Finite Group Databasebeta

← #464×D53 #20284155

Subgroups — #464×D53 #20284155

Order 6784.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D53C211yesmaximal, characteristic, complemented
2C2×SD16×D53C211yesmaximal, characteristic
3#124×D53C211yesmaximal, characteristic
4C4×Q8×D53C211yesmaximal, characteristic, complemented
5#16810848C211yesmaximal, characteristic, complemented
6#16810847C211yesmaximal, characteristic, complemented
7#16810846C211yesmaximal, characteristic, complemented
8#16810845C211yesmaximal, characteristic, complemented
9#16810844C211yesmaximal, characteristic, complemented
10#16810843C211yesmaximal, characteristic, complemented
11#16810842C211yesmaximal, characteristic, complemented
12C4⋊C8×D53C211yesmaximal, characteristic, complemented
13#103×D53C211yesmaximal, characteristic, complemented
14#102×D53C211yesmaximal, characteristic
15C53×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D53C2211yescharacteristic
17C2×Q8×D53C2211yescharacteristic
18C2×D4×D53C2211yescharacteristic
19C2×Dic212C2211yescharacteristic, complemented
20C2×#11719925C2211yescharacteristic, complemented
21C2×#11719925C2211yescharacteristic, complemented
22Q16×D53—24no—
23C2×#11719913C2211yescharacteristic
24C2×#11719923C2211yescharacteristic
25C2×#11719924C2211yescharacteristic
26SD16×D53—24no—
27C2×C8×D53C2211yescharacteristic
28C2×C8×D53C2211yescharacteristic
29#13133206C2211yescharacteristic
30#13133205C2211yescharacteristic
31#13133204C2211yescharacteristic
32#13133203—21no—
33#13133203—21no—
34Q8×Dic53C2211yescharacteristic, complemented
35C4×Dic106—21no—
36C4×Dic106C2211yescharacteristic, complemented
37#13133182—21no—
38#13133182C2211yescharacteristic, complemented
39C4⋊C4×D53—21no—
40C4⋊C4×D53C2211yescharacteristic
41C22⋊C4×D53—21no—
42C22⋊C4×D53—21no—
43C42×D53—21no—
44C42×D53C2211yescharacteristic
45C4⋊#88322C2211yescharacteristic, complemented
46#13133146C2211yescharacteristic, complemented
47#13133146C2211yescharacteristic, complemented
48#13133142C2211yescharacteristic, complemented
49#13133141C2211yescharacteristic, complemented
50#13133140C2211yescharacteristic, complemented
51#13133139C2211yescharacteristic
52#13133138C2211yescharacteristic
53#13133137C2211yescharacteristic
54C2×Q16×C53C2211yescharacteristic, complemented
55C2×SD16×C53C2211yescharacteristic
56#124×C53C2211yescharacteristic
57C4×Q8×C53C2211yescharacteristic, complemented
58C4⋊C8×C53C2211yescharacteristic, complemented
59#103×C53C2211yescharacteristic, complemented
60#102×C53C2211yescharacteristic
61C23×D53—21no—
62C2×Q8×C53C2311yescharacteristic
63C2×Q8×C53C2311yescharacteristic
64C2×D4×C53C2311yescharacteristic
65C2×C22⋊D53—21no—
66Q8×D53—22no—
67Q8×D53—22no—
68Q8×D53—22no—
69Q8×D53D414yes—
70D4×D53—22no—
71D4×D53—22no—
72C2×D212C2311yescharacteristic
73C2×C4×D53—21no—
74C2×C4×D53—21no—
75C2×C4×D53—21no—
76C2×C4×D53D411yescharacteristic
77C2×C4×D53D411yescharacteristic
78C2×C4×D53C2311yescharacteristic
79C2×Dic106—21no—
80C2×Dic106—21no—
81C2×Dic106C2311yescharacteristic
82C2×Dic106C2311yescharacteristic
83Q16×C53—22no—
84SD16×C53—22no—
85C2×C8×C53C2311yescharacteristic
86C2×C8×C53C2311yescharacteristic
87C4⋊C4×C53—21no—
88C4⋊C4×C53C2311yescharacteristic
89C22⋊C4×C53—21no—
90C22⋊C4×C53—21no—
91C42×C53—21no—
92C42×C53C2311yescharacteristic
93C22⋊Dic53—21no—
94C22⋊Dic53—21no—
95#11719925—22no—
96#11719925—22no—
97#11719924—22no—
98#11719923—22no—
99#11719921—21no—
100#11719921—21no—
101#11719921—21no—
102#11719921—21no—
103C4⋊Dic53—21no—
104C4⋊Dic53C2311yescharacteristic
105#11719919—21no—
106#11719919—21no—
107#11719919—21no—
108C4×Dic53—21no—
109C4×Dic53—21no—
110C4×Dic53—21no—
111C4×Dic53D411yescharacteristic
112C4×Dic53D411yescharacteristic
113C4×Dic53C2311yescharacteristic
114C2×#88322C2311yescharacteristic
115C2×#88322C2311yescharacteristic
116Dic212—22no—
117#11719913—22no—
118C8×D53—22no—
119C8×D53—22no—
120C23×C53—21no—
121C22×D53—21no—
122C22×D53—42no—
123C22×D53—42no—
124C22×D53—42no—
125C22×D53C2×D411yescharacteristic
126Q8×C53—21no—
127Q8×C53—21no—
128Q8×C53—21no—
129Q8×C53C2×D412yes—
130D4×C53—21no—
131D4×C53—21no—
132C2×C4×C53—21no—
133C2×C4×C53—21no—
134C2×C4×C53—21no—
135C2×C4×C53C2×D411yescharacteristic
136C2×C4×C53C2×D411yescharacteristic
137C2×C4×C53C2411yescharacteristic
138C22⋊D53—42no—
139C2×Dic53—21no—
140C2×Dic53—21no—
141C2×Dic53—21no—
142C2×Dic53C2×D411yescharacteristic
143C2×Dic53C2×D411yescharacteristic
144C2×Dic53C2×D411yescharacteristic
145D212—21no—
146D212—21no—
147C4×D53—24no—
148C4×D53—22no—
149C4×D53—22no—
150C4×D53—42no—
151C4×D53—42no—
152C4×D53C2×D412yes—
153C4×D53#4112yes—
154Dic106—21no—
155Dic106—24no—
156Dic106—21no—
157Dic106—21no—
158Dic106—42no—
159Dic106C2×D412yes—
160C8×C53—21no—
161C8×C53—21no—
162#88322—21no—
163#88322—21no—
164C22×C53—41no—
165C22×C53—41no—
166C22×C53—41no—
167C22×C53C22×D411yescharacteristic
168C2×D53—41no—
169C2×D53—41no—
170C2×D53—41no—
171C2×D53—84no—
172C2×D53#12112yes—
173C2×D53#13512yes—
174C2×D53#13712yes—
175C4×C53—22no—
176C4×C53—21no—
177C4×C53—21no—
178C4×C53—41no—
179C4×C53—41no—
180C4×C53C22×D411yescharacteristic
181C4×C53C2×#4111yescharacteristic
182Dic53—22no—
183Dic53—21no—
184Dic53—21no—
185Dic53—41no—
186Dic53—41no—
187Dic53#12112yes—
188C2×#464—531nomaximal, Sylow
189C2×C53—81no—
190C2×C53C2×#12111yescharacteristic
191C2×C53C2×#13511yescharacteristic
192C2×C53C2×#13711yescharacteristic
193D53—81no—
194D53#46414yesdirect product factor
195C22×Q16—531no—
196C22×SD16—531no—
197C2×#124—531no—
198C2×C4×Q8—531no—
199#464—531no—
200#464—531no—
201#464—531no—
202#464—531no—
203#464—531no—
204#464—531no—
205#464—531no—
206#464D5311yescharacteristic, direct product factor
207C2×C4⋊C8—531no—
208C2×#103—531no—
209C2×#102—531no—
210C53C2×#46411yescharacteristic, complemented, Sylow
211C22×Q8—531no—
212C22×Q8—531no—
213C22×D4—531no—
214C2×Q16—531no—
215C2×Q16—531no—
216C2×Q16—531no—
217C2×Q16—1064no—
218C2×Q16C2×D5311yescharacteristic, complemented
219C2×SD16—531no—
220C2×SD16—531no—
221C2×SD16—531no—
222C2×SD16—1064no—
223C2×SD16C2×D5311yescharacteristic
224C22×C8—531no—
225C22×C8—531no—
226#124—531no—
227#124—531no—
228#124—531no—
229#124—1061no—
230#124—1061no—
231#124C2×D5311yescharacteristic
232C4×Q8—531no—
233C4×Q8—531no—
234C4×Q8—531no—
235C4×Q8—1061no—
236C4×Q8—1061no—
237C4×Q8C2×D5311yescharacteristic, complemented
238C2×C4⋊C4—531no—
239C2×C4⋊C4—1061no—
240C2×C22⋊C4—1061no—
241C2×C22⋊C4—1061no—
242C2×C42—531no—
243C2×C42—1061no—
244C4⋊C8—531no—
245C4⋊C8—531no—
246C4⋊C8—531no—
247C4⋊C8C2×D5311yescharacteristic, complemented
248#103—531no—
249#103—531no—
250#103—531no—
251#103C2×D5311yescharacteristic, complemented
252#102—531no—
253#102—531no—
254#102—531no—
255#102C2×D5311yescharacteristic
256C24—1061no—
257C2×Q8—534no—
258C2×Q8—531no—
259C2×Q8—531no—
260C2×Q8—1061no—
261C2×Q8—1061no—
262C2×Q8—1062no—
263C2×Q8—1062no—
264C2×Q8—1062no—
265C2×Q8C22×D5311yescharacteristic
266C2×Q8C22×D5311yescharacteristic
267C2×D4—531no—
268C2×D4—1062no—
269C2×D4—1062no—
270C2×D4—1061no—
271C2×D4C22×D5311yescharacteristic
272C22×C4—531no—
273C22×C4—531no—
274C22×C4—531no—
275C22×C4—1061no—
276C22×C4—1061no—
277C22×C4—1061no—
278Q16—22no—
279Q16—1062no—
280Q16—1062no—
281Q16—1062no—
282SD16—22no—
283SD16—1062no—
284SD16—1062no—
285SD16—1062no—
286C2×C8—531no—
287C2×C8—531no—
288C2×C8—1062no—
289C2×C8—1062no—
290C2×C8C22×D5311yescharacteristic
291C2×C8C22×D5311yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—531no—
294C4⋊C4—1061no—
295C4⋊C4—1061no—
296C4⋊C4—1061no—
297C4⋊C4—1061no—
298C4⋊C4C22×D5311yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1061no—
302C22⋊C4—1061no—
303C22⋊C4—1061no—
304C22⋊C4—1061no—
305C22⋊C4—1061no—
306C22⋊C4—1061no—
307C42—21no—
308C42—531no—
309C42—531no—
310C42—531no—
311C42—1061no—
312C42—1061no—
313C42—1061no—
314C42C22×D5311yescharacteristic
315C23—21no—
316C23—531no—
317C23—1061no—
318C23—2122no—
319C23—2122no—
320C23—2122no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—532no—
325Q8—1064no—
326Q8—1061no—
327Q8—1061no—
328Q8—1061no—
329Q8—2122no—
330Q8D4×D5312yes—
331D4—21no—
332D4—21no—
333D4—1061no—
334D4—1061no—
335D4—2122no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—531no—
340C2×C4—532no—
341C2×C4—532no—
342C2×C4—531no—
343C2×C4—531no—
344C2×C4—1062no—
345C2×C4—1062no—
346C2×C4—1064no—
347C2×C4—1061no—
348C2×C4—1061no—
349C2×C4—1061no—
350C2×C4—2122no—
351C2×C4—2122no—
352C2×C4D4×D5311yescharacteristic
353C2×C4D4×D5311yescharacteristic
354C2×C4C23×D5311yescharacteristic
355C8—21no—
356C8—21no—
357C8—1061no—
358C8—1061no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—532no—
363C22—532no—
364C22—532no—
365C22—4244no—
366C22—2121no—
367C22—2121no—
368C22—2121no—
369C22C2×D4×D5311yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—532no—
376C4—1062no—
377C4—1061no—
378C4—1061no—
379C4—2121no—
380C4—2121no—
381C4C2×D4×D5311yescharacteristic
382C4#41×D5311yescharacteristic
383C2—81no—
384C2—534no—
385C2—4241no—
386C2#121×D5311yescharacteristic
387C2#135×D5311yescharacteristic
388C2#137×D5311yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC2×C4×C53C24
FrattiniC2×C4C23×D53
FittingC53×#464C2
socleC22×C53C22×D4
hypercenter#464D53
hypocenterC53C2×#464
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D53C2semidirect
4. C4×Q8×D53C2semidirect
5. #16810848C2semidirect
6. #16810847C2semidirect
7. #16810846C2semidirect
8. #16810845C2semidirect
9. #16810844C2semidirect
10. #16810843C2semidirect
11. #16810842C2semidirect
12. C4⋊C8×D53C2semidirect
13. #103×D53C2semidirect
15. C53×#464C2semidirect
19. C2×Dic212C22semidirect
20. C2×#11719925C22semidirect
21. C2×#11719925C22semidirect
34. Q8×Dic53C22semidirect
36. C4×Dic106C22semidirect
38. #13133182C22semidirect
45. C4⋊#88322C22semidirect
46. #13133146C22semidirect
47. #13133146C22semidirect
48. #13133142C22semidirect
49. #13133141C22semidirect
50. #13133140C22semidirect
54. C2×Q16×C53C22semidirect
57. C4×Q8×C53C22semidirect
58. C4⋊C8×C53C22semidirect
59. #103×C53C22semidirect
194. D53#464direct (N × H)
206. #464D53direct (N × H)
210. C53C2×#464semidirect
218. C2×Q16C2×D53semidirect
237. C4×Q8C2×D53semidirect
247. C4⋊C8C2×D53semidirect
251. #103C2×D53semidirect