Finite Group Databasebeta

← C43×#8101 #24928118

Subgroups — C43×#8101 #24928118

Order 11008.

2414 conjugacy classes of subgroups; only the 278 normal subgroups are shown.

normal subgroups only

This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 278 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
1C2×C43×#379C213yesmaximal
2C43×#1304C214yesmaximal, complemented
3C26×C43C2211yescharacteristic
4C22×C22⋊C4×C43—26no—
5C22×C22⋊C4×C43C416yescomplemented
6C43×#379—26no—
7C43×#379C416yescomplemented
8C43×#379C2216yes—
9C25×C43—412no—
10C25×C43C2×C413yes—
11C25×C43C2×C413yes—
12C25×C43D416yes—
13C25×C43Q812yes—
14C25×C43C2311yescharacteristic
15C23×C4×C43—26no—
16C2×C22⋊C4×C43—212no—
17C2×C22⋊C4×C43—26no—
18C2×C22⋊C4×C43—212no—
19C2×C22⋊C4×C43—424no—
20C2×C22⋊C4×C43—412no—
21C2×C22⋊C4×C43C2×C4112yescomplemented
22C24×C43—212no—
23C24×C43—224no—
24C24×C43—412no—
25C24×C43—412no—
26C24×C43—46no—
27C24×C43—412no—
28C24×C43—412no—
29C24×C43—412no—
30C24×C43—46no—
31C24×C43—464no—
32C24×C43C4213yes—
33C24×C43C4211yescharacteristic
34C24×C43C22⋊C413yes—
35C24×C43C22⋊C416yes—
36C24×C43C22⋊C413yes—
37C24×C43C4⋊C416yes—
38C24×C43C4⋊C416yes—
39C24×C43C22×C413yes—
40C24×C43C2×D413yes—
41C24×C43C2×Q811yescharacteristic
42C22×C4×C43—212no—
43C22×C4×C43—424no—
44C22×C4×C43—412no—
45C22⋊C4×C43—412no—
46C22⋊C4×C43—424no—
47C22⋊C4×C43—424no—
48C22⋊C4×C43—412no—
49C23×C43—212no—
50C23×C43—26no—
51C23×C43—212no—
52C23×C43—212no—
53C23×C43—212no—
54C23×C43—212no—
55C23×C43—212no—
56C23×C43—26no—
57C23×C43—212no—
58C23×C43—212no—
59C23×C43—43no—
60C23×C43—43no—
61C23×C43—46no—
62C23×C43—46no—
63C23×C43—46no—
64C23×C43—46no—
65C23×C43—46no—
66C23×C43—46no—
67C23×C43—43no—
68C23×C43—43no—
69C23×C43—448no—
70C23×C43—496no—
71C23×C43—448no—
72C23×C43—432no—
73C23×C43—416no—
74C23×C43#9512yes—
75C23×C43#9516yes—
76C23×C43#99112yes—
77C23×C43C2×C4211yescharacteristic
78C23×C43C2×C22⋊C413yes—
79C23×C43C2×C4⋊C413yes—
80C2×C4×C43—424no—
81C2×C4×C43—412no—
82C2×C4×C43—824no—
83#8101C4311yesmaximal, characteristic, direct product factor, Sylow
84C22×C43—224no—
85C22×C43—26no—
86C22×C43—26no—
87C22×C43—26no—
88C22×C43—26no—
89C22×C43—23no—
90C22×C43—23no—
91C22×C43—26no—
92C22×C43—412no—
93C22×C43—412no—
94C22×C43—424no—
95C22×C43—412no—
96C22×C43—424no—
97C22×C43—412no—
98C22×C43—424no—
99C22×C43—44no—
100C22×C43—44no—
101C22×C43#342112yes—
102C22×C43C2×#9511yescharacteristic
103C22×C43C2×#9916yes—
104C4×C43—812no—
105C2×#379C2×C4313yes—
106#1304C2×C4314yescomplemented
107C2×C43—26no—
108C2×C43—212no—
109C2×C43—42no—
110C2×C43—41no—
111C2×C43—43no—
112C2×C43C2×#34213yes—
113C26C22×C4311yescharacteristic
114C22×C22⋊C4—26no—
115C22×C22⋊C4C4×C4316yescomplemented
116#379—26no—
117#379C4×C4316yescomplemented
118#379C22×C4316yes—
119C43#810111yescharacteristic, direct product factor, Sylow
120C25—412no—
121C25C2×C4×C4313yes—
122C25C2×C4×C4313yes—
123C25D4×C4316yes—
124C25Q8×C4312yes—
125C25C23×C4311yescharacteristic
126C23×C4—26no—
127C2×C22⋊C4—212no—
128C2×C22⋊C4—26no—
129C2×C22⋊C4—212no—
130C2×C22⋊C4—424no—
131C2×C22⋊C4—412no—
132C2×C22⋊C4C2×C4×C43112yescomplemented
133C24—212no—
134C24—224no—
135C24—46no—
136C24—412no—
137C24—412no—
138C24—46no—
139C24—412no—
140C24—412no—
141C24—412no—
142C24—464no—
143C24C42×C4313yes—
144C24C42×C4311yescharacteristic
145C24C22⋊C4×C4313yes—
146C24C22⋊C4×C4316yes—
147C24C22⋊C4×C4313yes—
148C24C4⋊C4×C4316yes—
149C24C4⋊C4×C4316yes—
150C24C22×C4×C4313yes—
151C24C2×D4×C4313yes—
152C24C2×Q8×C4311yescharacteristic
153C22×C4—212no—
154C22×C4—424no—
155C22×C4—412no—
156C22⋊C4—424no—
157C22⋊C4—424no—
158C22⋊C4—412no—
159C22⋊C4—412no—
160C23—212no—
161C23—26no—
162C23—212no—
163C23—212no—
164C23—212no—
165C23—212no—
166C23—212no—
167C23—26no—
168C23—212no—
169C23—212no—
170C23—43no—
171C23—43no—
172C23—46no—
173C23—46no—
174C23—46no—
175C23—46no—
176C23—46no—
177C23—46no—
178C23—43no—
179C23—43no—
180C23—448no—
181C23—496no—
182C23—416no—
183C23—448no—
184C23—432no—
185C23#95×C4312yes—
186C23#95×C4316yes—
187C23#99×C43112yes—
188C23C2×C42×C4311yescharacteristic
189C23C2×C22⋊C4×C4313yes—
190C23C2×C4⋊C4×C4313yes—
191C2×C4—424no—
192C2×C4—412no—
193C2×C4—824no—
194C22—224no—
195C22—26no—
196C22—26no—
197C22—26no—
198C22—26no—
199C22—23no—
200C22—23no—
201C22—26no—
202C22—412no—
203C22—412no—
204C22—424no—
205C22—412no—
206C22—424no—
207C22—412no—
208C22—424no—
209C22—44no—
210C22—44no—
211C22C43×#342112yes—
212C22C2×#95×C4311yescharacteristic
213C22C2×#99×C4316yes—
214C4—812no—
215C2—26no—
216C2—212no—
217C2—42no—
218C2—41no—
219C2—43no—
220C2C2×C43×#34213yes—
subgroupG/H
center, socleC22×C43C2×#95
commutatorC23C2×C42×C43
Frattini, cosocleC25C23×C43
prime radicalC26×C43C22
LCSG ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C26×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1304C2semidirect
5. C22×C22⋊C4×C43C4semidirect
7. C43×#379C4semidirect
21. C2×C22⋊C4×C43C2×C4semidirect
83. #8101C43direct (N × H)
106. #1304C2×C43semidirect
115. C22×C22⋊C4C4×C43semidirect
117. #379C4×C43semidirect
119. C43#8101direct (N × H)
132. C2×C22⋊C4C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3792
C43×#13042
#810143