Finite Group Databasebeta

← #20244558

Subgroups — #20244558

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#15689676C211yesmaximal, characteristic, complemented
2C2×#13093951C211yesmaximal, characteristic
3#15689097C211yesmaximal, characteristic
4#15688894C211yesmaximal, characteristic, complemented
5#15688884C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#421C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9#13094023—21no—
10#13094015—21no—
11#13094001—22no—
12C4×Dic94—22no—
13#13093983C2211yescharacteristic
14#13093983C2211yescharacteristic
15C2×C4×Dic47C2211yescharacteristic
16#13093951—21no—
17#13093951—21no—
18#13093939—22no—
19C2×#41×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic
21#117×C47C2211yescharacteristic
22#104×C47—22no—
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×C47C2311yescharacteristic
32C22×Dic47—21no—
33C2×Dic94—22no—
34M16×C47—21no—
35M16×C47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C22⋊C4×C47—21no—
39C42×C47D412yes—
40C22⋊Dic47—21no—
41C22⋊Dic47D412yes—
42C4⋊Dic47—22no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45Dic47⋊C4—22no—
46Dic47⋊C4—22no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52#10625329—21no—
53#10625329—21no—
54C2×C47⋊C8—21no—
55C23×C47—21no—
56C23×C47C2×D411yescharacteristic
57Q8×C47—21no—
58Q8×C47—21no—
59D4×C47—21no—
60D4×C47—21no—
61D4×C47—41no—
62D4×C47—41no—
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×Q811yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—22no—
76C2×Dic47—42no—
77C2×Dic47—41no—
78Dic94—44no—
79C8×C47—41no—
80C47⋊C8—41no—
81C22×C47—41no—
82C22×C47—41no—
83C22×C47—81no—
84C22×C47#12011yescharacteristic
85C22×C47C22⋊Q811yescharacteristic
86C22×C47#12411yescharacteristic
87C4×C47—42no—
88C4×C47—41no—
89C4×C47C22⋊Q811yescharacteristic
90C4×C47C22⋊Q811yescharacteristic
91C4×C47#12411yescharacteristic
92C4×C47#12411yescharacteristic
93Dic47—22no—
94Dic47—42no—
95Dic47—41no—
96Dic47—81no—
97#2031—471nomaximal, Sylow
98C2×C47—21no—
99C2×C47—21no—
100C2×C47—21no—
101C2×C47—81no—
102C2×C47#39311yescharacteristic
103#533—471no—
104#421D4711yescharacteristic
105C2×#104—471no—
106#410—471no—
107#344—471no—
108#339—471no—
109H(3,ℤ/4)—471no—
110C47#203111yescharacteristic, complemented, Sylow
111C2×#41C2×D4711yescharacteristic
112C2×M16—471no—
113C2×M16C2×D4711yescharacteristic
114C4⋊Q8—941no—
115#125—941no—
116C22⋊Q8—942no—
117C4×Q8—942no—
118#117—471no—
119#117—471no—
120#117C2×D4711yescharacteristic
121C2×C42—471no—
122#104—22no—
123#104—941no—
124#104—941no—
125#99—942no—
126#41—21no—
127#41—21no—
128#41—21no—
129#41—21no—
130C2×Q8—942no—
131C2×Q8Dic9411yescharacteristic, complemented
132C2×D4—21no—
133C2×D4Dic9411yescharacteristic, complemented
134C22×C4—21no—
135C22×C4—941no—
136C22×C4C22×D4711yescharacteristic
137M16—21no—
138M16—21no—
139M16—941no—
140M16—941no—
141C2×C8—21no—
142C2×C8—941no—
143C4⋊C4—21no—
144C4⋊C4—942no—
145C4⋊C4—942no—
146C4⋊C4—942no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C22⋊C4—21no—
150C22⋊C4—472no—
151C22⋊C4—941no—
152C42—471no—
153C42—471no—
154C42—941no—
155C42—941no—
156C42—941no—
157C42C22⋊D4712yes—
158C23—21no—
159C23D4×D4711yescharacteristic
160Q8—21no—
161Q8—21no—
162Q8—1884no—
163D4—21no—
164D4—21no—
165D4—41no—
166D4—41no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—941no—
172C2×C4—941no—
173C2×C4—942no—
174C2×C4—1882no—
175C2×C4—1881no—
176C2×C4C2×Dic9411yescharacteristic
177C2×C4#1062535011yescharacteristic
178C2×C4D4×D4711yescharacteristic
179C2×C4#1062535211yescharacteristic
180C2×C4#1062535211yescharacteristic
181C2×C4C2×C22⋊D4711yescharacteristic
182C8—41no—
183C8—1881no—
184C22—41no—
185C22—41no—
186C22—81no—
187C22#1309399211yescharacteristic
188C22#1309400111yescharacteristic
189C22#1309401011yescharacteristic
190C4—42no—
191C4—41no—
192C4—942no—
193C4—3761no—
194C4—1881no—
195C4—1882no—
196C4#1309400111yescharacteristic
197C4#1309400311yescharacteristic
198C4#1309401011yescharacteristic
199C4#1309401111yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—81no—
204C2#1568903511yescharacteristic
subgroupG/H
centerC4#13094011
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#421C2
socleC2×C47#393
hypercenter#421D47
hypocenterC47#2031
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #15689676C2semidirect
4. #15688894C2semidirect
5. #15688884C2semidirect
6. #15688879C2semidirect
27. C2×Q8×C47Q8semidirect
29. C2×D4×C47Q8semidirect
110. C47#2031semidirect
131. C2×Q8Dic94semidirect
133. C2×D4Dic94semidirect