Finite Group Databasebeta

← #26103907

Subgroups — #26103907

Order 12032.

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

normal subgroups only

This group has 198 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#20244733C211yesmaximal, characteristic
2#20241334C211yesmaximal, characteristic
3C47×#1296C211yesmaximal, characteristic
4#15689754C411yescharacteristic
5#15689163—21no—
6#15688892C411yescharacteristic
7#15688883—21no—
8#15688849—21no—
9C2×C4⋊C8×C47—21no—
10C47×#384C2211yescharacteristic
11C2×#10625329—21no—
12#13094023—41no—
13#13094015—41no—
14#13094003—41no—
15#13093983—21no—
16#13093957—41no—
17#13093955—41no—
18C22⋊(C47⋊C8)—41no—
19C22×C8×C47—41no—
20C2×C4⋊C4×C47—41no—
21C2×C4⋊C4×C47C2×C411yescharacteristic
22C2×C4⋊C4×C47D411yescharacteristic
23C2×C42×C47D411yescharacteristic
24C4⋊C8×C47—22no—
25C4⋊C8×C47—41no—
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47C22⋊C411yescharacteristic
30C2×Dic94—41no—
31C2×C8×C47—42no—
32C2×C8×C47—81no—
33C2×C8×C47—81no—
34C4⋊C4×C47—41no—
35C4⋊C4×C47—41no—
36C4⋊C4×C47—81no—
37C4⋊C4×C47—81no—
38C42×C47—21no—
39C42×C47SD1611yescharacteristic
40C42×C47Q1611yescharacteristic
41C22⋊Dic47—41no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—41no—
45Dic47⋊C4—42no—
46C4×Dic47—41no—
47#10625329—22no—
48#10625329—41no—
49C2×C47⋊C8—41no—
50C2×C47⋊C8—81no—
51C23×C47#9911yescharacteristic
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—81no—
63C2×C4×C47—81no—
64C2×C4×C47#10311yescharacteristic
65C2×C4×C47#10411yescharacteristic
66C2×Dic47—41no—
67C2×Dic47—41no—
68Dic94—161no—
69C8×C47—82no—
70C47⋊C8—42no—
71C47⋊C8—161no—
72#7443—471nomaximal, Sylow
73C22×C47—21no—
74C22×C47—21no—
75C22×C47#32811yescharacteristic
76C22×C47AΣL(1,𝔽16)11yescharacteristic
77C22×C47#35611yescharacteristic
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—21no—
84C4×C47—81no—
85C4×C47—81no—
86Dic47—81no—
87Dic47—81no—
88#2060—471no—
89#1325—471no—
90#1296D4711yescharacteristic
91C2×C47—21no—
92C2×C47—21no—
93C2×C47#135411yescharacteristic
94C2×C47#140211yescharacteristic
95C2×C47#140511yescharacteristic
96#544—471no—
97#428—941no—
98C2×C4⋊C8—21no—
99#384C2×D4711yescharacteristic
100#343—471no—
101#339—941no—
102#324—941no—
103C47#744311yescharacteristic, complemented, Sylow
104C2×M16—941no—
105C22×C8—41no—
106C4⋊Q8—1881no—
107#125—1881no—
108C22⋊Q8—1881no—
109#117—941no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4C4×D4711yescharacteristic
112C2×C4⋊C4D18811yescharacteristic
113C2×C42C22⋊D4711yescharacteristic
114#107—1881no—
115#106—1881no—
116C4⋊C8—22no—
117C4⋊C8—41no—
118C22⋊C8—1881no—
119C2×Q8—1881no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4(C2×D47)⋊C411yescharacteristic
124M16—942no—
125M16—1881no—
126C2×C8—42no—
127C2×C8—81no—
128C2×C8—81no—
129C2×C8—3761no—
130C2×C8—1881no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4—81no—
134C4⋊C4—81no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C4⋊C4—1881no—
138C4⋊C4—1882no—
139C22⋊C4—1881no—
140C42—21no—
141C42—1881no—
142C42#1062533511yescharacteristic
143C42#1062533711yescharacteristic
144C23#1309393811yescharacteristic
145Q8—7521no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4#1309394711yescharacteristic
161C2×C4#1309395211yescharacteristic
162C8—82no—
163C8—1882no—
164C8—7521no—
165C22—21no—
166C22—21no—
167C22#1568885911yescharacteristic
168C22#1568891111yescharacteristic
169C22#1568892111yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—3761no—
179C4—3761no—
180C2—21no—
181C2—21no—
182C2#2024141711yescharacteristic
183C2#2024153411yescharacteristic
184C2#2024154311yescharacteristic
subgroupG/H
centerC22#15688911
commutatorC2×C4⋊C4×C47C2×C4
Frattini#384C2×D47
FittingC47×#1296C2
socleC22×C47AΣL(1,𝔽16)
prime radicalC23×C47#99
cosocleC47×#384C22
hypercenter#1296D47
hypocenterC47#7443
LCSG ▷ C2×C4⋊C4×C47 ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1296

Complements

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

NH ≅ G/Ntype
103. C47#7443semidirect

Maximal subgroups

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

subgroupindex
#202447332
#202413342
C47×#12962
#744347