Finite Group Databasebeta

← C4×#19104759 #35223339

Subgroups — C4×#19104759 #35223339

Order 20864.

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×#19104759C211yesmaximal, characteristic
2C4×#14579698C211yesmaximal, characteristic, complemented
3C4×D4×D163C211yesmaximal, characteristic, complemented
4#23781777C211yesmaximal, characteristic, complemented
5#23781774C211yesmaximal, characteristic, complemented
6#23781764C211yesmaximal, characteristic, complemented
7#23781762C211yesmaximal, characteristic, complemented
8C4×#14579688C211yesmaximal, characteristic, complemented
9C4×#14579687C211yesmaximal, characteristic, complemented
10C4×#14579684C211yesmaximal, characteristic, complemented
11#23781706C211yesmaximal, characteristic, complemented
12#23781668C211yesmaximal, characteristic, complemented
13#23781663C211yesmaximal, characteristic, complemented
14C4×#14579682C211yesmaximal, characteristic, complemented
15C4×D8×C163C211yesmaximal, characteristic, complemented
16C2×#14579698C2211yescharacteristic
17C2×D4×D163C2211yescharacteristic
18C22×C4×D163—21no—
19#19104759C418yesdirect product factor
20C2×#14579688C2211yescharacteristic
21C2×#14579687C2211yescharacteristic
22C2×#14579684C2211yescharacteristic
23C2×#14579682C2211yescharacteristic
24C2×#14579682C2211yescharacteristic
25C4×Dic326C2211yescharacteristic, complemented
26#19104700C2211yescharacteristic, complemented
27C4×D652C2211yescharacteristic
28D4×Dic163C2211yescharacteristic
29D4×Dic163C2211yescharacteristic, complemented
30#19104697C2211yescharacteristic
31C4×C22⋊D163—21no—
32C4×C22⋊D163—21no—
33(C22⋊D163)⋊C4—21no—
34(C22⋊D163)⋊C4—21no—
35#19104693C2211yescharacteristic
36#19104691—21no—
37C4⋊C4×D163C2211yescharacteristic
38C22⋊C4×D163—21no—
39C2×C4×Dic163—21no—
40C42×D163C2211yescharacteristic
41#19104668C2211yescharacteristic, complemented
42#19104667C2211yescharacteristic, complemented
43#19104666C2211yescharacteristic, complemented
44#19104660C2211yescharacteristic, complemented
45#19104658C2211yescharacteristic, complemented
46#19104657C2211yescharacteristic
47#19104656C2211yescharacteristic
48#19104656C2211yescharacteristic, complemented
49#19104655C2211yescharacteristic
50#19104645C2211yescharacteristic, complemented
51#19104645C2211yescharacteristic, complemented
52C4×C163⋊C8C2211yescharacteristic, complemented
53C2×D8×C163C2211yescharacteristic
54C4×D4×C163C2211yescharacteristic
55C4×D4×C163C2211yescharacteristic, complemented
56#107×C163C2211yescharacteristic, complemented
57#102×C163C2211yescharacteristic
58#102×C163C2211yescharacteristic, complemented
59C4×C8×C163C2211yescharacteristic, complemented
60C23×D163—21no—
61#14579698—22no—
62#14579698C2×C414yescomplemented
63C2×Dic326C2311yescharacteristic
64C2×D652C2311yescharacteristic
65C2×C22⋊D163—21no—
66C2×C22⋊D163—21no—
67D4×D163—22no—
68D4×D163C2×C414yescomplemented
69C22×Dic163—21no—
70C22×Dic163—21no—
71C22×Dic163—21no—
72C2×C4×D163—21no—
73C2×C4×D163—21no—
74C2×C4×D163—21no—
75C2×C4×D163—44no—
76C2×C4×D163D411yescharacteristic
77C2×C4×D163D411yescharacteristic
78C2×C4×D163C2311yescharacteristic
79#14579688C2×C414yescomplemented
80#14579687C2×C414yescomplemented
81#14579684C2×C414yescomplemented
82#14579682—22no—
83#14579682C2×C414yescomplemented
84C2×C163⋊C8C2311yescharacteristic
85C2×C163⋊C8C2311yescharacteristic
86C4⋊Dic163C2311yescharacteristic
87C4⋊Dic163C2311yescharacteristic
88Dic163⋊C4—21no—
89Dic163⋊C4—21no—
90Dic163⋊C4—21no—
91C22⋊Dic163—21no—
92C22⋊Dic163—21no—
93(C2×D163)⋊C4—21no—
94(C2×D163)⋊C4—21no—
95(C2×D163)⋊C4—21no—
96C4×Dic163—21no—
97C4×Dic163—21no—
98C4×Dic163—21no—
99C4×Dic163D411yescharacteristic
100C4×Dic163D411yescharacteristic
101C4×Dic163C2311yescharacteristic
102C2×D4×C163C2311yescharacteristic
103C2×D4×C163C2311yescharacteristic
104C22×C4×C163—21no—
105C22×C4×C163—21no—
106D8×C163C2×C414yescomplemented
107C2×C8×C163C2311yescharacteristic
108C2×C8×C163C2311yescharacteristic
109C4⋊C4×C163C2311yescharacteristic
110C4⋊C4×C163C2311yescharacteristic
111C22⋊C4×C163—21no—
112C22⋊C4×C163—21no—
113C42×C163C2311yescharacteristic
114C22×D163—21no—
115C22×D163—24no—
116C22×D163—42no—
117C22×D163—42no—
118C22×D163C2×D411yescharacteristic
119Dic326—21no—
120Dic326C22×C412yescomplemented
121D652—21no—
122D652C22×C412yes—
123C22⋊D163—24no—
124C22⋊D163—24no—
125C2×Dic163—21no—
126C2×Dic163—24no—
127C2×Dic163—21no—
128C2×Dic163—21no—
129C2×Dic163—42no—
130C2×Dic163—42no—
131C2×Dic163C2×D411yescharacteristic
132C2×Dic163C2×D411yescharacteristic
133C2×Dic163C2×D411yescharacteristic
134C4×D163—22no—
135C4×D163—41no—
136C4×D163—42no—
137C4×D163—42no—
138C4×D163—42no—
139C4×D163C22×C412yes—
140C4×D163#4112yes—
141C163⋊C8—21no—
142C163⋊C8C22×C412yescomplemented
143C23×C163—21no—
144C23×C163—21no—
145D4×C163—21no—
146D4×C163—21no—
147D4×C163C22×C412yes—
148D4×C163C22×C412yescomplemented
149C2×C4×C163—21no—
150C2×C4×C163—21no—
151C2×C4×C163—42no—
152C2×C4×C163—42no—
153C2×C4×C163C2×D411yescharacteristic
154C2×C4×C163C2×D411yescharacteristic
155C2×C4×C163C2411yescharacteristic
156C8×C163—21no—
157C8×C163C22×C412yescomplemented
158C22×C163—22no—
159C22×C163—22no—
160C22×C163—41no—
161C22×C163—41no—
162C22×C163—41no—
163C22×C163—41no—
164C22×C163C22×D411yescharacteristic
165C2×D163—21no—
166C2×D163—21no—
167C2×D163—22no—
168C2×D163—48no—
169C2×D163—41no—
170C2×D163—41no—
171C2×D163C4×D412yes—
172C4×C163—21no—
173C4×C163—41no—
174C4×C163—41no—
175C4×C163AGL(1,ℤ/8)12yescomplemented
176C4×C163C23×C411yescharacteristic
177C4×C163C2×#4111yescharacteristic
178Dic163—22no—
179Dic163—21no—
180Dic163—21no—
181Dic163—41no—
182Dic163—41no—
183Dic163C4×D412yes—
184C2×C163—42no—
185C2×C163—42no—
186C2×C163C2×C4×D411yescharacteristic
187C2×C163C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C163#57511yescharacteristic
189D163—22no—
190D163—42no—
191C163C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
192C4×AGL(1,ℤ/8)—1631nomaximal, Sylow
193C2×AGL(1,ℤ/8)—1631no—
194C4×#41—1631no—
195C2×C4×D4—1631no—
196#442—1631no—
197#442—1631no—
198#440—1631no—
199#440—1631no—
200C4×SD16—1631no—
201C4×SD16—1631no—
202C4×D8—1631no—
203C4×D8D16311yescharacteristic, complemented
204#428—1631no—
205#418—1631no—
206#417—1631no—
207C4×M16—1631no—
208C2×#41—1631no—
209C22×D4—1631no—
210C23×C4—3261no—
211AGL(1,ℤ/8)—1638no—
212C2×SD16—1631no—
213C2×SD16—1631no—
214C2×D8—1631no—
215C2×D8C2×D16311yescharacteristic
216C2×M16—1631no—
217C2×M16—1631no—
218C4×Q8—1631no—
219C4×Q8—1631no—
220C4×D4—3261no—
221C4×D4—3261no—
222C4×D4—3261no—
223C4×D4—3261no—
224C4×D4—1631no—
225C4×D4—1631no—
226C4×D4—1631no—
227C4×D4—1631no—
228C4×D4C2×D16311yescharacteristic
229C4×D4C2×D16311yescharacteristic, complemented
230#117—3261no—
231#117—1631no—
232C2×C4⋊C4—1631no—
233C2×C22⋊C4—3261no—
234C2×C42—3261no—
235C2×C42—1631no—
236#107—1631no—
237#107C2×D16311yescharacteristic, complemented
238#106—1631no—
239#106—1631no—
240#103—1631no—
241#103—1631no—
242#102—1631no—
243#102—1631no—
244#102—1631no—
245#102—1631no—
246#102C2×D16311yescharacteristic
247#102C2×D16311yescharacteristic, complemented
248#97—1631no—
249#97—1631no—
250C4×C8—1631no—
251C4×C8C2×D16311yescharacteristic, complemented
252C24—3261no—
253#41—3262no—
254#41—1634no—
255C2×Q8—1631no—
256C2×D4—3261no—
257C2×D4—3262no—
258C2×D4—3261no—
259C2×D4—1634no—
260C2×D4—1631no—
261C2×D4C22×D16311yescharacteristic
262C2×D4C22×D16311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—3261no—
266C22×C4—3261no—
267C22×C4—3261no—
268C22×C4—3261no—
269C22×C4—3261no—
270C22×C4—3261no—
271C22×C4—6524no—
272C22×C4—1631no—
273C22×C4—1631no—
274C22×C4—1631no—
275SD16—1634no—
276SD16—1634no—
277D8—1634no—
278D8C4×D16314yescomplemented
279M16—3262no—
280M16—1634no—
281C2×C8—1631no—
282C2×C8—1631no—
283C2×C8C22×D16311yescharacteristic
284C2×C8C22×D16311yescharacteristic
285C4⋊C4—3261no—
286C4⋊C4—3261no—
287C4⋊C4—3261no—
288C4⋊C4—1631no—
289C4⋊C4—1631no—
290C4⋊C4C22×D16311yescharacteristic
291C4⋊C4C22×D16311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—3261no—
295C22⋊C4—3261no—
296C22⋊C4—3261no—
297C22⋊C4—3261no—
298C22⋊C4—3261no—
299C42—3261no—
300C42—3261no—
301C42—3261no—
302C42—1631no—
303C42—1631no—
304C42—1631no—
305C42C22×D16311yescharacteristic
306C23—21no—
307C23—21no—
308C23—3264no—
309C23—3261no—
310C23—6522no—
311C23—6522no—
312C23—1631no—
313Q8—3261no—
314Q8—1632no—
315D4—21no—
316D4—21no—
317D4—3264no—
318D4—3264no—
319D4—3261no—
320D4—1632no—
321D4C2×C4×D16312yes—
322D4C2×C4×D16312yescomplemented
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—3261no—
328C2×C4—3264no—
329C2×C4—3262no—
330C2×C4—3261no—
331C2×C4—3261no—
332C2×C4—6521no—
333C2×C4—6522no—
334C2×C4—6522no—
335C2×C4—6522no—
336C2×C4—6522no—
337C2×C4—6522no—
338C2×C4—1631no—
339C2×C4—1631no—
340C2×C4—1631no—
341C2×C4—1632no—
342C2×C4—1632no—
343C2×C4D4×D16311yescharacteristic
344C2×C4D4×D16311yescharacteristic
345C2×C4C23×D16311yescharacteristic
346C8—21no—
347C8—3261no—
348C8—1632no—
349C8C2×C4×D16312yescomplemented
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—3261no—
357C22—3261no—
358C22—3262no—
359C22—6528no—
360C22—6521no—
361C22—6521no—
362C22—1632no—
363C22C2×D4×D16311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—3261no—
368C4—3261no—
369C4—3262no—
370C4—6521no—
371C4—6521no—
372C4—1632no—
373C4#1910475912yesdirect product factor
374C4C22×C4×D16311yescharacteristic
375C4#41×D16311yescharacteristic
376C2—42no—
377C2—42no—
378C2—3262no—
379C2—6522no—
380C2C4×D4×D16311yescharacteristic
381C2C2×#1910475911yescharacteristic
382C2#2378246211yescharacteristic
subgroupG/H
centerC2×C4D4×D163
commutatorC4×C163C23×C4
FrattiniC2×C4C23×D163
FittingC4×D8×C163C2
socleC22×C163C22×D4
prime radicalC2×#19104759C2
cosocleC2×C4×C163C24
hypercenterC4×D8D163
hypocenterC163C4×AGL(1,ℤ/8)
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×#14579698C2semidirect
3. C4×D4×D163C2semidirect
4. #23781777C2semidirect
5. #23781774C2semidirect
6. #23781764C2semidirect
7. #23781762C2semidirect
8. C4×#14579688C2semidirect
9. C4×#14579687C2semidirect
10. C4×#14579684C2semidirect
11. #23781706C2semidirect
12. #23781668C2semidirect
13. #23781663C2semidirect
14. C4×#14579682C2semidirect
15. C4×D8×C163C2semidirect
19. #19104759C4direct (N × H)
25. C4×Dic326C22semidirect
26. #19104700C22semidirect
29. D4×Dic163C22semidirect
41. #19104668C22semidirect
42. #19104667C22semidirect
43. #19104666C22semidirect
44. #19104660C22semidirect
45. #19104658C22semidirect
48. #19104656C22semidirect
50. #19104645C22semidirect
51. #19104645C22semidirect
52. C4×C163⋊C8C22semidirect
55. C4×D4×C163C22semidirect
56. #107×C163C22semidirect
58. #102×C163C22semidirect
59. C4×C8×C163C22semidirect
62. #14579698C2×C4semidirect
68. D4×D163C2×C4semidirect
79. #14579688C2×C4semidirect
80. #14579687C2×C4semidirect
81. #14579684C2×C4semidirect
83. #14579682C2×C4semidirect
106. D8×C163C2×C4semidirect
120. Dic326C22×C4semidirect
142. C163⋊C8C22×C4semidirect
148. D4×C163C22×C4semidirect
157. C8×C163C22×C4semidirect
175. C4×C163AGL(1,ℤ/8)semidirect
191. C163C4×AGL(1,ℤ/8)semidirect
203. C4×D8D163semidirect
229. C4×D4C2×D163semidirect
237. #107C2×D163semidirect
247. #102C2×D163semidirect
251. C4×C8C2×D163semidirect
278. D8C4×D163semidirect
322. D4C2×C4×D163semidirect
349. C8C2×C4×D163semidirect
373. C4#19104759direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191047592
C4×#145796982
C4×D4×D1632
#237817772
#237817742
#237817642
#237817622
C4×#145796882
C4×#145796872
C4×#145796842
#237817062
#237816682
#237816632
C4×#145796822
C4×D8×C1632
C4×AGL(1,ℤ/8)163