Finite Group Databasebeta

← C43×#13402 #24933419

Subgroups — C43×#13402 #24933419

Order 11008.

404 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#472C211yesmaximal, characteristic
2C43×#2155C211yesmaximal, characteristic, complemented
3C2×C43×#361C211yesmaximal, characteristic, complemented
4C43×#2140C211yesmaximal, characteristic, complemented
5C43×#2115C211yesmaximal, characteristic, complemented
6C43×#1814C211yesmaximal, characteristic, complemented
7C43×#1388C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C43—21no—
9C22×D8×C43C2211yescharacteristic
10C2×#131×C43C2211yescharacteristic
11C2×M32×C43C2211yescharacteristic
12C2×M32×C43C2211yescharacteristic
13C43×#472—22no—
14C43×#472—22no—
15C2×#108×C43C2211yescharacteristic
16C2×#108×C43C2211yescharacteristic
17C43×#427C2211yescharacteristic
18C43×#421—21no—
19C2×#100×C43—21no—
20C43×#365—22no—
21C43×#361—22no—
22C43×#357—22no—
23C43×#349—22no—
24C43×#344—21no—
25C2×#41×C43D411yescharacteristic
26C22×D4×C43—21no—
27AGL(1,ℤ/8)×C43—24no—
28AGL(1,ℤ/8)×C43—42no—
29C2×SD16×C43—41no—
30C2×D8×C43—21no—
31C2×D8×C43—21no—
32C2×D8×C43—21no—
33C2×D8×C43—21no—
34C2×D8×C43—21no—
35C2×D8×C43—41no—
36C2×D8×C43D412yes—
37#131×C43—21no—
38#131×C43—21no—
39#131×C43—21no—
40#131×C43—21no—
41C2×M16×C43—21no—
42C2×M16×C43—21no—
43C2×M16×C43—21no—
44C2×M16×C43D411yescharacteristic
45C22×C8×C43—21no—
46C22×C8×C43C2311yescharacteristic
47#117×C43—21no—
48M32×C43—21no—
49M32×C43—21no—
50M32×C43—21no—
51M32×C43D412yes—
52C2×C16×C43—21no—
53C2×C16×C43—21no—
54#108×C43—21no—
55#108×C43—21no—
56#108×C43—21no—
57#108×C43D412yes—
58#107×C43—21no—
59#106×C43—21no—
60#104×C43—42no—
61#100×C43—24no—
62C24×C43—41no—
63#41×C43—21no—
64#41×C43—21no—
65#41×C43—21no—
66#41×C43—21no—
67C2×Q8×C43SD1611yescharacteristic
68C2×D4×C43—21no—
69C2×D4×C43—22no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43SD1611yescharacteristic
76C22×C4×C43—21no—
77C22×C4×C43C2×D411yescharacteristic
78SD16×C43—44no—
79D8×C43—22no—
80D8×C43—22no—
81D8×C43—44no—
82D8×C43—41no—
83D8×C43—41no—
84M16×C43—21no—
85M16×C43—22no—
86M16×C43—21no—
87M16×C43—41no—
88M16×C43—41no—
89M16×C43—41no—
90M16×C43—41no—
91M16×C43—41no—
92C2×C8×C43—21no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C4⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C42×C43—41no—
106C16×C43—22no—
107C16×C43—41no—
108C23×C43—21no—
109C23×C43—42no—
110C23×C43—81no—
111C23×C43—81no—
112C23×C43—162no—
113C23×C43#13511yescharacteristic
114Q8×C43—21no—
115Q8×C43—21no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—41no—
119D4×C43—41no—
120D4×C43—42no—
121D4×C43—42no—
122D4×C43—81no—
123D4×C43—81no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—81no—
128C2×C4×C43#12011yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12311yescharacteristic
131C2×C4×C43C2×SD1611yescharacteristic
132C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
134C8×C43—41no—
135C8×C43—42no—
136C8×C43—81no—
137C8×C43#12111yescharacteristic
138C8×C43#12111yescharacteristic
139C8×C43#12311yescharacteristic
140C8×C43#12411yescharacteristic
141#13402C4311yesmaximal, characteristic, direct product factor, Sylow
142C22×C43—41no—
143C22×C43—41no—
144C22×C43—81no—
145C22×C43—82no—
146C22×C43—162no—
147C22×C43—162no—
148C22×C43—162no—
149C22×C43#44911yescharacteristic
150C22×C43#46511yescharacteristic
151C22×C43#48211yescharacteristic
152C4×C43—41no—
153C4×C43—161no—
154C4×C43#39411yescharacteristic
155C4×C43#45011yescharacteristic
156C4×C43#46911yescharacteristic
157C4×C43#48111yescharacteristic
158C2×#472C2×C4311yescharacteristic
159#2155C2×C4311yescharacteristic, complemented
160C2×#361C2×C4311yescharacteristic, complemented
161#2140C2×C4311yescharacteristic, complemented
162#2115C2×C4311yescharacteristic, complemented
163#1814C2×C4311yescharacteristic, complemented
164#1388C2×C4311yescharacteristic, complemented
165C2×C43—21no—
166C2×C43—21no—
167C2×C43—21no—
168C2×C43—81no—
169C2×C43—162no—
170C2×C43#203411yescharacteristic
171C2×AGL(1,ℤ/8)—21no—
172C22×D8C22×C4311yescharacteristic
173C2×#131C22×C4311yescharacteristic
174C2×M32C22×C4311yescharacteristic
175C2×M32C22×C4311yescharacteristic
176#472—22no—
177#472—22no—
178C2×#108C22×C4311yescharacteristic
179C2×#108C22×C4311yescharacteristic
180#427C22×C4311yescharacteristic
181#421—21no—
182C2×#100—21no—
183#365—22no—
184#361—22no—
185#357—22no—
186#349—22no—
187#344—21no—
188C43#1340211yescharacteristic, direct product factor, Sylow
189C2×#41D4×C4311yescharacteristic
190C22×D4—21no—
191AGL(1,ℤ/8)—24no—
192AGL(1,ℤ/8)—42no—
193C2×SD16—41no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8—41no—
200C2×D8D4×C4312yes—
201#131—21no—
202#131—21no—
203#131—21no—
204#131—21no—
205C2×M16—21no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16D4×C4311yescharacteristic
209C22×C8—21no—
210C22×C8C23×C4311yescharacteristic
211#117—21no—
212M32—21no—
213M32—21no—
214M32—21no—
215M32D4×C4312yes—
216C2×C16—21no—
217C2×C16—21no—
218#108—21no—
219#108—21no—
220#108—21no—
221#108D4×C4312yes—
222#107—21no—
223#106—21no—
224#104—42no—
225#100—24no—
226C24—41no—
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231C2×Q8SD16×C4311yescharacteristic
232C2×D4—21no—
233C2×D4—22no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4SD16×C4311yescharacteristic
240C22×C4—21no—
241C22×C4C2×D4×C4311yescharacteristic
242SD16—44no—
243D8—22no—
244D8—22no—
245D8—44no—
246D8—41no—
247D8—41no—
248M16—21no—
249M16—22no—
250M16—21no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—41no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8C2×D4×C4311yescharacteristic
262C2×C8C2×D4×C4311yescharacteristic
263C2×C8C2×D4×C4311yescharacteristic
264C2×C8#41×C4311yescharacteristic
265C2×C8#41×C4311yescharacteristic
266C2×C8#41×C4311yescharacteristic
267C4⋊C4—41no—
268C22⋊C4—41no—
269C42—41no—
270C16—22no—
271C16—41no—
272C23—21no—
273C23—42no—
274C23—81no—
275C23—81no—
276C23—162no—
277C23#135×C4311yescharacteristic
278Q8—21no—
279Q8—21no—
280D4—21no—
281D4—21no—
282D4—41no—
283D4—41no—
284D4—42no—
285D4—42no—
286D4—81no—
287D4—81no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4#120×C4311yescharacteristic
293C2×C4#121×C4311yescharacteristic
294C2×C4#123×C4311yescharacteristic
295C2×C4C2×SD16×C4311yescharacteristic
296C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
297C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
298C8—41no—
299C8—42no—
300C8—81no—
301C8#121×C4311yescharacteristic
302C8#121×C4311yescharacteristic
303C8#123×C4311yescharacteristic
304C8#124×C4311yescharacteristic
305C22—41no—
306C22—41no—
307C22—81no—
308C22—82no—
309C22—162no—
310C22—162no—
311C22—162no—
312C22C43×#44911yescharacteristic
313C22C43×#46511yescharacteristic
314C22C43×#48211yescharacteristic
315C4—41no—
316C4—161no—
317C4C43×#39411yescharacteristic
318C4C43×#45011yescharacteristic
319C4C43×#46911yescharacteristic
320C4C43×#48111yescharacteristic
321C2—21no—
322C2—21no—
323C2—21no—
324C2—81no—
325C2—162no—
326C2C43×#203411yescharacteristic
subgroupG/H
center, socleC2×C43#2034
commutator, Frattini, cosocleC22×C8C23×C43
prime radicalC2×C43×#472C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C4×C43 ◁ C2×#131×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2155C2semidirect
3. C2×C43×#361C2semidirect
4. C43×#2140C2semidirect
5. C43×#2115C2semidirect
6. C43×#1814C2semidirect
7. C43×#1388C2semidirect
141. #13402C43direct (N × H)
159. #2155C2×C43semidirect
160. C2×#361C2×C43semidirect
161. #2140C2×C43semidirect
162. #2115C2×C43semidirect
163. #1814C2×C43semidirect
164. #1388C2×C43semidirect
188. C43#13402direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4722
C43×#21552
C2×C43×#3612
C43×#21402
C43×#21152
C43×#18142
C43×#13882
#1340243