Finite Group Databasebeta

← C43×#34059 #24954076

Subgroups — C43×#34059 #24954076

Order 11008.

2250 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C43C211yesmaximal, characteristic
2C43×#2320C218yesmaximal, complemented
3C43×#2316C212yesmaximal
4C43×#2313C214yesmaximal
5C43×#2310C212yesmaximal
6C43×#2295C218yesmaximal, complemented
7C43×#2283C214yesmaximal
8C4×#117×C43C212yesmaximal
9C23×Q8×C43C2211yescharacteristic
10C2×C4×Q8×C43C4116yescomplemented
11C2×C4×Q8×C43C2214yes—
12C2×C4×Q8×C43C2214yes—
13C2×#117×C43C2214yes—
14C22×C4⋊C4×C43C2212yes—
15C22×C4⋊C4×C43C2211yescharacteristic
16C22×C42×C43C2211yescharacteristic
17C22×C42×C43C2212yes—
18C43×#391C22116yes—
19C43×#389C22116yes—
20C43×#387C22132yes—
21C43×#383C2218yes—
22C43×#382C2218yes—
23C43×#381C2218yes—
24C43×#380C2218yes—
25C4×C4⋊C4×C43C2214yes—
26C4×C4⋊C4×C43C2214yes—
27C4×C4⋊C4×C43C2218yes—
28C4×C22⋊C4×C43C2214yes—
29C4×C22⋊C4×C43C2214yes—
30C43×#376C2214yes—
31C43×#376C2218yes—
32C43×C43C2214yes—
33C22×Q8×C43—28no—
34C22×Q8×C43C2×C418yes—
35C22×Q8×C43C2314yes—
36C23×C4×C43C2312yes—
37C23×C4×C43C2311yescharacteristic
38C23×C4×C43C2311yescharacteristic
39C23×C4×C43C2312yes—
40C23×C4×C43C2311yescharacteristic
41C4×Q8×C43C2×C4132yes—
42C4×Q8×C43C2×C4132yes—
43#117×C43—216no—
44C2×C4⋊C4×C43C2×C4116yes—
45C2×C4⋊C4×C43C2×C418yes—
46C2×C4⋊C4×C43C2318yes—
47C2×C4⋊C4×C43C23116yes—
48C2×C4⋊C4×C43C2318yes—
49C2×C4⋊C4×C43C2314yes—
50C2×C22⋊C4×C43C2318yes—
51C2×C42×C43C2×C4116yes—
52C2×C42×C43C2×C418yes—
53C2×C42×C43C2318yes—
54C2×C42×C43C2318yes—
55C2×C42×C43C2318yes—
56C2×C42×C43C2312yes—
57C2×C42×C43C2314yes—
58C2×C42×C43C2312yes—
59C2×C42×C43C2314yes—
60#95×C43C2318yes—
61#95×C43C2318yes—
62#95×C43C23116yes—
63#95×C43C23116yes—
64#95×C43C23116yes—
65C24×C43C2411yescharacteristic
66C2×Q8×C43—232no—
67C2×Q8×C43—216no—
68C2×Q8×C43C22×C4116yes—
69C22×C4×C43—24no—
70C22×C4×C43—28no—
71C22×C4×C43—42no—
72C22×C4×C43—44no—
73C22×C4×C43C22×C414yes—
74C22×C4×C43C22×C418yes—
75C22×C4×C43C22×C414yes—
76C22×C4×C43C22×C418yes—
77C22×C4×C43C22×C414yes—
78C22×C4×C43#4118yes—
79C22×C4×C43C24116yes—
80C22×C4×C43C2411yescharacteristic
81C22×C4×C43C2414yes—
82C22×C4×C43C2412yes—
83C22×C4×C43C2414yes—
84C22×C4×C43C2412yes—
85C22×C4×C43C2411yescharacteristic
86C4⋊C4×C43—216no—
87C4⋊C4×C43—416no—
88C4⋊C4×C43C22×C4132yes—
89C4⋊C4×C43C22×C4116yes—
90C22⋊C4×C43—216no—
91C42×C43—216no—
92C42×C43—216no—
93C42×C43—48no—
94C42×C43C22×C4116yes—
95C42×C43C22×C418yes—
96C42×C43C22×C4116yes—
97C42×C43C22×C418yes—
98C23×C43—22no—
99C23×C43—22no—
100C23×C43C23×C412yes—
101C23×C43C2×#4114yes—
102C23×C43C2511yescharacteristic
103Q8×C43—232no—
104C2×C4×C43—216no—
105C2×C4×C43—28no—
106C2×C4×C43—22no—
107C2×C4×C43—24no—
108C2×C4×C43—28no—
109C2×C4×C43—28no—
110C2×C4×C43—216no—
111C2×C4×C43—216no—
112C2×C4×C43—216no—
113C2×C4×C43—44no—
114C2×C4×C43—48no—
115C2×C4×C43#117116yes—
116C2×C4×C43C23×C412yes—
117C2×C4×C43C23×C414yes—
118C2×C4×C43C23×C418yes—
119C2×C4×C43C23×C418yes—
120C2×C4×C43C23×C414yes—
121C2×C4×C43C23×C412yes—
122C2×C4×C43C2×#4118yes—
123C2×C4×C432−1+414yes—
124#34059C4311yesmaximal, characteristic, direct product factor, Sylow
125C22×C43—22no—
126C22×C43—22no—
127C22×C43—28no—
128C22×C43C2×#11714yes—
129C22×C43C24×C411yescharacteristic
130C22×C43C22×#4112yes—
131C22×C43C2×2−1+412yes—
132C22×C43#58512yes—
133C4×C43—28no—
134C4×C43—22no—
135C4×C43—24no—
136C4×C43—28no—
137C4×C43—416no—
138C4×C43C2×#11718yes—
139C4×C43#51914yes—
140C22×C4×Q8C2×C4311yescharacteristic
141#2320C2×C4318yescomplemented
142#2316C2×C4312yes—
143#2313C2×C4314yes—
144#2310C2×C4312yes—
145#2295C2×C4318yescomplemented
146#2283C2×C4314yes—
147C4×#117C2×C4312yes—
148C2×C43—24no—
149C2×C43C22×#11711yescharacteristic
150C2×C43C2×#51911yescharacteristic
151C2×C43#342811yescharacteristic
152C2×C43#346114yes—
153C23×Q8C22×C4311yescharacteristic
154C2×C4×Q8C4×C43116yescomplemented
155C2×C4×Q8C22×C4314yes—
156C2×C4×Q8C22×C4314yes—
157C2×#117C22×C4314yes—
158C22×C4⋊C4C22×C4312yes—
159C22×C4⋊C4C22×C4311yescharacteristic
160C22×C42C22×C4311yescharacteristic
161C22×C42C22×C4312yes—
162#391C22×C43116yes—
163#389C22×C43116yes—
164#387C22×C43132yes—
165#383C22×C4318yes—
166#382C22×C4318yes—
167#381C22×C4318yes—
168#380C22×C4318yes—
169C4×C4⋊C4C22×C4314yes—
170C4×C4⋊C4C22×C4314yes—
171C4×C4⋊C4C22×C4318yes—
172C4×C22⋊C4C22×C4314yes—
173C4×C22⋊C4C22×C4314yes—
174#376C22×C4314yes—
175#376C22×C4318yes—
176C43C22×C4314yes—
177C43#3405911yescharacteristic, direct product factor, Sylow
178C22×Q8—28no—
179C22×Q8C2×C4×C4318yes—
180C22×Q8C23×C4314yes—
181C23×C4C23×C4312yes—
182C23×C4C23×C4311yescharacteristic
183C23×C4C23×C4311yescharacteristic
184C23×C4C23×C4312yes—
185C23×C4C23×C4311yescharacteristic
186C4×Q8C2×C4×C43132yes—
187C4×Q8C2×C4×C43132yes—
188#117—216no—
189C2×C4⋊C4C2×C4×C43116yes—
190C2×C4⋊C4C2×C4×C4318yes—
191C2×C4⋊C4C23×C4318yes—
192C2×C4⋊C4C23×C43116yes—
193C2×C4⋊C4C23×C4318yes—
194C2×C4⋊C4C23×C4314yes—
195C2×C22⋊C4C23×C4318yes—
196C2×C42C2×C4×C43116yes—
197C2×C42C2×C4×C4318yes—
198C2×C42C23×C4318yes—
199C2×C42C23×C4318yes—
200C2×C42C23×C4318yes—
201C2×C42C23×C4312yes—
202C2×C42C23×C4312yes—
203C2×C42C23×C4314yes—
204C2×C42C23×C4314yes—
205#95C23×C4318yes—
206#95C23×C4318yes—
207#95C23×C43116yes—
208#95C23×C43116yes—
209#95C23×C43116yes—
210C24C24×C4311yescharacteristic
211C2×Q8—232no—
212C2×Q8—216no—
213C2×Q8C22×C4×C43116yes—
214C22×C4—28no—
215C22×C4—24no—
216C22×C4—42no—
217C22×C4—44no—
218C22×C4C22×C4×C4314yes—
219C22×C4C22×C4×C4318yes—
220C22×C4C22×C4×C4314yes—
221C22×C4C22×C4×C4318yes—
222C22×C4C22×C4×C4314yes—
223C22×C4#41×C4318yes—
224C22×C4C24×C43116yes—
225C22×C4C24×C4311yescharacteristic
226C22×C4C24×C4314yes—
227C22×C4C24×C4312yes—
228C22×C4C24×C4314yes—
229C22×C4C24×C4312yes—
230C22×C4C24×C4311yescharacteristic
231C4⋊C4—216no—
232C4⋊C4—416no—
233C4⋊C4C22×C4×C43132yes—
234C4⋊C4C22×C4×C43116yes—
235C22⋊C4—216no—
236C42—216no—
237C42—216no—
238C42—48no—
239C42C22×C4×C43116yes—
240C42C22×C4×C4318yes—
241C42C22×C4×C43116yes—
242C42C22×C4×C4318yes—
243C23—22no—
244C23—22no—
245C23C23×C4×C4312yes—
246C23C2×#41×C4314yes—
247C23C25×C4311yescharacteristic
248Q8—232no—
249C2×C4—216no—
250C2×C4—28no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—28no—
254C2×C4—28no—
255C2×C4—216no—
256C2×C4—216no—
257C2×C4—216no—
258C2×C4—44no—
259C2×C4—48no—
260C2×C4#117×C43116yes—
261C2×C4C23×C4×C4312yes—
262C2×C4C23×C4×C4314yes—
263C2×C4C23×C4×C4318yes—
264C2×C4C23×C4×C4318yes—
265C2×C4C23×C4×C4314yes—
266C2×C4C23×C4×C4312yes—
267C2×C4C2×#41×C4318yes—
268C2×C42−1+4×C4314yes—
269C22—22no—
270C22—22no—
271C22—28no—
272C22C2×#117×C4314yes—
273C22C24×C4×C4311yescharacteristic
274C22C22×#41×C4312yes—
275C22C2×2−1+4×C4312yes—
276C22C43×#58512yes—
277C4—28no—
278C4—22no—
279C4—24no—
280C4—28no—
281C4—416no—
282C4C2×#117×C4318yes—
283C4C43×#51914yes—
284C2—24no—
285C2C22×#117×C4311yescharacteristic
286C2C2×C43×#51911yescharacteristic
287C2C43×#342811yescharacteristic
288C2C43×#346114yes—
subgroupG/H
centerC22×C4×C43C24
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
socleC23×C43C25
prime radicalC24×C43C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2320C2semidirect
6. C43×#2295C2semidirect
10. C2×C4×Q8×C43C4semidirect
124. #34059C43direct (N × H)
141. #2320C2×C43semidirect
145. #2295C2×C43semidirect
154. C2×C4×Q8C4×C43semidirect
177. C43#34059direct (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×#23202
C43×#23162
C43×#23132
C43×#23102
C43×#22952
C43×#22832
C4×#117×C432
#3405943