Finite Group Databasebeta

← #20244492

Subgroups — #20244492

Order 6016.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#15689923C211yesmaximal, characteristic, complemented
2#15689921C212yesmaximal, complemented
3#15689089C212yesmaximal, complemented
4C47⋊#338C211yesmaximal, characteristic, complemented
5C47×#408C211yesmaximal, characteristic, complemented
6C2×#10625350C2212yes—
7#13094057—22no—
8#13094055—22no—
9#13094054—22no—
10#13094052—22no—
11#13094050—22no—
12#13094049—22no—
13#13094046—22no—
14#13094044—24no—
15C2×#10625329C2212yes—
16(C2×D47)⋊C8—24no—
17C2×#41×C47C2211yescharacteristic
18C2×M16×C47C2211yescharacteristic
19C22×C8×C47C2211yescharacteristic
20C22⋊C8×C47—22no—
21#41×C47—22no—
22#41×C47—22no—
23C2×Q8×C47D411yescharacteristic
24C2×D4×C47—21no—
25C2×D4×C47D411yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—22no—
29#10625350—22no—
30#10625350—22no—
31#10625350—22no—
32#10625350—22no—
33C2×D188D412yes—
34C2×C4×D47—22no—
35C2×Dic94D412yes—
36M16×C47—22no—
37C2×C8×C47—22no—
38C2×C8×C47—21no—
39C2×C8×C47D412yes—
40#10625337—24no—
41#10625336—24no—
42#10625335—24no—
43#10625334—24no—
44#10625329—22no—
45#10625329—22no—
46C2×C47⋊C8D414yes—
47Dic188—22no—
48D376—22no—
49#10625325—24no—
50C23×C47—21no—
51C23×C47#4111yescharacteristic
52C22×D47—22no—
53Q8×C47—22no—
54D4×C47—22no—
55D4×C47—42no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D412yes—
61C2×C4×C47C2×D412yes—
62C2×C4×C47C2×D411yescharacteristic
63C22⋊D47—42no—
64C22⋊D47—42no—
65C2×Dic47—22no—
66D188—22no—
67D188—22no—
68C4×D47—42no—
69C4×D47—42no—
70Dic94—22no—
71Dic94—22no—
72C8×C47—22no—
73C8×C47—41no—
74C47⋊C8—24no—
75C22×C47—41no—
76C22×C47—42no—
77C22×C47—41no—
78C22×C47#12112yes—
79C22×C47#12111yescharacteristic
80C2×D47—44no—
81C2×D47—42no—
82C4×C47—41no—
83C4×C47#12011yescharacteristic
84C4×C47#12012yes—
85C4×C47#12711yescharacteristic
86Dic47—42no—
87#2017—471nomaximal, Sylow
88C2×C47—22no—
89C2×C47—21no—
90C2×C47—81no—
91C2×C47#39211yescharacteristic
92D47—82no—
93#575—472no—
94#575—471no—
95#408—472no—
96#408D4711yescharacteristic, complemented
97#338—471no—
98C47#201711yescharacteristic, complemented, Sylow
99C2×#41—472no—
100C2×#41C2×D4711yescharacteristic
101#137—942no—
102#137—942no—
103#137—942no—
104AGL(1,ℤ/8)—942no—
105AGL(1,ℤ/8)—942no—
106AGL(1,ℤ/8)—942no—
107#135—944no—
108#135—942no—
109C2×M16—472no—
110C2×M16C2×D4711yescharacteristic
111C22×C8C2×D4711yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—944no—
114#41—22no—
115#41—22no—
116#41—942no—
117#41—942no—
118#41—942no—
119#41—942no—
120C2×Q8—472no—
121C2×Q8D18811yescharacteristic
122C2×D4—21no—
123C2×D4—472no—
124C2×D4—942no—
125C2×D4D18811yescharacteristic
126C22×C4—21no—
127C22×C4—942no—
128C22×C4C22×D4711yescharacteristic
129Q16—942no—
130Q16—944no—
131SD16—944no—
132SD16—944no—
133SD16—944no—
134D8—942no—
135D8—944no—
136M16—22no—
137M16—942no—
138M16—942no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—474no—
142C2×C8C22⋊D4712yes—
143C23—21no—
144C23—942no—
145C23#1062535011yescharacteristic
146Q8—22no—
147Q8—942no—
148Q8—942no—
149D4—22no—
150D4—42no—
151D4—942no—
152D4—942no—
153D4—1882no—
154D4—1882no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—942no—
159C2×C4—1882no—
160C2×C4—1882no—
161C2×C4C2×D18811yescharacteristic
162C2×C4D4×D4712yes—
163C2×C4D4×D4712yes—
164C2×C4C2×C22⋊D4711yescharacteristic
165C8—22no—
166C8—41no—
167C8—944no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—1884no—
172C22—1882no—
173C22#1309399712yes—
174C22#1309399811yescharacteristic
175C4—41no—
176C4—1882no—
177C4#1309399211yescharacteristic
178C4#1309399412yes—
179C4#1309402011yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—3762no—
184C2#1568903211yescharacteristic
subgroupG/H
centerC4#13094020
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#408C2
socleC2×C47#392
hypercenter#408D47
hypocenterC47#2017
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #15689923C2semidirect
2. #15689921C2semidirect
3. #15689089C2semidirect
4. C47⋊#338C2semidirect
5. C47×#408C2semidirect
96. #408D47semidirect
98. C47#2017semidirect