Finite Group Databasebeta

← #19143941

Subgroups — #19143941

Order 5504.

724 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583735C211yesmaximal, characteristic, complemented
2#14583697C211yesmaximal, characteristic, complemented
3#14583445C211yesmaximal, characteristic, complemented
4#14583080C212yesmaximal, complemented
5#14583075C212yesmaximal, complemented
6#14583070C212yesmaximal, complemented
7#14583065C212yesmaximal, complemented
8C2×#13063252C211yesmaximal, characteristic, complemented
9C2×#13063251C211yesmaximal, characteristic, complemented
10#14582881C211yesmaximal, characteristic, complemented
11C43×#575C211yesmaximal, characteristic, complemented
12#13063373—21no—
13#13063372—21no—
14#13063372C2212yes—
15#13063371—21no—
16#13063371C2212yes—
17#13063370—21no—
18#13063370—22no—
19C2×#10621898—22no—
20C2×#10621898C2211yescharacteristic
21C2×#10621898C2211yescharacteristic
22#41×D43—22no—
23#41×D43—22no—
24#13063356C2212yescomplemented
25#13063355—21no—
26#13063351C2212yescomplemented
27#13063350—21no—
28#13063345—22no—
29C2×#10621877C2211yescharacteristic, complemented
30#13063323C2211yescharacteristic, complemented
31#13063321C2211yescharacteristic, complemented
32#13063314C2211yescharacteristic, complemented
33#13063312C2211yescharacteristic, complemented
34#13063297—22no—
35C4×C22⋊D43—22no—
36C2×C4×Dic43C2211yescharacteristic, complemented
37#13063252C2212yescomplemented
38#13063252C2212yescomplemented
39#13063251C2212yescomplemented
40#13063251C2212yescomplemented
41#13063243C2212yescomplemented
42#13063241C2212yescomplemented
43C2×#41×C43C2211yescharacteristic
44C2×#41×C43C2211yescharacteristic, complemented
45#137×C43—21no—
46#137×C43C2212yescomplemented
47AGL(1,ℤ/8)×C43—21no—
48AGL(1,ℤ/8)×C43C2212yescomplemented
49#135×C43—22no—
50C2×M16×C43C2211yescharacteristic, complemented
51#41×C43—21no—
52#41×C43—21no—
53#41×C43—21no—
54#41×C43—21no—
55#41×C43—21no—
56#41×C43—21no—
57#41×C43D412yescomplemented
58#41×C43C2312yes—
59C2×Q8×C43D411yescharacteristic, complemented
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43D411yescharacteristic, complemented
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—24no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—22no—
71C2×C22⋊D43D412yes—
72C22×Dic43—21no—
73#10621902—22no—
74#10621902—22no—
75Q8×D43—22no—
76Q8×D43—22no—
77#10621900—24no—
78#10621900—22no—
79#10621900—22no—
80#10621900—24no—
81D4×D43—22no—
82D4×D43—24no—
83D4×D43—22no—
84D4×D43—24no—
85#10621898—24no—
86#10621898—24no—
87#10621898—21no—
88#10621898—21no—
89#10621898—21no—
90#10621898—21no—
91#10621898—21no—
92#10621898—21no—
93#10621898—22no—
94#10621898—22no—
95#10621898D412yescomplemented
96#10621898C2312yes—
97C2×D172—22no—
98C2×D172D411yescharacteristic, complemented
99C2×D172C2311yescharacteristic
100C2×C4×D43—24no—
101C2×C4×D43—21no—
102C2×C4×D43D412yes—
103C2×Dic86—22no—
104C2×Dic86D411yescharacteristic, complemented
105C2×Dic86C2311yescharacteristic
106Q16×C43—22no—
107SD16×C43—22no—
108SD16×C43—22no—
109D8×C43—22no—
110M16×C43—21no—
111M16×C43C2312yes—
112C2×C8×C43—21no—
113C22⋊Dic43—22no—
114#10621885—22no—
115#10621884—22no—
116#10621883—22no—
117#10621882—22no—
118(C2×D43)⋊C4—22no—
119Dic43⋊C4—22no—
120C4×Dic43—21no—
121C4×Dic43C2311yescharacteristic
122C4×Dic43C2311yescharacteristic
123#10621877—21no—
124#10621877C2312yes—
125C2×C43⋊C8—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43C2×D411yescharacteristic
129C22×D43—24no—
130C22×D43—21no—
131C22×D43C2×D412yes—
132Q8×C43—21no—
133Q8×C43—21no—
134Q8×C43—21no—
135Q8×C43C2×D412yes—
136D4×C43—22no—
137D4×C43—22no—
138D4×C43—21no—
139D4×C43—21no—
140D4×C43—21no—
141D4×C43—41no—
142D4×C43—41no—
143D4×C43C2×D412yes—
144C2×C4×C43—21no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—21no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43C2×D411yescharacteristic
151C2×C4×C43C2×D411yescharacteristic
152C2×C4×C43C2×D411yescharacteristic
153C2×C4×C43C2×D411yescharacteristic
154C2×C4×C43C2×D411yescharacteristic
155C2×C4×C43C2411yescharacteristic
156C22⋊D43—24no—
157C22⋊D43—24no—
158C22⋊D43—22no—
159C22⋊D43—22no—
160C22⋊D43—22no—
161C22⋊D43—22no—
162C22⋊D43—44no—
163C2×Dic43—24no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—42no—
168C2×Dic43C2×D412yes—
169D172—24no—
170D172—21no—
171D172—21no—
172D172—21no—
173D172C2×D412yes—
174C4×D43—24no—
175C4×D43—24no—
176C4×D43—22no—
177C4×D43—22no—
178C4×D43—22no—
179C4×D43—22no—
180Dic86—24no—
181Dic86—21no—
182Dic86—21no—
183Dic86—21no—
184Dic86C2×D412yes—
185C8×C43—22no—
186C43⋊C8—22no—
187C22×C43—22no—
188C22×C43—41no—
189C22×C43—42no—
190C22×C43—41no—
191C22×C43—81no—
192C22×C43#12011yescharacteristic
193C22×C43#12011yescharacteristic
194C22×C43C22×D411yescharacteristic
195C2×D43—22no—
196C2×D43—22no—
197C2×D43—42no—
198C2×D43—81no—
199C2×D43—84no—
200C4×C43—22no—
201C4×C43—41no—
202C4×C43#12011yescharacteristic
203C4×C43#12011yescharacteristic
204C4×C43C22×D411yescharacteristic
205C4×C43C22×D411yescharacteristic
206Dic43—22no—
207Dic43—22no—
208Dic43—22no—
209Dic43—41no—
210#3018—431nomaximal, Sylow
211C2×C43—21no—
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—42no—
215C2×C43—81no—
216C2×C43C2×#12011yescharacteristic
217D43—42no—
218D43—42no—
219#585—431no—
220#575—431no—
221#575D4311yescharacteristic, complemented
222#532—431no—
223#456—432no—
224#455—432no—
225#454—432no—
226#453—432no—
227C2×#104—431no—
228C2×#104—431no—
229#413—431no—
230C43#301811yescharacteristic, complemented, Sylow
2312−1+4—432no—
2322−1+4—861no—
2332−1+4—861no—
234H(5,𝔽2)—432no—
235H(5,𝔽2)—862no—
236H(5,𝔽2)—861no—
237H(5,𝔽2)—861no—
238C2×#41—431no—
239C2×#41—431no—
240C2×#41—862no—
241C2×#41—862no—
242C2×#41—862no—
243C2×#41C2×D4311yescharacteristic
244C2×#41C2×D4311yescharacteristic, complemented
245#137—21no—
246#137—432no—
247#137—861no—
248#137C2×D4312yescomplemented
249AGL(1,ℤ/8)—21no—
250AGL(1,ℤ/8)—432no—
251AGL(1,ℤ/8)—861no—
252AGL(1,ℤ/8)C2×D4312yescomplemented
253#135—22no—
254#135—862no—
255C2×M16—431no—
256C2×M16C2×D4311yescharacteristic, complemented
257C4⋊Q8—431no—
258#127—431no—
259#124—431no—
260#124—431no—
261#121—862no—
262C4×D4—862no—
263C2×C42—431no—
264#104—432no—
265#104—432no—
266#104—432no—
267#104—432no—
268#101—432no—
269#100—432no—
270#41—21no—
271#41—21no—
272#41—21no—
273#41—21no—
274#41—21no—
275#41—21no—
276#41—432no—
277#41—432no—
278#41—862no—
279#41—862no—
280#41—864no—
281#41—864no—
282#41—864no—
283#41—864no—
284#41—862no—
285#41—862no—
286#41—862no—
287#41—862no—
288#41—861no—
289#41—861no—
290#41—861no—
291#41—861no—
292#41—861no—
293#41—861no—
294#41C22⋊D4312yescomplemented
295#41C22×D4312yes—
296C2×Q8—431no—
297C2×Q8—431no—
298C2×Q8—862no—
299C2×Q8—862no—
300C2×Q8—862no—
301C2×Q8C22⋊D4311yescharacteristic, complemented
302C2×Q8C22×D4311yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—432no—
306C2×D4—431no—
307C2×D4—431no—
308C2×D4—862no—
309C2×D4—864no—
310C2×D4—864no—
311C2×D4—862no—
312C2×D4—864no—
313C2×D4—861no—
314C2×D4—862no—
315C2×D4—862no—
316C2×D4C22⋊D4311yescharacteristic, complemented
317C2×D4C22×D4311yescharacteristic
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—432no—
321C22×C4—864no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4C22×D4311yescharacteristic
325Q16—22no—
326Q16—862no—
327SD16—22no—
328SD16—22no—
329SD16—862no—
330SD16—862no—
331D8—22no—
332D8—862no—
333M16—21no—
334M16—432no—
335M16—861no—
336M16C22×D4312yes—
337C2×C8—21no—
338C2×C8—861no—
339C4⋊C4—862no—
340C22⋊C4—862no—
341C22⋊C4—862no—
342C42—431no—
343C42—431no—
344C42—861no—
345C23—21no—
346C23—21no—
347C23—432no—
348C23—864no—
349C23—861no—
350C23D4×D4311yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—21no—
354Q8—432no—
355Q8—864no—
356Q8—861no—
357Q8—861no—
358Q8—861no—
359Q8C2×C22⋊D4312yes—
360D4—22no—
361D4—22no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—41no—
366D4—41no—
367D4—432no—
368D4—864no—
369D4—864no—
370D4—864no—
371D4—862no—
372D4—862no—
373D4—862no—
374D4—862no—
375D4—861no—
376D4—861no—
377D4—861no—
378D4—1724no—
379D4C2×C22⋊D4312yes—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—432no—
387C2×C4—864no—
388C2×C4—864no—
389C2×C4—864no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—862no—
393C2×C4—862no—
394C2×C4—862no—
395C2×C4—862no—
396C2×C4—861no—
397C2×C4—1722no—
398C2×C4D4×D4311yescharacteristic
399C2×C4D4×D4311yescharacteristic
400C2×C4D4×D4311yescharacteristic
401C2×C4C2×C22⋊D4311yescharacteristic
402C2×C4C2×C22⋊D4311yescharacteristic
403C2×C4C23×D4311yescharacteristic
404C8—22no—
405C8—862no—
406C22—22no—
407C22—41no—
408C22—42no—
409C22—41no—
410C22—81no—
411C22—862no—
412C22—862no—
413C22—3441no—
414C22—3444no—
415C22—1722no—
416C22#1306329311yescharacteristic
417C22#1306329311yescharacteristic
418C22C2×D4×D4311yescharacteristic
419C4—22no—
420C4—41no—
421C4—862no—
422C4—862no—
423C4—862no—
424C4—1721no—
425C4#1306329311yescharacteristic
426C4#1306329311yescharacteristic
427C4C2×D4×D4311yescharacteristic
428C4C22×C22⋊D4311yescharacteristic
429C2—21no—
430C2—21no—
431C2—21no—
432C2—42no—
433C2—81no—
434C2—1722no—
435C2—1722no—
436C2C2×#1306329311yescharacteristic
subgroupG/H
centerC4#13063293
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#575C2
socleC2×C43C2×#120
hypercenter#575D43
hypocenterC43#3018
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14583735C2semidirect
2. #14583697C2semidirect
3. #14583445C2semidirect
4. #14583080C2semidirect
5. #14583075C2semidirect
6. #14583070C2semidirect
7. #14583065C2semidirect
8. C2×#13063252C2semidirect
9. C2×#13063251C2semidirect
10. #14582881C2semidirect
11. C43×#575C2semidirect
24. #13063356C22semidirect
26. #13063351C22semidirect
29. C2×#10621877C22semidirect
30. #13063323C22semidirect
31. #13063321C22semidirect
32. #13063314C22semidirect
33. #13063312C22semidirect
36. C2×C4×Dic43C22semidirect
37. #13063252C22semidirect
38. #13063252C22semidirect
39. #13063251C22semidirect
40. #13063251C22semidirect
41. #13063243C22semidirect
42. #13063241C22semidirect
44. C2×#41×C43C22semidirect
46. #137×C43C22semidirect
48. AGL(1,ℤ/8)×C43C22semidirect
50. C2×M16×C43C22semidirect
57. #41×C43D4semidirect
59. C2×Q8×C43D4semidirect
63. C2×D4×C43D4semidirect
95. #10621898D4semidirect
98. C2×D172D4semidirect
104. C2×Dic86D4semidirect
221. #575D43semidirect
230. C43#3018semidirect
244. C2×#41C2×D43semidirect
248. #137C2×D43semidirect
252. AGL(1,ℤ/8)C2×D43semidirect
256. C2×M16C2×D43semidirect
294. #41C22⋊D43semidirect
301. C2×Q8C22⋊D43semidirect
316. C2×D4C22⋊D43semidirect