Finite Group Databasebeta

← C4×#1882 #354243

Subgroups — C4×#1882 #354243

Order 512.

1998 conjugacy classes of subgroups.

The subgroup lattice has 697 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#137C211yesmaximal, characteristic
2C4×#520C211yesmaximal, characteristic
3C2×#1882C212yesmaximal
4C4×#419C211yesmaximal, characteristic, complemented
5C2×C4×#104C211yesmaximal, characteristic
6C4×#391C211yesmaximal, characteristic, complemented
7#10957C212yesmaximal, complemented
8#10899C212yesmaximal, complemented
9#10781C212yesmaximal
10C4×#343C211yesmaximal, characteristic, complemented
11C4×#339C211yesmaximal, characteristic, complemented
12C22×#137C2211yescharacteristic
13C2×#520C2212yes—
14C2×C4×#41C2211yescharacteristic
15C22×C4×Q8C2211yescharacteristic
16C4×#137—24no—
17C4×#137C418yescomplemented
18C2×#441—21no—
19C2×#440—21no—
20C2×C4×Q16—21no—
21C2×C4×SD16—21no—
22C2×#428C2211yescharacteristic
23C22×#104C2212yes—
24C2×#417C2211yescharacteristic
25C2×#419C2212yes—
26C2×#419C2211yescharacteristic
27C2×C4×M16C2211yescharacteristic
28C2×C4×M16C2211yescharacteristic
29C2×#391C2212yes—
30#2276—21no—
31#2275—22no—
32#2275—21no—
33#2274—22no—
34#2274C2212yes—
35C42×Q8—21no—
36C42×D4—22no—
37C42×D4—21no—
38C4×#117—21no—
39C4×#117C2211yescharacteristic
40C2×C4×C4⋊C4—21no—
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C43C2211yescharacteristic
43#1882C4116yesdirect product factor
44#1763—22no—
45C4×#103—21no—
46C4×#103—21no—
47C4×#104—24no—
48C2×#343C2212yes—
49C2×#343C2212yes—
50#1736C2212yes—
51C2×#339C2212yes—
52C2×#339C2212yes—
53C2×#339C2212yes—
54#1436—22no—
55C4⋊#95C2212yes—
56C4×#95—22no—
57C22×#41C2311yescharacteristic
58C23×Q8C2311yescharacteristic
59C2×#137—22no—
60C2×#137—24no—
61C2×#137C2×C418yes—
62C2×#137C2×C414yes—
63C22×Q16—21no—
64C22×SD16—21no—
65C22×M16C2311yescharacteristic
66C22×M16C2312yes—
67C22×M16C2311yescharacteristic
68#520—24no—
69#520—24no—
70#520—24no—
71#520C2×C418yes—
72C4×#41—22no—
73C4×#41—22no—
74C4×#41C2×C414yes—
75C4×#41D414yes—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—21no—
79C2×C4×Q8—21no—
80C2×C4×Q8—22no—
81C2×C4×Q8—21no—
82C2×C4×Q8—21no—
83C2×C4×Q8—22no—
84C2×C4×Q8C2×C414yescomplemented
85C2×C4×Q8D411yescharacteristic
86C2×C4×Q8D411yescharacteristic
87C2×C4×D4—22no—
88C2×C4×D4—21no—
89C2×C4×D4—21no—
90C2×C4×D4—24no—
91C2×C4×D4D411yescharacteristic
92C2×C4×D4D411yescharacteristic
93C2×#117—22no—
94C2×#117—21no—
95C2×#117C2311yescharacteristic
96C2×#117C2312yes—
97C22×C4⋊C4—22no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2312yes—
101C22×C42—21no—
102C22×C42—21no—
103C22×C42—21no—
104C22×C42—22no—
105C22×C42—21no—
106C22×C42D412yes—
107C22×C42C2312yes—
108C22×C42C2311yescharacteristic
109#441—28no—
110#440—28no—
111C4×Q16—28no—
112C4×SD16—28no—
113#428—22no—
114#428C2×C414yescomplemented
115C2×#107—21no—
116C2×#106—21no—
117C2×#104—24no—
118C2×#104—24no—
119C2×#104C2×C418yes—
120#419—22no—
121#419—24no—
122#419C2×C418yescomplemented
123#419C2×C414yescomplemented
124#417—22no—
125#417C2×C414yes—
126C2×#103—21no—
127C2×#103—21no—
128C2×#103—21no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#102—21no—
132C4×M16—22no—
133C4×M16—22no—
134C4×M16—22no—
135C4×M16C2×C414yescomplemented
136C2×#97—21no—
137C2×#97—21no—
138C2×C4×C8—21no—
139C2×C4×C8—21no—
140#391—24no—
141#391C2×C418yescomplemented
142C4×C4⋊C4—22no—
143C4×C4⋊C4—22no—
144C4×C4⋊C4—24no—
145C4×C4⋊C4—24no—
146C4×C4⋊C4—22no—
147C4×C4⋊C4—22no—
148C4×C4⋊C4—22no—
149C4×C4⋊C4—22no—
150C4×C4⋊C4—21no—
151C4×C4⋊C4—21no—
152C4×C4⋊C4—21no—
153C4×C4⋊C4—21no—
154C4×C4⋊C4D411yescharacteristic
155C4×C4⋊C4D411yescharacteristic
156C4×C4⋊C4D412yes—
157C4×C22⋊C4—22no—
158C4×C22⋊C4—22no—
159C4×C22⋊C4—24no—
160C4×C22⋊C4—24no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—24no—
164#376—22no—
165#376—21no—
166C2×#95—22no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95D412yes—
170C43—22no—
171C43—21no—
172C43—22no—
173C43—22no—
174#343—24no—
175#343C2×C418yescomplemented
176#340—22no—
177#340—22no—
178#339—24no—
179#339—24no—
180#339C2×C418yescomplemented
181C2×#41—21no—
182C2×#41—21no—
183C2×#41—22no—
184C2×#41—22no—
185C2×#41C22×C412yes—
186C2×#41C22×C414yes—
187C2×#41C2×D412yes—
188C2×#41#4114yes—
189C22×Q8—21no—
190C22×Q8—22no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—22no—
196C22×Q8—22no—
197C22×Q8C22×C412yes—
198C22×Q8C22×C414yes—
199C22×Q8C2×D411yescharacteristic
200C22×D4—21no—
201C22×D4C2×D411yescharacteristic
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—22no—
205C23×C4—24no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D414yes—
211C23×C4C2×D411yescharacteristic
212C23×C4C2411yescharacteristic
213#137—28no—
214#137—216no—
215#137C42116yescomplemented
216C2×Q16—24no—
217C2×Q16—28no—
218C2×SD16—24no—
219C2×SD16—28no—
220C2×M16—21no—
221C2×M16—22no—
222C2×M16—21no—
223C2×M16—22no—
224C2×M16—22no—
225C2×M16—22no—
226C2×M16—22no—
227C2×M16—22no—
228C2×M16—22no—
229C2×M16—22no—
230C2×M16C22×C414yes—
231C2×M16C22×C412yes—
232C2×M16C22×C414yes—
233C2×M16C22×C412yes—
234C22×C8—21no—
235C22×C8—22no—
236C22×C8—21no—
237C4×Q8—28no—
238C4×Q8—28no—
239C4×Q8—22no—
240C4×Q8—22no—
241C4×Q8—24no—
242C4×Q8—24no—
243C4×Q8—24no—
244C4×Q8—24no—
245C4×Q8—42no—
246C4×Q8—42no—
247C4×Q8—42no—
248C4×Q8—42no—
249C4×Q8C22⋊C414yes—
250C4×Q8C22⋊C414yes—
251C4×D4—216no—
252C4×D4—28no—
253C4×D4—28no—
254C4×D4—24no—
255C4×D4—24no—
256C4×D4—216no—
257C4×D4—24no—
258C4×D4—24no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4C22⋊C414yes—
262C4×D4C22⋊C414yes—
263#117—28no—
264#117—21no—
265#117—21no—
266#117—22no—
267#117—22no—
268#117—28no—
269#117—24no—
270#117—24no—
271#117C22×C412yes—
272#117C22×C414yes—
273#117C2×D412yes—
274#117#4114yes—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4C22×C412yes—
294C2×C4⋊C4C22×C414yes—
295C2×C4⋊C4C2×D411yescharacteristic
296C2×C4⋊C4C2×D411yescharacteristic
297C2×C4⋊C4C2×D412yes—
298C2×C4⋊C4C2×D412yes—
299C2×C4⋊C4#4114yes—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C42—24no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—22no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—24no—
317C2×C42—24no—
318C2×C42—21no—
319C2×C42—22no—
320C2×C42—21no—
321C2×C42—22no—
322C2×C42—24no—
323C2×C42—24no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42—42no—
327C2×C42—44no—
328C2×C42—41no—
329C2×C42—41no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—42no—
333C2×C42—44no—
334C2×C42—84no—
335C2×C42C22×C414yes—
336C2×C42C22×C412yes—
337C2×C42C2×D412yes—
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42#4112yes—
343C2×C42#4112yes—
344#107—24no—
345#106—24no—
346#104—216no—
347#103—24no—
348#103—24no—
349#103—24no—
350#103—28no—
351#103—28no—
352#102—24no—
353#97—24no—
354#97—42no—
355C4×C8—24no—
356C4×C8—42no—
357#95—24no—
358#95—24no—
359#95—216no—
360#95—21no—
361#95—22no—
362#95—22no—
363#95—21no—
364#95—22no—
365#95—48no—
366C24—21no—
367C24C22×D411yescharacteristic
368#41—22no—
369#41—24no—
370#41—22no—
371#41—24no—
372#41—24no—
373#41—24no—
374#41—24no—
375#41C2×C4214yes—
376#41#11714yes—
377#41C4×D418yes—
378C2×Q8—22no—
379C2×Q8—24no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—24no—
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—24no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—42no—
395C2×Q8—42no—
396C2×Q8—42no—
397C2×Q8C2×C4214yescomplemented
398C2×Q8C2×C22⋊C412yes—
399C2×Q8C4×D414yes—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4C2×C22⋊C412yes—
407C2×D4C4×D414yes—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—216no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4—41no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—82no—
446C22×C4—84no—
447C22×C4—84no—
448C22×C4C4×D412yes—
449C22×C4C4×D418yes—
450C22×C4C4×D412yes—
451C22×C4#12011yescharacteristic
452C22×C4#12011yescharacteristic
453C22×C4#12011yescharacteristic
454C22×C4#12011yescharacteristic
455C22×C4#12112yes—
456C22×C4#12112yes—
457C22×C4C23×C411yescharacteristic
458C22×C4C23×C412yes—
459C22×C4C22×D411yescharacteristic
460C22×C4C22×D411yescharacteristic
461C22×C4C22×D411yescharacteristic
462C22×C4C2×#4112yes—
463C22×C4C2×#4111yescharacteristic
464C22×C4C2×#4112yes—
465C22×C4C2×#4111yescharacteristic
466C22×C4C2×#4112yes—
467Q16—216no—
468SD16—216no—
469M16—22no—
470M16—24no—
471M16—24no—
472M16—22no—
473M16—22no—
474M16—24no—
475M16—42no—
476M16—42no—
477M16—42no—
478M16C2×C4214yescomplemented
479C2×C8—22no—
480C2×C8—24no—
481C2×C8—22no—
482C2×C8—24no—
483C2×C8—42no—
484C2×C8—42no—
485C2×C8—42no—
486C4⋊C4—216no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—44no—
502C4⋊C4—44no—
503C4⋊C4C2×C22⋊C412yes—
504C4⋊C4C2×C22⋊C412yes—
505C4⋊C4C4×D414yes—
506C4⋊C4C4×D414yes—
507C22⋊C4—216no—
508C22⋊C4—22no—
509C22⋊C4—24no—
510C22⋊C4—22no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C42—216no—
515C42—22no—
516C42—24no—
517C42—22no—
518C42—24no—
519C42—24no—
520C42—24no—
521C42—24no—
522C42—24no—
523C42—48no—
524C42—48no—
525C42—42no—
526C42—42no—
527C42—44no—
528C42—44no—
529C42—44no—
530C42—42no—
531C42—42no—
532C42—82no—
533C42—82no—
534C42—84no—
535C42—84no—
536C42C2×C22⋊C412yes—
537C42C2×C22⋊C412yes—
538C42C4×D412yes—
539C42C4×D412yes—
540C42#12112yes—
541C42#12112yes—
542C42#12312yes—
543C42#12312yes—
544C23—21no—
545C23—21no—
546C23—22no—
547C23—22no—
548C23—24no—
549C23—41no—
550C23—41no—
551C23—42no—
552C23C2×C4×D411yescharacteristic
553C23C2×C4×D412yes—
554C23C2×#12011yescharacteristic
555C23C2×#12111yescharacteristic
556C23#52512yes—
557Q8—22no—
558Q8—24no—
559Q8—24no—
560Q8—24no—
561Q8—42no—
562Q8—42no—
563Q8—44no—
564Q8—44no—
565Q8C4×C22⋊C414yes—
566D4—24no—
567D4—24no—
568D4—28no—
569D4—22no—
570D4—24no—
571D4C4×C22⋊C414yes—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—28no—
583C2×C4—28no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—28no—
589C2×C4—24no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—44no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—48no—
613C2×C4—44no—
614C2×C4—42no—
615C2×C4—84no—
616C2×C4—84no—
617C2×C4—816no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4#38612yes—
621C2×C4#38612yes—
622C2×C4#38612yes—
623C2×C4#38612yes—
624C2×C4#45512yes—
625C2×C4#45612yes—
626C2×C4C22×C4211yescharacteristic
627C2×C4C22×C22⋊C411yescharacteristic
628C2×C4C2×#11711yescharacteristic
629C2×C4C2×C4×D412yes—
630C2×C4C2×C4×D412yes—
631C2×C4C2×C4×D411yescharacteristic
632C2×C4C2×C4×D412yes—
633C2×C4C4×#4111yescharacteristic
634C2×C4C4×#4112yes—
635C2×C4C4×#4111yescharacteristic
636C2×C4C4×#4112yes—
637C2×C4C2×#12111yescharacteristic
638C2×C4C2×#12311yescharacteristic
639C2×C4#52512yes—
640C2×C4#52512yes—
641C2×C4#52912yes—
642C2×C4#52912yes—
643C2×C4#53212yes—
644C8—24no—
645C8—42no—
646C8—44no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—24no—
656C22—42no—
657C22—42no—
658C22—44no—
659C22—44no—
660C22C42×D411yescharacteristic
661C22C2×#38611yescharacteristic
662C22#229011yescharacteristic
663C22C4×#12012yes—
664C22C4×#12112yes—
665C22C2×#45511yescharacteristic
666C22C2×#45611yescharacteristic
667C22#301812yes—
668C4—24no—
669C4—22no—
670C4—22no—
671C4—22no—
672C4—48no—
673C4—44no—
674C4—42no—
675C4—42no—
676C4—48no—
677C4—44no—
678C4—44no—
679C4—82no—
680C4#188214yesdirect product factor
681C4C2×C4×C22⋊C411yescharacteristic
682C4C42×D411yescharacteristic
683C4#229011yescharacteristic
684C4#229711yescharacteristic
685C4C4×#12112yes—
686C4C4×#12312yes—
687C2—22no—
688C2—21no—
689C2—21no—
690C2—44no—
691C2C4×#38611yescharacteristic
692C2C2×#188211yescharacteristic
693C2#2094211yescharacteristic
694C2C4×#45512yes—
695C2C4×#45612yes—
subgroupG/H
centerC22×C4#120
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C2×#120
prime radicalC22×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C4×#419C2semidirect
6. C4×#391C2semidirect
7. #10957C2semidirect
8. #10899C2semidirect
10. C4×#343C2semidirect
11. C4×#339C2semidirect
17. C4×#137C4semidirect
43. #1882C4direct (N × H)
84. C2×C4×Q8C2×C4semidirect
114. #428C2×C4semidirect
122. #419C2×C4semidirect
123. #419C2×C4semidirect
135. C4×M16C2×C4semidirect
141. #391C2×C4semidirect
175. #343C2×C4semidirect
180. #339C2×C4semidirect
215. #137C42semidirect
397. C2×Q8C2×C42semidirect
478. M16C2×C42semidirect
680. C4#1882direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#1372
C4×#5202
C2×#18822
C4×#4192
C2×C4×#1042
C4×#3912
#109572
#108992
#107812
C4×#3432
C4×#3392