Finite Group Databasebeta

← D43×#1820 #25096328

Subgroups — D43×#1820 #25096328

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2#381×D43C212yesmaximal
3#19134672C211yesmaximal, characteristic, complemented
4#19134671C214yesmaximal, complemented
5#19134670C212yesmaximal, complemented
6#342×D43C214yesmaximal
7C43×#1820C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10C2×#13063283C412yescomplemented
11C2×#13063282C412yescomplemented
12C2×#13063281C2212yes—
13#117×D43—24no—
14#117×D43—24no—
15C2×C4⋊C4×D43C412yescomplemented
16C2×C22⋊C4×D43C2214yes—
17C2×C22⋊C4×D43C2212yes—
18C2×C42×D43C412yescomplemented
19#14582762C2212yes—
20#14582761—24no—
21#14582760C2214yes—
22#95×D43—24no—
23#14582666C2214yes—
24#14582665C2218yes—
25C2×#117×C43C2211yescharacteristic
26C43×#381C2212yes—
27C43×#342C2214yes—
28C24×D43C2311yescharacteristic
29C23×Dic43C2311yescharacteristic
30C22×C4×D43—28no—
31C22×C4×D43—24no—
32C22×C4×D43C2×C411yescharacteristic
33C22×C4×D43C2×C411yescharacteristic
34C22×C4×D43C2×C411yescharacteristic
35C22×C4×D43C2×C411yescharacteristic
36C22×C4×D43C2×C414yes—
37C22×C4×D43D414yes—
38C22×C4×D43D414yes—
39#13063284—24no—
40#13063283—28no—
41#13063282—28no—
42#13063281—28no—
43C2×C4⋊Dic43C2×C412yescomplemented
44C2×Dic43⋊C4C2×C414yescomplemented
45C4⋊C4×D43—24no—
46C4⋊C4×D43—24no—
47C2×C22⋊Dic43C2314yes—
48C2×C22⋊Dic43C2312yes—
49C2×(C2×D43)⋊C4—24no—
50C2×(C2×D43)⋊C4C2×C414yes—
51C22⋊C4×D43—24no—
52C22⋊C4×D43—24no—
53C22⋊C4×D43—216no—
54C2×C4×Dic43C2×C414yescomplemented
55C2×C4×Dic43C2×C412yescomplemented
56C42×D43—24no—
57C42×D43—24no—
58C43⋊#95—24no—
59C43⋊#95—28no—
60C23×C4×C43C2311yescharacteristic
61#117×C43—24no—
62C2×C4⋊C4×C43C2×C412yescomplemented
63C2×C22⋊C4×C43C2314yes—
64C2×C22⋊C4×C43C2312yes—
65C2×C42×C43C2×C412yescomplemented
66#95×C43—24no—
67C24×C43C2411yescharacteristic
68C23×D43—44no—
69C23×D43C22×C411yescharacteristic
70C23×D43C22×C411yescharacteristic
71C23×D43C2×D412yes—
72C23×D43C2×D412yes—
73C23×D43#4118yes—
74C22×C4×C43—24no—
75C22×C4×C43—24no—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C22×C414yes—
79C22×C4×C43C2×D414yes—
80C22×Dic43—24no—
81C22×Dic43—24no—
82C22×Dic43C22×C411yescharacteristic
83C22×Dic43C22×C411yescharacteristic
84C22×Dic43C22×C414yes—
85C22×Dic43C2×D414yes—
86C2×C4×D43—24no—
87C2×C4×D43—24no—
88C2×C4×D43—24no—
89C2×C4×D43—24no—
90C2×C4×D43—24no—
91C2×C4×D43—24no—
92C2×C4×D43—216no—
93C2×C4×D43—216no—
94C2×C4×D43—48no—
95C2×C4×D43—416no—
96C2×C4×D43—48no—
97C2×C4×D43C22⋊C412yes—
98C2×C4×D43C22⋊C412yes—
99C2×C4×D43C22⋊C412yes—
100C2×C4×D43C22⋊C412yes—
101C2×C4×D43C22⋊C414yes—
102C2×C4×D43C22⋊C414yes—
103C4⋊C4×C43—24no—
104C22⋊C4×C43—24no—
105C22⋊C4×C43—28no—
106C42×C43—24no—
107C22⋊Dic43—24no—
108C22⋊Dic43—28no—
109(C2×D43)⋊C4—28no—
110(C2×D43)⋊C4—48no—
111C4⋊Dic43—24no—
112Dic43⋊C4—28no—
113C4×Dic43—24no—
114C4×Dic43—28no—
115C23×C43—42no—
116C23×C43C23×C411yescharacteristic
117C23×C43C22×D412yes—
118C23×C43C2×#4114yes—
119C22×D43—24no—
120C22×D43—28no—
121C22×D43—416no—
122C22×D43—42no—
123C22×D43—44no—
124C22×D43C2×C22⋊C412yes—
125C22×D43C2×C22⋊C411yescharacteristic
126C22×D43C2×C22⋊C411yescharacteristic
127C22×D43#11714yes—
128C22×D43#11714yes—
129C22×D43#12318yes—
130C22×D43#12318yes—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—28no—
134C2×C4×C43—24no—
135C2×C4×C43—44no—
136C2×C4×C43—48no—
137C2×C4×C43—44no—
138C2×C4×C43C2×C22⋊C412yes—
139C2×C4×C43C2×C22⋊C412yes—
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—28no—
143C2×Dic43—24no—
144C2×Dic43—44no—
145C2×Dic43—48no—
146C2×Dic43—44no—
147C2×Dic43C2×C22⋊C412yes—
148C2×Dic43C2×C22⋊C412yes—
149C4×D43—24no—
150C4×D43—24no—
151C4×D43—28no—
152C4×D43—28no—
153C4×D43—24no—
154C4×D43—24no—
155C4×D43—48no—
156C4×D43—48no—
157C4×D43—816no—
158C2×#1820—431nomaximal, Sylow
159C22×C43—22no—
160C22×C43—24no—
161C22×C43—44no—
162C22×C43C22×C22⋊C411yescharacteristic
163C22×C43C2×#11712yes—
164C22×C43C2×#12314yes—
165C2×D43—24no—
166C2×D43—22no—
167C2×D43—28no—
168C2×D43—216no—
169C2×D43—44no—
170C2×D43—48no—
171C2×D43#38114yes—
172C2×D43#38112yes—
173C2×D43#38112yes—
174C2×D43#41014yes—
175C4×C43—22no—
176C4×C43—22no—
177C4×C43—44no—
178C4×C43—84no—
179Dic43—22no—
180Dic43—22no—
181Dic43—44no—
182Dic43—84no—
183C22×#117—431no—
184C2×#381—432no—
185#1820—432no—
186#1820—434no—
187#1820—431no—
188#1820D4311yescharacteristic, direct product factor
189C2×#342—434no—
190C2×C43—24no—
191C2×C43—22no—
192C2×C43C2×#38111yescharacteristic
193C2×C43C2×#41012yes—
194D43—24no—
195D43—22no—
196D43#182014yesdirect product factor
197C24×C4—431no—
198C2×#117—431no—
199C2×#117—432no—
200C2×#117—432no—
201C2×#117—432no—
202C2×#117—864no—
203C2×#117—864no—
204C2×#117C2×D4311yescharacteristic
205C22×C4⋊C4—432no—
206C22×C22⋊C4—432no—
207C22×C22⋊C4—434no—
208C22×C42—432no—
209#381—432no—
210#381—434no—
211#381—864no—
212#381C2×D4312yes—
213C2×#95—864no—
214#342—438no—
215#342—434no—
216#342C2×D4314yes—
217C43C2×#182011yescharacteristic, complemented, Sylow
218C25—431no—
219C23×C4—431no—
220C23×C4—431no—
221C23×C4—431no—
222C23×C4—431no—
223C23×C4—431no—
224C23×C4—434no—
225C23×C4—434no—
226C23×C4—434no—
227C23×C4—868no—
228C23×C4—864no—
229C23×C4C22×D4311yescharacteristic
230#117—24no—
231#117—868no—
232#117—868no—
233#117—868no—
234#117—864no—
235C2×C4⋊C4—434no—
236C2×C4⋊C4—432no—
237C2×C4⋊C4—864no—
238C2×C4⋊C4—864no—
239C2×C4⋊C4C4×D4312yescomplemented
240C2×C22⋊C4—432no—
241C2×C22⋊C4—434no—
242C2×C22⋊C4—434no—
243C2×C22⋊C4—864no—
244C2×C22⋊C4—864no—
245C2×C22⋊C4—8616no—
246C2×C22⋊C4—864no—
247C2×C22⋊C4C22×D4314yes—
248C2×C22⋊C4C22×D4312yes—
249C2×C42—434no—
250C2×C42—432no—
251C2×C42—864no—
252C2×C42—864no—
253C2×C42C4×D4312yescomplemented
254#95—24no—
255#95—868no—
256#95—864no—
257C24—431no—
258C24—432no—
259C24—431no—
260C24—432no—
261C24—438no—
262C24—1724no—
263C24C23×D4311yescharacteristic
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—434no—
269C22×C4—432no—
270C22×C4—432no—
271C22×C4—432no—
272C22×C4—432no—
273C22×C4—434no—
274C22×C4—434no—
275C22×C4—434no—
276C22×C4—864no—
277C22×C4—864no—
278C22×C4—864no—
279C22×C4—864no—
280C22×C4—8616no—
281C22×C4—8616no—
282C22×C4—864no—
283C22×C4—864no—
284C22×C4—864no—
285C22×C4—864no—
286C22×C4—1728no—
287C22×C4—17216no—
288C22×C4—1728no—
289C22×C4C2×C4×D4311yescharacteristic
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4C2×C4×D4314yes—
292C22×C4D4×D4314yes—
293C4⋊C4—24no—
294C4⋊C4—868no—
295C4⋊C4—864no—
296C22⋊C4—24no—
297C22⋊C4—28no—
298C22⋊C4—868no—
299C22⋊C4—864no—
300C22⋊C4—868no—
301C22⋊C4—1728no—
302C42—24no—
303C42—868no—
304C42—864no—
305C23—42no—
306C23—431no—
307C23—432no—
308C23—431no—
309C23—434no—
310C23—438no—
311C23—434no—
312C23—438no—
313C23—864no—
314C23—868no—
315C23—1722no—
316C23—1724no—
317C23—17216no—
318C23C22×C4×D4311yescharacteristic
319C23C2×D4×D4312yes—
320C23#41×D4314yes—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—28no—
324C2×C4—24no—
325C2×C4—44no—
326C2×C4—48no—
327C2×C4—44no—
328C2×C4—432no—
329C2×C4—432no—
330C2×C4—864no—
331C2×C4—864no—
332C2×C4—864no—
333C2×C4—864no—
334C2×C4—868no—
335C2×C4—868no—
336C2×C4—862no—
337C2×C4—862no—
338C2×C4—868no—
339C2×C4—864no—
340C2×C4—34416no—
341C2×C4—1728no—
342C2×C4—1728no—
343C2×C4—1728no—
344C2×C4—1724no—
345C2×C4—1724no—
346C2×C4C22⋊C4×D4312yes—
347C2×C4C22⋊C4×D4312yes—
348C22—22no—
349C22—24no—
350C22—44no—
351C22—434no—
352C22—432no—
353C22—434no—
354C22—432no—
355C22—8616no—
356C22—868no—
357C22—862no—
358C22—864no—
359C22—1728no—
360C22—1724no—
361C22C2×C22⋊C4×D4311yescharacteristic
362C22#117×D4312yes—
363C22#123×D4314yes—
364C4—22no—
365C4—22no—
366C4—44no—
367C4—84no—
368C4—862no—
369C4—862no—
370C4—3444no—
371C4—1724no—
372C2—24no—
373C2—22no—
374C2—434no—
375C2—864no—
376C2—862no—
377C2#381×D4311yescharacteristic
378C2#410×D4312yes—
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1820C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43C23
cosocleC24×C43C24
hypercenter#1820D43
hypocenterC43C2×#1820
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
3. #19134672C2semidirect
4. #19134671C2semidirect
5. #19134670C2semidirect
7. C43×#1820C2semidirect
10. C2×#13063283C4semidirect
11. C2×#13063282C4semidirect
15. C2×C4⋊C4×D43C4semidirect
18. C2×C42×D43C4semidirect
43. C2×C4⋊Dic43C2×C4semidirect
44. C2×Dic43⋊C4C2×C4semidirect
54. C2×C4×Dic43C2×C4semidirect
55. C2×C4×Dic43C2×C4semidirect
62. C2×C4⋊C4×C43C2×C4semidirect
65. C2×C42×C43C2×C4semidirect
188. #1820D43direct (N × H)
196. D43#1820direct (N × H)
217. C43C2×#1820semidirect
239. C2×C4⋊C4C4×D43semidirect
253. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
#381×D432
#191346722
#191346712
#191346702
#342×D432
C43×#18202
C2×#182043