Finite Group Databasebeta

← #20283540

Subgroups — #20283540

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×#13133241C211yesmaximal, characteristic
2#16811102C211yesmaximal, characteristic, complemented
3#16811095C211yesmaximal, characteristic, complemented
4#16810735C211yesmaximal, characteristic, complemented
5#16810733C211yesmaximal, characteristic, complemented
6#16810723C211yesmaximal, characteristic, complemented
7#16810722C211yesmaximal, characteristic, complemented
8#16810714C211yesmaximal, characteristic, complemented
9C4×#11719913C211yesmaximal, characteristic, complemented
10#16810703C211yesmaximal, characteristic, complemented
11#16810664C211yesmaximal, characteristic, complemented
12#16810616C211yesmaximal, characteristic, complemented
13#102×D53C211yesmaximal, characteristic, complemented
14#16810577C211yesmaximal, characteristic, complemented
15C4×D8×C53C211yesmaximal, characteristic, complemented
16C2×#11719947C2211yescharacteristic
17C2×D4×D53C2211yescharacteristic
18#13133241C418yescomplemented
19C2×#11719913C2211yescharacteristic
20C2×#11719923C2211yescharacteristic
21C2×#11719922C2211yescharacteristic
22C2×#11719912C2211yescharacteristic
23C2×C8×D53C2211yescharacteristic
24C4×Dic106C2211yescharacteristic, complemented
25#13133182C2211yescharacteristic, complemented
26C4×D212C2211yescharacteristic
27D4×Dic53C2211yescharacteristic
28D4×Dic53C2211yescharacteristic, complemented
29#13133179C2211yescharacteristic
30C4×C22⋊D53—21no—
31C4×C22⋊D53—21no—
32#13133177—21no—
33#13133177—21no—
34#13133175C2211yescharacteristic
35#13133174C2211yescharacteristic
36#13133173—21no—
37C2×#11719919—21no—
38C4⋊C4×D53C2211yescharacteristic
39C2×#11719921—21no—
40C22⋊C4×D53—21no—
41#13133150C2211yescharacteristic, complemented
42#13133149C2211yescharacteristic, complemented
43#13133148C2211yescharacteristic, complemented
44#13133142C2211yescharacteristic, complemented
45#13133140C2211yescharacteristic, complemented
46#13133139C2211yescharacteristic
47#13133138C2211yescharacteristic
48#13133138C2211yescharacteristic, complemented
49#13133137C2211yescharacteristic
50#13133128C2211yescharacteristic, complemented
51#13133127C2211yescharacteristic, complemented
52C8×Dic53C2211yescharacteristic, complemented
53C2×D8×C53C2211yescharacteristic
54C4×D4×C53C2211yescharacteristic
55C4×D4×C53C2211yescharacteristic, complemented
56#107×C53C2211yescharacteristic, complemented
57#102×C53C2211yescharacteristic
58#102×C53C2211yescharacteristic, complemented
59C4×C8×C53C2211yescharacteristic, complemented
60C23×D53—21no—
61C2×D4×C53C2311yescharacteristic
62C2×D4×C53C2311yescharacteristic
63C22×C4×C53—21no—
64C22×C4×C53—21no—
65C2×C22⋊D53—21no—
66C2×C22⋊D53—21no—
67C22×Dic53—21no—
68C22×Dic53—21no—
69C22×Dic53—21no—
70#11719947—22no—
71#11719947C2×C414yescomplemented
72D4×D53—22no—
73D4×D53C2×C414yescomplemented
74C2×D212C2311yescharacteristic
75C2×C4×D53—21no—
76C2×C4×D53—21no—
77C2×C4×D53—21no—
78C2×C4×D53C2311yescharacteristic
79C2×Dic106C2311yescharacteristic
80D8×C53C2×C414yescomplemented
81C2×C8×C53C2311yescharacteristic
82C2×C8×C53C2311yescharacteristic
83C4⋊C4×C53C2311yescharacteristic
84C4⋊C4×C53C2311yescharacteristic
85C22⋊C4×C53—21no—
86C22⋊C4×C53—21no—
87C42×C53C2311yescharacteristic
88C22⋊Dic53—21no—
89C22⋊Dic53—21no—
90#11719923C2×C414yescomplemented
91#11719922C2×C414yescomplemented
92#11719921—21no—
93#11719921—21no—
94#11719921—21no—
95#11719921D411yescharacteristic
96#11719921D411yescharacteristic
97C4⋊Dic53C2311yescharacteristic
98C4⋊Dic53C2311yescharacteristic
99#11719919—21no—
100#11719919—21no—
101#11719919—21no—
102#11719919D411yescharacteristic
103#11719919D411yescharacteristic
104C4×Dic53—21no—
105C4×Dic53—21no—
106C4×Dic53—21no—
107C4×Dic53C2311yescharacteristic
108C2×#88322C2311yescharacteristic
109C2×#88322C2311yescharacteristic
110#11719913C2×C414yescomplemented
111#11719912C2×C414yescomplemented
112C8×D53—22no—
113C23×C53—21no—
114C23×C53—21no—
115C22×D53—21no—
116C22×D53—24no—
117C22×D53—81no—
118C22×D53—81no—
119C22×D53C2×D411yescharacteristic
120D4×C53—21no—
121D4×C53—21no—
122D4×C53C22×C412yes—
123D4×C53C22×C412yes—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—81no—
127C2×C4×C53—81no—
128C2×C4×C53C2×D411yescharacteristic
129C2×C4×C53C2×D411yescharacteristic
130C2×C4×C53C2411yescharacteristic
131C22⋊D53—24no—
132C22⋊D53—24no—
133C2×Dic53—21no—
134C2×Dic53—24no—
135C2×Dic53—21no—
136C2×Dic53—21no—
137C2×Dic53—81no—
138C2×Dic53—81no—
139C2×Dic53C2×D411yescharacteristic
140C2×Dic53C2×D411yescharacteristic
141C2×Dic53C2×D411yescharacteristic
142D212—21no—
143D212C22×C412yes—
144C4×D53—81no—
145C4×D53—81no—
146C4×D53—81no—
147C4×D53C22×C412yes—
148C4×D53#4112yes—
149Dic106—21no—
150Dic106C22×C412yes—
151C8×C53—21no—
152C8×C53C22×C412yes—
153#88322—21no—
154#88322C22×C412yes—
155C22×C53—22no—
156C22×C53—22no—
157C22×C53—41no—
158C22×C53—41no—
159C22×C53—41no—
160C22×C53—41no—
161C22×C53C22×D411yescharacteristic
162C2×D53—21no—
163C2×D53—21no—
164C2×D53—22no—
165C2×D53—41no—
166C2×D53—41no—
167C2×D53—84no—
168C2×D53C4×D412yes—
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—
181#2946—531nomaximal, Sylow
182C2×C53—42no—
183C2×C53—42no—
184C2×C53C2×C4×D411yescharacteristic
185C2×C53#57611yescharacteristic
186C2×C53#57711yescharacteristic
187D53—22no—
188D53—42no—
189C2×AGL(1,ℤ/8)—531no—
190#520—531no—
191#518—531no—
192#442—531no—
193#442—531no—
194#440—531no—
195#440—531no—
196C4×SD16—531no—
197C4×SD16—531no—
198C4×D8—531no—
199C4×D8D5311yescharacteristic, complemented
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×SD16—531no—
210C2×D8—531no—
211C2×D8C2×D5311yescharacteristic
212C2×M16—531no—
213C22×C8—531no—
214C4×Q8—531no—
215C4×Q8—531no—
216C4×D4—531no—
217C4×D4—531no—
218C4×D4—531no—
219C4×D4—531no—
220C4×D4—1061no—
221C4×D4—1061no—
222C4×D4—1061no—
223C4×D4—1061no—
224C4×D4C2×D5311yescharacteristic
225C4×D4C2×D5311yescharacteristic, complemented
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#103—531no—
239#102—531no—
240#102—531no—
241#102—531no—
242#102—531no—
243#102C2×D5311yescharacteristic
244#102C2×D5311yescharacteristic, complemented
245#97—531no—
246#97—531no—
247C4×C8—531no—
248C4×C8C2×D5311yescharacteristic, complemented
249C24—1061no—
250#41—534no—
251#41—1062no—
252C2×Q8—531no—
253C2×D4—534no—
254C2×D4—531no—
255C2×D4—1062no—
256C2×D4—1061no—
257C2×D4—1061no—
258C2×D4C22×D5311yescharacteristic
259C2×D4C22×D5311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—531no—
263C22×C4—1061no—
264C22×C4—1061no—
265C22×C4—1061no—
266C22×C4—1061no—
267C22×C4—1061no—
268C22×C4—1061no—
269SD16—534no—
270SD16—534no—
271D8—534no—
272D8C4×D5314yescomplemented
273M16—534no—
274C2×C8—531no—
275C2×C8—531no—
276C2×C8—1062no—
277C2×C8C22×D5311yescharacteristic
278C2×C8C22×D5311yescharacteristic
279C4⋊C4—531no—
280C4⋊C4—531no—
281C4⋊C4—531no—
282C4⋊C4—531no—
283C4⋊C4—1061no—
284C4⋊C4—1061no—
285C4⋊C4—1061no—
286C4⋊C4C22×D5311yescharacteristic
287C4⋊C4C22×D5311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—531no—
291C22⋊C4—531no—
292C22⋊C4—1061no—
293C22⋊C4—1061no—
294C22⋊C4—1061no—
295C22⋊C4—1061no—
296C22⋊C4—1061no—
297C42—531no—
298C42—1061no—
299C42—1061no—
300C42—1061no—
301C42C22×D5311yescharacteristic
302C23—21no—
303C23—21no—
304C23—531no—
305C23—1064no—
306C23—1061no—
307C23—4241no—
308C23—4241no—
309Q8—532no—
310Q8—1061no—
311D4—21no—
312D4—21no—
313D4—532no—
314D4—1064no—
315D4—1064no—
316D4—1061no—
317D4C2×C4×D5312yes—
318D4C2×C4×D5312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
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—1061no—
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—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—532no—
351C22—1061no—
352C22—1061no—
353C22—1062no—
354C22—4244no—
355C22—2121no—
356C22—2121no—
357C22C2×D4×D5311yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—532no—
363C4—1062no—
364C4—1061no—
365C4—1061no—
366C4—2121no—
367C4—2121no—
368C4C22×C4×D5311yescharacteristic
369C4#41×D5311yescharacteristic
370C2—42no—
371C2—42no—
372C2—1062no—
373C2—2122no—
374C2C4×D4×D5311yescharacteristic
375C2#1681142411yescharacteristic
376C2#1681143011yescharacteristic
subgroupG/H
centerC22C2×D4×D53
commutatorC4×C53C23×C4
FrattiniC2×C4C23×D53
FittingC4×D8×C53C2
socleC22×C53C22×D4
hypercenterC4×D8D53
hypocenterC53#2946
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. #16811102C2semidirect
3. #16811095C2semidirect
4. #16810735C2semidirect
5. #16810733C2semidirect
6. #16810723C2semidirect
7. #16810722C2semidirect
8. #16810714C2semidirect
9. C4×#11719913C2semidirect
10. #16810703C2semidirect
11. #16810664C2semidirect
12. #16810616C2semidirect
13. #102×D53C2semidirect
14. #16810577C2semidirect
15. C4×D8×C53C2semidirect
18. #13133241C4semidirect
24. C4×Dic106C22semidirect
25. #13133182C22semidirect
28. D4×Dic53C22semidirect
41. #13133150C22semidirect
42. #13133149C22semidirect
43. #13133148C22semidirect
44. #13133142C22semidirect
45. #13133140C22semidirect
48. #13133138C22semidirect
50. #13133128C22semidirect
51. #13133127C22semidirect
52. C8×Dic53C22semidirect
55. C4×D4×C53C22semidirect
56. #107×C53C22semidirect
58. #102×C53C22semidirect
59. C4×C8×C53C22semidirect
71. #11719947C2×C4semidirect
73. D4×D53C2×C4semidirect
80. D8×C53C2×C4semidirect
90. #11719923C2×C4semidirect
91. #11719922C2×C4semidirect
110. #11719913C2×C4semidirect
111. #11719912C2×C4semidirect
199. C4×D8D53semidirect
204. C53#2946semidirect
225. C4×D4C2×D53semidirect
234. #107C2×D53semidirect
244. #102C2×D53semidirect
248. C4×C8C2×D53semidirect
272. D8C4×D53semidirect