Finite Group Databasebeta

← C2×#9043 #195115

Subgroups — C2×#9043 #195115

Order 512.

1934 conjugacy classes of subgroups.

The subgroup lattice has 685 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#480C211yesmaximal, characteristic
2C2×#2325C211yesmaximal, characteristic
3C2×#1823C211yesmaximal, characteristic, complemented
4C22×#327C211yesmaximal, characteristic
5C2×#1445C211yesmaximal, characteristic, complemented
6#9043C218yesmaximal, direct product factor
7C2×#1294C211yesmaximal, characteristic, complemented
8C2×#1280C211yesmaximal, characteristic, complemented
9C22×#121C2211yescharacteristic
10C22×C4×D4—21no—
11C23×C4⋊C4C2211yescharacteristic
12C2×#480—24no—
13C2×#480—22no—
14C2×#480C418yescomplemented
15C2×#480C2214yes—
16C22×#107—21no—
17C22×#102—21no—
18C22×C22⋊C8C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20#2325—22no—
21#2325—22no—
22#2325—22no—
23#2325C2214yes—
24C2×#388—21no—
25C2×#387—21no—
26C2×#386—21no—
27C2×#386—21no—
28C2×#385—21no—
29C2×#380C2211yescharacteristic
30C22×#95—21no—
31C22×#95—21no—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34#1823—22no—
35#1823C2214yescomplemented
36C2×#340—21no—
37C2×#340—21no—
38C2×#327—24no—
39C2×#327C2214yes—
40#1445—22no—
41#1445C2214yescomplemented
42#1294C2214yescomplemented
43#1280C2214yescomplemented
44C23×D4—21no—
45C23×D4D411yescharacteristic
46C24×C4—21no—
47C24×C4—21no—
48C24×C4—21no—
49C24×C4D411yescharacteristic
50C24×C4D411yescharacteristic
51C24×C4C2311yescharacteristic
52C23×C8—21no—
53C23×C8—21no—
54C2×#121—21no—
55C2×#121—21no—
56C2×#121—22no—
57C2×#121—22no—
58C2×#121C2×C414yes—
59C2×#121D414yes—
60C2×#121D412yes—
61C2×#121C2312yes—
62C2×C4×D4—24no—
63C2×C4×D4—24no—
64C2×C4×D4—44no—
65C2×C4×D4—44no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4C2×C414yescomplemented
76C22×C4⋊C4D411yescharacteristic
77C22×C4⋊C4D411yescharacteristic
78C22×C4⋊C4D411yescharacteristic
79C22×C4⋊C4C2312yes—
80C22×C22⋊C4—21no—
81C22×C22⋊C4—21no—
82C22×C22⋊C4—21no—
83C22×C22⋊C4—21no—
84C22×C22⋊C4—21no—
85C22×C42—21no—
86#480—216no—
87#480—28no—
88#480C2×C4116yescomplemented
89C2×#107—28no—
90C2×#107—24no—
91C2×#102—28no—
92C2×#102—24no—
93C2×C22⋊C8—21no—
94C2×C22⋊C8—22no—
95C2×C22⋊C8—22no—
96C2×C22⋊C8—22no—
97C2×C22⋊C8—21no—
98C2×C22⋊C8C2×C414yescomplemented
99C2×C22⋊C8C2312yes—
100C2×C22⋊C8C2312yes—
101#388—24no—
102#388—24no—
103#387—24no—
104#387—24no—
105#386—24no—
106#386—24no—
107#386—24no—
108#386—24no—
109#385—24no—
110#385—24no—
111#380—21no—
112#380—21no—
113#380D412yes—
114#380C2312yes—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—21no—
121C2×#95—21no—
122C2×#95—22no—
123C2×#95—22no—
124C2×#95—21no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—44no—
128C2×#95—44no—
129C2×#95D412yes—
130C2×#95C2312yes—
131C2×#95C2312yes—
132#340—24no—
133#340—24no—
134#327—28no—
135C25—21no—
136C25C2×D411yescharacteristic
137C22×D4—24no—
138C22×D4—22no—
139C22×D4—24no—
140C22×D4—22no—
141C22×D4—21no—
142C22×D4—22no—
143C22×D4—42no—
144C22×D4—42no—
145C22×D4—42no—
146C22×D4—42no—
147C22×D4—42no—
148C22×D4—42no—
149C22×D4C22⋊C414yes—
150C22×D4C2×D412yes—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—22no—
155C23×C4—24no—
156C23×C4—24no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—24no—
164C23×C4—21no—
165C23×C4—22no—
166C23×C4—42no—
167C23×C4—42no—
168C23×C4—44no—
169C23×C4—42no—
170C23×C4—42no—
171C23×C4—42no—
172C23×C4—42no—
173C23×C4—42no—
174C23×C4—42no—
175C23×C4—42no—
176C23×C4—41no—
177C23×C4—41no—
178C23×C4—42no—
179C23×C4—42no—
180C23×C4—42no—
181C23×C4—42no—
182C23×C4—42no—
183C23×C4—42no—
184C23×C4—42no—
185C23×C4—42no—
186C23×C4—82no—
187C23×C4—82no—
188C23×C4D814yes—
189C23×C4C22×C412yes—
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D412yes—
193C23×C4C2×D412yes—
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D412yes—
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4#4112yes—
199C23×C4#4112yes—
200C23×C4C2411yescharacteristic
201C22×C8—24no—
202C22×C8—22no—
203C22×C8—22no—
204C22×C8—42no—
205C22×C8—42no—
206C22×C8—42no—
207C22×C8—42no—
208C22×C8—42no—
209#121—24no—
210#121—24no—
211#121—24no—
212#121—24no—
213#121—24no—
214#121—22no—
215#121—22no—
216#121C22⋊C418yes—
217#121C22×C414yes—
218#121C2×D414yes—
219C4×D4—48no—
220C4×D4—416no—
221C4×D4—48no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—44no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4—42no—
241C2×C4⋊C4—42no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4—42no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4C22⋊C414yes—
248C2×C4⋊C4C22×C414yescomplemented
249C2×C4⋊C4C2×D412yes—
250C2×C4⋊C4C2×D412yes—
251C2×C4⋊C4C2×D412yes—
252C2×C22⋊C4—24no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—24no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—24no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—44no—
262C2×C22⋊C4—42no—
263C2×C22⋊C4—42no—
264C2×C22⋊C4—82no—
265C2×C22⋊C4—82no—
266C2×C42—24no—
267C2×C42—44no—
268#107—216no—
269#102—216no—
270C22⋊C8—24no—
271C22⋊C8—22no—
272C22⋊C8—22no—
273C22⋊C8—22no—
274C22⋊C8—42no—
275C22⋊C8C22×C414yescomplemented
276#95—24no—
277#95—24no—
278#95—22no—
279#95—22no—
280#95—22no—
281#95—22no—
282#95—22no—
283#95—22no—
284#95—22no—
285#95—22no—
286#95—48no—
287#95—42no—
288#95—48no—
289C24—22no—
290C24—22no—
291C24—22no—
292C24—22no—
293C24—22no—
294C24—24no—
295C24—42no—
296C24—42no—
297C24—42no—
298C24—42no—
299C24—42no—
300C24—42no—
301C24C4×D412yes—
302C24#12011yescharacteristic
303C24#12011yescharacteristic
304C24#12112yes—
305C24C2×D812yes—
306C24#13512yes—
307C24AGL(1,ℤ/8)12yes—
308C24AGL(1,ℤ/8)12yes—
309C24C22×D411yescharacteristic
310C2×D4—24no—
311C2×D4—24no—
312C2×D4—28no—
313C2×D4—22no—
314C2×D4—24no—
315C2×D4—48no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—42no—
320C2×D4—42no—
321C2×D4—42no—
322C2×D4—48no—
323C2×D4—48no—
324C2×D4—44no—
325C2×D4—44no—
326C2×D4—48no—
327C2×D4—48no—
328C2×D4—84no—
329C2×D4—81no—
330C2×D4—81no—
331C2×D4C2×C22⋊C414yes—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—44no—
358C22×C4—44no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—48no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—48no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—48no—
372C22×C4—48no—
373C22×C4—48no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—48no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—44no—
388C22×C4—44no—
389C22×C4—48no—
390C22×C4—48no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—84no—
402C22×C4—81no—
403C22×C4—81no—
404C22×C4—81no—
405C22×C4—81no—
406C22×C4—84no—
407C22×C4—84no—
408C22×C4—816no—
409C22×C4—84no—
410C22×C4—84no—
411C22×C4—84no—
412C22×C4—82no—
413C22×C4—82no—
414C22×C4—82no—
415C22×C4—82no—
416C22×C4—84no—
417C22×C4—84no—
418C22×C4—84no—
419C22×C4—84no—
420C22×C4C2×C22⋊C412yes—
421C22×C4C2×C22⋊C412yes—
422C22×C4C4×D412yes—
423C22×C4C4×D412yes—
424C22×C4C4×D412yes—
425C22×C4#12011yescharacteristic
426C22×C4#12011yescharacteristic
427C22×C4#12112yes—
428C22×C4#12112yes—
429C22×C4#12112yes—
430C22×C4#12312yes—
431C22×C4#12312yes—
432C22×C4C2×D814yes—
433C22×C4C23×C411yescharacteristic
434C22×C4C22×D411yescharacteristic
435C22×C4C22×D411yescharacteristic
436C22×C4C22×D411yescharacteristic
437C22×C4C2×#4111yescharacteristic
438C22×C4C2×#4111yescharacteristic
439C2×C8—24no—
440C2×C8—48no—
441C2×C8—42no—
442C2×C8—42no—
443C2×C8—42no—
444C2×C8—42no—
445C2×C8—42no—
446C2×C8—84no—
447C4⋊C4—22no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C4⋊C4—48no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—44no—
457C4⋊C4—44no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4C2×C22⋊C414yes—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—28no—
464C22⋊C4—48no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—44no—
468C22⋊C4—84no—
469C22⋊C4—84no—
470C42—48no—
471C23—24no—
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—24no—
492C23—48no—
493C23—48no—
494C23—48no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—84no—
502C23—84no—
503C23—84no—
504C23—84no—
505C23#38612yes—
506C23#38612yes—
507C23C4×D814yes—
508C23#44214yes—
509C23#44712yes—
510C23#44712yes—
511C23#44912yes—
512C23#44912yes—
513C23#45512yes—
514C23#45612yes—
515C23#45812yes—
516C23#45812yes—
517C23#45914yes—
518C23#46314yes—
519C23C2×C4×D411yescharacteristic
520C23C2×#12011yescharacteristic
521C23C2×#12111yescharacteristic
522C23C22×D811yescharacteristic
523C23C2×#13511yescharacteristic
524C23C2×AGL(1,ℤ/8)11yescharacteristic
525C23C2×AGL(1,ℤ/8)11yescharacteristic
526D4—44no—
527D4—416no—
528D4—44no—
529D4—44no—
530D4—44no—
531D4—44no—
532D4—82no—
533D4—84no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—48no—
559C2×C4—48no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—82no—
582C2×C4—84no—
583C2×C4—816no—
584C2×C4—816no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4—84no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—84no—
592C2×C4—88no—
593C2×C4—88no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4#38612yes—
601C2×C4#38612yes—
602C2×C4C22×C22⋊C411yescharacteristic
603C2×C4C2×C4×D411yescharacteristic
604C2×C4C2×#12111yescharacteristic
605C2×C4C2×#12311yescharacteristic
606C8—44no—
607C8—82no—
608C22—28no—
609C22—28no—
610C22—28no—
611C22—28no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—21no—
616C22—21no—
617C22—22no—
618C22—21no—
619C22—21no—
620C22—22no—
621C22—21no—
622C22—21no—
623C22—22no—
624C22—21no—
625C22—21no—
626C22—22no—
627C22—21no—
628C22—21no—
629C22—22no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—816no—
634C22—82no—
635C22—82no—
636C22—82no—
637C22—82no—
638C22#160714yes—
639C22#160914yes—
640C22#161014yes—
641C22#161214yes—
642C22#187914yes—
643C22#187914yes—
644C22#188214yes—
645C22#189014yes—
646C22C2×#38611yescharacteristic
647C22C2×C4×D811yescharacteristic
648C22C2×#44211yescharacteristic
649C22C2×#44711yescharacteristic
650C22C2×#44911yescharacteristic
651C22C2×#45511yescharacteristic
652C22C2×#45611yescharacteristic
653C22C2×#45811yescharacteristic
654C22C2×#45811yescharacteristic
655C22C2×#45911yescharacteristic
656C22C2×#46311yescharacteristic
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—22no—
662C4—22no—
663C4—44no—
664C4—44no—
665C4—84no—
666C4—82no—
667C4—84no—
668C4—82no—
669C4—82no—
670C2—21no—
671C2—24no—
672C2—21no—
673C2—21no—
674C2—21no—
675C2—84no—
676C2#904318yesdirect product factor
677C2C2×#160711yescharacteristic
678C2C2×#160911yescharacteristic
679C2C2×#161011yescharacteristic
680C2C2×#161211yescharacteristic
681C2C2×#187911yescharacteristic
682C2C2×#188211yescharacteristic
683C2C2×#189011yescharacteristic
subgroupG/H
center, socleC24#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1823C2semidirect
5. C2×#1445C2semidirect
6. #9043C2direct (N × H)
7. C2×#1294C2semidirect
8. C2×#1280C2semidirect
14. C2×#480C4semidirect
35. #1823C22semidirect
41. #1445C22semidirect
42. #1294C22semidirect
43. #1280C22semidirect
75. C22×C4⋊C4C2×C4semidirect
88. #480C2×C4semidirect
98. C2×C22⋊C8C2×C4semidirect
248. C2×C4⋊C4C22×C4semidirect
275. C22⋊C8C22×C4semidirect
676. C2#9043direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4802
C2×#23252
C2×#18232
C22×#3272
C2×#14452
#90432
C2×#12942
C2×#12802