Finite Group Databasebeta

← #19143963

Subgroups — #19143963

Order 5504.

736 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#14583734C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D43C212yesmaximal, complemented
3#14583462C211yesmaximal, characteristic, complemented
4#14583073C212yesmaximal, complemented
5#14583070C212yesmaximal, complemented
6#14583069C211yesmaximal, characteristic, complemented
7#14583067C211yesmaximal, characteristic, complemented
8#14583066C211yesmaximal, characteristic, complemented
9#14582914C212yesmaximal, complemented
10#14582880C211yesmaximal, characteristic, complemented
11C43×#453C211yesmaximal, characteristic, complemented
12#13063372—22no—
13#13063372C2212yescomplemented
14#13063370—22no—
15#13063370—22no—
16#13063370C2211yescharacteristic, complemented
17C2×#10621900—22no—
18C2×#10621900—22no—
19C2×#10621900C2211yescharacteristic
20#41×D43—22no—
21#41×D43C2212yes—
22C2×D4×D43C2211yescharacteristic, complemented
23#13063353C2212yescomplemented
24#13063352—22no—
25#13063351C2212yescomplemented
26#13063350C2212yescomplemented
27#13063349—22no—
28SD16×D43—22no—
29D8×D43—22no—
30M16×D43C2212yescomplemented
31#13063321C2211yescharacteristic, complemented
32#13063313C2211yescharacteristic, complemented
33#13063312C2211yescharacteristic, complemented
34#13063297—22no—
35#13063293—22no—
36#13063282C2211yescharacteristic, complemented
37#13063253C2212yescomplemented
38#13063252C2212yescomplemented
39#13063251C2212yescomplemented
40#13063243C2212yescomplemented
41#13063242C2211yescharacteristic, complemented
42H(5,𝔽2)×C43C2211yescharacteristic, complemented
43AGL(1,ℤ/8)×C43C2212yescomplemented
44#127×C43C2211yescharacteristic, complemented
45#104×C43C2212yescomplemented
46#100×C43C2211yescharacteristic, complemented
47C23×D43—21no—
48#41×C43—22no—
49#41×C43C2312yes—
50C2×D4×C43—22no—
51C2×D4×C43—22no—
52C2×D4×C43—22no—
53C2×D4×C43C2311yescharacteristic
54C2×D4×C43C2311yescharacteristic
55C2×C22⋊D43—22no—
56C2×C22⋊D43—24no—
57C2×C22⋊D43—21no—
58C2×C22⋊D43—22no—
59C2×C22⋊D43—22no—
60C2×C22⋊D43D412yes—
61C22×Dic43—22no—
62C22×Dic43D412yes—
63#10621902D412yescomplemented
64Q8×D43—22no—
65Q8×D43D412yescomplemented
66#10621900—24no—
67#10621900—24no—
68#10621900—24no—
69#10621900—22no—
70#10621900—22no—
71#10621900—24no—
72#10621900—22no—
73#10621900—22no—
74#10621900—22no—
75#10621900D412yescomplemented
76D4×D43—24no—
77D4×D43—22no—
78D4×D43—22no—
79D4×D43—22no—
80D4×D43—22no—
81D4×D43D412yescomplemented
82#10621898—24no—
83#10621898—22no—
84#10621898—22no—
85#10621898C2312yes—
86C2×D172C2311yescharacteristic
87C2×C4×D43—22no—
88C2×C4×D43—22no—
89C2×C4×D43C2311yescharacteristic
90C2×Dic86—22no—
91C2×Dic86—22no—
92C2×Dic86C2311yescharacteristic
93SD16×C43—22no—
94D8×C43—22no—
95M16×C43C2312yes—
96C42×C43C2311yescharacteristic
97C22⋊Dic43—22no—
98#10621884—22no—
99#10621883—22no—
100#10621882—22no—
101#10621882—22no—
102(C2×D43)⋊C4—22no—
103(C2×D43)⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43C2311yescharacteristic
106#10621877C2312yes—
107D344—22no—
108#10621873—22no—
109#10621872—22no—
110C8×D43—22no—
111C23×C43—22no—
112C23×C43—21no—
113C23×C43C2×D412yes—
114C22×D43—22no—
115C22×D43—22no—
116C22×D43—21no—
117C22×D43—42no—
118C22×D43—82no—
119C22×D43C2×D411yescharacteristic
120Q8×C43C2×D412yes—
121D4×C43—24no—
122D4×C43—22no—
123D4×C43—22no—
124D4×C43—22no—
125D4×C43—82no—
126D4×C43C2×D412yes—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—21no—
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—24no—
132C22⋊D43—24no—
133C22⋊D43—22no—
134C22⋊D43—24no—
135C22⋊D43—22no—
136C22⋊D43—22no—
137C22⋊D43—41no—
138C22⋊D43—41no—
139C22⋊D43—82no—
140C2×Dic43—24no—
141C2×Dic43—22no—
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43—22no—
145C2×Dic43—21no—
146C2×Dic43C2×D412yes—
147C2×Dic43C2×D411yescharacteristic
148D172—22no—
149D172—22no—
150D172C2×D412yes—
151C4×D43—24no—
152C4×D43—22no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43C2×D412yes—
156C4×D43C2×D412yes—
157Dic86—24no—
158Dic86—22no—
159Dic86—22no—
160Dic86C2×D412yes—
161C8×C43—22no—
162C43⋊C8—22no—
163C22×C43—22no—
164C22×C43—22no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43—41no—
168C22×C43—82no—
169C22×C43C22×D411yescharacteristic
170C2×D43—22no—
171C2×D43—41no—
172C2×D43—42no—
173C2×D43—41no—
174C2×D43—82no—
175C2×D43—84no—
176C2×D43—82no—
177C2×D43#12012yes—
178C4×C43—22no—
179C4×C43—41no—
180C4×C43C22×D412yes—
181Dic43—22no—
182Dic43—22no—
183Dic43—41no—
184Dic43#12011yescharacteristic
185Dic43#12011yescharacteristic
186#3021—431nomaximal, Sylow
187C2×C43—21no—
188C2×C43—42no—
189C2×C43—42no—
190C2×C43—81no—
191C2×C43C2×#12011yescharacteristic
192D43—22no—
193D43—42no—
194D43—81no—
195#585—431no—
196C2×AGL(1,ℤ/8)—432no—
197#535—431no—
198#454—432no—
199#454—432no—
200#453—431no—
201#453—431no—
202#453—431no—
203#453D4311yescharacteristic, complemented
204#421—432no—
205#413—431no—
206C43#302111yescharacteristic, complemented, Sylow
2072−1+4—432no—
2082−1+4—862no—
209H(5,𝔽2)—431no—
210H(5,𝔽2)—862no—
211H(5,𝔽2)—862no—
212H(5,𝔽2)C2×D4311yescharacteristic, complemented
213C2×#41—431no—
214C2×#41—432no—
215C2×#41—862no—
216C2×#41—862no—
217C2×#41—862no—
218C22×D4—431no—
219AGL(1,ℤ/8)—432no—
220AGL(1,ℤ/8)—432no—
221AGL(1,ℤ/8)—432no—
222AGL(1,ℤ/8)—862no—
223AGL(1,ℤ/8)—862no—
224AGL(1,ℤ/8)C2×D4312yescomplemented
225C2×SD16—862no—
226C2×D8—862no—
227C2×M16—432no—
228#127—431no—
229#127C2×D4311yescharacteristic, complemented
230#124—431no—
231#124—431no—
232#121—862no—
233#120—862no—
234#117—431no—
235#104—432no—
236#104—432no—
237#104—432no—
238#104C2×D4312yescomplemented
239#101—432no—
240#100—431no—
241#100C2×D4311yescharacteristic, complemented
242C24—861no—
243#41—22no—
244#41—432no—
245#41—432no—
246#41—432no—
247#41—862no—
248#41—862no—
249#41—864no—
250#41—862no—
251#41—862no—
252#41—862no—
253#41—864no—
254#41—862no—
255#41—864no—
256#41—864no—
257#41—864no—
258#41—862no—
259#41C22×D4312yes—
260C2×Q8—431no—
261C2×Q8—432no—
262C2×Q8—862no—
263C2×Q8—862no—
264C2×Q8—862no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—432no—
269C2×D4—432no—
270C2×D4—431no—
271C2×D4—862no—
272C2×D4—862no—
273C2×D4—861no—
274C2×D4—862no—
275C2×D4—862no—
276C2×D4—864no—
277C2×D4—862no—
278C2×D4—864no—
279C2×D4—862no—
280C2×D4—862no—
281C2×D4C22×D4311yescharacteristic
282C2×D4C22×D4311yescharacteristic
283C22×C4—431no—
284C22×C4—432no—
285C22×C4—862no—
286C22×C4—862no—
287C22×C4—862no—
288SD16—22no—
289SD16—862no—
290SD16—862no—
291SD16—862no—
292D8—22no—
293D8—862no—
294D8—862no—
295D8—862no—
296M16—432no—
297M16—862no—
298M16C22×D4312yes—
299C2×C8—862no—
300C4⋊C4—861no—
301C22⋊C4—862no—
302C22⋊C4—861no—
303C22⋊C4—862no—
304C42—431no—
305C42C22×D4311yescharacteristic
306C23—22no—
307C23—21no—
308C23—431no—
309C23—862no—
310C23—862no—
311C23—861no—
312C23—3442no—
313C23—1722no—
314C23D4×D4312yes—
315Q8—432no—
316Q8—862no—
317Q8—864no—
318Q8—862no—
319Q8D4×D4312yes—
320D4—24no—
321D4—22no—
322D4—22no—
323D4—22no—
324D4—82no—
325D4—432no—
326D4—862no—
327D4—862no—
328D4—864no—
329D4—862no—
330D4—864no—
331D4—864no—
332D4—862no—
333D4—862no—
334D4—3442no—
335D4—1721no—
336D4—1721no—
337D4D4×D4312yes—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—431no—
342C2×C4—432no—
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—864no—
352C2×C4—862no—
353C2×C4—862no—
354C2×C4—861no—
355C2×C4C23×D4311yescharacteristic
356C8—22no—
357C8—862no—
358C22—22no—
359C22—22no—
360C22—42no—
361C22—42no—
362C22—41no—
363C22—82no—
364C22—432no—
365C22—862no—
366C22—3442no—
367C22—3442no—
368C22—3444no—
369C22—1721no—
370C22—1722no—
371C22—1721no—
372C22C2×D4×D4311yescharacteristic
373C4—22no—
374C4—41no—
375C4—431no—
376C4—431no—
377C4—862no—
378C4—862no—
379C4—1721no—
380C4C2×D4×D4312yes—
381C2—21no—
382C2—42no—
383C2—42no—
384C2—81no—
385C2—862no—
386C2—3441no—
387C2—1722no—
388C2#120×D4311yescharacteristic
subgroupG/H
centerC2#120×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#453C2
socleC2×C43C2×#120
hypercenter#453D43
hypocenterC43#3021
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. #14583734C2semidirect
2. AGL(1,ℤ/8)×D43C2semidirect
3. #14583462C2semidirect
4. #14583073C2semidirect
5. #14583070C2semidirect
6. #14583069C2semidirect
7. #14583067C2semidirect
8. #14583066C2semidirect
9. #14582914C2semidirect
10. #14582880C2semidirect
11. C43×#453C2semidirect
13. #13063372C22semidirect
16. #13063370C22semidirect
22. C2×D4×D43C22semidirect
23. #13063353C22semidirect
25. #13063351C22semidirect
26. #13063350C22semidirect
30. M16×D43C22semidirect
31. #13063321C22semidirect
32. #13063313C22semidirect
33. #13063312C22semidirect
36. #13063282C22semidirect
37. #13063253C22semidirect
38. #13063252C22semidirect
39. #13063251C22semidirect
40. #13063243C22semidirect
41. #13063242C22semidirect
42. H(5,𝔽2)×C43C22semidirect
43. AGL(1,ℤ/8)×C43C22semidirect
44. #127×C43C22semidirect
45. #104×C43C22semidirect
46. #100×C43C22semidirect
63. #10621902D4semidirect
65. Q8×D43D4semidirect
75. #10621900D4semidirect
81. D4×D43D4semidirect
203. #453D43semidirect
206. C43#3021semidirect
212. H(5,𝔽2)C2×D43semidirect
224. AGL(1,ℤ/8)C2×D43semidirect
229. #127C2×D43semidirect
238. #104C2×D43semidirect
241. #100C2×D43semidirect