Finite Group Databasebeta

← #453×D43 #19143916

Subgroups — #453×D43 #19143916

Order 5504.

844 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(5,𝔽2)×D43C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D43C212yesmaximal, complemented
3#127×D43C211yesmaximal, characteristic, complemented
4#14583069C211yesmaximal, characteristic, complemented
5#14583068C212yesmaximal, complemented
6#14583067C211yesmaximal, characteristic, complemented
7#14583066C211yesmaximal, characteristic, complemented
8#14583065C212yesmaximal, complemented
9#104×D43C212yesmaximal, complemented
10#100×D43C211yesmaximal, characteristic, complemented
11C43×#453C211yesmaximal, characteristic, complemented
12#13063371—22no—
13#13063371C2212yescomplemented
14#13063370—22no—
15#13063370—22no—
16#13063370C2211yescharacteristic, complemented
17#41×D43—22no—
18#41×D43C2212yes—
19C2×D4×D43—22no—
20C2×D4×D43—22no—
21C2×D4×D43—22no—
22C2×D4×D43C2211yescharacteristic
23C2×D4×D43C2211yescharacteristic, complemented
24#13063353C2212yescomplemented
25#13063352—22no—
26#13063351C2212yescomplemented
27#13063350C2212yescomplemented
28#13063349—22no—
29SD16×D43—22no—
30D8×D43—22no—
31M16×D43C2212yescomplemented
32#13063322C2211yescharacteristic, complemented
33#13063321—22no—
34#13063321C2211yescharacteristic, complemented
35#13063321C2211yescharacteristic, complemented
36C42×D43C2211yescharacteristic, complemented
37#13063253C2212yescomplemented
38#13063252C2212yescomplemented
39#13063251C2212yescomplemented
40#13063242C2211yescharacteristic, complemented
41#13063241C2212yescomplemented
42H(5,𝔽2)×C43C2211yescharacteristic, complemented
43AGL(1,ℤ/8)×C43C2212yescomplemented
44#127×C43C2211yescharacteristic, complemented
45#104×C43C2212yescomplemented
46#100×C43C2211yescharacteristic, complemented
47C23×D43—22no—
48C23×D43—21no—
49C23×D43D412yes—
50#41×C43—22no—
51#41×C43C2312yes—
52C2×D4×C43—22no—
53C2×D4×C43—22no—
54C2×D4×C43—22no—
55C2×D4×C43C2311yescharacteristic
56C2×D4×C43C2311yescharacteristic, complemented
57C2×C22⋊D43—24no—
58C2×C22⋊D43—22no—
59C2×C22⋊D43—21no—
60C2×C22⋊D43—22no—
61C2×C22⋊D43—22no—
62C2×C22⋊D43—22no—
63C2×C22⋊D43D412yes—
64#10621902—22no—
65#10621902D412yescomplemented
66Q8×D43D412yescomplemented
67#10621900—24no—
68#10621900—22no—
69#10621900—22no—
70#10621900D412yescomplemented
71D4×D43—24no—
72D4×D43—24no—
73D4×D43—24no—
74D4×D43—22no—
75D4×D43—22no—
76D4×D43—22no—
77D4×D43—22no—
78D4×D43—22no—
79D4×D43—24no—
80D4×D43—22no—
81D4×D43—22no—
82D4×D43—48no—
83D4×D43D412yescomplemented
84#10621898—24no—
85#10621898—22no—
86#10621898—22no—
87#10621898C2312yes—
88C2×D172—22no—
89C2×D172—22no—
90C2×D172—22no—
91C2×D172C2311yescharacteristic
92C2×D172C2311yescharacteristic, complemented
93C2×C4×D43—22no—
94C2×C4×D43—22no—
95C2×C4×D43—21no—
96C2×C4×D43C2311yescharacteristic
97SD16×C43—22no—
98D8×C43—22no—
99M16×C43C2312yescomplemented
100C42×C43C2311yescharacteristic, complemented
101#10621884—22no—
102#10621883—22no—
103#10621882—22no—
104#10621882—22no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic, complemented
107#10621877C2312yescomplemented
108D344—22no—
109#10621873—22no—
110#10621872—22no—
111C8×D43—22no—
112C23×C43—22no—
113C23×C43—21no—
114C23×C43C2×D412yes—
115C22×D43—22no—
116C22×D43—24no—
117C22×D43—22no—
118C22×D43—22no—
119C22×D43—22no—
120C22×D43—21no—
121C22×D43—44no—
122C22×D43—44no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—84no—
126C22×D43C2×D411yescharacteristic
127C22×D43C2×D412yes—
128Q8×C43C2×D412yescomplemented
129D4×C43—24no—
130D4×C43—22no—
131D4×C43—22no—
132D4×C43—22no—
133D4×C43—44no—
134D4×C43C2×D412yescomplemented
135C2×C4×C43—22no—
136C2×C4×C43—21no—
137C2×C4×C43—22no—
138C2×C4×C43C2411yescharacteristic
139C22⋊D43—24no—
140C22⋊D43—24no—
141C22⋊D43—22no—
142C22⋊D43—22no—
143C22⋊D43—24no—
144C22⋊D43—22no—
145C22⋊D43—44no—
146C22⋊D43—44no—
147C22⋊D43—42no—
148C2×Dic43—22no—
149C2×Dic43—21no—
150C2×Dic43—22no—
151C2×Dic43C2×D411yescharacteristic
152D172—24no—
153D172—22no—
154D172—22no—
155D172—22no—
156D172—44no—
157D172C2×D412yescomplemented
158C4×D43—24no—
159C4×D43—24no—
160C4×D43—22no—
161C4×D43—22no—
162C4×D43—22no—
163C4×D43C2×D412yes—
164C4×D43C2×D412yes—
165Dic86—22no—
166Dic86C2×D412yescomplemented
167C8×C43—22no—
168C43⋊C8—22no—
169C22×C43—22no—
170C22×C43—22no—
171C22×C43—42no—
172C22×C43—42no—
173C22×C43—41no—
174C22×C43—82no—
175C22×C43C22×D411yescharacteristic
176C2×D43—22no—
177C2×D43—22no—
178C2×D43—22no—
179C2×D43—44no—
180C2×D43—44no—
181C2×D43—42no—
182C2×D43—42no—
183C2×D43—41no—
184C2×D43—82no—
185C2×D43—82no—
186C2×D43—84no—
187C2×D43—82no—
188C2×D43—82no—
189C2×D43#12011yescharacteristic
190C2×D43#12011yescharacteristic
191C4×C43—22no—
192C4×C43—22no—
193C4×C43C22×D412yes—
194Dic43—22no—
195Dic43—22no—
196Dic43#12012yes—
197C2×#453—431nomaximal, Sylow
198C2×C43—21no—
199C2×C43—42no—
200C2×C43—42no—
201C2×C43—81no—
202C2×C43C2×#12011yescharacteristic
203D43—21no—
204D43—42no—
205D43—42no—
206D43—81no—
207D43#45312yesdirect product factor
208C2×H(5,𝔽2)—431no—
209C2×AGL(1,ℤ/8)—432no—
210C2×#127—431no—
211#453—431no—
212#453—432no—
213#453—431no—
214#453—432no—
215#453—431no—
216#453D4311yescharacteristic, direct product factor
217C2×#104—432no—
218C2×#100—431no—
219C43C2×#45311yescharacteristic, complemented, Sylow
220H(5,𝔽2)—432no—
221H(5,𝔽2)—431no—
222H(5,𝔽2)—862no—
223H(5,𝔽2)—862no—
224H(5,𝔽2)—862no—
225H(5,𝔽2)C2×D4311yescharacteristic, complemented
226C2×#41—432no—
227C2×#41—862no—
228C22×D4—431no—
229C22×D4—431no—
230C22×D4—862no—
231C22×D4—862no—
232C22×D4—862no—
233AGL(1,ℤ/8)—432no—
234AGL(1,ℤ/8)—432no—
235AGL(1,ℤ/8)—432no—
236AGL(1,ℤ/8)—862no—
237AGL(1,ℤ/8)—862no—
238AGL(1,ℤ/8)C2×D4312yescomplemented
239C2×SD16—862no—
240C2×D8—862no—
241C2×M16—432no—
242#127—431no—
243#127—431no—
244#127—431no—
245#127—862no—
246#127C2×D4311yescharacteristic, complemented
247C2×C42—431no—
248#104—432no—
249#104—432no—
250#104—432no—
251#104C2×D4312yescomplemented
252#100—431no—
253#100—432no—
254#100C2×D4311yescharacteristic, complemented
255C24—432no—
256C24—861no—
257C24—862no—
258#41—22no—
259#41—432no—
260#41—432no—
261#41—432no—
262#41—862no—
263#41—862no—
264#41—864no—
265#41—862no—
266#41—862no—
267#41—864no—
268#41—862no—
269#41C22×D4312yes—
270C2×Q8—432no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—432no—
275C2×D4—432no—
276C2×D4—431no—
277C2×D4—431no—
278C2×D4—862no—
279C2×D4—862no—
280C2×D4—862no—
281C2×D4—862no—
282C2×D4—862no—
283C2×D4—862no—
284C2×D4—862no—
285C2×D4—861no—
286C2×D4—862no—
287C2×D4—862no—
288C2×D4—864no—
289C2×D4—864no—
290C2×D4—864no—
291C2×D4—864no—
292C2×D4—864no—
293C2×D4—862no—
294C2×D4—862no—
295C2×D4—862no—
296C2×D4—862no—
297C2×D4—862no—
298C2×D4—1728no—
299C2×D4C22×D4311yescharacteristic
300C2×D4C22×D4311yescharacteristic, complemented
301C22×C4—431no—
302C22×C4—862no—
303C22×C4—861no—
304C22×C4—862no—
305SD16—22no—
306SD16—862no—
307SD16—862no—
308SD16—862no—
309D8—22no—
310D8—862no—
311D8—862no—
312D8—862no—
313M16—432no—
314M16—862no—
315M16C22×D4312yescomplemented
316C2×C8—862no—
317C42—431no—
318C42—861no—
319C42C22×D4311yescharacteristic, complemented
320C23—22no—
321C23—21no—
322C23—431no—
323C23—432no—
324C23—862no—
325C23—862no—
326C23—862no—
327C23—862no—
328C23—864no—
329C23—861no—
330C23—3444no—
331C23—1721no—
332C23—1721no—
333C23—1724no—
334C23—1724no—
335C23D4×D4312yes—
336Q8—432no—
337Q8—862no—
338Q8D4×D4312yescomplemented
339D4—24no—
340D4—22no—
341D4—22no—
342D4—22no—
343D4—44no—
344D4—432no—
345D4—862no—
346D4—864no—
347D4—864no—
348D4—862no—
349D4—862no—
350D4—864no—
351D4—864no—
352D4—862no—
353D4—862no—
354D4—862no—
355D4—1724no—
356D4—1722no—
357D4—1724no—
358D4—1724no—
359D4D4×D4312yescomplemented
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—431no—
364C2×C4—432no—
365C2×C4—432no—
366C2×C4—862no—
367C2×C4—862no—
368C2×C4—864no—
369C2×C4—864no—
370C2×C4—862no—
371C2×C4—862no—
372C2×C4—861no—
373C2×C4—862no—
374C2×C4C23×D4311yescharacteristic
375C8—22no—
376C8—862no—
377C22—22no—
378C22—22no—
379C22—42no—
380C22—42no—
381C22—41no—
382C22—82no—
383C22—431no—
384C22—431no—
385C22—862no—
386C22—862no—
387C22—862no—
388C22—3442no—
389C22—3442no—
390C22—3444no—
391C22—3442no—
392C22—3442no—
393C22—1722no—
394C22—1722no—
395C22—1724no—
396C22—1724no—
397C22—1721no—
398C22C2×D4×D4311yescharacteristic
399C4—22no—
400C4—22no—
401C4—432no—
402C4—862no—
403C4—862no—
404C4C2×D4×D4312yes—
405C2—21no—
406C2—42no—
407C2—42no—
408C2—81no—
409C2—432no—
410C2—861no—
411C2—3441no—
412C2—1722no—
413C2—1722no—
414C2#120×D4311yescharacteristic
subgroupG/H
centerC2#120×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#453C2
socleC2×C43C2×#120
hypercenter#453D43
hypocenterC43C2×#453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. H(5,𝔽2)×D43C2semidirect
2. AGL(1,ℤ/8)×D43C2semidirect
3. #127×D43C2semidirect
4. #14583069C2semidirect
5. #14583068C2semidirect
6. #14583067C2semidirect
7. #14583066C2semidirect
8. #14583065C2semidirect
9. #104×D43C2semidirect
10. #100×D43C2semidirect
11. C43×#453C2semidirect
13. #13063371C22semidirect
16. #13063370C22semidirect
23. C2×D4×D43C22semidirect
24. #13063353C22semidirect
26. #13063351C22semidirect
27. #13063350C22semidirect
31. M16×D43C22semidirect
32. #13063322C22semidirect
34. #13063321C22semidirect
35. #13063321C22semidirect
36. C42×D43C22semidirect
37. #13063253C22semidirect
38. #13063252C22semidirect
39. #13063251C22semidirect
40. #13063242C22semidirect
41. #13063241C22semidirect
42. H(5,𝔽2)×C43C22semidirect
43. AGL(1,ℤ/8)×C43C22semidirect
44. #127×C43C22semidirect
45. #104×C43C22semidirect
46. #100×C43C22semidirect
56. C2×D4×C43C23semidirect
65. #10621902D4semidirect
66. Q8×D43D4semidirect
70. #10621900D4semidirect
83. D4×D43D4semidirect
92. C2×D172C23semidirect
99. M16×C43C23semidirect
100. C42×C43C23semidirect
106. C4×Dic43C23semidirect
107. #10621877C23semidirect
128. Q8×C43C2×D4semidirect
134. D4×C43C2×D4semidirect
157. D172C2×D4semidirect
166. Dic86C2×D4semidirect
207. D43#453direct (N × H)
216. #453D43direct (N × H)
219. C43C2×#453semidirect
225. H(5,𝔽2)C2×D43semidirect
238. AGL(1,ℤ/8)C2×D43semidirect
246. #127C2×D43semidirect
251. #104C2×D43semidirect
254. #100C2×D43semidirect
300. C2×D4C22×D43semidirect
315. M16C22×D43semidirect
319. C42C22×D43semidirect
338. Q8D4×D43semidirect
359. D4D4×D43semidirect