Finite Group Databasebeta

← C43×#13247 #24933264

Subgroups — C43×#13247 #24933264

Order 11008.

414 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#509C211yesmaximal, characteristic
2C43×#2155C211yesmaximal, characteristic, complemented
3C43×#2143C211yesmaximal, characteristic, complemented
4C43×#2140C211yesmaximal, characteristic, complemented
5C43×#2110C211yesmaximal, characteristic, complemented
6C43×#1978C211yesmaximal, characteristic, complemented
7C43×#1976C211yesmaximal, characteristic, complemented
8C2×#135×C43C2211yescharacteristic
9C22×D8×C43C2211yescharacteristic
10C43×#509—22no—
11C43×#509—22no—
12C2×SD32×C43C412yescomplemented
13C2×D16×C43C412yescomplemented
14C2×M32×C43C2211yescharacteristic
15C2×M32×C43C2211yescharacteristic
16C2×#108×C43C2211yescharacteristic
17C43×#427C2211yescharacteristic
18C43×#421—21no—
19C43×#418—21no—
20C2×#100×C43—21no—
21C43×#410—21no—
22C43×#405C2211yescharacteristic
23C43×#365—22no—
24C43×#359—22no—
25C43×#357—22no—
26C43×#347—22no—
27C2×#41×C43—21no—
28C22×D4×C43—21no—
29#135×C43—21no—
30#135×C43—21no—
31#135×C43—21no—
32#135×C43—21no—
33C2×Q16×C43C2×C411yescharacteristic
34C2×SD16×C43—21no—
35C2×D8×C43—21no—
36C2×D8×C43—21no—
37C2×D8×C43—21no—
38C2×D8×C43—21no—
39C2×D8×C43—21no—
40C2×D8×C43C2×C411yescharacteristic
41C2×D8×C43C2×C412yes—
42C2×M16×C43—21no—
43C2×M16×C43D411yescharacteristic
44C22×C8×C43C2311yescharacteristic
45#117×C43—21no—
46#117×C43D411yescharacteristic
47SD32×C43—24no—
48D16×C43—24no—
49M32×C43—21no—
50M32×C43—21no—
51M32×C43D412yes—
52M32×C43D412yes—
53C2×C16×C43C2×C412yes—
54C2×C16×C43D412yes—
55#108×C43—21no—
56#108×C43—21no—
57#107×C43—21no—
58#106×C43—21no—
59#104×C43—42no—
60#102×C43—42no—
61#100×C43—42no—
62#99×C43—42no—
63#97×C43—21no—
64C4×C8×C43—21no—
65C24×C43—41no—
66#41×C43—41no—
67#41×C43—41no—
68#41×C43—41no—
69#41×C43—41no—
70C2×Q8×C43—21no—
71C2×D4×C43—22no—
72C2×D4×C43—21no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D411yescharacteristic
81Q16×C43—21no—
82Q16×C43—21no—
83SD16×C43—41no—
84SD16×C43—41no—
85D8×C43—21no—
86D8×C43—22no—
87D8×C43—22no—
88D8×C43—21no—
89D8×C43—41no—
90D8×C43—41no—
91M16×C43—21no—
92M16×C43—21no—
93M16×C43—41no—
94M16×C43—41no—
95C2×C8×C43—21no—
96C2×C8×C43—41no—
97C2×C8×C43C22×C411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43—41no—
107C42×C43—21no—
108C42×C43—41no—
109C16×C43—22no—
110C16×C43C22⋊C414yes—
111C23×C43—41no—
112C23×C43—42no—
113C23×C43—81no—
114C23×C43—81no—
115C23×C43—162no—
116C23×C43AGL(1,ℤ/8)11yescharacteristic
117Q8×C43—41no—
118Q8×C43—41no—
119D4×C43—42no—
120D4×C43—41no—
121D4×C43—42no—
122D4×C43—41no—
123D4×C43—81no—
124D4×C43—81no—
125D4×C43—81no—
126D4×C43—81no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12711yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C8×C43—41no—
139C8×C43—81no—
140C8×C43C2×C22⋊C411yescharacteristic
141C8×C43C4×D411yescharacteristic
142C8×C43#12111yescharacteristic
143C8×C43#12411yescharacteristic
144#13247C4311yesmaximal, characteristic, direct product factor, Sylow
145C22×C43—41no—
146C22×C43—82no—
147C22×C43—81no—
148C22×C43—161no—
149C22×C43—162no—
150C22×C43—162no—
151C22×C43—162no—
152C22×C43#44211yescharacteristic
153C22×C43#46911yescharacteristic
154C22×C43#49611yescharacteristic
155C4×C43—81no—
156C4×C43—81no—
157C4×C43—161no—
158C4×C43#39011yescharacteristic
159C4×C43#44211yescharacteristic
160C4×C43#46911yescharacteristic
161C4×C43#49611yescharacteristic
162C2×#509C2×C4311yescharacteristic
163#2155C2×C4311yescharacteristic, complemented
164#2143C2×C4311yescharacteristic, complemented
165#2140C2×C4311yescharacteristic, complemented
166#2110C2×C4311yescharacteristic, complemented
167#1978C2×C4311yescharacteristic, complemented
168#1976C2×C4311yescharacteristic, complemented
169C2×C43—21no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—161no—
173C2×C43—162no—
174C2×C43#197211yescharacteristic
175C2×#135C22×C4311yescharacteristic
176C22×D8C22×C4311yescharacteristic
177#509—22no—
178#509—22no—
179C2×SD32C4×C4312yescomplemented
180C2×D16C4×C4312yescomplemented
181C2×M32C22×C4311yescharacteristic
182C2×M32C22×C4311yescharacteristic
183C2×#108C22×C4311yescharacteristic
184#427C22×C4311yescharacteristic
185#421—21no—
186#418—21no—
187C2×#100—21no—
188#410—21no—
189#405C22×C4311yescharacteristic
190#365—22no—
191#359—22no—
192#357—22no—
193#347—22no—
194C43#1324711yescharacteristic, direct product factor, Sylow
195C2×#41—21no—
196C22×D4—21no—
197#135—21no—
198#135—21no—
199#135—21no—
200#135—21no—
201C2×Q16C2×C4×C4311yescharacteristic
202C2×SD16—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8C2×C4×C4312yes—
209C2×D8C2×C4×C4311yescharacteristic
210C2×M16—21no—
211C2×M16D4×C4311yescharacteristic
212C22×C8C23×C4311yescharacteristic
213#117—21no—
214#117D4×C4311yescharacteristic
215SD32—24no—
216D16—24no—
217M32—21no—
218M32—21no—
219M32D4×C4312yes—
220M32D4×C4312yes—
221C2×C16C2×C4×C4312yes—
222C2×C16D4×C4312yes—
223#108—21no—
224#108—21no—
225#107—21no—
226#106—21no—
227#104—42no—
228#102—42no—
229#100—42no—
230#99—42no—
231#97—21no—
232C4×C8—21no—
233C24—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C22×C4—41no—
248C22×C4C2×D4×C4311yescharacteristic
249Q16—21no—
250Q16—21no—
251SD16—41no—
252SD16—41no—
253D8—21no—
254D8—22no—
255D8—22no—
256D8—21no—
257D8—41no—
258D8—41no—
259M16—21no—
260M16—21no—
261M16—41no—
262M16—41no—
263C2×C8—21no—
264C2×C8—41no—
265C2×C8C22×C4×C4311yescharacteristic
266C2×C8C2×D4×C4311yescharacteristic
267C2×C8C2×D4×C4311yescharacteristic
268C2×C8C2×D4×C4311yescharacteristic
269C2×C8#41×C4311yescharacteristic
270C2×C8#41×C4311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—41no—
273C22⋊C4—21no—
274C22⋊C4—41no—
275C42—21no—
276C42—41no—
277C16—22no—
278C16C22⋊C4×C4314yes—
279C23—41no—
280C23—42no—
281C23—81no—
282C23—81no—
283C23—162no—
284C23AGL(1,ℤ/8)×C4311yescharacteristic
285Q8—41no—
286Q8—41no—
287D4—42no—
288D4—41no—
289D4—42no—
290D4—41no—
291D4—81no—
292D4—81no—
293D4—81no—
294D4—81no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4C4×D4×C4311yescharacteristic
301C2×C4#121×C4311yescharacteristic
302C2×C4#127×C4311yescharacteristic
303C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
304C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
305C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
306C8—41no—
307C8—81no—
308C8C2×C22⋊C4×C4311yescharacteristic
309C8C4×D4×C4311yescharacteristic
310C8#121×C4311yescharacteristic
311C8#124×C4311yescharacteristic
312C22—41no—
313C22—81no—
314C22—82no—
315C22—162no—
316C22—161no—
317C22—162no—
318C22—162no—
319C22C43×#44211yescharacteristic
320C22C43×#46911yescharacteristic
321C22C43×#49611yescharacteristic
322C4—81no—
323C4—81no—
324C4—161no—
325C4C43×#39011yescharacteristic
326C4C43×#44211yescharacteristic
327C4C43×#46911yescharacteristic
328C4C43×#49611yescharacteristic
329C2—21no—
330C2—21no—
331C2—21no—
332C2—162no—
333C2—161no—
334C2C43×#197211yescharacteristic
subgroupG/H
center, socleC2×C43#1972
commutatorC2×C8C22×C4×C43
Frattini, cosocleC22×C8C23×C43
prime radicalC2×C43×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C43 ◁ C22×C4×C43 ◁ C43×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2155C2semidirect
3. C43×#2143C2semidirect
4. C43×#2140C2semidirect
5. C43×#2110C2semidirect
6. C43×#1978C2semidirect
7. C43×#1976C2semidirect
12. C2×SD32×C43C4semidirect
13. C2×D16×C43C4semidirect
144. #13247C43direct (N × H)
163. #2155C2×C43semidirect
164. #2143C2×C43semidirect
165. #2140C2×C43semidirect
166. #2110C2×C43semidirect
167. #1978C2×C43semidirect
168. #1976C2×C43semidirect
179. C2×SD32C4×C43semidirect
180. C2×D16C4×C43semidirect
194. C43#13247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5092
C43×#21552
C43×#21432
C43×#21402
C43×#21102
C43×#19782
C43×#19762
#1324743