Finite Group Databasebeta

← #26119014

Subgroups — #26119014

Order 12032.

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

normal subgroups only

This group has 528 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#20254336C212yesmaximal
2#20244365C211yesmaximal, characteristic
3#20242069C212yesmaximal
4#20241221C211yesmaximal, characteristic
5C47×#2862C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689502—22no—
8#15689473—22no—
9#15689330—24no—
10#15689279—24no—
11#15689176C2212yes—
12#15689147C2211yescharacteristic
13#15688883—22no—
14#15688872—24no—
15C2×C4⋊Q8×C47C2212yes—
16C47×#391—24no—
17C47×#382—22no—
18C43×C47C2211yescharacteristic
19C2×#10625337—28no—
20C2×#10625329—21no—
21#13094024D412yes—
22#13094016—21no—
23#13094003—22no—
24C4×Dic94—22no—
25#13093983—21no—
26C4⋊(C47⋊C8)—22no—
27C4⋊(C47⋊C8)D414yes—
28#13093948—28no—
29C22⋊(C47⋊C8)—22no—
30C4×C47⋊C8—22no—
31C22×Q8×C47D414yes—
32C4⋊Q8×C47—22no—
33C4⋊Q8×C47—22no—
34C4⋊Q8×C47—22no—
35C4⋊Q8×C47—22no—
36C2×C4⋊C4×C47—22no—
37C2×C4⋊C4×C47—22no—
38C2×C42×C47—22no—
39C2×C42×C47D412yes—
40C2×C42×C47C2311yescharacteristic
41#95×C47—28no—
42C2×Q8×C47—24no—
43C2×Q8×C47—24no—
44C2×Q8×C47—48no—
45C22×C4×C47—22no—
46C22×C4×C47—24no—
47C22×C4×C47C2×D412yes—
48C22×C4×C47C2×D411yescharacteristic
49C2×Dic94—22no—
50C4⋊C4×C47—42no—
51C4⋊C4×C47—42no—
52C4⋊C4×C47—42no—
53C4⋊C4×C47—42no—
54C42×C47—22no—
55C42×C47—44no—
56C42×C47Q1614yescomplemented
57C42×C47C2×D411yescharacteristic
58C42×C47C2×D412yes—
59C42×C47#4111yescharacteristic
60C22⋊Dic47—41no—
61#10625337—88no—
62C4⋊Dic47—22no—
63C4⋊Dic47—22no—
64Dic47⋊C4—42no—
65C4×Dic47—41no—
66#10625329—42no—
67C2×C47⋊C8—24no—
68C2×C47⋊C8—41no—
69C23×C47#12011yescharacteristic
70Q8×C47—48no—
71Q8×C47—84no—
72C2×C4×C47—24no—
73C2×C4×C47—24no—
74C2×C4×C47—44no—
75C2×C4×C47—48no—
76C2×C4×C47—44no—
77C2×C4×C47#12012yes—
78C2×C4×C47#12111yescharacteristic
79C2×C4×C47#12112yes—
80C2×C4×C47#12711yescharacteristic
81C2×C4×C47C2×Q1612yes—
82C2×C4×C47#13712yes—
83C2×Dic47—42no—
84Dic94—44no—
85C47⋊C8—44no—
86C47⋊C8—81no—
87#10297—471nomaximal, Sylow
88C22×C47—22no—
89C22×C47#39211yescharacteristic
90C22×C47#45112yes—
91C4×C47—22no—
92C4×C47—44no—
93C4×C47—84no—
94C4×C47#45514yes—
95C4×C47#46212yes—
96C4×C47#49411yescharacteristic
97C4×C47#49711yescharacteristic
98Dic47—82no—
99#3209—472no—
100#2862D4711yescharacteristic
101#1994—471no—
102#1548—472no—
103#1276—471no—
104C2×C47—22no—
105C2×C47#200412yes—
106C2×C47#201611yescharacteristic
107#533—471no—
108C2×C4⋊Q8C2×D4712yes—
109#494—942no—
110#487—942no—
111#462—944no—
112#451—944no—
113#431—472no—
114#423—471no—
115#391—24no—
116#382—22no—
117C43C2×D4711yescharacteristic
118#339—942no—
119#333—944no—
120C47#1029711yescharacteristic, complemented, Sylow
121C22×Q8C22⋊D4714yes—
122C2×Q16—948no—
123C2×M16—941no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—472no—
129#125—941no—
130C22⋊Q8—942no—
131C4×Q8—942no—
132#117—941no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C42—22no—
136C2×C42C22⋊D4712yes—
137C2×C42C22×D4711yescharacteristic
138C4⋊C8—474no—
139C4⋊C8—942no—
140#103—948no—
141C22⋊C8—942no—
142C4×C8—942no—
143#95—28no—
144C2×Q8—24no—
145C2×Q8—24no—
146C2×Q8—48no—
147C2×Q8—942no—
148C22×C4—22no—
149C22×C4—24no—
150C22×C4C2×C22⋊D4712yes—
151C22×C4C2×C22⋊D4711yescharacteristic
152Q16—3768no—
153M16—1882no—
154C2×C8—944no—
155C2×C8—1881no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—942no—
161C4⋊C4—942no—
162C4⋊C4—1882no—
163C22⋊C4—1881no—
164C42—22no—
165C42—44no—
166C42—1881no—
167C42#1062533714yescomplemented
168C42D4×D4711yescharacteristic
169C42D4×D4712yes—
170C42#1062535211yescharacteristic
171C23#1309399311yescharacteristic
172Q8—48no—
173Q8—84no—
174Q8—1884no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—48no—
179C2×C4—44no—
180C2×C4—1882no—
181C2×C4#1309399212yes—
182C2×C4#1309399511yescharacteristic
183C2×C4#1309399612yes—
184C2×C4#1309402011yescharacteristic
185C2×C4C2×#1062533712yes—
186C2×C4#1309405512yes—
187C8—3761no—
188C8—1884no—
189C22—22no—
190C22#1568903111yescharacteristic
191C22#1568927912yes—
192C4—22no—
193C4—44no—
194C4—84no—
195C4—3762no—
196C4#1568930014yes—
197C4#1568933012yes—
198C4#1568950211yescharacteristic
199C4#1568951511yescharacteristic
200C2—22no—
201C2#2024441712yes—
202C2#2024448811yescharacteristic
subgroupG/H
centerC22#15689031
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2862C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#2862D47
hypocenterC47#10297
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
56. C42×C47Q16semidirect
120. C47#10297semidirect
167. C42#10625337semidirect

Maximal subgroups

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

subgroupindex
#202543362
#202443652
#202420692
#202412212
C47×#28622
#1029747