Finite Group Databasebeta

← D43×#1453 #25062213

Subgroups — D43×#1453 #25062213

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#431×D43C212yesmaximal
2C4×M16×D43C211yesmaximal, characteristic
3#19132893C211yesmaximal, characteristic, complemented
4#19132892C211yesmaximal, characteristic, complemented
5#19132891C212yesmaximal, complemented
6#19132890C212yesmaximal, complemented
7#19132889C211yesmaximal, characteristic, complemented
8#322×D43C212yesmaximal, complemented
9#322×D43C211yesmaximal, characteristic, complemented
10C82×D43C211yesmaximal, characteristic, complemented
11C43×#1453C211yesmaximal, characteristic, complemented
12C2×M16×D43C412yes—
13C2×C42×D43C2211yescharacteristic
14#14582952C2212yes—
15#14582951C414yes—
16#14582950C2212yes—
17#14582950C2212yes—
18#14582949C414yes—
19C4⋊C8×D43C414yes—
20C22⋊C8×D43C414yes—
21C4×#10621877C2211yescharacteristic
22#14582851C412yes—
23M16×Dic43C412yes—
24C4×#10621872C2211yescharacteristic
25C4×#10621872C2211yescharacteristic
26#97×D43C412yes—
27C4×C8×D43C2212yes—
28C4×C8×D43C2212yes—
29C4×C8×D43C2211yescharacteristic
30C4×C8×D43C2211yescharacteristic
31#14582621C2212yescomplemented
32#14582621C2212yescomplemented
33#14582621C2212yescomplemented
34#14582620C2211yescharacteristic, complemented
35#14582620C2212yescomplemented
36C8×C43⋊C8C2212yescomplemented
37C8×C43⋊C8C2211yescharacteristic, complemented
38C43×#431C2212yes—
39C4×M16×C43C2211yescharacteristic
40C43×#322C2212yescomplemented
41C43×#322C2211yescharacteristic, complemented
42C82×C43C2211yescharacteristic, complemented
43C22×C4×D43C2×C412yes—
44C22×C4×D43C2×C411yescharacteristic
45C2×#10621877C2×C412yes—
46C2×#10621872C2×C412yes—
47C2×#10621872C2×C412yes—
48M16×D43—28no—
49C2×C8×D43C2×C412yes—
50C2×C8×D43C2×C414yes—
51C2×C8×D43C2×C414yes—
52C2×C8×D43C2×C412yes—
53C2×C4×Dic43C2×C411yescharacteristic
54C2×C4×Dic43C2×C412yes—
55C42×D43C2×C411yescharacteristic
56C42×D43C2×C411yescharacteristic
57C42×D43C2×C412yes—
58C42×D43C2×C412yes—
59C42×D43C2311yescharacteristic
60C42×D43C2311yescharacteristic
61C4⋊(C43⋊C8)C2×C414yes—
62Dic43⋊C8C2×C414yes—
63Dic43⋊C8C2×C414yes—
64C22⋊(C43⋊C8)C2×C414yes—
65(C2×D43)⋊C8C2×C414yes—
66(C2×D43)⋊C8C2×C414yes—
67#13063236C2×C412yes—
68#13063235C2×C412yes—
69#13063235C2×C412yes—
70C4×C43⋊C8C2311yescharacteristic
71C4×C43⋊C8C2311yescharacteristic
72C4×C43⋊C8C2312yes—
73C4×C43⋊C8C2312yes—
74C8×Dic43C2×C412yes—
75C8×Dic43C2×C412yes—
76C8×Dic43C2×C414yes—
77C8×Dic43C2×C414yes—
78C2×M16×C43C2×C412yes—
79C2×C42×C43C2311yescharacteristic
80C4⋊C8×C43C2×C414yes—
81C22⋊C8×C43C2×C414yes—
82#97×C43C2×C412yes—
83C4×C8×C43C2311yescharacteristic
84C4×C8×C43C2311yescharacteristic
85C4×C8×C43C2312yes—
86C4×C8×C43C2312yes—
87C23×D43C4211yescharacteristic
88C22×C4×C43C22×C412yes—
89C22×C4×C43C22×C411yescharacteristic
90C22×Dic43C4211yescharacteristic
91C22×Dic43C4212yes—
92C2×C4×D43—24no—
93C2×C4×D43—28no—
94C2×C4×D43C4211yescharacteristic
95C2×C4×D43C4212yes—
96C2×C4×D43C4211yescharacteristic
97C2×C4×D43C4212yes—
98C2×C4×D43C22×C412yes—
99C2×C4×D43C22×C411yescharacteristic
100C2×C4×D43C22×C411yescharacteristic
101C2×C4×D43C22×C412yes—
102M16×C43—24no—
103C2×C8×C43C22×C412yes—
104C2×C8×C43C22×C414yes—
105C2×C8×C43C22×C414yes—
106C2×C8×C43C22×C412yes—
107C42×C43C22×C411yescharacteristic
108C42×C43C22×C412yes—
109C42×C43C2411yescharacteristic
110C4×Dic43C4212yes—
111C4×Dic43C4212yes—
112C4×Dic43C4212yes—
113C4×Dic43C22×C412yes—
114C4×Dic43C22×C411yescharacteristic
115C4×Dic43C22×C411yescharacteristic
116C4×Dic43C22×C412yes—
117#10621877—24no—
118C2×C43⋊C8C22×C412yes—
119C2×C43⋊C8C22×C414yes—
120C2×C43⋊C8C22×C414yes—
121C2×C43⋊C8C22×C412yes—
122#10621872—24no—
123#10621872—24no—
124C8×D43—24no—
125C8×D43—28no—
126C8×D43—28no—
127C8×D43M1618yes—
128C23×C43C2×C4211yescharacteristic
129C22×D43—22no—
130C22×D43—24no—
131C22×D43C2×C4211yescharacteristic
132C22×D43C2×C4211yescharacteristic
133C2×C4×C43—22no—
134C2×C4×C43—24no—
135C2×C4×C43C2×C4211yescharacteristic
136C2×C4×C43C2×C4212yes—
137C2×C4×C43C23×C411yescharacteristic
138C2×C4×C43C23×C412yes—
139C2×Dic43—22no—
140C2×Dic43—24no—
141C2×Dic43C2×C4211yescharacteristic
142C2×Dic43C2×C4212yes—
143C2×Dic43C2×C4211yescharacteristic
144C2×Dic43C2×C4212yes—
145C4×D43—22no—
146C4×D43—24no—
147C4×D43—22no—
148C4×D43—24no—
149C4×D43—22no—
150C4×D43—24no—
151C4×D43C2×M1614yes—
152C4×D43#13118yes—
153C8×C43—22no—
154C8×C43—24no—
155C8×C43—24no—
156C8×C43C2×M1614yes—
157C43⋊C8—22no—
158C43⋊C8—24no—
159C43⋊C8—24no—
160C43⋊C8C2×M1614yes—
161C2×#1453—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—22no—
164C22×C43C22×C4211yescharacteristic
165C2×D43—21no—
166C2×D43—22no—
167C2×D43—44no—
168C2×D43C4×M1612yes—
169C2×D43#40514yes—
170C4×C43—21no—
171C4×C43—22no—
172C4×C43C22×M1612yes—
173C4×C43C2×#13114yes—
174Dic43—21no—
175Dic43—22no—
176Dic43C4×M1612yes—
177Dic43#40514yes—
178C2×#431—432no—
179C2×C4×M16—431no—
180#1453—432no—
181#1453—431no—
182#1453—432no—
183#1453—431no—
184#1453—431no—
185#1453D4311yescharacteristic, direct product factor
186C2×#322—431no—
187C2×#322—432no—
188C2×C82—431no—
189C2×C43—41no—
190C2×C43C2×C4×M1611yescharacteristic
191C2×C43C2×#40512yes—
192D43—41no—
193D43#145314yesdirect product factor
194C22×M16—432no—
195C22×C42—431no—
196#431—432no—
197#431—434no—
198#431—434no—
199#431—432no—
200#431—432no—
201#431C2×D4312yes—
202C2×C4⋊C8—434no—
203C2×C22⋊C8—434no—
204C4×M16—432no—
205C4×M16—431no—
206C4×M16—432no—
207C4×M16—431no—
208C4×M16—431no—
209C4×M16C2×D4311yescharacteristic
210C2×#97—432no—
211C2×C4×C8—431no—
212C2×C4×C8—431no—
213C2×C4×C8—432no—
214C2×C4×C8—432no—
215#322—432no—
216#322—431no—
217#322—432no—
218#322—432no—
219#322—432no—
220#322C2×D4311yescharacteristic, complemented
221#322C2×D4312yescomplemented
222C82—432no—
223C82—431no—
224C82C2×D4311yescharacteristic, complemented
225C43C2×#145311yescharacteristic, complemented, Sylow
226C23×C4—431no—
227C23×C4—432no—
228C2×M16—432no—
229C2×M16—432no—
230C2×M16—432no—
231C2×M16—868no—
232C2×M16C4×D4312yes—
233C22×C8—432no—
234C22×C8—432no—
235C22×C8—434no—
236C22×C8—434no—
237C2×C42—431no—
238C2×C42—432no—
239C2×C42—431no—
240C2×C42—431no—
241C2×C42—432no—
242C2×C42—432no—
243C2×C42—431no—
244C2×C42—431no—
245C2×C42C22×D4311yescharacteristic
246C4⋊C8—434no—
247C4⋊C8—434no—
248C4⋊C8—434no—
249C4⋊C8C4×D4314yes—
250C22⋊C8—434no—
251C22⋊C8—434no—
252C22⋊C8—434no—
253C22⋊C8C4×D4314yes—
254#97—432no—
255#97—432no—
256#97—432no—
257#97C4×D4312yes—
258C4×C8—432no—
259C4×C8—432no—
260C4×C8—434no—
261C4×C8—434no—
262C4×C8—431no—
263C4×C8—432no—
264C4×C8—431no—
265C4×C8—432no—
266C4×C8C22×D4311yescharacteristic
267C4×C8C22×D4312yes—
268C4×C8C22×D4311yescharacteristic
269C4×C8C22×D4312yes—
270C24—431no—
271C22×C4—431no—
272C22×C4—432no—
273C22×C4—432no—
274C22×C4—431no—
275C22×C4—432no—
276C22×C4—431no—
277C22×C4—432no—
278C22×C4—431no—
279C22×C4—432no—
280C22×C4—431no—
281C22×C4—864no—
282C22×C4—868no—
283C22×C4C2×C4×D4312yes—
284C22×C4C2×C4×D4311yescharacteristic
285M16—24no—
286M16—864no—
287M16—864no—
288M16—864no—
289C2×C8—432no—
290C2×C8—438no—
291C2×C8—432no—
292C2×C8—434no—
293C2×C8—434no—
294C2×C8—864no—
295C2×C8—868no—
296C2×C8—868no—
297C2×C8C2×C4×D4312yes—
298C2×C8C2×C4×D4314yes—
299C2×C8C2×C4×D4314yes—
300C2×C8C2×C4×D4312yes—
301C42—432no—
302C42—432no—
303C42—432no—
304C42—431no—
305C42—432no—
306C42—431no—
307C42—432no—
308C42C2×C4×D4311yescharacteristic
309C42C2×C4×D4312yes—
310C42C23×D4311yescharacteristic
311C23—431no—
312C23—431no—
313C23—862no—
314C23—864no—
315C23C42×D4311yescharacteristic
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—431no—
319C2×C4—432no—
320C2×C4—434no—
321C2×C4—438no—
322C2×C4—431no—
323C2×C4—432no—
324C2×C4—862no—
325C2×C4—864no—
326C2×C4—862no—
327C2×C4—864no—
328C2×C4—862no—
329C2×C4—864no—
330C2×C4—862no—
331C2×C4—864no—
332C2×C4C42×D4311yescharacteristic
333C2×C4C42×D4312yes—
334C2×C4C22×C4×D4311yescharacteristic
335C2×C4C22×C4×D4312yes—
336C8—22no—
337C8—24no—
338C8—24no—
339C8—434no—
340C8—862no—
341C8—864no—
342C8—864no—
343C8M16×D4314yes—
344C22—21no—
345C22—22no—
346C22—432no—
347C22—434no—
348C22—861no—
349C22—862no—
350C22—1724no—
351C22C2×C42×D4311yescharacteristic
352C4—21no—
353C4—22no—
354C4—432no—
355C4—434no—
356C4—861no—
357C4—862no—
358C4C2×M16×D4312yes—
359C4#131×D4314yes—
360C2—41no—
361C2—434no—
362C2—1721no—
363C2C4×M16×D4311yescharacteristic
364C2#405×D4312yes—
subgroupG/H
center, FrattiniC42C23×D43
commutator, socleC22×C43C22×C42
FittingC43×#1453C2
prime radicalC23×D43C42
cosocleC42×C43C24
hypercenter#1453D43
hypocenterC43C2×#1453
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C42 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. #19132893C2semidirect
4. #19132892C2semidirect
5. #19132891C2semidirect
6. #19132890C2semidirect
7. #19132889C2semidirect
8. #322×D43C2semidirect
9. #322×D43C2semidirect
10. C82×D43C2semidirect
11. C43×#1453C2semidirect
31. #14582621C22semidirect
32. #14582621C22semidirect
33. #14582621C22semidirect
34. #14582620C22semidirect
35. #14582620C22semidirect
36. C8×C43⋊C8C22semidirect
37. C8×C43⋊C8C22semidirect
40. C43×#322C22semidirect
41. C43×#322C22semidirect
42. C82×C43C22semidirect
185. #1453D43direct (N × H)
193. D43#1453direct (N × H)
220. #322C2×D43semidirect
221. #322C2×D43semidirect
224. C82C2×D43semidirect
225. C43C2×#1453semidirect

Maximal subgroups

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

subgroupindex
#431×D432
C4×M16×D432
#191328932
#191328922
#191328912
#191328902
#191328892
#322×D432
C82×D432
C43×#14532
C2×#145343