Finite Group Databasebeta

← C2×#19465 #6354531

Subgroups — C2×#19465 #6354531

Order 512.

1878 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3226C211yesmaximal, characteristic, complemented
2C2×#3109C211yesmaximal, characteristic
3C22×#476C211yesmaximal, characteristic, complemented
4C2×#2974C211yesmaximal, characteristic, complemented
5#19465C2116yesmaximal, direct product factor
6C2×#1697C212yesmaximal, complemented
7C2×#1695C212yesmaximal, complemented
8C2×#1677C212yesmaximal, complemented
9C2×#1675C212yesmaximal, complemented
10C2×#1573C211yesmaximal, characteristic, complemented
11C2×#1558C211yesmaximal, characteristic, complemented
12C2×#1551C211yesmaximal, characteristic, complemented
13C2×#532C2211yescharacteristic
14C22×C4⋊Q8C2211yescharacteristic
15C22×C4×D4C2211yescharacteristic
16#3226—24no—
17#3226C2218yescomplemented
18C2×#500C2212yescomplemented
19C2×#486C2212yescomplemented
20#3109—24no—
21#3109C2218yes—
22C2×#481—21no—
23C2×#480—21no—
24C2×#480—21no—
25C2×#476—24no—
26C2×#476—21no—
27C2×#476—21no—
28C2×#476C2212yes—
29C2×#476C2212yes—
30C2×#476C2211yescharacteristic
31C2×#476C2211yescharacteristic
32C2×#476C2218yescomplemented
33C2×#474—22no—
34C2×#459C2211yescharacteristic
35C2×#459C2211yescharacteristic
36C2×#447—21no—
37#2974—24no—
38#2974C2218yescomplemented
39C2×#442—21no—
40C2×#442—21no—
41C2×#436C2212yes—
42C2×#435—22no—
43C2×C8×D4C2212yes—
44C2×#432C2211yescharacteristic
45C2×#432C2211yescharacteristic
46C2×#431C2211yescharacteristic
47C22×#106—21no—
48C22×C4⋊C8C2211yescharacteristic
49C22×#102—21no—
50C2×#407—21no—
51C22×C22⋊C8—21no—
52#1697C22116yescomplemented
53#1695C22116yescomplemented
54#1677C22116yescomplemented
55#1675C22116yescomplemented
56#1573C2218yescomplemented
57C2×#335C2212yescomplemented
58C2×#334C2212yescomplemented
59#1558C2218yescomplemented
60#1551C2218yescomplemented
61C2×#333C2212yescomplemented
62C2×#333C2212yescomplemented
63C2×#333C2212yescomplemented
64C2×#331C2212yescomplemented
65C22×#41—21no—
66C23×Q8—21no—
67C23×D4D411yescharacteristic
68C24×C4—21no—
69C22×D8—21no—
70C22×D8—21no—
71C22×M16—22no—
72C23×C8—21no—
73C23×C8—22no—
74#532—22no—
75#532—22no—
76#532—22no—
77#532C2314yes—
78C2×C4⋊Q8—22no—
79C2×C4⋊Q8—21no—
80C2×C4⋊Q8—21no—
81C2×C4⋊Q8—22no—
82C2×C4⋊Q8—21no—
83C2×C4⋊Q8—22no—
84C2×C4⋊Q8C2312yes—
85C2×C4⋊Q8C2311yescharacteristic
86C2×C4⋊Q8C2314yes—
87C2×#127C2311yescharacteristic
88C2×#124—21no—
89C2×#121—21no—
90C2×#121—21no—
91C2×C4×D4—21no—
92C2×C4×D4—22no—
93C2×C4×D4—21no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4—22no—
97C2×C4×D4D414yes—
98C2×C4×D4D411yescharacteristic
99C2×C4×D4D411yescharacteristic
100C2×C4×D4C2314yes—
101C2×C4×D4C2311yescharacteristic
102C2×C4×D4C2311yescharacteristic
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4D411yescharacteristic
106C22×C22⋊C4—21no—
107C22×C42C2311yescharacteristic
108#500—24no—
109#500C2318yescomplemented
110#486—24no—
111#486C2318yescomplemented
112#481—28no—
113#480—28no—
114#480—28no—
115#476—22no—
116#476—22no—
117#476—24no—
118#476—24no—
119#476—28no—
120#476—28no—
121#476C2314yes—
122#476C2314yes—
123#476C2318yes—
124#476C2318yes—
125#474—216no—
126#459—22no—
127#459—22no—
128#459C2314yes—
129#459C2314yes—
130#447—28no—
131#442—28no—
132#442—28no—
133#436—24no—
134#436C2318yes—
135#435—216no—
136C8×D4—24no—
137C8×D4C2318yes—
138#432—22no—
139#432—22no—
140#432C2314yes—
141#432C2314yes—
142#431D414yes—
143#431C2314yes—
144C2×#107—22no—
145C2×#107—22no—
146C2×#106—21no—
147C2×#106—21no—
148C2×#106—22no—
149C2×#106—22no—
150C2×#106—28no—
151C2×C4⋊C8—21no—
152C2×C4⋊C8—22no—
153C2×C4⋊C8D412yes—
154C2×C4⋊C8C2312yes—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2311yescharacteristic
157C2×C4⋊C8C2311yescharacteristic
158C2×C4⋊C8C2314yes—
159C2×#102—22no—
160C2×#102—22no—
161C2×#102—28no—
162C2×#102—21no—
163C2×#102—21no—
164C2×#102—22no—
165C2×#102—22no—
166C2×#102—21no—
167C2×#102—21no—
168#407—28no—
169C2×C22⋊C8—21no—
170C2×C22⋊C8—21no—
171C2×C22⋊C8—22no—
172C2×C22⋊C8—22no—
173C2×C22⋊C8—28no—
174C2×C22⋊C8D411yescharacteristic
175C2×C22⋊C8D411yescharacteristic
176C2×#97—21no—
177C2×#97—21no—
178C2×C4×C8C2312yes—
179#335C2318yescomplemented
180#334C2318yescomplemented
181#333C2318yescomplemented
182#333C2318yescomplemented
183#333C2318yescomplemented
184#331C2318yescomplemented
185C25—21no—
186C2×#41—24no—
187C2×#41—42no—
188C2×#41—84no—
189C22×Q8—21no—
190C22×Q8—24no—
191C22×Q8—22no—
192C22×Q8—42no—
193C22×Q8—41no—
194C22×Q8—84no—
195C22×D4—24no—
196C22×D4—22no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—42no—
202C22×D4—41no—
203C22×D4C2×D411yescharacteristic
204C22×D4C2×D414yes—
205C22×D4C2×D411yescharacteristic
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—41no—
214C23×C4—41no—
215C23×C4—84no—
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4#4111yescharacteristic
219C2×D8—24no—
220C2×D8—24no—
221C2×D8—44no—
222C2×D8—44no—
223C2×M16—28no—
224C2×M16—84no—
225C22×C8—22no—
226C22×C8—24no—
227C22×C8—22no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—28no—
231C22×C8—44no—
232C22×C8—84no—
233C22×C8C2×D412yes—
234C22×C8C2×D412yes—
235C4⋊Q8—24no—
236C4⋊Q8—24no—
237C4⋊Q8—22no—
238C4⋊Q8—22no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—24no—
242C4⋊Q8—22no—
243C4⋊Q8—21no—
244C4⋊Q8—42no—
245C4⋊Q8—42no—
246C4⋊Q8—42no—
247C4⋊Q8C2414yes—
248C4⋊Q8C2412yes—
249#127—21no—
250#127—21no—
251#127—21no—
252#127C2412yes—
253#124—24no—
254#124—42no—
255#121—24no—
256#121—24no—
257#121—42no—
258#121—42no—
259C4×D4—24no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4—24no—
263C4×D4—21no—
264C4×D4—24no—
265C4×D4—21no—
266C4×D4—24no—
267C4×D4—24no—
268C4×D4—24no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—42no—
272C4×D4—42no—
273C4×D4C2×D414yes—
274C4×D4C2×D414yes—
275C4×D4C2×D412yes—
276C4×D4C2×D412yes—
277C4×D4C2412yes—
278C4×D4C2412yes—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4C2×D411yescharacteristic
292C2×C4⋊C4C2×D411yescharacteristic
293C2×C4⋊C4C2×D414yes—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—41no—
301C2×C22⋊C4—41no—
302C2×C42C2×D411yescharacteristic
303C2×C42C2×D411yescharacteristic
304C2×C42C2×D412yes—
305C2×C42C2×D412yes—
306C2×C42#4111yescharacteristic
307C2×C42#4112yes—
308C2×C42C2411yescharacteristic
309C2×C42C2412yes—
310#107—28no—
311#107—28no—
312#106—28no—
313#106—28no—
314#106—24no—
315#106—24no—
316C4⋊C8—24no—
317C4⋊C8—22no—
318C4⋊C8—22no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8C2×D418yes—
322C4⋊C8C2414yes—
323C4⋊C8C2414yes—
324C4⋊C8C2412yes—
325C4⋊C8C2412yes—
326#102—28no—
327#102—28no—
328#102—24no—
329#102—24no—
330#102—28no—
331#102—28no—
332#102—24no—
333#102—24no—
334C22⋊C8—24no—
335C22⋊C8—24no—
336C22⋊C8—28no—
337C22⋊C8—28no—
338C22⋊C8C2×D414yes—
339C22⋊C8C2×D414yes—
340#97—24no—
341#97—24no—
342C4×C8C2×D414yes—
343C4×C8C2414yes—
344C24—21no—
345C24—21no—
346C24—24no—
347C24—44no—
348C24—44no—
349C24—41no—
350C24—82no—
351C24#12111yescharacteristic
352#41—88no—
353#41—88no—
354C2×Q8—22no—
355C2×Q8—24no—
356C2×Q8—41no—
357C2×Q8—44no—
358C2×Q8—42no—
359C2×Q8—84no—
360C2×Q8—88no—
361C2×Q8—84no—
362C2×Q8—88no—
363C2×Q8—82no—
364C2×D4—28no—
365C2×D4—21no—
366C2×D4—24no—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—44no—
375C2×D4—48no—
376C2×D4—44no—
377C2×D4—44no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—44no—
384C2×D4—82no—
385C2×D4—84no—
386C2×D4#13714yes—
387C2×D4C22×D412yes—
388C2×D4C22×D412yes—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—41no—
406C22×C4—42no—
407C22×C4—44no—
408C22×C4—88no—
409C22×C4—88no—
410C22×C4—82no—
411C22×C4—82no—
412C22×C4—84no—
413C22×C4—82no—
414C22×C4—84no—
415C22×C4#12112yes—
416C22×C4#12112yes—
417C22×C4#12112yes—
418C22×C4#12111yescharacteristic
419C22×C4#12111yescharacteristic
420C22×C4#12111yescharacteristic
421C22×C4C22×D412yes—
422C22×C4C22×D412yes—
423C22×C4C22×D411yescharacteristic
424C22×C4C22×D411yescharacteristic
425C22×C4C2×#4112yes—
426C22×C4C2×#4111yescharacteristic
427D8—48no—
428D8—48no—
429M16—88no—
430C2×C8—24no—
431C2×C8—24no—
432C2×C8—24no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—24no—
436C2×C8—48no—
437C2×C8—42no—
438C2×C8—44no—
439C2×C8—42no—
440C2×C8—44no—
441C2×C8—88no—
442C2×C8C22×D414yes—
443C2×C8C22×D414yes—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—44no—
452C4⋊C4—44no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4C22×D412yes—
458C4⋊C4C22×D412yes—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—44no—
466C22⋊C4—44no—
467C42#12112yes—
468C42#12112yes—
469C42#12112yes—
470C42C22×D411yescharacteristic
471C42C22×D412yes—
472C42C22×D412yes—
473C42C22×D411yescharacteristic
474C42C2×#4112yes—
475C42C2×#4111yescharacteristic
476C42C2511yescharacteristic
477C23—22no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—22no—
482C23—48no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—48no—
488C23—42no—
489C23—42no—
490C23—84no—
491C23—816no—
492C23—82no—
493C23—82no—
494C23—82no—
495C23#47214yes—
496C23C2×#12112yes—
497C23C2×#12111yescharacteristic
498Q8—84no—
499Q8—82no—
500Q8—88no—
501Q8—84no—
502Q8—82no—
503D4—24no—
504D4—22no—
505D4—22no—
506D4—22no—
507D4—48no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—44no—
512D4—82no—
513D4—82no—
514D4—88no—
515D4—82no—
516D4—82no—
517D4C2×#13714yes—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—84no—
540C2×C4—84no—
541C2×C4—88no—
542C2×C4—84no—
543C2×C4—82no—
544C2×C4—88no—
545C2×C4—84no—
546C2×C4C2×#12112yes—
547C2×C4C2×#12111yescharacteristic
548C2×C4C2×#12112yes—
549C2×C4C2×#12112yes—
550C2×C4C2×#12111yescharacteristic
551C2×C4C2×#12111yescharacteristic
552C2×C4C2×#13712yes—
553C2×C4#57512yes—
554C2×C4#57714yes—
555C2×C4C23×D411yescharacteristic
556C2×C4C23×D411yescharacteristic
557C2×C4C22×#4111yescharacteristic
558C8—24no—
559C8—24no—
560C8—42no—
561C8—44no—
562C8—42no—
563C8—44no—
564C22—22no—
565C22—28no—
566C22—22no—
567C22—24no—
568C22—42no—
569C22—48no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—816no—
575C22—84no—
576C22—82no—
577C22—82no—
578C22—82no—
579C22—164no—
580C22#304212yes—
581C22#305612yes—
582C22C2×#47214yes—
583C22C2×#47212yes—
584C22C22×#12111yescharacteristic
585C4—22no—
586C4—22no—
587C4—22no—
588C4—21no—
589C4—21no—
590C4—42no—
591C4—42no—
592C4—82no—
593C4—84no—
594C4#304212yes—
595C4#305612yes—
596C4C22×#13711yescharacteristic
597C4C2×#57511yescharacteristic
598C4C2×#57712yes—
599C2—24no—
600C2—44no—
601C2—82no—
602C2—162no—
603C2#1946514yesdirect product factor
604C2C2×#304211yescharacteristic
605C2C2×#305611yescharacteristic
606C2C22×#47211yescharacteristic
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×#3226C2semidirect
3. C22×#476C2semidirect
4. C2×#2974C2semidirect
5. #19465C2direct (N × H)
6. C2×#1697C2semidirect
7. C2×#1695C2semidirect
8. C2×#1677C2semidirect
9. C2×#1675C2semidirect
10. C2×#1573C2semidirect
11. C2×#1558C2semidirect
12. C2×#1551C2semidirect
17. #3226C22semidirect
18. C2×#500C22semidirect
19. C2×#486C22semidirect
32. C2×#476C22semidirect
38. #2974C22semidirect
52. #1697C22semidirect
53. #1695C22semidirect
54. #1677C22semidirect
55. #1675C22semidirect
56. #1573C22semidirect
57. C2×#335C22semidirect
58. C2×#334C22semidirect
59. #1558C22semidirect
60. #1551C22semidirect
61. C2×#333C22semidirect
62. C2×#333C22semidirect
63. C2×#333C22semidirect
64. C2×#331C22semidirect
109. #500C23semidirect
111. #486C23semidirect
179. #335C23semidirect
180. #334C23semidirect
181. #333C23semidirect
182. #333C23semidirect
183. #333C23semidirect
184. #331C23semidirect
603. C2#19465direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32262
C2×#31092
C22×#4762
C2×#29742
#194652
C2×#16972
C2×#16952
C2×#16772
C2×#16752
C2×#15732
C2×#15582
C2×#15512