Finite Group Databasebeta

← C4×#13133241 #20283518

Subgroups — C4×#13133241 #20283518

Order 6784.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13133241C211yesmaximal, characteristic
2C4×#11719947C211yesmaximal, characteristic, complemented
3C4×D4×D53C211yesmaximal, characteristic, complemented
4#16810735C211yesmaximal, characteristic, complemented
5#16810732C211yesmaximal, characteristic, complemented
6#16810722C211yesmaximal, characteristic, complemented
7#16810720C211yesmaximal, characteristic, complemented
8C4×#11719913C211yesmaximal, characteristic, complemented
9C4×#11719923C211yesmaximal, characteristic, complemented
10C4×#11719922C211yesmaximal, characteristic, complemented
11#16810664C211yesmaximal, characteristic, complemented
12#16810626C211yesmaximal, characteristic, complemented
13#16810621C211yesmaximal, characteristic, complemented
14C4×#11719912C211yesmaximal, characteristic, complemented
15C4×D8×C53C211yesmaximal, characteristic, complemented
16C2×#11719947C2211yescharacteristic
17C2×D4×D53C2211yescharacteristic
18C22×C4×D53—21no—
19#13133241C418yesdirect product factor
20C2×#11719913C2211yescharacteristic
21C2×#11719923C2211yescharacteristic
22C2×#11719922C2211yescharacteristic
23C2×#11719912C2211yescharacteristic
24C2×#11719912C2211yescharacteristic
25C4×Dic106C2211yescharacteristic, complemented
26#13133182C2211yescharacteristic, complemented
27C4×D212C2211yescharacteristic
28D4×Dic53C2211yescharacteristic
29D4×Dic53C2211yescharacteristic, complemented
30#13133179C2211yescharacteristic
31C4×C22⋊D53—21no—
32C4×C22⋊D53—21no—
33#13133177—21no—
34#13133177—21no—
35#13133175C2211yescharacteristic
36#13133173—21no—
37C4⋊C4×D53C2211yescharacteristic
38C22⋊C4×D53—21no—
39C2×C4×Dic53—21no—
40C42×D53C2211yescharacteristic
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#13133127C2211yescharacteristic, complemented
51#13133127C2211yescharacteristic, complemented
52C4×#88322C2211yescharacteristic, 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×D53—44no—
79C2×C4×D53D411yescharacteristic
80C2×C4×D53D411yescharacteristic
81C2×C4×D53C2311yescharacteristic
82C2×Dic106C2311yescharacteristic
83D8×C53C2×C414yescomplemented
84C2×C8×C53C2311yescharacteristic
85C2×C8×C53C2311yescharacteristic
86C4⋊C4×C53C2311yescharacteristic
87C4⋊C4×C53C2311yescharacteristic
88C22⋊C4×C53—21no—
89C22⋊C4×C53—21no—
90C42×C53C2311yescharacteristic
91C22⋊Dic53—21no—
92C22⋊Dic53—21no—
93#11719923C2×C414yescomplemented
94#11719922C2×C414yescomplemented
95#11719921—21no—
96#11719921—21no—
97#11719921—21no—
98C4⋊Dic53C2311yescharacteristic
99C4⋊Dic53C2311yescharacteristic
100#11719919—21no—
101#11719919—21no—
102#11719919—21no—
103C4×Dic53—21no—
104C4×Dic53—21no—
105C4×Dic53—21no—
106C4×Dic53D411yescharacteristic
107C4×Dic53D411yescharacteristic
108C4×Dic53C2311yescharacteristic
109C2×#88322C2311yescharacteristic
110C2×#88322C2311yescharacteristic
111#11719913C2×C414yescomplemented
112#11719912—22no—
113#11719912C2×C414yescomplemented
114C23×C53—21no—
115C23×C53—21no—
116C22×D53—21no—
117C22×D53—24no—
118C22×D53—42no—
119C22×D53—42no—
120C22×D53C2×D411yescharacteristic
121D4×C53—21no—
122D4×C53—21no—
123D4×C53C22×C412yes—
124D4×C53C22×C412yescomplemented
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53—42no—
128C2×C4×C53—42no—
129C2×C4×C53C2×D411yescharacteristic
130C2×C4×C53C2×D411yescharacteristic
131C2×C4×C53C2411yescharacteristic
132C22⋊D53—24no—
133C22⋊D53—24no—
134C2×Dic53—21no—
135C2×Dic53—24no—
136C2×Dic53—21no—
137C2×Dic53—21no—
138C2×Dic53—42no—
139C2×Dic53—42no—
140C2×Dic53C2×D411yescharacteristic
141C2×Dic53C2×D411yescharacteristic
142C2×Dic53C2×D411yescharacteristic
143D212—21no—
144D212C22×C412yes—
145C4×D53—22no—
146C4×D53—41no—
147C4×D53—42no—
148C4×D53—42no—
149C4×D53—42no—
150C4×D53C22×C412yes—
151C4×D53#4112yes—
152Dic106—21no—
153Dic106C22×C412yescomplemented
154C8×C53—21no—
155C8×C53C22×C412yescomplemented
156#88322—21no—
157#88322C22×C412yescomplemented
158C22×C53—22no—
159C22×C53—22no—
160C22×C53—41no—
161C22×C53—41no—
162C22×C53—41no—
163C22×C53—41no—
164C22×C53C22×D411yescharacteristic
165C2×D53—21no—
166C2×D53—21no—
167C2×D53—22no—
168C2×D53—48no—
169C2×D53—41no—
170C2×D53—41no—
171C2×D53C4×D412yes—
172C4×C53—21no—
173C4×C53—41no—
174C4×C53—41no—
175C4×C53AGL(1,ℤ/8)12yescomplemented
176C4×C53C23×C411yescharacteristic
177C4×C53C2×#4111yescharacteristic
178Dic53—22no—
179Dic53—21no—
180Dic53—21no—
181Dic53—41no—
182Dic53—41no—
183Dic53C4×D412yes—
184C4×AGL(1,ℤ/8)—531nomaximal, Sylow
185C2×C53—42no—
186C2×C53—42no—
187C2×C53C2×C4×D411yescharacteristic
188C2×C53C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C53#57511yescharacteristic
190D53—22no—
191D53—42no—
192C2×AGL(1,ℤ/8)—531no—
193C4×#41—531no—
194C2×C4×D4—531no—
195#442—531no—
196#442—531no—
197#440—531no—
198#440—531no—
199C4×SD16—531no—
200C4×SD16—531no—
201C4×D8—531no—
202C4×D8D5311yescharacteristic, complemented
203#428—531no—
204#418—531no—
205#417—531no—
206C4×M16—531no—
207C53C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
208C2×#41—531no—
209C22×D4—531no—
210C23×C4—1061no—
211AGL(1,ℤ/8)—538no—
212C2×SD16—531no—
213C2×SD16—531no—
214C2×D8—531no—
215C2×D8C2×D5311yescharacteristic
216C2×M16—531no—
217C2×M16—531no—
218C4×Q8—531no—
219C4×Q8—531no—
220C4×D4—531no—
221C4×D4—531no—
222C4×D4—531no—
223C4×D4—531no—
224C4×D4—1061no—
225C4×D4—1061no—
226C4×D4—1061no—
227C4×D4—1061no—
228C4×D4C2×D5311yescharacteristic
229C4×D4C2×D5311yescharacteristic, complemented
230#117—531no—
231#117—1061no—
232C2×C4⋊C4—531no—
233C2×C22⋊C4—1061no—
234C2×C42—531no—
235C2×C42—1061no—
236#107—531no—
237#107C2×D5311yescharacteristic, complemented
238#106—531no—
239#106—531no—
240#103—531no—
241#103—531no—
242#102—531no—
243#102—531no—
244#102—531no—
245#102—531no—
246#102C2×D5311yescharacteristic
247#102C2×D5311yescharacteristic, complemented
248#97—531no—
249#97—531no—
250C4×C8—531no—
251C4×C8C2×D5311yescharacteristic, complemented
252C24—1061no—
253#41—534no—
254#41—1062no—
255C2×Q8—531no—
256C2×D4—534no—
257C2×D4—531no—
258C2×D4—1062no—
259C2×D4—1061no—
260C2×D4—1061no—
261C2×D4C22×D5311yescharacteristic
262C2×D4C22×D5311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—531no—
266C22×C4—531no—
267C22×C4—531no—
268C22×C4—1061no—
269C22×C4—1061no—
270C22×C4—1061no—
271C22×C4—1061no—
272C22×C4—1061no—
273C22×C4—1061no—
274C22×C4—2124no—
275SD16—534no—
276SD16—534no—
277D8—534no—
278D8C4×D5314yescomplemented
279M16—534no—
280M16—1062no—
281C2×C8—531no—
282C2×C8—531no—
283C2×C8C22×D5311yescharacteristic
284C2×C8C22×D5311yescharacteristic
285C4⋊C4—531no—
286C4⋊C4—531no—
287C4⋊C4—1061no—
288C4⋊C4—1061no—
289C4⋊C4—1061no—
290C4⋊C4C22×D5311yescharacteristic
291C4⋊C4C22×D5311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1061no—
295C22⋊C4—1061no—
296C22⋊C4—1061no—
297C22⋊C4—1061no—
298C22⋊C4—1061no—
299C42—531no—
300C42—531no—
301C42—531no—
302C42—1061no—
303C42—1061no—
304C42—1061no—
305C42C22×D5311yescharacteristic
306C23—21no—
307C23—21no—
308C23—531no—
309C23—1064no—
310C23—1061no—
311C23—2122no—
312C23—2122no—
313Q8—532no—
314Q8—1061no—
315D4—21no—
316D4—21no—
317D4—532no—
318D4—1064no—
319D4—1064no—
320D4—1061no—
321D4C2×C4×D5312yes—
322D4C2×C4×D5312yescomplemented
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—531no—
328C2×C4—532no—
329C2×C4—532no—
330C2×C4—531no—
331C2×C4—531no—
332C2×C4—1064no—
333C2×C4—1061no—
334C2×C4—1062no—
335C2×C4—1061no—
336C2×C4—1061no—
337C2×C4—2121no—
338C2×C4—2122no—
339C2×C4—2122no—
340C2×C4—2122no—
341C2×C4—2122no—
342C2×C4—2122no—
343C2×C4D4×D5311yescharacteristic
344C2×C4D4×D5311yescharacteristic
345C2×C4C23×D5311yescharacteristic
346C8—21no—
347C8—532no—
348C8—1061no—
349C8C2×C4×D5312yescomplemented
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—532no—
357C22—1061no—
358C22—1061no—
359C22—1062no—
360C22—2128no—
361C22—2121no—
362C22—2121no—
363C22C2×D4×D5311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—532no—
368C4—1062no—
369C4—1061no—
370C4—1061no—
371C4—2121no—
372C4—2121no—
373C4#1313324112yesdirect product factor
374C4C22×C4×D5311yescharacteristic
375C4#41×D5311yescharacteristic
376C2—42no—
377C2—42no—
378C2—1062no—
379C2—2122no—
380C2C4×D4×D5311yescharacteristic
381C2C2×#1313324111yescharacteristic
382C2#1681142011yescharacteristic
subgroupG/H
centerC2×C4D4×D53
commutatorC4×C53C23×C4
FrattiniC2×C4C23×D53
FittingC4×D8×C53C2
socleC22×C53C22×D4
hypercenterC4×D8D53
hypocenterC53C4×AGL(1,ℤ/8)
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×#11719947C2semidirect
3. C4×D4×D53C2semidirect
4. #16810735C2semidirect
5. #16810732C2semidirect
6. #16810722C2semidirect
7. #16810720C2semidirect
8. C4×#11719913C2semidirect
9. C4×#11719923C2semidirect
10. C4×#11719922C2semidirect
11. #16810664C2semidirect
12. #16810626C2semidirect
13. #16810621C2semidirect
14. C4×#11719912C2semidirect
15. C4×D8×C53C2semidirect
19. #13133241C4direct (N × H)
25. C4×Dic106C22semidirect
26. #13133182C22semidirect
29. D4×Dic53C22semidirect
41. #13133150C22semidirect
42. #13133149C22semidirect
43. #13133148C22semidirect
44. #13133142C22semidirect
45. #13133140C22semidirect
48. #13133138C22semidirect
50. #13133127C22semidirect
51. #13133127C22semidirect
52. C4×#88322C22semidirect
55. C4×D4×C53C22semidirect
56. #107×C53C22semidirect
58. #102×C53C22semidirect
59. C4×C8×C53C22semidirect
71. #11719947C2×C4semidirect
73. D4×D53C2×C4semidirect
83. D8×C53C2×C4semidirect
93. #11719923C2×C4semidirect
94. #11719922C2×C4semidirect
111. #11719913C2×C4semidirect
113. #11719912C2×C4semidirect
124. D4×C53C22×C4semidirect
153. Dic106C22×C4semidirect
155. C8×C53C22×C4semidirect
157. #88322C22×C4semidirect
175. C4×C53AGL(1,ℤ/8)semidirect
202. C4×D8D53semidirect
207. C53C4×AGL(1,ℤ/8)semidirect
229. C4×D4C2×D53semidirect
237. #107C2×D53semidirect
247. #102C2×D53semidirect
251. C4×C8C2×D53semidirect
278. D8C4×D53semidirect
322. D4C2×C4×D53semidirect
349. C8C2×C4×D53semidirect
373. C4#13133241direct (N × H)