Finite Group Databasebeta

← C43×#33382 #24953399

Subgroups — C43×#33382 #24953399

Order 11008.

1124 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#578C211yesmaximal, characteristic
2C2×C43×#504C211yesmaximal, characteristic, complemented
3C43×#2913C211yesmaximal, characteristic, complemented
4C43×#2141C213yesmaximal, complemented
5C43×#2139C213yesmaximal, complemented
6C43×#2138C213yesmaximal, complemented
7C2×C43×#358C213yesmaximal, complemented
8C2×2−1+4×C43—21no—
9C43×#578—24no—
10C43×#578C418yescomplemented
11C2×#137×C43—23no—
12C2×#135×C43C2213yes—
13C22×Q16×C43C2213yes—
14C2×#131×C43C2211yescharacteristic
15C43×#520—21no—
16C43×#504—24no—
17C2×M32×C43C2213yes—
18C22×C16×C43C2213yes—
19C43×#428—23no—
20C43×#427C2213yes—
21C2×#107×C43C2213yes—
22C43×#358C2213yes—
23C43×#358C2216yes—
24C43×#358C2213yes—
25C43×#357C2211yescharacteristic
26C43×#357C2213yes—
272−1+4×C43—28no—
282−1+4×C43—44no—
29C2×#41×C43—23no—
30C2×#41×C43—43no—
31C2×#41×C43D411yescharacteristic
32C22×Q8×C43—23no—
33C22×Q8×C43—41no—
34#137×C43—224no—
35#135×C43—26no—
36#135×C43C2×C4112yescomplemented
37C2×Q16×C43—23no—
38C2×Q16×C43—26no—
39C2×Q16×C43C2×C4112yescomplemented
40C2×Q16×C43C2313yes—
41C2×SD16×C43—23no—
42C2×D8×C43C2311yescharacteristic
43#131×C43C2×C414yes—
44#131×C43D414yes—
45C2×M16×C43D413yes—
46C22×C8×C43C2313yes—
47C4×Q8×C43—41no—
48C4×D4×C43—43no—
49#117×C43—23no—
50C2×C4⋊C4×C43—23no—
51M32×C43—26no—
52C2×C16×C43—26no—
53C2×C16×C43C2311yescharacteristic
54C2×C16×C43C2313yes—
55#107×C43—23no—
56#107×C43C2313yes—
57#107×C43C2311yescharacteristic
58#106×C43—23no—
59#41×C43—212no—
60#41×C43—424no—
61#41×C43—46no—
62#41×C43C22⋊C414yes—
63#41×C43SD1614yes—
64C2×Q8×C43—212no—
65C2×Q8×C43—23no—
66C2×Q8×C43—48no—
67C2×Q8×C43—43no—
68C2×Q8×C43—46no—
69C2×Q8×C43D811yescharacteristic
70C2×D4×C43—21no—
71C2×D4×C43—43no—
72C2×D4×C43D813yes—
73C22×C4×C43—43no—
74C22×C4×C43—43no—
75C22×C4×C43—43no—
76C22×C4×C43C2×D413yes—
77Q16×C43—212no—
78Q16×C43—23no—
79Q16×C43C22×C416yes—
80SD16×C43—212no—
81D8×C43—21no—
82D8×C43C22×C412yes—
83M16×C43C22⋊C4112yes—
84C2×C8×C43C22×C416yes—
85C2×C8×C43C2×D413yes—
86C2×C8×C43C2×D416yes—
87C2×C8×C43C2411yescharacteristic
88C4⋊C4×C43—21no—
89C4⋊C4×C43—23no—
90C4⋊C4×C43—43no—
91C22⋊C4×C43—43no—
92C42×C43—43no—
93C16×C43—21no—
94C16×C43—23no—
95C23×C43—41no—
96C23×C43C2×D813yes—
97Q8×C43—26no—
98Q8×C43—43no—
99Q8×C43—412no—
100Q8×C43#10214yes—
101D4×C43—22no—
102D4×C43—412no—
103D4×C43—41no—
104D4×C43#102112yes—
105C2×C4×C43—43no—
106C2×C4×C43—412no—
107C2×C4×C43—412no—
108C2×C4×C43—41no—
109C2×C4×C43—43no—
110C2×C4×C43—163no—
111C2×C4×C43C2×C22⋊C416yes—
112C2×C4×C43C2×D813yes—
113C2×C4×C43C2×SD1616yes—
114C2×C4×C43C22×D411yescharacteristic
115C8×C43C2×C22⋊C416yes—
116C8×C43C23×C411yescharacteristic
117C8×C43C22×D411yescharacteristic
118#33382C4311yesmaximal, characteristic, direct product factor, Sylow
119C22×C43—23no—
120C22×C43—23no—
121C22×C43—42no—
122C22×C43—81no—
123C22×C43—81no—
124C22×C43C2×#10216yes—
125C22×C43C22×D811yescharacteristic
126C4×C43—46no—
127C4×C43—83no—
128C4×C43—81no—
129C4×C43C2×#10216yes—
130C4×C43C22×C22⋊C411yescharacteristic
131C4×C43C22×SD1611yescharacteristic
132C2×#578C2×C4311yescharacteristic
133C2×#504C2×C4311yescharacteristic, complemented
134#2913C2×C4311yescharacteristic, complemented
135#2141C2×C4313yescomplemented
136#2139C2×C4313yescomplemented
137#2138C2×C4313yescomplemented
138C2×#358C2×C4313yescomplemented
139C2×C43—26no—
140C2×C43—82no—
141C2×C43C22×#10211yescharacteristic
142C2×C43#341611yescharacteristic
143C2×C43#341711yescharacteristic
144C2×2−1+4—21no—
145#578—24no—
146#578C4×C4318yescomplemented
147C2×#137—23no—
148C2×#135C22×C4313yes—
149C22×Q16C22×C4313yes—
150C2×#131C22×C4311yescharacteristic
151#520—21no—
152#504—24no—
153C2×M32C22×C4313yes—
154C22×C16C22×C4313yes—
155#428—23no—
156#427C22×C4313yes—
157C2×#107C22×C4313yes—
158#358C22×C4313yes—
159#358C22×C4316yes—
160#358C22×C4313yes—
161#357C22×C4311yescharacteristic
162#357C22×C4313yes—
163C43#3338211yescharacteristic, direct product factor, Sylow
1642−1+4—28no—
1652−1+4—44no—
166C2×#41—23no—
167C2×#41—43no—
168C2×#41D4×C4311yescharacteristic
169C22×Q8—23no—
170C22×Q8—41no—
171#137—224no—
172#135—26no—
173#135C2×C4×C43112yescomplemented
174C2×Q16—23no—
175C2×Q16—26no—
176C2×Q16C2×C4×C43112yescomplemented
177C2×Q16C23×C4313yes—
178C2×SD16—23no—
179C2×D8C23×C4311yescharacteristic
180#131C2×C4×C4314yes—
181#131D4×C4314yes—
182C2×M16D4×C4313yes—
183C22×C8C23×C4313yes—
184C4×Q8—41no—
185C4×D4—43no—
186#117—23no—
187C2×C4⋊C4—23no—
188M32—26no—
189C2×C16—26no—
190C2×C16C23×C4311yescharacteristic
191C2×C16C23×C4313yes—
192#107—23no—
193#107C23×C4313yes—
194#107C23×C4311yescharacteristic
195#106—23no—
196#41—212no—
197#41—424no—
198#41—46no—
199#41C22⋊C4×C4314yes—
200#41SD16×C4314yes—
201C2×Q8—212no—
202C2×Q8—23no—
203C2×Q8—48no—
204C2×Q8—43no—
205C2×Q8—46no—
206C2×Q8D8×C4311yescharacteristic
207C2×D4—21no—
208C2×D4—43no—
209C2×D4D8×C4313yes—
210C22×C4—43no—
211C22×C4—43no—
212C22×C4—43no—
213C22×C4C2×D4×C4313yes—
214Q16—212no—
215Q16—23no—
216Q16C22×C4×C4316yes—
217SD16—212no—
218D8—21no—
219D8C22×C4×C4312yes—
220M16C22⋊C4×C43112yes—
221C2×C8C22×C4×C4316yes—
222C2×C8C2×D4×C4313yes—
223C2×C8C2×D4×C4316yes—
224C2×C8C24×C4311yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—23no—
227C4⋊C4—43no—
228C22⋊C4—43no—
229C42—43no—
230C16—21no—
231C16—23no—
232C23—41no—
233C23C2×D8×C4313yes—
234Q8—26no—
235Q8—43no—
236Q8—412no—
237Q8#102×C4314yes—
238D4—22no—
239D4—412no—
240D4—41no—
241D4#102×C43112yes—
242C2×C4—43no—
243C2×C4—412no—
244C2×C4—412no—
245C2×C4—41no—
246C2×C4—43no—
247C2×C4—163no—
248C2×C4C2×C22⋊C4×C4316yes—
249C2×C4C2×D8×C4313yes—
250C2×C4C2×SD16×C4316yes—
251C2×C4C22×D4×C4311yescharacteristic
252C8C2×C22⋊C4×C4316yes—
253C8C23×C4×C4311yescharacteristic
254C8C22×D4×C4311yescharacteristic
255C22—23no—
256C22—23no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22C2×#102×C4316yes—
261C22C22×D8×C4311yescharacteristic
262C4—46no—
263C4—83no—
264C4—81no—
265C4C2×#102×C4316yes—
266C4C22×C22⋊C4×C4311yescharacteristic
267C4C22×SD16×C4311yescharacteristic
268C2—26no—
269C2—82no—
270C2C22×#102×C4311yescharacteristic
271C2C43×#341611yescharacteristic
272C2C43×#341711yescharacteristic
subgroupG/H
center, socleC22×C43C22×D8
commutatorC8C23×C4×C43
Frattini, cosocleC2×C8C24×C43
prime radicalC2×C43×#578C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×#41×C43 ◁ C2×#131×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#504C2semidirect
3. C43×#2913C2semidirect
4. C43×#2141C2semidirect
5. C43×#2139C2semidirect
6. C43×#2138C2semidirect
7. C2×C43×#358C2semidirect
10. C43×#578C4semidirect
36. #135×C43C2×C4semidirect
39. C2×Q16×C43C2×C4semidirect
118. #33382C43direct (N × H)
133. C2×#504C2×C43semidirect
134. #2913C2×C43semidirect
135. #2141C2×C43semidirect
136. #2139C2×C43semidirect
137. #2138C2×C43semidirect
138. C2×#358C2×C43semidirect
146. #578C4×C43semidirect
163. C43#33382direct (N × H)
173. #135C2×C4×C43semidirect
176. C2×Q16C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5782
C2×C43×#5042
C43×#29132
C43×#21412
C43×#21392
C43×#21382
C2×C43×#3582
#3338243