Finite Group Databasebeta

← C43×#13584 #24933601

Subgroups — C43×#13584 #24933601

Order 11008.

474 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3151C211yesmaximal, characteristic
2C2×C43×#353C212yesmaximal, complemented
3C43×#1409C212yesmaximal, complemented
4C43×#1408C212yesmaximal, complemented
5C2×AGL(1,ℤ/8)×C43—22no—
6C43×#532C411yescharacteristic, complemented
7C2×#127×C43C2211yescharacteristic
8C43×#496—22no—
9C43×#493C411yescharacteristic, complemented
10C43×#493C2211yescharacteristic
11C43×#492C411yescharacteristic, complemented
12C43×#492C2211yescharacteristic
13C2×#99×C43—22no—
14C4×M16×C43C411yescharacteristic, complemented
15C43×#353—22no—
16C43×#353C2214yes—
17C2×#41×C43—21no—
18C22×D4×C43—41no—
19C22×D4×C43D412yes—
20AGL(1,ℤ/8)×C43—44no—
21AGL(1,ℤ/8)×C43—44no—
22C2×SD16×C43—22no—
23C2×SD16×C43—22no—
24C2×D8×C43—22no—
25C2×D8×C43—22no—
26C2×M16×C43—21no—
27C4⋊Q8×C43C2×C411yescharacteristic, complemented
28#127×C43—41no—
29#127×C43C2×C411yescharacteristic
30#127×C43C2×C411yescharacteristic, complemented
31#127×C43D412yes—
32#127×C43C2311yescharacteristic
33#124×C43—21no—
34#121×C43—41no—
35C4×D4×C43—41no—
36C2×C22⋊C4×C43—42no—
37C2×C42×C43C2×C411yescharacteristic
38#99×C43—24no—
39#99×C43—42no—
40#97×C43—21no—
41C4×C8×C43C2×C411yescharacteristic, complemented
42C4×C8×C43C2×C411yescharacteristic, complemented
43C24×C43—22no—
44#41×C43—42no—
45#41×C43—42no—
46C2×Q8×C43—21no—
47C2×D4×C43—22no—
48C2×D4×C43—21no—
49C2×D4×C43—41no—
50C2×D4×C43—42no—
51C2×D4×C43—41no—
52C2×D4×C43—41no—
53C2×D4×C43—42no—
54C2×D4×C43—42no—
55C2×D4×C43—41no—
56C2×D4×C43—84no—
57C2×D4×C43C22⋊C412yes—
58C2×D4×C43C2×D412yes—
59C22×C4×C43—21no—
60C22×C4×C43—41no—
61C22×C4×C43—82no—
62C22×C4×C43C22⋊C411yescharacteristic
63SD16×C43—44no—
64SD16×C43—44no—
65D8×C43—44no—
66D8×C43—44no—
67M16×C43—24no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C4⋊C4×C43—41no—
71C22⋊C4×C43—44no—
72C22⋊C4×C43—42no—
73C22⋊C4×C43—82no—
74C42×C43—21no—
75C42×C43C22⋊C411yescharacteristic
76C42×C43C22×C411yescharacteristic
77C23×C43—22no—
78C23×C43—22no—
79C23×C43—42no—
80C23×C43—42no—
81C23×C43—41no—
82C23×C43—84no—
83C23×C43#9911yescharacteristic
84Q8×C43—42no—
85D4×C43—42no—
86D4×C43—42no—
87D4×C43—42no—
88D4×C43—82no—
89D4×C43—82no—
90D4×C43—82no—
91D4×C43—82no—
92D4×C43—84no—
93D4×C43—82no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—42no—
98C2×C4×C43—41no—
99C2×C4×C43—81no—
100C2×C4×C43—81no—
101C2×C4×C43—84no—
102C2×C4×C43—164no—
103C2×C4×C43#9911yescharacteristic
104C2×C4×C43C2×C22⋊C411yescharacteristic
105C8×C43—22no—
106C8×C43—22no—
107#13584C4311yesmaximal, characteristic, direct product factor, Sylow
108C22×C43—41no—
109C22×C43—42no—
110C22×C43—42no—
111C22×C43—82no—
112C22×C43—82no—
113C22×C43—84no—
114C22×C43—82no—
115C22×C43—81no—
116C22×C43—162no—
117C22×C43#35312yes—
118C22×C43C2×#9911yescharacteristic
119C4×C43—22no—
120C4×C43—21no—
121C4×C43—21no—
122C4×C43—41no—
123C4×C43—81no—
124C4×C43—164no—
125#3151C2×C4311yescharacteristic
126C2×#353C2×C4312yescomplemented
127#1409C2×C4312yescomplemented
128#1408C2×C4312yescomplemented
129C2×C43—21no—
130C2×C43—22no—
131C2×C43—82no—
132C2×C43—82no—
133C2×C43—161no—
134C2×C43C2×#35311yescharacteristic
135C2×AGL(1,ℤ/8)—22no—
136#532C4×C4311yescharacteristic, complemented
137C2×#127C22×C4311yescharacteristic
138#496—22no—
139#493C4×C4311yescharacteristic, complemented
140#493C22×C4311yescharacteristic
141#492C4×C4311yescharacteristic, complemented
142#492C22×C4311yescharacteristic
143C2×#99—22no—
144C4×M16C4×C4311yescharacteristic, complemented
145#353—22no—
146#353C22×C4314yes—
147C43#1358411yescharacteristic, direct product factor, Sylow
148C2×#41—21no—
149C22×D4—41no—
150C22×D4D4×C4312yes—
151AGL(1,ℤ/8)—44no—
152AGL(1,ℤ/8)—44no—
153C2×SD16—22no—
154C2×SD16—22no—
155C2×D8—22no—
156C2×D8—22no—
157C2×M16—21no—
158C4⋊Q8C2×C4×C4311yescharacteristic, complemented
159#127—41no—
160#127C2×C4×C4311yescharacteristic
161#127C2×C4×C4311yescharacteristic, complemented
162#127D4×C4312yes—
163#127C23×C4311yescharacteristic
164#124—21no—
165#121—41no—
166C4×D4—41no—
167C2×C22⋊C4—42no—
168C2×C42C2×C4×C4311yescharacteristic
169#99—24no—
170#99—42no—
171#97—21no—
172C4×C8C2×C4×C4311yescharacteristic, complemented
173C4×C8C2×C4×C4311yescharacteristic, complemented
174C24—22no—
175#41—42no—
176#41—42no—
177C2×Q8—21no—
178C2×D4—22no—
179C2×D4—21no—
180C2×D4—42no—
181C2×D4—42no—
182C2×D4—41no—
183C2×D4—41no—
184C2×D4—42no—
185C2×D4—41no—
186C2×D4—41no—
187C2×D4—84no—
188C2×D4C22⋊C4×C4312yes—
189C2×D4C2×D4×C4312yes—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—82no—
193C22×C4C22⋊C4×C4311yescharacteristic
194SD16—44no—
195SD16—44no—
196D8—44no—
197D8—44no—
198M16—24no—
199C2×C8—21no—
200C2×C8—21no—
201C4⋊C4—41no—
202C22⋊C4—42no—
203C22⋊C4—44no—
204C22⋊C4—82no—
205C42—21no—
206C42C22⋊C4×C4311yescharacteristic
207C42C22×C4×C4311yescharacteristic
208C23—22no—
209C23—22no—
210C23—42no—
211C23—42no—
212C23—41no—
213C23—84no—
214C23#99×C4311yescharacteristic
215Q8—42no—
216D4—42no—
217D4—42no—
218D4—42no—
219D4—82no—
220D4—82no—
221D4—82no—
222D4—82no—
223D4—84no—
224D4—82no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—84no—
233C2×C4—164no—
234C2×C4#99×C4311yescharacteristic
235C2×C4C2×C22⋊C4×C4311yescharacteristic
236C8—22no—
237C8—22no—
238C22—41no—
239C22—42no—
240C22—42no—
241C22—82no—
242C22—82no—
243C22—84no—
244C22—82no—
245C22—81no—
246C22—162no—
247C22C43×#35312yes—
248C22C2×#99×C4311yescharacteristic
249C4—22no—
250C4—21no—
251C4—21no—
252C4—41no—
253C4—81no—
254C4—164no—
255C2—21no—
256C2—22no—
257C2—82no—
258C2—82no—
259C2—161no—
260C2C2×C43×#35311yescharacteristic
subgroupG/H
center, socleC2×C43C2×#353
commutatorC42C22×C4×C43
Frattini, cosocle#127C23×C43
prime radicalC43×#3151C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C23×C43 ◁ C22×C4×C43 ◁ C2×#127×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#353C2semidirect
3. C43×#1409C2semidirect
4. C43×#1408C2semidirect
6. C43×#532C4semidirect
9. C43×#493C4semidirect
11. C43×#492C4semidirect
14. C4×M16×C43C4semidirect
27. C4⋊Q8×C43C2×C4semidirect
30. #127×C43C2×C4semidirect
41. C4×C8×C43C2×C4semidirect
42. C4×C8×C43C2×C4semidirect
107. #13584C43direct (N × H)
126. C2×#353C2×C43semidirect
127. #1409C2×C43semidirect
128. #1408C2×C43semidirect
136. #532C4×C43semidirect
139. #493C4×C43semidirect
141. #492C4×C43semidirect
144. C4×M16C4×C43semidirect
147. C43#13584direct (N × H)
158. C4⋊Q8C2×C4×C43semidirect
161. #127C2×C4×C43semidirect
172. C4×C8C2×C4×C43semidirect
173. C4×C8C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31512
C2×C43×#3532
C43×#14092
C43×#14082
#1358443