Finite Group Databasebeta

← C43×#9022 #24929039

Subgroups — C43×#9022 #24929039

Order 11008.

572 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×C43×#400C211yesmaximal, characteristic
2C43×#2313C211yesmaximal, characteristic
3C43×#1824C212yesmaximal
4C2×C43×#324C211yesmaximal, characteristic
5C43×#1294C212yesmaximal
6C22×C4⋊C4×C43C2211yescharacteristic
7C22×C4⋊C4×C43C2211yescharacteristic
8C2×C22⋊C8×C43C2212yes—
9C43×#400—22no—
10C43×#400C414yescomplemented
11C43×#387—24no—
12C43×#381—21no—
13C43×#380C2212yes—
14C4×C22⋊C4×C43—21no—
15C2×#95×C43—21no—
16C2×#95×C43—21no—
17C2×#95×C43C2211yescharacteristic
18C43×#340—24no—
19C43×#324—22no—
20C23×C4×C43—21no—
21C23×C4×C43—21no—
22C23×C4×C43D411yescharacteristic
23C23×C4×C43D411yescharacteristic
24C23×C4×C43C2311yescharacteristic
25C22×C8×C43—22no—
26C2×C4⋊C4×C43—22no—
27C2×C4⋊C4×C43—22no—
28C2×C4⋊C4×C43—22no—
29C2×C4⋊C4×C43—22no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43C2×C412yes—
32C2×C4⋊C4×C43C2×C412yes—
33C2×C4⋊C4×C43D412yes—
34C2×C4⋊C4×C43D414yes—
35C2×C22⋊C4×C43—22no—
36C2×C42×C43—22no—
37C22⋊C8×C43—22no—
38C22⋊C8×C43—22no—
39#95×C43—22no—
40#95×C43—24no—
41#95×C43—24no—
42#95×C43—24no—
43#95×C43—21no—
44#95×C43—22no—
45#95×C43C2×C412yes—
46C24×C43C2×D411yescharacteristic
47C22×C4×C43—22no—
48C22×C4×C43—22no—
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43—24no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—42no—
57C22×C4×C43—42no—
58C22×C4×C43—42no—
59C22×C4×C43—44no—
60C22×C4×C43—42no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43—42no—
64C22×C4×C43C22⋊C412yes—
65C22×C4×C43C22⋊C412yes—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D412yes—
69C22×C4×C43#4112yes—
70C2×C8×C43—44no—
71C2×C8×C43—42no—
72C4⋊C4×C43—24no—
73C4⋊C4×C43—24no—
74C4⋊C4×C43—24no—
75C4⋊C4×C43—44no—
76C4⋊C4×C43—42no—
77C22⋊C4×C43—42no—
78C22⋊C4×C43—42no—
79C42×C43—82no—
80C23×C43—22no—
81C23×C43—22no—
82C23×C43C2×C22⋊C411yescharacteristic
83C23×C43#12011yescharacteristic
84C23×C43#12311yescharacteristic
85C23×C43#13512yes—
86C23×C43#13712yes—
87C2×C4×C43—24no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—41no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—44no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—44no—
105C2×C4×C43—44no—
106C2×C4×C43—44no—
107C2×C4×C43—81no—
108C2×C4×C43—84no—
109C2×C4×C43—82no—
110C2×C4×C43—82no—
111C2×C4×C43C4×D412yes—
112C2×C4×C43#12112yes—
113C8×C43—82no—
114#9022C4311yesmaximal, characteristic, direct product factor, Sylow
115C22×C43—24no—
116C22×C43—24no—
117C22×C43—21no—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43—21no—
121C22×C43#38611yescharacteristic
122C22×C43#41611yescharacteristic
123C22×C43#41911yescharacteristic
124C22×C43#45212yes—
125C22×C43#45412yes—
126C22×C43#45812yes—
127C22×C43#48512yes—
128C4×C43—22no—
129C4×C43—22no—
130C4×C43—42no—
131C4×C43—42no—
132C4×C43—82no—
133C4×C43—84no—
134C4×C43—82no—
135C2×#400C2×C4311yescharacteristic
136#2313C2×C4311yescharacteristic
137#1824C2×C4312yes—
138C2×#324C2×C4311yescharacteristic
139#1294C2×C4312yes—
140C2×C43—21no—
141C2×C43—21no—
142C2×C43—22no—
143C2×C43#161514yes—
144C2×C43#187311yescharacteristic
145C2×C43#188811yescharacteristic
146C2×C43#189011yescharacteristic
147C22×C4⋊C4C22×C4311yescharacteristic
148C22×C4⋊C4C22×C4311yescharacteristic
149C2×C22⋊C8C22×C4312yes—
150#400—22no—
151#400C4×C4314yescomplemented
152#387—24no—
153#381—21no—
154#380C22×C4312yes—
155C4×C22⋊C4—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95C22×C4311yescharacteristic
159#340—24no—
160#324—22no—
161C43#902211yescharacteristic, direct product factor, Sylow
162C23×C4—21no—
163C23×C4—21no—
164C23×C4D4×C4311yescharacteristic
165C23×C4D4×C4311yescharacteristic
166C23×C4C23×C4311yescharacteristic
167C22×C8—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×C4×C4312yes—
174C2×C4⋊C4C2×C4×C4312yes—
175C2×C4⋊C4D4×C4312yes—
176C2×C4⋊C4D4×C4314yes—
177C2×C22⋊C4—22no—
178C2×C42—22no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181#95—22no—
182#95—24no—
183#95—24no—
184#95—24no—
185#95—21no—
186#95—22no—
187#95C2×C4×C4312yes—
188C24C2×D4×C4311yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—24no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—44no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—42no—
206C22×C4C22⋊C4×C4312yes—
207C22×C4C22⋊C4×C4312yes—
208C22×C4C22×C4×C4311yescharacteristic
209C22×C4C2×D4×C4312yes—
210C22×C4C2×D4×C4311yescharacteristic
211C22×C4#41×C4312yes—
212C2×C8—44no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—44no—
218C4⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C42—82no—
222C23—22no—
223C23—22no—
224C23C2×C22⋊C4×C4311yescharacteristic
225C23#120×C4311yescharacteristic
226C23#123×C4311yescharacteristic
227C23#135×C4312yes—
228C23#137×C4312yes—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—44no—
247C2×C4—44no—
248C2×C4—44no—
249C2×C4—81no—
250C2×C4—84no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4C4×D4×C4312yes—
254C2×C4#121×C4312yes—
255C8—82no—
256C22—24no—
257C22—24no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22C43×#38611yescharacteristic
263C22C43×#41611yescharacteristic
264C22C43×#41911yescharacteristic
265C22C43×#45212yes—
266C22C43×#45412yes—
267C22C43×#45812yes—
268C22C43×#48512yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—82no—
274C4—84no—
275C4—82no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2C43×#161514yes—
280C2C43×#187311yescharacteristic
281C2C43×#188811yescharacteristic
282C2C43×#189011yescharacteristic
subgroupG/H
center, socleC23×C43#120
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
10. C43×#400C4semidirect
114. #9022C43direct (N × H)
151. #400C4×C43semidirect
161. C43#9022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4002
C43×#23132
C43×#18242
C2×C43×#3242
C43×#12942
#902243