Finite Group Databasebeta

← C43×#7435 #24927452

Subgroups — C43×#7435 #24927452

Order 11008.

224 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C43×#2094C211yesmaximal, characteristic
2C43×#1393C211yesmaximal, characteristic
3C43×#1318C211yesmaximal, characteristic
4C2×#106×C43—21no—
5C2×#102×C43—21no—
6C2×#99×C43—21no—
7C43×#390C2211yescharacteristic
8C43×#384C411yescharacteristic, complemented
9C43×#336C411yescharacteristic, complemented
10C43×#324—21no—
11C22×D4×C43D411yescharacteristic
12C22×C8×C43—21no—
13C2×C4⋊C4×C43—21no—
14C2×C4⋊C4×C43—41no—
15C2×C4⋊C4×C43D411yescharacteristic
16C2×C22⋊C4×C43—41no—
17C2×C22⋊C4×C43—41no—
18C2×C42×C43C2×C411yescharacteristic
19#106×C43—42no—
20#102×C43—42no—
21#99×C43—22no—
22#99×C43—41no—
23C22⋊C8×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—41no—
33C22×C4×C43—81no—
34C22×C4×C43C22⋊C411yescharacteristic
35C2×C8×C43—22no—
36C2×C8×C43—41no—
37C2×C8×C43—41no—
38C2×C8×C43—81no—
39C4⋊C4×C43—41no—
40C4⋊C4×C43—41no—
41C4⋊C4×C43—41no—
42C4⋊C4×C43—82no—
43C22⋊C4×C43—42no—
44C22⋊C4×C43—81no—
45C22⋊C4×C43—82no—
46C42×C43—41no—
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—82no—
66C2×C4×C43—81no—
67C2×C4×C43—161no—
68C2×C4×C43—161no—
69C2×C4×C43#10311yescharacteristic
70C2×C4×C43#10411yescharacteristic
71C8×C43—42no—
72C8×C43—161no—
73#7435C4311yesmaximal, characteristic, direct product factor, 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—
91C4×C43—161no—
92#2094C2×C4311yescharacteristic
93#1393C2×C4311yescharacteristic
94#1318C2×C4311yescharacteristic
95C2×C43—21no—
96C2×C43—21no—
97C2×C43—81no—
98C2×C43—81no—
99C2×C43#135211yescharacteristic
100C2×C43#140611yescharacteristic
101C2×C43#140911yescharacteristic
102C2×#106—21no—
103C2×#102—21no—
104C2×#99—21no—
105#390C22×C4311yescharacteristic
106#384C4×C4311yescharacteristic, complemented
107#336C4×C4311yescharacteristic, complemented
108#324—21no—
109C43#743511yescharacteristic, direct product factor, Sylow
110C22×D4D4×C4311yescharacteristic
111C22×C8—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4D4×C4311yescharacteristic
115C2×C22⋊C4—41no—
116C2×C22⋊C4—41no—
117C2×C42C2×C4×C4311yescharacteristic
118#106—42no—
119#102—42no—
120#99—22no—
121#99—41no—
122C22⋊C8—41no—
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4SD16×C4311yescharacteristic
128C2×D4Q16×C4311yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—41no—
132C22×C4—81no—
133C22×C4C22⋊C4×C4311yescharacteristic
134C2×C8—22no—
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—81no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—82no—
142C22⋊C4—42no—
143C22⋊C4—82no—
144C22⋊C4—81no—
145C42—41no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#99×C4311yescharacteristic
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—82no—
165C2×C4—81no—
166C2×C4—161no—
167C2×C4—161no—
168C2×C4#103×C4311yescharacteristic
169C2×C4#104×C4311yescharacteristic
170C8—42no—
171C8—161no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22C43×#32811yescharacteristic
182C22C43×#35211yescharacteristic
183C22C43×#35311yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—162no—
189C4—161no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2C43×#135211yescharacteristic
195C2C43×#140611yescharacteristic
196C2C43×#140911yescharacteristic
subgroupG/H
center, socleC22×C43#353
commutatorC2×C42C2×C4×C43
Frattini, cosocle#390C22×C43
prime radicalC22×D4×C43D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C43 ◁ C22×C4×C43 ◁ C43×#390 ◁ G

Complements

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

NH ≅ G/Ntype
8. C43×#384C4semidirect
9. C43×#336C4semidirect
73. #7435C43direct (N × H)
106. #384C4×C43semidirect
107. #336C4×C43semidirect
109. C43#7435direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#20942
C43×#13932
C43×#13182
#743543