Finite Group Databasebeta

← C4×#1879 #354252

Subgroups — C4×#1879 #354252

Order 512.

2688 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D8C211yesmaximal, characteristic
2C2×C42×D4C211yesmaximal, characteristic, complemented
3C2×#1879C212yesmaximal
4C2×C4×#102C211yesmaximal, characteristic, complemented
5C2×C4×#102C211yesmaximal, characteristic, complemented
6C4×#390C211yesmaximal, characteristic, complemented
7#10931C212yesmaximal, complemented
8#10907C212yesmaximal, complemented
9#10788C212yesmaximal, complemented
10C4×#340C211yesmaximal, characteristic, complemented
11C4×#336C211yesmaximal, characteristic, complemented
12C23×D8C2211yescharacteristic
13C22×C4×D4C2212yes—
14C22×C4×D4C2211yescharacteristic
15C22×C4×D4C2211yescharacteristic
16C23×C42—21no—
17C2×C4×D8—24no—
18C2×C4×D8—24no—
19C2×C4×D8C418yescomplemented
20C22×#107C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2212yes—
23C22×#102C2211yescharacteristic
24C22×#102C2212yes—
25C22×C4×C8C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27C2×#390C2212yes—
28C42×D4—24no—
29C42×D4—24no—
30C2×C4×C4⋊C4C2212yes—
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4—22no—
34C2×C4×C22⋊C4—21no—
35C2×C4×C22⋊C4—21no—
36C2×C4×C22⋊C4—21no—
37C2×C43C2211yescharacteristic
38#1879C4116yesdirect product factor
39C4×#102—24no—
40C4×#102—24no—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#336C2212yes—
46C2×#336C2212yes—
47#1437—22no—
48C4⋊#95C2212yes—
49C23×D4C2311yescharacteristic
50C23×D4C2311yescharacteristic
51C24×C4—22no—
52C24×C4—21no—
53C24×C4—21no—
54C22×D8—22no—
55C22×D8—22no—
56C22×D8—24no—
57C22×D8C2×C418yes—
58C22×D8C2×C414yes—
59C23×C8C2312yes—
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C2×C4×D4—24no—
63C2×C4×D4—24no—
64C2×C4×D4—24no—
65C2×C4×D4—24no—
66C2×C4×D4—22no—
67C2×C4×D4—22no—
68C2×C4×D4—22no—
69C2×C4×D4—22no—
70C2×C4×D4—24no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4C2×C414yes—
76C2×C4×D4C2×C418yescomplemented
77C2×C4×D4C2×C414yescomplemented
78C2×C4×D4D414yes—
79C2×C4×D4D414yes—
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2312yes—
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2312yes—
84C22×C22⋊C4—22no—
85C22×C22⋊C4—21no—
86C22×C22⋊C4—21no—
87C22×C22⋊C4—22no—
88C22×C22⋊C4—22no—
89C22×C42—28no—
90C22×C42—22no—
91C22×C42—21no—
92C22×C42—21no—
93C22×C42—44no—
94C22×C42—44no—
95C22×C42D411yescharacteristic
96C22×C42D412yes—
97C22×C42D411yescharacteristic
98C22×C42C2312yes—
99C22×C42C2311yescharacteristic
100C4×D8—232no—
101C2×#107—22no—
102C2×#107—22no—
103C2×#107C2×C414yescomplemented
104C2×#102—22no—
105C2×#102—22no—
106C2×#102—24no—
107C2×#102—24no—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—24no—
111C2×#102—24no—
112C2×#102C2×C414yes—
113C2×#102C2×C418yescomplemented
114C2×#102C2×C418yescomplemented
115C2×#102C2×C414yescomplemented
116C2×C4×C8—22no—
117C2×C4×C8—22no—
118C2×C4×C8—22no—
119C2×C4×C8—22no—
120C2×C4×C8—22no—
121C2×C4×C8C2×C414yescomplemented
122#390—24no—
123#390C2×C418yescomplemented
124C4×C4⋊C4—24no—
125C4×C4⋊C4—24no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—22no—
128C4×C4⋊C4—22no—
129C4×C4⋊C4D414yes—
130C4×C22⋊C4—28no—
131C4×C22⋊C4—216no—
132C4×C22⋊C4—44no—
133C4×C22⋊C4—44no—
134C2×#95—22no—
135C2×#95—21no—
136C2×#95—22no—
137C2×#95—22no—
138C2×#95—21no—
139C43—22no—
140C43—22no—
141#340—24no—
142#340—24no—
143#340—24no—
144#340C2×C418yescomplemented
145#336—24no—
146#336C2×C418yescomplemented
147C25—21no—
148C25—21no—
149C22×D4—21no—
150C22×D4—21no—
151C22×D4—21no—
152C22×D4—21no—
153C22×D4—21no—
154C22×D4—22no—
155C22×D4—21no—
156C22×D4—22no—
157C22×D4—21no—
158C22×D4—22no—
159C22×D4—22no—
160C22×D4—21no—
161C22×D4—22no—
162C22×D4C22×C412yes—
163C22×D4C22×C414yes—
164C22×D4C22×C412yes—
165C22×D4C22×C414yes—
166C22×D4C2×D412yes—
167C22×D4C2×D412yes—
168C22×D4#4114yes—
169C23×C4—28no—
170C23×C4—28no—
171C23×C4—21no—
172C23×C4—22no—
173C23×C4—24no—
174C23×C4—28no—
175C23×C4—24no—
176C23×C4—24no—
177C23×C4—22no—
178C23×C4—21no—
179C23×C4—24no—
180C23×C4—44no—
181C23×C4—44no—
182C23×C4—44no—
183C23×C4—42no—
184C23×C4—44no—
185C23×C4—42no—
186C23×C4—42no—
187C23×C4—42no—
188C23×C4—42no—
189C23×C4—42no—
190C23×C4—42no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4C2×D412yes—
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D412yes—
197C23×C4C2×D411yescharacteristic
198C23×C4C2411yescharacteristic
199C2×D8—28no—
200C2×D8—28no—
201C2×D8—216no—
202C2×D8—216no—
203C2×D8C42116yescomplemented
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—22no—
207C22×C8—22no—
208C22×C8—22no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—22no—
212C22×C8—22no—
213C22×C8—22no—
214C22×C8—22no—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8C22×C414yes—
218C22×C8C22×C412yes—
219C22×C8C22×C414yes—
220C22×C8C22×C412yes—
221C4×D4—216no—
222C4×D4—216no—
223C4×D4—216no—
224C4×D4—216no—
225C4×D4—28no—
226C4×D4—28no—
227C4×D4—28no—
228C4×D4—28no—
229C4×D4—28no—
230C4×D4—44no—
231C4×D4—44no—
232C4×D4C22⋊C4116yescomplemented
233C2×C4⋊C4—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4C22×C412yes—
250C2×C4⋊C4C22×C414yes—
251C2×C4⋊C4C22×C412yes—
252C2×C4⋊C4C22×C414yes—
253C2×C4⋊C4C2×D412yes—
254C2×C4⋊C4C2×D412yes—
255C2×C4⋊C4C2×D414yes—
256C2×C4⋊C4#4114yes—
257C2×C22⋊C4—28no—
258C2×C22⋊C4—28no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—28no—
261C2×C22⋊C4—24no—
262C2×C22⋊C4—24no—
263C2×C22⋊C4—24no—
264C2×C22⋊C4—28no—
265C2×C22⋊C4—28no—
266C2×C22⋊C4—44no—
267C2×C22⋊C4—44no—
268C2×C22⋊C4—42no—
269C2×C22⋊C4—42no—
270C2×C22⋊C4—44no—
271C2×C22⋊C4—44no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42—22no—
278C2×C42—28no—
279C2×C42—24no—
280C2×C42—22no—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—22no—
284C2×C42—22no—
285C2×C42—432no—
286C2×C42—42no—
287C2×C42—44no—
288C2×C42—44no—
289C2×C42—42no—
290C2×C42—42no—
291C2×C42—42no—
292C2×C42—42no—
293C2×C42—42no—
294C2×C42D814yescomplemented
295C2×C42C22×C414yes—
296C2×C42C22×C412yes—
297C2×C42C2×D412yes—
298C2×C42C2×D412yes—
299C2×C42C2×D412yes—
300C2×C42#4114yes—
301C2×C42#4112yes—
302C2×C42#4112yes—
303#107—28no—
304#102—28no—
305#102—216no—
306#102—28no—
307#102—216no—
308C4×C8—28no—
309C4×C8—44no—
310#95—28no—
311#95—24no—
312#95—44no—
313#95—42no—
314#95—44no—
315C24—22no—
316C24—24no—
317C24—22no—
318C24—22no—
319C24—24no—
320C24—24no—
321C24—22no—
322C24—41no—
323C24—41no—
324C24—42no—
325C24—41no—
326C24—41no—
327C24—42no—
328C24—41no—
329C24—41no—
330C24—42no—
331C24—41no—
332C24—42no—
333C24—41no—
334C24—41no—
335C24—41no—
336C24—42no—
337C24C22×D411yescharacteristic
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—24no—
342C2×D4—24no—
343C2×D4—22no—
344C2×D4—24no—
345C2×D4—24no—
346C2×D4—22no—
347C2×D4—24no—
348C2×D4—22no—
349C2×D4—24no—
350C2×D4—22no—
351C2×D4—24no—
352C2×D4—22no—
353C2×D4—24no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—24no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4C2×C4214yes—
369C2×D4C2×C4214yescomplemented
370C2×D4C2×C22⋊C414yes—
371C2×D4#11714yes—
372C2×D4C4×D418yes—
373C2×D4C4×D418yes—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—232no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—216no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—416no—
397C22×C4—416no—
398C22×C4—416no—
399C22×C4—416no—
400C22×C4—416no—
401C22×C4—42no—
402C22×C4—41no—
403C22×C4—42no—
404C22×C4—41no—
405C22×C4—42no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—42no—
409C22×C4—48no—
410C22×C4—416no—
411C22×C4—48no—
412C22×C4—48no—
413C22×C4—48no—
414C22×C4—48no—
415C22×C4—48no—
416C22×C4—41no—
417C22×C4—42no—
418C22×C4—41no—
419C22×C4—42no—
420C22×C4—41no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—42no—
426C22×C4—41no—
427C22×C4—42no—
428C22×C4—48no—
429C22×C4—48no—
430C22×C4—48no—
431C22×C4—84no—
432C22×C4—84no—
433C22×C4—84no—
434C22×C4—84no—
435C22×C4C4×D414yes—
436C22×C4C4×D412yes—
437C22×C4C4×D414yes—
438C22×C4C4×D412yes—
439C22×C4#12012yes—
440C22×C4#12012yes—
441C22×C4#12112yes—
442C22×C4#12112yes—
443C22×C4C2×D814yes—
444C22×C4C2×D812yes—
445C22×C4#13514yes—
446C22×C4#13512yes—
447C22×C4AGL(1,ℤ/8)12yes—
448C22×C4AGL(1,ℤ/8)12yes—
449C22×C4C23×C411yescharacteristic
450C22×C4C23×C412yes—
451C22×C4C22×D411yescharacteristic
452C22×C4C22×D411yescharacteristic
453C22×C4C22×D411yescharacteristic
454C22×C4C2×#4112yes—
455C22×C4C2×#4111yescharacteristic
456C22×C4C2×#4112yes—
457C22×C4C2×#4111yescharacteristic
458C22×C4C2×#4112yes—
459D8—232no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—24no—
463C2×C8—24no—
464C2×C8—22no—
465C2×C8—24no—
466C2×C8—24no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—24no—
470C2×C8—42no—
471C2×C8—42no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8—42no—
475C2×C8—42no—
476C2×C8C2×C4214yescomplemented
477C4⋊C4—22no—
478C4⋊C4—24no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—24no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4C2×C22⋊C414yes—
492C4⋊C4C4×D418yes—
493C22⋊C4—232no—
494C22⋊C4—216no—
495C22⋊C4—416no—
496C22⋊C4—48no—
497C22⋊C4—416no—
498C42—24no—
499C42—24no—
500C42—24no—
501C42—24no—
502C42—28no—
503C42—48no—
504C42—416no—
505C42—48no—
506C42—44no—
507C42—84no—
508C42C2×C22⋊C414yes—
509C42C4×D414yes—
510C42#12114yes—
511C42#12314yes—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—28no—
516C23—28no—
517C23—24no—
518C23—44no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—42no—
523C23—44no—
524C23—42no—
525C23—44no—
526C23—42no—
527C23—42no—
528C23—44no—
529C23—44no—
530C23—42no—
531C23—42no—
532C23—44no—
533C23—42no—
534C23—42no—
535C23—44no—
536C23—44no—
537C23—42no—
538C23—42no—
539C23—44no—
540C23—42no—
541C23—42no—
542C23—44no—
543C23—44no—
544C23—42no—
545C23—42no—
546C23—44no—
547C23—44no—
548C23—82no—
549C23—82no—
550C23—82no—
551C23—82no—
552C23—81no—
553C23—81no—
554C23—82no—
555C23—81no—
556C23—81no—
557C23—82no—
558C23C2×C4×D411yescharacteristic
559C23C2×C4×D412yes—
560C23C2×#12011yescharacteristic
561C23C2×#12111yescharacteristic
562C23#52512yes—
563C23C22×D811yescharacteristic
564C23C2×#13511yescharacteristic
565C23C2×#13512yes—
566C23C2×AGL(1,ℤ/8)11yescharacteristic
567C23C2×AGL(1,ℤ/8)11yescharacteristic
568C23#57512yes—
569D4—24no—
570D4—24no—
571D4—24no—
572D4—24no—
573D4—24no—
574D4—28no—
575D4—28no—
576D4—42no—
577D4—42no—
578D4—44no—
579D4—44no—
580D4C4×C22⋊C418yescomplemented
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—28no—
596C2×C4—464no—
597C2×C4—44no—
598C2×C4—42no—
599C2×C4—44no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—44no—
603C2×C4—42no—
604C2×C4—44no—
605C2×C4—42no—
606C2×C4—44no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—432no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—44no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—82no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4—82no—
628C2×C4—816no—
629C2×C4#38614yes—
630C2×C4#38614yes—
631C2×C4C4×D814yes—
632C2×C4C4×D818yescomplemented
633C2×C4#44214yes—
634C2×C4#44714yes—
635C2×C4#44914yes—
636C2×C4#45914yes—
637C2×C4#46314yes—
638C2×C4C22×C4211yescharacteristic
639C2×C4C22×C22⋊C411yescharacteristic
640C2×C4C2×#11711yescharacteristic
641C2×C4C2×C4×D412yes—
642C2×C4C2×C4×D412yes—
643C2×C4C2×C4×D411yescharacteristic
644C2×C4C2×C4×D412yes—
645C2×C4C4×#4111yescharacteristic
646C2×C4C4×#4112yes—
647C2×C4C4×#4111yescharacteristic
648C2×C4C4×#4112yes—
649C2×C4C2×#12111yescharacteristic
650C2×C4C2×#12311yescharacteristic
651C2×C4#52512yes—
652C2×C4#52512yes—
653C2×C4#52912yes—
654C2×C4#52912yes—
655C2×C4#53212yes—
656C8—24no—
657C8—42no—
658C8—44no—
659C22—28no—
660C22—44no—
661C22—44no—
662C22—44no—
663C22—44no—
664C22—44no—
665C22—44no—
666C22—48no—
667C22—48no—
668C22—48no—
669C22—48no—
670C22—44no—
671C22—44no—
672C22—44no—
673C22—82no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—84no—
678C22—84no—
679C22—84no—
680C22—84no—
681C22C42×D411yescharacteristic
682C22C2×#38611yescharacteristic
683C22#229011yescharacteristic
684C22C4×#12012yes—
685C22C4×#12112yes—
686C22C2×C4×D811yescharacteristic
687C22C2×C4×D812yes—
688C22C4×#13511yescharacteristic
689C22C4×#13512yes—
690C22C2×#44211yescharacteristic
691C22#294311yescharacteristic
692C22C4×AGL(1,ℤ/8)12yes—
693C22C4×AGL(1,ℤ/8)12yes—
694C22C2×#44711yescharacteristic
695C22C2×#44911yescharacteristic
696C22#300212yes—
697C22C2×#45911yescharacteristic
698C22C2×#46311yescharacteristic
699C22#303512yes—
700C22#310012yes—
701C22#310212yes—
702C22#310512yes—
703C22#310612yes—
704C4—24no—
705C4—28no—
706C4—44no—
707C4—48no—
708C4—44no—
709C4—82no—
710C4—84no—
711C4#187918yesdirect product factor
712C4C2×C4×C22⋊C411yescharacteristic
713C4C42×D411yescharacteristic
714C4#229011yescharacteristic
715C4#229711yescharacteristic
716C4C4×#12112yes—
717C4C4×#12312yes—
718C2—48no—
719C2—84no—
720C2C4×#38611yescharacteristic
721C2C42×D811yescharacteristic
722C2C4×#44211yescharacteristic
723C2C2×#187911yescharacteristic
724C2#2092411yescharacteristic
725C2#2111311yescharacteristic
726C2#2111811yescharacteristic
727C2C4×#44712yes—
728C2C4×#44912yes—
729C2C4×#45912yes—
730C2C4×#46312yes—
subgroupG/H
centerC23×C4C2×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC24C22×D4
prime radicalC23×D8C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C42×D4C2semidirect
4. C2×C4×#102C2semidirect
5. C2×C4×#102C2semidirect
6. C4×#390C2semidirect
7. #10931C2semidirect
8. #10907C2semidirect
9. #10788C2semidirect
10. C4×#340C2semidirect
11. C4×#336C2semidirect
19. C2×C4×D8C4semidirect
38. #1879C4direct (N × H)
76. C2×C4×D4C2×C4semidirect
77. C2×C4×D4C2×C4semidirect
103. C2×#107C2×C4semidirect
113. C2×#102C2×C4semidirect
114. C2×#102C2×C4semidirect
115. C2×#102C2×C4semidirect
121. C2×C4×C8C2×C4semidirect
123. #390C2×C4semidirect
144. #340C2×C4semidirect
146. #336C2×C4semidirect
203. C2×D8C42semidirect
232. C4×D4C22⋊C4semidirect
294. C2×C42D8semidirect
369. C2×D4C2×C42semidirect
476. C2×C8C2×C42semidirect
580. D4C4×C22⋊C4semidirect
632. C2×C4C4×D8semidirect
711. C4#1879direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D82
C2×C42×D42
C2×#18792
C2×C4×#1022
C4×#3902
#109312
#109072
#107882
C4×#3402
C4×#3362