Finite Group Databasebeta

← C4×#1629 #209661

Subgroups — C4×#1629 #209661

Order 512.

1656 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D42C211yesmaximal, characteristic
2C4×#492C211yesmaximal, characteristic, complemented
3C4×#476C212yesmaximal, complemented
4C2×#1629C211yesmaximal, characteristic
5#9064C211yesmaximal, characteristic, complemented
6#8973C212yesmaximal, complemented
7#8924C211yesmaximal, characteristic, complemented
8#8886C212yesmaximal, complemented
9#8443C211yesmaximal, characteristic
10C4×#331C211yesmaximal, characteristic, complemented
11C4×D4⋊C8C212yesmaximal, complemented
12C2×D42C2211yescharacteristic
13C22×C4×D4—22no—
14C2×#492C2211yescharacteristic
15C2×#476C2212yes—
16C2×C4×SD16—22no—
17#2366C2211yescharacteristic
18#2361—22no—
19#2358—22no—
20D4×C4⋊C4C2212yes—
21D4×C22⋊C4—22no—
22C4×C4⋊Q8C2211yescharacteristic, complemented
23C4×#127C2211yescharacteristic
24C4×#121—22no—
25C4×#120—22no—
26C42×D4C2212yes—
27#1987C2212yescomplemented
28#1968—22no—
29#1957C2211yescharacteristic
30#1956C2211yescharacteristic, complemented
31#1948C2212yescomplemented
32#1920—22no—
33#1864—22no—
34#1844C2211yescharacteristic, complemented
35#1802C2212yes—
36C4×#106—22no—
37C4×C4⋊C8C2212yescomplemented
38C4×#102—22no—
39C42×C8C2211yescharacteristic, complemented
40#1629C418yesdirect product factor
41C2×#331C2211yescharacteristic
42C2×#331C2211yescharacteristic
43C2×D4⋊C8C2212yes—
44C2×D4⋊C8C2212yes—
45#1296C2212yescomplemented
46#1279C2212yescomplemented
47#1279C2212yescomplemented
48C23×D4—22no—
49C24×C4—22no—
50C22×SD16—22no—
51D42—22no—
52D42—24no—
53D42C2×C414yes—
54C2×C4⋊Q8C2311yescharacteristic
55C2×#127C2311yescharacteristic
56C2×#121—22no—
57C2×#120—22no—
58C2×C4×Q8—21no—
59C2×C4×D4—24no—
60C2×C4×D4—24no—
61C2×C4×D4—22no—
62C2×C4×D4—22no—
63C2×C4×D4—22no—
64C2×C4×D4—48no—
65C2×C4×D4—48no—
66C2×C4×D4D412yes—
67C2×C4×D4D412yes—
68C2×C4×D4D412yes—
69C2×C4×D4C2312yes—
70C22×C4⋊C4—22no—
71C22×C22⋊C4—24no—
72C22×C42—22no—
73#492—22no—
74#492C2×C414yescomplemented
75#476—24no—
76#476C2×C418yescomplemented
77C4×SD16—48no—
78C2×#106—22no—
79C2×#106—22no—
80C2×#106—22no—
81C2×C4⋊C8C2312yes—
82C2×C4⋊C8C2312yes—
83C2×#103—22no—
84C2×#102—22no—
85C2×#102—22no—
86C2×#102—22no—
87C2×C4×C8—21no—
88C2×C4×C8—21no—
89C2×C4×C8—22no—
90C2×C4×C8C2311yescharacteristic
91C2×C4×C8C2311yescharacteristic
92#391—21no—
93#390—22no—
94#390—22no—
95#390D412yes—
96#389—22no—
97#389—22no—
98#388—24no—
99#386—24no—
100#386—24no—
101#386—22no—
102#385—22no—
103#385—24no—
104#384C2311yescharacteristic
105#384C2311yescharacteristic
106#380—22no—
107#379—22no—
108C4×C4⋊C4—22no—
109C4×C4⋊C4D412yes—
110C4×C4⋊C4D412yes—
111C4×C4⋊C4C2312yes—
112C4×C22⋊C4—22no—
113C4×C22⋊C4—22no—
114C4×C22⋊C4—22no—
115C4×C22⋊C4—22no—
116C43C2311yescharacteristic
117#340—22no—
118#340—22no—
119#340—22no—
120#340—22no—
121#336—22no—
122#331—22no—
123#331C2×C414yescomplemented
124D4⋊C8—24no—
125D4⋊C8C2×C418yescomplemented
126C25—22no—
127C22×Q8—21no—
128C22×D4—24no—
129C22×D4—28no—
130C22×D4—28no—
131C22×D4—22no—
132C22×D4—44no—
133C22×D4—44no—
134C22×D4—44no—
135C22×D4—44no—
136C22×D4C2×D412yes—
137C22×D4C2×D412yes—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—24no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—416no—
145C23×C4—84no—
146C2×SD16—28no—
147C2×SD16—44no—
148C2×SD16—44no—
149C22×C8—21no—
150C22×C8—22no—
151C22×C8—21no—
152C22×C8—22no—
153C4⋊Q8—22no—
154C4⋊Q8—21no—
155C4⋊Q8C22×C412yescomplemented
156#127—22no—
157#127C22×C412yes—
158#127#4112yes—
159#121—28no—
160#121—28no—
161#120—28no—
162#120—28no—
163C4×Q8—44no—
164C4×D4—24no—
165C4×D4—24no—
166C4×D4—22no—
167C4×D4—22no—
168C4×D4—42no—
169C4×D4—44no—
170C4×D4—416no—
171C4×D4—44no—
172C4×D4—416no—
173C4×D4—44no—
174C4×D4—44no—
175C4×D4—44no—
176C4×D4—44no—
177C4×D4—44no—
178C4×D4SD1618yescomplemented
179C4×D4C22×C414yes—
180C4×D4#4114yes—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4C2×D412yes—
190C2×C4⋊C4C2×D412yes—
191C2×C4⋊C4C2×D412yes—
192C2×C4⋊C4C2×D412yes—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—416no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—44no—
207C2×C42—44no—
208C2×C42—41no—
209C2×C42C2×D412yes—
210C2×C42C2×D411yescharacteristic
211C2×C42C2×D411yescharacteristic
212C2×C42C2×D412yes—
213C2×C42C2411yescharacteristic
214#106—28no—
215#106—44no—
216#106—44no—
217C4⋊C8—22no—
218C4⋊C8—22no—
219C4⋊C8—22no—
220C4⋊C8C22×C414yescomplemented
221#103—44no—
222#102—28no—
223#102—44no—
224#102—44no—
225C4×C8—24no—
226C4×C8—21no—
227C4×C8—22no—
228C4×C8—42no—
229C4×C8—44no—
230C4×C8C22×C412yescomplemented
231#95—24no—
232#95—22no—
233#95—22no—
234#95—22no—
235#95—42no—
236C24—22no—
237C24—28no—
238C24—22no—
239C24—48no—
240C24—48no—
241C24—82no—
242C24—82no—
243C2×Q8—22no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—41no—
247C2×D4—216no—
248C2×D4—24no—
249C2×D4—22no—
250C2×D4—24no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—42no—
255C2×D4—42no—
256C2×D4—416no—
257C2×D4—416no—
258C2×D4—416no—
259C2×D4—48no—
260C2×D4—48no—
261C2×D4—416no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4C4×D414yes—
267C2×D4C4×D414yes—
268C2×D4C2×SD1614yes—
269C2×D4#13514yes—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—28no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—44no—
278C22×C4—48no—
279C22×C4—48no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—44no—
285C22×C4—44no—
286C22×C4—48no—
287C22×C4—41no—
288C22×C4—44no—
289C22×C4—48no—
290C22×C4—44no—
291C22×C4—41no—
292C22×C4—82no—
293C22×C4—82no—
294C22×C4—84no—
295C22×C4—832no—
296C22×C4#12011yescharacteristic
297C22×C4#12012yes—
298C22×C4#12011yescharacteristic
299C22×C4C22×D411yescharacteristic
300C22×C4C22×D412yes—
301SD16—416no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—24no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—42no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—42no—
320C4⋊C4—48no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—82no—
328C4⋊C4C4×D414yes—
329C4⋊C4C2×SD1614yes—
330C22⋊C4—28no—
331C22⋊C4—24no—
332C22⋊C4—24no—
333C22⋊C4—28no—
334C22⋊C4—44no—
335C22⋊C4—48no—
336C22⋊C4—48no—
337C22⋊C4—48no—
338C22⋊C4—82no—
339C22⋊C4—82no—
340C42—22no—
341C42—22no—
342C42—22no—
343C42—41no—
344C42—42no—
345C42—42no—
346C42—44no—
347C42—44no—
348C42—82no—
349C42C2×SD1614yes—
350C42AGL(1,ℤ/8)14yes—
351C42C23×C411yescharacteristic
352C42C2×#4111yescharacteristic
353C42C2×#4112yes—
354C23—24no—
355C23—24no—
356C23—24no—
357C23—24no—
358C23—432no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—44no—
364C23—44no—
365C23—42no—
366C23—42no—
367C23—88no—
368C23—88no—
369C23—88no—
370C23—816no—
371C23C2×#12011yescharacteristic
372Q8—44no—
373Q8—82no—
374D4—24no—
375D4—24no—
376D4—24no—
377D4—44no—
378D4—432no—
379D4—44no—
380D4—44no—
381D4—44no—
382D4—44no—
383D4—82no—
384D4C4×SD1618yescomplemented
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—24no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—416no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—88no—
409C2×C4—88no—
410C2×C4—816no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—88no—
414C2×C4—82no—
415C2×C4—81no—
416C2×C4#45014yes—
417C2×C4#45014yes—
418C2×C4#45312yes—
419C2×C4C2×C4×D411yescharacteristic
420C2×C4C2×C4×D412yes—
421C2×C4#52511yescharacteristic
422C2×C4#52512yes—
423C2×C4C22×SD1612yes—
424C2×C4C2×#13512yes—
425C2×C4C2×AGL(1,ℤ/8)12yes—
426C2×C4#57512yes—
427C8—24no—
428C8—42no—
429C8—44no—
430C8—82no—
431C22—28no—
432C22—44no—
433C22—44no—
434C22—44no—
435C22—44no—
436C22—44no—
437C22—44no—
438C22—48no—
439C22—44no—
440C22—832no—
441C22—82no—
442C22—82no—
443C22—84no—
444C22C4×#12011yescharacteristic
445C22C2×#45012yes—
446C22#300212yes—
447C22C2×#45311yescharacteristic
448C22#301811yescharacteristic
449C4—24no—
450C4—21no—
451C4—21no—
452C4—44no—
453C4—41no—
454C4—44no—
455C4—82no—
456C4—82no—
457C4—82no—
458C4—161no—
459C4#162914yesdirect product factor
460C4C2×C4×SD1612yes—
461C4C4×AGL(1,ℤ/8)12yes—
462C4#310112yes—
463C4#310512yes—
464C2—48no—
465C2—84no—
466C2C2×#162911yescharacteristic
467C2#1848011yescharacteristic
468C2#1851712yes—
469C2C4×#45012yes—
470C2C4×#45311yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
socleC23C2×#120
prime radicalC2×D42C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#492C2semidirect
3. C4×#476C2semidirect
5. #9064C2semidirect
6. #8973C2semidirect
7. #8924C2semidirect
8. #8886C2semidirect
10. C4×#331C2semidirect
11. C4×D4⋊C8C2semidirect
22. C4×C4⋊Q8C22semidirect
27. #1987C22semidirect
30. #1956C22semidirect
31. #1948C22semidirect
34. #1844C22semidirect
37. C4×C4⋊C8C22semidirect
39. C42×C8C22semidirect
40. #1629C4direct (N × H)
45. #1296C22semidirect
46. #1279C22semidirect
47. #1279C22semidirect
74. #492C2×C4semidirect
76. #476C2×C4semidirect
123. #331C2×C4semidirect
125. D4⋊C8C2×C4semidirect
155. C4⋊Q8C22×C4semidirect
178. C4×D4SD16semidirect
220. C4⋊C8C22×C4semidirect
230. C4×C8C22×C4semidirect
384. D4C4×SD16semidirect
459. C4#1629direct (N × H)

Maximal subgroups

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

subgroupindex
C4×D422
C4×#4922
C4×#4762
C2×#16292
#90642
#89732
#89242
#88862
#84432
C4×#3312
C4×D4⋊C82