Finite Group Databasebeta

← #19143406

Subgroups — #19143406

Order 5504.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063349C211yesmaximal, characteristic
2C4×#10621900C211yesmaximal, characteristic, complemented
3C4×D4×D43C211yesmaximal, characteristic, complemented
4#14583009C211yesmaximal, characteristic, complemented
5#14583001C211yesmaximal, characteristic, complemented
6#14582999C211yesmaximal, characteristic, complemented
7#14582990C211yesmaximal, characteristic, complemented
8#14582986C211yesmaximal, characteristic, complemented
9D8×Dic43C211yesmaximal, characteristic, complemented
10#14582979C211yesmaximal, characteristic, complemented
11#14582938C211yesmaximal, characteristic, complemented
12#14582902C211yesmaximal, characteristic, complemented
13#14582897C211yesmaximal, characteristic, complemented
14#14582851C211yesmaximal, characteristic, complemented
15C43×#442C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C22×C4×D43—21no—
19#13063349C418yescomplemented
20C2×#10621873C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621872C2211yescharacteristic
24C2×#10621872C2211yescharacteristic
25C4×Dic86C2211yescharacteristic, complemented
26#13063290C2211yescharacteristic, complemented
27C4×D172C2211yescharacteristic
28D4×Dic43C2211yescharacteristic
29D4×Dic43C2211yescharacteristic, complemented
30#13063287C2211yescharacteristic
31C4×C22⋊D43—21no—
32C4×C22⋊D43—21no—
33(C22⋊D43)⋊C4—21no—
34(C22⋊D43)⋊C4—21no—
35#13063283C2211yescharacteristic
36#13063281—21no—
37C4⋊C4×D43C2211yescharacteristic
38C22⋊C4×D43—21no—
39C2×C4×Dic43—21no—
40C42×D43C2211yescharacteristic
41#13063259C2211yescharacteristic, complemented
42#13063258C2211yescharacteristic, complemented
43#13063256C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063248C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic, complemented
49#13063245C2211yescharacteristic
50#13063236C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C8×Dic43C2211yescharacteristic, complemented
53C2×D8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic, complemented
56#106×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic, complemented
59#97×C43C2211yescharacteristic, complemented
60C23×D43—21no—
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70#10621900—22no—
71#10621900C2×C414yescomplemented
72D4×D43—22no—
73D4×D43C2×C414yescomplemented
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—44no—
79C2×C4×D43D411yescharacteristic
80C2×C4×D43D411yescharacteristic
81C2×C4×D43C2311yescharacteristic
82C2×Dic86C2311yescharacteristic
83D8×C43C2×C414yescomplemented
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93#10621883C2×C414yescomplemented
94#10621882C2×C414yescomplemented
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43D411yescharacteristic
107C4×Dic43D411yescharacteristic
108C4×Dic43C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111#10621873C2×C414yescomplemented
112#10621872—22no—
113#10621872C2×C414yescomplemented
114C23×C43—21no—
115C23×C43—21no—
116C22×D43—21no—
117C22×D43—24no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43C2×D411yescharacteristic
121D4×C43—21no—
122D4×C43—21no—
123D4×C43C22×C412yes—
124D4×C43C22×C412yescomplemented
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—24no—
133C22⋊D43—24no—
134C2×Dic43—21no—
135C2×Dic43—24no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143D172—21no—
144D172C22×C412yes—
145C4×D43—22no—
146C4×D43—41no—
147C4×D43—42no—
148C4×D43—42no—
149C4×D43—42no—
150C4×D43C22×C412yes—
151C4×D43#4112yes—
152Dic86—21no—
153Dic86C22×C412yescomplemented
154C8×C43—21no—
155C8×C43C22×C412yescomplemented
156C43⋊C8—21no—
157C43⋊C8C22×C412yescomplemented
158C22×C43—22no—
159C22×C43—22no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43C22×D411yescharacteristic
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—22no—
168C2×D43—48no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43C4×D412yes—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43C23×C411yescharacteristic
177C4×C43C2×#4111yescharacteristic
178Dic43—22no—
179Dic43—21no—
180Dic43—41no—
181Dic43—41no—
182Dic43C4×D412yes—
183Dic43AGL(1,ℤ/8)12yescomplemented
184C4×AGL(1,ℤ/8)—431nomaximal, Sylow
185C2×C43—42no—
186C2×C43—42no—
187C2×C43C2×C4×D411yescharacteristic
188C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C43#57511yescharacteristic
190D43—22no—
191D43—42no—
192C2×AGL(1,ℤ/8)—431no—
193C4×#41—431no—
194C2×C4×D4—431no—
195#442—431no—
196#442D4311yescharacteristic, complemented
197#440—431no—
198#440—431no—
199C4×SD16—431no—
200C4×SD16—431no—
201C4×D8—431no—
202C4×D8—431no—
203#428—431no—
204#418—431no—
205#417—431no—
206C4×M16—431no—
207C43C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4—431no—
210C23×C4—861no—
211AGL(1,ℤ/8)—438no—
212C2×SD16—431no—
213C2×SD16—431no—
214C2×D8—431no—
215C2×D8C2×D4311yescharacteristic
216C2×M16—431no—
217C2×M16—431no—
218C4×Q8—431no—
219C4×Q8—431no—
220C4×D4—431no—
221C4×D4—431no—
222C4×D4—431no—
223C4×D4—431no—
224C4×D4—861no—
225C4×D4—861no—
226C4×D4—861no—
227C4×D4—861no—
228C4×D4C2×D4311yescharacteristic
229C4×D4C2×D4311yescharacteristic, complemented
230#117—431no—
231#117—861no—
232C2×C4⋊C4—431no—
233C2×C22⋊C4—861no—
234C2×C42—431no—
235C2×C42—861no—
236#107—431no—
237#107—431no—
238#106—431no—
239#106C2×D4311yescharacteristic, complemented
240#103—431no—
241#103—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102C2×D4311yescharacteristic
247#102C2×D4311yescharacteristic, complemented
248#97—431no—
249#97C2×D4311yescharacteristic, complemented
250C4×C8—431no—
251C4×C8—431no—
252C24—861no—
253#41—434no—
254#41—862no—
255C2×Q8—431no—
256C2×D4—434no—
257C2×D4—431no—
258C2×D4—862no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4C22×D4311yescharacteristic
262C2×D4C22×D4311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—1724no—
275SD16—434no—
276SD16—434no—
277D8—434no—
278D8C4×D4314yescomplemented
279M16—434no—
280M16—862no—
281C2×C8—431no—
282C2×C8—431no—
283C2×C8C22×D4311yescharacteristic
284C2×C8C22×D4311yescharacteristic
285C4⋊C4—431no—
286C4⋊C4—431no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4C22×D4311yescharacteristic
291C4⋊C4C22×D4311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C42—431no—
300C42—431no—
301C42—431no—
302C42—861no—
303C42—861no—
304C42—861no—
305C42C22×D4311yescharacteristic
306C23—21no—
307C23—21no—
308C23—431no—
309C23—864no—
310C23—861no—
311C23—1722no—
312C23—1722no—
313Q8—432no—
314Q8—861no—
315D4—21no—
316D4—21no—
317D4—432no—
318D4—864no—
319D4—864no—
320D4—861no—
321D4C2×C4×D4312yes—
322D4C2×C4×D4312yescomplemented
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—431no—
328C2×C4—431no—
329C2×C4—432no—
330C2×C4—432no—
331C2×C4—431no—
332C2×C4—862no—
333C2×C4—864no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—1721no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4D4×D4311yescharacteristic
344C2×C4D4×D4311yescharacteristic
345C2×C4C23×D4311yescharacteristic
346C8—21no—
347C8—432no—
348C8—861no—
349C8C2×C4×D4312yescomplemented
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—432no—
357C22—861no—
358C22—861no—
359C22—862no—
360C22—1728no—
361C22—1721no—
362C22—1721no—
363C22C2×D4×D4311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—432no—
369C4—432no—
370C4—862no—
371C4—861no—
372C4—1721no—
373C4—1721no—
374C4C22×C4×D4311yescharacteristic
375C4#41×D4311yescharacteristic
376C2—42no—
377C2—42no—
378C2—862no—
379C2—1722no—
380C2C4×D4×D4311yescharacteristic
381C2AGL(1,ℤ/8)×D4311yescharacteristic
382C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC4×C43C23×C4
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43C4×AGL(1,ℤ/8)
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×#10621900C2semidirect
3. C4×D4×D43C2semidirect
4. #14583009C2semidirect
5. #14583001C2semidirect
6. #14582999C2semidirect
7. #14582990C2semidirect
8. #14582986C2semidirect
9. D8×Dic43C2semidirect
10. #14582979C2semidirect
11. #14582938C2semidirect
12. #14582902C2semidirect
13. #14582897C2semidirect
14. #14582851C2semidirect
15. C43×#442C2semidirect
19. #13063349C4semidirect
25. C4×Dic86C22semidirect
26. #13063290C22semidirect
29. D4×Dic43C22semidirect
41. #13063259C22semidirect
42. #13063258C22semidirect
43. #13063256C22semidirect
44. #13063250C22semidirect
45. #13063248C22semidirect
48. #13063246C22semidirect
50. #13063236C22semidirect
51. C8×Dic43C22semidirect
52. C8×Dic43C22semidirect
55. C4×D4×C43C22semidirect
56. #106×C43C22semidirect
58. #102×C43C22semidirect
59. #97×C43C22semidirect
71. #10621900C2×C4semidirect
73. D4×D43C2×C4semidirect
83. D8×C43C2×C4semidirect
93. #10621883C2×C4semidirect
94. #10621882C2×C4semidirect
111. #10621873C2×C4semidirect
113. #10621872C2×C4semidirect
124. D4×C43C22×C4semidirect
153. Dic86C22×C4semidirect
155. C8×C43C22×C4semidirect
157. C43⋊C8C22×C4semidirect
183. Dic43AGL(1,ℤ/8)semidirect
196. #442D43semidirect
207. C43C4×AGL(1,ℤ/8)semidirect
229. C4×D4C2×D43semidirect
239. #106C2×D43semidirect
247. #102C2×D43semidirect
249. #97C2×D43semidirect
278. D8C4×D43semidirect
322. D4C2×C4×D43semidirect
349. C8C2×C4×D43semidirect