Finite Group Databasebeta

← #24984202

Subgroups — #24984202

Order 11008.

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#19136128C211yesmaximal, characteristic
2#19132527C211yesmaximal, characteristic
3C43×#1393C211yesmaximal, characteristic
4C2×#13063256—21no—
5C2×#13063246—21no—
6#14582769C411yescharacteristic, complemented
7#14582654C411yescharacteristic, complemented
8#14582625—21no—
9C2×#99×C43—21no—
10C43×#390C2211yescharacteristic
11C22×C43⋊C8—21no—
12C2×C4⋊Dic43—21no—
13C2×C4⋊Dic43—41no—
14#13063256—42no—
15#13063246—42no—
16C22⋊(C43⋊C8)—41no—
17C22×D4×C43D411yescharacteristic
18C2×C4⋊C4×C43D411yescharacteristic
19C2×C22⋊C4×C43—41no—
20C2×C22⋊C4×C43—41no—
21C2×C42×C43C2×C411yescharacteristic
22#99×C43—22no—
23#99×C43—41no—
24C24×C43—21no—
25C2×D4×C43—21no—
26C2×D4×C43—41no—
27C2×D4×C43—41no—
28C2×D4×C43SD1611yescharacteristic
29C2×D4×C43Q1611yescharacteristic
30C22×C4×C43—21no—
31C22×C4×C43—21no—
32C22×C4×C43—81no—
33C22×C4×C43C22⋊C411yescharacteristic
34C22×Dic43—41no—
35C4⋊C4×C43—41no—
36C22⋊C4×C43—42no—
37C22⋊C4×C43—81no—
38C22⋊C4×C43—82no—
39C42×C43—41no—
40C4⋊Dic43—41no—
41C4⋊Dic43—41no—
42C4⋊Dic43—82no—
43C2×C43⋊C8—22no—
44C2×C43⋊C8—41no—
45C2×C43⋊C8—41no—
46C2×C43⋊C8—81no—
47C23×C43—21no—
48C23×C43—21no—
49C23×C43—41no—
50C23×C43—41no—
51C23×C43—81no—
52C23×C43—81no—
53C23×C43#9911yescharacteristic
54D4×C43—41no—
55D4×C43—41no—
56D4×C43—81no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—22no—
60C2×C4×C43—41no—
61C2×C4×C43—41no—
62C2×C4×C43—41no—
63C2×C4×C43—81no—
64C2×C4×C43—82no—
65C2×C4×C43—161no—
66C2×C4×C43—161no—
67C2×C4×C43#10311yescharacteristic
68C2×C4×C43#10411yescharacteristic
69C2×Dic43—82no—
70C2×Dic43—81no—
71C43⋊C8—42no—
72C43⋊C8—161no—
73#7435—431nomaximal, Sylow
74C22×C43—21no—
75C22×C43—21no—
76C22×C43—41no—
77C22×C43—41no—
78C22×C43—81no—
79C22×C43—81no—
80C22×C43—81no—
81C22×C43—81no—
82C22×C43—161no—
83C22×C43#32811yescharacteristic
84C22×C43#35211yescharacteristic
85C22×C43#35311yescharacteristic
86C4×C43—21no—
87C4×C43—21no—
88C4×C43—42no—
89C4×C43—81no—
90C4×C43—162no—
91Dic43—161no—
92#2094—431no—
93#1393D4311yescharacteristic
94#1318—431no—
95C2×C43—21no—
96C2×C43—21no—
97C2×C43—81no—
98C2×C43—81no—
99C2×C43#135211yescharacteristic
100C2×C43#140611yescharacteristic
101C2×C43#140911yescharacteristic
102C2×#106—861no—
103C2×#102—861no—
104C2×#99—21no—
105#390C2×D4311yescharacteristic
106#384—431no—
107#336—431no—
108#324—861no—
109C43#743511yescharacteristic, complemented, Sylow
110C22×D4C22⋊D4311yescharacteristic
111C22×C8—861no—
112C2×C4⋊C4—861no—
113C2×C4⋊C4—1721no—
114C2×C4⋊C4D17211yescharacteristic
115C2×C22⋊C4—41no—
116C2×C22⋊C4—41no—
117C2×C42C4×D4311yescharacteristic
118#106—1722no—
119#102—1722no—
120#99—22no—
121#99—41no—
122C22⋊C8—1721no—
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4#1062188311yescharacteristic
128C2×D4#1062188511yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—81no—
132C22×C4—1721no—
133C22×C4(C2×D43)⋊C411yescharacteristic
134C2×C8—862no—
135C2×C8—3441no—
136C2×C8—1721no—
137C2×C8—1721no—
138C4⋊C4—41no—
139C4⋊C4—3442no—
140C4⋊C4—1721no—
141C4⋊C4—1721no—
142C22⋊C4—42no—
143C22⋊C4—82no—
144C22⋊C4—81no—
145C42—41no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#1306323911yescharacteristic
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—82no—
164C2×C4—161no—
165C2×C4—161no—
166C2×C4—3442no—
167C2×C4—3441no—
168C2×C4#1306324811yescharacteristic
169C2×C4#1306325311yescharacteristic
170C8—1722no—
171C8—6881no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#1458263511yescharacteristic
182C22#1458268811yescharacteristic
183C22#1458269111yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—162no—
189C4—6881no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2#1913261811yescharacteristic
195C2#1913275111yescharacteristic
196C2#1913275911yescharacteristic
subgroupG/H
centerC22#14582691
commutatorC2×C42×C43C2×C4
Frattini#390C2×D43
FittingC43×#1393C2
socleC22×C43#353
prime radicalC22×D4×C43D4
cosocleC43×#390C22
hypercenter#1393D43
hypocenterC43#7435
LCSG ▷ C2×C42×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1393

Complements

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

NH ≅ G/Ntype
6. #14582769C4semidirect
7. #14582654C4semidirect
109. C43#7435semidirect

Maximal subgroups

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

subgroupindex
#191361282
#191325272
C43×#13932
#743543