Finite Group Databasebeta

← #19146091

Subgroups — #19146091

Order 5504.

546 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
1C2×#13063350C211yesmaximal, characteristic, complemented
2C22×#10621884C211yesmaximal, characteristic, complemented
3D4×D172C211yesmaximal, characteristic, complemented
4#14583289C211yesmaximal, characteristic, complemented
5#14583147C211yesmaximal, characteristic, complemented
6#14583133C211yesmaximal, characteristic, complemented
7#14583111C211yesmaximal, characteristic, complemented
8#14583099C211yesmaximal, characteristic, complemented
9#14583049C211yesmaximal, characteristic, complemented
10#14583044C211yesmaximal, characteristic, complemented
11#14583038C211yesmaximal, characteristic, complemented
12#14583032C211yesmaximal, characteristic, complemented
13#14582997C211yesmaximal, characteristic, complemented
14#14582971C211yesmaximal, characteristic, complemented
15C43×#548C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×D4×D43—21no—
19#13063350—24no—
20C2×#10621884—24no—
21C2×#10621884C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23C2×#10621884C2211yescharacteristic, complemented
24C2×#10621884C2211yescharacteristic, complemented
25C2×#10621884C2211yescharacteristic, complemented
26C2×#10621884C2211yescharacteristic, complemented
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic, complemented
29C2×#10621882C2211yescharacteristic, complemented
30C2×#10621877C2211yescharacteristic, complemented
31C22×C43⋊C8C2211yescharacteristic, complemented
32#13063322C2211yescharacteristic
33#13063300—21no—
34#13063299C2211yescharacteristic
35#13063299C2211yescharacteristic
36#13063295—21no—
37#13063295—21no—
38C4×D172C2211yescharacteristic
39#13063258C2211yescharacteristic, complemented
40C4⋊(C43⋊C8)C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063246C2211yescharacteristic, complemented
44#13063245C2211yescharacteristic
45#13063245C2211yescharacteristic, complemented
46#13063245C2211yescharacteristic, complemented
47C22⋊(C43⋊C8)C2211yescharacteristic, complemented
48C22⋊(C43⋊C8)C2211yescharacteristic, complemented
49#13063236C2211yescharacteristic, complemented
50C2×#41×C43C2211yescharacteristic, complemented
51C22×Q8×C43C2211yescharacteristic, complemented
52#124×C43—21no—
53#124×C43C2211yescharacteristic, complemented
54C22⋊Q8×C43—21no—
55C22⋊Q8×C43C2211yescharacteristic, complemented
56#121×C43—21no—
57#121×C43C2211yescharacteristic, complemented
58C4×Q8×C43C2211yescharacteristic, complemented
59C4×D4×C43—21no—
60C4×D4×C43C2211yescharacteristic
61C23×D43—21no—
62C23×D43—21no—
63#41×C43—22no—
64#41×C43—41no—
65C2×Q8×C43—21no—
66C2×Q8×C43—22no—
67C2×Q8×C43—41no—
68C2×Q8×C43C2311yescharacteristic
69C2×Q8×C43C2311yescharacteristic
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43D411yescharacteristic
73C2×D4×C43C2311yescharacteristic
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43C2311yescharacteristic
77C22×C4×C43C2311yescharacteristic
78C2×C22⋊D43—21no—
79C2×C22⋊D43—21no—
80D4×D43—44no—
81C2×D172—21no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172C2311yescharacteristic
90C2×D172C2311yescharacteristic
91C2×D172C2311yescharacteristic
92C2×C4×D43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43D411yescharacteristic
96C4⋊C4×C43C2311yescharacteristic
97C22⋊C4×C43—21no—
98C22⋊C4×C43—21no—
99C22⋊C4×C43—21no—
100C22⋊C4×C43—21no—
101C22⋊C4×C43D411yescharacteristic
102C22⋊C4×C43D411yescharacteristic
103C42×C43—21no—
104C42×C43C2311yescharacteristic
105#10621884—22no—
106#10621884—22no—
107#10621884—22no—
108#10621884—22no—
109#10621884—41no—
110#10621884D414yescomplemented
111#10621882—22no—
112#10621882—22no—
113#10621882—41no—
114(C2×D43)⋊C4—21no—
115(C2×D43)⋊C4—21no—
116(C2×D43)⋊C4—21no—
117C4⋊Dic43C2311yescharacteristic
118#10621877—22no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8C2311yescharacteristic
121C2×C43⋊C8C2311yescharacteristic
122C2×C43⋊C8C2311yescharacteristic
123C2×C43⋊C8C2311yescharacteristic
124C23×C43—21no—
125C23×C43C2×D411yescharacteristic
126C23×C43C2×D411yescharacteristic
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—42no—
131C22×D43—42no—
132C22×D43—42no—
133C22×D43—42no—
134C22×D43—81no—
135C22×D43—81no—
136Q8×C43—21no—
137Q8×C43—21no—
138Q8×C43—21no—
139Q8×C43—42no—
140Q8×C43C2×D412yescomplemented
141D4×C43—22no—
142D4×C43—21no—
143D4×C43—21no—
144D4×C43—42no—
145D4×C43—42no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43C2×D411yescharacteristic
156C2×C4×C43C2×D411yescharacteristic
157C2×C4×C43C2×D411yescharacteristic
158C2×C4×C43C2×D411yescharacteristic
159C2×C4×C43C2411yescharacteristic
160C22⋊D43—42no—
161C22⋊D43—42no—
162C2×Dic43—21no—
163D172—21no—
164D172—21no—
165D172—21no—
166D172—21no—
167D172—21no—
168D172—42no—
169D172—42no—
170D172—42no—
171D172—81no—
172D172C2×D412yes—
173C4×D43—42no—
174C43⋊C8—21no—
175C43⋊C8—21no—
176C43⋊C8—21no—
177C43⋊C8C2×D412yescomplemented
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43AGL(1,ℤ/8)12yescomplemented
187C22×C43C22×D411yescharacteristic
188C2×D43—22no—
189C2×D43—41no—
190C2×D43—41no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—41no—
197C2×D43—84no—
198C2×D43—84no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—22no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—41no—
205C4×C43—41no—
206C4×C43C22×D411yescharacteristic
207C4×C43H(5,𝔽2)11yescharacteristic
208Dic43—41no—
209#3265—431nomaximal, Sylow
210C2×C43—22no—
211C2×C43—41no—
212C2×C43—81no—
213C2×C43D4211yescharacteristic
214C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C43#57711yescharacteristic
216D43—42no—
217D43—81no—
218D43—81no—
219C2×AGL(1,ℤ/8)—431no—
220C22×SD16—431no—
221#548D4311yescharacteristic, complemented
222D42—431no—
223#496—431no—
224#468—431no—
225#466—431no—
226#463—431no—
227#460—431no—
228#450—431no—
229#449—431no—
230#448—431no—
231#447—431no—
232#440—431no—
233#435—431no—
234C43#326511yescharacteristic, complemented, Sylow
235C2×#41C2×D4311yescharacteristic, complemented
236C22×Q8C2×D4311yescharacteristic, complemented
237C22×D4—431no—
238C22×D4—431no—
239C22×D4—861no—
240AGL(1,ℤ/8)—864no—
241C2×SD16—431no—
242C2×SD16—431no—
243C2×SD16—431no—
244C2×SD16—431no—
245C2×SD16—431no—
246C2×SD16—431no—
247C2×SD16—864no—
248C2×D8—431no—
249C2×D8—431no—
250C2×D8—431no—
251C2×M16—431no—
252C22×C8—431no—
253#127—431no—
254#124—21no—
255#124C2×D4311yescharacteristic, complemented
256C22⋊Q8—21no—
257C22⋊Q8C2×D4311yescharacteristic, complemented
258#121—21no—
259#121—431no—
260#121—431no—
261#121—861no—
262#121C2×D4311yescharacteristic, complemented
263#120—861no—
264#120—861no—
265C4×Q8C2×D4311yescharacteristic, complemented
266C4×D4—21no—
267C4×D4—431no—
268C4×D4C2×D4311yescharacteristic
269#107—431no—
270C4⋊C8—431no—
271#103—431no—
272#103—431no—
273#102—431no—
274#102—431no—
275#102—431no—
276#102—431no—
277C22⋊C8—431no—
278C22⋊C8—431no—
279#97—431no—
280C24—861no—
281C24—861no—
282#41—22no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D4311yescharacteristic
288C2×Q8C22×D4311yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—431no—
292C2×D4—431no—
293C2×D4—431no—
294C2×D4—862no—
295C2×D4—862no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—861no—
301C2×D4—861no—
302C2×D4—1721no—
303C2×D4—1721no—
304C2×D4—1724no—
305C2×D4C22⋊D4311yescharacteristic
306C2×D4C22×D4311yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—861no—
310C22×C4C22×D4311yescharacteristic
311C22×C4C22×D4311yescharacteristic
312SD16—434no—
313SD16—862no—
314SD16—862no—
315SD16—862no—
316SD16—862no—
317SD16—1721no—
318D8—862no—
319D8—862no—
320D8—1721no—
321M16—862no—
322C2×C8—431no—
323C2×C8—431no—
324C2×C8—431no—
325C2×C8—431no—
326C2×C8—862no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—431no—
330C4⋊C4C22⋊D4311yescharacteristic
331C4⋊C4C22×D4311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—861no—
337C22⋊C4—861no—
338C22⋊C4—861no—
339C22⋊C4C22⋊D4311yescharacteristic
340C22⋊C4C22⋊D4311yescharacteristic
341C42—21no—
342C42C22×D4311yescharacteristic
343C23—21no—
344C23—861no—
345C23—861no—
346C23—861no—
347C23—3441no—
348C23—3441no—
349C23—1722no—
350C23—1722no—
351C23—1722no—
352C23—1722no—
353C23C2×C22⋊D4311yescharacteristic
354C23C2×C22⋊D4311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8D4×D4312yescomplemented
360D4—22no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—432no—
366D4—861no—
367D4—861no—
368D4—861no—
369D4—861no—
370D4—861no—
371D4—3441no—
372D4—1722no—
373D4—1722no—
374D4—1722no—
375D4—1722no—
376D4—1722no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—861no—
387C2×C4—1722no—
388C2×C4C2×C22⋊D4311yescharacteristic
389C2×C4C2×C22⋊D4311yescharacteristic
390C2×C4C2×C22⋊D4311yescharacteristic
391C2×C4C2×C22⋊D4311yescharacteristic
392C2×C4C23×D4311yescharacteristic
393C8—432no—
394C8—861no—
395C8—861no—
396C8—861no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—862no—
406C22—3444no—
407C22—3444no—
408C22—1721no—
409C22—1721no—
410C22—1721no—
411C22—1721no—
412C22—1721no—
413C22—1721no—
414C22—1721no—
415C22—1721no—
416C22#1306335012yescomplemented
417C22C22×C22⋊D4311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—22no—
423C4—41no—
424C4—41no—
425C4—1721no—
426C4C2×D4×D4311yescharacteristic
427C4#1306337011yescharacteristic
428C2—22no—
429C2—41no—
430C2—81no—
431C2—3441no—
432C2—3441no—
433C2—1722no—
434C2D4×C22⋊D4311yescharacteristic
435C2C2×#1306335011yescharacteristic
436C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#548C2
socleC22×C43C22×D4
hypercenter#548D43
hypocenterC43#3265
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#13063350C2semidirect
2. C22×#10621884C2semidirect
3. D4×D172C2semidirect
4. #14583289C2semidirect
5. #14583147C2semidirect
6. #14583133C2semidirect
7. #14583111C2semidirect
8. #14583099C2semidirect
9. #14583049C2semidirect
10. #14583044C2semidirect
11. #14583038C2semidirect
12. #14583032C2semidirect
13. #14582997C2semidirect
14. #14582971C2semidirect
15. C43×#548C2semidirect
23. C2×#10621884C22semidirect
24. C2×#10621884C22semidirect
25. C2×#10621884C22semidirect
26. C2×#10621884C22semidirect
28. C2×#10621882C22semidirect
29. C2×#10621882C22semidirect
30. C2×#10621877C22semidirect
31. C22×C43⋊C8C22semidirect
39. #13063258C22semidirect
40. C4⋊(C43⋊C8)C22semidirect
41. #13063249C22semidirect
42. #13063249C22semidirect
43. #13063246C22semidirect
45. #13063245C22semidirect
46. #13063245C22semidirect
47. C22⋊(C43⋊C8)C22semidirect
48. C22⋊(C43⋊C8)C22semidirect
49. #13063236C22semidirect
50. C2×#41×C43C22semidirect
51. C22×Q8×C43C22semidirect
53. #124×C43C22semidirect
55. C22⋊Q8×C43C22semidirect
57. #121×C43C22semidirect
58. C4×Q8×C43C22semidirect
110. #10621884D4semidirect
140. Q8×C43C2×D4semidirect
177. C43⋊C8C2×D4semidirect
186. C22×C43AGL(1,ℤ/8)semidirect
221. #548D43semidirect
234. C43#3265semidirect
235. C2×#41C2×D43semidirect
236. C22×Q8C2×D43semidirect
255. #124C2×D43semidirect
257. C22⋊Q8C2×D43semidirect
262. #121C2×D43semidirect
265. C4×Q8C2×D43semidirect
359. Q8D4×D43semidirect
416. C22#13063350semidirect