Finite Group Databasebeta

← #440×D53 #20283490

Subgroups — #440×D53 #20283490

Order 6784.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D53C211yesmaximal, characteristic
2C4×Q8×D53C211yesmaximal, characteristic, complemented
3C4×D4×D53C211yesmaximal, characteristic
4#16810726C211yesmaximal, characteristic, complemented
5#16810725C211yesmaximal, characteristic, complemented
6#16810724C211yesmaximal, characteristic, complemented
7#16810723C211yesmaximal, characteristic, complemented
8#16810722C211yesmaximal, characteristic, complemented
9#16810721C211yesmaximal, characteristic, complemented
10#16810720C211yesmaximal, characteristic, complemented
11#107×D53C211yesmaximal, characteristic, complemented
12#103×D53C211yesmaximal, characteristic, complemented
13#102×D53C211yesmaximal, characteristic
14#97×D53C211yesmaximal, characteristic, complemented
15C53×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D53C2211yescharacteristic
17C2×D4×D53C2211yescharacteristic
18C22×C4×D53—21no—
19C2×#11719913C2211yescharacteristic
20C2×#11719923C2211yescharacteristic
21C2×#11719924C2211yescharacteristic
22SD16×D53C418yescomplemented
23C2×C8×D53C2211yescharacteristic
24C2×C8×D53C2211yescharacteristic
25Q8×Dic53C2211yescharacteristic, complemented
26C4×Dic106—21no—
27C4×Dic106C2211yescharacteristic, complemented
28#13133182—21no—
29#13133182C2211yescharacteristic, complemented
30C4×D212C2211yescharacteristic
31D4×Dic53C2211yescharacteristic
32#13133179C2211yescharacteristic
33C4×C22⋊D53—21no—
34#13133177—21no—
35C4⋊C4×D53—21no—
36C4⋊C4×D53C2211yescharacteristic
37C4⋊C4×D53C2211yescharacteristic
38C22⋊C4×D53—21no—
39C42×D53—21no—
40C42×D53C2211yescharacteristic
41#13133151C2211yescharacteristic, complemented
42#13133150C2211yescharacteristic, complemented
43#13133150C2211yescharacteristic, complemented
44#13133142C2211yescharacteristic, complemented
45#13133141C2211yescharacteristic, complemented
46#13133140C2211yescharacteristic, complemented
47#13133139C2211yescharacteristic
48#13133138C2211yescharacteristic
49#13133137C2211yescharacteristic
50#13133128C2211yescharacteristic, complemented
51#13133127C2211yescharacteristic, complemented
52#13133127C2211yescharacteristic, complemented
53C2×SD16×C53C2211yescharacteristic
54C4×Q8×C53C2211yescharacteristic, complemented
55C4×D4×C53C2211yescharacteristic
56#107×C53C2211yescharacteristic, complemented
57#103×C53C2211yescharacteristic, complemented
58#102×C53C2211yescharacteristic
59#97×C53C2211yescharacteristic, complemented
60C23×D53—21no—
61C2×Q8×C53C2311yescharacteristic
62C2×D4×C53C2311yescharacteristic
63C22×C4×C53—21no—
64C2×C22⋊D53—21no—
65C22×Dic53—21no—
66Q8×D53—22no—
67Q8×D53C2×C414yescomplemented
68D4×D53—22no—
69D4×D53C2×C414yes—
70C2×D212C2311yescharacteristic
71C2×C4×D53—21no—
72C2×C4×D53—21no—
73C2×C4×D53—21no—
74C2×C4×D53—21no—
75C2×C4×D53—21no—
76C2×C4×D53—44no—
77C2×C4×D53D411yescharacteristic
78C2×C4×D53D411yescharacteristic
79C2×C4×D53C2311yescharacteristic
80C2×Dic106—21no—
81C2×Dic106C2311yescharacteristic
82SD16×C53C2×C414yescomplemented
83C2×C8×C53C2311yescharacteristic
84C2×C8×C53C2311yescharacteristic
85C4⋊C4×C53—21no—
86C4⋊C4×C53C2311yescharacteristic
87C4⋊C4×C53C2311yescharacteristic
88C22⋊C4×C53—21no—
89C42×C53—21no—
90C42×C53C2311yescharacteristic
91C22⋊Dic53—21no—
92#11719924C2×C414yescomplemented
93#11719923C2×C414yescomplemented
94#11719921—21no—
95#11719921—21no—
96C4⋊Dic53—21no—
97C4⋊Dic53C2311yescharacteristic
98C4⋊Dic53C2311yescharacteristic
99#11719919—21no—
100#11719919—21no—
101#11719919—21no—
102#11719919—21no—
103C4×Dic53—21no—
104C4×Dic53—21no—
105C4×Dic53—21no—
106C4×Dic53D411yescharacteristic
107C4×Dic53D411yescharacteristic
108C4×Dic53C2311yescharacteristic
109C2×#88322C2311yescharacteristic
110C2×#88322C2311yescharacteristic
111#11719913C2×C414yescomplemented
112C8×D53—22no—
113C8×D53C2×C414yescomplemented
114C23×C53—21no—
115C22×D53—21no—
116C22×D53—24no—
117C22×D53—42no—
118C22×D53—42no—
119C22×D53C2×D411yescharacteristic
120Q8×C53—21no—
121Q8×C53C22×C412yescomplemented
122D4×C53—21no—
123D4×C53C22×C412yes—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53—42no—
128C2×C4×C53C2×D411yescharacteristic
129C2×C4×C53C2×D411yescharacteristic
130C2×C4×C53C2411yescharacteristic
131C22⋊D53—24no—
132C2×Dic53—21no—
133C2×Dic53—21no—
134C2×Dic53—21no—
135C2×Dic53—42no—
136C2×Dic53C2×D411yescharacteristic
137C2×Dic53C2×D411yescharacteristic
138C2×Dic53C2×D411yescharacteristic
139D212—21no—
140D212C22×C412yes—
141C4×D53—24no—
142C4×D53—22no—
143C4×D53—22no—
144C4×D53—42no—
145C4×D53—42no—
146C4×D53—42no—
147C4×D53—42no—
148C4×D53C22×C412yes—
149C4×D53#4112yes—
150Dic106—21no—
151Dic106—24no—
152Dic106C22×C412yescomplemented
153C8×C53—21no—
154C8×C53C22×C412yescomplemented
155#88322—21no—
156#88322C22×C412yescomplemented
157C22×C53—22no—
158C22×C53—41no—
159C22×C53—41no—
160C22×C53C22×D411yescharacteristic
161C2×D53—22no—
162C2×D53—41no—
163C2×D53—41no—
164C2×D53—48no—
165C2×D53C4×D412yes—
166C2×D53AGL(1,ℤ/8)12yes—
167C2×D53#13712yes—
168C4×C53—22no—
169C4×C53—21no—
170C4×C53—21no—
171C4×C53—41no—
172C4×C53—41no—
173C4×C53C23×C411yescharacteristic
174C4×C53C2×#4111yescharacteristic
175Dic53—22no—
176Dic53—21no—
177Dic53—21no—
178Dic53—41no—
179Dic53—41no—
180Dic53C4×D412yes—
181C2×#440—531nomaximal, Sylow
182C2×C53—42no—
183C2×C53C2×C4×D411yescharacteristic
184C2×C53C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C53C2×#13711yescharacteristic
186D53—42no—
187D53#44014yesdirect product factor
188C22×SD16—531no—
189C2×C4×Q8—531no—
190C2×C4×D4—531no—
191#440—531no—
192#440—531no—
193#440—531no—
194#440—531no—
195#440—531no—
196#440—531no—
197#440—531no—
198#440D5311yescharacteristic, direct product factor
199C2×#107—531no—
200C2×#103—531no—
201C2×#102—531no—
202C2×#97—531no—
203C53C2×#44011yescharacteristic, complemented, Sylow
204C22×Q8—531no—
205C22×D4—531no—
206C23×C4—1061no—
207C2×SD16—531no—
208C2×SD16—531no—
209C2×SD16—538no—
210C2×SD16—531no—
211C2×SD16C2×D5311yescharacteristic
212C22×C8—531no—
213C22×C8—531no—
214C4×Q8—531no—
215C4×Q8—531no—
216C4×Q8—531no—
217C4×Q8—1061no—
218C4×Q8—1061no—
219C4×Q8C2×D5311yescharacteristic, complemented
220C4×D4—531no—
221C4×D4—531no—
222C4×D4—531no—
223C4×D4—1061no—
224C4×D4—1061no—
225C4×D4C2×D5311yescharacteristic
226C2×C4⋊C4—531no—
227C2×C4⋊C4—531no—
228C2×C4⋊C4—1061no—
229C2×C22⋊C4—1061no—
230C2×C42—531no—
231C2×C42—1061no—
232#107—531no—
233#107—531no—
234#107—531no—
235#107C2×D5311yescharacteristic, complemented
236#103—531no—
237#103—531no—
238#103—531no—
239#103C2×D5311yescharacteristic, complemented
240#102—531no—
241#102—531no—
242#102—531no—
243#102C2×D5311yescharacteristic
244#97—531no—
245#97—531no—
246#97—531no—
247#97C2×D5311yescharacteristic, complemented
248C24—1061no—
249C2×Q8—534no—
250C2×Q8—531no—
251C2×Q8—1061no—
252C2×Q8—1062no—
253C2×Q8C22×D5311yescharacteristic
254C2×D4—534no—
255C2×D4—531no—
256C2×D4—1062no—
257C2×D4—1061no—
258C2×D4C22×D5311yescharacteristic
259C22×C4—21no—
260C22×C4—531no—
261C22×C4—531no—
262C22×C4—531no—
263C22×C4—1061no—
264C22×C4—1061no—
265C22×C4—1061no—
266C22×C4—1061no—
267C22×C4—1061no—
268C22×C4—1061no—
269C22×C4—2124no—
270SD16—534no—
271SD16—534no—
272SD16—534no—
273SD16C4×D5314yescomplemented
274C2×C8—531no—
275C2×C8—534no—
276C2×C8—531no—
277C2×C8—1062no—
278C2×C8C22×D5311yescharacteristic
279C2×C8C22×D5311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—531no—
282C4⋊C4—531no—
283C4⋊C4—1061no—
284C4⋊C4—1061no—
285C4⋊C4—1061no—
286C4⋊C4—1061no—
287C4⋊C4—1061no—
288C4⋊C4C22×D5311yescharacteristic
289C4⋊C4C22×D5311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—1061no—
292C22⋊C4—1061no—
293C22⋊C4—1061no—
294C42—21no—
295C42—531no—
296C42—531no—
297C42—531no—
298C42—1061no—
299C42—1061no—
300C42—1061no—
301C42C22×D5311yescharacteristic
302C23—21no—
303C23—531no—
304C23—1064no—
305C23—1061no—
306C23—2122no—
307C23—2122no—
308Q8—21no—
309Q8—532no—
310Q8—1064no—
311Q8—1061no—
312Q8C2×C4×D5312yescomplemented
313D4—21no—
314D4—532no—
315D4—1064no—
316D4—1061no—
317D4C2×C4×D5312yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—531no—
323C2×C4—532no—
324C2×C4—532no—
325C2×C4—531no—
326C2×C4—531no—
327C2×C4—1062no—
328C2×C4—1062no—
329C2×C4—1064no—
330C2×C4—1061no—
331C2×C4—1061no—
332C2×C4—1061no—
333C2×C4—2122no—
334C2×C4—2122no—
335C2×C4—2122no—
336C2×C4—2122no—
337C2×C4—2122no—
338C2×C4D4×D5311yescharacteristic
339C2×C4D4×D5311yescharacteristic
340C2×C4C23×D5311yescharacteristic
341C8—21no—
342C8—532no—
343C8—1061no—
344C8C2×C4×D5312yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—532no—
349C22—532no—
350C22—532no—
351C22—1062no—
352C22—2128no—
353C22—2121no—
354C22—2121no—
355C22C2×D4×D5311yescharacteristic
356C4—22no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—532no—
362C4—1062no—
363C4—1061no—
364C4—1061no—
365C4—2121no—
366C4—2121no—
367C4C22×C4×D5311yescharacteristic
368C4#41×D5311yescharacteristic
369C2—42no—
370C2—534no—
371C2—2122no—
372C2C4×D4×D5311yescharacteristic
373C2AGL(1,ℤ/8)×D5311yescharacteristic
374C2#137×D5311yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC4×C53C23×C4
FrattiniC2×C4C23×D53
FittingC53×#440C2
socleC22×C53C22×D4
hypercenter#440D53
hypocenterC53C2×#440
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D53C2semidirect
4. #16810726C2semidirect
5. #16810725C2semidirect
6. #16810724C2semidirect
7. #16810723C2semidirect
8. #16810722C2semidirect
9. #16810721C2semidirect
10. #16810720C2semidirect
11. #107×D53C2semidirect
12. #103×D53C2semidirect
14. #97×D53C2semidirect
15. C53×#440C2semidirect
22. SD16×D53C4semidirect
25. Q8×Dic53C22semidirect
27. C4×Dic106C22semidirect
29. #13133182C22semidirect
41. #13133151C22semidirect
42. #13133150C22semidirect
43. #13133150C22semidirect
44. #13133142C22semidirect
45. #13133141C22semidirect
46. #13133140C22semidirect
50. #13133128C22semidirect
51. #13133127C22semidirect
52. #13133127C22semidirect
54. C4×Q8×C53C22semidirect
56. #107×C53C22semidirect
57. #103×C53C22semidirect
59. #97×C53C22semidirect
67. Q8×D53C2×C4semidirect
82. SD16×C53C2×C4semidirect
92. #11719924C2×C4semidirect
93. #11719923C2×C4semidirect
111. #11719913C2×C4semidirect
113. C8×D53C2×C4semidirect
121. Q8×C53C22×C4semidirect
152. Dic106C22×C4semidirect
154. C8×C53C22×C4semidirect
156. #88322C22×C4semidirect
187. D53#440direct (N × H)
198. #440D53direct (N × H)
203. C53C2×#440semidirect
219. C4×Q8C2×D53semidirect
235. #107C2×D53semidirect
239. #103C2×D53semidirect
247. #97C2×D53semidirect
273. SD16C4×D53semidirect
312. Q8C2×C4×D53semidirect
344. C8C2×C4×D53semidirect