Finite Group Databasebeta

← C2×C43×#2986 #24980263

Subgroups — C2×C43×#2986 #24980263

Order 11008.

1794 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#533C211yesmaximal, characteristic
2C43×#2986C2116yesmaximal, direct product factor
3C2×C43×#446C214yesmaximal, complemented
4C2×C8×Q8×C43C214yesmaximal, complemented
5C2×C43×#433C214yesmaximal
6C2×C43×#431C212yesmaximal
7C43×#533C418yes—
8C43×#533C2218yes—
9C2×C4⋊Q8×C43C412yes—
10C2×#125×C43C412yes—
11C2×C22⋊Q8×C43C414yes—
12C2×C4×Q8×C43C2214yes—
13C2×#117×C43C2212yes—
14C22×C42×C43C2211yescharacteristic
15C43×#446C22132yescomplemented
16C8×Q8×C43C22132yescomplemented
17C43×#433C22132yes—
18C43×#431C22116yes—
19C2×C4⋊C8×C43C2212yes—
20C2×C4⋊C8×C43C2212yes—
21C2×C4⋊C8×C43C2218yes—
22C2×C22⋊C8×C43C2214yes—
23C2×#97×C43C2214yes—
24C2×C4×C8×C43C2214yes—
25C2×C4×C8×C43C2214yes—
26C22×Q8×C43C2×C414yes—
27C23×C4×C43C2×C412yes—
28C23×C4×C43C2311yescharacteristic
29C22×C8×C43C2314yes—
30C22×C8×C43C2314yes—
31C4⋊Q8×C43C2×C4116yes—
32#125×C43C2×C4116yes—
33C22⋊Q8×C43C2×C4132yes—
34C4×Q8×C43C2×C4116yes—
35C4×Q8×C43C23116yes—
36#117×C43C2×C418yes—
37#117×C43C2318yes—
38C2×C4⋊C4×C43C2×C414yes—
39C2×C4⋊C4×C43C2×C418yes—
40C2×C4⋊C4×C43C2×C414yes—
41C2×C22⋊C4×C43C2×C414yes—
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43C2×C414yes—
45C2×C42×C43C2314yes—
46C2×C42×C43C2312yes—
47C2×C42×C43C2314yes—
48C4⋊C8×C43C2318yes—
49C4⋊C8×C43C2318yes—
50C4⋊C8×C43C23132yes—
51C22⋊C8×C43C23116yes—
52#97×C43C23116yes—
53C4×C8×C43C23116yes—
54C4×C8×C43C23116yes—
55C24×C43C22×C411yescharacteristic
56C2×Q8×C43—216no—
57C2×Q8×C43C22×C4116yes—
58C22×C4×C43—28no—
59C22×C4×C43—24no—
60C22×C4×C43C22×C411yescharacteristic
61C22×C4×C43C22×C412yes—
62C22×C4×C43C22×C412yes—
63C22×C4×C43C22×C418yes—
64C22×C4×C43C22×C418yes—
65C22×C4×C43C22×C412yes—
66C22×C4×C43C2412yes—
67C22×C4×C43C2411yescharacteristic
68C2×C8×C43—28no—
69C2×C8×C43—28no—
70C2×C8×C43C2418yes—
71C2×C8×C43C2418yes—
72C4⋊C4×C43C22×C4116yes—
73C4⋊C4×C43C22×C4132yes—
74C4⋊C4×C43C22×C4116yes—
75C22⋊C4×C43C22×C4116yes—
76C42×C43C22×C414yes—
77C42×C43C22×C414yes—
78C42×C43C22×C414yes—
79C42×C43C22×C418yes—
80C42×C43C2414yes—
81C42×C43C2418yes—
82C23×C43—22no—
83C23×C43—24no—
84C23×C43C23×C412yes—
85C23×C43C23×C411yescharacteristic
86Q8×C43—232no—
87C2×C4×C43—22no—
88C2×C4×C43—24no—
89C2×C4×C43—216no—
90C2×C4×C43—24no—
91C2×C4×C43—216no—
92C2×C4×C43—24no—
93C2×C4×C43#13118yes—
94C2×C4×C43C23×C412yes—
95C2×C4×C43C23×C414yes—
96C2×C4×C43C23×C4116yes—
97C2×C4×C43C23×C411yescharacteristic
98C2×C4×C43C23×C414yes—
99C2×C4×C432−1+414yes—
100C2×C4×C43C2511yescharacteristic
101C8×C43—28no—
102C8×C43—28no—
103C2×#2986C4311yesmaximal, characteristic, direct product factor, Sylow
104C22×C43—22no—
105C22×C43—24no—
106C22×C43—44no—
107C22×C43#51912yes—
108C22×C43C2×#13114yes—
109C22×C43C24×C411yescharacteristic
110C4×C43—22no—
111C4×C43—24no—
112C4×C43—216no—
113C4×C43#51912yes—
114C4×C43C2×#13118yes—
115C4×C43C2×2−1+412yes—
116C2×#533C2×C4311yescharacteristic
117#2986C2×C43116yesdirect product factor
118C2×#446C2×C4314yescomplemented
119C2×C8×Q8C2×C4314yescomplemented
120C2×#433C2×C4314yes—
121C2×#431C2×C4312yes—
122C2×C43—42no—
123C2×C43#298614yesdirect product factor
124C2×C43C2×#51911yescharacteristic
125C2×C43C22×#13112yes—
126#533C4×C4318yes—
127#533C22×C4318yes—
128C2×C4⋊Q8C4×C4312yes—
129C2×#125C4×C4312yes—
130C2×C22⋊Q8C4×C4314yes—
131C2×C4×Q8C22×C4314yes—
132C2×#117C22×C4312yes—
133C22×C42C22×C4311yescharacteristic
134#446C22×C43132yescomplemented
135C8×Q8C22×C43132yescomplemented
136#433C22×C43132yes—
137#431C22×C43116yes—
138C2×C4⋊C8C22×C4312yes—
139C2×C4⋊C8C22×C4312yes—
140C2×C4⋊C8C22×C4318yes—
141C2×C22⋊C8C22×C4314yes—
142C2×#97C22×C4314yes—
143C2×C4×C8C22×C4314yes—
144C2×C4×C8C22×C4314yes—
145C43C2×#298611yescharacteristic, direct product factor, Sylow
146C22×Q8C2×C4×C4314yes—
147C23×C4C2×C4×C4312yes—
148C23×C4C23×C4311yescharacteristic
149C22×C8C23×C4314yes—
150C22×C8C23×C4314yes—
151C4⋊Q8C2×C4×C43116yes—
152#125C2×C4×C43116yes—
153C22⋊Q8C2×C4×C43132yes—
154C4×Q8C2×C4×C43116yes—
155C4×Q8C23×C43116yes—
156#117C2×C4×C4318yes—
157#117C23×C4318yes—
158C2×C4⋊C4C2×C4×C4314yes—
159C2×C4⋊C4C2×C4×C4318yes—
160C2×C4⋊C4C2×C4×C4314yes—
161C2×C22⋊C4C2×C4×C4314yes—
162C2×C42C2×C4×C4311yescharacteristic
163C2×C42C2×C4×C4311yescharacteristic
164C2×C42C2×C4×C4314yes—
165C2×C42C23×C4314yes—
166C2×C42C23×C4312yes—
167C2×C42C23×C4314yes—
168C4⋊C8C23×C4318yes—
169C4⋊C8C23×C4318yes—
170C4⋊C8C23×C43132yes—
171C22⋊C8C23×C43116yes—
172#97C23×C43116yes—
173C4×C8C23×C43116yes—
174C4×C8C23×C43116yes—
175C24C22×C4×C4311yescharacteristic
176C2×Q8—216no—
177C2×Q8C22×C4×C43116yes—
178C22×C4—28no—
179C22×C4—24no—
180C22×C4C22×C4×C4312yes—
181C22×C4C22×C4×C4318yes—
182C22×C4C22×C4×C4318yes—
183C22×C4C22×C4×C4311yescharacteristic
184C22×C4C22×C4×C4312yes—
185C22×C4C22×C4×C4312yes—
186C22×C4C24×C4312yes—
187C22×C4C24×C4311yescharacteristic
188C2×C8—28no—
189C2×C8—28no—
190C2×C8C24×C4318yes—
191C2×C8C24×C4318yes—
192C4⋊C4C22×C4×C43116yes—
193C4⋊C4C22×C4×C43132yes—
194C4⋊C4C22×C4×C43116yes—
195C22⋊C4C22×C4×C43116yes—
196C42C22×C4×C4314yes—
197C42C22×C4×C4314yes—
198C42C22×C4×C4314yes—
199C42C22×C4×C4318yes—
200C42C24×C4314yes—
201C42C24×C4318yes—
202C23—22no—
203C23—24no—
204C23C23×C4×C4312yes—
205C23C23×C4×C4311yescharacteristic
206Q8—232no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—216no—
210C2×C4—24no—
211C2×C4—216no—
212C2×C4—24no—
213C2×C4#131×C4318yes—
214C2×C4C23×C4×C4312yes—
215C2×C4C23×C4×C4314yes—
216C2×C4C23×C4×C43116yes—
217C2×C4C23×C4×C4311yescharacteristic
218C2×C4C23×C4×C4314yes—
219C2×C42−1+4×C4314yes—
220C2×C4C25×C4311yescharacteristic
221C8—28no—
222C8—28no—
223C22—22no—
224C22—24no—
225C22—44no—
226C22C43×#51912yes—
227C22C2×#131×C4314yes—
228C22C24×C4×C4311yescharacteristic
229C4—22no—
230C4—24no—
231C4—216no—
232C4C43×#51912yes—
233C4C2×#131×C4318yes—
234C4C2×2−1+4×C4312yes—
235C2—42no—
236C2C43×#298614yesdirect product factor
237C2C2×C43×#51911yescharacteristic
238C2C22×#131×C4312yes—
subgroupG/H
centerC22×C4×C43C24
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC23×C43C23×C4
prime radicalC24×C43C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2986C2direct (N × H)
3. C2×C43×#446C2semidirect
4. C2×C8×Q8×C43C2semidirect
15. C43×#446C22semidirect
16. C8×Q8×C43C22semidirect
103. C2×#2986C43direct (N × H)
117. #2986C2×C43direct (N × H)
118. C2×#446C2×C43semidirect
119. C2×C8×Q8C2×C43semidirect
123. C2×C43#2986direct (N × H)
134. #446C22×C43semidirect
135. C8×Q8C22×C43semidirect
145. C43C2×#2986direct (N × H)
236. C2C43×#2986direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5332
C43×#29862
C2×C43×#4462
C2×C8×Q8×C432
C2×C43×#4332
C2×C43×#4312
C2×#298643