Finite Group Databasebeta

← #19143953

Subgroups — #19143953

Order 5504.

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

normal subgroups only

This group has 762 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
1H(5,𝔽2)×D43C211yesmaximal, characteristic, complemented
2#14583698C212yesmaximal, complemented
3#14583467C211yesmaximal, characteristic, complemented
4#14583076C211yesmaximal, characteristic, complemented
5#14583075C212yesmaximal, complemented
6#14583069C211yesmaximal, characteristic, complemented
7#14583068C212yesmaximal, complemented
8#14583067C211yesmaximal, characteristic, complemented
9#14582914C212yesmaximal, complemented
10#100×D43C211yesmaximal, characteristic, complemented
11C43×#455C211yesmaximal, characteristic, complemented
12#13063371—22no—
13#13063371C2212yes—
14#13063370—22no—
15#13063370—22no—
16#13063370C2211yescharacteristic
17C2×#10621902C2211yescharacteristic, complemented
18#41×D43—22no—
19#41×D43C2212yes—
20C2×D4×D43—22no—
21C2×D4×D43—22no—
22C2×D4×D43C2211yescharacteristic
23#13063357—22no—
24#13063356C2212yescomplemented
25#13063353C2212yescomplemented
26#13063352—22no—
27#13063350C2212yescomplemented
28#13063348—22no—
29#13063346—22no—
30M16×D43C2212yescomplemented
31#13063322C2211yescharacteristic, complemented
32#13063321C2211yescharacteristic, complemented
33#13063314C2211yescharacteristic, complemented
34#13063298—22no—
35#13063295—22no—
36#13063282C2211yescharacteristic, 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⋊D43—22no—
59C2×C22⋊D43D412yes—
60#10621902—22no—
61#10621902—22no—
62#10621902—22no—
63#10621902D412yescomplemented
64Q8×D43D412yescomplemented
65#10621900—24no—
66#10621900—22no—
67#10621900—22no—
68#10621900D412yescomplemented
69D4×D43—24no—
70D4×D43—24no—
71D4×D43—24no—
72D4×D43—22no—
73D4×D43—22no—
74D4×D43—22no—
75D4×D43—22no—
76D4×D43—22no—
77D4×D43—24no—
78D4×D43D412yescomplemented
79#10621898—24no—
80#10621898—22no—
81#10621898—22no—
82#10621898C2312yes—
83C2×D172—22no—
84C2×D172—22no—
85C2×D172—21no—
86C2×D172—22no—
87C2×D172C2311yescharacteristic
88C2×D172C2311yescharacteristic, complemented
89C2×C4×D43—22no—
90C2×C4×D43—22no—
91C2×C4×D43—21no—
92C2×C4×D43C2311yescharacteristic
93Q16×C43—22no—
94SD16×C43—22no—
95M16×C43C2312yescomplemented
96C22⋊C4×C43—22no—
97C42×C43C2311yescharacteristic, complemented
98#10621885—22no—
99#10621884—22no—
100#10621884—22no—
101#10621882—22no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—22no—
104Dic43⋊C4—21no—
105C4×Dic43C2311yescharacteristic, complemented
106#10621877C2312yescomplemented
107D344—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—21no—
119C22×D43—82no—
120C22×D43—84no—
121C22×D43C2×D412yes—
122C22×D43C2×D411yescharacteristic
123Q8×C43—22no—
124Q8×C43C2×D412yes—
125D4×C43—24no—
126D4×C43—22no—
127D4×C43—22no—
128D4×C43C2×D412yes—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—24no—
135C22⋊D43—24no—
136C22⋊D43—22no—
137C22⋊D43—22no—
138C22⋊D43—24no—
139C22⋊D43—22no—
140C22⋊D43—82no—
141C2×Dic43—22no—
142C2×Dic43—22no—
143C2×Dic43—21no—
144C2×Dic43C2×D411yescharacteristic
145D172—24no—
146D172—22no—
147D172—22no—
148D172—22no—
149D172—41no—
150D172—41no—
151D172—82no—
152D172C2×D412yes—
153C4×D43—24no—
154C4×D43—22no—
155C4×D43—22no—
156C4×D43—22no—
157C4×D43—42no—
158C4×D43C2×D412yes—
159C4×D43C2×D412yes—
160Dic86—22no—
161Dic86C2×D412yes—
162C8×C43—22no—
163C43⋊C8—22no—
164C22×C43—22no—
165C22×C43—22no—
166C22×C43—42no—
167C22×C43—82no—
168C22×C43C22×D411yescharacteristic
169C2×D43—22no—
170C2×D43—22no—
171C2×D43—41no—
172C2×D43—44no—
173C2×D43—44no—
174C2×D43—42no—
175C2×D43—42no—
176C2×D43—41no—
177C2×D43—82no—
178C2×D43—84no—
179C2×D43—82no—
180C2×D43#12011yescharacteristic
181C2×D43#12011yescharacteristic
182C4×C43—22no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43C22×D412yes—
186Dic43—22no—
187Dic43—41no—
188Dic43#12012yes—
189#3019—431nomaximal, Sylow
190C2×C43—21no—
191C2×C43—42no—
192C2×C43—42no—
193C2×C43C2×#12011yescharacteristic
194D43—21no—
195D43—21no—
196D43—42no—
197D43—42no—
198D43—81no—
199C2×H(5,𝔽2)—431no—
200#575—432no—
201#535—431no—
202#455—432no—
203#455—431no—
204#455D4311yescharacteristic, complemented
205#453—431no—
206#453—432no—
207#453—431no—
208#421—432no—
209C2×#100—431no—
210C43#301911yescharacteristic, complemented, Sylow
211H(5,𝔽2)—432no—
212H(5,𝔽2)—431no—
213H(5,𝔽2)—862no—
214H(5,𝔽2)—862no—
215H(5,𝔽2)—862no—
216H(5,𝔽2)C2×D4311yescharacteristic
217C2×#41—432no—
218C2×#41—431no—
219C2×#41—862no—
220C22×D4—431no—
221C22×D4—862no—
222C22×D4—862no—
223#137—432no—
224#137—862no—
225#137C2×D4312yescomplemented
226AGL(1,ℤ/8)—432no—
227AGL(1,ℤ/8)—432no—
228AGL(1,ℤ/8)—862no—
229#135—862no—
230#135—862no—
231C2×M16—432no—
232#127—431no—
233#127—431no—
234#124—431no—
235#124C2×D4311yescharacteristic, complemented
236#121—862no—
237#120—862no—
238#117—431no—
239#104—432no—
240#104—432no—
241#104—432no—
242#104C2×D4312yescomplemented
243#100—431no—
244#100—432no—
245#100C2×D4311yescharacteristic, complemented
246C24—432no—
247C24—862no—
248#41—22no—
249#41—432no—
250#41—432no—
251#41—432no—
252#41—862no—
253#41—862no—
254#41—864no—
255#41—862no—
256#41—862no—
257#41—862no—
258#41—862no—
259#41—864no—
260#41—862no—
261#41C22×D4312yes—
262C2×Q8—432no—
263C2×Q8C22×D4311yescharacteristic, complemented
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—432no—
267C2×D4—432no—
268C2×D4—431no—
269C2×D4—431no—
270C2×D4—862no—
271C2×D4—862no—
272C2×D4—862no—
273C2×D4—861no—
274C2×D4—862no—
275C2×D4—862no—
276C2×D4—862no—
277C2×D4—862no—
278C2×D4—864no—
279C2×D4—864no—
280C2×D4—864no—
281C2×D4—864no—
282C2×D4—864no—
283C2×D4—862no—
284C2×D4—862no—
285C2×D4—862no—
286C2×D4—862no—
287C2×D4C22×D4311yescharacteristic
288C22×C4—431no—
289C22×C4—862no—
290C22×C4—861no—
291C22×C4—862no—
292Q16—22no—
293Q16—862no—
294SD16—22no—
295SD16—862no—
296SD16—862no—
297SD16—862no—
298D8—862no—
299D8—862no—
300M16—432no—
301M16—862no—
302M16C22×D4312yescomplemented
303C2×C8—862no—
304C4⋊C4—861no—
305C22⋊C4—22no—
306C22⋊C4—861no—
307C22⋊C4—862no—
308C42—431no—
309C42C22×D4311yescharacteristic, complemented
310C23—22no—
311C23—431no—
312C23—432no—
313C23—862no—
314C23—862no—
315C23—862no—
316C23—862no—
317C23—864no—
318C23—861no—
319C23—3442no—
320C23—3444no—
321C23D4×D4312yes—
322Q8—22no—
323Q8—432no—
324Q8—862no—
325Q8D4×D4312yes—
326D4—24no—
327D4—22no—
328D4—22no—
329D4—432no—
330D4—862no—
331D4—864no—
332D4—864no—
333D4—862no—
334D4—862no—
335D4—864no—
336D4—864no—
337D4—862no—
338D4—862no—
339D4—862no—
340D4—3442no—
341D4—3442no—
342D4—1721no—
343D4—1721no—
344D4D4×D4312yes—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—431no—
350C2×C4—432no—
351C2×C4—432no—
352C2×C4—862no—
353C2×C4—862no—
354C2×C4—864no—
355C2×C4—862no—
356C2×C4—862no—
357C2×C4—862no—
358C2×C4—861no—
359C2×C4—1722no—
360C2×C4C23×D4311yescharacteristic
361C8—22no—
362C8—862no—
363C22—22no—
364C22—22no—
365C22—42no—
366C22—82no—
367C22—431no—
368C22—431no—
369C22—862no—
370C22—862no—
371C22—3442no—
372C22—3442no—
373C22—3444no—
374C22—1721no—
375C22—1722no—
376C22—1722no—
377C22—1724no—
378C22—1724no—
379C22—1721no—
380C22C2×D4×D4311yescharacteristic
381C4—22no—
382C4—41no—
383C4—41no—
384C4—432no—
385C4—862no—
386C4—1721no—
387C4C2×D4×D4312yes—
388C2—21no—
389C2—42no—
390C2—42no—
391C2—861no—
392C2—861no—
393C2—3441no—
394C2—1722no—
395C2—1722no—
396C2#120×D4311yescharacteristic
subgroupG/H
centerC2#120×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#455C2
socleC2×C43C2×#120
hypercenter#455D43
hypocenterC43#3019
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
1. H(5,𝔽2)×D43C2semidirect
2. #14583698C2semidirect
3. #14583467C2semidirect
4. #14583076C2semidirect
5. #14583075C2semidirect
6. #14583069C2semidirect
7. #14583068C2semidirect
8. #14583067C2semidirect
9. #14582914C2semidirect
10. #100×D43C2semidirect
11. C43×#455C2semidirect
17. C2×#10621902C22semidirect
24. #13063356C22semidirect
25. #13063353C22semidirect
27. #13063350C22semidirect
30. M16×D43C22semidirect
31. #13063322C22semidirect
32. #13063321C22semidirect
33. #13063314C22semidirect
36. #13063282C22semidirect
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
63. #10621902D4semidirect
64. Q8×D43D4semidirect
68. #10621900D4semidirect
78. D4×D43D4semidirect
88. C2×D172C23semidirect
95. M16×C43C23semidirect
97. C42×C43C23semidirect
105. C4×Dic43C23semidirect
106. #10621877C23semidirect
204. #455D43semidirect
210. C43#3019semidirect
225. #137C2×D43semidirect
235. #124C2×D43semidirect
242. #104C2×D43semidirect
245. #100C2×D43semidirect
263. C2×Q8C22×D43semidirect
302. M16C22×D43semidirect
309. C42C22×D43semidirect