Finite Group Databasebeta

← C43×#19137 #24939154

Subgroups — C43×#19137 #24939154

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3160C211yesmaximal, characteristic, complemented
2C43×#3101C212yesmaximal
3C2×C43×#436C211yesmaximal, characteristic
4C43×#1695C212yesmaximal, complemented
5C43×#1693C212yesmaximal, complemented
6C43×#1691C214yesmaximal, complemented
7C43×#1564C211yesmaximal, characteristic, complemented
8C43×#1542C212yesmaximal, complemented
9C22×M16×C43—21no—
10C43×#533C2212yes—
11C2×C4×D4×C43C2211yescharacteristic
12C43×#500C2211yescharacteristic, complemented
13C43×#500C2211yescharacteristic, complemented
14C43×#499—21no—
15C43×#499—21no—
16C43×#498C2212yescomplemented
17C43×#483—22no—
18C43×#476C2214yes—
19C43×#461C2214yes—
20C43×#450—22no—
21C4×SD16×C43—24no—
22C43×#436—21no—
23C43×#436—21no—
24C43×#436C2212yes—
25C43×#436C2212yes—
26C43×#431C2212yes—
27C43×#427—21no—
28C43×#427—21no—
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C22⋊C8×C43—21no—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#335C2212yescomplemented
33C43×#334C2212yescomplemented
34C43×#333C2214yescomplemented
35C43×#332C2214yescomplemented
36C22×D4×C43D411yescharacteristic
37C23×C4×C43—21no—
38C2×SD16×C43—24no—
39C2×M16×C43—22no—
40C2×M16×C43—22no—
41C2×M16×C43—44no—
42C22×C8×C43—21no—
43C22×C8×C43D411yescharacteristic
44C22×C8×C43D411yescharacteristic
45C4⋊Q8×C43C2312yes—
46C4⋊Q8×C43C2312yes—
47#125×C43—22no—
48C22⋊Q8×C43—22no—
49C22⋊Q8×C43—22no—
50C4×Q8×C43—22no—
51C4×Q8×C43—22no—
52C4×D4×C43—21no—
53C4×D4×C43—21no—
54C4×D4×C43D412yes—
55C4×D4×C43C2312yes—
56#117×C43—22no—
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C42×C43C2311yescharacteristic
60#107×C43—21no—
61#107×C43—21no—
62#107×C43—21no—
63#107×C43—21no—
64#106×C43—22no—
65#106×C43—22no—
66#106×C43—24no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43C2312yes—
69C4⋊C8×C43C2314yes—
70#103×C43—24no—
71#102×C43—24no—
72C22⋊C8×C43—22no—
73C22⋊C8×C43—22no—
74C22⋊C8×C43—22no—
75C4×C8×C43—22no—
76C4×C8×C43D411yescharacteristic
77C4×C8×C43D411yescharacteristic
78C4×C8×C43C2311yescharacteristic
79C4×C8×C43C2311yescharacteristic
80C24×C43—21no—
81C2×Q8×C43—22no—
82C2×Q8×C43—22no—
83C2×D4×C43—21no—
84C2×D4×C43—42no—
85C2×D4×C43C2×D412yes—
86C22×C4×C43—22no—
87C22×C4×C43—22no—
88C22×C4×C43—21no—
89C22×C4×C43—42no—
90C22×C4×C43—42no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94SD16×C43—48no—
95M16×C43—44no—
96M16×C43—44no—
97C2×C8×C43—22no—
98C2×C8×C43—24no—
99C2×C8×C43—22no—
100C2×C8×C43—42no—
101C2×C8×C43SD1614yescomplemented
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C4⋊C4×C43—21no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—42no—
112C4⋊C4×C43—42no—
113C4⋊C4×C43C2×D412yes—
114C22⋊C4×C43—22no—
115C22⋊C4×C43—22no—
116C22⋊C4×C43—42no—
117C42×C43—42no—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C42×C43C2411yescharacteristic
122C23×C43—22no—
123C23×C43—42no—
124C23×C43—42no—
125C23×C43—42no—
126C23×C43#12111yescharacteristic
127Q8×C43—44no—
128Q8×C43—82no—
129D4×C43—24no—
130D4×C43—42no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—44no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43C2×SD1612yes—
144C2×C4×C43#13712yes—
145C2×C4×C43C22×D411yescharacteristic
146C2×C4×C43C22×D411yescharacteristic
147C2×C4×C43C2×#4111yescharacteristic
148C8×C43—21no—
149C8×C43—21no—
150C8×C43—42no—
151C8×C43—44no—
152C8×C43C2×SD1612yes—
153C8×C43C2×SD1612yes—
154#19137C4311yesmaximal, characteristic, direct product factor, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—42no—
158C22×C43—42no—
159C22×C43—42no—
160C22×C43—84no—
161C22×C43#46112yes—
162C22×C43C2×#12111yescharacteristic
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—42no—
167C4×C43—82no—
168C4×C43—82no—
169C4×C43#46112yes—
170C4×C43C22×SD1611yescharacteristic
171C4×C43C2×#13711yescharacteristic
172C4×C43#57512yes—
173#3160C2×C4311yescharacteristic, complemented
174#3101C2×C4312yes—
175C2×#436C2×C4311yescharacteristic
176#1695C2×C4312yescomplemented
177#1693C2×C4312yescomplemented
178#1691C2×C4314yescomplemented
179#1564C2×C4311yescharacteristic, complemented
180#1542C2×C4312yescomplemented
181C2×C43—22no—
182C2×C43—82no—
183C2×C43C2×#46111yescharacteristic
184C2×C43#305411yescharacteristic
185C2×C43#306711yescharacteristic
186C22×M16—21no—
187#533C22×C4312yes—
188C2×C4×D4C22×C4311yescharacteristic
189#500C22×C4311yescharacteristic, complemented
190#500C22×C4311yescharacteristic, complemented
191#499—21no—
192#499—21no—
193#498C22×C4312yescomplemented
194#483—22no—
195#476C22×C4314yes—
196#461C22×C4314yes—
197#450—22no—
198C4×SD16—24no—
199#436—21no—
200#436—21no—
201#436C22×C4312yes—
202#436C22×C4312yes—
203#431C22×C4312yes—
204#427—21no—
205#427—21no—
206C2×C4⋊C8C22×C4311yescharacteristic
207C2×C22⋊C8—21no—
208C2×C4×C8C22×C4311yescharacteristic
209#335C22×C4312yescomplemented
210#334C22×C4312yescomplemented
211#333C22×C4314yescomplemented
212#332C22×C4314yescomplemented
213C43#1913711yescharacteristic, direct product factor, Sylow
214C22×D4D4×C4311yescharacteristic
215C23×C4—21no—
216C2×SD16—24no—
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—44no—
220C22×C8—21no—
221C22×C8D4×C4311yescharacteristic
222C22×C8D4×C4311yescharacteristic
223C4⋊Q8C23×C4312yes—
224C4⋊Q8C23×C4312yes—
225#125—22no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C4×Q8—22no—
229C4×Q8—22no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4D4×C4312yes—
233C4×D4C23×C4312yes—
234#117—22no—
235C2×C4⋊C4D4×C4311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C42C23×C4311yescharacteristic
238#107—21no—
239#107—21no—
240#107—21no—
241#107—21no—
242#106—22no—
243#106—22no—
244#106—24no—
245C4⋊C8—21no—
246C4⋊C8C23×C4312yes—
247C4⋊C8C23×C4314yes—
248#103—24no—
249#102—24no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C22⋊C8—22no—
253C4×C8—22no—
254C4×C8D4×C4311yescharacteristic
255C4×C8D4×C4311yescharacteristic
256C4×C8C23×C4311yescharacteristic
257C4×C8C23×C4311yescharacteristic
258C24—21no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×D4—21no—
262C2×D4—42no—
263C2×D4C2×D4×C4312yes—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4C2×D4×C4311yescharacteristic
270C22×C4C2×D4×C4311yescharacteristic
271C22×C4#41×C4311yescharacteristic
272SD16—48no—
273M16—44no—
274M16—44no—
275C2×C8—22no—
276C2×C8—24no—
277C2×C8—22no—
278C2×C8—42no—
279C2×C8SD16×C4314yescomplemented
280C2×C8C2×D4×C4311yescharacteristic
281C2×C8C2×D4×C4311yescharacteristic
282C2×C8C2×D4×C4311yescharacteristic
283C2×C8C2×D4×C4311yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4C2×D4×C4312yes—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—42no—
295C42—42no—
296C42C2×D4×C4311yescharacteristic
297C42C2×D4×C4311yescharacteristic
298C42#41×C4311yescharacteristic
299C42C24×C4311yescharacteristic
300C23—22no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23#121×C4311yescharacteristic
305Q8—44no—
306Q8—82no—
307D4—24no—
308D4—42no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4#121×C4311yescharacteristic
319C2×C4#121×C4311yescharacteristic
320C2×C4#121×C4311yescharacteristic
321C2×C4C2×SD16×C4312yes—
322C2×C4#137×C4312yes—
323C2×C4C22×D4×C4311yescharacteristic
324C2×C4C22×D4×C4311yescharacteristic
325C2×C4C2×#41×C4311yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8—44no—
330C8C2×SD16×C4312yes—
331C8C2×SD16×C4312yes—
332C22—21no—
333C22—21no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—84no—
338C22C43×#46112yes—
339C22C2×#121×C4311yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—42no—
344C4—82no—
345C4—82no—
346C4C43×#46112yes—
347C4C22×SD16×C4311yescharacteristic
348C4C2×#137×C4311yescharacteristic
349C4C43×#57512yes—
350C2—22no—
351C2—82no—
352C2C2×C43×#46111yescharacteristic
353C2C43×#305411yescharacteristic
354C2C43×#306711yescharacteristic
subgroupG/H
centerC2×C4×C43#121
commutator, Frattini, cosocleC42C24×C43
socleC22×C43C2×#121
prime radicalC22×D4×C43D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3160C2semidirect
4. C43×#1695C2semidirect
5. C43×#1693C2semidirect
6. C43×#1691C2semidirect
7. C43×#1564C2semidirect
8. C43×#1542C2semidirect
12. C43×#500C22semidirect
13. C43×#500C22semidirect
16. C43×#498C22semidirect
32. C43×#335C22semidirect
33. C43×#334C22semidirect
34. C43×#333C22semidirect
35. C43×#332C22semidirect
101. C2×C8×C43SD16semidirect
154. #19137C43direct (N × H)
173. #3160C2×C43semidirect
176. #1695C2×C43semidirect
177. #1693C2×C43semidirect
178. #1691C2×C43semidirect
179. #1564C2×C43semidirect
180. #1542C2×C43semidirect
189. #500C22×C43semidirect
190. #500C22×C43semidirect
193. #498C22×C43semidirect
209. #335C22×C43semidirect
210. #334C22×C43semidirect
211. #333C22×C43semidirect
212. #332C22×C43semidirect
213. C43#19137direct (N × H)
279. C2×C8SD16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31602
C43×#31012
C2×C43×#4362
C43×#16952
C43×#16932
C43×#16912
C43×#15642
C43×#15422
#1913743