Finite Group Databasebeta

← #26103885

Subgroups — #26103885

Order 12032.

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

normal subgroups only

This group has 224 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#20244921C211yesmaximal, characteristic
2#20241513C211yesmaximal, characteristic
3C47×#1318C211yesmaximal, characteristic
4C2×#13093955—21no—
5C2×#13093945—21no—
6C2×#13093939—21no—
7#15688993C411yescharacteristic, complemented
8#15688878C411yescharacteristic, complemented
9C47×#390C2211yescharacteristic
10C47×#324—21no—
11C22×C47⋊C8—21no—
12C2×C4⋊Dic47—21no—
13C2×C4⋊Dic47—41no—
14C2×C22⋊Dic47—41no—
15#13093955—42no—
16#13093945—42no—
17#13093939—22no—
18#13093939—41no—
19C22×D4×C47D411yescharacteristic
20C2×C4⋊C4×C47D411yescharacteristic
21C2×C22⋊C4×C47—41no—
22C2×C42×C47C2×C411yescharacteristic
23C22⋊C8×C47—41no—
24C24×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—41no—
27C2×D4×C47—41no—
28C2×D4×C47SD1611yescharacteristic
29C2×D4×C47Q1611yescharacteristic
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47C22⋊C411yescharacteristic
33C22×Dic47—41no—
34C22×Dic47—81no—
35C2×C8×C47—81no—
36C4⋊C4×C47—41no—
37C22⋊C4×C47—82no—
38C42×C47—41no—
39C22⋊Dic47—42no—
40C22⋊Dic47—81no—
41C4⋊Dic47—41no—
42C4⋊Dic47—41no—
43C4⋊Dic47—82no—
44C2×C47⋊C8—22no—
45C2×C47⋊C8—41no—
46C2×C47⋊C8—41no—
47C23×C47—21no—
48C23×C47—21no—
49C23×C47—41no—
50C23×C47—41no—
51C23×C47—81no—
52C23×C47—81no—
53C23×C47#9911yescharacteristic
54D4×C47—41no—
55D4×C47—41no—
56D4×C47—81no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—22no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—81no—
64C2×C4×C47#10311yescharacteristic
65C2×C4×C47#10411yescharacteristic
66C2×Dic47—82no—
67C2×Dic47—82no—
68C2×Dic47—81no—
69C2×Dic47—161no—
70C2×Dic47—161no—
71C8×C47—161no—
72C47⋊C8—42no—
73#7435—471nomaximal, Sylow
74C22×C47—21no—
75C22×C47—21no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47—81no—
79C22×C47—81no—
80C22×C47—81no—
81C22×C47—81no—
82C22×C47—161no—
83C22×C47#32811yescharacteristic
84C22×C47#35211yescharacteristic
85C22×C47#35311yescharacteristic
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—42no—
89C4×C47—81no—
90Dic47—162no—
91Dic47—161no—
92#2094—471no—
93#1393—471no—
94#1318D4711yescharacteristic
95C2×C47—21no—
96C2×C47—21no—
97C2×C47—81no—
98C2×C47—81no—
99C2×C47#135211yescharacteristic
100C2×C47#140611yescharacteristic
101C2×C47#140911yescharacteristic
102C2×#106—941no—
103C2×#102—941no—
104C2×#99—941no—
105#390C2×D4711yescharacteristic
106#384—471no—
107#336—471no—
108#324—21no—
109C47#743511yescharacteristic, complemented, Sylow
110C22×D4D18811yescharacteristic
111C22×C8—941no—
112C2×C4⋊C4—941no—
113C2×C4⋊C4—1881no—
114C2×C4⋊C4C22⋊D4711yescharacteristic
115C2×C22⋊C4—41no—
116C2×C22⋊C4—1881no—
117C2×C42C4×D4711yescharacteristic
118#106—1882no—
119#102—1882no—
120#99—942no—
121#99—1881no—
122C22⋊C8—41no—
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4#1062532511yescharacteristic
128C2×D4Dic18811yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—3761no—
132C22×C4—1881no—
133C22×C4(C2×D47)⋊C411yescharacteristic
134C2×C8—81no—
135C2×C8—942no—
136C2×C8—1881no—
137C2×C8—1881no—
138C4⋊C4—41no—
139C4⋊C4—3762no—
140C4⋊C4—1881no—
141C4⋊C4—1881no—
142C22⋊C4—82no—
143C22⋊C4—3761no—
144C22⋊C4—1882no—
145C42—41no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#1309393811yescharacteristic
153D4—41no—
154D4—41no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—3762no—
164C2×C4—3762no—
165C2×C4—3761no—
166C2×C4—7521no—
167C2×C4—7521no—
168C2×C4#1309394911yescharacteristic
169C2×C4#1309395011yescharacteristic
170C8—161no—
171C8—1882no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#1568886111yescharacteristic
182C22#1568891411yescharacteristic
183C22#1568891511yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—7522no—
189C4—7521no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#2024141311yescharacteristic
195C2#2024154611yescharacteristic
196C2#2024155211yescharacteristic
subgroupG/H
centerC22#15688915
commutatorC2×C42×C47C2×C4
Frattini#390C2×D47
FittingC47×#1318C2
socleC22×C47#353
prime radicalC22×D4×C47D4
cosocleC47×#390C22
hypercenter#1318D47
hypocenterC47#7435
LCSG ▷ C2×C42×C47 ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1318

Complements

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

NH ≅ G/Ntype
7. #15688993C4semidirect
8. #15688878C4semidirect
109. C47#7435semidirect

Maximal subgroups

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

subgroupindex
#202449212
#202415132
C47×#13182
#743547