Finite Group Databasebeta

← #26119013

Subgroups — #26119013

Order 12032.

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

normal subgroups only

This group has 528 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#20254333C212yesmaximal
2#20251766C211yesmaximal, characteristic
3#20242070C212yesmaximal
4#20241221C211yesmaximal, characteristic
5C47×#1994C211yesmaximal, characteristic
6C2×#13094024C2212yes—
7#15689502—22no—
8#15689475—22no—
9#15689333—24no—
10#15689278—24no—
11#15689176C2212yes—
12#15689029—24no—
13#15688989—22no—
14#15688871—24no—
15C47×#533C2211yescharacteristic
16C47×#423C2211yescharacteristic
17C43×C47C2211yescharacteristic
18C47×#339—22no—
19C22×Dic94D414yes—
20C2×#10625337—28no—
21#13094024—22no—
22#13094024—22no—
23#13094024—22no—
24#13094024—22no—
25C2×C4⋊Dic47—22no—
26C2×C4⋊Dic47—22no—
27C4⋊(C47⋊C8)D414yes—
28#13093947—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—24no—
48C2×Dic94—24no—
49C2×Dic94—48no—
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×C47Q1614yescomplemented
60C42×C47C2×D411yescharacteristic
61C42×C47C2×D412yes—
62C42×C47#4111yescharacteristic
63#10625337—88no—
64C4⋊Dic47—42no—
65C4⋊Dic47—42no—
66C4⋊Dic47—42no—
67C4⋊Dic47—42no—
68C2×C47⋊C8—24no—
69C23×C47#12011yescharacteristic
70Q8×C47—44no—
71C2×C4×C47—24no—
72C2×C4×C47—24no—
73C2×C4×C47—44no—
74C2×C4×C47—42no—
75C2×C4×C47#12012yes—
76C2×C4×C47#12112yes—
77C2×C4×C47#12111yescharacteristic
78C2×C4×C47#12711yescharacteristic
79C2×C4×C47C2×Q1612yes—
80C2×C4×C47#13712yes—
81C2×Dic47—48no—
82C2×Dic47—44no—
83Dic94—48no—
84Dic94—84no—
85C8×C47—81no—
86C47⋊C8—44no—
87#10297—471nomaximal, Sylow
88C22×C47—22no—
89C22×C47#39211yescharacteristic
90C22×C47#45112yes—
91C4×C47—22no—
92C4×C47—44no—
93C4×C47—82no—
94C4×C47#45514yes—
95C4×C47#46212yes—
96C4×C47#49411yescharacteristic
97C4×C47#49711yescharacteristic
98Dic47—84no—
99#3209—472no—
100#2862—471no—
101#1994D4711yescharacteristic
102#1548—472no—
103#1276—471no—
104C2×C47—22no—
105C2×C47#200412yes—
106C2×C47#201611yescharacteristic
107#533C2×D4711yescharacteristic
108C2×C4⋊Q8—472no—
109#494—942no—
110#487—942no—
111#462—944no—
112#451—944no—
113#431—472no—
114#423C2×D4711yescharacteristic
115#391—944no—
116#382—942no—
117C43C2×D4711yescharacteristic
118#339—22no—
119#333—944no—
120C47#1029711yescharacteristic, complemented, Sylow
121C22×Q8—474no—
122C2×Q16—948no—
123C2×M16—21no—
124C4⋊Q8—942no—
125C4⋊Q8—942no—
126C4⋊Q8—942no—
127C4⋊Q8—942no—
128C4⋊Q8D18812yes—
129#125—21no—
130C22⋊Q8—22no—
131C4×Q8—22no—
132#117—21no—
133C2×C4⋊C4—942no—
134C2×C4⋊C4—942no—
135C2×C42—22no—
136C2×C42C22⋊D4712yes—
137C2×C42C22×D4711yescharacteristic
138C4⋊C8—22no—
139C4⋊C8—474no—
140#103—948no—
141C22⋊C8—942no—
142C4×C8—942no—
143#95—948no—
144C2×Q8—22no—
145C2×Q8—944no—
146C2×Q8—944no—
147C2×Q8—1888no—
148C22×C4—22no—
149C22×C4—944no—
150C22×C4D4×D4712yes—
151C22×C4C2×C22⋊D4711yescharacteristic
152Q16—3768no—
153M16—42no—
154C2×C8—41no—
155C2×C8—944no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C4⋊C4—1882no—
162C4⋊C4—1882no—
163C22⋊C4—41no—
164C42—22no—
165C42—44no—
166C42—41no—
167C42#1062533714yescomplemented
168C42C2×D18811yescharacteristic
169C42#1062535011yescharacteristic
170C42D4×D4712yes—
171C23#1309399211yescharacteristic
172Q8—44no—
173Q8—3764no—
174Q8—1888no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—42no—
179C2×C4—1888no—
180C2×C4—1884no—
181C2×C4#1309399412yes—
182C2×C4#1309399712yes—
183C2×C4#1309399811yescharacteristic
184C2×C4#1309402011yescharacteristic
185C2×C4C2×#1062533712yes—
186C2×C4#1309405412yes—
187C8—81no—
188C8—1884no—
189C22—22no—
190C22#1568903211yescharacteristic
191C22#1568927812yes—
192C4—22no—
193C4—44no—
194C4—82no—
195C4—3764no—
196C4#1568930214yes—
197C4#1568933312yes—
198C4#1568950211yescharacteristic
199C4#1568951811yescharacteristic
200C2—22no—
201C2#2024441612yes—
202C2#2024448711yescharacteristic
subgroupG/H
centerC22#15689032
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1994C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#1994D47
hypocenterC47#10297
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
59. 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
#202543332
#202517662
#202420702
#202412212
C47×#19942
#1029747