Finite Group Databasebeta

← #19143449

Subgroups — #19143449

Order 5504.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D43C211yesmaximal, characteristic
2#14583375C211yesmaximal, characteristic, complemented
3#14583371C211yesmaximal, characteristic
4#14583002C211yesmaximal, characteristic, complemented
5#14582999C211yesmaximal, characteristic, complemented
6#14582997C211yesmaximal, characteristic, complemented
7#14582996C211yesmaximal, characteristic, complemented
8C4×#10621873C211yesmaximal, characteristic, complemented
9SD16×Dic43C211yesmaximal, characteristic, complemented
10#14582986C211yesmaximal, characteristic, complemented
11#14582934C211yesmaximal, characteristic, complemented
12#14582906C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic
14#14582853C211yesmaximal, characteristic, complemented
15C4×SD16×C43C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21SD16×D43C418yescomplemented
22C2×#10621872C2211yescharacteristic
23C2×C8×D43C2211yescharacteristic
24Q8×Dic43C2211yescharacteristic, complemented
25C4×Dic86—21no—
26C4×Dic86C2211yescharacteristic, complemented
27#13063290—21no—
28#13063290C2211yescharacteristic, complemented
29C4×D172C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31#13063287C2211yescharacteristic
32C4×C22⋊D43—21no—
33(C22⋊D43)⋊C4—21no—
34#13063283—21no—
35#13063283C2211yescharacteristic
36#13063283C2211yescharacteristic
37#13063282—21no—
38#13063282C2211yescharacteristic
39C2×(C2×D43)⋊C4—21no—
40C22⋊C4×D43—21no—
41#13063258C2211yescharacteristic, complemented
42#13063258C2211yescharacteristic, complemented
43#13063257C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063249C2211yescharacteristic, complemented
46#13063248C2211yescharacteristic, complemented
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063236C2211yescharacteristic, complemented
51#13063235C2211yescharacteristic, complemented
52C8×Dic43C2211yescharacteristic, complemented
53C2×SD16×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic, complemented
55C4×D4×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic
59C4×C8×C43C2211yescharacteristic, complemented
60C23×D43—21no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C2×C22⋊D43—21no—
65C22×Dic43—21no—
66Q8×D43—22no—
67Q8×D43C2×C414yescomplemented
68D4×D43—22no—
69D4×D43C2×C414yes—
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43C2311yescharacteristic
75C2×Dic86—21no—
76C2×Dic86C2311yescharacteristic
77SD16×C43C2×C414yescomplemented
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C42×C43—21no—
85C42×C43C2311yescharacteristic
86C22⋊Dic43—21no—
87#10621884C2×C414yescomplemented
88#10621883C2×C414yescomplemented
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621873C2×C414yescomplemented
111#10621872—22no—
112C8×D43C2×C414yescomplemented
113C23×C43—21no—
114C22×D43—21no—
115C22×D43—24no—
116C22×D43—81no—
117C22×D43—81no—
118C22×D43C2×D411yescharacteristic
119Q8×C43—21no—
120Q8×C43C22×C412yes—
121D4×C43—21no—
122D4×C43C22×C412yes—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—81no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—24no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—81no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138D172—21no—
139D172C22×C412yes—
140C4×D43—24no—
141C4×D43—81no—
142C4×D43—81no—
143C4×D43C22×C412yes—
144C4×D43#4112yes—
145Dic86—21no—
146Dic86—24no—
147Dic86C22×C412yes—
148C8×C43—21no—
149C8×C43C22×C412yes—
150C43⋊C8—21no—
151C43⋊C8C22×C412yes—
152C22×C43—22no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—22no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—84no—
162C2×D43C4×D412yes—
163C4×C43—22no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43C23×C411yescharacteristic
169C4×C43C2×#4111yescharacteristic
170Dic43—22no—
171Dic43—21no—
172Dic43—21no—
173Dic43—41no—
174Dic43—41no—
175Dic43C4×D412yes—
176#2949—431nomaximal, Sylow
177C2×C43—42no—
178C2×C43C2×C4×D411yescharacteristic
179C2×C43#57711yescharacteristic
180C2×C43#57711yescharacteristic
181D43—22no—
182D43—42no—
183C22×SD16—431no—
184#519—431no—
185#518—431no—
186#440—431no—
187#440—431no—
188#440—431no—
189#440—431no—
190C4×SD16—431no—
191C4×SD16—431no—
192C4×SD16—431no—
193C4×SD16D4311yescharacteristic, complemented
194#427—431no—
195#419—431no—
196#418—431no—
197#405—431no—
198C43#294911yescharacteristic, complemented, Sylow
199C22×Q8—431no—
200C22×D4—431no—
201C2×SD16—431no—
202C2×SD16—431no—
203C2×SD16—438no—
204C2×SD16—431no—
205C2×SD16C2×D4311yescharacteristic
206C2×M16—431no—
207C22×C8—431no—
208C4×Q8—431no—
209C4×Q8—431no—
210C4×Q8—431no—
211C4×Q8—861no—
212C4×Q8—861no—
213C4×Q8C2×D4311yescharacteristic, complemented
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—431no—
217C4×D4—861no—
218C4×D4—861no—
219C4×D4C2×D4311yescharacteristic
220#117—431no—
221#117—431no—
222#117—431no—
223#117—861no—
224#117—861no—
225C2×C22⋊C4—861no—
226C2×C22⋊C4—861no—
227#107—431no—
228#107—431no—
229#106—431no—
230#106C2×D4311yescharacteristic, complemented
231#103—431no—
232#103—431no—
233#103—431no—
234#103C2×D4311yescharacteristic, complemented
235#102—431no—
236#102—431no—
237#102—431no—
238#102C2×D4311yescharacteristic
239#97—431no—
240#97—431no—
241C4×C8—431no—
242C4×C8C2×D4311yescharacteristic, complemented
243C24—861no—
244C2×Q8—434no—
245C2×Q8—431no—
246C2×Q8—861no—
247C2×Q8—862no—
248C2×Q8C22×D4311yescharacteristic
249C2×D4—434no—
250C2×D4—431no—
251C2×D4—862no—
252C2×D4—861no—
253C2×D4C22×D4311yescharacteristic
254C22×C4—21no—
255C22×C4—431no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260SD16—434no—
261SD16—434no—
262SD16—434no—
263SD16C4×D4314yescomplemented
264M16—862no—
265C2×C8—431no—
266C2×C8—434no—
267C2×C8—431no—
268C2×C8C22×D4311yescharacteristic
269C2×C8C22×D4311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—431no—
272C4⋊C4—431no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4C22×D4311yescharacteristic
279C4⋊C4C22×D4311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—431no—
282C22⋊C4—431no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C42—21no—
289C42—431no—
290C42—861no—
291C42—861no—
292C42—861no—
293C42—861no—
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—21no—
297C23—431no—
298C23—864no—
299C23—861no—
300C23—3441no—
301C23—3441no—
302Q8—21no—
303Q8—432no—
304Q8—864no—
305Q8—861no—
306Q8C2×C4×D4312yes—
307D4—21no—
308D4—432no—
309D4—864no—
310D4—861no—
311D4C2×C4×D4312yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—431no—
317C2×C4—432no—
318C2×C4—432no—
319C2×C4—431no—
320C2×C4—431no—
321C2×C4—864no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4D4×D4311yescharacteristic
329C2×C4D4×D4311yescharacteristic
330C2×C4C23×D4311yescharacteristic
331C8—21no—
332C8—432no—
333C8—861no—
334C8C2×C4×D4312yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—432no—
339C22—861no—
340C22—861no—
341C22—862no—
342C22—3444no—
343C22—1721no—
344C22—1721no—
345C22C2×D4×D4311yescharacteristic
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—432no—
352C4—862no—
353C4—861no—
354C4—861no—
355C4—1721no—
356C4—1721no—
357C4C22×C4×D4311yescharacteristic
358C4#41×D4311yescharacteristic
359C2—42no—
360C2—862no—
361C2—1722no—
362C2C4×D4×D4311yescharacteristic
363C2#1458370511yescharacteristic
364C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC4×C43C23×C4
FrattiniC2×C4C23×D43
FittingC4×SD16×C43C2
socleC22×C43C22×D4
hypercenterC4×SD16D43
hypocenterC43#2949
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #14583375C2semidirect
4. #14583002C2semidirect
5. #14582999C2semidirect
6. #14582997C2semidirect
7. #14582996C2semidirect
8. C4×#10621873C2semidirect
9. SD16×Dic43C2semidirect
10. #14582986C2semidirect
11. #14582934C2semidirect
12. #14582906C2semidirect
14. #14582853C2semidirect
15. C4×SD16×C43C2semidirect
21. SD16×D43C4semidirect
24. Q8×Dic43C22semidirect
26. C4×Dic86C22semidirect
28. #13063290C22semidirect
41. #13063258C22semidirect
42. #13063258C22semidirect
43. #13063257C22semidirect
44. #13063250C22semidirect
45. #13063249C22semidirect
46. #13063248C22semidirect
50. #13063236C22semidirect
51. #13063235C22semidirect
52. C8×Dic43C22semidirect
54. C4×Q8×C43C22semidirect
56. #106×C43C22semidirect
57. #103×C43C22semidirect
59. C4×C8×C43C22semidirect
67. Q8×D43C2×C4semidirect
77. SD16×C43C2×C4semidirect
87. #10621884C2×C4semidirect
88. #10621883C2×C4semidirect
110. #10621873C2×C4semidirect
112. C8×D43C2×C4semidirect
193. C4×SD16D43semidirect
198. C43#2949semidirect
213. C4×Q8C2×D43semidirect
230. #106C2×D43semidirect
234. #103C2×D43semidirect
242. C4×C8C2×D43semidirect
263. SD16C4×D43semidirect