Finite Group Databasebeta

← #26103906

Subgroups — #26103906

Order 12032.

194 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 41 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#20244738C211yesmaximal, characteristic
2#20241269C211yesmaximal, characteristic
3C47×#1324C211yesmaximal, characteristic
4#15689754C411yescharacteristic
5#15689163—21no—
6C2×#13093935—21no—
7#15688892C411yescharacteristic
8#15688883—21no—
9C47×#382C2211yescharacteristic
10C47×#324—21no—
11C2×#10625329—21no—
12C22×C47⋊C8—41no—
13#13094023—41no—
14#13094015—41no—
15#13094003—41no—
16#13093983—21no—
17#13093957—41no—
18#13093955—41no—
19#13093935—22no—
20#13093935—41no—
21C2×C4⋊C4×C47C2×C411yescharacteristic
22C2×C4⋊C4×C47D411yescharacteristic
23C2×C42×C47D411yescharacteristic
24C22⋊C8×C47—41no—
25#95×C47—41no—
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47C22⋊C411yescharacteristic
30C2×Dic94—41no—
31C2×C8×C47—81no—
32C4⋊C4×C47—41no—
33C4⋊C4×C47—41no—
34C42×C47—21no—
35C42×C47SD1611yescharacteristic
36C42×C47Q1611yescharacteristic
37C22⋊Dic47—41no—
38C4⋊Dic47—21no—
39C4⋊Dic47—21no—
40C4⋊Dic47—41no—
41Dic47⋊C4—42no—
42C4×Dic47—41no—
43#10625329—22no—
44#10625329—41no—
45C2×C47⋊C8—42no—
46C2×C47⋊C8—41no—
47C2×C47⋊C8—42no—
48C2×C47⋊C8—42no—
49C23×C47#9911yescharacteristic
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—81no—
59C2×C4×C47—81no—
60C2×C4×C47#10311yescharacteristic
61C2×C4×C47#10411yescharacteristic
62C2×Dic47—41no—
63C2×Dic47—41no—
64Dic94—161no—
65C8×C47—161no—
66C47⋊C8—42no—
67C47⋊C8—44no—
68#7442—471nomaximal, Sylow
69C22×C47—21no—
70C22×C47—21no—
71C22×C47#32811yescharacteristic
72C22×C47AΣL(1,𝔽16)11yescharacteristic
73C22×C47#35611yescharacteristic
74C4×C47—21no—
75C4×C47—21no—
76C4×C47—41no—
77C4×C47—41no—
78C4×C47—81no—
79C4×C47—81no—
80Dic47—81no—
81Dic47—81no—
82#2061—471no—
83#1324D4711yescharacteristic
84#1295—471no—
85C2×C47—21no—
86C2×C47—21no—
87C2×C47#135411yescharacteristic
88C2×C47#140311yescharacteristic
89C2×C47#140411yescharacteristic
90#544—471no—
91#428—941no—
92C2×#97—941no—
93#382C2×D4711yescharacteristic
94#343—471no—
95#339—941no—
96#324—21no—
97C47#744211yescharacteristic, complemented, Sylow
98C2×M16—941no—
99C22×C8—1881no—
100C4⋊Q8—1881no—
101#125—1881no—
102C22⋊Q8—1881no—
103#117—941no—
104C2×C4⋊C4C4×D4711yescharacteristic
105C2×C4⋊C4C22⋊D4711yescharacteristic
106C2×C42D18811yescharacteristic
107#107—1881no—
108#106—1881no—
109C22⋊C8—41no—
110#97—942no—
111#97—1881no—
112#95—41no—
113C2×Q8—1881no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4(C2×D47)⋊C411yescharacteristic
118M16—942no—
119M16—1881no—
120C2×C8—81no—
121C2×C8—1882no—
122C2×C8—1881no—
123C2×C8—1882no—
124C2×C8—1882no—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—941no—
128C4⋊C4—941no—
129C4⋊C4—1881no—
130C4⋊C4—1882no—
131C22⋊C4—1881no—
132C42—21no—
133C42—1881no—
134C42#1062532511yescharacteristic
135C42Dic18811yescharacteristic
136C23#1309393811yescharacteristic
137Q8—7521no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—1881no—
149C2×C4—1881no—
150C2×C4#1309394911yescharacteristic
151C2×C4#1309395011yescharacteristic
152C8—161no—
153C8—1882no—
154C8—1884no—
155C22—21no—
156C22—21no—
157C22#1568886111yescharacteristic
158C22#1568890911yescharacteristic
159C22#1568892111yescharacteristic
160C4—21no—
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—3761no—
167C4—3761no—
168C2—21no—
169C2—21no—
170C2#2024141911yescharacteristic
171C2#2024153511yescharacteristic
172C2#2024153811yescharacteristic
subgroupG/H
centerC22#15688909
commutatorC2×C4⋊C4×C47C2×C4
Frattini#382C2×D47
FittingC47×#1324C2
socleC22×C47AΣL(1,𝔽16)
prime radicalC23×C47#99
cosocleC47×#382C22
hypercenter#1324D47
hypocenterC47#7442
LCSG ▷ C2×C4⋊C4×C47 ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
97. C47#7442semidirect

Maximal subgroups

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

subgroupindex
#202447382
#202412692
C47×#13242
#744247