Finite Group Databasebeta

← C2×C43×#2984 #24980261

Subgroups — C2×C43×#2984 #24980261

Order 11008.

2022 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C43C211yesmaximal, characteristic
2C43×#2984C2116yesmaximal, direct product factor
3C2×C43×#446C216yesmaximal, complemented
4C2×C8×Q8×C43C212yesmaximal, complemented
5C2×C43×#432C213yesmaximal
6C2×C43×#431C213yesmaximal
7C23×Q8×C43C411yescharacteristic
8C2×C4×Q8×C43C418yes—
9C2×C4×Q8×C43C413yes—
10C2×C4×Q8×C43C411yescharacteristic
11C2×C4×Q8×C43C2211yescharacteristic
12C2×C4×Q8×C43C2213yes—
13C2×C4×Q8×C43C2218yes—
14C22×C4⋊C4×C43C413yes—
15C22×C42×C43C2213yes—
16C43×#446C22148yescomplemented
17C8×Q8×C43C22116yescomplemented
18C43×#432C22124yes—
19C43×#431C22124yes—
20C2×C4⋊C8×C43C2216yes—
21C2×C4⋊C8×C43C2216yes—
22C2×C22⋊C8×C43C2211yescharacteristic
23C2×C22⋊C8×C43C2213yes—
24C2×#97×C43C2216yes—
25C2×C4×C8×C43C2216yes—
26C22×Q8×C43—28no—
27C22×Q8×C43C2×C418yes—
28C22×Q8×C43C2×C413yes—
29C22×Q8×C43C2×C411yescharacteristic
30C23×C4×C43C2×C413yes—
31C23×C4×C43C2×C413yes—
32C23×C4×C43C2311yescharacteristic
33C22×C8×C43C2312yes—
34C22×C8×C43C2316yes—
35C4×Q8×C43C2×C4112yes—
36C4×Q8×C43C2×C4124yes—
37C4×Q8×C43C2×C414yes—
38C4×Q8×C43C2×C418yes—
39C4×Q8×C43C2314yes—
40C4×Q8×C43C23112yes—
41C2×C4⋊C4×C43C2×C416yes—
42C2×C4⋊C4×C43C2×C4124yes—
43C2×C4⋊C4×C43C2×C413yes—
44C2×C4⋊C4×C43C2×C413yes—
45C2×C42×C43C2×C413yes—
46C2×C42×C43C2×C4112yes—
47C2×C42×C43C2×C413yes—
48C2×C42×C43C23112yes—
49C2×C42×C43C2313yes—
50C2×C42×C43C2313yes—
51C4⋊C8×C43C23124yes—
52C4⋊C8×C43C23124yes—
53C22⋊C8×C43C2314yes—
54C22⋊C8×C43C23112yes—
55#97×C43C23124yes—
56C4×C8×C43C23124yes—
57C24×C43C22×C411yescharacteristic
58C2×Q8×C43—232no—
59C2×Q8×C43—212no—
60C2×Q8×C43M1618yes—
61C2×Q8×C43C22×C4112yes—
62C2×Q8×C43C22×C414yes—
63C22×C4×C43—212no—
64C22×C4×C43—24no—
65C22×C4×C43—212no—
66C22×C4×C43C22×C412yes—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C22×C4112yes—
69C22×C4×C43C22×C413yes—
70C22×C4×C43C22×C413yes—
71C22×C4×C43C22×C4112yes—
72C22×C4×C43C22×C413yes—
73C22×C4×C43C22×C413yes—
74C22×C4×C43C2412yes—
75C22×C4×C43C2411yescharacteristic
76C2×C8×C43—24no—
77C2×C8×C43—212no—
78C2×C8×C43C2414yes—
79C2×C8×C43C24112yes—
80C4⋊C4×C43C22×C4124yes—
81C4⋊C4×C43C22×C4112yes—
82C4⋊C4×C43C22×C4112yes—
83C42×C43C22×C4112yes—
84C42×C43C22×C4112yes—
85C42×C43C22×C416yes—
86C42×C43C22×C416yes—
87C42×C43C2416yes—
88C42×C43C2416yes—
89C23×C43—22no—
90C23×C43—22no—
91C23×C43#13114yes—
92C23×C43C23×C412yes—
93C23×C43C23×C411yescharacteristic
94Q8×C43—224no—
95Q8×C43C2×M16116yes—
96C2×C4×C43—22no—
97C2×C4×C43—26no—
98C2×C4×C43—224no—
99C2×C4×C43—26no—
100C2×C4×C43—26no—
101C2×C4×C43—24no—
102C2×C4×C43—224no—
103C2×C4×C43—24no—
104C2×C4×C43C2×M16112yes—
105C2×C4×C43C23×C412yes—
106C2×C4×C43C23×C416yes—
107C2×C4×C43C23×C416yes—
108C2×C4×C43C23×C416yes—
109C2×C4×C43C23×C411yescharacteristic
110C2×C4×C43C23×C416yes—
111C2×C4×C432−1+414yes—
112C2×C4×C43C2511yescharacteristic
113C8×C43—24no—
114C8×C43—212no—
115C2×#2984C4311yesmaximal, characteristic, direct product factor, Sylow
116C22×C43—22no—
117C22×C43—28no—
118C22×C43—22no—
119C22×C43#51912yes—
120C22×C43C22×M1612yes—
121C22×C43C2×#13114yes—
122C22×C43C2×#13112yes—
123C22×C43C24×C411yescharacteristic
124C4×C43—22no—
125C4×C43—26no—
126C4×C43—26no—
127C4×C43—26no—
128C4×C43#51912yes—
129C4×C43C22×M16112yes—
130C4×C43C2×2−1+412yes—
131C22×C4×Q8C2×C4311yescharacteristic
132#2984C2×C43116yesdirect product factor
133C2×#446C2×C4316yescomplemented
134C2×C8×Q8C2×C4312yescomplemented
135C2×#432C2×C4313yes—
136C2×#431C2×C4313yes—
137C2×C43—24no—
138C2×C43#298414yesdirect product factor
139C2×C43C2×#51911yescharacteristic
140C2×C43C23×M1611yescharacteristic
141C2×C43C22×#13111yescharacteristic
142C23×Q8C4×C4311yescharacteristic
143C2×C4×Q8C4×C4318yes—
144C2×C4×Q8C4×C4313yes—
145C2×C4×Q8C4×C4311yescharacteristic
146C2×C4×Q8C22×C4311yescharacteristic
147C2×C4×Q8C22×C4313yes—
148C2×C4×Q8C22×C4318yes—
149C22×C4⋊C4C4×C4313yes—
150C22×C42C22×C4313yes—
151#446C22×C43148yescomplemented
152C8×Q8C22×C43116yescomplemented
153#432C22×C43124yes—
154#431C22×C43124yes—
155C2×C4⋊C8C22×C4316yes—
156C2×C4⋊C8C22×C4316yes—
157C2×C22⋊C8C22×C4311yescharacteristic
158C2×C22⋊C8C22×C4313yes—
159C2×#97C22×C4316yes—
160C2×C4×C8C22×C4316yes—
161C43C2×#298411yescharacteristic, direct product factor, Sylow
162C22×Q8—28no—
163C22×Q8C2×C4×C4318yes—
164C22×Q8C2×C4×C4313yes—
165C22×Q8C2×C4×C4311yescharacteristic
166C23×C4C2×C4×C4313yes—
167C23×C4C2×C4×C4313yes—
168C23×C4C23×C4311yescharacteristic
169C22×C8C23×C4312yes—
170C22×C8C23×C4316yes—
171C4×Q8C2×C4×C43112yes—
172C4×Q8C2×C4×C43124yes—
173C4×Q8C2×C4×C4314yes—
174C4×Q8C2×C4×C4318yes—
175C4×Q8C23×C4314yes—
176C4×Q8C23×C43112yes—
177C2×C4⋊C4C2×C4×C4316yes—
178C2×C4⋊C4C2×C4×C43124yes—
179C2×C4⋊C4C2×C4×C4313yes—
180C2×C4⋊C4C2×C4×C4313yes—
181C2×C42C2×C4×C4313yes—
182C2×C42C2×C4×C43112yes—
183C2×C42C2×C4×C4313yes—
184C2×C42C23×C4313yes—
185C2×C42C23×C4313yes—
186C2×C42C23×C43112yes—
187C4⋊C8C23×C43124yes—
188C4⋊C8C23×C43124yes—
189C22⋊C8C23×C4314yes—
190C22⋊C8C23×C43112yes—
191#97C23×C43124yes—
192C4×C8C23×C43124yes—
193C24C22×C4×C4311yescharacteristic
194C2×Q8—232no—
195C2×Q8—212no—
196C2×Q8M16×C4318yes—
197C2×Q8C22×C4×C43112yes—
198C2×Q8C22×C4×C4314yes—
199C22×C4—212no—
200C22×C4—212no—
201C22×C4—24no—
202C22×C4C22×C4×C43112yes—
203C22×C4C22×C4×C4313yes—
204C22×C4C22×C4×C4313yes—
205C22×C4C22×C4×C4313yes—
206C22×C4C22×C4×C43112yes—
207C22×C4C22×C4×C4311yescharacteristic
208C22×C4C22×C4×C4312yes—
209C22×C4C22×C4×C4313yes—
210C22×C4C24×C4312yes—
211C22×C4C24×C4311yescharacteristic
212C2×C8—24no—
213C2×C8—212no—
214C2×C8C24×C4314yes—
215C2×C8C24×C43112yes—
216C4⋊C4C22×C4×C43124yes—
217C4⋊C4C22×C4×C43112yes—
218C4⋊C4C22×C4×C43112yes—
219C42C22×C4×C43112yes—
220C42C22×C4×C43112yes—
221C42C22×C4×C4316yes—
222C42C22×C4×C4316yes—
223C42C24×C4316yes—
224C42C24×C4316yes—
225C23—22no—
226C23—22no—
227C23#131×C4314yes—
228C23C23×C4×C4312yes—
229C23C23×C4×C4311yescharacteristic
230Q8—224no—
231Q8C2×M16×C43116yes—
232C2×C4—22no—
233C2×C4—26no—
234C2×C4—224no—
235C2×C4—26no—
236C2×C4—26no—
237C2×C4—24no—
238C2×C4—224no—
239C2×C4—24no—
240C2×C4C2×M16×C43112yes—
241C2×C4C23×C4×C4312yes—
242C2×C4C23×C4×C4316yes—
243C2×C4C23×C4×C4316yes—
244C2×C4C23×C4×C4316yes—
245C2×C4C23×C4×C4311yescharacteristic
246C2×C4C23×C4×C4316yes—
247C2×C42−1+4×C4314yes—
248C2×C4C25×C4311yescharacteristic
249C8—24no—
250C8—212no—
251C22—22no—
252C22—28no—
253C22—22no—
254C22C43×#51912yes—
255C22C22×M16×C4312yes—
256C22C2×#131×C4314yes—
257C22C2×#131×C4312yes—
258C22C24×C4×C4311yescharacteristic
259C4—22no—
260C4—26no—
261C4—26no—
262C4—26no—
263C4C43×#51912yes—
264C4C22×M16×C43112yes—
265C4C2×2−1+4×C4312yes—
266C2—24no—
267C2C43×#298414yesdirect product factor
268C2C2×C43×#51911yescharacteristic
269C2C23×M16×C4311yescharacteristic
270C2C22×#131×C4311yescharacteristic
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×#2984C2direct (N × H)
3. C2×C43×#446C2semidirect
4. C2×C8×Q8×C43C2semidirect
16. C43×#446C22semidirect
17. C8×Q8×C43C22semidirect
115. C2×#2984C43direct (N × H)
132. #2984C2×C43direct (N × H)
133. C2×#446C2×C43semidirect
134. C2×C8×Q8C2×C43semidirect
138. C2×C43#2984direct (N × H)
151. #446C22×C43semidirect
152. C8×Q8C22×C43semidirect
161. C43C2×#2984direct (N × H)
267. C2C43×#2984direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C432
C43×#29842
C2×C43×#4462
C2×C8×Q8×C432
C2×C43×#4322
C2×C43×#4312
C2×#298443