Finite Group Databasebeta

← C43×#13146 #24933163

Subgroups — C43×#13146 #24933163

Order 11008.

312 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×#2148C211yesmaximal, characteristic
2C2×C43×#359C211yesmaximal, characteristic
3C43×#2108C211yesmaximal, characteristic, complemented
4C43×#1976C211yesmaximal, characteristic
5C43×#1953C211yesmaximal, characteristic, complemented
6C43×#1389C211yesmaximal, characteristic, complemented
7C43×#1382C211yesmaximal, characteristic, complemented
8C2×#135×C43C2211yescharacteristic
9C2×M32×C43C2211yescharacteristic
10C22×C16×C43C2211yescharacteristic
11C43×#430—21no—
12C2×#108×C43C2211yescharacteristic
13C2×#108×C43C2211yescharacteristic
14C43×#427C2211yescharacteristic
15C43×#421—21no—
16C43×#410—21no—
17C43×#405C2211yescharacteristic
18C43×#362C412yescomplemented
19C43×#361C412yescomplemented
20C43×#359—21no—
21C43×#359—21no—
22C43×#346—21no—
23C4×C16×C43—21no—
24C43×#344—21no—
25C2×#41×C43—21no—
26#135×C43—21no—
27#135×C43—21no—
28#135×C43—21no—
29#135×C43—21no—
30C2×Q16×C43C2×C411yescharacteristic
31C2×SD16×C43—21no—
32C2×D8×C43C2×C411yescharacteristic
33C2×M16×C43—21no—
34C2×M16×C43—21no—
35C2×M16×C43D411yescharacteristic
36C22×C8×C43C2311yescharacteristic
37#117×C43—21no—
38#117×C43D411yescharacteristic
39M32×C43—21no—
40M32×C43C2×C412yes—
41C2×C16×C43—21no—
42C2×C16×C43—21no—
43C2×C16×C43—21no—
44C2×C16×C43D411yescharacteristic
45C2×C16×C43D411yescharacteristic
46#108×C43—21no—
47#108×C43—21no—
48#108×C43—21no—
49#108×C43—42no—
50#108×C43C2×C412yes—
51#107×C43—21no—
52#106×C43—21no—
53#104×C43—42no—
54#99×C43—42no—
55#97×C43—21no—
56C4×C8×C43—21no—
57#41×C43—41no—
58#41×C43—41no—
59#41×C43—41no—
60#41×C43—41no—
61C2×Q8×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43C2×D411yescharacteristic
66Q16×C43—21no—
67Q16×C43—21no—
68SD16×C43—41no—
69SD16×C43—41no—
70D8×C43—21no—
71D8×C43—21no—
72M16×C43—21no—
73M16×C43—22no—
74M16×C43—41no—
75M16×C43—41no—
76M16×C43—41no—
77M16×C43D812yes—
78C2×C8×C43—21no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43C22×C411yescharacteristic
82C2×C8×C43C2×D411yescharacteristic
83C2×C8×C43#4111yescharacteristic
84C2×C8×C43#4111yescharacteristic
85C2×C8×C43#4111yescharacteristic
86C2×C8×C43#4111yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43SD1612yes—
91C42×C43—21no—
92C42×C43—41no—
93C16×C43—22no—
94C16×C43—21no—
95C16×C43—21no—
96C23×C43—41no—
97C23×C43C2×SD1611yescharacteristic
98Q8×C43—41no—
99Q8×C43—41no—
100D4×C43—41no—
101D4×C43—41no—
102D4×C43—81no—
103D4×C43—81no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—81no—
107C2×C4×C43—81no—
108C2×C4×C43—81no—
109C2×C4×C43C4×D411yescharacteristic
110C2×C4×C43#12111yescharacteristic
111C2×C4×C43#12411yescharacteristic
112C2×C4×C43C2×D811yescharacteristic
113C2×C4×C43#13511yescharacteristic
114C2×C4×C43#13511yescharacteristic
115C8×C43—22no—
116C8×C43—42no—
117C8×C43—81no—
118C8×C43#11711yescharacteristic
119C8×C43C4×D411yescharacteristic
120C8×C43#12311yescharacteristic
121C8×C43#12611yescharacteristic
122#13146C4311yesmaximal, characteristic, direct product factor, Sylow
123C22×C43—41no—
124C22×C43—81no—
125C22×C43—161no—
126C22×C43C4×SD1611yescharacteristic
127C22×C43#46511yescharacteristic
128C22×C43#48611yescharacteristic
129C4×C43—42no—
130C4×C43—81no—
131C4×C43—161no—
132C4×C43#38811yescharacteristic
133C4×C43C4×D811yescharacteristic
134C4×C43#46611yescharacteristic
135C4×C43#48811yescharacteristic
136#2148C2×C4311yescharacteristic
137C2×#359C2×C4311yescharacteristic
138#2108C2×C4311yescharacteristic, complemented
139#1976C2×C4311yescharacteristic
140#1953C2×C4311yescharacteristic, complemented
141#1389C2×C4311yescharacteristic, complemented
142#1382C2×C4311yescharacteristic, complemented
143C2×C43—21no—
144C2×C43—21no—
145C2×C43—21no—
146C2×C43—161no—
147C2×C43#193411yescharacteristic
148C2×#135C22×C4311yescharacteristic
149C2×M32C22×C4311yescharacteristic
150C22×C16C22×C4311yescharacteristic
151#430—21no—
152C2×#108C22×C4311yescharacteristic
153C2×#108C22×C4311yescharacteristic
154#427C22×C4311yescharacteristic
155#421—21no—
156#410—21no—
157#405C22×C4311yescharacteristic
158#362C4×C4312yescomplemented
159#361C4×C4312yescomplemented
160#359—21no—
161#359—21no—
162#346—21no—
163C4×C16—21no—
164#344—21no—
165C43#1314611yescharacteristic, direct product factor, Sylow
166C2×#41—21no—
167#135—21no—
168#135—21no—
169#135—21no—
170#135—21no—
171C2×Q16C2×C4×C4311yescharacteristic
172C2×SD16—21no—
173C2×D8C2×C4×C4311yescharacteristic
174C2×M16—21no—
175C2×M16—21no—
176C2×M16D4×C4311yescharacteristic
177C22×C8C23×C4311yescharacteristic
178#117—21no—
179#117D4×C4311yescharacteristic
180M32—21no—
181M32C2×C4×C4312yes—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—21no—
185C2×C16D4×C4311yescharacteristic
186C2×C16D4×C4311yescharacteristic
187#108—21no—
188#108—21no—
189#108—21no—
190#108—42no—
191#108C2×C4×C4312yes—
192#107—21no—
193#106—21no—
194#104—42no—
195#99—42no—
196#97—21no—
197C4×C8—21no—
198#41—41no—
199#41—41no—
200#41—41no—
201#41—41no—
202C2×Q8—21no—
203C2×D4—21no—
204C2×D4—41no—
205C22×C4—41no—
206C22×C4C2×D4×C4311yescharacteristic
207Q16—21no—
208Q16—21no—
209SD16—41no—
210SD16—41no—
211D8—21no—
212D8—21no—
213M16—21no—
214M16—22no—
215M16—41no—
216M16—41no—
217M16—41no—
218M16D8×C4312yes—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C22×C4×C4311yescharacteristic
223C2×C8C2×D4×C4311yescharacteristic
224C2×C8#41×C4311yescharacteristic
225C2×C8#41×C4311yescharacteristic
226C2×C8#41×C4311yescharacteristic
227C2×C8#41×C4311yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4SD16×C4312yes—
232C42—21no—
233C42—41no—
234C16—22no—
235C16—21no—
236C16—21no—
237C23—41no—
238C23C2×SD16×C4311yescharacteristic
239Q8—41no—
240Q8—41no—
241D4—41no—
242D4—41no—
243D4—81no—
244D4—81no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4C4×D4×C4311yescharacteristic
251C2×C4#121×C4311yescharacteristic
252C2×C4#124×C4311yescharacteristic
253C2×C4C2×D8×C4311yescharacteristic
254C2×C4#135×C4311yescharacteristic
255C2×C4#135×C4311yescharacteristic
256C8—22no—
257C8—42no—
258C8—81no—
259C8#117×C4311yescharacteristic
260C8C4×D4×C4311yescharacteristic
261C8#123×C4311yescharacteristic
262C8#126×C4311yescharacteristic
263C22—41no—
264C22—81no—
265C22—161no—
266C22C4×SD16×C4311yescharacteristic
267C22C43×#46511yescharacteristic
268C22C43×#48611yescharacteristic
269C4—42no—
270C4—81no—
271C4—161no—
272C4C43×#38811yescharacteristic
273C4C4×D8×C4311yescharacteristic
274C4C43×#46611yescharacteristic
275C4C43×#48811yescharacteristic
276C2—21no—
277C2—21no—
278C2—21no—
279C2—161no—
280C2C43×#193411yescharacteristic
subgroupG/H
centerC4×C43#466
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
socleC2×C43#1934
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
3. C43×#2108C2semidirect
5. C43×#1953C2semidirect
6. C43×#1389C2semidirect
7. C43×#1382C2semidirect
18. C43×#362C4semidirect
19. C43×#361C4semidirect
122. #13146C43direct (N × H)
138. #2108C2×C43semidirect
140. #1953C2×C43semidirect
141. #1389C2×C43semidirect
142. #1382C2×C43semidirect
158. #362C4×C43semidirect
159. #361C4×C43semidirect
165. C43#13146direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#21482
C2×C43×#3592
C43×#21082
C43×#19762
C43×#19532
C43×#13892
C43×#13822
#1314643