C4—942no—
173C2×C4—1881no—
174C2×C4C2×Dic9411yescharacteristic
175C2×C4#1062535011yescharacteristic
176C2×C4D4×D4711yescharacteristic
177C2×C4#1062535211yescharacteristic
178C2×C4#1062535211yescharacteristic
179C2×C4C2×C22⋊D4711yescharacteristic
180C8—41no—
181C8—1881no—
182C22—41no—
183C22—41no—
184C22—81no—
185C22#1309399211yescharacteristic
186C22#1309400111yescharacteristic
187C22#1309401011yescharacteristic
188C4—22no—
189C4—41no—
190C4—41no—
191C4—3761no—
192C4—1882no—
193C4—1882no—
194C4#1309400111yescharacteristic
195C4#1309400311yescharacteristic
196C4#1309401011yescharacteristic
197C4#1309401111yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#1568903511yescharacteristic
subgroupG/H
centerC4#13094010
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC2×C47#393
hypercenterC2×#104D47
hypocenterC47#2031
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
4. #15688895C2semidirect
5. #15688883C2semidirect
6. #15688880C2semidirect
27. C2×Q8×C47Q8semidirect
29. C2×D4×C47Q8semidirect
109. C47#2031semidirect
130. C2×Q8Dic94semidirect
132. C2×D4Dic94semidirect