Finite Group Databasebeta

← #26119002

Subgroups — #26119002

Order 12032.

504 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 113 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#20254539C212yesmaximal
2#20244365C211yesmaximal, characteristic
3#20242073C212yesmaximal
4#20241221C211yesmaximal, characteristic
5C47×#2862C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689526—22no—
8#15689475—22no—
9#15689458—24no—
10#15689415—24no—
11#15689176C2212yes—
12#15689147C2211yescharacteristic
13#15688883—22no—
14#15688869—24no—
15C2×C4⋊Q8×C47C2212yes—
16C47×#391—24no—
17C47×#382—22no—
18C43×C47C2211yescharacteristic
19C2×#10625329—21no—
20#13094024D412yes—
21#13094016—21no—
22#13094003—22no—
23C4×Dic94—22no—
24#13093983—21no—
25#13093957—28no—
26C4⋊(C47⋊C8)—22no—
27C4⋊(C47⋊C8)D414yes—
28#13093947—28no—
29C22⋊(C47⋊C8)—22no—
30C4×C47⋊C8—22no—
31C22×Q8×C47—22no—
32C4⋊Q8×C47—22no—
33C4⋊Q8×C47—22no—
34C4⋊Q8×C47—22no—
35C4⋊Q8×C47—22no—
36C2×C4⋊C4×C47—22no—
37C2×C4⋊C4×C47D414yes—
38C2×C42×C47—22no—
39C2×C42×C47D412yes—
40C2×C42×C47C2311yescharacteristic
41#95×C47—28no—
42C2×Q8×C47—48no—
43C2×Q8×C47—42no—
44C2×Q8×C47—42no—
45C22×C4×C47—22no—
46C22×C4×C47—24no—
47C22×C4×C47C2×D412yes—
48C22×C4×C47C2×D411yescharacteristic
49C2×Dic94—22no—
50C4⋊C4×C47—24no—
51C4⋊C4×C47—24no—
52C4⋊C4×C47—42no—
53C4⋊C4×C47—42no—
54C42×C47—22no—
55C42×C47—44no—
56C42×C47Q1614yes—
57C42×C47C2×D411yescharacteristic
58C42×C47C2×D412yes—
59C42×C47#4111yescharacteristic
60C22⋊Dic47—41no—
61C4⋊Dic47—22no—
62C4⋊Dic47—22no—
63Dic47⋊C4—42no—
64C4×Dic47—41no—
65#10625329—42no—
66C2×C47⋊C8—24no—
67C2×C47⋊C8—41no—
68C23×C47#12011yescharacteristic
69Q8×C47—84no—
70Q8×C47—84no—
71C2×C4×C47—24no—
72C2×C4×C47—24no—
73C2×C4×C47—44no—
74C2×C4×C47—48no—
75C2×C4×C47—44no—
76C2×C4×C47#12012yes—
77C2×C4×C47#12111yescharacteristic
78C2×C4×C47#12112yes—
79C2×C4×C47#12711yescharacteristic
80C2×C4×C47C2×Q1612yes—
81C2×C4×C47#13712yes—
82C2×Dic47—42no—
83Dic94—44no—
84C47⋊C8—44no—
85C47⋊C8—81no—
86#10295—471nomaximal, Sylow
87C22×C47—22no—
88C22×C47#39211yescharacteristic
89C22×C47#45112yes—
90C4×C47—22no—
91C4×C47—44no—
92C4×C47—84no—
93C4×C47#45414yes—
94C4×C47#46212yes—
95C4×C47#49411yescharacteristic
96C4×C47#49711yescharacteristic
97Dic47—82no—
98#3230—472no—
99#2862D4711yescharacteristic
100#1994—471no—
101#1549—472no—
102#1276—471no—
103C2×C47—22no—
104C2×C47#200312yes—
105C2×C47#201611yescharacteristic
106#533—471no—
107C2×C4⋊Q8C2×D4712yes—
108#500—942no—
109#487—942no—
110#484—944no—
111#477—944no—
112#431—472no—
113#423—471no—
114#391—24no—
115#382—22no—
116C43C2×D4711yescharacteristic
117#339—942no—
118#332—944no—
119C47#1029511yescharacteristic, complemented, Sylow
120C22×Q8—22no—
121C2×M16—941no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—472no—
127#125—941no—
128C22⋊Q8—942no—
129C4×Q8—942no—
130#117—941no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4C22⋊D4714yes—
133C2×C42—22no—
134C2×C42C22⋊D4712yes—
135C2×C42C22×D4711yescharacteristic
136#107—948no—
137C4⋊C8—474no—
138C4⋊C8—942no—
139#103—948no—
140C22⋊C8—942no—
141C4×C8—942no—
142#95—28no—
143C2×Q8—48no—
144C2×Q8—42no—
145C2×Q8—42no—
146C2×Q8—942no—
147C22×C4—22no—
148C22×C4—24no—
149C22×C4C2×C22⋊D4712yes—
150C22×C4C2×C22⋊D4711yescharacteristic
151M16—1882no—
152C2×C8—944no—
153C2×C8—1881no—
154C4⋊C4—24no—
155C4⋊C4—24no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4—1882no—
161C22⋊C4—1881no—
162C42—22no—
163C42—44no—
164C42—1881no—
165C42#1062533714yes—
166C42D4×D4711yescharacteristic
167C42D4×D4712yes—
168C42#1062535211yescharacteristic
169C23#1309399311yescharacteristic
170Q8—84no—
171Q8—84no—
172Q8—1884no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—1882no—
179C2×C4#1309399212yes—
180C2×C4#1309399511yescharacteristic
181C2×C4#1309399612yes—
182C2×C4#1309402011yescharacteristic
183C2×C4C2×#1062533712yes—
184C2×C4#1309405512yes—
185C8—3761no—
186C8—1884no—
187C22—22no—
188C22#1568903111yescharacteristic
189C22#1568927912yes—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—3762no—
194C4#1568929514yes—
195C4#1568933012yes—
196C4#1568950211yescharacteristic
197C4#1568951511yescharacteristic
198C2—22no—
199C2#2024441012yes—
200C2#2024448811yescharacteristic
subgroupG/H
centerC22#15689031
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2862C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#2862D47
hypocenterC47#10295
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

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
#202545392
#202443652
#202420732
#202412212
C47×#28622
#1029547