Finite Group Databasebeta

← #465×D53 #20284271

Subgroups — #465×D53 #20284271

Order 6784.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D53C211yesmaximal, characteristic, complemented
2C22×C8×D53C211yesmaximal, characteristic, complemented
3C22⋊Q8×D53C211yesmaximal, characteristic, complemented
4#121×D53C211yesmaximal, characteristic
5#16810855C211yesmaximal, characteristic, complemented
6#16810854C211yesmaximal, characteristic, complemented
7#16810853C211yesmaximal, characteristic, complemented
8#16810852C211yesmaximal, characteristic, complemented
9#16810851C211yesmaximal, characteristic, complemented
10#16810850C211yesmaximal, characteristic, complemented
11#16810849C211yesmaximal, characteristic, complemented
12#106×D53C211yesmaximal, characteristic, complemented
13#103×D53C211yesmaximal, characteristic, complemented
14#102×D53C211yesmaximal, characteristic, complemented
15C53×#465C211yesmaximal, characteristic, complemented
16C2×Q8×D53C2211yescharacteristic
17C2×D4×D53—21no—
18C2×D4×D53C2211yescharacteristic
19C22×C4×D53C2211yescharacteristic
20C2×#11719913C2211yescharacteristic, complemented
21C2×#11719923C2211yescharacteristic, complemented
22C2×#11719924C2211yescharacteristic, complemented
23SD16×D53—24no—
24C22×#88322C2211yescharacteristic, complemented
25C2×C8×D53—24no—
26C2×C8×D53C2211yescharacteristic
27C2×C8×D53C2211yescharacteristic
28C2×C8×D53C2211yescharacteristic, complemented
29C2×C8×D53C2211yescharacteristic, complemented
30#13133197C2211yescharacteristic, complemented
31#13133196C2211yescharacteristic, complemented
32#13133195—21no—
33#13133194—21no—
34#13133193C2211yescharacteristic, complemented
35#13133192C2211yescharacteristic
36#13133191C2211yescharacteristic
37#13133190—21no—
38#13133189—21no—
39#13133188C2211yescharacteristic
40C4⋊C4×D53—21no—
41C4⋊C4×D53C2211yescharacteristic
42C4⋊C4×D53C2211yescharacteristic
43C22⋊C4×D53—21no—
44C22⋊C4×D53—21no—
45#13133149C2211yescharacteristic, complemented
46#13133148C2211yescharacteristic, complemented
47#13133148C2211yescharacteristic, complemented
48#13133142C2211yescharacteristic, complemented
49#13133141C2211yescharacteristic, complemented
50#13133140C2211yescharacteristic, complemented
51#13133139C2211yescharacteristic, complemented
52#13133138C2211yescharacteristic, complemented
53#13133137C2211yescharacteristic, complemented
54C2×SD16×C53C2211yescharacteristic, complemented
55C22×C8×C53C2211yescharacteristic, complemented
56C22⋊Q8×C53C2211yescharacteristic, complemented
57#121×C53C2211yescharacteristic
58#106×C53C2211yescharacteristic, complemented
59#103×C53C2211yescharacteristic, complemented
60#102×C53C2211yescharacteristic, complemented
61C23×D53—21no—
62C23×D53D411yescharacteristic
63C2×Q8×C53C2311yescharacteristic
64C2×D4×C53—21no—
65C2×D4×C53C2311yescharacteristic
66C22×C4×C53C2311yescharacteristic
67C2×C22⋊D53—21no—
68C2×C22⋊D53—21no—
69C2×C22⋊D53—21no—
70C22×Dic53D411yescharacteristic
71Q8×D53—22no—
72Q8×D53—22no—
73D4×D53—22no—
74D4×D53—22no—
75D4×D53—44no—
76C2×D212—21no—
77C2×D212C2311yescharacteristic
78C2×C4×D53—22no—
79C2×C4×D53—22no—
80C2×C4×D53—21no—
81C2×C4×D53—21no—
82C2×C4×D53—21no—
83C2×C4×D53D411yescharacteristic
84C2×C4×D53D411yescharacteristic
85C2×C4×D53C2311yescharacteristic
86C2×C4×D53C2311yescharacteristic
87C2×Dic106—21no—
88C2×Dic106C2311yescharacteristic
89SD16×C53—22no—
90C2×C8×C53—22no—
91C2×C8×C53C2311yescharacteristic
92C2×C8×C53C2311yescharacteristic
93C4⋊C4×C53—21no—
94C4⋊C4×C53C2311yescharacteristic
95C4⋊C4×C53C2311yescharacteristic
96C22⋊C4×C53—21no—
97C22⋊C4×C53—21no—
98C22⋊Dic53—21no—
99C22⋊Dic53—21no—
100#11719924—22no—
101#11719923—22no—
102#11719921—21no—
103#11719921—21no—
104#11719921—21no—
105#11719921—21no—
106C4⋊Dic53—21no—
107C4⋊Dic53C2311yescharacteristic
108C4⋊Dic53C2311yescharacteristic
109#11719919—21no—
110#11719919—21no—
111#11719919—21no—
112#11719919—21no—
113C2×#88322—22no—
114C2×#88322C2311yescharacteristic
115C2×#88322C2311yescharacteristic
116#11719913—22no—
117C8×D53—22no—
118C8×D53—22no—
119C8×D53—22no—
120C8×D53D414yescomplemented
121C23×C53—21no—
122C23×C53C2×D411yescharacteristic
123C22×D53—22no—
124C22×D53—22no—
125C22×D53—21no—
126C22×D53—42no—
127C22×D53—42no—
128C22×D53—42no—
129C22×D53SD1614yescomplemented
130C22×D53C2×D411yescharacteristic
131C22×D53C2×D411yescharacteristic
132Q8×C53—21no—
133Q8×C53—21no—
134D4×C53—21no—
135D4×C53—21no—
136D4×C53—42no—
137C2×C4×C53—21no—
138C2×C4×C53—21no—
139C2×C4×C53—21no—
140C2×C4×C53—21no—
141C2×C4×C53—21no—
142C2×C4×C53C2×D411yescharacteristic
143C2×C4×C53C2411yescharacteristic
144C22⋊D53—42no—
145C22⋊D53—42no—
146C22⋊D53—42no—
147C2×Dic53—22no—
148C2×Dic53—21no—
149C2×Dic53—21no—
150C2×Dic53—21no—
151C2×Dic53C2×D411yescharacteristic
152C2×Dic53C2×D411yescharacteristic
153D212—21no—
154D212—21no—
155D212—42no—
156C4×D53—22no—
157C4×D53—21no—
158C4×D53—21no—
159C4×D53—22no—
160C4×D53—42no—
161C4×D53—42no—
162C4×D53—42no—
163C4×D53C2×D412yes—
164C4×D53#4112yes—
165Dic106—21no—
166Dic106—21no—
167Dic106—42no—
168C8×C53—21no—
169C8×C53C2×D412yescomplemented
170#88322—21no—
171#88322C2×D412yescomplemented
172C22×C53—21no—
173C22×C53—21no—
174C22×C53—41no—
175C22×C53—41no—
176C22×C53—41no—
177C22×C53C2×SD1612yescomplemented
178C22×C53C22×D411yescharacteristic
179C2×D53—21no—
180C2×D53—21no—
181C2×D53—28no—
182C2×D53—41no—
183C2×D53—41no—
184C2×D53—41no—
185C2×D53—84no—
186C2×D53#12112yes—
187C2×D53C2×SD1612yes—
188C2×D53C2×SD1612yescomplemented
189C2×D53#13512yes—
190C4×C53—21no—
191C4×C53—41no—
192C4×C53—41no—
193C4×C53—41no—
194C4×C53C22×D411yescharacteristic
195C4×C53C2×#4111yescharacteristic
196Dic53—21no—
197Dic53—41no—
198Dic53—41no—
199Dic53—41no—
200Dic53#12112yes—
201C2×#465—531nomaximal, Sylow
202C2×C53—22no—
203C2×C53—81no—
204C2×C53C2×#12111yescharacteristic
205C2×C53C22×SD1611yescharacteristic
206C2×C53C2×#13511yescharacteristic
207D53—22no—
208D53—81no—
209D53#46514yesdirect product factor
210C22×SD16—531no—
211C23×C8—531no—
212C2×C22⋊Q8—531no—
213C2×#121—531no—
214#465—531no—
215#465—531no—
216#465—531no—
217#465—531no—
218#465—531no—
219#465—531no—
220#465—531no—
221#465D5311yescharacteristic, direct product factor
222C2×#106—531no—
223C2×#103—531no—
224C2×#102—531no—
225C53C2×#46511yescharacteristic, complemented, Sylow
226C22×Q8—531no—
227C22×D4—531no—
228C22×D4—1061no—
229C23×C4—531no—
230C2×SD16—531no—
231C2×SD16—531no—
232C2×SD16—531no—
233C2×SD16—1064no—
234C2×SD16C2×D5311yescharacteristic, complemented
235C22×C8—531no—
236C22×C8—531no—
237C22×C8—531no—
238C22×C8—531no—
239C22×C8—531no—
240C22×C8—1064no—
241C22×C8C2×D5311yescharacteristic, complemented
242C22⋊Q8—531no—
243C22⋊Q8—531no—
244C22⋊Q8—531no—
245C22⋊Q8—1061no—
246C22⋊Q8—1061no—
247C22⋊Q8C2×D5311yescharacteristic, complemented
248#121—531no—
249#121—531no—
250#121—531no—
251#121—1061no—
252#121—1061no—
253#121C2×D5311yescharacteristic
254C2×C4⋊C4—531no—
255C2×C4⋊C4—531no—
256C2×C4⋊C4—1061no—
257C2×C22⋊C4—1061no—
258C2×C22⋊C4—1061no—
259#106—531no—
260#106—531no—
261#106—531no—
262#106C2×D5311yescharacteristic, complemented
263#103—531no—
264#103—531no—
265#103—531no—
266#103C2×D5311yescharacteristic, complemented
267#102—531no—
268#102—531no—
269#102—531no—
270#102C2×D5311yescharacteristic, complemented
271C24—531no—
272C24—1061no—
273C2×Q8—531no—
274C2×Q8—1061no—
275C2×Q8—1062no—
276C2×Q8—1062no—
277C2×Q8C22×D5311yescharacteristic
278C2×D4—21no—
279C2×D4—531no—
280C2×D4—1061no—
281C2×D4—1062no—
282C2×D4—1062no—
283C2×D4—1061no—
284C2×D4—1061no—
285C2×D4—1061no—
286C2×D4—2124no—
287C2×D4C22×D5311yescharacteristic
288C22×C4—531no—
289C22×C4—531no—
290C22×C4—531no—
291C22×C4—531no—
292C22×C4—531no—
293C22×C4—1062no—
294C22×C4—1062no—
295C22×C4—1061no—
296C22×C4—1061no—
297C22×C4—1061no—
298C22×C4C22×D5311yescharacteristic
299SD16—22no—
300SD16—1062no—
301SD16—1062no—
302SD16—1062no—
303C2×C8—22no—
304C2×C8—531no—
305C2×C8—534no—
306C2×C8—531no—
307C2×C8—1062no—
308C2×C8—1062no—
309C2×C8—1062no—
310C2×C8—1062no—
311C2×C8C22×D5311yescharacteristic
312C2×C8C22×D5311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—531no—
315C4⋊C4—531no—
316C4⋊C4—1061no—
317C4⋊C4—1061no—
318C4⋊C4—1061no—
319C4⋊C4—1061no—
320C4⋊C4—1061no—
321C4⋊C4C22×D5311yescharacteristic
322C4⋊C4C22×D5311yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—1061no—
326C22⋊C4—1061no—
327C22⋊C4—1061no—
328C22⋊C4—1061no—
329C22⋊C4—1061no—
330C22⋊C4—1061no—
331C23—21no—
332C23—531no—
333C23—534no—
334C23—531no—
335C23—1062no—
336C23—1062no—
337C23—1061no—
338C23—2122no—
339C23—2122no—
340C23—2122no—
341C23D4×D5311yescharacteristic
342Q8—21no—
343Q8—21no—
344Q8—1061no—
345Q8—1061no—
346Q8—2122no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—1061no—
351D4—1061no—
352D4—2122no—
353D4—2122no—
354D4—2122no—
355D4—2122no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—531no—
362C2×C4—532no—
363C2×C4—532no—
364C2×C4—531no—
365C2×C4—1062no—
366C2×C4—1062no—
367C2×C4—1062no—
368C2×C4—1061no—
369C2×C4—1061no—
370C2×C4—1061no—
371C2×C4—1061no—
372C2×C4—1061no—
373C2×C4—2122no—
374C2×C4—2122no—
375C2×C4—2122no—
376C2×C4D4×D5311yescharacteristic
377C2×C4C23×D5311yescharacteristic
378C8—21no—
379C8—532no—
380C8—1061no—
381C8D4×D5312yescomplemented
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—532no—
388C22—532no—
389C22—532no—
390C22—532no—
391C22—1068no—
392C22—1061no—
393C22—1061no—
394C22—4244no—
395C22—2121no—
396C22—2121no—
397C22—2121no—
398C22SD16×D5312yescomplemented
399C22C2×D4×D5311yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—532no—
405C4—1061no—
406C4—2121no—
407C4—2121no—
408C4—2121no—
409C4C2×D4×D5311yescharacteristic
410C4#41×D5311yescharacteristic
411C2—22no—
412C2—81no—
413C2—534no—
414C2—1062no—
415C2—4241no—
416C2#121×D5311yescharacteristic
417C2C2×SD16×D5311yescharacteristic
418C2#135×D5311yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC2×C4×C53C24
FrattiniC2×C4C23×D53
FittingC53×#465C2
socleC22×C53C22×D4
hypercenter#465D53
hypocenterC53C2×#465
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D53C2semidirect
2. C22×C8×D53C2semidirect
3. C22⋊Q8×D53C2semidirect
5. #16810855C2semidirect
6. #16810854C2semidirect
7. #16810853C2semidirect
8. #16810852C2semidirect
9. #16810851C2semidirect
10. #16810850C2semidirect
11. #16810849C2semidirect
12. #106×D53C2semidirect
13. #103×D53C2semidirect
14. #102×D53C2semidirect
15. C53×#465C2semidirect
20. C2×#11719913C22semidirect
21. C2×#11719923C22semidirect
22. C2×#11719924C22semidirect
24. C22×#88322C22semidirect
28. C2×C8×D53C22semidirect
29. C2×C8×D53C22semidirect
30. #13133197C22semidirect
31. #13133196C22semidirect
34. #13133193C22semidirect
45. #13133149C22semidirect
46. #13133148C22semidirect
47. #13133148C22semidirect
48. #13133142C22semidirect
49. #13133141C22semidirect
50. #13133140C22semidirect
51. #13133139C22semidirect
52. #13133138C22semidirect
53. #13133137C22semidirect
54. C2×SD16×C53C22semidirect
55. C22×C8×C53C22semidirect
56. C22⋊Q8×C53C22semidirect
58. #106×C53C22semidirect
59. #103×C53C22semidirect
60. #102×C53C22semidirect
120. C8×D53D4semidirect
129. C22×D53SD16semidirect
169. C8×C53C2×D4semidirect
171. #88322C2×D4semidirect
177. C22×C53C2×SD16semidirect
188. C2×D53C2×SD16semidirect
209. D53#465direct (N × H)
221. #465D53direct (N × H)
225. C53C2×#465semidirect
234. C2×SD16C2×D53semidirect
241. C22×C8C2×D53semidirect
247. C22⋊Q8C2×D53semidirect
262. #106C2×D53semidirect
266. #103C2×D53semidirect
270. #102C2×D53semidirect
381. C8D4×D53semidirect
398. C22SD16×D53semidirect