Finite Group Databasebeta

← #19146116

Subgroups — #19146116

Order 5504.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063351C211yesmaximal, characteristic, complemented
2C2×#13063345C211yesmaximal, characteristic, complemented
3#14583554C211yesmaximal, characteristic, complemented
4#14583294C211yesmaximal, characteristic, complemented
5#14583155C211yesmaximal, characteristic, complemented
6#14583126C211yesmaximal, characteristic, complemented
7#14583111C211yesmaximal, characteristic, complemented
8#14583104C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583059C211yesmaximal, characteristic, complemented
11#14583050C211yesmaximal, characteristic, complemented
12#14583042C211yesmaximal, characteristic, complemented
13#14583009C211yesmaximal, characteristic, complemented
14#14582971C211yesmaximal, characteristic, complemented
15C43×#546C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic, complemented
18#13063351—24no—
19#13063345—24no—
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621885C2211yescharacteristic, complemented
22C2×#10621883C2211yescharacteristic
23C2×#10621883C2211yescharacteristic
24C2×#10621883C2211yescharacteristic
25C2×#10621883C2211yescharacteristic
26C2×#10621884C2211yescharacteristic, complemented
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C2×#10621877C2211yescharacteristic
30C22×C43⋊C8C2211yescharacteristic, complemented
31#13063325C2211yescharacteristic, complemented
32#13063307—21no—
33#13063307—21no—
34#13063304C2211yescharacteristic
35#13063304C2211yescharacteristic, complemented
36#13063296—21no—
37C4×D172C2211yescharacteristic, complemented
38C4⋊C4×D43—21no—
39#13063256C2211yescharacteristic, complemented
40C4⋊(C43⋊C8)C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063248C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063246C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063245C2211yescharacteristic, complemented
47C22⋊(C43⋊C8)C2211yescharacteristic
48C22⋊(C43⋊C8)C2211yescharacteristic, complemented
49#13063236C2211yescharacteristic, complemented
50C2×#41×C43C2211yescharacteristic
51C22×D4×C43C2211yescharacteristic
52#124×C43C2211yescharacteristic
53#123×C43—21no—
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43—21no—
56#121×C43C2211yescharacteristic
57#120×C43—21no—
58C4×D4×C43C2211yescharacteristic
59C4×D4×C43C2211yescharacteristic
60C2×C22⋊C4×C43—21no—
61C24×C43—21no—
62#41×C43—22no—
63#41×C43—41no—
64C2×Q8×C43C2311yescharacteristic
65C2×D4×C43—21no—
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—22no—
69C2×D4×C43—41no—
70C2×D4×C43D411yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C2×D4×C43C2311yescharacteristic
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43C2311yescharacteristic
76C22×C4×C43C2311yescharacteristic
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79#10621898—22no—
80#10621898—22no—
81#10621898—41no—
82#10621898—41no—
83C2×D172C2311yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×Dic86C2311yescharacteristic
88C2×Dic86C2311yescharacteristic
89C4⋊C4×C43—21no—
90C4⋊C4×C43D411yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊C4×C43D411yescharacteristic
98C22⋊C4×C43D411yescharacteristic
99C42×C43C2311yescharacteristic
100C22⋊Dic43—21no—
101C22⋊Dic43—21no—
102#10621885—22no—
103#10621885—41no—
104#10621884—22no—
105#10621883—22no—
106#10621883—22no—
107#10621883—22no—
108#10621883—41no—
109#10621882—22no—
110#10621882D414yescomplemented
111(C2×D43)⋊C4—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43C2311yescharacteristic
115Dic43⋊C4—21no—
116Dic43⋊C4—21no—
117#10621877—22no—
118C2×C43⋊C8—22no—
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121C2×C43⋊C8C2311yescharacteristic
122C2×C43⋊C8C2311yescharacteristic
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43—81no—
128C23×C43C2×D411yescharacteristic
129C23×C43C2×D411yescharacteristic
130C22×D43—21no—
131Q8×C43—21no—
132Q8×C43—21no—
133D4×C43—21no—
134D4×C43—21no—
135D4×C43—21no—
136D4×C43—41no—
137D4×C43—42no—
138D4×C43—42no—
139D4×C43—81no—
140D4×C43C2×D412yes—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—42no—
148C2×C4×C43—81no—
149C2×C4×C43C2×D411yescharacteristic
150C2×C4×C43C2×D411yescharacteristic
151C2×C4×C43C2×D411yescharacteristic
152C2×C4×C43C2×D411yescharacteristic
153C2×C4×C43C2411yescharacteristic
154C22⋊D43—42no—
155C22⋊D43—42no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159D172—21no—
160D172C2×D412yes—
161C4×D43—42no—
162C4×D43—42no—
163C4×D43—42no—
164Dic86—21no—
165Dic86—21no—
166Dic86—21no—
167Dic86—21no—
168C43⋊C8—21no—
169C43⋊C8—21no—
170C43⋊C8—21no—
171C43⋊C8C2×D412yes—
172C22×C43—22no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—84no—
185C22×C43C22×D411yescharacteristic
186C2×D43—22no—
187C2×D43—41no—
188C2×D43—41no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—41no—
194C4×C43—41no—
195C4×C43C22×D411yescharacteristic
196C4×C43H(5,𝔽2)11yescharacteristic
197Dic43—41no—
198Dic43—41no—
199Dic43—41no—
200#3267—431nomaximal, Sylow
201C2×C43—41no—
202C2×C43—41no—
203C2×C43—42no—
204C2×C43—81no—
205C2×C43D4211yescharacteristic
206C2×C43#57511yescharacteristic
207C2×C43#57711yescharacteristic
208D43—42no—
209C2×AGL(1,ℤ/8)—431no—
210C2×#135—431no—
211#547—431no—
212#546D4311yescharacteristic, complemented
213#497—431no—
214#470—431no—
215#465—431no—
216#463—431no—
217#461—431no—
218#452—431no—
219#452—431no—
220#450—431no—
221#449—431no—
222#442—431no—
223#435—431no—
224C43#326711yescharacteristic, complemented, Sylow
225C2×#41—431no—
226C2×#41—431no—
227C2×#41C2×D4311yescharacteristic
228C22×D4C2×D4311yescharacteristic
229AGL(1,ℤ/8)—864no—
230#135—864no—
231C2×Q16—431no—
232C2×Q16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16—431no—
237C2×SD16—431no—
238C2×D8—431no—
239C2×D8—431no—
240C2×M16—431no—
241C22×C8—431no—
242C4⋊Q8—431no—
243#124C2×D4311yescharacteristic
244#123—21no—
245#123—861no—
246#123—861no—
247C22⋊Q8—431no—
248C22⋊Q8—431no—
249C22⋊Q8C2×D4311yescharacteristic
250#121—21no—
251#121—861no—
252#121C2×D4311yescharacteristic
253#120—21no—
254C4×D4—431no—
255C4×D4C2×D4311yescharacteristic
256C4×D4C2×D4311yescharacteristic
257C2×C4⋊C4—861no—
258C2×C22⋊C4—21no—
259#106—431no—
260C4⋊C8—431no—
261#103—431no—
262#103—431no—
263#103—431no—
264#102—431no—
265#102—431no—
266#102—431no—
267C22⋊C8—431no—
268C22⋊C8—431no—
269#97—431no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—862no—
274#41—862no—
275#41—1721no—
276#41—1721no—
277C2×Q8—431no—
278C2×Q8—431no—
279C2×Q8C22×D4311yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—431no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4C22⋊D4311yescharacteristic
289C2×D4C22×D4311yescharacteristic
290C2×D4C22×D4311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4C22×D4311yescharacteristic
297C22×C4C22×D4311yescharacteristic
298Q16—862no—
299Q16—1721no—
300SD16—862no—
301SD16—862no—
302SD16—862no—
303SD16—862no—
304SD16—1721no—
305D8—434no—
306D8—862no—
307M16—862no—
308C2×C8—431no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8—431no—
312C2×C8—862no—
313C4⋊C4—21no—
314C4⋊C4—431no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4C22⋊D4311yescharacteristic
320C4⋊C4C22×D4311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C22⋊C4C22⋊D4311yescharacteristic
330C22⋊C4C22⋊D4311yescharacteristic
331C42C22×D4311yescharacteristic
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—861no—
338C23C2×C22⋊D4311yescharacteristic
339C23C2×C22⋊D4311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—861no—
343Q8—861no—
344Q8—861no—
345Q8—861no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—81no—
353D4—432no—
354D4—861no—
355D4—1722no—
356D4—1722no—
357D4D4×D4312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4—1722no—
372C2×C4C2×C22⋊D4311yescharacteristic
373C2×C4C2×C22⋊D4311yescharacteristic
374C2×C4C2×C22⋊D4311yescharacteristic
375C2×C4C2×C22⋊D4311yescharacteristic
376C2×C4C23×D4311yescharacteristic
377C8—432no—
378C8—861no—
379C8—861no—
380C8—861no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—862no—
395C22—1721no—
396C22—1721no—
397C22C22×C22⋊D4311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—1721no—
405C4—1721no—
406C4—1721no—
407C4C2×D4×D4311yescharacteristic
408C4#1306337011yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—81no—
413C2—1722no—
414C2D4×C22⋊D4311yescharacteristic
415C2#1458369711yescharacteristic
416C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#546C2
socleC22×C43C22×D4
hypercenter#546D43
hypocenterC43#3267
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#13063351C2semidirect
2. C2×#13063345C2semidirect
3. #14583554C2semidirect
4. #14583294C2semidirect
5. #14583155C2semidirect
6. #14583126C2semidirect
7. #14583111C2semidirect
8. #14583104C2semidirect
9. #14583061C2semidirect
10. #14583059C2semidirect
11. #14583050C2semidirect
12. #14583042C2semidirect
13. #14583009C2semidirect
14. #14582971C2semidirect
15. C43×#546C2semidirect
17. C2×#10621898C22semidirect
20. C2×#10621885C22semidirect
21. C2×#10621885C22semidirect
26. C2×#10621884C22semidirect
30. C22×C43⋊C8C22semidirect
31. #13063325C22semidirect
35. #13063304C22semidirect
37. C4×D172C22semidirect
39. #13063256C22semidirect
40. C4⋊(C43⋊C8)C22semidirect
41. #13063249C22semidirect
42. #13063248C22semidirect
43. #13063248C22semidirect
46. #13063245C22semidirect
48. C22⋊(C43⋊C8)C22semidirect
49. #13063236C22semidirect
110. #10621882D4semidirect
212. #546D43semidirect
224. C43#3267semidirect