Finite Group Databasebeta

← C43×#9412 #24929429

Subgroups — C43×#9412 #24929429

Order 11008.

526 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2583C211yesmaximal, characteristic
2C43×#2313C211yesmaximal, characteristic
3C43×#1508C212yesmaximal
4C43×#1463C211yesmaximal, characteristic
5C43×#1297C212yesmaximal
6C2×C22⋊Q8×C43C2211yescharacteristic
7C22×C4⋊C4×C43C2211yescharacteristic
8C43×#407C2212yes—
9C43×#398C412yescomplemented
10C43×#395C412yescomplemented
11C43×#389—22no—
12C43×#387—24no—
13C43×#385—21no—
14C43×#385—21no—
15C43×#381—21no—
16C43×#380—21no—
17C4×C22⋊C4×C43C2211yescharacteristic
18C4×C22⋊C4×C43C2212yes—
19C43×#328—24no—
20C43×#324—22no—
21C22×Q8×C43C2×C411yescharacteristic
22C23×C4×C43D411yescharacteristic
23C23×C4×C43D411yescharacteristic
24C23×C4×C43C2311yescharacteristic
25C2×M16×C43—22no—
26C22⋊Q8×C43—22no—
27C22⋊Q8×C43—22no—
28C2×C4⋊C4×C43—22no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43—22no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—22no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43C2×C411yescharacteristic
35C2×C4⋊C4×C43C2×C412yes—
36C2×C4⋊C4×C43D412yes—
37C2×C22⋊C4×C43—21no—
38C2×C22⋊C4×C43—21no—
39C2×C22⋊C4×C43—22no—
40C2×C42×C43—22no—
41C2×C42×C43—21no—
42C22⋊C8×C43—22no—
43C22⋊C8×C43—22no—
44#95×C43—22no—
45#95×C43—24no—
46#95×C43—22no—
47#95×C43—22no—
48#95×C43C2×C412yes—
49#95×C43D414yes—
50C24×C43C2×D411yescharacteristic
51C2×Q8×C43—22no—
52C2×Q8×C43—81no—
53C22×C4×C43—22no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—24no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—42no—
62C22×C4×C43—81no—
63C22×C4×C43—81no—
64C22×C4×C43C22⋊C412yes—
65C22×C4×C43C22⋊C412yes—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D412yes—
69C22×C4×C43#4112yes—
70M16×C43—82no—
71C2×C8×C43—42no—
72C4⋊C4×C43—24no—
73C4⋊C4×C43—24no—
74C4⋊C4×C43—22no—
75C4⋊C4×C43—44no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—82no—
78C4⋊C4×C43—82no—
79C22⋊C4×C43—24no—
80C22⋊C4×C43—44no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C42×C43—81no—
84C42×C43—82no—
85C23×C43—22no—
86C23×C43—22no—
87C23×C43—41no—
88C23×C43C2×C22⋊C411yescharacteristic
89C23×C43#12011yescharacteristic
90C23×C43#12311yescharacteristic
91Q8×C43—82no—
92C2×C4×C43—24no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—41no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—41no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—44no—
108C2×C4×C43—44no—
109C2×C4×C43—42no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—44no—
114C2×C4×C43—81no—
115C2×C4×C43C4×D412yes—
116C2×C4×C43#12112yes—
117C8×C43—82no—
118#9412C4311yesmaximal, characteristic, direct product factor, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—44no—
127C22×C43#38611yescharacteristic
128C22×C43#42112yes—
129C22×C43#45612yes—
130C4×C43—22no—
131C4×C43—22no—
132C4×C43—44no—
133C4×C43—42no—
134C4×C43—42no—
135C4×C43—84no—
136C4×C43—81no—
137C4×C43—81no—
138#2583C2×C4311yescharacteristic
139#2313C2×C4311yescharacteristic
140#1508C2×C4312yes—
141#1463C2×C4311yescharacteristic
142#1297C2×C4312yes—
143C2×C43—22no—
144C2×C43—22no—
145C2×C43—41no—
146C2×C43#188611yescharacteristic
147C2×C43#189711yescharacteristic
148C2×C43#191311yescharacteristic
149C2×C22⋊Q8C22×C4311yescharacteristic
150C22×C4⋊C4C22×C4311yescharacteristic
151#407C22×C4312yes—
152#398C4×C4312yescomplemented
153#395C4×C4312yescomplemented
154#389—22no—
155#387—24no—
156#385—21no—
157#385—21no—
158#381—21no—
159#380—21no—
160C4×C22⋊C4C22×C4311yescharacteristic
161C4×C22⋊C4C22×C4312yes—
162#328—24no—
163#324—22no—
164C43#941211yescharacteristic, direct product factor, Sylow
165C22×Q8C2×C4×C4311yescharacteristic
166C23×C4D4×C4311yescharacteristic
167C23×C4D4×C4311yescharacteristic
168C23×C4C23×C4311yescharacteristic
169C2×M16—22no—
170C22⋊Q8—22no—
171C22⋊Q8—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4C2×C4×C4311yescharacteristic
179C2×C4⋊C4C2×C4×C4312yes—
180C2×C4⋊C4D4×C4312yes—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—22no—
184C2×C42—22no—
185C2×C42—21no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188#95—22no—
189#95—24no—
190#95—22no—
191#95—22no—
192#95C2×C4×C4312yes—
193#95D4×C4314yes—
194C24C2×D4×C4311yescharacteristic
195C2×Q8—22no—
196C2×Q8—81no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—24no—
205C22×C4—42no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4C22⋊C4×C4312yes—
209C22×C4C22⋊C4×C4312yes—
210C22×C4C22×C4×C4311yescharacteristic
211C22×C4C2×D4×C4312yes—
212C22×C4C2×D4×C4311yescharacteristic
213C22×C4#41×C4312yes—
214M16—82no—
215C2×C8—42no—
216C4⋊C4—24no—
217C4⋊C4—24no—
218C4⋊C4—22no—
219C4⋊C4—44no—
220C4⋊C4—42no—
221C4⋊C4—82no—
222C4⋊C4—82no—
223C22⋊C4—24no—
224C22⋊C4—44no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C42—81no—
228C42—82no—
229C23—22no—
230C23—22no—
231C23—41no—
232C23C2×C22⋊C4×C4311yescharacteristic
233C23#120×C4311yescharacteristic
234C23#123×C4311yescharacteristic
235Q8—82no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—44no—
252C2×C4—44no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—44no—
258C2×C4—81no—
259C2×C4C4×D4×C4312yes—
260C2×C4#121×C4312yes—
261C8—82no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22C43×#38611yescharacteristic
271C22C43×#42112yes—
272C22C43×#45612yes—
273C4—22no—
274C4—22no—
275C4—44no—
276C4—42no—
277C4—42no—
278C4—84no—
279C4—81no—
280C4—81no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2C43×#188611yescharacteristic
285C2C43×#189711yescharacteristic
286C2C43×#191311yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
9. C43×#398C4semidirect
10. C43×#395C4semidirect
118. #9412C43direct (N × H)
152. #398C4×C43semidirect
153. #395C4×C43semidirect
164. C43#9412direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25832
C43×#23132
C43×#15082
C43×#14632
C43×#12972
#941243