Finite Group Databasebeta

← C2×#14882 #607869

Subgroups — C2×#14882 #607869

Order 512.

5906 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Q8C211yesmaximal, characteristic, complemented
2C22×#397C211yesmaximal, characteristic
3C22×#393C211yesmaximal, characteristic
4C22×#388C211yesmaximal, characteristic
5#14882C2116yesmaximal, direct product factor
6C2×#1446C211yesmaximal, characteristic, complemented
7C2×#1445C211yesmaximal, characteristic, complemented
8C2×#1442C212yesmaximal, complemented
9C2×#1439C212yesmaximal
10C2×#1437C212yesmaximal
11C2×#1436C212yesmaximal, complemented
12C2×#1434C211yesmaximal, characteristic, complemented
13C24×Q8C2211yescharacteristic
14C22×C4×Q8—28no—
15C22×C4×Q8—28no—
16C22×C4×Q8—28no—
17C22×C4×Q8C2218yescomplemented
18C23×C4⋊C4C2212yes—
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2212yes—
26C23×C42C2212yes—
27C23×C42C2211yescharacteristic
28C2×#397—28no—
29C2×#397C2218yes—
30C2×#393—28no—
31C2×#393C2218yes—
32C2×#388—28no—
33C2×#388C2218yes—
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2212yes—
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2212yes—
44C22×#95C2212yes—
45C22×#95C2212yes—
46#1446C2218yescomplemented
47#1445C2218yescomplemented
48#1442C22116yescomplemented
49#1439C22116yes—
50#1437C22116yes—
51#1436C22116yescomplemented
52#1434C2218yescomplemented
53C26C2311yescharacteristic
54C23×Q8—24no—
55C23×Q8—24no—
56C23×Q8—28no—
57C23×Q8—28no—
58C23×Q8D418yes—
59C23×Q8C2314yes—
60C24×C4C2311yescharacteristic
61C24×C4C2312yes—
62C24×C4C2311yescharacteristic
63C24×C4C2312yes—
64C24×C4C2311yescharacteristic
65C24×C4C2312yes—
66C24×C4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C24×C4C2312yes—
69C24×C4C2311yescharacteristic
70C2×C4×Q8—2128no—
71C2×C4×Q8—232no—
72C2×C4×Q8—232no—
73C2×C4×Q8—232no—
74C22×C4⋊C4—28no—
75C22×C4⋊C4—28no—
76C22×C4⋊C4—28no—
77C22×C4⋊C4—24no—
78C22×C4⋊C4—24no—
79C22×C4⋊C4—24no—
80C22×C4⋊C4—28no—
81C22×C4⋊C4D418yes—
82C22×C4⋊C4C2318yes—
83C22×C4⋊C4C2314yes—
84C22×C4⋊C4C2314yes—
85C22×C22⋊C4—24no—
86C22×C22⋊C4—24no—
87C22×C22⋊C4—24no—
88C22×C22⋊C4—28no—
89C22×C22⋊C4—24no—
90C22×C22⋊C4—28no—
91C22×C22⋊C4—28no—
92C22×C22⋊C4—24no—
93C22×C22⋊C4—24no—
94C22×C22⋊C4—24no—
95C22×C22⋊C4—28no—
96C22×C22⋊C4—28no—
97C22×C22⋊C4—28no—
98C22×C22⋊C4—44no—
99C22×C22⋊C4C2314yes—
100C22×C22⋊C4C2318yes—
101C22×C22⋊C4C2314yes—
102C22×C22⋊C4C2314yes—
103C22×C22⋊C4C2318yes—
104C22×C42—28no—
105C22×C42—28no—
106C22×C42—28no—
107C22×C42—24no—
108C22×C42—24no—
109C22×C42D418yes—
110C22×C42C2318yes—
111C22×C42C2314yes—
112#397—232no—
113#393—232no—
114#388—232no—
115C2×#95—24no—
116C2×#95—28no—
117C2×#95—28no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—28no—
122C2×#95—28no—
123C2×#95—28no—
124C2×#95—28no—
125C2×#95—44no—
126C2×#95—44no—
127C2×#95C2314yes—
128C2×#95C2318yes—
129C2×#95C2314yes—
130C2×#95C2318yes—
131C2×#95C2318yes—
132C2×#95C2318yes—
133C2×#95C2318yes—
134C2×#95C2318yes—
135C2×#95C2314yes—
136C2×#95C2314yes—
137C2×#95C2318yes—
138C2×#95C2318yes—
139C25—22no—
140C25—22no—
141C25—22no—
142C25—22no—
143C25—24no—
144C25—24no—
145C25—24no—
146C25—22no—
147C25—22no—
148C25—24no—
149C25#4114yes—
150C25C2412yes—
151C25C2411yescharacteristic
152C22×Q8—232no—
153C22×Q8—232no—
154C22×Q8—264no—
155C22×Q8—232no—
156C22×Q8—264no—
157C22×Q8—28no—
158C22×Q8—28no—
159C22×Q8—216no—
160C22×Q8—216no—
161C22×Q8C2×D4116yes—
162C23×C4—24no—
163C23×C4—24no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—24no—
167C23×C4—24no—
168C23×C4—24no—
169C23×C4—24no—
170C23×C4—24no—
171C23×C4—22no—
172C23×C4—24no—
173C23×C4—22no—
174C23×C4—24no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—24no—
180C23×C4—24no—
181C23×C4—24no—
182C23×C4—24no—
183C23×C4—24no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—24no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—24no—
191C23×C4—22no—
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—24no—
195C23×C4—24no—
196C23×C4—24no—
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—24no—
204C23×C4—24no—
205C23×C4—22no—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—22no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4C2×D414yes—
212C23×C4C2×D418yes—
213C23×C4C2×D414yes—
214C23×C4C2×D414yes—
215C23×C4C2×D414yes—
216C23×C4C2×D418yes—
217C23×C4C2×D414yes—
218C23×C4#4114yes—
219C23×C4#4118yes—
220C23×C4#4118yes—
221C23×C4#4118yes—
222C23×C4C2412yes—
223C23×C4C2414yes—
224C23×C4C2414yes—
225C23×C4C2412yes—
226C23×C4C2414yes—
227C23×C4C2412yes—
228C23×C4C2412yes—
229C23×C4C2412yes—
230C23×C4C2414yes—
231C23×C4C2412yes—
232C4×Q8—2256no—
233C2×C4⋊C4—264no—
234C2×C4⋊C4—232no—
235C2×C4⋊C4—216no—
236C2×C4⋊C4—216no—
237C2×C4⋊C4—216no—
238C2×C4⋊C4—28no—
239C2×C4⋊C4—28no—
240C2×C4⋊C4—28no—
241C2×C4⋊C4—216no—
242C2×C4⋊C4—416no—
243C2×C4⋊C4C2×D4116yes—
244C2×C22⋊C4—232no—
245C2×C22⋊C4—28no—
246C2×C22⋊C4—28no—
247C2×C22⋊C4—28no—
248C2×C22⋊C4—216no—
249C2×C22⋊C4—28no—
250C2×C22⋊C4—28no—
251C2×C22⋊C4—28no—
252C2×C22⋊C4—216no—
253C2×C22⋊C4—216no—
254C2×C22⋊C4—28no—
255C2×C22⋊C4—216no—
256C2×C22⋊C4—216no—
257C2×C22⋊C4—216no—
258C2×C22⋊C4—48no—
259C2×C22⋊C4—432no—
260C2×C22⋊C4—416no—
261C2×C22⋊C4—432no—
262C2×C22⋊C4—416no—
263C2×C42—264no—
264C2×C42—232no—
265C2×C42—216no—
266C2×C42—216no—
267C2×C42—216no—
268C2×C42—28no—
269C2×C42—28no—
270C2×C42C2×D4116yes—
271#95—28no—
272#95—28no—
273#95—28no—
274#95—216no—
275#95—216no—
276#95—28no—
277#95—216no—
278#95—216no—
279#95—216no—
280#95—216no—
281#95—48no—
282#95—48no—
283C24—28no—
284C24—216no—
285C24—28no—
286C24—28no—
287C24—216no—
288C24—22no—
289C24—22no—
290C24—22no—
291C24—22no—
292C24—24no—
293C24—24no—
294C24—24no—
295C24—22no—
296C24—22no—
297C24—24no—
298C24—44no—
299C24—48no—
300C24—44no—
301C24—44no—
302C24—48no—
303C24—44no—
304C24—48no—
305C24—44no—
306C24—44no—
307C24—48no—
308C24—48no—
309C24—44no—
310C24—48no—
311C24—48no—
312C24—44no—
313C24—48no—
314C24—48no—
315C24—48no—
316C24C22×D412yes—
317C24C22×D412yes—
318C24C22×D412yes—
319C24C2×#4114yes—
320C24C2×#4114yes—
321C24C2×#4114yes—
322C24C2×#4112yes—
323C24C2×#4112yes—
324C24C2×#4114yes—
325C24H(5,𝔽2)12yes—
326C242−1+414yes—
327C242−1+412yes—
328C24C2511yescharacteristic
329C2×Q8—2256no—
330C2×Q8—232no—
331C2×Q8—232no—
332C2×Q8—264no—
333C2×Q8—232no—
334C2×Q8—264no—
335C22×C4—28no—
336C22×C4—216no—
337C22×C4—216no—
338C22×C4—216no—
339C22×C4—28no—
340C22×C4—28no—
341C22×C4—216no—
342C22×C4—216no—
343C22×C4—216no—
344C22×C4—216no—
345C22×C4—216no—
346C22×C4—28no—
347C22×C4—216no—
348C22×C4—216no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—216no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—28no—
362C22×C4—216no—
363C22×C4—28no—
364C22×C4—216no—
365C22×C4—216no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—44no—
407C22×C4—48no—
408C22×C4—44no—
409C22×C4—48no—
410C22×C4—48no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—48no—
415C22×C4—44no—
416C22×C4—48no—
417C22×C4—44no—
418C22×C4—48no—
419C22×C4—44no—
420C22×C4—48no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—48no—
424C22×C4—48no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—48no—
428C22×C4—48no—
429C22×C4—48no—
430C22×C4—48no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—48no—
437C22×C4—48no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4#120116yes—
442C22×C4#123132yes—
443C22×C4#124116yes—
444C22×C4C22×D418yes—
445C22×C4C22×D414yes—
446C22×C4C22×D414yes—
447C22×C4C22×D414yes—
448C22×C4C22×D414yes—
449C22×C4C22×D418yes—
450C22×C4C22×D414yes—
451C22×C4C2×#4114yes—
452C22×C4C2×#4118yes—
453C22×C4C2×#4118yes—
454C22×C4C2×#4118yes—
455C4⋊C4—264no—
456C4⋊C4—232no—
457C4⋊C4—416no—
458C22⋊C4—232no—
459C22⋊C4—432no—
460C22⋊C4—416no—
461C22⋊C4—432no—
462C22⋊C4—416no—
463C42—264no—
464C42—232no—
465C23—24no—
466C23—28no—
467C23—24no—
468C23—24no—
469C23—28no—
470C23—416no—
471C23—416no—
472C23—416no—
473C23—42no—
474C23—44no—
475C23—42no—
476C23—44no—
477C23—42no—
478C23—42no—
479C23—44no—
480C23—432no—
481C23—42no—
482C23—42no—
483C23—44no—
484C23—44no—
485C23—42no—
486C23—44no—
487C23—44no—
488C23—42no—
489C23—44no—
490C23—44no—
491C23—44no—
492C23—432no—
493C23—88no—
494C23—88no—
495C23—88no—
496C23—88no—
497C23—816no—
498C23—816no—
499C23C2×#12014yes—
500C23C2×#12318yes—
501C23#52514yes—
502C23#52514yes—
503C23#52518yes—
504C23#52514yes—
505C23C2×#12414yes—
506C23#52918yes—
507C23#52918yes—
508C23#53614yes—
509C23#53714yes—
510C23#54118yes—
511C23#54218yes—
512C23#54614yes—
513C23#54714yes—
514C23#54814yes—
515C23#54818yes—
516C23#54818yes—
517C23#55014yes—
518C23#55218yes—
519C23#55618yes—
520C23#55618yes—
521C23#55918yes—
522C23C23×D411yescharacteristic
523C23C23×D411yescharacteristic
524C23C23×D411yescharacteristic
525C23C22×#4112yes—
526C23C22×#4112yes—
527C23C22×#4111yescharacteristic
528C23C22×#4111yescharacteristic
529C23C22×#4112yes—
530C23C2×H(5,𝔽2)11yescharacteristic
531C23C2×2−1+412yes—
532C23C2×2−1+411yescharacteristic
533Q8—2128no—
534C2×C4—232no—
535C2×C4—264no—
536C2×C4—24no—
537C2×C4—28no—
538C2×C4—28no—
539C2×C4—28no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—28no—
543C2×C4—28no—
544C2×C4—28no—
545C2×C4—28no—
546C2×C4—28no—
547C2×C4—24no—
548C2×C4—232no—
549C2×C4—28no—
550C2×C4—28no—
551C2×C4—28no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—28no—
556C2×C4—24no—
557C2×C4—28no—
558C2×C4—28no—
559C2×C4—416no—
560C2×C4—416no—
561C2×C4—432no—
562C2×C4—44no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—88no—
598C2×C4—88no—
599C2×C4—816no—
600C2×C4—816no—
601C2×C4C2×#12018yes—
602C2×C4C2×#123116yes—
603C2×C4C2×#12418yes—
604C22—44no—
605C22—48no—
606C22—48no—
607C22—44no—
608C22—44no—
609C22—82no—
610C22—832no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—84no—
615C22—84no—
616C22#239818yes—
617C22#240718yes—
618C22#2421116yes—
619C22#243618yes—
620C22#2448116yes—
621C22#2458116yes—
622C22#2469116yes—
623C22#259218yes—
624C22#259918yes—
625C22#263718yes—
626C22#284918yes—
627C22C22×#12011yescharacteristic
628C22C22×#12312yes—
629C22C2×#52511yescharacteristic
630C22C2×#52511yescharacteristic
631C22C2×#52512yes—
632C22C2×#52511yescharacteristic
633C22C22×#12411yescharacteristic
634C22C2×#52912yes—
635C22C2×#52912yes—
636C22C2×#53611yescharacteristic
637C22C2×#53711yescharacteristic
638C22C2×#54112yes—
639C22C2×#54212yes—
640C22C2×#54611yescharacteristic
641C22C2×#54711yescharacteristic
642C22C2×#54812yes—
643C22C2×#54812yes—
644C22C2×#54811yescharacteristic
645C22C2×#55011yescharacteristic
646C22C2×#55212yes—
647C22C2×#55612yes—
648C22C2×#55612yes—
649C22C2×#55912yes—
650C4—28no—
651C4—216no—
652C4—28no—
653C4—44no—
654C4—48no—
655C4—44no—
656C4—82no—
657C4—82no—
658C4—84no—
659C4—84no—
660C2—84no—
661C2#14882116yesdirect product factor
662C2C2×#239811yescharacteristic
663C2C2×#263711yescharacteristic
664C2C2×#243611yescharacteristic
665C2C2×#246912yes—
666C2C2×#245812yes—
667C2C2×#242112yes—
668C2C2×#244812yes—
669C2C2×#240711yescharacteristic
670C2C2×#259911yescharacteristic
671C2C2×#259211yescharacteristic
672C2C2×#284911yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×C4×Q8C2semidirect
5. #14882C2direct (N × H)
6. C2×#1446C2semidirect
7. C2×#1445C2semidirect
8. C2×#1442C2semidirect
11. C2×#1436C2semidirect
12. C2×#1434C2semidirect
17. C22×C4×Q8C22semidirect
46. #1446C22semidirect
47. #1445C22semidirect
48. #1442C22semidirect
51. #1436C22semidirect
52. #1434C22semidirect
661. C2#14882direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×Q82
C22×#3972
C22×#3932
C22×#3882
#148822
C2×#14462
C2×#14452
C2×#14422
C2×#14392
C2×#14372
C2×#14362
C2×#14342