Finite Group Databasebeta

← #26119025

Subgroups — #26119025

Order 12032.

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

normal subgroups only

This group has 576 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#20254529C212yesmaximal
2#20251786C211yesmaximal, characteristic
3#20242061C212yesmaximal
4#20241221C211yesmaximal, characteristic
5C47×#1994C211yesmaximal, characteristic
6C2×#13094024—22no—
7C2×#13094024C2212yes—
8#15689519—22no—
9#15689473—22no—
10#15689451—24no—
11#15689408—24no—
12#15689176C2212yes—
13#15688993—24no—
14#15688870—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—
24#13094024—44no—
25#13094024—44no—
26C2×C4⋊Dic47—28no—
27C2×C4⋊Dic47—22no—
28C2×C4⋊Dic47D414yes—
29#13093955—28no—
30C4⋊(C47⋊C8)D414yes—
31#13093948—28no—
32C22⋊(C47⋊C8)—22no—
33C4×C47⋊C8—22no—
34C2×M16×C47—21no—
35C4⋊Q8×C47D412yes—
36#125×C47—21no—
37C22⋊Q8×C47—22no—
38C4×Q8×C47—22no—
39#117×C47—21no—
40C2×C42×C47—22no—
41C2×C42×C47D412yes—
42C2×C42×C47C2311yescharacteristic
43C4⋊C8×C47—22no—
44C2×Q8×C47—22no—
45C22×C4×C47—22no—
46C22×C4×C47C2×D412yes—
47C22×C4×C47C2×D411yescharacteristic
48C22×Dic47—24no—
49C2×Dic94—42no—
50C2×Dic94—42no—
51C2×Dic94—44no—
52C2×Dic94—44no—
53M16×C47—42no—
54C2×C8×C47—41no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—22no—
57C4⋊C4×C47—42no—
58C22⋊C4×C47—41no—
59C42×C47—28no—
60C42×C47—22no—
61C42×C47—41no—
62C42×C47SD1614yes—
63C42×C47C2×D411yescharacteristic
64C42×C47C2×D412yes—
65C42×C47#4111yescharacteristic
66C4⋊Dic47—24no—
67C4⋊Dic47—24no—
68C4⋊Dic47—416no—
69C4⋊Dic47—42no—
70C4⋊Dic47—42no—
71C2×C47⋊C8—24no—
72C23×C47#12011yescharacteristic
73Q8×C47—44no—
74C2×C4×C47—28no—
75C2×C4×C47—24no—
76C2×C4×C47—24no—
77C2×C4×C47—42no—
78C2×C4×C47#12012yes—
79C2×C4×C47#12112yes—
80C2×C4×C47#12111yescharacteristic
81C2×C4×C47#12711yescharacteristic
82C2×C4×C47C2×SD1612yes—
83C2×C4×C47AGL(1,ℤ/8)12yes—
84C2×Dic47—44no—
85C2×Dic47—48no—
86Dic94—84no—
87Dic94—82no—
88Dic94—82no—
89C8×C47—81no—
90C47⋊C8—44no—
91#10299—471nomaximal, Sylow
92C22×C47—22no—
93C22×C47#39211yescharacteristic
94C22×C47#45012yes—
95C4×C47—28no—
96C4×C47—22no—
97C4×C47—82no—
98C4×C47#45614yes—
99C4×C47#46012yes—
100C4×C47#49211yescharacteristic
101C4×C47#49611yescharacteristic
102Dic47—84no—
103#3229—472no—
104#2868—471no—
105#1994D4711yescharacteristic
106#1546—472no—
107#1276—471no—
108C2×C47—22no—
109C2×C47#200512yes—
110C2×C47#201411yescharacteristic
111#533C2×D4711yescharacteristic
112C2×C4⋊Q8—472no—
113C2×C4⋊Q8—942no—
114#498—942no—
115#487—942no—
116#483—944no—
117#475—944no—
118#431—472no—
119#423C2×D4711yescharacteristic
120#384—944no—
121C43C2×D4711yescharacteristic
122#339—22no—
123#332—944no—
124C47#1029911yescharacteristic, complemented, Sylow
125C22×Q8—942no—
126C2×M16—21no—
127C4⋊Q8—942no—
128C4⋊Q8—942no—
129C4⋊Q8—942no—
130C4⋊Q8—942no—
131C4⋊Q8—1884no—
132C4⋊Q8—1884no—
133C4⋊Q8D18812yes—
134#125—21no—
135C22⋊Q8—22no—
136C4×Q8—22no—
137#117—21no—
138C2×C4⋊C4—474no—
139C2×C4⋊C4—948no—
140C2×C4⋊C4—942no—
141C2×C42—22no—
142C2×C42C22⋊D4712yes—
143C2×C42C22×D4711yescharacteristic
144#106—948no—
145C4⋊C8—22no—
146C4⋊C8—474no—
147#103—948no—
148C22⋊C8—942no—
149C4×C8—942no—
150C2×Q8—22no—
151C2×Q8—1882no—
152C2×Q8—1882no—
153C2×Q8—1884no—
154C2×Q8—1884no—
155C22×C4—22no—
156C22×C4—944no—
157C22×C4D4×D4712yes—
158C22×C4C2×C22⋊D4711yescharacteristic
159M16—42no—
160C2×C8—41no—
161C2×C8—944no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—944no—
166C4⋊C4—944no—
167C4⋊C4—18816no—
168C4⋊C4—1882no—
169C4⋊C4—1882no—
170C22⋊C4—41no—
171C42—28no—
172C42—22no—
173C42—41no—
174C42#1062533614yes—
175C42C2×D18811yescharacteristic
176C42#1062535011yescharacteristic
177C42D4×D4712yes—
178C23#1309399211yescharacteristic
179Q8—44no—
180Q8—3762no—
181Q8—3762no—
182Q8—3764no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—1888no—
188C2×C4—1884no—
189C2×C4#1309399412yes—
190C2×C4#1309399712yes—
191C2×C4#1309399811yescharacteristic
192C2×C4#1309402011yescharacteristic
193C2×C4C2×#1062533612yes—
194C2×C4#1309404912yes—
195C8—81no—
196C8—1884no—
197C22—22no—
198C22#1568903211yescharacteristic
199C22#1568927312yes—
200C4—28no—
201C4—22no—
202C4—82no—
203C4—3764no—
204C4#1568930714yes—
205C4#1568932312yes—
206C4#1568949711yescharacteristic
207C4#1568951311yescharacteristic
208C2—22no—
209C2#2024442312yes—
210C2#2024447511yescharacteristic
subgroupG/H
centerC22#15689032
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1994C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#1994D47
hypocenterC47#10299
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
124. C47#10299semidirect

Maximal subgroups

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

subgroupindex
#202545292
#202517862
#202420612
#202412212
C47×#19942
#1029947