Finite Group Databasebeta

← C43×#29533 #24949550

Subgroups — C43×#29533 #24949550

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2293C212yesmaximal, complemented
2C43×#2087C211yesmaximal, characteristic, complemented
3C43×#2065C212yesmaximal, complemented
4C43×#2054C211yesmaximal, characteristic
5C43×#1925C212yesmaximal, complemented
6C43×#1920C212yesmaximal, complemented
7C43×#1879C212yesmaximal
8C43×#1864C212yesmaximal, complemented
9C43×#1831C211yesmaximal, characteristic, complemented
10C22×D8×C43C2211yescharacteristic
11C2×C4×D4×C43C2212yes—
12C2×#117×C43—22no—
13C2×#107×C43C2211yescharacteristic
14C2×#106×C43C2212yes—
15C2×C4⋊C8×C43C2211yescharacteristic
16C2×C4⋊C8×C43C2211yescharacteristic
17C2×#102×C43C2212yes—
18C2×#102×C43C2212yes—
19C2×#102×C43C2212yes—
20C43×#390C2212yes—
21C43×#390C2212yes—
22C43×#389C2212yes—
23C43×#389C2212yes—
24C43×#388—22no—
25C43×#388—22no—
26C4×C4⋊C4×C43C2212yes—
27C4×C22⋊C4×C43—22no—
28C43×C43C2211yescharacteristic
29C43×#340C2212yes—
30C43×#340C2211yescharacteristic
31C43×#340C2212yes—
32C43×#340C2211yescharacteristic
33C43×#336C2212yes—
34C43×#336C2212yes—
35C22×D4×C43C2312yes—
36C23×C4×C43—22no—
37C2×D8×C43—24no—
38C2×D8×C43—41no—
39C22×C8×C43C2311yescharacteristic
40C22×C8×C43C2312yes—
41C22×C8×C43C2311yescharacteristic
42C4×D4×C43—24no—
43C4×D4×C43—24no—
44#117×C43—48no—
45C2×C4⋊C4×C43—22no—
46C2×C4⋊C4×C43—22no—
47C2×C4⋊C4×C43C2312yes—
48C2×C4⋊C4×C43C2312yes—
49C2×C4⋊C4×C43C2312yes—
50C2×C22⋊C4×C43—22no—
51C2×C22⋊C4×C43—22no—
52C2×C22⋊C4×C43—22no—
53C2×C22⋊C4×C43—22no—
54C2×C22⋊C4×C43—22no—
55C2×C42×C43—22no—
56C2×C42×C43D412yes—
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43C2312yes—
60C2×C42×C43C2311yescharacteristic
61#107×C43—41no—
62#106×C43—24no—
63C4⋊C8×C43—41no—
64C4⋊C8×C43—41no—
65#102×C43—24no—
66#102×C43—24no—
67#102×C43—42no—
68#95×C43—22no—
69#95×C43—22no—
70#95×C43—22no—
71C24×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—22no—
74C2×D4×C43—22no—
75C2×D4×C43—22no—
76C2×D4×C43—22no—
77C2×D4×C43#4114yes—
78C22×C4×C43—28no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—44no—
83C22×C4×C43—44no—
84C22×C4×C43C2×D412yes—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2411yescharacteristic
89D8×C43—44no—
90C2×C8×C43—22no—
91C2×C8×C43—22no—
92C2×C8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43—22no—
95C2×C8×C43—21no—
96C2×C8×C43—21no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—44no—
103C4⋊C4×C43—44no—
104C4⋊C4×C43#4114yes—
105C22⋊C4×C43—28no—
106C22⋊C4×C43—44no—
107C22⋊C4×C43—44no—
108C22⋊C4×C43—44no—
109C22⋊C4×C43—44no—
110C42×C43—22no—
111C42×C43—24no—
112C42×C43—22no—
113C42×C43—22no—
114C42×C43—21no—
115C42×C43—21no—
116C42×C43—41no—
117C42×C43—44no—
118C23×C43—24no—
119C23×C43—42no—
120C23×C43—42no—
121C23×C43—42no—
122C23×C43—42no—
123C23×C43—42no—
124C23×C43—42no—
125C23×C43C22×D411yescharacteristic
126D4×C43—24no—
127D4×C43—24no—
128D4×C43—42no—
129D4×C43—42no—
130C2×C4×C43—22no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—24no—
136C2×C4×C43—21no—
137C2×C4×C43—22no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—416no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43#13512yes—
150C2×C4×C43AGL(1,ℤ/8)14yes—
151C2×C4×C43C2×#4112yes—
152C2×C4×C43C2×#4112yes—
153C2×C4×C43H(5,𝔽2)11yescharacteristic
154C2×C4×C432−1+411yescharacteristic
155C8×C43—41no—
156C8×C43—41no—
157C8×C43—42no—
158#29533C4311yesmaximal, characteristic, direct product factor, Sylow
159C22×C43—44no—
160C22×C43—44no—
161C22×C43—44no—
162C22×C43—82no—
163C22×C43—82no—
164C22×C43—82no—
165C22×C43—82no—
166C22×C43#52512yes—
167C22×C43#53711yescharacteristic
168C22×C43C2×#13511yescharacteristic
169C22×C43C2×AGL(1,ℤ/8)12yes—
170C22×C43#57511yescharacteristic
171C4×C43—24no—
172C4×C43—22no—
173C4×C43—42no—
174C4×C43—44no—
175C4×C43—41no—
176C4×C43—82no—
177C4×C43—82no—
178C4×C43#55111yescharacteristic
179C4×C43#55212yes—
180C4×C43#55511yescharacteristic
181#2293C2×C4312yescomplemented
182#2087C2×C4311yescharacteristic, complemented
183#2065C2×C4312yescomplemented
184#2054C2×C4311yescharacteristic
185#1925C2×C4312yescomplemented
186#1920C2×C4312yescomplemented
187#1879C2×C4312yes—
188#1864C2×C4312yescomplemented
189#1831C2×C4311yescharacteristic, complemented
190C2×C43—84no—
191C2×C43#260911yescharacteristic
192C2×C43#310612yes—
193C2×C43#311412yes—
194C2×C43#325011yescharacteristic
195C2×C43#325311yescharacteristic
196C22×D8C22×C4311yescharacteristic
197C2×C4×D4C22×C4312yes—
198C2×#117—22no—
199C2×#107C22×C4311yescharacteristic
200C2×#106C22×C4312yes—
201C2×C4⋊C8C22×C4311yescharacteristic
202C2×C4⋊C8C22×C4311yescharacteristic
203C2×#102C22×C4312yes—
204C2×#102C22×C4312yes—
205C2×#102C22×C4312yes—
206#390C22×C4312yes—
207#390C22×C4312yes—
208#389C22×C4312yes—
209#389C22×C4312yes—
210#388—22no—
211#388—22no—
212C4×C4⋊C4C22×C4312yes—
213C4×C22⋊C4—22no—
214C43C22×C4311yescharacteristic
215#340C22×C4311yescharacteristic
216#340C22×C4312yes—
217#340C22×C4311yescharacteristic
218#340C22×C4312yes—
219#336C22×C4312yes—
220#336C22×C4312yes—
221C43#2953311yescharacteristic, direct product factor, Sylow
222C22×D4C23×C4312yes—
223C23×C4—22no—
224C2×D8—24no—
225C2×D8—41no—
226C22×C8C23×C4311yescharacteristic
227C22×C8C23×C4312yes—
228C22×C8C23×C4311yescharacteristic
229C4×D4—24no—
230C4×D4—24no—
231#117—48no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4C23×C4312yes—
235C2×C4⋊C4C23×C4312yes—
236C2×C4⋊C4C23×C4312yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C42—22no—
243C2×C42D4×C4312yes—
244C2×C42D4×C4311yescharacteristic
245C2×C42D4×C4311yescharacteristic
246C2×C42C23×C4312yes—
247C2×C42C23×C4311yescharacteristic
248#107—41no—
249#106—24no—
250C4⋊C8—41no—
251C4⋊C8—41no—
252#102—24no—
253#102—24no—
254#102—42no—
255#95—22no—
256#95—22no—
257#95—22no—
258C24—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4#41×C4314yes—
265C22×C4—28no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—44no—
270C22×C4—44no—
271C22×C4C2×D4×C4312yes—
272C22×C4C2×D4×C4311yescharacteristic
273C22×C4C2×D4×C4311yescharacteristic
274C22×C4C2×D4×C4312yes—
275C22×C4C24×C4311yescharacteristic
276D8—44no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—21no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—44no—
290C4⋊C4—44no—
291C4⋊C4#41×C4314yes—
292C22⋊C4—28no—
293C22⋊C4—44no—
294C22⋊C4—44no—
295C22⋊C4—44no—
296C22⋊C4—44no—
297C42—22no—
298C42—24no—
299C42—22no—
300C42—22no—
301C42—21no—
302C42—21no—
303C42—41no—
304C42—44no—
305C23—24no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23C22×D4×C4311yescharacteristic
313D4—24no—
314D4—24no—
315D4—42no—
316D4—42no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—416no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4#135×C4312yes—
337C2×C4AGL(1,ℤ/8)×C4314yes—
338C2×C4C2×#41×C4312yes—
339C2×C4C2×#41×C4312yes—
340C2×C4H(5,𝔽2)×C4311yescharacteristic
341C2×C42−1+4×C4311yescharacteristic
342C8—41no—
343C8—41no—
344C8—42no—
345C22—44no—
346C22—44no—
347C22—44no—
348C22—82no—
349C22—82no—
350C22—82no—
351C22—82no—
352C22C43×#52512yes—
353C22C43×#53711yescharacteristic
354C22C2×#135×C4311yescharacteristic
355C22C2×AGL(1,ℤ/8)×C4312yes—
356C22C43×#57511yescharacteristic
357C4—24no—
358C4—22no—
359C4—42no—
360C4—44no—
361C4—41no—
362C4—82no—
363C4—82no—
364C4C43×#55111yescharacteristic
365C4C43×#55212yes—
366C4C43×#55511yescharacteristic
367C2—84no—
368C2C43×#260911yescharacteristic
369C2C43×#310612yes—
370C2C43×#311412yes—
371C2C43×#325011yescharacteristic
372C2C43×#325311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D8×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2293C2semidirect
2. C43×#2087C2semidirect
3. C43×#2065C2semidirect
5. C43×#1925C2semidirect
6. C43×#1920C2semidirect
8. C43×#1864C2semidirect
9. C43×#1831C2semidirect
158. #29533C43direct (N × H)
181. #2293C2×C43semidirect
182. #2087C2×C43semidirect
183. #2065C2×C43semidirect
185. #1925C2×C43semidirect
186. #1920C2×C43semidirect
188. #1864C2×C43semidirect
189. #1831C2×C43semidirect
221. C43#29533direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#22932
C43×#20872
C43×#20652
C43×#20542
C43×#19252
C43×#19202
C43×#18792
C43×#18642
C43×#18312
#2953343