Finite Group Databasebeta

← #26119422

Subgroups — #26119422

Order 12032.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#20246693C211yesmaximal, characteristic
2#20244369C211yesmaximal, characteristic
3#20241888C212yesmaximal
4#20241290C212yesmaximal
5C47×#1274C211yesmaximal, characteristic
6#15689680C2211yescharacteristic
7#15689147C2211yescharacteristic
8#15689065—22no—
9#15689057—22no—
10C4×Dic47⋊C4—22no—
11C4×C4⋊Dic47C2212yes—
12#15688883—22no—
13#15688861—22no—
14#15688861—22no—
15C47×#431C2212yes—
16C47×#376C2211yescharacteristic
17C2×#10625329—21no—
18#13094024Q812yes—
19#13094016—21no—
20#13094003—22no—
21C4×Dic94—22no—
22#13093983—21no—
23C2×C4⋊Dic47—22no—
24C2×Dic47⋊C4—22no—
25C2×Dic47⋊C4—22no—
26C2×C4×Dic47—22no—
27C4⋊(C47⋊C8)—22no—
28C47⋊#95—22no—
29C47⋊#95—22no—
30C47⋊#95D412yes—
31C47⋊#95D412yes—
32C2×C42×C47D412yes—
33C2×C42×C47C2311yescharacteristic
34C4⋊C8×C47—22no—
35C22⋊C8×C47—22no—
36C4×C8×C47—22no—
37#95×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47C2×D412yes—
40C22×C4×C47C2×D411yescharacteristic
41C22×Dic47—22no—
42C22×Dic47—22no—
43C2×Dic94—22no—
44C2×C8×C47—42no—
45C42×C47—22no—
46C42×C47—22no—
47C42×C47C2×Q811yescharacteristic
48C42×C47#4112yes—
49C42×C47#4111yescharacteristic
50C22⋊Dic47—41no—
51C4⋊Dic47—22no—
52C4⋊Dic47—22no—
53C4⋊Dic47—44no—
54Dic47⋊C4—44no—
55Dic47⋊C4—44no—
56Dic47⋊C4—42no—
57C4×Dic47—41no—
58C4×Dic47—42no—
59C4×Dic47—42no—
60#10625329—42no—
61C2×C47⋊C8—41no—
62C23×C47#12011yescharacteristic
63C2×C4×C47—42no—
64C2×C4×C47—42no—
65C2×C4×C47—42no—
66C2×C4×C47—42no—
67C2×C4×C47C22⋊Q812yes—
68C2×C4×C47C22⋊Q811yescharacteristic
69C2×C4×C47#12412yes—
70C2×C4×C47#12411yescharacteristic
71C2×C4×C47#13512yes—
72C2×C4×C47#13712yes—
73C2×Dic47—24no—
74C2×Dic47—42no—
75C2×Dic47—42no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78C2×Dic47—42no—
79C2×Dic47—42no—
80Dic94—82no—
81C8×C47—82no—
82C47⋊C8—81no—
83#10373—471nomaximal, Sylow
84C22×C47—22no—
85C22×C47#39311yescharacteristic
86C22×C47#45212yes—
87C4×C47—22no—
88C4×C47—22no—
89C4×C47—82no—
90C4×C47#47912yes—
91C4×C47#48811yescharacteristic
92C4×C47#49111yescharacteristic
93Dic47—44no—
94Dic47—82no—
95Dic47—82no—
96#2402—471no—
97#1995—471no—
98#1503—472no—
99#1303—472no—
100#1274D4711yescharacteristic
101C2×C47—22no—
102C2×C47#202611yescharacteristic
103C2×C47#203112yes—
104#533—471no—
105#431C2×D4712yes—
106#423—471no—
107#400—942no—
108#398—942no—
109C4×C4⋊C4—472no—
110C4×C4⋊C4—942no—
111#376C2×D4711yescharacteristic
112#339—942no—
113#328—942no—
114#328—942no—
115C47#1037311yescharacteristic, complemented, Sylow
116C2×M16—941no—
117C4⋊Q8—472no—
118#125—941no—
119C22⋊Q8—942no—
120C4×Q8—942no—
121#117—941no—
122C2×C4⋊C4—942no—
123C2×C4⋊C4—942no—
124C2×C4⋊C4—942no—
125C2×C42—942no—
126C2×C42D18812yes—
127C2×C42C22×D4711yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—942no—
130C22⋊C8—22no—
131C4×C8—22no—
132#95—22no—
133#95—472no—
134#95—472no—
135#95—942no—
136#95—942no—
137C2×Q8—942no—
138C22×C4—22no—
139C22×C4—942no—
140C22×C4—942no—
141C22×C4C2×D18811yescharacteristic
142C22×C4D4×D4712yes—
143M16—1882no—
144C2×C8—42no—
145C2×C8—1881no—
146C4⋊C4—942no—
147C4⋊C4—942no—
148C4⋊C4—1884no—
149C4⋊C4—1884no—
150C4⋊C4—1884no—
151C4⋊C4—1882no—
152C22⋊C4—1881no—
153C42—22no—
154C42—22no—
155C42—1881no—
156C42—1882no—
157C42—1882no—
158C42#1062535012yes—
159C42#1062535211yescharacteristic
160C42Q8×D4711yescharacteristic
161C23#1309399411yescharacteristic
162Q8—3762no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—944no—
168C2×C4—1882no—
169C2×C4—1882no—
170C2×C4—1882no—
171C2×C4—1882no—
172C2×C4—1882no—
173C2×C4—1882no—
174C2×C4#1309400212yes—
175C2×C4#1309400411yescharacteristic
176C2×C4#1309401012yes—
177C2×C4#1309401211yescharacteristic
178C2×C4#1309404612yes—
179C2×C4#1309405712yes—
180C8—82no—
181C8—3761no—
182C22—22no—
183C22#1568903611yescharacteristic
184C22#1568928712yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—3762no—
189C4—3762no—
190C4—1884no—
191C4#1568943112yes—
192C4#1568947811yescharacteristic
193C4#1568949211yescharacteristic
194C2—22no—
195C2#2024454011yescharacteristic
196C2#2024455912yes—
subgroupG/H
centerC2×C4#13094012
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1274C2
socleC22×C47#393
prime radicalC23×C47#120
hypercenter#1274D47
hypocenterC47#10373
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
115. C47#10373semidirect

Maximal subgroups

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

subgroupindex
#202466932
#202443692
#202418882
#202412902
C47×#12742
#1037347