Finite Group Databasebeta

← #26102955

Subgroups — #26102955

Order 12032.

218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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#20244816C211yesmaximal, characteristic
2#20241256C211yesmaximal, characteristic
3C47×#1314C211yesmaximal, characteristic
4C2×#13093958C411yescharacteristic, complemented
5#15688983—21no—
6#15688983—21no—
7#15688886—21no—
8#15688886C411yescharacteristic, complemented
9C2×C22⋊C8×C47C2211yescharacteristic
10C47×C22⋊C16—21no—
11C2×C4⋊Dic47—21no—
12C2×C4⋊Dic47—21no—
13C2×C4⋊Dic47—41no—
14C2×C22⋊Dic47—41no—
15C2×C22⋊Dic47—41no—
16#13093958—41no—
17C47⋊#95—22no—
18C47⋊#95—41no—
19C23×C4×C47D411yescharacteristic
20C22×C8×C47C2×C411yescharacteristic
21C22×C8×C47D411yescharacteristic
22C2×C16×C47—41no—
23C22⋊C8×C47—41no—
24C24×C47D811yescharacteristic
25C22×C4×C47—21no—
26C22×C4×C47—21no—
27C22×C4×C47—41no—
28C22×C4×C47—41no—
29C22×C4×C47C22⋊C411yescharacteristic
30C22×C4×C47SD1611yescharacteristic
31C22×Dic47—42no—
32C22×Dic47—41no—
33C22×Dic47—41no—
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C2×C8×C47—41no—
37C2×C8×C47—41no—
38C22⋊Dic47—81no—
39C22⋊Dic47—82no—
40C22⋊Dic47—81no—
41C4⋊Dic47—41no—
42C4⋊Dic47—41no—
43C4⋊Dic47—41no—
44C4⋊Dic47—41no—
45C4⋊Dic47—81no—
46C4⋊Dic47—81no—
47C16×C47—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#9911yescharacteristic
63C2×C4×C47#10411yescharacteristic
64C2×Dic47—81no—
65C2×Dic47—81no—
66C2×Dic47—82no—
67C2×Dic47—81no—
68C2×Dic47—81no—
69C2×Dic47—82no—
70C2×Dic47—82no—
71C2×Dic47—81no—
72C2×Dic47—81no—
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#35211yescharacteristic
91C4×C47#35411yescharacteristic
92Dic47—161no—
93Dic47—162no—
94Dic47—161no—
95#2076—471no—
96#1314D4711yescharacteristic
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×#107—471no—
106C2×C22⋊C8C2×D4711yescharacteristic
107#380—941no—
108#380—941no—
109C22⋊C16—21no—
110#340—471no—
111#340—941no—
112C47#707711yescharacteristic, complemented, Sylow
113C23×C4D18811yescharacteristic
114C22×C8C4×D4711yescharacteristic
115C22×C8C22⋊D4711yescharacteristic
116C2×C4⋊C4—941no—
117C2×C4⋊C4—941no—
118C2×C4⋊C4—1881no—
119C2×C22⋊C4—1881no—
120C2×C22⋊C4—1881no—
121C2×C16—41no—
122#107—1881no—
123C22⋊C8—41no—
124#95—942no—
125#95—1881no—
126C24D37611yescharacteristic
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—41no—
130C22×C4—41no—
131C22×C4—1882no—
132C22×C4—1881no—
133C22×C4—1881no—
134C22×C4#1062532511yescharacteristic
135C22×C4(C2×D47)⋊C411yescharacteristic
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—41no—
140C4⋊C4—3761no—
141C4⋊C4—3761no—
142C4⋊C4—1881no—
143C4⋊C4—1881no—
144C4⋊C4—1881no—
145C4⋊C4—1881no—
146C22⋊C4—3761no—
147C22⋊C4—3762no—
148C22⋊C4—3761no—
149C16—81no—
150C23—21no—
151C23—21no—
152C23—41no—
153C23—41no—
154C23#1309394611yescharacteristic
155C23#1309396911yescharacteristic
156C23Dic37611yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—81no—
164C2×C4—3761no—
165C2×C4—3762no—
166C2×C4—3761no—
167C2×C4—3761no—
168C2×C4—3761no—
169C2×C4—3762no—
170C2×C4—3762no—
171C2×C4—3761no—
172C2×C4—3761no—
173C2×C4#1309393811yescharacteristic
174C2×C4#1309395011yescharacteristic
175C8—41no—
176C8—41no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22—81no—
186C22#1568885811yescharacteristic
187C22#1568892811yescharacteristic
188C22#1568893411yescharacteristic
189C4—21no—
190C4—41no—
191C4—7521no—
192C4—7522no—
193C4—7521no—
194C4#1568891411yescharacteristic
195C4#1568891711yescharacteristic
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2#2024137411yescharacteristic
201C2#2024138911yescharacteristic
202C2#2024140111yescharacteristic
subgroupG/H
centerC22#15688858
commutatorC22×C8×C47C2×C4
FrattiniC2×C22⋊C8C2×D47
FittingC47×#1314C2
socleC22×C47#327
prime radicalC24×C47D8
cosocleC2×C22⋊C8×C47C22
hypercenter#1314D47
hypocenterC47#7077
LCSG ▷ C22×C8×C47 ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
4. C2×#13093958C4semidirect
8. #15688886C4semidirect
112. C47#7077semidirect

Maximal subgroups

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

subgroupindex
#202448162
#202412562
C47×#13142
#707747