Finite Group Databasebeta

← #455×D43 #19143922

Subgroups — #455×D43 #19143922

Order 5504.

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

normal subgroups only

This group has 760 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
2#137×D43C212yesmaximal, complemented
3#124×D43C211yesmaximal, characteristic, complemented
4#14583079C211yesmaximal, characteristic, complemented
5#14583078C212yesmaximal, complemented
6#14583077C211yesmaximal, characteristic, complemented
7#14583076C211yesmaximal, characteristic, complemented
8#14583075C212yesmaximal, complemented
9#104×D43C212yesmaximal, complemented
10#100×D43C211yesmaximal, characteristic, complemented
11C43×#455C211yesmaximal, characteristic, complemented
12#13063371—22no—
13#13063371C2212yes—
14#13063370—22no—
15#13063370—22no—
16#13063370C2211yescharacteristic
17#41×D43—22no—
18#41×D43C2212yes—
19C2×Q8×D43C2211yescharacteristic, complemented
20C2×D4×D43—22no—
21C2×D4×D43—22no—
22C2×D4×D43C2211yescharacteristic
23#13063358C2212yescomplemented
24#13063357—22no—
25#13063356C2212yescomplemented
26#13063355C2212yescomplemented
27#13063354—22no—
28Q16×D43—22no—
29SD16×D43—22no—
30M16×D43C2212yescomplemented
31#13063314C2211yescharacteristic, complemented
32#13063313C2211yescharacteristic, complemented
33#13063312C2211yescharacteristic, complemented
34#13063311—22no—
35C22⋊C4×D43—22no—
36C42×D43C2211yescharacteristic, complemented
37#13063253C2212yescomplemented
38#13063252C2212yescomplemented
39#13063251C2212yescomplemented
40#13063242C2211yescharacteristic, complemented
41#13063241C2212yescomplemented
42H(5,𝔽2)×C43C2211yescharacteristic
43#137×C43C2212yescomplemented
44#124×C43C2211yescharacteristic, complemented
45#104×C43C2212yescomplemented
46#100×C43C2211yescharacteristic, complemented
47C23×D43—22no—
48C23×D43D412yes—
49#41×C43—22no—
50#41×C43C2312yes—
51C2×Q8×C43C2311yescharacteristic, complemented
52C2×D4×C43—22no—
53C2×D4×C43—22no—
54C2×D4×C43C2311yescharacteristic
55C2×C22⋊D43—24no—
56C2×C22⋊D43—22no—
57C2×C22⋊D43—22no—
58C2×C22⋊D43D412yes—
59#10621902—22no—
60#10621902D412yes—
61Q8×D43—22no—
62Q8×D43—22no—
63Q8×D43D412yes—
64#10621900—24no—
65#10621900—22no—
66#10621900—22no—
67#10621900D412yes—
68D4×D43—24no—
69D4×D43—24no—
70D4×D43—24no—
71D4×D43—22no—
72D4×D43—22no—
73D4×D43—22no—
74D4×D43—22no—
75D4×D43—22no—
76D4×D43—24no—
77D4×D43D412yes—
78#10621898—24no—
79#10621898—22no—
80#10621898—22no—
81#10621898C2312yes—
82C2×D172—22no—
83C2×D172—22no—
84C2×D172C2311yescharacteristic
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43C2311yescharacteristic
90C2×Dic86—21no—
91C2×Dic86C2311yescharacteristic, complemented
92Q16×C43—22no—
93SD16×C43—22no—
94M16×C43C2312yescomplemented
95C22⋊C4×C43—22no—
96C42×C43C2311yescharacteristic, complemented
97C22⋊Dic43—22no—
98#10621885—22no—
99#10621885—22no—
100#10621884—22no—
101#10621883—22no—
102(C2×D43)⋊C4—22no—
103(C2×D43)⋊C4—22no—
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic, complemented
106#10621877C2312yescomplemented
107Dic172—22no—
108#10621873—22no—
109#10621872—22no—
110C8×D43—22no—
111C23×C43—22no—
112C23×C43C2×D412yes—
113C22×D43—22no—
114C22×D43—24no—
115C22×D43—22no—
116C22×D43—22no—
117C22×D43—22no—
118C22×D43—44no—
119C22×D43—84no—
120C22×D43C2×D411yescharacteristic
121C22×D43C2×D412yes—
122Q8×C43—22no—
123Q8×C43C2×D412yes—
124D4×C43—24no—
125D4×C43—22no—
126D4×C43—22no—
127D4×C43C2×D412yes—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—24no—
134C22⋊D43—24no—
135C22⋊D43—22no—
136C22⋊D43—22no—
137C22⋊D43—24no—
138C22⋊D43—22no—
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43C2×D411yescharacteristic
144D172—24no—
145D172—22no—
146D172—22no—
147D172C2×D412yes—
148C4×D43—24no—
149C4×D43—22no—
150C4×D43—22no—
151C4×D43—22no—
152C4×D43—42no—
153C4×D43—41no—
154C4×D43—41no—
155C4×D43C2×D412yes—
156C4×D43C2×D412yes—
157Dic86—22no—
158Dic86—22no—
159Dic86—42no—
160Dic86C2×D412yes—
161C8×C43—22no—
162C43⋊C8—22no—
163C22×C43—22no—
164C22×C43—22no—
165C22×C43—42no—
166C22×C43—82no—
167C22×C43C22×D411yescharacteristic
168C2×D43—22no—
169C2×D43—22no—
170C2×D43—22no—
171C2×D43—44no—
172C2×D43—44no—
173C2×D43—42no—
174C2×D43—82no—
175C2×D43—84no—
176C2×D43—82no—
177C2×D43#12011yescharacteristic
178C2×D43#12011yescharacteristic
179C4×C43—22no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43C22×D412yes—
183Dic43—22no—
184Dic43—41no—
185Dic43—41no—
186Dic43#12012yes—
187C2×#455—431nomaximal, Sylow
188C2×C43—21no—
189C2×C43—42no—
190C2×C43—42no—
191C2×C43C2×#12011yescharacteristic
192D43—21no—
193D43—42no—
194D43—42no—
195D43#45512yesdirect product factor
196C2×H(5,𝔽2)—431no—
197C2×#137—432no—
198C2×#124—431no—
199#455—431no—
200#455—432no—
201#455—431no—
202#455—432no—
203#455—431no—
204#455D4311yescharacteristic, direct product factor
205C2×#104—432no—
206C2×#100—431no—
207C43C2×#45511yescharacteristic, complemented, Sylow
208H(5,𝔽2)—432no—
209H(5,𝔽2)—431no—
210H(5,𝔽2)—862no—
211H(5,𝔽2)—862no—
212H(5,𝔽2)—862no—
213H(5,𝔽2)C2×D4311yescharacteristic
214C2×#41—432no—
215C2×#41—862no—
216C22×Q8—431no—
217C22×D4—431no—
218C22×D4—862no—
219C22×D4—862no—
220#137—432no—
221#137—432no—
222#137—432no—
223#137—862no—
224#137—862no—
225#137C2×D4312yescomplemented
226C2×Q16—862no—
227C2×SD16—862no—
228C2×M16—432no—
229#124—431no—
230#124—431no—
231#124—431no—
232#124—862no—
233#124C2×D4311yescharacteristic, complemented
234C2×C22⋊C4—862no—
235C2×C42—431no—
236#104—432no—
237#104—432no—
238#104—432no—
239#104C2×D4312yescomplemented
240#100—431no—
241#100—432no—
242#100C2×D4311yescharacteristic, complemented
243C24—432no—
244C24—862no—
245#41—22no—
246#41—432no—
247#41—432no—
248#41—432no—
249#41—862no—
250#41—862no—
251#41—864no—
252#41—862no—
253#41—862no—
254#41—864no—
255#41—862no—
256#41C22×D4312yes—
257C2×Q8—432no—
258C2×Q8—431no—
259C2×Q8—861no—
260C2×Q8—862no—
261C2×Q8—862no—
262C2×Q8C22×D4311yescharacteristic, complemented
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—432no—
266C2×D4—432no—
267C2×D4—431no—
268C2×D4—862no—
269C2×D4—862no—
270C2×D4—862no—
271C2×D4—862no—
272C2×D4—862no—
273C2×D4—862no—
274C2×D4—864no—
275C2×D4—864no—
276C2×D4—864no—
277C2×D4—864no—
278C2×D4—864no—
279C2×D4—862no—
280C2×D4—862no—
281C2×D4—862no—
282C2×D4C22×D4311yescharacteristic
283C22×C4—431no—
284C22×C4—862no—
285C22×C4—862no—
286C22×C4—861no—
287C22×C4—861no—
288Q16—22no—
289Q16—862no—
290Q16—862no—
291Q16—862no—
292SD16—22no—
293SD16—862no—
294SD16—862no—
295SD16—862no—
296M16—432no—
297M16—862no—
298M16C22×D4312yescomplemented
299C2×C8—862no—
300C22⋊C4—22no—
301C22⋊C4—862no—
302C22⋊C4—862no—
303C22⋊C4—862no—
304C42—431no—
305C42—861no—
306C42C22×D4311yescharacteristic, complemented
307C23—22no—
308C23—431no—
309C23—432no—
310C23—862no—
311C23—862no—
312C23—862no—
313C23—862no—
314C23—864no—
315C23—3444no—
316C23—1724no—
317C23D4×D4312yes—
318Q8—22no—
319Q8—432no—
320Q8—862no—
321Q8—862no—
322Q8—1722no—
323Q8D4×D4312yes—
324D4—24no—
325D4—22no—
326D4—22no—
327D4—432no—
328D4—862no—
329D4—864no—
330D4—864no—
331D4—862no—
332D4—862no—
333D4—864no—
334D4—864no—
335D4—862no—
336D4—862no—
337D4D4×D4312yes—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—431no—
343C2×C4—432no—
344C2×C4—432no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—864no—
348C2×C4—862no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1722no—
356C2×C4C23×D4311yescharacteristic
357C8—22no—
358C8—862no—
359C22—22no—
360C22—22no—
361C22—42no—
362C22—82no—
363C22—431no—
364C22—431no—
365C22—862no—
366C22—862no—
367C22—862no—
368C22—3442no—
369C22—3442no—
370C22—3444no—
371C22—1722no—
372C22—1724no—
373C22—1724no—
374C22C2×D4×D4311yescharacteristic
375C4—22no—
376C4—41no—
377C4—41no—
378C4—432no—
379C4—862no—
380C4—1721no—
381C4—1721no—
382C4C2×D4×D4312yes—
383C2—21no—
384C2—42no—
385C2—42no—
386C2—432no—
387C2—861no—
388C2—1722no—
389C2—1722no—
390C2#120×D4311yescharacteristic
subgroupG/H
centerC2#120×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#455C2
socleC2×C43C2×#120
hypercenter#455D43
hypocenterC43C2×#455
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
2. #137×D43C2semidirect
3. #124×D43C2semidirect
4. #14583079C2semidirect
5. #14583078C2semidirect
6. #14583077C2semidirect
7. #14583076C2semidirect
8. #14583075C2semidirect
9. #104×D43C2semidirect
10. #100×D43C2semidirect
11. C43×#455C2semidirect
19. C2×Q8×D43C22semidirect
23. #13063358C22semidirect
25. #13063356C22semidirect
26. #13063355C22semidirect
30. M16×D43C22semidirect
31. #13063314C22semidirect
32. #13063313C22semidirect
33. #13063312C22semidirect
36. C42×D43C22semidirect
37. #13063253C22semidirect
38. #13063252C22semidirect
39. #13063251C22semidirect
40. #13063242C22semidirect
41. #13063241C22semidirect
43. #137×C43C22semidirect
44. #124×C43C22semidirect
45. #104×C43C22semidirect
46. #100×C43C22semidirect
51. C2×Q8×C43C23semidirect
91. C2×Dic86C23semidirect
94. M16×C43C23semidirect
96. C42×C43C23semidirect
105. C4×Dic43C23semidirect
106. #10621877C23semidirect
195. D43#455direct (N × H)
204. #455D43direct (N × H)
207. C43C2×#455semidirect
225. #137C2×D43semidirect
233. #124C2×D43semidirect
239. #104C2×D43semidirect
242. #100C2×D43semidirect
262. C2×Q8C22×D43semidirect
298. M16C22×D43semidirect
306. C42C22×D43semidirect