Finite Group Databasebeta

← C43×#13140 #24933157

Subgroups — C43×#13140 #24933157

Order 11008.

314 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2155C211yesmaximal, characteristic, complemented
2C43×#2148C211yesmaximal, characteristic
3C43×#2145C211yesmaximal, characteristic
4C43×#1975C211yesmaximal, characteristic
5C43×#1773C211yesmaximal, characteristic, complemented
6C43×#1385C211yesmaximal, characteristic, complemented
7C43×#1377C211yesmaximal, characteristic, complemented
8C2×#135×C43C2211yescharacteristic
9C2×M32×C43C2211yescharacteristic
10C2×M32×C43C2211yescharacteristic
11C2×#108×C43C2211yescharacteristic
12C2×#108×C43C2211yescharacteristic
13C43×#427C2211yescharacteristic
14C2×#104×C43—21no—
15C43×#408—21no—
16C43×#405—21no—
17C2×#97×C43C2211yescharacteristic
18C43×#365—22no—
19C43×#362C412yescomplemented
20C43×#361C412yescomplemented
21C43×#360—22no—
22C43×#339—21no—
23C2×#41×C43—21no—
24#135×C43—21no—
25#135×C43—21no—
26#135×C43—21no—
27#135×C43—21no—
28C2×Q16×C43C2×C411yescharacteristic
29C2×SD16×C43—21no—
30C2×D8×C43C2×C411yescharacteristic
31C2×M16×C43—21no—
32C2×M16×C43—21no—
33C22×C8×C43D411yescharacteristic
34C22×C8×C43C2311yescharacteristic
35#117×C43—21no—
36C2×C42×C43D411yescharacteristic
37M32×C43—21no—
38M32×C43—21no—
39M32×C43—21no—
40M32×C43C2×C412yes—
41C2×C16×C43—21no—
42C2×C16×C43—21no—
43#108×C43—21no—
44#108×C43—21no—
45#108×C43—21no—
46#108×C43C2×C412yes—
47#107×C43—21no—
48#106×C43D412yes—
49#104×C43—42no—
50C22⋊C8×C43—42no—
51#97×C43—21no—
52#97×C43—21no—
53#97×C43—41no—
54C4×C8×C43—41no—
55#41×C43—41no—
56#41×C43—41no—
57#41×C43—41no—
58#41×C43—41no—
59C2×Q8×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—41no—
62C22×C4×C43—21no—
63C22×C4×C43—41no—
64C22×C4×C43C2×D411yescharacteristic
65Q16×C43—21no—
66Q16×C43—21no—
67SD16×C43—41no—
68SD16×C43—41no—
69D8×C43—21no—
70D8×C43—21no—
71M16×C43—22no—
72M16×C43—41no—
73M16×C43—41no—
74M16×C43—41no—
75C2×C8×C43—21no—
76C2×C8×C43—21no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43SD1612yes—
80C2×C8×C43C22×C411yescharacteristic
81C2×C8×C43C2×D411yescharacteristic
82C2×C8×C43#4111yescharacteristic
83C2×C8×C43#4111yescharacteristic
84C2×C8×C43#4111yescharacteristic
85C2×C8×C43#4111yescharacteristic
86C4⋊C4×C43—22no—
87C22⋊C4×C43—41no—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43—41no—
91C16×C43—22no—
92C16×C43—41no—
93C23×C43—41no—
94C23×C43#13511yescharacteristic
95Q8×C43—41no—
96Q8×C43—41no—
97D4×C43—41no—
98D4×C43—41no—
99D4×C43—81no—
100D4×C43—81no—
101C2×C4×C43—41no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43—81no—
105C2×C4×C43—81no—
106C2×C4×C43—81no—
107C2×C4×C43C4×D411yescharacteristic
108C2×C4×C43#12111yescharacteristic
109C2×C4×C43#12311yescharacteristic
110C2×C4×C43C2×SD1611yescharacteristic
111C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
113C8×C43—22no—
114C8×C43—42no—
115C8×C43—81no—
116C8×C43#11711yescharacteristic
117C8×C43C4×D411yescharacteristic
118C8×C43#12411yescharacteristic
119C8×C43#12611yescharacteristic
120#13140C4311yesmaximal, characteristic, direct product factor, Sylow
121C22×C43—41no—
122C22×C43—82no—
123C22×C43—81no—
124C22×C43C4×SD1611yescharacteristic
125C22×C43#46311yescharacteristic
126C22×C43#48211yescharacteristic
127C4×C43—82no—
128C4×C43—81no—
129C4×C43—81no—
130C4×C43#38811yescharacteristic
131C4×C43#44211yescharacteristic
132C4×C43#46011yescharacteristic
133C4×C43#48111yescharacteristic
134#2155C2×C4311yescharacteristic, complemented
135#2148C2×C4311yescharacteristic
136#2145C2×C4311yescharacteristic
137#1975C2×C4311yescharacteristic
138#1773C2×C4311yescharacteristic, complemented
139#1385C2×C4311yescharacteristic, complemented
140#1377C2×C4311yescharacteristic, complemented
141C2×C43—21no—
142C2×C43—21no—
143C2×C43—21no—
144C2×C43—161no—
145C2×C43#192611yescharacteristic
146C2×#135C22×C4311yescharacteristic
147C2×M32C22×C4311yescharacteristic
148C2×M32C22×C4311yescharacteristic
149C2×#108C22×C4311yescharacteristic
150C2×#108C22×C4311yescharacteristic
151#427C22×C4311yescharacteristic
152C2×#104—21no—
153#408—21no—
154#405—21no—
155C2×#97C22×C4311yescharacteristic
156#365—22no—
157#362C4×C4312yescomplemented
158#361C4×C4312yescomplemented
159#360—22no—
160#339—21no—
161C43#1314011yescharacteristic, direct product factor, Sylow
162C2×#41—21no—
163#135—21no—
164#135—21no—
165#135—21no—
166#135—21no—
167C2×Q16C2×C4×C4311yescharacteristic
168C2×SD16—21no—
169C2×D8C2×C4×C4311yescharacteristic
170C2×M16—21no—
171C2×M16—21no—
172C22×C8D4×C4311yescharacteristic
173C22×C8C23×C4311yescharacteristic
174#117—21no—
175C2×C42D4×C4311yescharacteristic
176M32—21no—
177M32—21no—
178M32—21no—
179M32C2×C4×C4312yes—
180C2×C16—21no—
181C2×C16—21no—
182#108—21no—
183#108—21no—
184#108—21no—
185#108C2×C4×C4312yes—
186#107—21no—
187#106D4×C4312yes—
188#104—42no—
189C22⋊C8—42no—
190#97—21no—
191#97—21no—
192#97—41no—
193C4×C8—41no—
194#41—41no—
195#41—41no—
196#41—41no—
197#41—41no—
198C2×Q8—21no—
199C2×D4—21no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4C2×D4×C4311yescharacteristic
204Q16—21no—
205Q16—21no—
206SD16—41no—
207SD16—41no—
208D8—21no—
209D8—21no—
210M16—22no—
211M16—41no—
212M16—41no—
213M16—41no—
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8SD16×C4312yes—
219C2×C8C22×C4×C4311yescharacteristic
220C2×C8C2×D4×C4311yescharacteristic
221C2×C8#41×C4311yescharacteristic
222C2×C8#41×C4311yescharacteristic
223C2×C8#41×C4311yescharacteristic
224C2×C8#41×C4311yescharacteristic
225C4⋊C4—22no—
226C22⋊C4—41no—
227C42—21no—
228C42—21no—
229C42—41no—
230C16—22no—
231C16—41no—
232C23—41no—
233C23#135×C4311yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—81no—
239D4—81no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C4×D4×C4311yescharacteristic
247C2×C4#121×C4311yescharacteristic
248C2×C4#123×C4311yescharacteristic
249C2×C4C2×SD16×C4311yescharacteristic
250C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
251C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
252C8—22no—
253C8—42no—
254C8—81no—
255C8#117×C4311yescharacteristic
256C8C4×D4×C4311yescharacteristic
257C8#124×C4311yescharacteristic
258C8#126×C4311yescharacteristic
259C22—41no—
260C22—82no—
261C22—81no—
262C22C4×SD16×C4311yescharacteristic
263C22C43×#46311yescharacteristic
264C22C43×#48211yescharacteristic
265C4—81no—
266C4—82no—
267C4—81no—
268C4C43×#38811yescharacteristic
269C4C43×#44211yescharacteristic
270C4C43×#46011yescharacteristic
271C4C43×#48111yescharacteristic
272C2—21no—
273C2—21no—
274C2—21no—
275C2—161no—
276C2C43×#192611yescharacteristic
subgroupG/H
centerC4×C43#481
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
socleC2×C43#1926
prime radicalC2×#135×C43C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C43 ◁ C22×C4×C43 ◁ C2×#97×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2155C2semidirect
5. C43×#1773C2semidirect
6. C43×#1385C2semidirect
7. C43×#1377C2semidirect
19. C43×#362C4semidirect
20. C43×#361C4semidirect
120. #13140C43direct (N × H)
134. #2155C2×C43semidirect
138. #1773C2×C43semidirect
139. #1385C2×C43semidirect
140. #1377C2×C43semidirect
157. #362C4×C43semidirect
158. #361C4×C43semidirect
161. C43#13140direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#21552
C43×#21482
C43×#21452
C43×#19752
C43×#17732
C43×#13852
C43×#13772
#1314043