Finite Group Databasebeta

← C43×#9408 #24929425

Subgroups — C43×#9408 #24929425

Order 11008.

618 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2274C211yesmaximal, characteristic
3C43×#1508C212yesmaximal
4C43×#1463C211yesmaximal, characteristic
5C43×#1297C212yesmaximal
6C2×C22⋊Q8×C43C2211yescharacteristic
7C2×#117×C43—21no—
8C22×C4⋊C4×C43C2211yescharacteristic
9C43×#407C2212yes—
10C43×#398C412yescomplemented
11C43×#395C412yescomplemented
12C43×#389—22no—
13C43×#385—21no—
14C43×#385—21no—
15C4×C4⋊C4×C43—24no—
16C4×C22⋊C4×C43—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—
28#117×C43—28no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43—22no—
31C2×C4⋊C4×C43—22no—
32C2×C4⋊C4×C43—22no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43C2×C411yescharacteristic
36C2×C4⋊C4×C43C2×C412yes—
37C2×C4⋊C4×C43D412yes—
38C2×C22⋊C4×C43—22no—
39C2×C22⋊C4×C43—21no—
40C2×C22⋊C4×C43—21no—
41C2×C42×C43—22no—
42C2×C42×C43—22no—
43C2×C42×C43—22no—
44C2×C42×C43—21no—
45C22⋊C8×C43—22no—
46C22⋊C8×C43—22no—
47#95×C43—22no—
48#95×C43—22no—
49#95×C43—22no—
50#95×C43C2×C412yes—
51#95×C43D414yes—
52C24×C43C2×D411yescharacteristic
53C2×Q8×C43—22no—
54C2×Q8×C43—81no—
55C22×C4×C43—24no—
56C22×C4×C43—22no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—24no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—81no—
65C22×C4×C43—81no—
66C22×C4×C43C22⋊C412yes—
67C22×C4×C43C22⋊C412yes—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D412yes—
71C22×C4×C43#4112yes—
72M16×C43—82no—
73C2×C8×C43—42no—
74C4⋊C4×C43—28no—
75C4⋊C4×C43—24no—
76C4⋊C4×C43—24no—
77C4⋊C4×C43—22no—
78C4⋊C4×C43—44no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43—82no—
81C22⋊C4×C43—24no—
82C22⋊C4×C43—28no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C42×C43—28no—
86C42×C43—82no—
87C42×C43—81no—
88C42×C43—82no—
89C23×C43—22no—
90C23×C43—22no—
91C23×C43—41no—
92C23×C43C2×C22⋊C411yescharacteristic
93C23×C43#12011yescharacteristic
94C23×C43#12311yescharacteristic
95Q8×C43—82no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—24no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—28no—
102C2×C4×C43—24no—
103C2×C4×C43—22no—
104C2×C4×C43—41no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—41no—
108C2×C4×C43—44no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—44no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—42no—
118C2×C4×C43—81no—
119C2×C4×C43#10414yes—
120C2×C4×C43C4×D412yes—
121C2×C4×C43#12112yes—
122C8×C43—82no—
123#9408C4311yesmaximal, characteristic, direct product factor, Sylow
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—21no—
127C22×C43—21no—
128C22×C43—21no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—44no—
132C22×C43#38611yescharacteristic
133C22×C43C2×#10412yes—
134C22×C43#45612yes—
135C4×C43—24no—
136C4×C43—22no—
137C4×C43—22no—
138C4×C43—48no—
139C4×C43—44no—
140C4×C43—42no—
141C4×C43—81no—
142C4×C43—81no—
143#2583C2×C4311yescharacteristic
144#2274C2×C4311yescharacteristic
145#1508C2×C4312yes—
146#1463C2×C4311yescharacteristic
147#1297C2×C4312yes—
148C2×C43—22no—
149C2×C43—22no—
150C2×C43—41no—
151C2×C43#188611yescharacteristic
152C2×C43#189611yescharacteristic
153C2×C43#191311yescharacteristic
154C2×C22⋊Q8C22×C4311yescharacteristic
155C2×#117—21no—
156C22×C4⋊C4C22×C4311yescharacteristic
157#407C22×C4312yes—
158#398C4×C4312yescomplemented
159#395C4×C4312yescomplemented
160#389—22no—
161#385—21no—
162#385—21no—
163C4×C4⋊C4—24no—
164C4×C22⋊C4—21no—
165C4×C22⋊C4C22×C4311yescharacteristic
166C4×C22⋊C4C22×C4312yes—
167#328—24no—
168#324—22no—
169C43#940811yescharacteristic, direct product factor, Sylow
170C22×Q8C2×C4×C4311yescharacteristic
171C23×C4D4×C4311yescharacteristic
172C23×C4D4×C4311yescharacteristic
173C23×C4C23×C4311yescharacteristic
174C2×M16—22no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177#117—28no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4C2×C4×C4311yescharacteristic
185C2×C4⋊C4C2×C4×C4312yes—
186C2×C4⋊C4D4×C4312yes—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—21no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—21no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#95—22no—
197#95—22no—
198#95—22no—
199#95C2×C4×C4312yes—
200#95D4×C4314yes—
201C24C2×D4×C4311yescharacteristic
202C2×Q8—22no—
203C2×Q8—81no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—24no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—81no—
214C22×C4—81no—
215C22×C4C22⋊C4×C4312yes—
216C22×C4C22⋊C4×C4312yes—
217C22×C4C22×C4×C4311yescharacteristic
218C22×C4C2×D4×C4312yes—
219C22×C4C2×D4×C4311yescharacteristic
220C22×C4#41×C4312yes—
221M16—82no—
222C2×C8—42no—
223C4⋊C4—28no—
224C4⋊C4—24no—
225C4⋊C4—24no—
226C4⋊C4—22no—
227C4⋊C4—44no—
228C4⋊C4—42no—
229C4⋊C4—82no—
230C22⋊C4—28no—
231C22⋊C4—24no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C42—28no—
235C42—82no—
236C42—81no—
237C42—82no—
238C23—22no—
239C23—22no—
240C23—41no—
241C23C2×C22⋊C4×C4311yescharacteristic
242C23#120×C4311yescharacteristic
243C23#123×C4311yescharacteristic
244Q8—82no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—28no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—81no—
268C2×C4#104×C4314yes—
269C2×C4C4×D4×C4312yes—
270C2×C4#121×C4312yes—
271C8—82no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22C43×#38611yescharacteristic
281C22C2×#104×C4312yes—
282C22C43×#45612yes—
283C4—24no—
284C4—22no—
285C4—22no—
286C4—48no—
287C4—44no—
288C4—42no—
289C4—81no—
290C4—81no—
291C2—22no—
292C2—22no—
293C2—41no—
294C2C43×#188611yescharacteristic
295C2C43×#189611yescharacteristic
296C2C43×#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
10. C43×#398C4semidirect
11. C43×#395C4semidirect
123. #9408C43direct (N × H)
158. #398C4×C43semidirect
159. #395C4×C43semidirect
169. C43#9408direct (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×#22742
C43×#15082
C43×#14632
C43×#12972
#940843