Finite Group Databasebeta

← C4×#14524070 #22569018

Subgroups — C4×#14524070 #22569018

Order 8576.

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×#14524070C211yesmaximal, characteristic
2C4×#11761629C211yesmaximal, characteristic, complemented
3C4×D4×D67C211yesmaximal, characteristic, complemented
4#16863507C211yesmaximal, characteristic, complemented
5#16863505C211yesmaximal, characteristic, complemented
6#16863499C211yesmaximal, characteristic, complemented
7#16863497C211yesmaximal, characteristic, complemented
8C4×#11761615C211yesmaximal, characteristic, complemented
9C4×D536C211yesmaximal, characteristic, complemented
10C4×#11761613C211yesmaximal, characteristic, complemented
11#16863435C211yesmaximal, characteristic, complemented
12#16863399C211yesmaximal, characteristic, complemented
13#16863396C211yesmaximal, characteristic, complemented
14C4×#11761611C211yesmaximal, characteristic, complemented
15C4×SD16×C67C211yesmaximal, characteristic, complemented
16C2×#11761629C2211yescharacteristic
17C2×D4×D67C2211yescharacteristic
18C22×C4×D67—21no—
19#14524070C418yesdirect product factor
20C2×#11761615C2211yescharacteristic
21C2×D536C2211yescharacteristic
22C2×#11761613C2211yescharacteristic
23C2×#11761611C2211yescharacteristic
24C2×#11761611C2211yescharacteristic
25Q8×Dic67C2211yescharacteristic, complemented
26C4×D268—21no—
27C4×D268C2211yescharacteristic
28C4×D268C2211yescharacteristic, complemented
29D4×Dic67C2211yescharacteristic
30#14524005—21no—
31#14524005C2211yescharacteristic
32#14524005C2211yescharacteristic, complemented
33C4×C22⋊D67—21no—
34(C22⋊D67)⋊C4—21no—
35#14524001—21no—
36#14524001C2211yescharacteristic
37C4⋊C4×D67C2211yescharacteristic
38C22⋊C4×D67—21no—
39C42×D67—21no—
40C42×D67C2211yescharacteristic
41#14523977C2211yescharacteristic, complemented
42#14523976C2211yescharacteristic, complemented
43#14523974C2211yescharacteristic, complemented
44#14523967C2211yescharacteristic, complemented
45#14523965C2211yescharacteristic
46#14523965C2211yescharacteristic, complemented
47#14523964C2211yescharacteristic
48#14523963C2211yescharacteristic
49#14523963C2211yescharacteristic, complemented
50#14523953C2211yescharacteristic, complemented
51#14523953C2211yescharacteristic, complemented
52C4×C67⋊C8C2211yescharacteristic, complemented
53C2×SD16×C67C2211yescharacteristic
54C4×Q8×C67C2211yescharacteristic, complemented
55C4×D4×C67C2211yescharacteristic
56#106×C67C2211yescharacteristic, complemented
57#103×C67C2211yescharacteristic, complemented
58#102×C67C2211yescharacteristic
59C4×C8×C67C2211yescharacteristic, complemented
60C23×D67—21no—
61#11761629—22no—
62#11761629C2×C414yescomplemented
63C2×D268—21no—
64C2×D268C2311yescharacteristic
65C2×D268C2311yescharacteristic
66C2×C22⋊D67—21no—
67D4×D67—22no—
68D4×D67C2×C414yescomplemented
69C22×Dic67—21no—
70C2×C4×D67—21no—
71C2×C4×D67—21no—
72C2×C4×D67—21no—
73C2×C4×D67—21no—
74C2×C4×D67—21no—
75C2×C4×D67—21no—
76C2×C4×D67—44no—
77C2×C4×D67D411yescharacteristic
78C2×C4×D67D411yescharacteristic
79C2×C4×D67C2311yescharacteristic
80#11761615C2×C414yescomplemented
81D536C2×C414yescomplemented
82#11761613C2×C414yescomplemented
83#11761611—22no—
84#11761611C2×C414yescomplemented
85C2×C67⋊C8C2311yescharacteristic
86C2×C67⋊C8C2311yescharacteristic
87C4⋊Dic67—21no—
88C4⋊Dic67C2311yescharacteristic
89C4⋊Dic67C2311yescharacteristic
90Dic67⋊C4—21no—
91C22⋊Dic67—21no—
92(C2×D67)⋊C4—21no—
93(C2×D67)⋊C4—21no—
94(C2×D67)⋊C4—21no—
95(C2×D67)⋊C4—21no—
96(C2×D67)⋊C4—21no—
97C4×Dic67—21no—
98C4×Dic67—21no—
99C4×Dic67D411yescharacteristic
100C4×Dic67D411yescharacteristic
101C4×Dic67C2311yescharacteristic
102C2×Q8×C67C2311yescharacteristic
103C2×D4×C67C2311yescharacteristic
104C22×C4×C67—21no—
105SD16×C67C2×C414yescomplemented
106C2×C8×C67C2311yescharacteristic
107C2×C8×C67C2311yescharacteristic
108C4⋊C4×C67—21no—
109C4⋊C4×C67C2311yescharacteristic
110C4⋊C4×C67C2311yescharacteristic
111C22⋊C4×C67—21no—
112C42×C67—21no—
113C42×C67C2311yescharacteristic
114C23×C67—21no—
115C22×D67—21no—
116C22×D67—21no—
117C22×D67—24no—
118C22×D67—42no—
119C22×D67—42no—
120C22×D67C2×D411yescharacteristic
121Q8×C67—21no—
122Q8×C67C22×C412yescomplemented
123D4×C67—21no—
124D4×C67C22×C412yes—
125C2×C4×C67—21no—
126C2×C4×C67—21no—
127C2×C4×C67—21no—
128C2×C4×C67—42no—
129C2×C4×C67C2×D411yescharacteristic
130C2×C4×C67C2×D411yescharacteristic
131C2×C4×C67C2411yescharacteristic
132C22⋊D67—24no—
133C2×Dic67—21no—
134C2×Dic67—21no—
135C2×Dic67—42no—
136C2×Dic67C2×D411yescharacteristic
137C2×Dic67C2×D411yescharacteristic
138C2×Dic67C2×D411yescharacteristic
139D268—24no—
140D268—21no—
141D268—21no—
142D268C22×C412yes—
143D268C22×C412yescomplemented
144C4×D67—22no—
145C4×D67—24no—
146C4×D67—41no—
147C4×D67—42no—
148C4×D67—42no—
149C4×D67—42no—
150C4×D67—42no—
151C4×D67—42no—
152C4×D67C22×C412yes—
153C4×D67#4112yes—
154C8×C67—21no—
155C8×C67C22×C412yescomplemented
156C67⋊C8—21no—
157C67⋊C8C22×C412yescomplemented
158C22×C67—22no—
159C22×C67—41no—
160C22×C67—41no—
161C22×C67C22×D411yescharacteristic
162C2×D67—21no—
163C2×D67—21no—
164C2×D67—22no—
165C2×D67—22no—
166C2×D67—48no—
167C2×D67—41no—
168C2×D67—41no—
169C2×D67—41no—
170C2×D67—41no—
171C2×D67C4×D412yes—
172C4×C67—22no—
173C4×C67—21no—
174C4×C67—41no—
175C4×C67—41no—
176C4×C67AGL(1,ℤ/8)12yescomplemented
177C4×C67C23×C411yescharacteristic
178C4×C67C2×#4111yescharacteristic
179Dic67—21no—
180Dic67—21no—
181Dic67—41no—
182Dic67—41no—
183Dic67C4×D412yes—
184C2×C67—42no—
185C2×C67C2×C4×D411yescharacteristic
186C2×C67C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C67#57511yescharacteristic
188D67—22no—
189D67—42no—
190D67—42no—
191C4×AGL(1,ℤ/8)—671nomaximal, Sylow
192C67C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
193C2×AGL(1,ℤ/8)—671no—
194C4×#41—671no—
195C2×C4×D4—671no—
196#442—671no—
197#442—671no—
198#440—671no—
199#440—671no—
200C4×SD16—671no—
201C4×SD16D6711yescharacteristic, complemented
202C4×D8—671no—
203C4×D8—671no—
204#428—671no—
205#418—671no—
206#417—671no—
207C4×M16—671no—
208C2×#41—671no—
209C22×D4—671no—
210C23×C4—1341no—
211AGL(1,ℤ/8)—678no—
212C2×SD16—671no—
213C2×SD16C2×D6711yescharacteristic
214C2×D8—671no—
215C2×D8—671no—
216C2×M16—671no—
217C2×M16—671no—
218C4×Q8—671no—
219C4×Q8C2×D6711yescharacteristic, complemented
220C4×D4—671no—
221C4×D4—671no—
222C4×D4—671no—
223C4×D4—671no—
224C4×D4—671no—
225C4×D4—1341no—
226C4×D4—1341no—
227C4×D4—1341no—
228C4×D4—1341no—
229C4×D4C2×D6711yescharacteristic
230#117—671no—
231#117—1341no—
232C2×C4⋊C4—671no—
233C2×C22⋊C4—1341no—
234C2×C42—671no—
235C2×C42—1341no—
236#107—671no—
237#107—671no—
238#106—671no—
239#106C2×D6711yescharacteristic, complemented
240#103—671no—
241#103C2×D6711yescharacteristic, complemented
242#102—671no—
243#102—671no—
244#102—671no—
245#102—671no—
246#102—671no—
247#102C2×D6711yescharacteristic
248#97—671no—
249#97—671no—
250C4×C8—671no—
251C4×C8C2×D6711yescharacteristic, complemented
252C24—1341no—
253#41—674no—
254#41—1342no—
255C2×Q8C22×D6711yescharacteristic
256C2×D4—674no—
257C2×D4—671no—
258C2×D4—671no—
259C2×D4—1341no—
260C2×D4—1342no—
261C2×D4—1341no—
262C2×D4C22×D6711yescharacteristic
263C22×C4—21no—
264C22×C4—2684no—
265C22×C4—671no—
266C22×C4—671no—
267C22×C4—671no—
268C22×C4—1341no—
269C22×C4—1341no—
270C22×C4—1341no—
271C22×C4—1341no—
272C22×C4—1341no—
273C22×C4—1341no—
274C22×C4—1341no—
275SD16—674no—
276SD16C4×D6714yescomplemented
277D8—674no—
278D8—674no—
279M16—674no—
280M16—1342no—
281C2×C8—671no—
282C2×C8—671no—
283C2×C8C22×D6711yescharacteristic
284C2×C8C22×D6711yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—671no—
287C4⋊C4—671no—
288C4⋊C4—1341no—
289C4⋊C4—1341no—
290C4⋊C4C22×D6711yescharacteristic
291C4⋊C4C22×D6711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—1341no—
294C22⋊C4—1341no—
295C22⋊C4—1341no—
296C22⋊C4—1341no—
297C22⋊C4—1341no—
298C22⋊C4—1341no—
299C42—21no—
300C42—671no—
301C42—671no—
302C42—671no—
303C42—1341no—
304C42—1341no—
305C42C22×D6711yescharacteristic
306C23—21no—
307C23—2682no—
308C23—2682no—
309C23—671no—
310C23—1344no—
311C23—1341no—
312C23—1341no—
313Q8—21no—
314Q8C2×C4×D6712yescomplemented
315D4—21no—
316D4—672no—
317D4—672no—
318D4—1344no—
319D4—1344no—
320D4—1341no—
321D4—1341no—
322D4C2×C4×D6712yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—2681no—
328C2×C4—2682no—
329C2×C4—2682no—
330C2×C4—2682no—
331C2×C4—2682no—
332C2×C4—2682no—
333C2×C4—2682no—
334C2×C4—671no—
335C2×C4—672no—
336C2×C4—672no—
337C2×C4—671no—
338C2×C4—671no—
339C2×C4—1344no—
340C2×C4—1341no—
341C2×C4—1341no—
342C2×C4—1342no—
343C2×C4D4×D6711yescharacteristic
344C2×C4D4×D6711yescharacteristic
345C2×C4C23×D6711yescharacteristic
346C8—21no—
347C8—672no—
348C8—1341no—
349C8C2×C4×D6712yescomplemented
350C22—22no—
351C22—41no—
352C22—41no—
353C22—2688no—
354C22—2681no—
355C22—2681no—
356C22—2681no—
357C22—2681no—
358C22—672no—
359C22—1342no—
360C22—1342no—
361C22—1341no—
362C22—1341no—
363C22C2×D4×D6711yescharacteristic
364C4—22no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—2681no—
369C4—2681no—
370C4—672no—
371C4—1341no—
372C4—1341no—
373C4#1452407012yesdirect product factor
374C4C22×C4×D6711yescharacteristic
375C4#41×D6711yescharacteristic
376C2—42no—
377C2—2682no—
378C2—2682no—
379C2—1342no—
380C2C4×D4×D6711yescharacteristic
381C2C2×#1452407011yescharacteristic
382C2#1686419311yescharacteristic
subgroupG/H
centerC2×C4D4×D67
commutatorC4×C67C23×C4
FrattiniC2×C4C23×D67
FittingC4×SD16×C67C2
socleC22×C67C22×D4
hypercenterC4×SD16D67
hypocenterC67C4×AGL(1,ℤ/8)
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#11761629C2semidirect
3. C4×D4×D67C2semidirect
4. #16863507C2semidirect
5. #16863505C2semidirect
6. #16863499C2semidirect
7. #16863497C2semidirect
8. C4×#11761615C2semidirect
9. C4×D536C2semidirect
10. C4×#11761613C2semidirect
11. #16863435C2semidirect
12. #16863399C2semidirect
13. #16863396C2semidirect
14. C4×#11761611C2semidirect
15. C4×SD16×C67C2semidirect
19. #14524070C4direct (N × H)
25. Q8×Dic67C22semidirect
28. C4×D268C22semidirect
32. #14524005C22semidirect
41. #14523977C22semidirect
42. #14523976C22semidirect
43. #14523974C22semidirect
44. #14523967C22semidirect
46. #14523965C22semidirect
49. #14523963C22semidirect
50. #14523953C22semidirect
51. #14523953C22semidirect
52. C4×C67⋊C8C22semidirect
54. C4×Q8×C67C22semidirect
56. #106×C67C22semidirect
57. #103×C67C22semidirect
59. C4×C8×C67C22semidirect
62. #11761629C2×C4semidirect
68. D4×D67C2×C4semidirect
80. #11761615C2×C4semidirect
81. D536C2×C4semidirect
82. #11761613C2×C4semidirect
84. #11761611C2×C4semidirect
105. SD16×C67C2×C4semidirect
122. Q8×C67C22×C4semidirect
143. D268C22×C4semidirect
155. C8×C67C22×C4semidirect
157. C67⋊C8C22×C4semidirect
176. C4×C67AGL(1,ℤ/8)semidirect
192. C67C4×AGL(1,ℤ/8)semidirect
201. C4×SD16D67semidirect
219. C4×Q8C2×D67semidirect
239. #106C2×D67semidirect
241. #103C2×D67semidirect
251. C4×C8C2×D67semidirect
276. SD16C4×D67semidirect
314. Q8C2×C4×D67semidirect
349. C8C2×C4×D67semidirect
373. C4#14524070direct (N × H)