Finite Group Databasebeta

← #19144534

Subgroups — #19144534

Order 5504.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D43C211yesmaximal, characteristic
2#117×D43C211yesmaximal, characteristic, complemented
3#14583224C211yesmaximal, characteristic, complemented
4#14583223C211yesmaximal, characteristic, complemented
5#14583220C211yesmaximal, characteristic, complemented
6#14583219C211yesmaximal, characteristic, complemented
7#14583216C211yesmaximal, characteristic, complemented
8#14583214C211yesmaximal, characteristic, complemented
9#14583211C211yesmaximal, characteristic, complemented
10#14582940C211yesmaximal, characteristic, complemented
11#14582938C211yesmaximal, characteristic, complemented
12#14582902C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582861C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C2×D4×D43—21no—
17C2×D4×D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C2×#10621872C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063300C2211yescharacteristic
22#13063299C2211yescharacteristic
23#13063298—21no—
24#13063297—21no—
25#13063296C2211yescharacteristic
26#13063284C2211yescharacteristic, complemented
27#13063283C2211yescharacteristic
28#13063283C2211yescharacteristic
29#13063282—21no—
30#13063281—21no—
31C4⋊C4×D43C2211yescharacteristic
32C4⋊C4×D43C2211yescharacteristic, complemented
33C4⋊C4×D43C2211yescharacteristic, complemented
34C22⋊C4×D43—21no—
35C22⋊C4×D43—21no—
36C42×D43—21no—
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063258C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52#121×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic, complemented
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43D411yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43D411yescharacteristic
68D4×D43—22no—
69D4×D43—22no—
70D4×D43—44no—
71C2×D172—21no—
72C2×D172C2311yescharacteristic
73C2×C4×D43—22no—
74C2×C4×D43—22no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43D411yescharacteristic
79C2×C4×D43D411yescharacteristic
80C2×C4×D43C2311yescharacteristic
81C2×C4×D43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C42×C43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107#10621872—22no—
108#10621872—22no—
109C23×C43—21no—
110C23×C43C2×D411yescharacteristic
111C22×D43—22no—
112C22×D43—22no—
113C22×D43—21no—
114C22×D43—41no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43C2×D411yescharacteristic
119C22×D43C2×D411yescharacteristic
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—42no—
131C22⋊D43—42no—
132C22⋊D43—42no—
133C2×Dic43—22no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139D172—21no—
140D172—21no—
141D172—42no—
142C4×D43—22no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—22no—
146C4×D43—42no—
147C4×D43—42no—
148C4×D43—42no—
149C4×D43#4112yes—
150C4×D43#4112yes—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—44no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—84no—
171C2×D43#12312yes—
172C2×D43AGL(1,ℤ/8)12yes—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43C2×#4111yescharacteristic
178C4×C43C2×#4111yescharacteristic
179Dic43—21no—
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183Dic43#12312yes—
184#3094—431nomaximal, Sylow
185C2×C43—41no—
186C2×C43—81no—
187C2×C43C2×#12311yescharacteristic
188C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C43#57511yescharacteristic
190D43—22no—
191D43—22no—
192D43—81no—
193C2×#121—431no—
194C2×#117—431no—
195#482—431no—
196#482—431no—
197#482—431no—
198#482D4311yescharacteristic, complemented
199#481—431no—
200#481—431no—
201#480—431no—
202#480—431no—
203#428—431no—
204#428—431no—
205#418—431no—
206#418—431no—
207#407—431no—
208C43#309411yescharacteristic, complemented, Sylow
209C22×D4—431no—
210C22×D4—861no—
211C23×C4—431no—
212C2×M16—431no—
213C2×M16—431no—
214#121—431no—
215#121—431no—
216#121—431no—
217#121—861no—
218#121—861no—
219#121C2×D4311yescharacteristic
220#117—431no—
221#117—431no—
222#117—431no—
223#117—861no—
224#117—861no—
225#117C2×D4311yescharacteristic, complemented
226C2×C4⋊C4—431no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C42—861no—
232#107—431no—
233#107—431no—
234#107—431no—
235#107C2×D4311yescharacteristic, complemented
236#106—431no—
237#106—431no—
238#106—431no—
239#106C2×D4311yescharacteristic, complemented
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102C2×D4311yescharacteristic, complemented
247#102C2×D4311yescharacteristic, complemented
248C22⋊C8—431no—
249C22⋊C8—431no—
250C22⋊C8—431no—
251C22⋊C8C2×D4311yescharacteristic, complemented
252C24—431no—
253C24—861no—
254C2×D4—21no—
255C2×D4—431no—
256C2×D4—861no—
257C2×D4—862no—
258C2×D4—862no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—1724no—
263C2×D4C22×D4311yescharacteristic
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—431no—
269C22×C4—862no—
270C22×C4—862no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4C22×D4311yescharacteristic
275M16—862no—
276M16—862no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—431no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C42—21no—
299C42—861no—
300C42—861no—
301C42—861no—
302C23—21no—
303C23—431no—
304C23—431no—
305C23—862no—
306C23—862no—
307C23—861no—
308C23—1721no—
309C23—1722no—
310C23—1722no—
311C23—1722no—
312C23D4×D4311yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—861no—
317D4—861no—
318D4—1722no—
319D4—1722no—
320D4—1722no—
321D4—1722no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—431no—
328C2×C4—432no—
329C2×C4—432no—
330C2×C4—431no—
331C2×C4—862no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4D4×D4311yescharacteristic
343C2×C4C23×D4311yescharacteristic
344C8—21no—
345C8—21no—
346C8—861no—
347C8—861no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—432no—
355C22—432no—
356C22—861no—
357C22—861no—
358C22—861no—
359C22—861no—
360C22—3444no—
361C22—1724no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22C2×D4×D4311yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—432no—
371C4—861no—
372C4—1721no—
373C4—1721no—
374C4—1721no—
375C4#41×D4311yescharacteristic
376C4#41×D4311yescharacteristic
377C2—41no—
378C2—81no—
379C2—862no—
380C2—862no—
381C2—3441no—
382C2#123×D4311yescharacteristic
383C2AGL(1,ℤ/8)×D4311yescharacteristic
384C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3094
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D43C2semidirect
3. #14583224C2semidirect
4. #14583223C2semidirect
5. #14583220C2semidirect
6. #14583219C2semidirect
7. #14583216C2semidirect
8. #14583214C2semidirect
9. #14583211C2semidirect
10. #14582940C2semidirect
11. #14582938C2semidirect
12. #14582902C2semidirect
13. #14582902C2semidirect
14. #14582861C2semidirect
15. C43×#482C2semidirect
26. #13063284C22semidirect
32. C4⋊C4×D43C22semidirect
33. C4⋊C4×D43C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063258C22semidirect
40. #13063257C22semidirect
41. #13063256C22semidirect
42. #13063256C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
45. #13063246C22semidirect
46. #13063246C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
53. #117×C43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. #102×C43C22semidirect
57. #102×C43C22semidirect
58. C22⋊C8×C43C22semidirect
198. #482D43semidirect
208. C43#3094semidirect
225. #117C2×D43semidirect
235. #107C2×D43semidirect
239. #106C2×D43semidirect
246. #102C2×D43semidirect
247. #102C2×D43semidirect
251. C22⋊C8C2×D43semidirect