Finite Group Databasebeta

← #20244666

Subgroups — #20244666

Order 6016.

254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#13094055C211yesmaximal, characteristic
2#15689171C211yesmaximal, characteristic, complemented
3#15689141C211yesmaximal, characteristic
4#15689105C211yesmaximal, characteristic
5C2×#13093943C211yesmaximal, characteristic, complemented
6#15688893C211yesmaximal, characteristic, complemented
7C47×#419C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—22no—
10#13094055—22no—
11C2×#10625337—21no—
12C2×#10625336—21no—
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15C2×#10625329C2211yescharacteristic
16#13093959—22no—
17#13093952—22no—
18#13093943—22no—
19#13093942—21no—
20#13093940—21no—
21C22×Q8×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23#117×C47C2211yescharacteristic
24#103×C47—22no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47D412yes—
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33C2×C22⋊D47—21no—
34#10625350—21no—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38C2×D188D411yescharacteristic
39C2×C4×D47—21no—
40C2×Dic94D411yescharacteristic
41M16×C47—21no—
42M16×C47—21no—
43C2×C8×C47—21no—
44C4⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C42×C47—21no—
47#10625337—24no—
48#10625336—24no—
49#10625329—21no—
50#10625329—21no—
51#10625329—21no—
52#10625329—21no—
53#10625329D412yes—
54#10625329D412yes—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C23×C47#4111yescharacteristic
59C22×D47—21no—
60Q8×C47—22no—
61Q8×C47—22no—
62Q8×C47—41no—
63Q8×C47—41no—
64C2×C4×C47—22no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C22⋊D47—41no—
75C22⋊D47—41no—
76C2×Dic47—21no—
77D188—21no—
78D188—21no—
79C4×D47—41no—
80C4×D47—41no—
81Dic94—21no—
82Dic94—21no—
83C8×C47—41no—
84C47⋊C8—22no—
85C47⋊C8—22no—
86C47⋊C8—41no—
87C22×C47—41no—
88C22×C47#12111yescharacteristic
89C22×C47#12311yescharacteristic
90C22×C47#12411yescharacteristic
91C2×D47—41no—
92C2×D47—81no—
93C4×C47—42no—
94C4×C47—81no—
95C4×C47#12011yescharacteristic
96C4×C47#12111yescharacteristic
97C4×C47#12111yescharacteristic
98C4×C47#12311yescharacteristic
99Dic47—41no—
100#2049—471nomaximal, Sylow
101C2×C47—21no—
102C2×C47—21no—
103C2×C47—21no—
104C2×C47#39411yescharacteristic
105D47—81no—
106C2×#137—471no—
107#430—471no—
108#421—471no—
109#419D4711yescharacteristic, complemented
110#413—471no—
111C2×#101—471no—
112#344—471no—
113C47#204911yescharacteristic, complemented, Sylow
114C2×#41—471no—
115C22×Q8C2×D4711yescharacteristic
116#137—942no—
117#137—942no—
118C2×Q16—941no—
119C2×SD16—941no—
120C2×M16—471no—
121C2×M16—471no—
122C2×M16—471no—
123C2×M16C2×D4711yescharacteristic
124#117C2×D4711yescharacteristic
125#108—942no—
126#104—942no—
127#103—22no—
128#101—941no—
129#101—942no—
130#100—941no—
131#41—941no—
132#41—941no—
133#41—941no—
134#41—941no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—471no—
141C2×Q8C22⋊D4712yes—
142C2×D4—471no—
143C2×D4—941no—
144C22×C4—21no—
145C22×C4—941no—
146C22×C4C22×D4711yescharacteristic
147Q16—944no—
148SD16—944no—
149M16—21no—
150M16—21no—
151M16—472no—
152M16—472no—
153M16—941no—
154M16—941no—
155M16—941no—
156M16—941no—
157C2×C8—21no—
158C2×C8—941no—
159C2×C8—941no—
160C2×C8—941no—
161C4⋊C4—21no—
162C22⋊C4—21no—
163C42—21no—
164C23—941no—
165C23#1062535211yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—941no—
171Q8—941no—
172D4—941no—
173D4—941no—
174D4—1881no—
175D4—1881no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—941no—
181C2×C4—1881no—
182C2×C4—1881no—
183C2×C4#1062535011yescharacteristic
184C2×C4#1062535011yescharacteristic
185C2×C4D4×D4711yescharacteristic
186C2×C4D4×D4711yescharacteristic
187C2×C4D4×D4711yescharacteristic
188C2×C4C2×C22⋊D4711yescharacteristic
189C8—41no—
190C8—942no—
191C8—942no—
192C8—1881no—
193C22—41no—
194C22—3761no—
195C22—1881no—
196C22#1309399611yescharacteristic
197C22#1309400611yescharacteristic
198C22#1309401011yescharacteristic
199C4—42no—
200C4—81no—
201C4—1881no—
202C4#1309399211yescharacteristic
203C4#1309399711yescharacteristic
204C4#1309399711yescharacteristic
205C4#1309400711yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—3761no—
210C2#1568903811yescharacteristic
subgroupG/H
centerC2#15689038
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#419C2
socleC2×C47#394
hypercenter#419D47
hypocenterC47#2049
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #15689171C2semidirect
5. C2×#13093943C2semidirect
6. #15688893C2semidirect
7. C47×#419C2semidirect
109. #419D47semidirect
113. C47#2049semidirect