Finite Group Databasebeta

← #20283546

Subgroups — #20283546

Order 6784.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13133244C211yesmaximal, characteristic
2#16811105C211yesmaximal, characteristic, complemented
3#16811095C211yesmaximal, characteristic, complemented
4#16810736C211yesmaximal, characteristic, complemented
5#16810732C211yesmaximal, characteristic, complemented
6#16810726C211yesmaximal, characteristic, complemented
7SD16×Dic53C211yesmaximal, characteristic, complemented
8C4×#11719924C211yesmaximal, characteristic, complemented
9#16810705C211yesmaximal, characteristic, complemented
10C4×#11719922C211yesmaximal, characteristic, complemented
11#16810664C211yesmaximal, characteristic, complemented
12#16810618C211yesmaximal, characteristic, complemented
13#102×D53C211yesmaximal, characteristic, complemented
14#16810580C211yesmaximal, characteristic, complemented
15C53×#440C211yesmaximal, characteristic, complemented
16C2×#11719949C2211yescharacteristic
17C2×D4×D53C2211yescharacteristic
18#13133244C418yescomplemented
19C2×#11719924C2211yescharacteristic
20C2×D424C2211yescharacteristic
21C2×#11719922C2211yescharacteristic
22C2×#11719912C2211yescharacteristic
23C2×C8×D53C2211yescharacteristic
24Q8×Dic53C2211yescharacteristic, complemented
25C4×D212—21no—
26C4×D212C2211yescharacteristic
27C4×D212C2211yescharacteristic, complemented
28D4×Dic53C2211yescharacteristic
29#13133179—21no—
30#13133179C2211yescharacteristic
31#13133179C2211yescharacteristic, complemented
32C4×C22⋊D53—21no—
33#13133177—21no—
34#13133175C2211yescharacteristic
35#13133174—21no—
36#13133174C2211yescharacteristic
37C4⋊C4×D53—21no—
38C4⋊C4×D53C2211yescharacteristic
39C2×#11719921—21no—
40C22⋊C4×D53—21no—
41#13133150C2211yescharacteristic, complemented
42#13133149C2211yescharacteristic, complemented
43#13133148C2211yescharacteristic, complemented
44#13133141C2211yescharacteristic, complemented
45#13133139C2211yescharacteristic
46#13133139C2211yescharacteristic, complemented
47#13133138C2211yescharacteristic
48#13133137C2211yescharacteristic
49#13133137C2211yescharacteristic, complemented
50#13133127C2211yescharacteristic, complemented
51C4×#88322C2211yescharacteristic, complemented
52C8×Dic53C2211yescharacteristic, 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—
66#11719949—22no—
67#11719949C2×C414yescomplemented
68D4×D53—22no—
69D4×D53C2×C414yescomplemented
70C2×D212—21no—
71C2×D212C2311yescharacteristic
72C2×D212C2311yescharacteristic
73C2×C4×D53—21no—
74C2×C4×D53—21no—
75C2×C4×D53—21no—
76C2×C4×D53—21no—
77C2×C4×D53—21no—
78C2×C4×D53—21no—
79C2×C4×D53C2311yescharacteristic
80SD16×C53C2×C414yescomplemented
81C2×C8×C53C2311yescharacteristic
82C2×C8×C53C2311yescharacteristic
83C4⋊C4×C53—21no—
84C4⋊C4×C53C2311yescharacteristic
85C4⋊C4×C53C2311yescharacteristic
86C22⋊C4×C53—21no—
87C42×C53—21no—
88C42×C53C2311yescharacteristic
89C22⋊Dic53—21no—
90#11719924C2×C414yescomplemented
91#11719922C2×C414yescomplemented
92#11719921—21no—
93#11719921—21no—
94#11719921—21no—
95#11719921—21no—
96#11719921—21no—
97#11719921D411yescharacteristic
98#11719921D411yescharacteristic
99C4⋊Dic53—21no—
100C4⋊Dic53C2311yescharacteristic
101C4⋊Dic53C2311yescharacteristic
102#11719919—21no—
103#11719919D411yescharacteristic
104#11719919D411yescharacteristic
105C4×Dic53—21no—
106C4×Dic53—21no—
107C4×Dic53C2311yescharacteristic
108C2×#88322C2311yescharacteristic
109C2×#88322C2311yescharacteristic
110D424C2×C414yescomplemented
111#11719912C2×C414yescomplemented
112C8×D53—22no—
113C23×C53—21no—
114C22×D53—21no—
115C22×D53—21no—
116C22×D53—24no—
117C22×D53—81no—
118C22×D53—81no—
119C22×D53C2×D411yescharacteristic
120Q8×C53—21no—
121Q8×C53C22×C412yes—
122D4×C53—21no—
123D4×C53C22×C412yes—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53—81no—
128C2×C4×C53C2×D411yescharacteristic
129C2×C4×C53C2×D411yescharacteristic
130C2×C4×C53C2411yescharacteristic
131C22⋊D53—24no—
132C2×Dic53—21no—
133C2×Dic53—21no—
134C2×Dic53—81no—
135C2×Dic53C2×D411yescharacteristic
136C2×Dic53C2×D411yescharacteristic
137C2×Dic53C2×D411yescharacteristic
138D212—24no—
139D212—21no—
140D212—21no—
141D212C22×C412yes—
142D212C22×C412yes—
143C4×D53—24no—
144C4×D53—81no—
145C4×D53—81no—
146C4×D53—81no—
147C4×D53—81no—
148C4×D53—81no—
149C4×D53C22×C412yes—
150C4×D53#4112yes—
151C8×C53—21no—
152C8×C53C22×C412yes—
153#88322—21no—
154#88322C22×C412yes—
155C22×C53—22no—
156C22×C53—41no—
157C22×C53—41no—
158C22×C53C22×D411yescharacteristic
159C2×D53—21no—
160C2×D53—21no—
161C2×D53—22no—
162C2×D53—22no—
163C2×D53—41no—
164C2×D53—41no—
165C2×D53—41no—
166C2×D53—41no—
167C2×D53—84no—
168C2×D53C4×D412yes—
169C4×C53—22no—
170C4×C53—21no—
171C4×C53—21no—
172C4×C53—41no—
173C4×C53—41no—
174C4×C53C23×C411yescharacteristic
175C4×C53C2×#4111yescharacteristic
176Dic53—21no—
177Dic53—21no—
178Dic53—41no—
179Dic53—41no—
180Dic53C4×D412yes—
181#2946—531nomaximal, Sylow
182C2×C53—42no—
183C2×C53C2×C4×D411yescharacteristic
184C2×C53#57611yescharacteristic
185C2×C53#57711yescharacteristic
186D53—22no—
187D53—42no—
188D53—42no—
189C2×AGL(1,ℤ/8)—531no—
190#520—531no—
191#518—531no—
192#442—531no—
193#442—531no—
194#440—531no—
195#440D5311yescharacteristic, complemented
196C4×SD16—531no—
197C4×SD16—531no—
198C4×D8—531no—
199C4×D8—531no—
200#428—531no—
201#416—531no—
202C2×#102—531no—
203#405—531no—
204C53#294611yescharacteristic, complemented, Sylow
205C2×#41—531no—
206C22×D4—531no—
207AGL(1,ℤ/8)—538no—
208C2×SD16—531no—
209C2×SD16C2×D5311yescharacteristic
210C2×D8—531no—
211C2×D8—531no—
212C2×M16—531no—
213C22×C8—531no—
214C4×Q8—531no—
215C4×Q8C2×D5311yescharacteristic, complemented
216C4×D4—531no—
217C4×D4—531no—
218C4×D4—531no—
219C4×D4—531no—
220C4×D4—531no—
221C4×D4—1061no—
222C4×D4—1061no—
223C4×D4—1061no—
224C4×D4—1061no—
225C4×D4C2×D5311yescharacteristic
226#117—531no—
227#117—531no—
228#117—1061no—
229C2×C4⋊C4—531no—
230C2×C4⋊C4—1061no—
231C2×C22⋊C4—1061no—
232C2×C22⋊C4—1061no—
233#107—531no—
234#107C2×D5311yescharacteristic, complemented
235#106—531no—
236#106—531no—
237#103—531no—
238#103C2×D5311yescharacteristic, complemented
239#102—531no—
240#102—531no—
241#102—531no—
242#102—531no—
243#102—531no—
244#102C2×D5311yescharacteristic
245#97—531no—
246#97C2×D5311yescharacteristic, complemented
247C4×C8—531no—
248C4×C8—531no—
249C24—1061no—
250#41—534no—
251#41—1062no—
252C2×Q8C22×D5311yescharacteristic
253C2×D4—534no—
254C2×D4—531no—
255C2×D4—531no—
256C2×D4—1061no—
257C2×D4—1062no—
258C2×D4—1061no—
259C2×D4C22×D5311yescharacteristic
260C22×C4—21no—
261C22×C4—531no—
262C22×C4—1061no—
263C22×C4—1061no—
264C22×C4—1061no—
265C22×C4—1061no—
266C22×C4—1061no—
267C22×C4—1061no—
268C22×C4—1061no—
269SD16—534no—
270SD16C4×D5314yescomplemented
271D8—534no—
272D8—534no—
273M16—534no—
274C2×C8—531no—
275C2×C8—531no—
276C2×C8—1062no—
277C2×C8C22×D5311yescharacteristic
278C2×C8C22×D5311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—531no—
281C4⋊C4—531no—
282C4⋊C4—531no—
283C4⋊C4—531no—
284C4⋊C4—1061no—
285C4⋊C4—1061no—
286C4⋊C4C22×D5311yescharacteristic
287C4⋊C4C22×D5311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—531no—
290C22⋊C4—531no—
291C22⋊C4—1061no—
292C22⋊C4—1061no—
293C22⋊C4—1061no—
294C22⋊C4—1061no—
295C22⋊C4—1061no—
296C22⋊C4—1061no—
297C42—21no—
298C42—531no—
299C42—1061no—
300C42—1061no—
301C42C22×D5311yescharacteristic
302C23—21no—
303C23—531no—
304C23—1064no—
305C23—1061no—
306C23—1061no—
307C23—4241no—
308C23—4241no—
309Q8—21no—
310Q8C2×C4×D5312yes—
311D4—21no—
312D4—532no—
313D4—532no—
314D4—1064no—
315D4—1064no—
316D4—1061no—
317D4—1061no—
318D4C2×C4×D5312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—531no—
324C2×C4—532no—
325C2×C4—532no—
326C2×C4—531no—
327C2×C4—531no—
328C2×C4—1064no—
329C2×C4—1061no—
330C2×C4—1061no—
331C2×C4—4241no—
332C2×C4—4241no—
333C2×C4—4241no—
334C2×C4—4241no—
335C2×C4—4241no—
336C2×C4—4241no—
337C2×C4D4×D5311yescharacteristic
338C2×C4D4×D5311yescharacteristic
339C2×C4C23×D5311yescharacteristic
340C8—21no—
341C8—532no—
342C8—1061no—
343C8C2×C4×D5312yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—532no—
348C22—1061no—
349C22—1061no—
350C22—1062no—
351C22—1062no—
352C22—4244no—
353C22—2121no—
354C22—2121no—
355C22—2121no—
356C22—2121no—
357C22C2×D4×D5311yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—532no—
364C4—1061no—
365C4—1061no—
366C4—2121no—
367C4—2121no—
368C4C22×C4×D5311yescharacteristic
369C4#41×D5311yescharacteristic
370C2—42no—
371C2—1062no—
372C2—2122no—
373C2—2122no—
374C2C4×D4×D5311yescharacteristic
375C2#1681142711yescharacteristic
376C2#1681143211yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC4×C53C23×C4
FrattiniC2×C4C23×D53
FittingC53×#440C2
socleC22×C53C22×D4
hypercenter#440D53
hypocenterC53#2946
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. #16811105C2semidirect
3. #16811095C2semidirect
4. #16810736C2semidirect
5. #16810732C2semidirect
6. #16810726C2semidirect
7. SD16×Dic53C2semidirect
8. C4×#11719924C2semidirect
9. #16810705C2semidirect
10. C4×#11719922C2semidirect
11. #16810664C2semidirect
12. #16810618C2semidirect
13. #102×D53C2semidirect
14. #16810580C2semidirect
15. C53×#440C2semidirect
18. #13133244C4semidirect
24. Q8×Dic53C22semidirect
27. C4×D212C22semidirect
31. #13133179C22semidirect
41. #13133150C22semidirect
42. #13133149C22semidirect
43. #13133148C22semidirect
44. #13133141C22semidirect
46. #13133139C22semidirect
49. #13133137C22semidirect
50. #13133127C22semidirect
51. C4×#88322C22semidirect
52. C8×Dic53C22semidirect
54. C4×Q8×C53C22semidirect
56. #107×C53C22semidirect
57. #103×C53C22semidirect
59. #97×C53C22semidirect
67. #11719949C2×C4semidirect
69. D4×D53C2×C4semidirect
80. SD16×C53C2×C4semidirect
90. #11719924C2×C4semidirect
91. #11719922C2×C4semidirect
110. D424C2×C4semidirect
111. #11719912C2×C4semidirect
195. #440D53semidirect
204. C53#2946semidirect
215. C4×Q8C2×D53semidirect
234. #107C2×D53semidirect
238. #103C2×D53semidirect
246. #97C2×D53semidirect
270. SD16C4×D53semidirect