Finite Group Databasebeta

← C43×#13144 #24933161

Subgroups — C43×#13144 #24933161

Order 11008.

334 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#361C211yesmaximal, characteristic
2C2×C43×#357C211yesmaximal, characteristic
3C43×#2108C211yesmaximal, characteristic, complemented
4C43×#1978C211yesmaximal, characteristic
5C43×#1952C211yesmaximal, characteristic, complemented
6C43×#1387C211yesmaximal, characteristic, complemented
7C43×#1381C211yesmaximal, characteristic, complemented
8C22×D8×C43C2211yescharacteristic
9C2×M32×C43C2211yescharacteristic
10C22×C16×C43C2211yescharacteristic
11C2×#108×C43C2211yescharacteristic
12C2×#108×C43C2211yescharacteristic
13C43×#428—21no—
14C2×#107×C43C2211yescharacteristic
15C43×#418—21no—
16C2×#100×C43—21no—
17C43×#405C2211yescharacteristic
18C43×#361C414yescomplemented
19C43×#357—21no—
20C43×#357—21no—
21C43×#346—21no—
22C4×C16×C43—21no—
23C43×#343—21no—
24C22×D4×C43—21no—
25C2×D8×C43—21no—
26C2×D8×C43—21no—
27C2×D8×C43—21no—
28C2×D8×C43—21no—
29C2×D8×C43—21no—
30C2×D8×C43C2×C412yes—
31C2×M16×C43—21no—
32C2×M16×C43—21no—
33C2×M16×C43D411yescharacteristic
34C22×C8×C43C2311yescharacteristic
35#117×C43D411yescharacteristic
36C2×C4⋊C4×C43—21no—
37M32×C43—21no—
38M32×C43C2×C412yes—
39C2×C16×C43—21no—
40C2×C16×C43—21no—
41C2×C16×C43—21no—
42C2×C16×C43D411yescharacteristic
43C2×C16×C43D411yescharacteristic
44#108×C43—21no—
45#108×C43—21no—
46#108×C43—21no—
47#108×C43C2×C412yes—
48#107×C43—21no—
49#107×C43—21no—
50#107×C43—41no—
51#106×C43—41no—
52#102×C43—41no—
53#102×C43—41no—
54#100×C43—42no—
55#97×C43—21no—
56C4×C8×C43—21no—
57C24×C43—41no—
58C2×D4×C43—22no—
59C2×D4×C43—41no—
60C2×D4×C43—41no—
61C2×D4×C43—41no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43C2×D411yescharacteristic
66D8×C43—22no—
67D8×C43—22no—
68D8×C43—41no—
69D8×C43—41no—
70M16×C43—21no—
71M16×C43—22no—
72M16×C43—41no—
73M16×C43—41no—
74M16×C43—41no—
75M16×C43SD1612yes—
76C2×C8×C43—21no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43C22×C411yescharacteristic
80C2×C8×C43C2×D411yescharacteristic
81C2×C8×C43#4111yescharacteristic
82C2×C8×C43#4111yescharacteristic
83C2×C8×C43#4111yescharacteristic
84C2×C8×C43#4111yescharacteristic
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43D811yescharacteristic
88C4⋊C4×C43D811yescharacteristic
89C22⋊C4×C43—21no—
90C42×C43—21no—
91C16×C43—22no—
92C16×C43—21no—
93C16×C43—21no—
94C23×C43—42no—
95C23×C43—81no—
96C23×C43—81no—
97C23×C43—161no—
98C23×C43—161no—
99C23×C43#13511yescharacteristic
100D4×C43—42no—
101D4×C43—42no—
102D4×C43—81no—
103D4×C43—81no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—81no—
107C2×C4×C43—161no—
108C2×C4×C43C4×D411yescharacteristic
109C2×C4×C43#12111yescharacteristic
110C2×C4×C43#12411yescharacteristic
111C2×C4×C43C2×D811yescharacteristic
112C2×C4×C43C2×SD1611yescharacteristic
113C2×C4×C43#13511yescharacteristic
114C8×C43—22no—
115C8×C43—42no—
116C8×C43—81no—
117C8×C43#11711yescharacteristic
118C8×C43C4×D411yescharacteristic
119C8×C43#12311yescharacteristic
120C8×C43#12611yescharacteristic
121#13144C4311yesmaximal, characteristic, direct product factor, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—82no—
125C22×C43—162no—
126C22×C43—162no—
127C22×C43—161no—
128C22×C43—161no—
129C22×C43C4×SD1611yescharacteristic
130C22×C43#46611yescharacteristic
131C22×C43#48811yescharacteristic
132C4×C43—41no—
133C4×C43—41no—
134C4×C43—161no—
135C4×C43#38811yescharacteristic
136C4×C43C4×D811yescharacteristic
137C4×C43#46511yescharacteristic
138C4×C43#48611yescharacteristic
139C2×#361C2×C4311yescharacteristic
140C2×#357C2×C4311yescharacteristic
141#2108C2×C4311yescharacteristic, complemented
142#1978C2×C4311yescharacteristic
143#1952C2×C4311yescharacteristic, complemented
144#1387C2×C4311yescharacteristic, complemented
145#1381C2×C4311yescharacteristic, complemented
146C2×C43—21no—
147C2×C43—21no—
148C2×C43—162no—
149C2×C43#193411yescharacteristic
150C2×C43#222111yescharacteristic
151C2×C43#222311yescharacteristic
152C22×D8C22×C4311yescharacteristic
153C2×M32C22×C4311yescharacteristic
154C22×C16C22×C4311yescharacteristic
155C2×#108C22×C4311yescharacteristic
156C2×#108C22×C4311yescharacteristic
157#428—21no—
158C2×#107C22×C4311yescharacteristic
159#418—21no—
160C2×#100—21no—
161#405C22×C4311yescharacteristic
162#361C4×C4314yescomplemented
163#357—21no—
164#357—21no—
165#346—21no—
166C4×C16—21no—
167#343—21no—
168C43#1314411yescharacteristic, direct product factor, Sylow
169C22×D4—21no—
170C2×D8—21no—
171C2×D8—21no—
172C2×D8—21no—
173C2×D8—21no—
174C2×D8—21no—
175C2×D8C2×C4×C4312yes—
176C2×M16—21no—
177C2×M16—21no—
178C2×M16D4×C4311yescharacteristic
179C22×C8C23×C4311yescharacteristic
180#117D4×C4311yescharacteristic
181C2×C4⋊C4—21no—
182M32—21no—
183M32C2×C4×C4312yes—
184C2×C16—21no—
185C2×C16—21no—
186C2×C16—21no—
187C2×C16D4×C4311yescharacteristic
188C2×C16D4×C4311yescharacteristic
189#108—21no—
190#108—21no—
191#108—21no—
192#108C2×C4×C4312yes—
193#107—21no—
194#107—21no—
195#107—41no—
196#106—41no—
197#102—41no—
198#102—41no—
199#100—42no—
200#97—21no—
201C4×C8—21no—
202C24—41no—
203C2×D4—22no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C22×C4—41no—
210C22×C4C2×D4×C4311yescharacteristic
211D8—22no—
212D8—22no—
213D8—41no—
214D8—41no—
215M16—21no—
216M16—22no—
217M16—41no—
218M16—41no—
219M16—41no—
220M16SD16×C4312yes—
221C2×C8—21no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8C22×C4×C4311yescharacteristic
225C2×C8C2×D4×C4311yescharacteristic
226C2×C8#41×C4311yescharacteristic
227C2×C8#41×C4311yescharacteristic
228C2×C8#41×C4311yescharacteristic
229C2×C8#41×C4311yescharacteristic
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4D8×C4311yescharacteristic
233C4⋊C4D8×C4311yescharacteristic
234C22⋊C4—21no—
235C42—21no—
236C16—22no—
237C16—21no—
238C16—21no—
239C23—42no—
240C23—81no—
241C23—81no—
242C23—161no—
243C23—161no—
244C23#135×C4311yescharacteristic
245D4—42no—
246D4—42no—
247D4—81no—
248D4—81no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—81no—
252C2×C4—161no—
253C2×C4C4×D4×C4311yescharacteristic
254C2×C4#121×C4311yescharacteristic
255C2×C4#124×C4311yescharacteristic
256C2×C4C2×D8×C4311yescharacteristic
257C2×C4C2×SD16×C4311yescharacteristic
258C2×C4#135×C4311yescharacteristic
259C8—22no—
260C8—42no—
261C8—81no—
262C8#117×C4311yescharacteristic
263C8C4×D4×C4311yescharacteristic
264C8#123×C4311yescharacteristic
265C8#126×C4311yescharacteristic
266C22—21no—
267C22—21no—
268C22—82no—
269C22—162no—
270C22—162no—
271C22—161no—
272C22—161no—
273C22C4×SD16×C4311yescharacteristic
274C22C43×#46611yescharacteristic
275C22C43×#48811yescharacteristic
276C4—41no—
277C4—41no—
278C4—161no—
279C4C43×#38811yescharacteristic
280C4C4×D8×C4311yescharacteristic
281C4C43×#46511yescharacteristic
282C4C43×#48611yescharacteristic
283C2—21no—
284C2—21no—
285C2—162no—
286C2C43×#193411yescharacteristic
287C2C43×#222111yescharacteristic
288C2C43×#222311yescharacteristic
subgroupG/H
center, socleC22×C43#466
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
prime radicalC22×D8×C43C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×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×#1952C2semidirect
6. C43×#1387C2semidirect
7. C43×#1381C2semidirect
18. C43×#361C4semidirect
121. #13144C43direct (N × H)
141. #2108C2×C43semidirect
143. #1952C2×C43semidirect
144. #1387C2×C43semidirect
145. #1381C2×C43semidirect
162. #361C4×C43semidirect
168. C43#13144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#3612
C2×C43×#3572
C43×#21082
C43×#19782
C43×#19522
C43×#13872
C43×#13812
#1314443