Finite Group Databasebeta

← #26119026

Subgroups — #26119026

Order 12032.

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

normal subgroups only

This group has 576 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#20254532C212yesmaximal
2#20244365C211yesmaximal, characteristic
3#20242060C212yesmaximal
4#20241221C211yesmaximal, characteristic
5C47×#2868C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689519—22no—
8#15689475—22no—
9#15689453—24no—
10#15689405—24no—
11#15689176C2212yes—
12#15689147C2211yescharacteristic
13#15688883—22no—
14#15688869—24no—
15C2×C4⋊Q8×C47—22no—
16C2×C4⋊Q8×C47C2212yes—
17C47×#384—24no—
18C43×C47C2211yescharacteristic
19C2×#10625329—21no—
20#13094024D412yes—
21#13094016—21no—
22#13094003—22no—
23C4×Dic94—22no—
24#13093983—21no—
25#13093955—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—
36C4⋊Q8×C47—44no—
37C4⋊Q8×C47—44no—
38C2×C4⋊C4×C47—28no—
39C2×C4⋊C4×C47—22no—
40C2×C4⋊C4×C47D414yes—
41C2×C42×C47—22no—
42C2×C42×C47D412yes—
43C2×C42×C47C2311yescharacteristic
44C2×Q8×C47—42no—
45C2×Q8×C47—42no—
46C2×Q8×C47—44no—
47C2×Q8×C47—44no—
48C22×C4×C47—22no—
49C22×C4×C47—24no—
50C22×C4×C47C2×D412yes—
51C22×C4×C47C2×D411yescharacteristic
52C2×Dic94—22no—
53C4⋊C4×C47—24no—
54C4⋊C4×C47—24no—
55C4⋊C4×C47—416no—
56C4⋊C4×C47—42no—
57C4⋊C4×C47—42no—
58C42×C47—28no—
59C42×C47—22no—
60C42×C47SD1614yes—
61C42×C47C2×D411yescharacteristic
62C42×C47C2×D412yes—
63C42×C47#4111yescharacteristic
64C22⋊Dic47—41no—
65C4⋊Dic47—22no—
66C4⋊Dic47—22no—
67Dic47⋊C4—42no—
68C4×Dic47—41no—
69#10625329—42no—
70C2×C47⋊C8—24no—
71C2×C47⋊C8—41no—
72C23×C47#12011yescharacteristic
73Q8×C47—84no—
74Q8×C47—82no—
75Q8×C47—82no—
76C2×C4×C47—28no—
77C2×C4×C47—24no—
78C2×C4×C47—24no—
79C2×C4×C47—44no—
80C2×C4×C47—48no—
81C2×C4×C47#12012yes—
82C2×C4×C47#12111yescharacteristic
83C2×C4×C47#12112yes—
84C2×C4×C47#12711yescharacteristic
85C2×C4×C47C2×SD1612yes—
86C2×C4×C47AGL(1,ℤ/8)12yes—
87C2×Dic47—42no—
88Dic94—44no—
89C47⋊C8—44no—
90C47⋊C8—81no—
91#10299—471nomaximal, Sylow
92C22×C47—22no—
93C22×C47#39211yescharacteristic
94C22×C47#45012yes—
95C4×C47—28no—
96C4×C47—22no—
97C4×C47—84no—
98C4×C47#45614yes—
99C4×C47#46012yes—
100C4×C47#49211yescharacteristic
101C4×C47#49611yescharacteristic
102Dic47—82no—
103#3229—472no—
104#2868D4711yescharacteristic
105#1994—471no—
106#1546—472no—
107#1276—471no—
108C2×C47—22no—
109C2×C47#200512yes—
110C2×C47#201411yescharacteristic
111#533—471no—
112C2×C4⋊Q8—22no—
113C2×C4⋊Q8C2×D4712yes—
114#498—942no—
115#487—942no—
116#483—944no—
117#475—944no—
118#431—472no—
119#423—471no—
120#384—24no—
121C43C2×D4711yescharacteristic
122#339—942no—
123#332—944no—
124C47#1029911yescharacteristic, complemented, Sylow
125C22×Q8—22no—
126C2×M16—941no—
127C4⋊Q8—22no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—22no—
131C4⋊Q8—44no—
132C4⋊Q8—44no—
133C4⋊Q8—472no—
134#125—941no—
135C22⋊Q8—942no—
136C4×Q8—942no—
137#117—941no—
138C2×C4⋊C4—28no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4C22⋊D4714yes—
141C2×C42—22no—
142C2×C42C22⋊D4712yes—
143C2×C42C22×D4711yescharacteristic
144#106—948no—
145C4⋊C8—474no—
146C4⋊C8—942no—
147#103—948no—
148C22⋊C8—942no—
149C4×C8—942no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—44no—
153C2×Q8—44no—
154C2×Q8—942no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4C2×C22⋊D4712yes—
158C22×C4C2×C22⋊D4711yescharacteristic
159M16—1882no—
160C2×C8—944no—
161C2×C8—1881no—
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—416no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—1882no—
170C22⋊C4—1881no—
171C42—28no—
172C42—22no—
173C42—1881no—
174C42#1062533514yes—
175C42D4×D4711yescharacteristic
176C42D4×D4712yes—
177C42#1062535211yescharacteristic
178C23#1309399311yescharacteristic
179Q8—82no—
180Q8—82no—
181Q8—84no—
182Q8—1884no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—48no—
187C2×C4—44no—
188C2×C4—1882no—
189C2×C4#1309399212yes—
190C2×C4#1309399511yescharacteristic
191C2×C4#1309399612yes—
192C2×C4#1309402011yescharacteristic
193C2×C4C2×#1062533512yes—
194C2×C4#1309405012yes—
195C8—3761no—
196C8—1884no—
197C22—22no—
198C22#1568903111yescharacteristic
199C22#1568927412yes—
200C4—28no—
201C4—22no—
202C4—84no—
203C4—3762no—
204C4#1568930514yes—
205C4#1568932012yes—
206C4#1568949511yescharacteristic
207C4#1568951011yescharacteristic
208C2—22no—
209C2#2024442412yes—
210C2#2024447611yescharacteristic
subgroupG/H
centerC22#15689031
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2868C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#2868D47
hypocenterC47#10299
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2868

Complements

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

NH ≅ G/Ntype
124. C47#10299semidirect

Maximal subgroups

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

subgroupindex
#202545322
#202443652
#202420602
#202412212
C47×#28682
#1029947