Finite Group Databasebeta

← C4×#1619 #209660

Subgroups — C4×#1619 #209660

Order 512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D42C211yesmaximal, characteristic, complemented
2C4×#493C211yesmaximal, characteristic, complemented
3C4×#459C212yesmaximal, complemented
4C2×#1619C211yesmaximal, characteristic
5#9061C211yesmaximal, characteristic, complemented
6#8977C212yesmaximal, complemented
7#8920C211yesmaximal, characteristic, complemented
8#8882C212yesmaximal, complemented
9#8443C211yesmaximal, characteristic, complemented
10C4×#331C211yesmaximal, characteristic, complemented
11C4×D4⋊C8C212yesmaximal, complemented
12C2×D42C2211yescharacteristic
13C22×C4×D4—22no—
14C2×#493C2211yescharacteristic
15C2×#459C2212yes—
16C2×C4×D8—22no—
17C2×C4×D8—22no—
18#2366C2211yescharacteristic
19#2361—22no—
20#2358—22no—
21D4×C4⋊C4C2212yes—
22D4×C22⋊C4—22no—
23C4×#127C2211yescharacteristic
24C4×#127C2211yescharacteristic, complemented
25C4×#121—22no—
26C4×#120—22no—
27C42×D4C2212yes—
28#1982C2212yescomplemented
29#1970—22no—
30#1957C2211yescharacteristic
31#1957C2211yescharacteristic, complemented
32#1947C2212yescomplemented
33#1925—22no—
34#1879—22no—
35#1845C2211yescharacteristic, complemented
36#1802C2212yes—
37C4×C4⋊C8C2212yescomplemented
38C4×#102—22no—
39C42×C8C2211yescharacteristic, complemented
40#1619C418yesdirect 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×D8—22no—
51C22×D8—22no—
52D42—22no—
53D42—24no—
54D42C2×C414yescomplemented
55C2×#127C2311yescharacteristic
56C2×#127C2311yescharacteristic
57C2×#121—22no—
58C2×#120—22no—
59C2×C4×D4—24no—
60C2×C4×D4—24no—
61C2×C4×D4—22no—
62C2×C4×D4—22no—
63C2×C4×D4—22no—
64C2×C4×D4—21no—
65C2×C4×D4—22no—
66C2×C4×D4—48no—
67C2×C4×D4—48no—
68C2×C4×D4D412yes—
69C2×C4×D4D412yes—
70C2×C4×D4D412yes—
71C2×C4×D4C2312yes—
72C22×C4⋊C4—22no—
73C22×C22⋊C4—24no—
74C22×C42—22no—
75#493—22no—
76#493C2×C414yescomplemented
77#459—24no—
78#459C2×C418yescomplemented
79C4×D8—48no—
80C4×D8—48no—
81C2×#107—22no—
82C2×#107—22no—
83C2×C4⋊C8C2312yes—
84C2×C4⋊C8C2312yes—
85C2×#102—22no—
86C2×#102—22no—
87C2×#102—22no—
88C2×#102—22no—
89C2×#102—22no—
90C2×#102—22no—
91C2×C4×C8—21no—
92C2×C4×C8—22no—
93C2×C4×C8—21no—
94C2×C4×C8C2311yescharacteristic
95C2×C4×C8C2311yescharacteristic
96#390—22no—
97#390—22no—
98#390—22no—
99#390—21no—
100#390D412yes—
101#389—22no—
102#388—24no—
103#386—24no—
104#386—24no—
105#386—22no—
106#385—22no—
107#385—24no—
108#384C2311yescharacteristic
109#384C2311yescharacteristic
110#380—22no—
111#379—22no—
112C4×C4⋊C4D412yes—
113C4×C4⋊C4D412yes—
114C4×C4⋊C4C2312yes—
115C4×C22⋊C4—22no—
116C4×C22⋊C4—22no—
117C4×C22⋊C4—22no—
118C4×C22⋊C4—22no—
119C43C2311yescharacteristic
120#340—22no—
121#340—22no—
122#336—22no—
123#331—22no—
124#331C2×C414yescomplemented
125D4⋊C8—24no—
126D4⋊C8C2×C418yescomplemented
127C25—22no—
128C22×D4—24no—
129C22×D4—28no—
130C22×D4—28no—
131C22×D4—22no—
132C22×D4—21no—
133C22×D4—22no—
134C22×D4—44no—
135C22×D4—44no—
136C22×D4—44no—
137C22×D4—44no—
138C22×D4C2×D412yes—
139C22×D4C2×D412yes—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—24no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—416no—
147C23×C4—41no—
148C23×C4—84no—
149C2×D8—28no—
150C2×D8—28no—
151C2×D8—44no—
152C2×D8—44no—
153C2×D8—44no—
154C2×D8—44no—
155C22×C8—21no—
156C22×C8—22no—
157C22×C8—21no—
158C22×C8—22no—
159#127—22no—
160#127—22no—
161#127—21no—
162#127C22×C412yes—
163#127C22×C412yescomplemented
164#127#4112yes—
165#121—28no—
166#121—28no—
167#120—28no—
168#120—28no—
169C4×D4—24no—
170C4×D4—24no—
171C4×D4—22no—
172C4×D4—22no—
173C4×D4—42no—
174C4×D4—44no—
175C4×D4—44no—
176C4×D4—416no—
177C4×D4—44no—
178C4×D4—416no—
179C4×D4—44no—
180C4×D4—44no—
181C4×D4—44no—
182C4×D4—44no—
183C4×D4—44no—
184C4×D4—44no—
185C4×D4—44no—
186C4×D4D818yescomplemented
187C4×D4C22×C414yes—
188C4×D4#4114yes—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4C2×D412yes—
196C2×C4⋊C4C2×D412yes—
197C2×C4⋊C4C2×D412yes—
198C2×C4⋊C4C2×D412yes—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—416no—
209C2×C22⋊C4—41no—
210C2×C22⋊C4—42no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—44no—
215C2×C42—44no—
216C2×C42C2×D412yes—
217C2×C42C2×D411yescharacteristic
218C2×C42C2×D411yescharacteristic
219C2×C42C2×D412yes—
220C2×C42C2411yescharacteristic
221#107—44no—
222#107—44no—
223C4⋊C8—22no—
224C4⋊C8—22no—
225C4⋊C8—22no—
226C4⋊C8C22×C414yescomplemented
227#102—28no—
228#102—44no—
229#102—44no—
230#102—44no—
231#102—44no—
232#102—44no—
233C4×C8—24no—
234C4×C8—21no—
235C4×C8—22no—
236C4×C8—42no—
237C4×C8—44no—
238C4×C8C22×C412yescomplemented
239#95—24no—
240#95—22no—
241#95—22no—
242#95—22no—
243C24—22no—
244C24—28no—
245C24—22no—
246C24—48no—
247C24—48no—
248C24—41no—
249C24—82no—
250C24—82no—
251C2×D4—216no—
252C2×D4—24no—
253C2×D4—24no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—24no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—416no—
265C2×D4—416no—
266C2×D4—416no—
267C2×D4—48no—
268C2×D4—48no—
269C2×D4—416no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4C4×D414yes—
281C2×D4C4×D414yes—
282C2×D4C2×D814yes—
283C2×D4#13514yes—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—28no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—44no—
292C22×C4—48no—
293C22×C4—48no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—44no—
299C22×C4—44no—
300C22×C4—48no—
301C22×C4—44no—
302C22×C4—48no—
303C22×C4—44no—
304C22×C4—41no—
305C22×C4—82no—
306C22×C4—82no—
307C22×C4—84no—
308C22×C4—832no—
309C22×C4—84no—
310C22×C4—82no—
311C22×C4#12011yescharacteristic
312C22×C4#12012yes—
313C22×C4#12011yescharacteristic
314C22×C4C22×D411yescharacteristic
315C22×C4C22×D412yes—
316D8—416no—
317D8—416no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—24no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—42no—
335C4⋊C4—48no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4C4×D414yes—
342C4⋊C4C2×D814yes—
343C22⋊C4—28no—
344C22⋊C4—24no—
345C22⋊C4—24no—
346C22⋊C4—28no—
347C22⋊C4—44no—
348C22⋊C4—48no—
349C22⋊C4—48no—
350C22⋊C4—48no—
351C22⋊C4—82no—
352C22⋊C4—82no—
353C22⋊C4—82no—
354C22⋊C4—84no—
355C42—22no—
356C42—22no—
357C42—22no—
358C42—41no—
359C42—42no—
360C42—42no—
361C42—44no—
362C42—44no—
363C42C2×D814yes—
364C42AGL(1,ℤ/8)14yes—
365C42C23×C411yescharacteristic
366C42C2×#4111yescharacteristic
367C42C2×#4112yes—
368C23—24no—
369C23—24no—
370C23—24no—
371C23—24no—
372C23—432no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—44no—
378C23—44no—
379C23—42no—
380C23—42no—
381C23—42no—
382C23—88no—
383C23—88no—
384C23—88no—
385C23—816no—
386C23—82no—
387C23—82no—
388C23—81no—
389C23—81no—
390C23C2×#12011yescharacteristic
391D4—24no—
392D4—24no—
393D4—24no—
394D4—44no—
395D4—44no—
396D4—432no—
397D4—44no—
398D4—44no—
399D4—44no—
400D4—44no—
401D4—44no—
402D4—44no—
403D4—82no—
404D4—82no—
405D4—82no—
406D4—82no—
407D4C4×D818yescomplemented
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—416no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—88no—
431C2×C4—88no—
432C2×C4—816no—
433C2×C4—88no—
434C2×C4—82no—
435C2×C4—81no—
436C2×C4—164no—
437C2×C4#44714yes—
438C2×C4#44714yes—
439C2×C4#45312yes—
440C2×C4C2×C4×D411yescharacteristic
441C2×C4C2×C4×D412yes—
442C2×C4#52511yescharacteristic
443C2×C4#52512yes—
444C2×C4C22×D812yes—
445C2×C4C2×#13512yes—
446C2×C4C2×AGL(1,ℤ/8)12yes—
447C2×C4#57512yes—
448C8—24no—
449C8—42no—
450C8—44no—
451C8—82no—
452C22—28no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—44no—
457C22—44no—
458C22—44no—
459C22—48no—
460C22—44no—
461C22—832no—
462C22—82no—
463C22—82no—
464C22—84no—
465C22—84no—
466C22—82no—
467C22—161no—
468C22—161no—
469C22—162no—
470C22C4×#12011yescharacteristic
471C22C2×#44712yes—
472C22#300212yes—
473C22C2×#45311yescharacteristic
474C22#301811yescharacteristic
475C4—24no—
476C4—21no—
477C4—21no—
478C4—44no—
479C4—41no—
480C4—44no—
481C4—82no—
482C4—82no—
483C4—161no—
484C4#161914yesdirect product factor
485C4C2×C4×D812yes—
486C4C4×AGL(1,ℤ/8)12yes—
487C4#310012yes—
488C4#310512yes—
489C2—48no—
490C2—84no—
491C2—162no—
492C2C2×#161911yescharacteristic
493C2#1848011yescharacteristic
494C2#1851612yes—
495C2C4×#44712yes—
496C2C4×#45311yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
socleC23C2×#120
prime radicalC2×#1619C2
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
1. C4×D42C2semidirect
2. C4×#493C2semidirect
3. C4×#459C2semidirect
5. #9061C2semidirect
6. #8977C2semidirect
7. #8920C2semidirect
8. #8882C2semidirect
9. #8443C2semidirect
10. C4×#331C2semidirect
11. C4×D4⋊C8C2semidirect
24. C4×#127C22semidirect
28. #1982C22semidirect
31. #1957C22semidirect
32. #1947C22semidirect
35. #1845C22semidirect
37. C4×C4⋊C8C22semidirect
39. C42×C8C22semidirect
40. #1619C4direct (N × H)
45. #1296C22semidirect
46. #1279C22semidirect
47. #1279C22semidirect
54. D42C2×C4semidirect
76. #493C2×C4semidirect
78. #459C2×C4semidirect
124. #331C2×C4semidirect
126. D4⋊C8C2×C4semidirect
163. #127C22×C4semidirect
186. C4×D4D8semidirect
226. C4⋊C8C22×C4semidirect
238. C4×C8C22×C4semidirect
407. D4C4×D8semidirect
484. C4#1619direct (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×#4932
C4×#4592
C2×#16192
#90612
#89772
#89202
#88822
#84432
C4×#3312
C4×D4⋊C82