Finite Group Databasebeta

← C43×#12830 #24932847

Subgroups — C43×#12830 #24932847

Order 11008.

378 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2957C211yesmaximal, characteristic
2C43×#2151C211yesmaximal, characteristic, complemented
3C43×#2145C211yesmaximal, characteristic
4C2×C43×#359C211yesmaximal, characteristic
5C43×#1833C211yesmaximal, characteristic, complemented
6C43×#1388C211yesmaximal, characteristic, complemented
7C43×#1382C211yesmaximal, characteristic, complemented
8C2×#135×C43C2211yescharacteristic
9C43×#568—21no—
10C2×M32×C43C2211yescharacteristic
11C22×C16×C43C2211yescharacteristic
12C43×#444C414yescomplemented
13C43×#443—22no—
14C2×#108×C43C2211yescharacteristic
15C2×#108×C43C2211yescharacteristic
16C43×#427C2211yescharacteristic
17C43×#421—21no—
18C43×#405C2211yescharacteristic
19C43×C4⋊C16—22no—
20C43×#360—22no—
21C43×#359—22no—
22C43×#344—21no—
23C43×H(3,ℤ/4)—21no—
24C2×#41×C43—21no—
25#135×C43—21no—
26#135×C43—21no—
27#135×C43C2×C412yes—
28#135×C43D412yes—
29C2×Q16×C43Q811yescharacteristic
30C2×SD16×C43—21no—
31C2×D8×C43Q811yescharacteristic
32#131×C43—24no—
33#131×C43—42no—
34C2×M16×C43—21no—
35C2×M16×C43—21no—
36C2×M16×C43—42no—
37C2×M16×C43D411yescharacteristic
38C22×C8×C43C2311yescharacteristic
39#117×C43—21no—
40#117×C43D411yescharacteristic
41M32×C43—21no—
42M32×C43—21no—
43C2×C16×C43—21no—
44C2×C16×C43—21no—
45C2×C16×C43—21no—
46C2×C16×C43—21no—
47#108×C43—21no—
48#108×C43—21no—
49#108×C43—21no—
50#108×C43C2×C412yes—
51#107×C43—21no—
52#106×C43—21no—
53#104×C43—24no—
54#97×C43C2×C412yes—
55C4×C8×C43D412yes—
56#41×C43—22no—
57#41×C43—22no—
58#41×C43—41no—
59#41×C43—41no—
60C2×Q8×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43C2×D411yescharacteristic
65Q16×C43—21no—
66Q16×C43C4⋊C412yes—
67SD16×C43—22no—
68SD16×C43—22no—
69D8×C43—21no—
70D8×C43C4⋊C412yes—
71M16×C43—21no—
72M16×C43—21no—
73M16×C43—22no—
74M16×C43—44no—
75M16×C43—41no—
76M16×C43—41no—
77M16×C43—41no—
78C2×C8×C43—44no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43C22⋊C412yes—
82C2×C8×C43C22×C411yescharacteristic
83C2×C8×C43C2×D411yescharacteristic
84C2×C8×C43C2×D411yescharacteristic
85C2×C8×C43C2×Q811yescharacteristic
86C2×C8×C43#4111yescharacteristic
87C2×C8×C43#4111yescharacteristic
88C4⋊C4×C43—21no—
89C4⋊C4×C43—41no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—41no—
92C42×C43—41no—
93C42×C43C22⋊C412yes—
94C16×C43—41no—
95C16×C43—41no—
96C23×C43—41no—
97C23×C43#13511yescharacteristic
98Q8×C43—22no—
99Q8×C43—41no—
100D4×C43—22no—
101D4×C43—42no—
102D4×C43—42no—
103D4×C43—41no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—81no—
109C2×C4×C43C2×C22⋊C411yescharacteristic
110C2×C4×C43#12111yescharacteristic
111C2×C4×C43C22⋊Q811yescharacteristic
112C2×C4×C43#13511yescharacteristic
113C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
115C8×C43—22no—
116C8×C43—42no—
117C8×C43—81no—
118C8×C43C2×C4⋊C411yescharacteristic
119C8×C43#11711yescharacteristic
120C8×C43#12111yescharacteristic
121C8×C43C22⋊Q811yescharacteristic
122#12830C4311yesmaximal, characteristic, direct product factor, Sylow
123C22×C43—41no—
124C22×C43—42no—
125C22×C43—161no—
126C22×C43#41611yescharacteristic
127C22×C43#46311yescharacteristic
128C22×C43#47811yescharacteristic
129C4×C43—42no—
130C4×C43—42no—
131C4×C43—161no—
132C4×C43#38011yescharacteristic
133C4×C43#41811yescharacteristic
134C4×C43#46311yescharacteristic
135C4×C43#47811yescharacteristic
136#2957C2×C4311yescharacteristic
137#2151C2×C4311yescharacteristic, complemented
138#2145C2×C4311yescharacteristic
139C2×#359C2×C4311yescharacteristic
140#1833C2×C4311yescharacteristic, complemented
141#1388C2×C4311yescharacteristic, complemented
142#1382C2×C4311yescharacteristic, complemented
143C2×C43—21no—
144C2×C43—21no—
145C2×C43—21no—
146C2×C43—82no—
147C2×C43#180411yescharacteristic
148C2×#135C22×C4311yescharacteristic
149#568—21no—
150C2×M32C22×C4311yescharacteristic
151C22×C16C22×C4311yescharacteristic
152#444C4×C4314yescomplemented
153#443—22no—
154C2×#108C22×C4311yescharacteristic
155C2×#108C22×C4311yescharacteristic
156#427C22×C4311yescharacteristic
157#421—21no—
158#405C22×C4311yescharacteristic
159C4⋊C16—22no—
160#360—22no—
161#359—22no—
162#344—21no—
163H(3,ℤ/4)—21no—
164C43#1283011yescharacteristic, direct product factor, Sylow
165C2×#41—21no—
166#135—21no—
167#135—21no—
168#135C2×C4×C4312yes—
169#135D4×C4312yes—
170C2×Q16Q8×C4311yescharacteristic
171C2×SD16—21no—
172C2×D8Q8×C4311yescharacteristic
173#131—24no—
174#131—42no—
175C2×M16—21no—
176C2×M16—21no—
177C2×M16—42no—
178C2×M16D4×C4311yescharacteristic
179C22×C8C23×C4311yescharacteristic
180#117—21no—
181#117D4×C4311yescharacteristic
182M32—21no—
183M32—21no—
184C2×C16—21no—
185C2×C16—21no—
186C2×C16—21no—
187C2×C16—21no—
188#108—21no—
189#108—21no—
190#108—21no—
191#108C2×C4×C4312yes—
192#107—21no—
193#106—21no—
194#104—24no—
195#97C2×C4×C4312yes—
196C4×C8D4×C4312yes—
197#41—22no—
198#41—22no—
199#41—41no—
200#41—41no—
201C2×Q8—21no—
202C2×D4—21no—
203C2×D4—41no—
204C22×C4—41no—
205C22×C4C2×D4×C4311yescharacteristic
206Q16—21no—
207Q16C4⋊C4×C4312yes—
208SD16—22no—
209SD16—22no—
210D8—21no—
211D8C4⋊C4×C4312yes—
212M16—21no—
213M16—21no—
214M16—22no—
215M16—44no—
216M16—41no—
217M16—41no—
218M16—41no—
219C2×C8—44no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C22⋊C4×C4312yes—
223C2×C8C22×C4×C4311yescharacteristic
224C2×C8C2×D4×C4311yescharacteristic
225C2×C8C2×D4×C4311yescharacteristic
226C2×C8C2×Q8×C4311yescharacteristic
227C2×C8#41×C4311yescharacteristic
228C2×C8#41×C4311yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—41no—
231C22⋊C4—21no—
232C22⋊C4—41no—
233C42—41no—
234C42C22⋊C4×C4312yes—
235C16—41no—
236C16—41no—
237C23—41no—
238C23#135×C4311yescharacteristic
239Q8—22no—
240Q8—41no—
241D4—22no—
242D4—42no—
243D4—42no—
244D4—41no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4C2×C22⋊C4×C4311yescharacteristic
251C2×C4#121×C4311yescharacteristic
252C2×C4C22⋊Q8×C4311yescharacteristic
253C2×C4#135×C4311yescharacteristic
254C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
255C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
256C8—22no—
257C8—42no—
258C8—81no—
259C8C2×C4⋊C4×C4311yescharacteristic
260C8#117×C4311yescharacteristic
261C8#121×C4311yescharacteristic
262C8C22⋊Q8×C4311yescharacteristic
263C22—41no—
264C22—42no—
265C22—161no—
266C22C43×#41611yescharacteristic
267C22C43×#46311yescharacteristic
268C22C43×#47811yescharacteristic
269C4—42no—
270C4—42no—
271C4—161no—
272C4C43×#38011yescharacteristic
273C4C43×#41811yescharacteristic
274C4C43×#46311yescharacteristic
275C4C43×#47811yescharacteristic
276C2—21no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2C43×#180411yescharacteristic
subgroupG/H
centerC4×C43#418
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
socleC2×C43#1804
prime radicalC2×#135×C43C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C43 ◁ C22×C4×C43 ◁ C43×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2151C2semidirect
5. C43×#1833C2semidirect
6. C43×#1388C2semidirect
7. C43×#1382C2semidirect
12. C43×#444C4semidirect
122. #12830C43direct (N × H)
137. #2151C2×C43semidirect
140. #1833C2×C43semidirect
141. #1388C2×C43semidirect
142. #1382C2×C43semidirect
152. #444C4×C43semidirect
164. C43#12830direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#29572
C43×#21512
C43×#21452
C2×C43×#3592
C43×#18332
C43×#13882
C43×#13822
#1283043