Finite Group Databasebeta

← #26102954

Subgroups — #26102954

Order 12032.

218 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 51 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#20241312C211yesmaximal, characteristic
2#20241256C211yesmaximal, characteristic
3C47×#2076C211yesmaximal, characteristic
4#15688983—21no—
5C22⋊(C47⋊C16)—21no—
6C2×#107×C47C411yescharacteristic, complemented
7C2×C22⋊C8×C47C2211yescharacteristic
8C47×#380—21no—
9C47×#340—21no—
10C47×#340C411yescharacteristic, complemented
11C2×C4⋊Dic47—41no—
12C2×C22⋊Dic47—41no—
13C2×C47⋊C16—41no—
14C47⋊#95—22no—
15C23×C4×C47D411yescharacteristic
16C22×C8×C47C2×C411yescharacteristic
17C22×C8×C47D411yescharacteristic
18C2×C4⋊C4×C47—21no—
19C2×C4⋊C4×C47—21no—
20C2×C22⋊C4×C47—41no—
21#107×C47—41no—
22C22⋊C8×C47—41no—
23#95×C47—41no—
24C24×C47D811yescharacteristic
25C22×C4×C47—21no—
26C22×C4×C47—21no—
27C22×C4×C47—41no—
28C22×C4×C47—41no—
29C22×C4×C47—41no—
30C22×C4×C47—41no—
31C22×C4×C47C22⋊C411yescharacteristic
32C22×C4×C47SD1611yescharacteristic
33C22×Dic47—42no—
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C2×C8×C47—41no—
37C2×C8×C47—41no—
38C4⋊C4×C47—41no—
39C4⋊C4×C47—41no—
40C4⋊C4×C47—41no—
41C4⋊C4×C47—41no—
42C22⋊C4×C47—82no—
43C22⋊Dic47—81no—
44C22⋊Dic47—81no—
45C4⋊Dic47—81no—
46C4⋊Dic47—81no—
47C47⋊C16—81no—
48C23×C47—21no—
49C23×C47—21no—
50C23×C47—41no—
51C23×C47—41no—
52C23×C47#10211yescharacteristic
53C23×C47SD3211yescharacteristic
54C23×C47Q3211yescharacteristic
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—81no—
62C2×C4×C47—81no—
63C2×C4×C47—81no—
64C2×C4×C47—81no—
65C2×C4×C47—81no—
66C2×C4×C47—81no—
67C2×C4×C47—81no—
68C2×C4×C47#9911yescharacteristic
69C2×C4×C47#10411yescharacteristic
70C2×Dic47—82no—
71C2×Dic47—82no—
72C2×Dic47—82no—
73C8×C47—41no—
74C8×C47—41no—
75#7077—471nomaximal, Sylow
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—21no—
79C22×C47—21no—
80C22×C47—41no—
81C22×C47—41no—
82C22×C47—41no—
83C22×C47—41no—
84C22×C47—81no—
85C22×C47#32711yescharacteristic
86C22×C47#35811yescharacteristic
87C22×C47#36011yescharacteristic
88C4×C47—21no—
89C4×C47—41no—
90C4×C47—161no—
91C4×C47—161no—
92C4×C47#35211yescharacteristic
93C4×C47#35411yescharacteristic
94Dic47—162no—
95#2076D4711yescharacteristic
96#1314—471no—
97#1289—471no—
98C2×C47—21no—
99C2×C47—21no—
100C2×C47—41no—
101C2×C47—41no—
102C2×C47#133911yescharacteristic
103C2×C47#134411yescharacteristic
104C2×C47#134811yescharacteristic
105C2×#107Dic4711yescharacteristic, complemented
106C2×C22⋊C8C2×D4711yescharacteristic
107#380—21no—
108#380—941no—
109C22⋊C16—941no—
110#340—21no—
111#340Dic4711yescharacteristic, complemented
112C47#707711yescharacteristic, complemented, Sylow
113C23×C4C22⋊D4711yescharacteristic
114C22×C8C2×Dic4711yescharacteristic
115C22×C8C22⋊D4711yescharacteristic
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—1881no—
119C2×C22⋊C4—41no—
120C2×C22⋊C4—1881no—
121C2×C16—1881no—
122#107—41no—
123C22⋊C8—41no—
124#95—41no—
125#95—942no—
126C24#1062533411yescharacteristic
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—41no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4—41no—
133C22×C4—1882no—
134C22×C4#1062533511yescharacteristic
135C22×C4C22⋊Dic4711yescharacteristic
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—41no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—3761no—
145C4⋊C4—3761no—
146C22⋊C4—82no—
147C22⋊C4—3761no—
148C22⋊C4—3761no—
149C16—3761no—
150C23—21no—
151C23—21no—
152C23—41no—
153C23—41no—
154C23#1309394511yescharacteristic
155C23#1309396711yescharacteristic
156C23#1309397011yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4—3762no—
171C2×C4—3762no—
172C2×C4—3762no—
173C2×C4#1309393911yescharacteristic
174C2×C4#1309395111yescharacteristic
175C8—41no—
176C8—41no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22—81no—
186C22#1568885711yescharacteristic
187C22#1568892711yescharacteristic
188C22#1568893311yescharacteristic
189C4—21no—
190C4—41no—
191C4—161no—
192C4—161no—
193C4—7522no—
194C4#1568891311yescharacteristic
195C4#1568891811yescharacteristic
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2#2024137311yescharacteristic
201C2#2024138811yescharacteristic
202C2#2024140011yescharacteristic
subgroupG/H
centerC22#15688857
commutatorC22×C8×C47C2×C4
FrattiniC2×C22⋊C8C2×D47
FittingC47×#2076C2
socleC22×C47#327
prime radicalC24×C47D8
cosocleC2×C22⋊C8×C47C22
hypercenter#2076D47
hypocenterC47#7077
LCSG ▷ C22×C8×C47 ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2076

Complements

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

NH ≅ G/Ntype
6. C2×#107×C47C4semidirect
10. C47×#340C4semidirect
105. C2×#107Dic47semidirect
111. #340Dic47semidirect
112. C47#7077semidirect

Maximal subgroups

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

subgroupindex
#202413122
#202412562
C47×#20762
#707747