Finite Group Databasebeta

← #26119028

Subgroups — #26119028

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#20254534C212yesmaximal
2#20251786C211yesmaximal, characteristic
3#20244365C211yesmaximal, characteristic
4#20242059C212yesmaximal
5C47×#1276C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7C2×#13094024—22no—
8C2×#13094024C2212yes—
9#15689521—22no—
10#15689474—22no—
11#15689454—24no—
12#15689409—24no—
13#15689147C2211yescharacteristic
14#15688993—24no—
15#15688883—22no—
16#15688868—24no—
17C47×#431C2212yes—
18C43×C47C2211yescharacteristic
19C22×Dic94—22no—
20C2×#10625329—21no—
21#13094024—22no—
22#13094024—22no—
23#13094024—22no—
24#13094024—22no—
25#13094024—44no—
26#13094024—44no—
27#13094024D412yes—
28#13094016—21no—
29#13094003—22no—
30C4×Dic94—22no—
31#13093983—21no—
32C2×C4⋊Dic47—28no—
33C2×C4⋊Dic47—22no—
34C2×C4⋊Dic47D414yes—
35#13093956—28no—
36C4⋊(C47⋊C8)—22no—
37#13093949—28no—
38C2×C42×C47—22no—
39C2×C42×C47D412yes—
40C2×C42×C47C2311yescharacteristic
41C4⋊C8×C47D414yes—
42C22⋊C8×C47—22no—
43C4×C8×C47—22no—
44C22×C4×C47—22no—
45C22×C4×C47C2×D412yes—
46C22×C4×C47C2×D411yescharacteristic
47C22×Dic47—24no—
48C2×Dic94—22no—
49C2×Dic94—42no—
50C2×Dic94—42no—
51C2×Dic94—44no—
52C2×Dic94—44no—
53C2×C8×C47—24no—
54C42×C47—28no—
55C42×C47—22no—
56C42×C47SD1614yes—
57C42×C47C2×D411yescharacteristic
58C42×C47C2×D412yes—
59C42×C47#4111yescharacteristic
60C22⋊Dic47—41no—
61C4⋊Dic47—24no—
62C4⋊Dic47—22no—
63C4⋊Dic47—24no—
64C4⋊Dic47—22no—
65C4⋊Dic47—416no—
66C4⋊Dic47—42no—
67C4⋊Dic47—42no—
68Dic47⋊C4—42no—
69C4×Dic47—41no—
70#10625329—42no—
71C2×C47⋊C8—41no—
72C23×C47#12011yescharacteristic
73C2×C4×C47—28no—
74C2×C4×C47—24no—
75C2×C4×C47—24no—
76C2×C4×C47#12012yes—
77C2×C4×C47#12112yes—
78C2×C4×C47#12111yescharacteristic
79C2×C4×C47#12711yescharacteristic
80C2×C4×C47C2×SD1612yes—
81C2×C4×C47AGL(1,ℤ/8)12yes—
82C2×Dic47—42no—
83C2×Dic47—44no—
84C2×Dic47—48no—
85Dic94—44no—
86Dic94—84no—
87Dic94—82no—
88Dic94—82no—
89C8×C47—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#45614yes—
98C4×C47#46012yes—
99C4×C47#49211yescharacteristic
100C4×C47#49611yescharacteristic
101Dic47—82no—
102Dic47—84no—
103#3229—472no—
104#2868—471no—
105#1994—471no—
106#1546—472no—
107#1276D4711yescharacteristic
108C2×C47—22no—
109C2×C47#200512yes—
110C2×C47#201411yescharacteristic
111#533—471no—
112C2×C4⋊Q8—472no—
113C2×C4⋊Q8—942no—
114#498—942no—
115#487—942no—
116#483—944no—
117#475—944no—
118#431C2×D4712yes—
119#423—471no—
120#384—944no—
121C43C2×D4711yescharacteristic
122#339—942no—
123#332—944no—
124C47#1029911yescharacteristic, complemented, Sylow
125C22×Q8—942no—
126C2×M16—941no—
127C4⋊Q8—472no—
128C4⋊Q8—942no—
129C4⋊Q8—942no—
130C4⋊Q8—942no—
131C4⋊Q8—942no—
132C4⋊Q8—1884no—
133C4⋊Q8—1884no—
134#125—941no—
135C22⋊Q8—942no—
136C4×Q8—942no—
137#117—941no—
138C2×C4⋊C4—474no—
139C2×C4⋊C4—948no—
140C2×C4⋊C4—942no—
141C2×C42—22no—
142C2×C42D18812yes—
143C2×C42C22×D4711yescharacteristic
144#106—948no—
145C4⋊C8—942no—
146C4⋊C8D18814yes—
147#103—948no—
148C22⋊C8—22no—
149C4×C8—22no—
150C2×Q8—942no—
151C2×Q8—1882no—
152C2×Q8—1882no—
153C2×Q8—1884no—
154C2×Q8—1884no—
155C22×C4—22no—
156C22×C4—944no—
157C22×C4C2×D18811yescharacteristic
158C22×C4D4×D4712yes—
159M16—1882no—
160C2×C8—24no—
161C2×C8—1881no—
162C4⋊C4—944no—
163C4⋊C4—942no—
164C4⋊C4—944no—
165C4⋊C4—942no—
166C4⋊C4—18816no—
167C4⋊C4—1882no—
168C4⋊C4—1882no—
169C4⋊C4—1882no—
170C22⋊C4—1881no—
171C42—28no—
172C42—22no—
173C42—1881no—
174C42#1062532514yes—
175C42C2×D18812yes—
176C42D4×D4711yescharacteristic
177C42#1062535411yescharacteristic
178C23#1309399411yescharacteristic
179Q8—3762no—
180Q8—3762no—
181Q8—3764no—
182Q8—1884no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—1888no—
187C2×C4—1882no—
188C2×C4—1884no—
189C2×C4#1309399412yes—
190C2×C4#1309399912yes—
191C2×C4#1309399911yescharacteristic
192C2×C4#1309402111yescharacteristic
193C2×C4C2×#1062532512yes—
194C2×C4#1309405212yes—
195C8—44no—
196C8—3761no—
197C22—22no—
198C22#1568903311yescharacteristic
199C22#1568927612yes—
200C4—28no—
201C4—22no—
202C4—3762no—
203C4—3764no—
204C4#1568930714yes—
205C4#1568932412yes—
206C4#1568949611yescharacteristic
207C4#1568951211yescharacteristic
208C2—22no—
209C2#2024442712yes—
210C2#2024447811yescharacteristic
subgroupG/H
centerC22#15689033
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1276C2
socleC22×C47#392
prime radicalC23×C47#120
hypercenter#1276D47
hypocenterC47#10299
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

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
#202545342
#202517862
#202443652
#202420592
C47×#12762
#1029947