Finite Group Databasebeta

← C2×C43×#2911 #24980122

Subgroups — C2×C43×#2911 #24980122

Order 11008.

2878 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C43C211yesmaximal, characteristic
2C22×#117×C43C212yesmaximal
3C43×#2911C2116yesmaximal, direct product factor
4C2×C43×#428C218yesmaximal, complemented
5C2×C43×#427C214yesmaximal, complemented
6C24×C4×C43C2211yescharacteristic
7C22×M16×C43C4116yescomplemented
8C22×M16×C43C2214yes—
9C22×M16×C43C2218yes—
10C23×C8×C43C2212yes—
11C2×#117×C43—22no—
12C2×#117×C43—28no—
13C2×#117×C43—22no—
14C2×#117×C43C2214yes—
15C2×#117×C43C2214yes—
16C2×#117×C43C22116yes—
17C22×C4⋊C4×C43C2214yes—
18C22×C22⋊C4×C43—22no—
19C22×C42×C43—22no—
20C43×#428C22164yescomplemented
21C43×#427C22132yescomplemented
22C2×#107×C43C2218yescomplemented
23C2×#106×C43C2218yescomplemented
24C25×C43D411yescharacteristic
25C23×C4×C43—24no—
26C23×C4×C43C2×C418yes—
27C23×C4×C43D411yescharacteristic
28C23×C4×C43D414yes—
29C23×C4×C43D412yes—
30C23×C4×C43Q818yes—
31C23×C4×C43C2312yes—
32C23×C4×C43C2314yes—
33C23×C4×C43C2311yescharacteristic
34C2×M16×C43C2×C4132yescomplemented
35C2×M16×C43C2×C4164yescomplemented
36C2×M16×C43C23116yes—
37C22×C8×C43C2×C4116yescomplemented
38C22×C8×C43C2314yes—
39C22×C8×C43C2318yes—
40#117×C43—216no—
41#117×C43—28no—
42#117×C43—28no—
43#117×C43—216no—
44#117×C43C23116yes—
45#117×C43C23116yes—
46C2×C4⋊C4×C43—24no—
47C2×C4⋊C4×C43—28no—
48C2×C4⋊C4×C43C2318yes—
49C2×C4⋊C4×C43C23116yes—
50C2×C22⋊C4×C43—24no—
51C2×C22⋊C4×C43—24no—
52C2×C22⋊C4×C43—216no—
53C2×C42×C43—24no—
54C2×C42×C43—216no—
55C2×C42×C43—24no—
56#107×C43C23132yescomplemented
57#106×C43C23132yescomplemented
58C24×C43—44no—
59C24×C43C4⋊C418yes—
60C24×C43C2×D411yescharacteristic
61C24×C43C2×D412yes—
62C24×C43C2×D414yes—
63C22×C4×C43—216no—
64C22×C4×C43—28no—
65C22×C4×C43—416no—
66C22×C4×C43C4⋊C418yes—
67C22×C4×C43C4⋊C4116yes—
68C22×C4×C43C4⋊C4132yes—
69C22×C4×C43C22×C414yes—
70C22×C4×C43C22×C418yes—
71C22×C4×C43C22×C4116yes—
72C22×C4×C43C2×D412yes—
73C22×C4×C43C2×D418yes—
74C22×C4×C43C2×D414yes—
75C22×C4×C43C2×D412yes—
76C22×C4×C43C2×D414yes—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×Q818yes—
79C22×C4×C43C2×Q814yes—
80C22×C4×C43C2×Q8116yes—
81C22×C4×C43C2411yescharacteristic
82C22×C4×C43C2414yes—
83C22×C4×C43C2412yes—
84M16×C43C22×C4164yescomplemented
85C2×C8×C43C22×C4116yes—
86C2×C8×C43C22×C4132yescomplemented
87C2×C8×C43C2418yes—
88C4⋊C4×C43—216no—
89C4⋊C4×C43—28no—
90C4⋊C4×C43C24116yes—
91C22⋊C4×C43—216no—
92C22⋊C4×C43—216no—
93C42×C43—216no—
94C42×C43—216no—
95C23×C43—28no—
96C23×C43—24no—
97C23×C43—416no—
98C23×C43—48no—
99C23×C43C2×C4⋊C414yes—
100C23×C43C2×C4⋊C418yes—
101C23×C43C2×C4⋊C4116yes—
102C23×C43C22×D412yes—
103C23×C43C22×D414yes—
104C23×C43C22×D411yescharacteristic
105C2×C4×C43—216no—
106C2×C4×C43—432no—
107C2×C4×C43—416no—
108C2×C4×C43C2×C4⋊C418yes—
109C2×C4×C43C2×C4⋊C4132yes—
110C2×C4×C43C2×C4⋊C4116yes—
111C2×C4×C43C2×C4⋊C4116yes—
112C2×C4×C43C2×C4⋊C418yes—
113C2×C4×C43C2×C4⋊C414yes—
114C2×C4×C43C23×C412yes—
115C2×C4×C43C23×C414yes—
116C2×C4×C43C23×C418yes—
117C2×C4×C43C22×D412yes—
118C2×C4×C43C22×D414yes—
119C2×C4×C43C22×D411yescharacteristic
120C2×C4×C43C22×Q818yes—
121C2×C4×C43C22×Q814yes—
122C2×C4×C43C22×Q812yes—
123C2×C4×C43C2511yescharacteristic
124C8×C43C23×C4116yes—
125C2×#2911C4311yesmaximal, characteristic, direct product factor, Sylow
126C22×C43—216no—
127C22×C43—28no—
128C22×C43—24no—
129C22×C43—28no—
130C22×C43—416no—
131C22×C43C22×C4⋊C414yes—
132C22×C43C22×C4⋊C418yes—
133C22×C43C22×C4⋊C412yes—
134C22×C43#57514yes—
135C22×C43C23×D411yescharacteristic
136C4×C43—416no—
137C4×C43C22×C4⋊C412yes—
138C4×C43C22×C4⋊C418yes—
139C4×C43C22×C4⋊C414yes—
140C4×C43C24×C411yescharacteristic
141C4×C43C23×Q811yescharacteristic
142C23×M16C2×C4311yescharacteristic
143C22×#117C2×C4312yes—
144#2911C2×C43116yesdirect product factor
145C2×#428C2×C4318yescomplemented
146C2×#427C2×C4314yescomplemented
147C2×C43—24no—
148C2×C43—28no—
149C2×C43#291114yesdirect product factor
150C2×C43C23×C4⋊C411yescharacteristic
151C2×C43C2×#57512yes—
152C24×C4C22×C4311yescharacteristic
153C22×M16C4×C43116yescomplemented
154C22×M16C22×C4314yes—
155C22×M16C22×C4318yes—
156C23×C8C22×C4312yes—
157C2×#117—22no—
158C2×#117—28no—
159C2×#117—22no—
160C2×#117C22×C4314yes—
161C2×#117C22×C4314yes—
162C2×#117C22×C43116yes—
163C22×C4⋊C4C22×C4314yes—
164C22×C22⋊C4—22no—
165C22×C42—22no—
166#428C22×C43164yescomplemented
167#427C22×C43132yescomplemented
168C2×#107C22×C4318yescomplemented
169C2×#106C22×C4318yescomplemented
170C43C2×#291111yescharacteristic, direct product factor, Sylow
171C25D4×C4311yescharacteristic
172C23×C4—24no—
173C23×C4C2×C4×C4318yes—
174C23×C4D4×C4311yescharacteristic
175C23×C4D4×C4314yes—
176C23×C4D4×C4312yes—
177C23×C4Q8×C4318yes—
178C23×C4C23×C4312yes—
179C23×C4C23×C4311yescharacteristic
180C23×C4C23×C4314yes—
181C2×M16C2×C4×C43132yescomplemented
182C2×M16C2×C4×C43164yescomplemented
183C2×M16C23×C43116yes—
184C22×C8C2×C4×C43116yescomplemented
185C22×C8C23×C4314yes—
186C22×C8C23×C4318yes—
187#117—216no—
188#117—28no—
189#117—28no—
190#117—216no—
191#117C23×C43116yes—
192#117C23×C43116yes—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—28no—
195C2×C4⋊C4C23×C4318yes—
196C2×C4⋊C4C23×C43116yes—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—216no—
200C2×C42—24no—
201C2×C42—24no—
202C2×C42—216no—
203#107C23×C43132yescomplemented
204#106C23×C43132yescomplemented
205C24—44no—
206C24C4⋊C4×C4318yes—
207C24C2×D4×C4311yescharacteristic
208C24C2×D4×C4312yes—
209C24C2×D4×C4314yes—
210C22×C4—216no—
211C22×C4—28no—
212C22×C4—416no—
213C22×C4C4⋊C4×C4318yes—
214C22×C4C4⋊C4×C43116yes—
215C22×C4C4⋊C4×C43132yes—
216C22×C4C22×C4×C4314yes—
217C22×C4C22×C4×C4318yes—
218C22×C4C22×C4×C43116yes—
219C22×C4C2×D4×C4311yescharacteristic
220C22×C4C2×D4×C4312yes—
221C22×C4C2×D4×C4318yes—
222C22×C4C2×D4×C4314yes—
223C22×C4C2×D4×C4312yes—
224C22×C4C2×D4×C4314yes—
225C22×C4C2×Q8×C4318yes—
226C22×C4C2×Q8×C4314yes—
227C22×C4C2×Q8×C43116yes—
228C22×C4C24×C4311yescharacteristic
229C22×C4C24×C4314yes—
230C22×C4C24×C4312yes—
231M16C22×C4×C43164yescomplemented
232C2×C8C22×C4×C43116yes—
233C2×C8C22×C4×C43132yescomplemented
234C2×C8C24×C4318yes—
235C4⋊C4—216no—
236C4⋊C4—28no—
237C4⋊C4C24×C43116yes—
238C22⋊C4—216no—
239C22⋊C4—216no—
240C42—216no—
241C42—216no—
242C23—28no—
243C23—24no—
244C23—416no—
245C23—48no—
246C23C2×C4⋊C4×C4314yes—
247C23C2×C4⋊C4×C4318yes—
248C23C2×C4⋊C4×C43116yes—
249C23C22×D4×C4312yes—
250C23C22×D4×C4314yes—
251C23C22×D4×C4311yescharacteristic
252C2×C4—216no—
253C2×C4—432no—
254C2×C4—416no—
255C2×C4C2×C4⋊C4×C4318yes—
256C2×C4C2×C4⋊C4×C43132yes—
257C2×C4C2×C4⋊C4×C43116yes—
258C2×C4C2×C4⋊C4×C43116yes—
259C2×C4C2×C4⋊C4×C4314yes—
260C2×C4C2×C4⋊C4×C4318yes—
261C2×C4C23×C4×C4312yes—
262C2×C4C23×C4×C4314yes—
263C2×C4C23×C4×C4318yes—
264C2×C4C22×D4×C4312yes—
265C2×C4C22×D4×C4314yes—
266C2×C4C22×D4×C4311yescharacteristic
267C2×C4C22×Q8×C4318yes—
268C2×C4C22×Q8×C4314yes—
269C2×C4C22×Q8×C4312yes—
270C2×C4C25×C4311yescharacteristic
271C8C23×C4×C43116yes—
272C22—216no—
273C22—28no—
274C22—28no—
275C22—24no—
276C22—416no—
277C22C22×C4⋊C4×C4314yes—
278C22C22×C4⋊C4×C4318yes—
279C22C22×C4⋊C4×C4312yes—
280C22C43×#57514yes—
281C22C23×D4×C4311yescharacteristic
282C4—416no—
283C4C22×C4⋊C4×C4312yes—
284C4C22×C4⋊C4×C4314yes—
285C4C22×C4⋊C4×C4318yes—
286C4C24×C4×C4311yescharacteristic
287C4C23×Q8×C4311yescharacteristic
288C2—28no—
289C2—24no—
290C2C43×#291114yesdirect product factor
291C2C23×C4⋊C4×C4311yescharacteristic
292C2C2×C43×#57512yes—
subgroupG/H
centerC22×C4×C43C2×D4
commutatorC4C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC23×C43C22×D4
prime radicalC25×C43D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2911C2direct (N × H)
4. C2×C43×#428C2semidirect
5. C2×C43×#427C2semidirect
7. C22×M16×C43C4semidirect
20. C43×#428C22semidirect
21. C43×#427C22semidirect
22. C2×#107×C43C22semidirect
23. C2×#106×C43C22semidirect
34. C2×M16×C43C2×C4semidirect
35. C2×M16×C43C2×C4semidirect
37. C22×C8×C43C2×C4semidirect
56. #107×C43C23semidirect
57. #106×C43C23semidirect
84. M16×C43C22×C4semidirect
86. C2×C8×C43C22×C4semidirect
125. C2×#2911C43direct (N × H)
144. #2911C2×C43direct (N × H)
145. C2×#428C2×C43semidirect
146. C2×#427C2×C43semidirect
149. C2×C43#2911direct (N × H)
153. C22×M16C4×C43semidirect
166. #428C22×C43semidirect
167. #427C22×C43semidirect
168. C2×#107C22×C43semidirect
169. C2×#106C22×C43semidirect
170. C43C2×#2911direct (N × H)
181. C2×M16C2×C4×C43semidirect
182. C2×M16C2×C4×C43semidirect
184. C22×C8C2×C4×C43semidirect
203. #107C23×C43semidirect
204. #106C23×C43semidirect
231. M16C22×C4×C43semidirect
233. C2×C8C22×C4×C43semidirect
290. C2C43×#2911direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C432
C22×#117×C432
C43×#29112
C2×C43×#4282
C2×C43×#4272
C2×#291143