Finite Group Databasebeta

← C43×#20385 #24940402

Subgroups — C43×#20385 #24940402

Order 11008.

1774 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C8×C43C211yesmaximal, characteristic
2C2×C43×#407C211yesmaximal, characteristic
3C2×C43×#405C212yesmaximal, complemented
4C43×#2280C211yesmaximal, characteristic
5C43×#1752C214yesmaximal, complemented
6C8×C22⋊C4×C43C214yesmaximal, complemented
7C43×#1729C212yesmaximal, complemented
8C24×C4×C43C2211yescharacteristic
9C22×M16×C43C2212yes—
10C23×C8×C43—28no—
11C23×C8×C43C418yescomplemented
12C23×C8×C43C2211yescharacteristic
13C23×C8×C43C2212yes—
14C23×C8×C43C2212yes—
15C23×C8×C43C2211yescharacteristic
16C2×#117×C43C2212yes—
17C43×#407C418yescomplemented
18C2×C22⋊C8×C43C2214yes—
19C43×#405—28no—
20C2×#97×C43C2214yescomplemented
21C2×C4×C8×C43C2214yescomplemented
22C43×#381C412yes—
23C43×#380C414yes—
24C43×#379C412yes—
25C4×C22⋊C4×C43C2214yes—
26C43×#336C2218yescomplemented
27C25×C43C2×C411yescharacteristic
28C23×C4×C43—24no—
29C23×C4×C43—24no—
30C23×C4×C43C2×C412yes—
31C23×C4×C43C2×C411yescharacteristic
32C23×C4×C43C2×C414yes—
33C23×C4×C43C2×C414yes—
34C23×C4×C43C2312yes—
35C23×C4×C43C2311yescharacteristic
36C2×M16×C43—24no—
37C2×M16×C43—24no—
38C2×M16×C43C2×C418yes—
39C22×C8×C43—24no—
40C22×C8×C43—232no—
41C22×C8×C43—28no—
42C22×C8×C43—28no—
43C22×C8×C43C2×C414yes—
44C22×C8×C43C2×C418yes—
45C22×C8×C43C2×C418yes—
46C22×C8×C43C2×C414yes—
47C22×C8×C43D418yes—
48C22×C8×C43C2312yes—
49C22×C8×C43C2314yes—
50C22×C8×C43C2311yescharacteristic
51C22×C8×C43C2311yescharacteristic
52#117×C43—24no—
53#117×C43—24no—
54C2×C4⋊C4×C43C2×C414yes—
55C2×C22⋊C4×C43C2×C414yes—
56C2×C22⋊C4×C43C2×C418yes—
57C2×C42×C43C2314yes—
58C22⋊C8×C43C2×C4116yes—
59#97×C43—28no—
60C4×C8×C43—28no—
61#95×C43C2×C418yes—
62C24×C43—24no—
63C24×C43—28no—
64C24×C43C4214yes—
65C24×C43C22×C411yescharacteristic
66C24×C43C22×C412yes—
67C22×C4×C43—28no—
68C22×C4×C43—28no—
69C22×C4×C43—28no—
70C22×C4×C43—216no—
71C22×C4×C43—24no—
72C22×C4×C43—24no—
73C22×C4×C43—24no—
74C22×C4×C43C4214yes—
75C22×C4×C43C4218yes—
76C22×C4×C43C22×C414yes—
77C22×C4×C43C22×C414yes—
78C22×C4×C43C22×C412yes—
79C22×C4×C43C22×C412yes—
80C22×C4×C43C22×C418yes—
81C22×C4×C43C22×C412yes—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D414yes—
84C22×C4×C43#4114yes—
85C22×C4×C43C2411yescharacteristic
86M16×C43—216no—
87C2×C8×C43—28no—
88C2×C8×C43—24no—
89C2×C8×C43—24no—
90C2×C8×C43—24no—
91C2×C8×C43—216no—
92C2×C8×C43—216no—
93C2×C8×C43C22⋊C4116yescomplemented
94C2×C8×C43C22×C418yes—
95C2×C8×C43C22×C414yes—
96C2×C8×C43C22×C412yes—
97C2×C8×C43C22×C412yes—
98C2×C8×C43C2×D414yes—
99C2×C8×C43C2×D414yes—
100C4⋊C4×C43—28no—
101C22⋊C4×C43—28no—
102C22⋊C4×C43—216no—
103C42×C43—24no—
104C42×C43—24no—
105C23×C43—232no—
106C23×C43—24no—
107C23×C43—24no—
108C23×C43—24no—
109C23×C43—28no—
110C23×C43—216no—
111C23×C43C2×C4212yes—
112C23×C43C2×C4214yes—
113C23×C43C4×D414yes—
114C23×C43#13118yes—
115C23×C43C23×C411yescharacteristic
116C2×C4×C43—24no—
117C2×C4×C43—28no—
118C2×C4×C43—24no—
119C2×C4×C43—24no—
120C2×C4×C43—28no—
121C2×C4×C43—216no—
122C2×C4×C43—28no—
123C2×C4×C43—216no—
124C2×C4×C43C2×C4214yes—
125C2×C4×C43C2×C4212yes—
126C2×C4×C43C2×C22⋊C414yes—
127C2×C4×C43#11714yes—
128C2×C4×C43C4×D418yes—
129C2×C4×C43C4×D414yes—
130C2×C4×C43C23×C411yescharacteristic
131C2×C4×C43C23×C411yescharacteristic
132C2×C4×C43C22×D412yes—
133C2×C4×C43C2×#4112yes—
134C8×C43—24no—
135C8×C43—28no—
136C8×C43C2×C22⋊C414yes—
137C8×C43C2×C22⋊C414yes—
138#20385C4311yesmaximal, characteristic, direct product factor, Sylow
139C22×C43—232no—
140C22×C43—24no—
141C22×C43—24no—
142C22×C43—28no—
143C22×C43—216no—
144C22×C43—24no—
145C22×C43C4×C22⋊C414yes—
146C22×C43#40518yescomplemented
147C22×C43C22×C4211yescharacteristic
148C22×C43C2×C4×D412yes—
149C22×C43C2×#13114yes—
150C4×C43—24no—
151C4×C43—48no—
152C4×C43C4×C22⋊C414yes—
153C4×C43C22×C22⋊C411yescharacteristic
154C4×C43C2×#11711yescharacteristic
155C4×C43C2×C4×D412yes—
156C24×C8C2×C4311yescharacteristic
157C2×#407C2×C4311yescharacteristic
158C2×#405C2×C4312yescomplemented
159#2280C2×C4311yescharacteristic
160#1752C2×C4314yescomplemented
161C8×C22⋊C4C2×C4314yescomplemented
162#1729C2×C4312yescomplemented
163C2×C43—24no—
164C2×C43—28no—
165C2×C43C2×C4×C22⋊C411yescharacteristic
166C2×C43C2×#40512yes—
167C2×C43#292914yes—
168C24×C4C22×C4311yescharacteristic
169C22×M16C22×C4312yes—
170C23×C8—28no—
171C23×C8C4×C4318yescomplemented
172C23×C8C22×C4311yescharacteristic
173C23×C8C22×C4312yes—
174C23×C8C22×C4312yes—
175C23×C8C22×C4311yescharacteristic
176C2×#117C22×C4312yes—
177#407C4×C4318yescomplemented
178C2×C22⋊C8C22×C4314yes—
179#405—28no—
180C2×#97C22×C4314yescomplemented
181C2×C4×C8C22×C4314yescomplemented
182#381C4×C4312yes—
183#380C4×C4314yes—
184#379C4×C4312yes—
185C4×C22⋊C4C22×C4314yes—
186#336C22×C4318yescomplemented
187C43#2038511yescharacteristic, direct product factor, Sylow
188C25C2×C4×C4311yescharacteristic
189C23×C4—24no—
190C23×C4—24no—
191C23×C4C2×C4×C4312yes—
192C23×C4C2×C4×C4311yescharacteristic
193C23×C4C2×C4×C4314yes—
194C23×C4C2×C4×C4314yes—
195C23×C4C23×C4312yes—
196C23×C4C23×C4311yescharacteristic
197C2×M16—24no—
198C2×M16—24no—
199C2×M16C2×C4×C4318yes—
200C22×C8—24no—
201C22×C8—232no—
202C22×C8—28no—
203C22×C8—28no—
204C22×C8C2×C4×C4314yes—
205C22×C8C2×C4×C4318yes—
206C22×C8C2×C4×C4318yes—
207C22×C8C2×C4×C4314yes—
208C22×C8D4×C4318yes—
209C22×C8C23×C4312yes—
210C22×C8C23×C4314yes—
211C22×C8C23×C4311yescharacteristic
212C22×C8C23×C4311yescharacteristic
213#117—24no—
214#117—24no—
215C2×C4⋊C4C2×C4×C4314yes—
216C2×C22⋊C4C2×C4×C4314yes—
217C2×C22⋊C4C2×C4×C4318yes—
218C2×C42C23×C4314yes—
219C22⋊C8C2×C4×C43116yes—
220#97—28no—
221C4×C8—28no—
222#95C2×C4×C4318yes—
223C24—24no—
224C24—28no—
225C24C42×C4314yes—
226C24C22×C4×C4311yescharacteristic
227C24C22×C4×C4312yes—
228C22×C4—24no—
229C22×C4—28no—
230C22×C4—28no—
231C22×C4—28no—
232C22×C4—216no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4C42×C4314yes—
236C22×C4C42×C4318yes—
237C22×C4C22×C4×C4318yes—
238C22×C4C22×C4×C4312yes—
239C22×C4C22×C4×C4314yes—
240C22×C4C22×C4×C4314yes—
241C22×C4C22×C4×C4311yescharacteristic
242C22×C4C22×C4×C4312yes—
243C22×C4C22×C4×C4312yes—
244C22×C4C2×D4×C4314yes—
245C22×C4#41×C4314yes—
246C22×C4C24×C4311yescharacteristic
247M16—216no—
248C2×C8—28no—
249C2×C8—24no—
250C2×C8—24no—
251C2×C8—24no—
252C2×C8—216no—
253C2×C8—216no—
254C2×C8C22⋊C4×C43116yescomplemented
255C2×C8C22×C4×C4318yes—
256C2×C8C22×C4×C4314yes—
257C2×C8C22×C4×C4312yes—
258C2×C8C22×C4×C4312yes—
259C2×C8C2×D4×C4314yes—
260C2×C8C2×D4×C4314yes—
261C4⋊C4—28no—
262C22⋊C4—28no—
263C22⋊C4—216no—
264C42—24no—
265C42—24no—
266C23—232no—
267C23—24no—
268C23—24no—
269C23—24no—
270C23—28no—
271C23—216no—
272C23C2×C42×C4312yes—
273C23C2×C42×C4314yes—
274C23C4×D4×C4314yes—
275C23#131×C4318yes—
276C23C23×C4×C4311yescharacteristic
277C2×C4—24no—
278C2×C4—28no—
279C2×C4—24no—
280C2×C4—24no—
281C2×C4—28no—
282C2×C4—216no—
283C2×C4—28no—
284C2×C4—216no—
285C2×C4C2×C42×C4314yes—
286C2×C4C2×C42×C4312yes—
287C2×C4C2×C22⋊C4×C4314yes—
288C2×C4#117×C4314yes—
289C2×C4C4×D4×C4318yes—
290C2×C4C4×D4×C4314yes—
291C2×C4C23×C4×C4311yescharacteristic
292C2×C4C23×C4×C4311yescharacteristic
293C2×C4C22×D4×C4312yes—
294C2×C4C2×#41×C4312yes—
295C8—24no—
296C8—28no—
297C8C2×C22⋊C4×C4314yes—
298C8C2×C22⋊C4×C4314yes—
299C22—232no—
300C22—24no—
301C22—24no—
302C22—28no—
303C22—216no—
304C22—24no—
305C22C4×C22⋊C4×C4314yes—
306C22C43×#40518yescomplemented
307C22C22×C42×C4311yescharacteristic
308C22C2×C4×D4×C4312yes—
309C22C2×#131×C4314yes—
310C4—24no—
311C4—48no—
312C4C4×C22⋊C4×C4314yes—
313C4C22×C22⋊C4×C4311yescharacteristic
314C4C2×#117×C4311yescharacteristic
315C4C2×C4×D4×C4312yes—
316C2—24no—
317C2—28no—
318C2C2×C4×C22⋊C4×C4311yescharacteristic
319C2C2×C43×#40512yes—
320C2C43×#292914yes—
subgroupG/H
centerC22×C8×C43C23
commutatorC22C22×C42×C43
Frattini, cosocleC22×C4C24×C43
socleC23×C43C23×C4
prime radicalC25×C43C2×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C43×#405C2semidirect
5. C43×#1752C2semidirect
6. C8×C22⋊C4×C43C2semidirect
7. C43×#1729C2semidirect
11. C23×C8×C43C4semidirect
17. C43×#407C4semidirect
20. C2×#97×C43C22semidirect
21. C2×C4×C8×C43C22semidirect
26. C43×#336C22semidirect
93. C2×C8×C43C22⋊C4semidirect
138. #20385C43direct (N × H)
146. C22×C43#405semidirect
158. C2×#405C2×C43semidirect
160. #1752C2×C43semidirect
161. C8×C22⋊C4C2×C43semidirect
162. #1729C2×C43semidirect
171. C23×C8C4×C43semidirect
177. #407C4×C43semidirect
180. C2×#97C22×C43semidirect
181. C2×C4×C8C22×C43semidirect
186. #336C22×C43semidirect
187. C43#20385direct (N × H)
254. C2×C8C22⋊C4×C43semidirect
306. C22C43×#405semidirect

Maximal subgroups

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

subgroupindex
C24×C8×C432
C2×C43×#4072
C2×C43×#4052
C43×#22802
C43×#17522
C8×C22⋊C4×C432
C43×#17292
#2038543