Finite Group Databasebeta

← #20283569

Subgroups — #20283569

Order 6784.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D53C211yesmaximal, characteristic
2#16811099C211yesmaximal, characteristic, complemented
3#16811095C211yesmaximal, characteristic
4#16810726C211yesmaximal, characteristic, complemented
5#16810723C211yesmaximal, characteristic, complemented
6#16810721C211yesmaximal, characteristic, complemented
7#16810720C211yesmaximal, characteristic, complemented
8C4×#11719913C211yesmaximal, characteristic, complemented
9SD16×Dic53C211yesmaximal, characteristic, complemented
10#16810710C211yesmaximal, characteristic, complemented
11#16810658C211yesmaximal, characteristic, complemented
12#16810630C211yesmaximal, characteristic, complemented
13#16810626C211yesmaximal, characteristic
14#16810577C211yesmaximal, characteristic, complemented
15C4×SD16×C53C211yesmaximal, characteristic, complemented
16C2×Q8×D53C2211yescharacteristic
17C2×D4×D53C2211yescharacteristic
18C2×#11719913C2211yescharacteristic
19C2×#11719923C2211yescharacteristic
20C2×#11719924C2211yescharacteristic
21SD16×D53C418yescomplemented
22C2×#11719912C2211yescharacteristic
23C2×C8×D53C2211yescharacteristic
24Q8×Dic53C2211yescharacteristic, complemented
25C4×Dic106—21no—
26C4×Dic106C2211yescharacteristic, complemented
27#13133182—21no—
28#13133182C2211yescharacteristic, complemented
29C4×D212C2211yescharacteristic
30D4×Dic53C2211yescharacteristic
31#13133179C2211yescharacteristic
32C4×C22⋊D53—21no—
33#13133177—21no—
34#13133175—21no—
35#13133175C2211yescharacteristic
36#13133175C2211yescharacteristic
37#13133174—21no—
38#13133174C2211yescharacteristic
39C2×#11719921—21no—
40C22⋊C4×D53—21no—
41#13133150C2211yescharacteristic, complemented
42#13133150C2211yescharacteristic, complemented
43#13133149C2211yescharacteristic, complemented
44#13133142C2211yescharacteristic, complemented
45#13133141C2211yescharacteristic, complemented
46#13133140C2211yescharacteristic, complemented
47#13133139C2211yescharacteristic
48#13133138C2211yescharacteristic
49#13133137C2211yescharacteristic
50#13133128C2211yescharacteristic, complemented
51#13133127C2211yescharacteristic, complemented
52C8×Dic53C2211yescharacteristic, complemented
53C2×SD16×C53C2211yescharacteristic
54C4×Q8×C53C2211yescharacteristic, complemented
55C4×D4×C53C2211yescharacteristic
56#106×C53C2211yescharacteristic, complemented
57#103×C53C2211yescharacteristic, complemented
58#102×C53C2211yescharacteristic
59C4×C8×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×D53C2311yescharacteristic
75C2×Dic106—21no—
76C2×Dic106C2311yescharacteristic
77SD16×C53C2×C414yescomplemented
78C2×C8×C53C2311yescharacteristic
79C2×C8×C53C2311yescharacteristic
80C4⋊C4×C53—21no—
81C4⋊C4×C53C2311yescharacteristic
82C4⋊C4×C53C2311yescharacteristic
83C22⋊C4×C53—21no—
84C42×C53—21no—
85C42×C53C2311yescharacteristic
86C22⋊Dic53—21no—
87#11719924C2×C414yescomplemented
88#11719923C2×C414yescomplemented
89#11719921—21no—
90#11719921—21no—
91#11719921—21no—
92#11719921—21no—
93#11719921D411yescharacteristic
94#11719921D411yescharacteristic
95C4⋊Dic53—21no—
96C4⋊Dic53C2311yescharacteristic
97C4⋊Dic53C2311yescharacteristic
98#11719919—21no—
99#11719919—21no—
100#11719919D411yescharacteristic
101#11719919D411yescharacteristic
102C4×Dic53—21no—
103C4×Dic53—21no—
104C4×Dic53—21no—
105C4×Dic53—21no—
106C4×Dic53—21no—
107C4×Dic53C2311yescharacteristic
108C2×#88322C2311yescharacteristic
109C2×#88322C2311yescharacteristic
110#11719913C2×C414yescomplemented
111#11719912—22no—
112C8×D53C2×C414yescomplemented
113C23×C53—21no—
114C22×D53—21no—
115C22×D53—24no—
116C22×D53—81no—
117C22×D53—81no—
118C22×D53C2×D411yescharacteristic
119Q8×C53—21no—
120Q8×C53C22×C412yes—
121D4×C53—21no—
122D4×C53C22×C412yes—
123C2×C4×C53—21no—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—81no—
127C2×C4×C53C2×D411yescharacteristic
128C2×C4×C53C2×D411yescharacteristic
129C2×C4×C53C2411yescharacteristic
130C22⋊D53—24no—
131C2×Dic53—21no—
132C2×Dic53—21no—
133C2×Dic53—21no—
134C2×Dic53—81no—
135C2×Dic53C2×D411yescharacteristic
136C2×Dic53C2×D411yescharacteristic
137C2×Dic53C2×D411yescharacteristic
138D212—21no—
139D212C22×C412yes—
140C4×D53—24no—
141C4×D53—81no—
142C4×D53—81no—
143C4×D53C22×C412yes—
144C4×D53#4112yes—
145Dic106—21no—
146Dic106—24no—
147Dic106C22×C412yes—
148C8×C53—21no—
149C8×C53C22×C412yes—
150#88322—21no—
151#88322C22×C412yes—
152C22×C53—22no—
153C22×C53—41no—
154C22×C53—41no—
155C22×C53C22×D411yescharacteristic
156C2×D53—21no—
157C2×D53—21no—
158C2×D53—22no—
159C2×D53—41no—
160C2×D53—41no—
161C2×D53—84no—
162C2×D53C4×D412yes—
163C4×C53—22no—
164C4×C53—21no—
165C4×C53—21no—
166C4×C53—41no—
167C4×C53—41no—
168C4×C53C23×C411yescharacteristic
169C4×C53C2×#4111yescharacteristic
170Dic53—22no—
171Dic53—21no—
172Dic53—21no—
173Dic53—41no—
174Dic53—41no—
175Dic53C4×D412yes—
176#2949—531nomaximal, Sylow
177C2×C53—42no—
178C2×C53C2×C4×D411yescharacteristic
179C2×C53#57711yescharacteristic
180C2×C53#57711yescharacteristic
181D53—22no—
182D53—42no—
183C22×SD16—531no—
184#519—531no—
185#518—531no—
186#440—531no—
187#440—531no—
188#440—531no—
189#440—531no—
190C4×SD16—531no—
191C4×SD16—531no—
192C4×SD16—531no—
193C4×SD16D5311yescharacteristic, complemented
194#427—531no—
195#419—531no—
196#418—531no—
197#405—531no—
198C53#294911yescharacteristic, complemented, Sylow
199C22×Q8—531no—
200C22×D4—531no—
201C2×SD16—531no—
202C2×SD16—531no—
203C2×SD16—538no—
204C2×SD16—531no—
205C2×SD16C2×D5311yescharacteristic
206C2×M16—531no—
207C22×C8—531no—
208C4×Q8—531no—
209C4×Q8—531no—
210C4×Q8—531no—
211C4×Q8—1061no—
212C4×Q8—1061no—
213C4×Q8C2×D5311yescharacteristic, complemented
214C4×D4—531no—
215C4×D4—531no—
216C4×D4—531no—
217C4×D4—1061no—
218C4×D4—1061no—
219C4×D4C2×D5311yescharacteristic
220#117—531no—
221#117—531no—
222#117—531no—
223#117—1061no—
224#117—1061no—
225C2×C22⋊C4—1061no—
226C2×C22⋊C4—1061no—
227#107—531no—
228#107—531no—
229#106—531no—
230#106C2×D5311yescharacteristic, complemented
231#103—531no—
232#103—531no—
233#103—531no—
234#103C2×D5311yescharacteristic, complemented
235#102—531no—
236#102—531no—
237#102—531no—
238#102C2×D5311yescharacteristic
239#97—531no—
240#97—531no—
241C4×C8—531no—
242C4×C8C2×D5311yescharacteristic, complemented
243C24—1061no—
244C2×Q8—534no—
245C2×Q8—531no—
246C2×Q8—1061no—
247C2×Q8—1062no—
248C2×Q8C22×D5311yescharacteristic
249C2×D4—534no—
250C2×D4—531no—
251C2×D4—1062no—
252C2×D4—1061no—
253C2×D4C22×D5311yescharacteristic
254C22×C4—21no—
255C22×C4—531no—
256C22×C4—1061no—
257C22×C4—1061no—
258C22×C4—1061no—
259C22×C4—1061no—
260SD16—534no—
261SD16—534no—
262SD16—534no—
263SD16C4×D5314yescomplemented
264M16—1062no—
265C2×C8—531no—
266C2×C8—534no—
267C2×C8—531no—
268C2×C8C22×D5311yescharacteristic
269C2×C8C22×D5311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—531no—
272C4⋊C4—531no—
273C4⋊C4—531no—
274C4⋊C4—531no—
275C4⋊C4—1061no—
276C4⋊C4—1061no—
277C4⋊C4—1061no—
278C4⋊C4C22×D5311yescharacteristic
279C4⋊C4C22×D5311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—531no—
282C22⋊C4—531no—
283C22⋊C4—1061no—
284C22⋊C4—1061no—
285C22⋊C4—1061no—
286C22⋊C4—1061no—
287C22⋊C4—1061no—
288C42—21no—
289C42—531no—
290C42—1061no—
291C42—1061no—
292C42—1061no—
293C42—1061no—
294C42—1061no—
295C42C22×D5311yescharacteristic
296C23—21no—
297C23—531no—
298C23—1064no—
299C23—1061no—
300C23—4241no—
301C23—4241no—
302Q8—21no—
303Q8—532no—
304Q8—1064no—
305Q8—1061no—
306Q8C2×C4×D5312yes—
307D4—21no—
308D4—532no—
309D4—1064no—
310D4—1061no—
311D4C2×C4×D5312yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—531no—
317C2×C4—532no—
318C2×C4—532no—
319C2×C4—531no—
320C2×C4—531no—
321C2×C4—1064no—
322C2×C4—1061no—
323C2×C4—1061no—
324C2×C4—1061no—
325C2×C4—4241no—
326C2×C4—4241no—
327C2×C4—4241no—
328C2×C4D4×D5311yescharacteristic
329C2×C4D4×D5311yescharacteristic
330C2×C4C23×D5311yescharacteristic
331C8—21no—
332C8—532no—
333C8—1061no—
334C8C2×C4×D5312yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—532no—
339C22—1061no—
340C22—1061no—
341C22—1062no—
342C22—4244no—
343C22—2121no—
344C22—2121no—
345C22C2×D4×D5311yescharacteristic
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—532no—
352C4—1062no—
353C4—1061no—
354C4—1061no—
355C4—2121no—
356C4—2121no—
357C4C22×C4×D5311yescharacteristic
358C4#41×D5311yescharacteristic
359C2—42no—
360C2—1062no—
361C2—2122no—
362C2C4×D4×D5311yescharacteristic
363C2#1681142911yescharacteristic
364C2#1681143011yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC4×C53C23×C4
FrattiniC2×C4C23×D53
FittingC4×SD16×C53C2
socleC22×C53C22×D4
hypercenterC4×SD16D53
hypocenterC53#2949
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #16811099C2semidirect
4. #16810726C2semidirect
5. #16810723C2semidirect
6. #16810721C2semidirect
7. #16810720C2semidirect
8. C4×#11719913C2semidirect
9. SD16×Dic53C2semidirect
10. #16810710C2semidirect
11. #16810658C2semidirect
12. #16810630C2semidirect
14. #16810577C2semidirect
15. C4×SD16×C53C2semidirect
21. SD16×D53C4semidirect
24. Q8×Dic53C22semidirect
26. C4×Dic106C22semidirect
28. #13133182C22semidirect
41. #13133150C22semidirect
42. #13133150C22semidirect
43. #13133149C22semidirect
44. #13133142C22semidirect
45. #13133141C22semidirect
46. #13133140C22semidirect
50. #13133128C22semidirect
51. #13133127C22semidirect
52. C8×Dic53C22semidirect
54. C4×Q8×C53C22semidirect
56. #106×C53C22semidirect
57. #103×C53C22semidirect
59. C4×C8×C53C22semidirect
67. Q8×D53C2×C4semidirect
77. SD16×C53C2×C4semidirect
87. #11719924C2×C4semidirect
88. #11719923C2×C4semidirect
110. #11719913C2×C4semidirect
112. C8×D53C2×C4semidirect
193. C4×SD16D53semidirect
198. C53#2949semidirect
213. C4×Q8C2×D53semidirect
230. #106C2×D53semidirect
234. #103C2×D53semidirect
242. C4×C8C2×D53semidirect
263. SD16C4×D53semidirect