Finite Group Databasebeta

← C2×C43×#2383 #24954366

Subgroups — C2×C43×#2383 #24954366

Order 11008.

2502 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C43C211yesmaximal, characteristic
2C43×#2383C2116yesmaximal, direct product factor
3C2×C43×#389C213yesmaximal, complemented
4C2×C43×#388C213yesmaximal
5C2×C43×#387C213yesmaximal, complemented
6C2×C43×#385C213yesmaximal
7C2×C43×#384C211yesmaximal, characteristic, complemented
8C2×C43×#383C211yesmaximal, characteristic, complemented
9C24×C4×C43C2211yescharacteristic
10C2×#126×C43C4116yescomplemented
11C2×#126×C43C2218yes—
12C22×C4⋊C4×C43C2213yes—
13C22×C4⋊C4×C43C2213yes—
14C22×C4⋊C4×C43C2213yes—
15C22×C4⋊C4×C43C2213yes—
16C22×C22⋊C4×C43C2213yes—
17C22×C22⋊C4×C43C2213yes—
18C22×C42×C43C2213yes—
19C22×C42×C43C2211yescharacteristic
20C43×#389C22124yescomplemented
21C43×#388C22124yes—
22C43×#387C22124yescomplemented
23C43×#385C22124yes—
24C43×#384C2218yescomplemented
25C43×#383C2218yescomplemented
26C2×#95×C43C2213yes—
27C2×#95×C43C2213yes—
28C2×#95×C43C2213yes—
29C2×#95×C43C2213yes—
30C25×C43C2311yescharacteristic
31C23×C4×C43—46no—
32C23×C4×C43C2313yes—
33C23×C4×C43C2313yes—
34C23×C4×C43C2311yescharacteristic
35C23×C4×C43C2311yescharacteristic
36C23×C4×C43C2313yes—
37C23×C4×C43C2313yes—
38C23×C4×C43C2314yes—
39#126×C43C2×C4164yescomplemented
40C2×C4⋊C4×C43—46no—
41C2×C4⋊C4×C43—46no—
42C2×C4⋊C4×C43—46no—
43C2×C4⋊C4×C43C2×C4124yescomplemented
44C2×C4⋊C4×C43C23112yes—
45C2×C4⋊C4×C43C23112yes—
46C2×C4⋊C4×C43C23112yes—
47C2×C4⋊C4×C43C23112yes—
48C2×C22⋊C4×C43—46no—
49C2×C22⋊C4×C43C2×C4124yes—
50C2×C22⋊C4×C43C23112yes—
51C2×C22⋊C4×C43C23112yes—
52C2×C42×C43—46no—
53C2×C42×C43C2×C418yescomplemented
54C2×C42×C43C23112yes—
55C2×C42×C43C2314yes—
56#95×C43C23112yes—
57#95×C43C23112yes—
58#95×C43C23112yes—
59#95×C43C23112yes—
60C24×C43—26no—
61C24×C43—26no—
62C24×C43C22×C414yes—
63C24×C43C2412yes—
64C24×C43C2411yescharacteristic
65C22×C4×C43—26no—
66C22×C4×C43—26no—
67C22×C4×C43—26no—
68C22×C4×C43—26no—
69C22×C4×C43—26no—
70C22×C4×C43—26no—
71C22×C4×C43—26no—
72C22×C4×C43—26no—
73C22×C4×C43—26no—
74C22×C4×C43—26no—
75C22×C4×C43—212no—
76C22×C4×C43—412no—
77C22×C4×C43—416no—
78C22×C4×C43C22×C4112yes—
79C22×C4×C43C22×C4112yes—
80C22×C4×C43C2416yes—
81C22×C4×C43C2412yes—
82C22×C4×C43C2412yes—
83C22×C4×C43C2416yes—
84C22×C4×C43C2416yes—
85C22×C4×C43C2416yes—
86C4⋊C4×C43—412no—
87C4⋊C4×C43—412no—
88C4⋊C4×C43—412no—
89C4⋊C4×C43C22×C4148yescomplemented
90C22⋊C4×C43—412no—
91C22⋊C4×C43C22×C4148yes—
92C42×C43—412no—
93C42×C43C22×C4116yescomplemented
94C23×C43—224no—
95C23×C43—26no—
96C23×C43—26no—
97C23×C43—44no—
98C23×C43—412no—
99C23×C43C23×C414yes—
100C23×C43C23×C412yes—
101C23×C43H(5,𝔽2)16yes—
102C23×C432−1+416yes—
103C23×C43C2511yescharacteristic
104C2×C4×C43—224no—
105C2×C4×C43—224no—
106C2×C4×C43—26no—
107C2×C4×C43—26no—
108C2×C4×C43—26no—
109C2×C4×C43—26no—
110C2×C4×C43—26no—
111C2×C4×C43—26no—
112C2×C4×C43—26no—
113C2×C4×C43—26no—
114C2×C4×C43—26no—
115C2×C4×C43—26no—
116C2×C4×C43—212no—
117C2×C4×C43—416no—
118C2×C4×C43—412no—
119C2×C4×C43—44no—
120C2×C4×C43—44no—
121C2×C4×C43—412no—
122C2×C4×C43C23×C4112yes—
123C2×C4×C43C23×C4112yes—
124C2×#2383C4311yesmaximal, characteristic, direct product factor, Sylow
125C22×C43—212no—
126C22×C43—416no—
127C22×C43—42no—
128C22×C43—46no—
129C22×C43#520112yes—
130C22×C43#56014yes—
131C22×C43#563112yes—
132C22×C43C24×C411yescharacteristic
133C22×C43C2×H(5,𝔽2)13yes—
134C22×C43C2×2−1+413yes—
135C4×C43—212no—
136C4×C43—212no—
137C4×C43—46no—
138C4×C43—42no—
139C4×C43—42no—
140C4×C43—46no—
141C22×#126C2×C4311yescharacteristic
142#2383C2×C43116yesdirect product factor
143C2×#389C2×C4313yescomplemented
144C2×#388C2×C4313yes—
145C2×#387C2×C4313yescomplemented
146C2×#385C2×C4313yes—
147C2×#384C2×C4311yescharacteristic, complemented
148C2×#383C2×C4311yescharacteristic, complemented
149C2×C43—44no—
150C2×C43#238318yesdirect product factor
151C2×C43C2×#52013yes—
152C2×C43C2×#56011yescharacteristic
153C2×C43C2×#56313yes—
154C24×C4C22×C4311yescharacteristic
155C2×#126C4×C43116yescomplemented
156C2×#126C22×C4318yes—
157C22×C4⋊C4C22×C4313yes—
158C22×C4⋊C4C22×C4313yes—
159C22×C4⋊C4C22×C4313yes—
160C22×C4⋊C4C22×C4313yes—
161C22×C22⋊C4C22×C4313yes—
162C22×C22⋊C4C22×C4313yes—
163C22×C42C22×C4313yes—
164C22×C42C22×C4311yescharacteristic
165#389C22×C43124yescomplemented
166#388C22×C43124yes—
167#387C22×C43124yescomplemented
168#385C22×C43124yes—
169#384C22×C4318yescomplemented
170#383C22×C4318yescomplemented
171C2×#95C22×C4313yes—
172C2×#95C22×C4313yes—
173C2×#95C22×C4313yes—
174C2×#95C22×C4313yes—
175C43C2×#238311yescharacteristic, direct product factor, Sylow
176C25C23×C4311yescharacteristic
177C23×C4—46no—
178C23×C4C23×C4313yes—
179C23×C4C23×C4313yes—
180C23×C4C23×C4311yescharacteristic
181C23×C4C23×C4311yescharacteristic
182C23×C4C23×C4313yes—
183C23×C4C23×C4313yes—
184C23×C4C23×C4314yes—
185#126C2×C4×C43164yescomplemented
186C2×C4⋊C4—46no—
187C2×C4⋊C4—46no—
188C2×C4⋊C4—46no—
189C2×C4⋊C4C2×C4×C43124yescomplemented
190C2×C4⋊C4C23×C43112yes—
191C2×C4⋊C4C23×C43112yes—
192C2×C4⋊C4C23×C43112yes—
193C2×C4⋊C4C23×C43112yes—
194C2×C22⋊C4—46no—
195C2×C22⋊C4C2×C4×C43124yes—
196C2×C22⋊C4C23×C43112yes—
197C2×C22⋊C4C23×C43112yes—
198C2×C42—46no—
199C2×C42C2×C4×C4318yescomplemented
200C2×C42C23×C43112yes—
201C2×C42C23×C4314yes—
202#95C23×C43112yes—
203#95C23×C43112yes—
204#95C23×C43112yes—
205#95C23×C43112yes—
206C24—26no—
207C24—26no—
208C24C22×C4×C4314yes—
209C24C24×C4312yes—
210C24C24×C4311yescharacteristic
211C22×C4—26no—
212C22×C4—26no—
213C22×C4—26no—
214C22×C4—26no—
215C22×C4—26no—
216C22×C4—26no—
217C22×C4—26no—
218C22×C4—26no—
219C22×C4—26no—
220C22×C4—26no—
221C22×C4—212no—
222C22×C4—412no—
223C22×C4—416no—
224C22×C4C22×C4×C43112yes—
225C22×C4C22×C4×C43112yes—
226C22×C4C24×C4316yes—
227C22×C4C24×C4312yes—
228C22×C4C24×C4312yes—
229C22×C4C24×C4316yes—
230C22×C4C24×C4316yes—
231C22×C4C24×C4316yes—
232C4⋊C4—412no—
233C4⋊C4—412no—
234C4⋊C4—412no—
235C4⋊C4C22×C4×C43148yescomplemented
236C22⋊C4—412no—
237C22⋊C4C22×C4×C43148yes—
238C42—412no—
239C42C22×C4×C43116yescomplemented
240C23—224no—
241C23—26no—
242C23—26no—
243C23—44no—
244C23—412no—
245C23C23×C4×C4314yes—
246C23C23×C4×C4312yes—
247C23H(5,𝔽2)×C4316yes—
248C232−1+4×C4316yes—
249C23C25×C4311yescharacteristic
250C2×C4—224no—
251C2×C4—224no—
252C2×C4—26no—
253C2×C4—26no—
254C2×C4—26no—
255C2×C4—26no—
256C2×C4—26no—
257C2×C4—26no—
258C2×C4—26no—
259C2×C4—26no—
260C2×C4—26no—
261C2×C4—26no—
262C2×C4—212no—
263C2×C4—416no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—412no—
267C2×C4—412no—
268C2×C4C23×C4×C43112yes—
269C2×C4C23×C4×C43112yes—
270C22—212no—
271C22—416no—
272C22—42no—
273C22—46no—
274C22C43×#520112yes—
275C22C43×#56014yes—
276C22C43×#563112yes—
277C22C24×C4×C4311yescharacteristic
278C22C2×H(5,𝔽2)×C4313yes—
279C22C2×2−1+4×C4313yes—
280C4—212no—
281C4—212no—
282C4—42no—
283C4—42no—
284C4—46no—
285C4—46no—
286C2—44no—
287C2C43×#238318yesdirect product factor
288C2C2×C43×#52013yes—
289C2C2×C43×#56011yescharacteristic
290C2C2×C43×#56313yes—
subgroupG/H
center, socleC24×C43C24
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
prime radicalC25×C43C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2383C2direct (N × H)
3. C2×C43×#389C2semidirect
5. C2×C43×#387C2semidirect
7. C2×C43×#384C2semidirect
8. C2×C43×#383C2semidirect
10. C2×#126×C43C4semidirect
20. C43×#389C22semidirect
22. C43×#387C22semidirect
24. C43×#384C22semidirect
25. C43×#383C22semidirect
39. #126×C43C2×C4semidirect
43. C2×C4⋊C4×C43C2×C4semidirect
53. C2×C42×C43C2×C4semidirect
89. C4⋊C4×C43C22×C4semidirect
93. C42×C43C22×C4semidirect
124. C2×#2383C43direct (N × H)
142. #2383C2×C43direct (N × H)
143. C2×#389C2×C43semidirect
145. C2×#387C2×C43semidirect
147. C2×#384C2×C43semidirect
148. C2×#383C2×C43semidirect
150. C2×C43#2383direct (N × H)
155. C2×#126C4×C43semidirect
165. #389C22×C43semidirect
167. #387C22×C43semidirect
169. #384C22×C43semidirect
170. #383C22×C43semidirect
175. C43C2×#2383direct (N × H)
185. #126C2×C4×C43semidirect
189. C2×C4⋊C4C2×C4×C43semidirect
199. C2×C42C2×C4×C43semidirect
235. C4⋊C4C22×C4×C43semidirect
239. C42C22×C4×C43semidirect
287. C2C43×#2383direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#126×C432
C43×#23832
C2×C43×#3892
C2×C43×#3882
C2×C43×#3872
C2×C43×#3852
C2×C43×#3842
C2×C43×#3832
C2×#238343