Finite Group Databasebeta

← #19143424

Subgroups — #19143424

Order 5504.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063349C211yesmaximal, characteristic
2#14583378C211yesmaximal, characteristic, complemented
3#14583371C211yesmaximal, characteristic, complemented
4#14583008C211yesmaximal, characteristic, complemented
5#14583001C211yesmaximal, characteristic, complemented
6#14582996C211yesmaximal, characteristic, complemented
7#14582986C211yesmaximal, characteristic, complemented
8C4×#10621883C211yesmaximal, characteristic, complemented
9D8×Dic43C211yesmaximal, characteristic, complemented
10C4×#10621882C211yesmaximal, characteristic, complemented
11#14582938C211yesmaximal, characteristic, complemented
12#14582892C211yesmaximal, characteristic, complemented
13#102×D43C211yesmaximal, characteristic, complemented
14#14582856C211yesmaximal, characteristic, complemented
15C43×#442C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18#13063349C418yescomplemented
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621882C2211yescharacteristic
22C2×#10621872C2211yescharacteristic
23C2×C8×D43C2211yescharacteristic
24C4×Dic86C2211yescharacteristic, complemented
25#13063290C2211yescharacteristic, complemented
26C4×D172C2211yescharacteristic
27D4×Dic43C2211yescharacteristic
28D4×Dic43C2211yescharacteristic, complemented
29#13063287C2211yescharacteristic
30C4×C22⋊D43—21no—
31C4×C22⋊D43—21no—
32(C22⋊D43)⋊C4—21no—
33(C22⋊D43)⋊C4—21no—
34#13063283C2211yescharacteristic
35#13063282C2211yescharacteristic
36#13063281—21no—
37C2×Dic43⋊C4—21no—
38C4⋊C4×D43C2211yescharacteristic
39C2×(C2×D43)⋊C4—21no—
40C22⋊C4×D43—21no—
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#13063235C2211yescharacteristic, complemented
51C4×C43⋊C8C2211yescharacteristic, 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×D43C2311yescharacteristic
79C2×Dic86C2311yescharacteristic
80D8×C43C2×C414yescomplemented
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C42×C43C2311yescharacteristic
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90#10621883C2×C414yescomplemented
91#10621882C2×C414yescomplemented
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4D411yescharacteristic
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621873C2×C414yescomplemented
111#10621872C2×C414yescomplemented
112C8×D43—22no—
113C23×C43—21no—
114C23×C43—21no—
115C22×D43—21no—
116C22×D43—24no—
117C22×D43—81no—
118C22×D43—81no—
119C22×D43C2×D411yescharacteristic
120D4×C43—21no—
121D4×C43—21no—
122D4×C43C22×C412yes—
123D4×C43C22×C412yes—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—24no—
132C22⋊D43—24no—
133C2×Dic43—21no—
134C2×Dic43—24no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142D172—21no—
143D172C22×C412yes—
144C4×D43—81no—
145C4×D43—81no—
146C4×D43—81no—
147C4×D43C22×C412yes—
148C4×D43#4112yes—
149Dic86—21no—
150Dic86C22×C412yes—
151C8×C43—21no—
152C8×C43C22×C412yes—
153C43⋊C8—21no—
154C43⋊C8C22×C412yes—
155C22×C43—22no—
156C22×C43—22no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—22no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—84no—
168C2×D43C4×D412yes—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43C23×C411yescharacteristic
174C4×C43C2×#4111yescharacteristic
175Dic43—22no—
176Dic43—21no—
177Dic43—21no—
178Dic43—41no—
179Dic43—41no—
180Dic43C4×D412yes—
181#2946—431nomaximal, Sylow
182C2×C43—42no—
183C2×C43—42no—
184C2×C43C2×C4×D411yescharacteristic
185C2×C43#57611yescharacteristic
186C2×C43#57711yescharacteristic
187D43—22no—
188D43—42no—
189C2×AGL(1,ℤ/8)—431no—
190#520—431no—
191#518—431no—
192#442—431no—
193#442D4311yescharacteristic, complemented
194#440—431no—
195#440—431no—
196C4×SD16—431no—
197C4×SD16—431no—
198C4×D8—431no—
199C4×D8—431no—
200#428—431no—
201#416—431no—
202C2×#102—431no—
203#405—431no—
204C43#294611yescharacteristic, complemented, Sylow
205C2×#41—431no—
206C22×D4—431no—
207AGL(1,ℤ/8)—438no—
208C2×SD16—431no—
209C2×SD16—431no—
210C2×D8—431no—
211C2×D8C2×D4311yescharacteristic
212C2×M16—431no—
213C22×C8—431no—
214C4×Q8—431no—
215C4×Q8—431no—
216C4×D4—431no—
217C4×D4—431no—
218C4×D4—431no—
219C4×D4—431no—
220C4×D4—861no—
221C4×D4—861no—
222C4×D4—861no—
223C4×D4—861no—
224C4×D4C2×D4311yescharacteristic
225C4×D4C2×D4311yescharacteristic, complemented
226#117—431no—
227#117—431no—
228#117—861no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—861no—
231C2×C22⋊C4—861no—
232C2×C22⋊C4—861no—
233#107—431no—
234#107—431no—
235#106—431no—
236#106C2×D4311yescharacteristic, complemented
237#103—431no—
238#103—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102C2×D4311yescharacteristic
244#102C2×D4311yescharacteristic, complemented
245#97—431no—
246#97C2×D4311yescharacteristic, complemented
247C4×C8—431no—
248C4×C8—431no—
249C24—861no—
250#41—434no—
251#41—862no—
252C2×Q8—431no—
253C2×D4—434no—
254C2×D4—431no—
255C2×D4—862no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4C22×D4311yescharacteristic
259C2×D4C22×D4311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—431no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269SD16—434no—
270SD16—434no—
271D8—434no—
272D8C4×D4314yescomplemented
273M16—434no—
274C2×C8—431no—
275C2×C8—431no—
276C2×C8—862no—
277C2×C8C22×D4311yescharacteristic
278C2×C8C22×D4311yescharacteristic
279C4⋊C4—431no—
280C4⋊C4—431no—
281C4⋊C4—431no—
282C4⋊C4—431no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C42—431no—
298C42—861no—
299C42—861no—
300C42—861no—
301C42C22×D4311yescharacteristic
302C23—21no—
303C23—21no—
304C23—431no—
305C23—864no—
306C23—861no—
307C23—3441no—
308C23—3441no—
309Q8—432no—
310Q8—861no—
311D4—21no—
312D4—21no—
313D4—432no—
314D4—864no—
315D4—864no—
316D4—861no—
317D4C2×C4×D4312yes—
318D4C2×C4×D4312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—431no—
324C2×C4—432no—
325C2×C4—432no—
326C2×C4—431no—
327C2×C4—431no—
328C2×C4—864no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4D4×D4311yescharacteristic
338C2×C4D4×D4311yescharacteristic
339C2×C4C23×D4311yescharacteristic
340C8—21no—
341C8—432no—
342C8—861no—
343C8C2×C4×D4312yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—432no—
351C22—861no—
352C22—861no—
353C22—862no—
354C22—3444no—
355C22—1721no—
356C22—1721no—
357C22C2×D4×D4311yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—432no—
363C4—862no—
364C4—861no—
365C4—861no—
366C4—1721no—
367C4—1721no—
368C4C22×C4×D4311yescharacteristic
369C4#41×D4311yescharacteristic
370C2—42no—
371C2—42no—
372C2—862no—
373C2—1722no—
374C2C4×D4×D4311yescharacteristic
375C2#1458370311yescharacteristic
376C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC4×C43C23×C4
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#2946
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. #14583378C2semidirect
3. #14583371C2semidirect
4. #14583008C2semidirect
5. #14583001C2semidirect
6. #14582996C2semidirect
7. #14582986C2semidirect
8. C4×#10621883C2semidirect
9. D8×Dic43C2semidirect
10. C4×#10621882C2semidirect
11. #14582938C2semidirect
12. #14582892C2semidirect
13. #102×D43C2semidirect
14. #14582856C2semidirect
15. C43×#442C2semidirect
18. #13063349C4semidirect
24. C4×Dic86C22semidirect
25. #13063290C22semidirect
28. D4×Dic43C22semidirect
41. #13063259C22semidirect
42. #13063258C22semidirect
43. #13063256C22semidirect
44. #13063250C22semidirect
45. #13063248C22semidirect
48. #13063246C22semidirect
50. #13063235C22semidirect
51. C4×C43⋊C8C22semidirect
52. C8×Dic43C22semidirect
55. C4×D4×C43C22semidirect
56. #106×C43C22semidirect
58. #102×C43C22semidirect
59. #97×C43C22semidirect
71. #10621900C2×C4semidirect
73. D4×D43C2×C4semidirect
80. D8×C43C2×C4semidirect
90. #10621883C2×C4semidirect
91. #10621882C2×C4semidirect
110. #10621873C2×C4semidirect
111. #10621872C2×C4semidirect
193. #442D43semidirect
204. C43#2946semidirect
225. C4×D4C2×D43semidirect
236. #106C2×D43semidirect
244. #102C2×D43semidirect
246. #97C2×D43semidirect
272. D8C4×D43semidirect