Finite Group Databasebeta

← C2×#19462 #6354528

Subgroups — C2×#19462 #6354528

Order 512.

1986 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3227C211yesmaximal, characteristic, complemented
2C2×#3109C211yesmaximal, characteristic
3C22×#461C211yesmaximal, characteristic, complemented
4C2×#2974C211yesmaximal, characteristic, complemented
5#19462C2116yesmaximal, direct product factor
6C2×#1701C212yesmaximal, complemented
7C2×#1691C212yesmaximal, complemented
8C2×#1681C212yesmaximal, complemented
9C2×#1671C212yesmaximal, complemented
10C2×#1573C211yesmaximal, characteristic, complemented
11C2×#1556C211yesmaximal, characteristic, complemented
12C2×#1551C211yesmaximal, characteristic, complemented
13C23×SD16—21no—
14C2×#532C2211yescharacteristic
15C22×C4⋊Q8C2211yescharacteristic
16C22×C4×D4C2211yescharacteristic
17#3227—24no—
18#3227C2218yescomplemented
19C2×#498C2212yescomplemented
20C2×#486C2212yescomplemented
21#3109—24no—
22#3109C2218yes—
23C2×#481—21no—
24C2×#481—21no—
25C2×#481—21no—
26C2×#476—22no—
27C2×#476C2211yescharacteristic
28C2×#476C2211yescharacteristic
29C2×#461—24no—
30C2×#461—21no—
31C2×#461—21no—
32C2×#461C2212yes—
33C2×#461C2212yes—
34C2×#461C2218yescomplemented
35C2×#459C2211yescharacteristic
36C2×#459C2211yescharacteristic
37C2×#447—21no—
38#2974—24no—
39#2974C2218yescomplemented
40C2×#442—21no—
41C2×#442—21no—
42C2×#436C2212yes—
43C2×#435—22no—
44C2×C8×D4C2212yes—
45C2×#432C2211yescharacteristic
46C2×#432C2211yescharacteristic
47C2×#431C2211yescharacteristic
48C22×C4⋊C8C2211yescharacteristic
49C22×#103—21no—
50C2×#407—21no—
51C22×C22⋊C8—21no—
52#1701C22116yescomplemented
53#1691C22116yescomplemented
54#1681C22116yescomplemented
55#1671C22116yescomplemented
56#1573C2218yescomplemented
57C2×#335C2212yescomplemented
58C2×#334C2212yescomplemented
59#1556C2218yescomplemented
60#1551C2218yescomplemented
61C2×#333C2212yescomplemented
62C2×#332C2212yescomplemented
63C2×#332C2212yescomplemented
64C2×#331C2212yescomplemented
65C22×#41—21no—
66C23×Q8—21no—
67C23×D4D411yescharacteristic
68C24×C4—21no—
69C22×SD16—22no—
70C22×SD16—22no—
71C22×SD16—28no—
72C22×SD16—48no—
73C22×D8—21no—
74C22×D8—21no—
75C22×M16—22no—
76C23×C8—21no—
77C23×C8—22no—
78#532—22no—
79#532—22no—
80#532—22no—
81#532C2314yes—
82C2×C4⋊Q8—22no—
83C2×C4⋊Q8—21no—
84C2×C4⋊Q8—21no—
85C2×C4⋊Q8—22no—
86C2×C4⋊Q8—21no—
87C2×C4⋊Q8—22no—
88C2×C4⋊Q8C2312yes—
89C2×C4⋊Q8C2311yescharacteristic
90C2×C4⋊Q8C2314yes—
91C2×#127C2311yescharacteristic
92C2×#124—21no—
93C2×#121—21no—
94C2×#121—21no—
95C2×C4×D4—21no—
96C2×C4×D4—22no—
97C2×C4×D4—21no—
98C2×C4×D4—21no—
99C2×C4×D4—21no—
100C2×C4×D4—22no—
101C2×C4×D4D414yes—
102C2×C4×D4D411yescharacteristic
103C2×C4×D4D411yescharacteristic
104C2×C4×D4C2314yes—
105C2×C4×D4C2311yescharacteristic
106C2×C4×D4C2311yescharacteristic
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4D411yescharacteristic
110C22×C22⋊C4—21no—
111C22×C42C2311yescharacteristic
112#498—24no—
113#498C2318yescomplemented
114#486—24no—
115#486C2318yescomplemented
116#481—28no—
117#481—28no—
118#481—28no—
119#476—22no—
120#476—22no—
121#476—216no—
122#476C2314yes—
123#476C2314yes—
124#461—24no—
125#461—24no—
126#461—28no—
127#461—28no—
128#461C2318yes—
129#461C2318yes—
130#459—22no—
131#459—22no—
132#459C2314yes—
133#459C2314yes—
134#447—28no—
135#442—28no—
136#442—28no—
137#436—24no—
138#436C2318yes—
139#435—216no—
140C8×D4—24no—
141C8×D4C2318yes—
142#432—22no—
143#432—22no—
144#432C2314yes—
145#432C2314yes—
146#431D414yes—
147#431C2314yes—
148C2×#106—22no—
149C2×#106—22no—
150C2×#106—21no—
151C2×#106—21no—
152C2×C4⋊C8—21no—
153C2×C4⋊C8—22no—
154C2×C4⋊C8D412yes—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2312yes—
157C2×C4⋊C8C2311yescharacteristic
158C2×C4⋊C8C2311yescharacteristic
159C2×C4⋊C8C2314yes—
160C2×#103—22no—
161C2×#103—22no—
162C2×#103—28no—
163C2×#102—21no—
164C2×#102—21no—
165C2×#102—22no—
166C2×#102—22no—
167C2×#102—21no—
168C2×#102—21no—
169#407—28no—
170C2×C22⋊C8—21no—
171C2×C22⋊C8—21no—
172C2×C22⋊C8—22no—
173C2×C22⋊C8—22no—
174C2×C22⋊C8—28no—
175C2×C22⋊C8D411yescharacteristic
176C2×C22⋊C8D411yescharacteristic
177C2×#97—21no—
178C2×#97—21no—
179C2×C4×C8C2312yes—
180#335C2318yescomplemented
181#334C2318yescomplemented
182#333C2318yescomplemented
183#332C2318yescomplemented
184#332C2318yescomplemented
185#331C2318yescomplemented
186C25—21no—
187C2×#41—24no—
188C2×#41—42no—
189C2×#41—84no—
190C22×Q8—24no—
191C22×Q8—22no—
192C22×Q8—21no—
193C22×Q8—44no—
194C22×Q8—44no—
195C22×Q8—42no—
196C22×Q8—41no—
197C22×D4—24no—
198C22×D4—22no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—42no—
204C22×D4—41no—
205C22×D4C2×D411yescharacteristic
206C22×D4C2×D414yes—
207C22×D4C2×D411yescharacteristic
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—41no—
216C23×C4—41no—
217C23×C4—84no—
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4#4111yescharacteristic
221C2×SD16—28no—
222C2×SD16—28no—
223C2×SD16—432no—
224C2×SD16—48no—
225C2×SD16—48no—
226C2×D8—24no—
227C2×D8—24no—
228C2×D8—44no—
229C2×D8—44no—
230C2×M16—28no—
231C2×M16—84no—
232C22×C8—22no—
233C22×C8—24no—
234C22×C8—22no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—28no—
238C22×C8—44no—
239C22×C8—84no—
240C22×C8C2×D412yes—
241C22×C8C2×D412yes—
242C4⋊Q8—24no—
243C4⋊Q8—22no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—24no—
247C4⋊Q8—22no—
248C4⋊Q8—24no—
249C4⋊Q8—22no—
250C4⋊Q8—21no—
251C4⋊Q8—42no—
252C4⋊Q8—42no—
253C4⋊Q8—42no—
254C4⋊Q8C2414yes—
255C4⋊Q8C2412yes—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C2412yes—
260#124—24no—
261#124—42no—
262#121—24no—
263#121—24no—
264#121—42no—
265#121—42no—
266C4×D4—24no—
267C4×D4—22no—
268C4×D4—22no—
269C4×D4—24no—
270C4×D4—21no—
271C4×D4—24no—
272C4×D4—21no—
273C4×D4—24no—
274C4×D4—24no—
275C4×D4—24no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—42no—
279C4×D4—42no—
280C4×D4C2×D414yes—
281C4×D4C2×D414yes—
282C4×D4C2×D412yes—
283C4×D4C2×D412yes—
284C4×D4C2412yes—
285C4×D4C2412yes—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4C2×D411yescharacteristic
299C2×C4⋊C4C2×D411yescharacteristic
300C2×C4⋊C4C2×D414yes—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—41no—
308C2×C22⋊C4—41no—
309C2×C42C2×D411yescharacteristic
310C2×C42C2×D411yescharacteristic
311C2×C42C2×D412yes—
312C2×C42C2×D412yes—
313C2×C42#4111yescharacteristic
314C2×C42#4112yes—
315C2×C42C2411yescharacteristic
316C2×C42C2412yes—
317#106—28no—
318#106—28no—
319#106—24no—
320#106—24no—
321C4⋊C8—24no—
322C4⋊C8—22no—
323C4⋊C8—22no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8C2×D418yes—
327C4⋊C8C2414yes—
328C4⋊C8C2414yes—
329C4⋊C8C2412yes—
330C4⋊C8C2412yes—
331#103—28no—
332#103—28no—
333#102—24no—
334#102—24no—
335#102—28no—
336#102—28no—
337#102—24no—
338#102—24no—
339C22⋊C8—24no—
340C22⋊C8—24no—
341C22⋊C8—28no—
342C22⋊C8—28no—
343C22⋊C8C2×D414yes—
344C22⋊C8C2×D414yes—
345#97—24no—
346#97—24no—
347C4×C8C2×D414yes—
348C4×C8C2414yes—
349C24—21no—
350C24—21no—
351C24—24no—
352C24—44no—
353C24—44no—
354C24—41no—
355C24—82no—
356C24#12111yescharacteristic
357#41—88no—
358#41—88no—
359C2×Q8—24no—
360C2×Q8—22no—
361C2×Q8—48no—
362C2×Q8—48no—
363C2×Q8—41no—
364C2×Q8—44no—
365C2×Q8—42no—
366C2×Q8—44no—
367C2×Q8—44no—
368C2×Q8—84no—
369C2×Q8—88no—
370C2×Q8—82no—
371C2×D4—28no—
372C2×D4—21no—
373C2×D4—24no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—44no—
382C2×D4—48no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—44no—
391C2×D4—82no—
392C2×D4—84no—
393C2×D4AGL(1,ℤ/8)14yes—
394C2×D4C22×D412yes—
395C2×D4C22×D412yes—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—44no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—41no—
413C22×C4—42no—
414C22×C4—44no—
415C22×C4—88no—
416C22×C4—88no—
417C22×C4—82no—
418C22×C4—82no—
419C22×C4—84no—
420C22×C4—82no—
421C22×C4—84no—
422C22×C4#12112yes—
423C22×C4#12112yes—
424C22×C4#12112yes—
425C22×C4#12111yescharacteristic
426C22×C4#12111yescharacteristic
427C22×C4#12111yescharacteristic
428C22×C4C22×D412yes—
429C22×C4C22×D412yes—
430C22×C4C22×D411yescharacteristic
431C22×C4C22×D411yescharacteristic
432C22×C4C2×#4112yes—
433C22×C4C2×#4111yescharacteristic
434SD16—416no—
435SD16—416no—
436D8—48no—
437D8—48no—
438M16—88no—
439C2×C8—24no—
440C2×C8—24no—
441C2×C8—24no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—24no—
445C2×C8—48no—
446C2×C8—44no—
447C2×C8—42no—
448C2×C8—42no—
449C2×C8—44no—
450C2×C8—88no—
451C2×C8C22×D414yes—
452C2×C8C22×D414yes—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—44no—
461C4⋊C4—42no—
462C4⋊C4—44no—
463C4⋊C4—42no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C22×D412yes—
467C4⋊C4C22×D412yes—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C42#12112yes—
477C42#12112yes—
478C42#12112yes—
479C42C22×D411yescharacteristic
480C42C22×D412yes—
481C42C22×D412yes—
482C42C22×D411yescharacteristic
483C42C2×#4112yes—
484C42C2×#4111yescharacteristic
485C42C2511yescharacteristic
486C23—22no—
487C23—22no—
488C23—22no—
489C23—24no—
490C23—22no—
491C23—48no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—48no—
497C23—42no—
498C23—42no—
499C23—84no—
500C23—816no—
501C23—82no—
502C23—82no—
503C23—82no—
504C23#47114yes—
505C23C2×#12112yes—
506C23C2×#12111yescharacteristic
507Q8—44no—
508Q8—44no—
509Q8—82no—
510Q8—88no—
511Q8—82no—
512Q8—84no—
513D4—24no—
514D4—22no—
515D4—22no—
516D4—22no—
517D4—48no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—44no—
522D4—82no—
523D4—82no—
524D4—88no—
525D4—82no—
526D4—82no—
527D4C2×AGL(1,ℤ/8)14yes—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—84no—
550C2×C4—84no—
551C2×C4—88no—
552C2×C4—84no—
553C2×C4—88no—
554C2×C4—84no—
555C2×C4—82no—
556C2×C4C2×#12112yes—
557C2×C4C2×#12111yescharacteristic
558C2×C4C2×#12112yes—
559C2×C4C2×#12112yes—
560C2×C4C2×#12111yescharacteristic
561C2×C4C2×#12111yescharacteristic
562C2×C4C2×AGL(1,ℤ/8)12yes—
563C2×C4#57512yes—
564C2×C4#57714yes—
565C2×C4C23×D411yescharacteristic
566C2×C4C23×D411yescharacteristic
567C2×C4C22×#4111yescharacteristic
568C8—24no—
569C8—24no—
570C8—44no—
571C8—42no—
572C8—42no—
573C8—44no—
574C22—22no—
575C22—28no—
576C22—22no—
577C22—24no—
578C22—42no—
579C22—48no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—816no—
585C22—84no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—164no—
590C22#304212yes—
591C22#305512yes—
592C22C2×#47114yes—
593C22C2×#47112yes—
594C22C22×#12111yescharacteristic
595C4—22no—
596C4—22no—
597C4—22no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—42no—
602C4—84no—
603C4—82no—
604C4#304212yes—
605C4#305512yes—
606C4C22×AGL(1,ℤ/8)11yescharacteristic
607C4C2×#57511yescharacteristic
608C4C2×#57712yes—
609C2—24no—
610C2—44no—
611C2—82no—
612C2—162no—
613C2#1946214yesdirect product factor
614C2C2×#304211yescharacteristic
615C2C2×#305511yescharacteristic
616C2C22×#47111yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
prime radicalC2×#3109C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3227C2semidirect
3. C22×#461C2semidirect
4. C2×#2974C2semidirect
5. #19462C2direct (N × H)
6. C2×#1701C2semidirect
7. C2×#1691C2semidirect
8. C2×#1681C2semidirect
9. C2×#1671C2semidirect
10. C2×#1573C2semidirect
11. C2×#1556C2semidirect
12. C2×#1551C2semidirect
18. #3227C22semidirect
19. C2×#498C22semidirect
20. C2×#486C22semidirect
34. C2×#461C22semidirect
39. #2974C22semidirect
52. #1701C22semidirect
53. #1691C22semidirect
54. #1681C22semidirect
55. #1671C22semidirect
56. #1573C22semidirect
57. C2×#335C22semidirect
58. C2×#334C22semidirect
59. #1556C22semidirect
60. #1551C22semidirect
61. C2×#333C22semidirect
62. C2×#332C22semidirect
63. C2×#332C22semidirect
64. C2×#331C22semidirect
113. #498C23semidirect
115. #486C23semidirect
180. #335C23semidirect
181. #334C23semidirect
182. #333C23semidirect
183. #332C23semidirect
184. #332C23semidirect
185. #331C23semidirect
613. C2#19462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32272
C2×#31092
C22×#4612
C2×#29742
#194622
C2×#17012
C2×#16912
C2×#16812
C2×#16712
C2×#15732
C2×#15562
C2×#15512