Finite Group Databasebeta

← #19143950

Subgroups — #19143950

Order 5504.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#13063371C211yesmaximal, characteristic, complemented
2#14583697C211yesmaximal, characteristic, complemented
3#14583463C211yesmaximal, characteristic, complemented
4#14583075C214yesmaximal, complemented
5#14583065C214yesmaximal, complemented
6#14582916C211yesmaximal, characteristic, complemented
7#14582915C211yesmaximal, characteristic, complemented
8C2×#13063241C211yesmaximal, characteristic, complemented
9C43×#575C211yesmaximal, characteristic, complemented
10#13063371—22no—
11#13063371—22no—
12#13063371—22no—
13#13063371C2214yes—
14C2×#10621902—21no—
15C2×#10621898—21no—
16C2×#10621898C2211yescharacteristic
17C22×D172—21no—
18C22×D172C2211yescharacteristic
19C2×D4×D43—22no—
20C2×D4×D43—21no—
21#13063356C2212yescomplemented
22#13063355—21no—
23#13063351C2212yescomplemented
24#13063350—21no—
25#13063345—22no—
26C2×#10621877C2211yescharacteristic, complemented
27#13063321C2212yescomplemented
28#13063314C2212yescomplemented
29#13063299—22no—
30#13063293—22no—
31#13063284C2211yescharacteristic, complemented
32#13063252C2214yescomplemented
33#13063251C2214yescomplemented
34#13063241C2214yescomplemented
35C2×#41×C43C2211yescharacteristic
36C2×#41×C43C2211yescharacteristic, complemented
37#137×C43—21no—
38#137×C43C2212yescomplemented
39AGL(1,ℤ/8)×C43—21no—
40AGL(1,ℤ/8)×C43C2212yescomplemented
41#135×C43—22no—
42C2×M16×C43C2211yescharacteristic, complemented
43C23×D43—22no—
44C23×D43D412yes—
45#41×C43—21no—
46#41×C43—21no—
47#41×C43—21no—
48#41×C43—21no—
49#41×C43—21no—
50#41×C43—21no—
51#41×C43D412yescomplemented
52#41×C43C2312yes—
53C2×Q8×C43D411yescharacteristic, complemented
54C2×Q8×C43C2311yescharacteristic, complemented
55C2×D4×C43—21no—
56C2×D4×C43—21no—
57C2×D4×C43D411yescharacteristic, complemented
58C2×D4×C43C2311yescharacteristic, complemented
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—22no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—24no—
65#10621902—24no—
66#10621902—24no—
67D4×D43—24no—
68D4×D43—28no—
69D4×D43—24no—
70D4×D43—28no—
71#10621898—24no—
72#10621898—21no—
73#10621898—21no—
74#10621898—24no—
75#10621898D412yescomplemented
76#10621898C2312yes—
77C2×D172—22no—
78C2×D172—24no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172—21no—
82C2×D172—21no—
83C2×D172—24no—
84C2×D172D412yes—
85C2×D172D411yescharacteristic, complemented
86C2×D172C2312yes—
87C2×C4×D43—22no—
88C2×C4×D43—21no—
89C2×Dic86D411yescharacteristic, complemented
90Q16×C43—22no—
91SD16×C43—22no—
92SD16×C43—22no—
93D8×C43—22no—
94M16×C43—21no—
95M16×C43C2312yescomplemented
96C2×C8×C43—21no—
97C22⋊Dic43—21no—
98#10621885—22no—
99#10621884—22no—
100#10621883—22no—
101#10621882—22no—
102(C2×D43)⋊C4—24no—
103C4⋊Dic43—21no—
104C4×Dic43C2312yescomplemented
105#10621877—21no—
106#10621877C2312yescomplemented
107C2×C43⋊C8—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43C2×D411yescharacteristic
111C22×D43—22no—
112C22×D43—21no—
113C22×D43—28no—
114C22×D43—22no—
115C22×D43—82no—
116C22×D43—84no—
117C22×D43C2×D414yes—
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43C2×D412yes—
122D4×C43—22no—
123D4×C43—22no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—41no—
128D4×C43—41no—
129D4×C43C2×D412yes—
130C2×C4×C43—21no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2×D411yescharacteristic
141C2×C4×C43C2411yescharacteristic
142C22⋊D43—28no—
143C22⋊D43—22no—
144C22⋊D43—22no—
145C22⋊D43—84no—
146C2×Dic43—21no—
147C2×Dic43—22no—
148D172—28no—
149D172—22no—
150D172—21no—
151D172—22no—
152D172—22no—
153D172—22no—
154D172C2×D412yes—
155C4×D43—28no—
156C4×D43—22no—
157C4×D43—22no—
158Dic86—21no—
159Dic86C2×D412yes—
160C8×C43—22no—
161C43⋊C8—22no—
162C22×C43—22no—
163C22×C43—41no—
164C22×C43—42no—
165C22×C43—42no—
166C22×C43—41no—
167C22×C43#12011yescharacteristic
168C22×C43#12011yescharacteristic
169C22×C43C22×D411yescharacteristic
170C2×D43—22no—
171C2×D43—24no—
172C2×D43—44no—
173C2×D43—42no—
174C2×D43—44no—
175C2×D43—82no—
176C2×D43—88no—
177C4×C43—22no—
178C4×C43—41no—
179C4×C43#12011yescharacteristic
180C4×C43#12011yescharacteristic
181C4×C43C22×D411yescharacteristic
182C4×C43C22×D411yescharacteristic
183Dic43—22no—
184Dic43—42no—
185#3019—431nomaximal, Sylow
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—42no—
190C2×C43—81no—
191C2×C43C2×#12011yescharacteristic
192D43—44no—
193D43—42no—
194C2×H(5,𝔽2)—431no—
195#575—431no—
196#575D4311yescharacteristic, complemented
197#535—431no—
198#455—434no—
199#453—434no—
200#421—431no—
201#421—431no—
202C2×#100—431no—
203C43#301911yescharacteristic, complemented, Sylow
204H(5,𝔽2)—434no—
205H(5,𝔽2)—862no—
206H(5,𝔽2)—862no—
207H(5,𝔽2)—862no—
208C2×#41—431no—
209C2×#41—861no—
210C2×#41—861no—
211C2×#41C2×D4311yescharacteristic
212C2×#41C2×D4311yescharacteristic, complemented
213C22×D4—431no—
214C22×D4—861no—
215C22×D4—862no—
216C22×D4—861no—
217#137—21no—
218#137—432no—
219#137—861no—
220#137C2×D4312yescomplemented
221AGL(1,ℤ/8)—21no—
222AGL(1,ℤ/8)—432no—
223AGL(1,ℤ/8)—861no—
224AGL(1,ℤ/8)C2×D4312yescomplemented
225#135—22no—
226#135—862no—
227C2×M16—431no—
228C2×M16C2×D4311yescharacteristic, complemented
229#127—432no—
230#124—432no—
231#121—862no—
232#120—862no—
233#117—431no—
234#104—434no—
235#104—434no—
236#100—434no—
237C24—432no—
238C24—862no—
239#41—21no—
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244#41—21no—
245#41—432no—
246#41—432no—
247#41—864no—
248#41—864no—
249#41—864no—
250#41—864no—
251#41—861no—
252#41—861no—
253#41C22⋊D4312yescomplemented
254#41C22×D4312yes—
255C2×Q8—431no—
256C2×Q8C22⋊D4311yescharacteristic, complemented
257C2×Q8C22×D4311yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—431no—
261C2×D4—432no—
262C2×D4—432no—
263C2×D4—864no—
264C2×D4—862no—
265C2×D4—864no—
266C2×D4—868no—
267C2×D4—868no—
268C2×D4—864no—
269C2×D4—862no—
270C2×D4—861no—
271C2×D4—864no—
272C2×D4—864no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4C22⋊D4311yescharacteristic, complemented
278C2×D4C22×D4311yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—862no—
282C22×C4—861no—
283C22×C4C22×D4311yescharacteristic
284Q16—22no—
285Q16—862no—
286SD16—22no—
287SD16—22no—
288SD16—862no—
289SD16—862no—
290D8—22no—
291D8—862no—
292M16—21no—
293M16—432no—
294M16—861no—
295M16C22×D4312yescomplemented
296C2×C8—21no—
297C2×C8—861no—
298C4⋊C4—861no—
299C22⋊C4—864no—
300C22⋊C4—861no—
301C42—432no—
302C23—21no—
303C23—21no—
304C23—434no—
305C23—868no—
306C23—862no—
307C23—861no—
308C23—862no—
309C23—3444no—
310C23—3442no—
311C23D4×D4311yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—432no—
316Q8—861no—
317Q8C2×C22⋊D4312yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—432no—
326D4—868no—
327D4—868no—
328D4—862no—
329D4—862no—
330D4—861no—
331D4—862no—
332D4—862no—
333D4—862no—
334D4—862no—
335D4—3444no—
336D4C2×C22⋊D4312yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—868no—
344C2×C4—861no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—862no—
348C2×C4D4×D4311yescharacteristic
349C2×C4D4×D4311yescharacteristic
350C2×C4D4×D4311yescharacteristic
351C2×C4C2×C22⋊D4311yescharacteristic
352C2×C4C2×C22⋊D4311yescharacteristic
353C2×C4C23×D4311yescharacteristic
354C8—22no—
355C8—862no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—862no—
362C22—864no—
363C22—3442no—
364C22—3448no—
365C22—1724no—
366C22—1722no—
367C22—1724no—
368C22#1306329311yescharacteristic
369C22#1306329311yescharacteristic
370C22C2×D4×D4311yescharacteristic
371C4—22no—
372C4—41no—
373C4—862no—
374C4—1722no—
375C4#1306329311yescharacteristic
376C4#1306329311yescharacteristic
377C4C2×D4×D4311yescharacteristic
378C4C22×C22⋊D4311yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—81no—
384C2—1722no—
385C2—1724no—
386C2C2×#1306329311yescharacteristic
subgroupG/H
centerC2C2×#13063293
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#575C2
socleC2×C43C2×#120
hypercenter#575D43
hypocenterC43#3019
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#13063371C2semidirect
2. #14583697C2semidirect
3. #14583463C2semidirect
4. #14583075C2semidirect
5. #14583065C2semidirect
6. #14582916C2semidirect
7. #14582915C2semidirect
8. C2×#13063241C2semidirect
9. C43×#575C2semidirect
21. #13063356C22semidirect
23. #13063351C22semidirect
26. C2×#10621877C22semidirect
27. #13063321C22semidirect
28. #13063314C22semidirect
31. #13063284C22semidirect
32. #13063252C22semidirect
33. #13063251C22semidirect
34. #13063241C22semidirect
36. C2×#41×C43C22semidirect
38. #137×C43C22semidirect
40. AGL(1,ℤ/8)×C43C22semidirect
42. C2×M16×C43C22semidirect
51. #41×C43D4semidirect
53. C2×Q8×C43D4semidirect
54. C2×Q8×C43C23semidirect
57. C2×D4×C43D4semidirect
58. C2×D4×C43C23semidirect
75. #10621898D4semidirect
85. C2×D172D4semidirect
89. C2×Dic86D4semidirect
95. M16×C43C23semidirect
104. C4×Dic43C23semidirect
106. #10621877C23semidirect
196. #575D43semidirect
203. C43#3019semidirect
212. C2×#41C2×D43semidirect
220. #137C2×D43semidirect
224. AGL(1,ℤ/8)C2×D43semidirect
228. C2×M16C2×D43semidirect
253. #41C22⋊D43semidirect
256. C2×Q8C22⋊D43semidirect
257. C2×Q8C22×D43semidirect
277. C2×D4C22⋊D43semidirect
278. C2×D4C22×D43semidirect
295. M16C22×D43semidirect