Finite Group Databasebeta

← C2×#14907 #607914

Subgroups — C2×#14907 #607914

Order 512.

6478 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#117C211yesmaximal, characteristic
2C22×#398C211yesmaximal, characteristic, complemented
3C22×#397C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic, complemented
5C22×#385C212yesmaximal
6#14907C2116yesmaximal, direct product factor
7C2×#1441C211yesmaximal, characteristic, complemented
8C2×#1441C212yesmaximal, complemented
9C2×#1440C212yesmaximal
10C2×#1439C211yesmaximal, characteristic
11C2×#1436C212yesmaximal, complemented
12C2×#1434C211yesmaximal, characteristic, complemented
13C25×C4C2211yescharacteristic
14C22×#117—28no—
15C22×#117—28no—
16C22×#117—28no—
17C22×#117C2218yes—
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2212yes—
21C23×C4⋊C4C2212yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2212yes—
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2212yes—
27C23×C22⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29C23×C42C2211yescharacteristic
30C2×#398—28no—
31C2×#398C2218yescomplemented
32C2×#397—28no—
33C2×#397C2218yes—
34C2×#389—28no—
35C2×#389C2218yescomplemented
36C2×#385—216no—
37C2×#385C22116yes—
38C22×#95C2212yes—
39C22×#95C2211yescharacteristic
40C22×#95C2212yes—
41C22×#95C2212yes—
42C22×#95C2212yes—
43C22×#95C2212yes—
44C22×#95C2212yes—
45C22×#95C2211yescharacteristic
46C22×#95C2212yes—
47C22×#95C2212yes—
48#1441C22116yescomplemented
49#1441C2218yescomplemented
50#1440C22116yes—
51#1439C2218yes—
52#1436C22116yescomplemented
53#1434C2218yescomplemented
54C26C2311yescharacteristic
55C24×C4—24no—
56C24×C4—24no—
57C24×C4—24no—
58C24×C4—24no—
59C24×C4—24no—
60C24×C4—24no—
61C24×C4D418yes—
62C24×C4C2312yes—
63C24×C4C2312yes—
64C24×C4C2314yes—
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C24×C4C2312yes—
69C24×C4C2312yes—
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C2×#117—2128no—
74C2×#117—232no—
75C2×#117—232no—
76C2×#117—232no—
77C22×C4⋊C4—24no—
78C22×C4⋊C4—24no—
79C22×C4⋊C4—24no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—24no—
82C22×C4⋊C4—24no—
83C22×C4⋊C4—28no—
84C22×C4⋊C4—24no—
85C22×C4⋊C4—24no—
86C22×C4⋊C4—28no—
87C22×C4⋊C4—28no—
88C22×C4⋊C4—28no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—28no—
91C22×C4⋊C4—28no—
92C22×C4⋊C4—28no—
93C22×C4⋊C4D418yes—
94C22×C4⋊C4C2314yes—
95C22×C4⋊C4C2318yes—
96C22×C4⋊C4C2314yes—
97C22×C4⋊C4C2318yes—
98C22×C4⋊C4C2314yes—
99C22×C4⋊C4C2314yes—
100C22×C22⋊C4—24no—
101C22×C22⋊C4—28no—
102C22×C22⋊C4—24no—
103C22×C22⋊C4—24no—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—24no—
106C22×C22⋊C4—28no—
107C22×C22⋊C4—28no—
108C22×C22⋊C4—28no—
109C22×C22⋊C4—28no—
110C22×C22⋊C4—28no—
111C22×C22⋊C4D418yes—
112C22×C22⋊C4C2318yes—
113C22×C22⋊C4C2314yes—
114C22×C22⋊C4C2318yes—
115C22×C22⋊C4C2314yes—
116C22×C42—24no—
117C22×C42—24no—
118C22×C42—24no—
119C22×C42—24no—
120C22×C42—24no—
121C22×C42D418yes—
122C22×C42C2314yes—
123C22×C42C2314yes—
124#398—232no—
125#397—232no—
126#389—232no—
127#385—264no—
128C2×#95—28no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—28no—
132C2×#95—28no—
133C2×#95—28no—
134C2×#95—28no—
135C2×#95—28no—
136C2×#95—28no—
137C2×#95—28no—
138C2×#95C2314yes—
139C2×#95C2318yes—
140C2×#95C2314yes—
141C2×#95C2318yes—
142C2×#95C2318yes—
143C2×#95C2318yes—
144C2×#95C2318yes—
145C2×#95C2318yes—
146C2×#95C2318yes—
147C2×#95C2318yes—
148C25—22no—
149C25—22no—
150C25—24no—
151C25—24no—
152C25—22no—
153C25—22no—
154C25—24no—
155C25—24no—
156C25C2×D414yes—
157C25C2×D414yes—
158C25#4114yes—
159C25C2412yes—
160C25C2411yescharacteristic
161C23×C4—232no—
162C23×C4—232no—
163C23×C4—232no—
164C23×C4—232no—
165C23×C4—232no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—28no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—24no—
172C23×C4—28no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—24no—
178C23×C4—232no—
179C23×C4—232no—
180C23×C4—28no—
181C23×C4—28no—
182C23×C4—28no—
183C23×C4—28no—
184C23×C4—24no—
185C23×C4—24no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
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—24no—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4C2×D414yes—
223C23×C4C2×D414yes—
224C23×C4C2×D414yes—
225C23×C4C2×D4116yes—
226C23×C4C2×D414yes—
227C23×C4C2×D414yes—
228C23×C4C2×D414yes—
229C23×C4C2×D414yes—
230C23×C4C2×D414yes—
231C23×C4C2×D414yes—
232C23×C4C2×D414yes—
233C23×C4#4118yes—
234C23×C4#4118yes—
235C23×C4#4114yes—
236C23×C4#4114yes—
237C23×C4C2414yes—
238C23×C4C2414yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2414yes—
243C23×C4C2414yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247#117—2256no—
248C2×C4⋊C4—232no—
249C2×C4⋊C4—232no—
250C2×C4⋊C4—232no—
251C2×C4⋊C4—28no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—28no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—28no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—216no—
258C2×C4⋊C4—216no—
259C2×C4⋊C4—216no—
260C2×C4⋊C4—28no—
261C2×C4⋊C4—216no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—216no—
265C2×C4⋊C4—216no—
266C2×C4⋊C4—216no—
267C2×C4⋊C4—416no—
268C2×C4⋊C4—432no—
269C2×C4⋊C4—432no—
270C2×C4⋊C4C2×D4116yes—
271C2×C22⋊C4—264no—
272C2×C22⋊C4—232no—
273C2×C22⋊C4—28no—
274C2×C22⋊C4—216no—
275C2×C22⋊C4—232no—
276C2×C22⋊C4—28no—
277C2×C22⋊C4—28no—
278C2×C22⋊C4—28no—
279C2×C22⋊C4—28no—
280C2×C22⋊C4—216no—
281C2×C22⋊C4—216no—
282C2×C22⋊C4—216no—
283C2×C22⋊C4—216no—
284C2×C22⋊C4—216no—
285C2×C22⋊C4—432no—
286C2×C22⋊C4C2×D4116yes—
287C2×C42—232no—
288C2×C42—232no—
289C2×C42—28no—
290C2×C42—28no—
291C2×C42—28no—
292C2×C42—28no—
293C2×C42—28no—
294C2×C42C2×D4116yes—
295#95—216no—
296#95—216no—
297#95—216no—
298#95—28no—
299#95—216no—
300#95—28no—
301#95—216no—
302#95—216no—
303#95—216no—
304#95—216no—
305C24—28no—
306C24—28no—
307C24—28no—
308C24—216no—
309C24—28no—
310C24—28no—
311C24—28no—
312C24—216no—
313C24—216no—
314C24—216no—
315C24—216no—
316C24—216no—
317C24—22no—
318C24—22no—
319C24—24no—
320C24—24no—
321C24—22no—
322C24—22no—
323C24—24no—
324C24—24no—
325C24—44no—
326C24—48no—
327C24—44no—
328C24—44no—
329C24—44no—
330C24—48no—
331C24—48no—
332C24—48no—
333C24—48no—
334C24—48no—
335C24#121116yes—
336C24C22×D414yes—
337C24C22×D414yes—
338C24C22×D412yes—
339C24C22×D412yes—
340C24C22×D412yes—
341C24C22×D412yes—
342C24C2×#4114yes—
343C24C2×#4112yes—
344C24C2×#4112yes—
345C24C2×#4112yes—
346C24C2×#4114yes—
347C24C2×#4114yes—
348C242−1+414yes—
349C242−1+414yes—
350C24C2511yescharacteristic
351C22×C4—232no—
352C22×C4—2256no—
353C22×C4—232no—
354C22×C4—232no—
355C22×C4—232no—
356C22×C4—28no—
357C22×C4—28no—
358C22×C4—232no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—28no—
362C22×C4—28no—
363C22×C4—28no—
364C22×C4—28no—
365C22×C4—28no—
366C22×C4—28no—
367C22×C4—28no—
368C22×C4—28no—
369C22×C4—28no—
370C22×C4—28no—
371C22×C4—216no—
372C22×C4—216no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—232no—
384C22×C4—232no—
385C22×C4—28no—
386C22×C4—28no—
387C22×C4—28no—
388C22×C4—216no—
389C22×C4—216no—
390C22×C4—216no—
391C22×C4—216no—
392C22×C4—28no—
393C22×C4—28no—
394C22×C4—216no—
395C22×C4—216no—
396C22×C4—216no—
397C22×C4—216no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—48no—
437C22×C4—48no—
438C22×C4—48no—
439C22×C4—44no—
440C22×C4—48no—
441C22×C4—48no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—48no—
445C22×C4—44no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—48no—
449C22×C4—48no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—48no—
454C22×C4—48no—
455C22×C4—48no—
456C22×C4—48no—
457C22×C4—48no—
458C22×C4—48no—
459C22×C4—48no—
460C22×C4—48no—
461C22×C4—48no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4#120116yes—
467C22×C4#121116yes—
468C22×C4#121116yes—
469C22×C4C22×D414yes—
470C22×C4C22×D414yes—
471C22×C4C22×D414yes—
472C22×C4C22×D414yes—
473C22×C4C22×D414yes—
474C22×C4C22×D414yes—
475C22×C4C22×D414yes—
476C22×C4C22×D414yes—
477C22×C4C22×D414yes—
478C22×C4C22×D414yes—
479C22×C4C2×#4118yes—
480C22×C4C2×#4118yes—
481C22×C4C2×#4114yes—
482C22×C4C2×#4114yes—
483C4⋊C4—232no—
484C4⋊C4—232no—
485C4⋊C4—232no—
486C4⋊C4—416no—
487C4⋊C4—432no—
488C4⋊C4—432no—
489C22⋊C4—264no—
490C22⋊C4—232no—
491C22⋊C4—232no—
492C22⋊C4—432no—
493C42—232no—
494C42—232no—
495C23—232no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—28no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—264no—
504C23—28no—
505C23—28no—
506C23—28no—
507C23—28no—
508C23—28no—
509C23—416no—
510C23—416no—
511C23—416no—
512C23—416no—
513C23—416no—
514C23—42no—
515C23—432no—
516C23—44no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—44no—
521C23—416no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—432no—
527C23—432no—
528C23C2×#12014yes—
529C23C2×#12118yes—
530C23C2×#12114yes—
531C23C2×#12114yes—
532C23C2×#12114yes—
533C23#52514yes—
534C23#52514yes—
535C23#52514yes—
536C23#52514yes—
537C23#52518yes—
538C23#52918yes—
539C23#53214yes—
540C23#53614yes—
541C23#53614yes—
542C23#53618yes—
543C23#54118yes—
544C23#54718yes—
545C23#54718yes—
546C23#54718yes—
547C23#54818yes—
548C23#55218yes—
549C23#55218yes—
550C23#55218yes—
551C23#55618yes—
552C23C23×D411yescharacteristic
553C23C23×D411yescharacteristic
554C23C23×D411yescharacteristic
555C23C23×D411yescharacteristic
556C23C22×#4111yescharacteristic
557C23C22×#4111yescharacteristic
558C23C22×#4111yescharacteristic
559C23C22×#4112yes—
560C23C22×#4112yes—
561C23C2×2−1+412yes—
562C23C2×2−1+412yes—
563C2×C4—2128no—
564C2×C4—232no—
565C2×C4—232no—
566C2×C4—232no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—28no—
582C2×C4—28no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—28no—
587C2×C4—28no—
588C2×C4—28no—
589C2×C4—28no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—28no—
593C2×C4—28no—
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—432no—
597C2×C4—416no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—42no—
601C2×C4—44no—
602C2×C4—432no—
603C2×C4—44no—
604C2×C4—42no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—416no—
610C2×C4—416no—
611C2×C4—44no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—44no—
631C2×C4—816no—
632C2×C4—816no—
633C2×C4C2×#12018yes—
634C2×C4C2×#12118yes—
635C2×C4C2×#12118yes—
636C22—28no—
637C22—216no—
638C22—44no—
639C22—44no—
640C22—464no—
641C22—44no—
642C22—48no—
643C22—44no—
644C22—48no—
645C22—48no—
646C22—44no—
647C22—44no—
648C22#239218yes—
649C22#240618yes—
650C22#2413116yes—
651C22#2415116yes—
652C22#243218yes—
653C22#2475116yes—
654C22#2478116yes—
655C22#259918yes—
656C22#261118yes—
657C22#262118yes—
658C22#284718yes—
659C22C22×#12011yescharacteristic
660C22C22×#12111yescharacteristic
661C22C22×#12111yescharacteristic
662C22C22×#12111yescharacteristic
663C22C2×#52511yescharacteristic
664C22C2×#52511yescharacteristic
665C22C2×#52511yescharacteristic
666C22C2×#52511yescharacteristic
667C22C2×#52512yes—
668C22C2×#52912yes—
669C22C2×#53211yescharacteristic
670C22C2×#53611yescharacteristic
671C22C2×#53611yescharacteristic
672C22C2×#53612yes—
673C22C2×#54112yes—
674C22C2×#54712yes—
675C22C2×#54712yes—
676C22C2×#54712yes—
677C22C2×#54812yes—
678C22C2×#55212yes—
679C22C2×#55212yes—
680C22C2×#55212yes—
681C22C2×#55612yes—
682C4—28no—
683C4—28no—
684C4—28no—
685C4—48no—
686C4—44no—
687C4—44no—
688C4—44no—
689C4—48no—
690C4—84no—
691C4—84no—
692C2—48no—
693C2#14907116yesdirect product factor
694C2C2×#239211yescharacteristic
695C2C2×#262111yescharacteristic
696C2C2×#241512yes—
697C2C2×#243211yescharacteristic
698C2C2×#247512yes—
699C2C2×#247812yes—
700C2C2×#240611yescharacteristic
701C2C2×#241312yes—
702C2C2×#259911yescharacteristic
703C2C2×#261111yescharacteristic
704C2C2×#284711yescharacteristic
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
2. C22×#398C2semidirect
4. C22×#389C2semidirect
6. #14907C2direct (N × H)
7. C2×#1441C2semidirect
8. C2×#1441C2semidirect
11. C2×#1436C2semidirect
12. C2×#1434C2semidirect
31. C2×#398C22semidirect
35. C2×#389C22semidirect
48. #1441C22semidirect
49. #1441C22semidirect
52. #1436C22semidirect
53. #1434C22semidirect
693. C2#14907direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1172
C22×#3982
C22×#3972
C22×#3892
C22×#3852
#149072
C2×#14412
C2×#14402
C2×#14392
C2×#14362
C2×#14342