Finite Group Databasebeta

← #26119001

Subgroups — #26119001

Order 12032.

504 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 111 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#20254536C212yesmaximal
2#20251766C211yesmaximal, characteristic
3#20242074C212yesmaximal
4#20241221C211yesmaximal, characteristic
5C47×#1994C211yesmaximal, characteristic
6C2×#13094024C2212yes—
7#15689526—22no—
8#15689473—22no—
9#15689456—24no—
10#15689418—24no—
11#15689176C2212yes—
12#15689029—24no—
13#15688989—22no—
14#15688868—24no—
15C47×#533C2211yescharacteristic
16C47×#423C2211yescharacteristic
17C43×C47C2211yescharacteristic
18C47×#339—22no—
19C22×Dic94—22no—
20#13094024—22no—
21#13094024—22no—
22#13094024—22no—
23#13094024—22no—
24C2×C4⋊Dic47—22no—
25C2×C4⋊Dic47D414yes—
26#13093957—28no—
27C4⋊(C47⋊C8)D414yes—
28#13093948—28no—
29C22⋊(C47⋊C8)—22no—
30C4×C47⋊C8—22no—
31C47⋊#95—28no—
32C2×M16×C47—21no—
33C4⋊Q8×C47D412yes—
34#125×C47—21no—
35C22⋊Q8×C47—22no—
36C4×Q8×C47—22no—
37#117×C47—21no—
38C2×C42×C47—22no—
39C2×C42×C47D412yes—
40C2×C42×C47C2311yescharacteristic
41C4⋊C8×C47—22no—
42C2×Q8×C47—22no—
43C22×C4×C47—22no—
44C22×C4×C47C2×D412yes—
45C22×C4×C47C2×D411yescharacteristic
46C22×Dic47—24no—
47C2×Dic94—48no—
48C2×Dic94—42no—
49C2×Dic94—42no—
50M16×C47—42no—
51C2×C8×C47—41no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—22no—
54C4⋊C4×C47—42no—
55C22⋊C4×C47—41no—
56C42×C47—22no—
57C42×C47—44no—
58C42×C47—41no—
59C42×C47Q1614yes—
60C42×C47C2×D411yescharacteristic
61C42×C47C2×D412yes—
62C42×C47#4111yescharacteristic
63C4⋊Dic47—24no—
64C4⋊Dic47—24no—
65C4⋊Dic47—42no—
66C4⋊Dic47—42no—
67C2×C47⋊C8—24no—
68C23×C47#12011yescharacteristic
69Q8×C47—44no—
70C2×C4×C47—24no—
71C2×C4×C47—24no—
72C2×C4×C47—44no—
73C2×C4×C47—42no—
74C2×C4×C47#12012yes—
75C2×C4×C47#12112yes—
76C2×C4×C47#12111yescharacteristic
77C2×C4×C47#12711yescharacteristic
78C2×C4×C47C2×Q1612yes—
79C2×C4×C47#13712yes—
80C2×Dic47—48no—
81C2×Dic47—44no—
82Dic94—84no—
83Dic94—84no—
84C8×C47—81no—
85C47⋊C8—44no—
86#10295—471nomaximal, Sylow
87C22×C47—22no—
88C22×C47#39211yescharacteristic
89C22×C47#45112yes—
90C4×C47—22no—
91C4×C47—44no—
92C4×C47—82no—
93C4×C47#45414yes—
94C4×C47#46212yes—
95C4×C47#49411yescharacteristic
96C4×C47#49711yescharacteristic
97Dic47—84no—
98#3230—472no—
99#2862—471no—
100#1994D4711yescharacteristic
101#1549—472no—
102#1276—471no—
103C2×C47—22no—
104C2×C47#200312yes—
105C2×C47#201611yescharacteristic
106#533C2×D4711yescharacteristic
107C2×C4⋊Q8—472no—
108#500—942no—
109#487—942no—
110#484—944no—
111#477—944no—
112#431—472no—
113#423C2×D4711yescharacteristic
114#391—944no—
115#382—942no—
116C43C2×D4711yescharacteristic
117#339—22no—
118#332—944no—
119C47#1029511yescharacteristic, complemented, Sylow
120C22×Q8—942no—
121C2×M16—21no—
122C4⋊Q8—942no—
123C4⋊Q8—942no—
124C4⋊Q8—942no—
125C4⋊Q8—942no—
126C4⋊Q8D18812yes—
127#125—21no—
128C22⋊Q8—22no—
129C4×Q8—22no—
130#117—21no—
131C2×C4⋊C4—474no—
132C2×C4⋊C4—942no—
133C2×C42—22no—
134C2×C42C22⋊D4712yes—
135C2×C42C22×D4711yescharacteristic
136#107—948no—
137C4⋊C8—22no—
138C4⋊C8—474no—
139#103—948no—
140C22⋊C8—942no—
141C4×C8—942no—
142#95—948no—
143C2×Q8—22no—
144C2×Q8—1888no—
145C2×Q8—1882no—
146C2×Q8—1882no—
147C22×C4—22no—
148C22×C4—944no—
149C22×C4D4×D4712yes—
150C22×C4C2×C22⋊D4711yescharacteristic
151M16—42no—
152C2×C8—41no—
153C2×C8—944no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—42no—
157C4⋊C4—944no—
158C4⋊C4—944no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C22⋊C4—41no—
162C42—22no—
163C42—44no—
164C42—41no—
165C42#1062533714yes—
166C42C2×D18811yescharacteristic
167C42#1062535011yescharacteristic
168C42D4×D4712yes—
169C23#1309399211yescharacteristic
170Q8—44no—
171Q8—3764no—
172Q8—3764no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—42no—
177C2×C4—1888no—
178C2×C4—1884no—
179C2×C4#1309399412yes—
180C2×C4#1309399712yes—
181C2×C4#1309399811yescharacteristic
182C2×C4#1309402011yescharacteristic
183C2×C4C2×#1062533712yes—
184C2×C4#1309405412yes—
185C8—81no—
186C8—1884no—
187C22—22no—
188C22#1568903211yescharacteristic
189C22#1568927812yes—
190C4—22no—
191C4—44no—
192C4—82no—
193C4—3764no—
194C4#1568929714yes—
195C4#1568933312yes—
196C4#1568950211yescharacteristic
197C4#1568951811yescharacteristic
198C2—22no—
199C2#2024440912yes—
200C2#2024448711yescharacteristic
subgroupG/H
centerC22#15689032
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1994C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#1994D47
hypocenterC47#10295
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
119. C47#10295semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202545362
#202517662
#202420742
#202412212
C47×#19942
#1029547