Finite Group Databasebeta

← C43×#11677 #24931694

Subgroups — C43×#11677 #24931694

Order 11008.

332 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×#3168C211yesmaximal, characteristic
2C2×C43×#346C211yesmaximal, characteristic, complemented
3C43×#1566C211yesmaximal, characteristic, complemented
4C43×#1334C212yesmaximal, complemented
5C43×#1333C212yesmaximal, complemented
6C43×#529—21no—
7C22×C16×C43—21no—
8C43×#499C411yescharacteristic
9C43×#495C411yescharacteristic
10C43×#488—21no—
11C43×#467C411yescharacteristic
12C43×#466C411yescharacteristic
13C43×#465—21no—
14C4×Q16×C43C2211yescharacteristic
15C4×SD16×C43—21no—
16C4×D8×C43C2211yescharacteristic
17C43×#423—21no—
18C2×C4×C8×C43C2211yescharacteristic
19C43×#346—21no—
20C43×#346C2212yes—
21C43×#334—21no—
22C43×#334C2212yes—
23C2×Q16×C43C2×C411yescharacteristic
24C2×SD16×C43—21no—
25C2×D8×C43C2×C411yescharacteristic
26C2×M16×C43—41no—
27C22×C8×C43C2×C411yescharacteristic
28C22×C8×C43D411yescharacteristic
29#126×C43—41no—
30#125×C43—21no—
31#124×C43—21no—
32#123×C43—41no—
33C22⋊Q8×C43—21no—
34#121×C43—21no—
35C4×Q8×C43—21no—
36C4×D4×C43—21no—
37C4×D4×C43—41no—
38#117×C43—41no—
39C2×C42×C43D411yescharacteristic
40C2×C16×C43—24no—
41C2×C16×C43—22no—
42#107×C43C2×C411yescharacteristic
43#107×C43C2×C411yescharacteristic
44#106×C43—21no—
45C4⋊C8×C43—22no—
46C4⋊C8×C43—41no—
47#103×C43—21no—
48#103×C43—21no—
49#102×C43—21no—
50#102×C43—21no—
51C4×C8×C43C2×C411yescharacteristic
52C4×C8×C43D411yescharacteristic
53C4×C8×C43D411yescharacteristic
54C4×C8×C43C2311yescharacteristic
55C2×Q8×C43—21no—
56C2×D4×C43—21no—
57C2×D4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43C22⋊C411yescharacteristic
60C22×C4×C43D811yescharacteristic
61C22×C4×C43SD1611yescharacteristic
62Q16×C43—22no—
63SD16×C43—42no—
64D8×C43—22no—
65M16×C43—82no—
66C2×C8×C43—22no—
67C2×C8×C43—22no—
68C2×C8×C43—42no—
69C2×C8×C43C22⋊C411yescharacteristic
70C2×C8×C43C22⋊C411yescharacteristic
71C2×C8×C43C22×C411yescharacteristic
72C2×C8×C43C2×D411yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C42×C43—41no—
85C42×C43C22⋊C411yescharacteristic
86C42×C43D811yescharacteristic
87C42×C43SD1611yescharacteristic
88C42×C43C2×D411yescharacteristic
89C16×C43—24no—
90C23×C43—41no—
91C23×C43#10211yescharacteristic
92Q8×C43—41no—
93Q8×C43—41no—
94D4×C43—41no—
95D4×C43—41no—
96D4×C43—82no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—82no—
105C2×C4×C43#10211yescharacteristic
106C2×C4×C43#10211yescharacteristic
107C2×C4×C43#10211yescharacteristic
108C2×C4×C43C2×C22⋊C411yescharacteristic
109C2×C4×C43C2×D811yescharacteristic
110C2×C4×C43C2×SD1611yescharacteristic
111C8×C43—21no—
112C8×C43—21no—
113C8×C43—82no—
114C8×C43#10412yes—
115C8×C43#13112yes—
116#11677C4311yesmaximal, characteristic, direct product factor, Sylow
117C22×C43—21no—
118C22×C43—21no—
119C22×C43—81no—
120C22×C43—81no—
121C22×C43—81no—
122C22×C43#36012yes—
123C22×C43C2×#10211yescharacteristic
124C4×C43—21no—
125C4×C43—21no—
126C4×C43—21no—
127C4×C43—21no—
128C4×C43—21no—
129C4×C43—81no—
130C4×C43—81no—
131C4×C43—81no—
132C4×C43#40811yescharacteristic
133C4×C43C2×#10411yescharacteristic
134#3168C2×C4311yescharacteristic
135C2×#346C2×C4311yescharacteristic, complemented
136#1566C2×C4311yescharacteristic, complemented
137#1334C2×C4312yescomplemented
138#1333C2×C4312yescomplemented
139C2×C43—22no—
140C2×C43—161no—
141C2×C43#149211yescharacteristic
142C2×C43C2×#36011yescharacteristic
143C2×C43#214811yescharacteristic
144#529—21no—
145C22×C16—21no—
146#499C4×C4311yescharacteristic
147#495C4×C4311yescharacteristic
148#488—21no—
149#467C4×C4311yescharacteristic
150#466C4×C4311yescharacteristic
151#465—21no—
152C4×Q16C22×C4311yescharacteristic
153C4×SD16—21no—
154C4×D8C22×C4311yescharacteristic
155#423—21no—
156C2×C4×C8C22×C4311yescharacteristic
157#346—21no—
158#346C22×C4312yes—
159#334—21no—
160#334C22×C4312yes—
161C43#1167711yescharacteristic, direct product factor, Sylow
162C2×Q16C2×C4×C4311yescharacteristic
163C2×SD16—21no—
164C2×D8C2×C4×C4311yescharacteristic
165C2×M16—41no—
166C22×C8C2×C4×C4311yescharacteristic
167C22×C8D4×C4311yescharacteristic
168#126—41no—
169#125—21no—
170#124—21no—
171#123—41no—
172C22⋊Q8—21no—
173#121—21no—
174C4×Q8—21no—
175C4×D4—21no—
176C4×D4—41no—
177#117—41no—
178C2×C42D4×C4311yescharacteristic
179C2×C16—24no—
180C2×C16—22no—
181#107C2×C4×C4311yescharacteristic
182#107C2×C4×C4311yescharacteristic
183#106—21no—
184C4⋊C8—22no—
185C4⋊C8—41no—
186#103—21no—
187#103—21no—
188#102—21no—
189#102—21no—
190C4×C8C2×C4×C4311yescharacteristic
191C4×C8D4×C4311yescharacteristic
192C4×C8D4×C4311yescharacteristic
193C4×C8C23×C4311yescharacteristic
194C2×Q8—21no—
195C2×D4—21no—
196C2×D4—41no—
197C22×C4—41no—
198C22×C4C22⋊C4×C4311yescharacteristic
199C22×C4D8×C4311yescharacteristic
200C22×C4SD16×C4311yescharacteristic
201Q16—22no—
202SD16—42no—
203D8—22no—
204M16—82no—
205C2×C8—22no—
206C2×C8—22no—
207C2×C8—42no—
208C2×C8C22⋊C4×C4311yescharacteristic
209C2×C8C22⋊C4×C4311yescharacteristic
210C2×C8C22×C4×C4311yescharacteristic
211C2×C8C2×D4×C4311yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C42—41no—
224C42C22⋊C4×C4311yescharacteristic
225C42D8×C4311yescharacteristic
226C42SD16×C4311yescharacteristic
227C42C2×D4×C4311yescharacteristic
228C16—24no—
229C23—41no—
230C23#102×C4311yescharacteristic
231Q8—41no—
232Q8—41no—
233D4—41no—
234D4—41no—
235D4—82no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—82no—
244C2×C4#102×C4311yescharacteristic
245C2×C4#102×C4311yescharacteristic
246C2×C4#102×C4311yescharacteristic
247C2×C4C2×C22⋊C4×C4311yescharacteristic
248C2×C4C2×D8×C4311yescharacteristic
249C2×C4C2×SD16×C4311yescharacteristic
250C8—21no—
251C8—21no—
252C8—82no—
253C8#104×C4312yes—
254C8#131×C4312yes—
255C22—21no—
256C22—21no—
257C22—81no—
258C22—81no—
259C22—81no—
260C22C43×#36012yes—
261C22C2×#102×C4311yescharacteristic
262C4—21no—
263C4—21no—
264C4—21no—
265C4—21no—
266C4—21no—
267C4—81no—
268C4—81no—
269C4—81no—
270C4C43×#40811yescharacteristic
271C4C2×#104×C4311yescharacteristic
272C2—22no—
273C2—161no—
274C2C43×#149211yescharacteristic
275C2C2×C43×#36011yescharacteristic
276C2C43×#214811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#102
commutatorC2×C8C22×C4×C43
Frattini, cosocleC4×C8C23×C43
prime radicalC43×#466C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ C2×C4×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#346C2semidirect
3. C43×#1566C2semidirect
4. C43×#1334C2semidirect
5. C43×#1333C2semidirect
116. #11677C43direct (N × H)
135. C2×#346C2×C43semidirect
136. #1566C2×C43semidirect
137. #1334C2×C43semidirect
138. #1333C2×C43semidirect
161. C43#11677direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31682
C2×C43×#3462
C43×#15662
C43×#13342
C43×#13332
#1167743