Finite Group Databasebeta

← C4×#19127842 #35409999

Subgroups — C4×#19127842 #35409999

Order 21248.

1532 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic166C211yesmaximal, characteristic, complemented
2C2×#19127842C211yesmaximal, characteristic
3C2×C4×#13050579C212yesmaximal, complemented
4C4×#14581766C211yesmaximal, characteristic
5#24907817C212yesmaximal, complemented
6#24907778C211yesmaximal, characteristic
7#24907734C212yesmaximal, complemented
8#24907658C211yesmaximal, characteristic, complemented
9#24907399C211yesmaximal, characteristic, complemented
10C4×#14581717C212yesmaximal, complemented
11C4×C22⋊C8×C83C211yesmaximal, characteristic, complemented
12C23×Dic166C2211yescharacteristic
13C22×#13050579C2212yes—
14C2×#14581766C2211yescharacteristic
15C2×C4×Dic166—28no—
16C2×C4×Dic166—21no—
17C2×C4×Dic166—21no—
18C2×C4×Dic166C2212yes—
19C2×C4×Dic166C2212yes—
20C2×C4×D332C2211yescharacteristic
21C2×C4×C22⋊D83—21no—
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4—21no—
24C22×C4×Dic83—21no—
25#19127842C418yesdirect product factor
26C4×#13050579—28no—
27C2×#14581724C2212yes—
28C2×#14581717C2212yes—
29C2×#14581717C2212yes—
30C2×#14581717C2212yes—
31C2×#14581714C2212yes—
32#19127603C2211yescharacteristic
33#19127599C2211yescharacteristic
34#19127592—21no—
35#19127580—21no—
36#19127561C2211yescharacteristic
37C4×C4⋊Dic83C2211yescharacteristic
38C4×(C2×D83)⋊C4—21no—
39#19127464C2212yes—
40#19127464C2212yes—
41C22×C42×C83C2211yescharacteristic
42C2×C22⋊C8×C83C2211yescharacteristic
43C2×C22⋊C8×C83C2211yescharacteristic
44C2×C4×C8×C83C2212yes—
45#336×C83C2212yes—
46C22×Dic166—24no—
47C22×Dic166—24no—
48C22×Dic166—21no—
49C22×Dic166—22no—
50C22×Dic166C2×C414yescomplemented
51C22×Dic166C2312yes—
52C22×D332C2311yescharacteristic
53C22×C22⋊D83—21no—
54C23×Dic83—21no—
55C23×Dic83—21no—
56C22×C4×D83—21no—
57C2×#13050579—24no—
58C2×#13050579—24no—
59C2×#13050579C2×C418yescomplemented
60#14581766—22no—
61#14581766C2×C414yes—
62C4×Dic166—28no—
63C4×Dic166—28no—
64C4×Dic166—24no—
65C4×Dic166—24no—
66C4×Dic166—24no—
67C4×Dic166D418yescomplemented
68C4×D332—24no—
69C4×C22⋊D83—44no—
70C2×C4⋊Dic83—24no—
71C2×C4⋊Dic83—21no—
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2312yes—
76C2×Dic83⋊C4—28no—
77C2×Dic83⋊C4—22no—
78C2×Dic83⋊C4—22no—
79C2×Dic83⋊C4—21no—
80C2×C22⋊Dic83—21no—
81C2×(C2×D83)⋊C4—21no—
82C2×(C2×D83)⋊C4—21no—
83C2×(C2×D83)⋊C4—21no—
84C2×(C2×D83)⋊C4—21no—
85C2×C4×Dic83—28no—
86C2×C4×Dic83—22no—
87C2×C4×Dic83—22no—
88C2×C4×Dic83—21no—
89#14581724—24no—
90#14581717—24no—
91#14581717—24no—
92#14581717C2×C418yescomplemented
93#14581714—24no—
94C83⋊#95—21no—
95C83⋊#95—21no—
96C83⋊#95—21no—
97C23×C4×C83D411yescharacteristic
98C23×C4×C83D411yescharacteristic
99C23×C4×C83C2311yescharacteristic
100C22×C8×C83C2312yes—
101C22×C8×C83C2312yes—
102C2×C42×C83—24no—
103C2×C42×C83D411yescharacteristic
104C2×C42×C83D411yescharacteristic
105C2×C42×C83C2311yescharacteristic
106C2×C42×C83C2311yescharacteristic
107C22⋊C8×C83—22no—
108C22⋊C8×C83C2×C414yescomplemented
109C4×C8×C83—24no—
110C23×D83—21no—
111C2×Dic166—24no—
112C2×Dic166—216no—
113C2×Dic166—24no—
114C2×Dic166—24no—
115C2×Dic166—22no—
116C2×Dic166—22no—
117C2×Dic166—22no—
118C2×Dic166—216no—
119C2×Dic166C22×C414yes—
120C2×Dic166C2×D414yes—
121C2×Dic166#4114yes—
122C2×D332—22no—
123C2×D332—22no—
124C2×D332—21no—
125C2×D332C22×C412yes—
126C2×C22⋊D83—24no—
127C2×C22⋊D83—42no—
128C2×C22⋊D83—42no—
129C22×Dic83—24no—
130C22×Dic83—24no—
131C22×Dic83—24no—
132C22×Dic83—22no—
133C22×Dic83—24no—
134C22×Dic83—22no—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—42no—
139C22×Dic83—42no—
140C2×C4×D83—42no—
141C2×C4×D83—42no—
142C2×C4×D83—42no—
143#13050579—216no—
144C4⋊Dic83—24no—
145C4⋊Dic83—22no—
146C4⋊Dic83—21no—
147C4⋊Dic83—22no—
148C4⋊Dic83—22no—
149C4⋊Dic83C22×C412yes—
150C4⋊Dic83C2×D414yes—
151Dic83⋊C4—28no—
152Dic83⋊C4—28no—
153Dic83⋊C4—42no—
154C22⋊Dic83—42no—
155(C2×D83)⋊C4—24no—
156(C2×D83)⋊C4—42no—
157(C2×D83)⋊C4—42no—
158(C2×D83)⋊C4—42no—
159C4×Dic83—28no—
160C4×Dic83—28no—
161C4×Dic83—42no—
162C24×C83C2×D411yescharacteristic
163C22×C4×C83—22no—
164C22×C4×C83—22no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—41no—
170C22×C4×C83SD1614yescomplemented
171C22×C4×C83C22×C412yes—
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83#4112yes—
178C22×C4×C83C2411yescharacteristic
179C2×C8×C83—22no—
180C2×C8×C83—22no—
181C2×C8×C83—22no—
182C2×C8×C83—22no—
183C2×C8×C83—22no—
184C2×C8×C83C22×C414yes—
185C42×C83—22no—
186C42×C83—22no—
187C42×C83—22no—
188C42×C83C2×D414yes—
189C23×C83—21no—
190C23×C83—21no—
191C23×C83—21no—
192C23×C83—21no—
193C23×C83C4×D412yes—
194C23×C83C2×SD1612yes—
195C23×C83#13512yes—
196C23×C83C22×D411yescharacteristic
197C22×D83—22no—
198C22×D83—41no—
199C22×D83—41no—
200C22×D83—41no—
201C22×D83—41no—
202C22×D83—41no—
203C22×D83—41no—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—21no—
207C2×C4×C83—21no—
208C2×C4×C83—21no—
209C2×C4×C83—21no—
210C2×C4×C83—24no—
211C2×C4×C83—24no—
212C2×C4×C83—28no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—44no—
217C2×C4×C83C4×D412yes—
218C2×C4×C83#12012yes—
219C2×C4×C83#12012yes—
220C2×C4×C83C2×SD1612yes—
221C2×C4×C83C2×SD1612yes—
222C2×C4×C83#13712yes—
223C2×C4×C83C23×C411yescharacteristic
224C2×C4×C83C22×D412yes—
225C2×C4×C83C2×#4112yes—
226C2×C4×C83C2×#4111yescharacteristic
227C22⋊D83—48no—
228C2×Dic83—216no—
229C2×Dic83—24no—
230C2×Dic83—24no—
231C2×Dic83—24no—
232C2×Dic83—22no—
233C2×Dic83—24no—
234C2×Dic83—48no—
235C2×Dic83—41no—
236C2×Dic83—42no—
237C2×Dic83—41no—
238C2×Dic83—42no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245D332—24no—
246D332—42no—
247C4×D83—84no—
248Dic166—216no—
249Dic166—24no—
250Dic166—24no—
251Dic166—24no—
252Dic166C4×D418yescomplemented
253C8×C83—24no—
254C8×C83—42no—
255C22×C83—22no—
256C22×C83—22no—
257C22×C83—22no—
258C22×C83—22no—
259C22×C83—22no—
260C22×C83—22no—
261C22×C83C4×SD1614yescomplemented
262C22×C83C2×C4×D411yescharacteristic
263C22×C83C2×#12011yescharacteristic
264C22×C83#52511yescharacteristic
265C22×C83C22×SD1611yescharacteristic
266C22×C83C2×#13511yescharacteristic
267C22×C83C2×#13711yescharacteristic
268C22×C83#57511yescharacteristic
269C2×D83—42no—
270C2×D83—42no—
271C2×D83—42no—
272C2×D83—81no—
273C2×D83—81no—
274C2×D83—81no—
275C2×D83—81no—
276C4×C83—22no—
277C4×C83—22no—
278C4×C83—22no—
279C4×C83—41no—
280C4×C83#44814yescomplemented
281C4×C83C2×C4×D412yes—
282C4×C83#52512yes—
283Dic83—28no—
284Dic83—42no—
285Dic83—44no—
286Dic83—81no—
287Dic83—81no—
288C4×#448—831nomaximal, Sylow
289C2×C83—24no—
290C2×C83C4×#12011yescharacteristic
291C2×C83C2×C4×SD1611yescharacteristic
292C2×C83C4×#13711yescharacteristic
293C2×C83C2×#44811yescharacteristic
294C2×C83#300211yescharacteristic
295C2×C83#310311yescharacteristic
296C2×C83#310811yescharacteristic
297D83—82no—
298C22×C4×Q8—831no—
299C2×#448—831no—
300C2×C4×SD16—832no—
301C4×#121—831no—
302#1880—832no—
303#1874—831no—
304#1865—832no—
305#1853—831no—
306#1787—831no—
307C4×#103—832no—
308C4×C22⋊C8D8311yescharacteristic, complemented
309C83C4×#44811yescharacteristic, complemented, Sylow
310C23×Q8—831no—
311C22×SD16—832no—
312C2×#121—831no—
313C2×C4×Q8—832no—
314C2×C4×Q8—832no—
315C2×C4×Q8—1668no—
316C2×C4×Q8—1661no—
317C2×C4×Q8—1661no—
318C2×C4×D4—831no—
319C2×C4×D4—1661no—
320C22×C4⋊C4—831no—
321C22×C4⋊C4—1661no—
322C22×C42—1661no—
323C22×C42C2×D8311yescharacteristic
324#448—838no—
325C4×SD16—1668no—
326C2×#106—832no—
327C2×#103—832no—
328C2×#103—832no—
329C2×#103—832no—
330C2×#102—832no—
331C2×C22⋊C8C2×D8311yescharacteristic
332C2×C22⋊C8C2×D8311yescharacteristic
333C2×C4×C8C2×D8312yes—
334#390—831no—
335#389—831no—
336#388—1661no—
337#386—1661no—
338#380—831no—
339C4×C4⋊C4—831no—
340C4×C22⋊C4—1661no—
341#340—832no—
342#340—832no—
343#336C2×D8312yes—
344C22×Q8—834no—
345C22×Q8—832no—
346C22×Q8—1664no—
347C22×Q8—1664no—
348C22×Q8—1661no—
349C22×Q8—1662no—
350C22×D4—831no—
351C22×D4—1661no—
352C23×C4—1661no—
353C23×C4—1661no—
354C23×C4—1661no—
355C23×C4D33211yescharacteristic
356C23×C4D33211yescharacteristic
357C23×C4C22×D8311yescharacteristic
358C2×SD16—838no—
359C2×SD16—1664no—
360C2×SD16—1664no—
361C22×C8C22×D8312yes—
362C22×C8C22×D8312yes—
363#121—834no—
364#121—1662no—
365C4×Q8—838no—
366C4×Q8—1664no—
367C4×Q8—1664no—
368C4×Q8—1668no—
369C4×Q8—1668no—
370C4×Q8—1664no—
371C4×D4—3324no—
372C4×D4—1664no—
373C2×C4⋊C4—832no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4—831no—
376C2×C4⋊C4—831no—
377C2×C4⋊C4—1661no—
378C2×C4⋊C4—1664no—
379C2×C4⋊C4—1668no—
380C2×C4⋊C4—1661no—
381C2×C4⋊C4—1662no—
382C2×C4⋊C4—1662no—
383C2×C22⋊C4—1661no—
384C2×C22⋊C4—1661no—
385C2×C22⋊C4—1661no—
386C2×C22⋊C4—1661no—
387C2×C22⋊C4—1661no—
388C2×C42—24no—
389C2×C42—1661no—
390C2×C42—1668no—
391C2×C42—1662no—
392C2×C42—1662no—
393C2×C42D33211yescharacteristic
394C2×C42D33211yescharacteristic
395C2×C42C22×D8311yescharacteristic
396C2×C42C22×D8311yescharacteristic
397#106—1664no—
398#103—838no—
399#103—1664no—
400#103—1664no—
401#102—1664no—
402C22⋊C8—22no—
403C22⋊C8C4×D8314yescomplemented
404C4×C8—24no—
405#95—1661no—
406#95—1661no—
407#95—1661no—
408C24—1661no—
409C24C2×D33211yescharacteristic
410C2×Q8—834no—
411C2×Q8—834no—
412C2×Q8—834no—
413C2×Q8—16616no—
414C2×Q8—1664no—
415C2×Q8—1664no—
416C2×Q8—16616no—
417C2×Q8—1662no—
418C2×Q8—1662no—
419C2×Q8—1662no—
420C2×Q8—1664no—
421C2×D4—3322no—
422C2×D4—3322no—
423C2×D4—832no—
424C2×D4—1664no—
425C2×D4—1662no—
426C2×D4—1662no—
427C2×D4—1661no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—41no—
435C22×C4—3322no—
436C22×C4—3322no—
437C22×C4—3322no—
438C22×C4—3322no—
439C22×C4—3322no—
440C22×C4—1661no—
441C22×C4—1661no—
442C22×C4—1664no—
443C22×C4—1661no—
444C22×C4—1662no—
445C22×C4—1664no—
446C22×C4—1664no—
447C22×C4—1662no—
448C22×C4—1664no—
449C22×C4#1305057914yescomplemented
450C22×C4C2×C4×D8312yes—
451C22×C4C2×D33211yescharacteristic
452C22×C4C2×D33211yescharacteristic
453C22×C4C2×D33211yescharacteristic
454C22×C4C2×D33211yescharacteristic
455C22×C4C2×D33211yescharacteristic
456C22×C4#1305059012yes—
457C22×C4C23×D8311yescharacteristic
458SD16—16616no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8C2×C4×D8314yes—
465C4⋊C4—3322no—
466C4⋊C4—832no—
467C4⋊C4—834no—
468C4⋊C4—1668no—
469C4⋊C4—1664no—
470C4⋊C4—1662no—
471C4⋊C4—1662no—
472C4⋊C4—1668no—
473C4⋊C4—1662no—
474C4⋊C4—1661no—
475C22⋊C4—3322no—
476C22⋊C4—3322no—
477C22⋊C4—3322no—
478C22⋊C4—3322no—
479C22⋊C4—1664no—
480C42—22no—
481C42—22no—
482C42—22no—
483C42—3322no—
484C42—1668no—
485C42—1668no—
486C42D4×D8314yes—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—3321no—
492C23—3321no—
493C23—3321no—
494C23—3321no—
495C23—3321no—
496C23—3321no—
497C23—1662no—
498C23C4×D33212yes—
499C23C2×#1305057912yes—
500C23#1458181412yes—
501C23C22×D33211yescharacteristic
502Q8—838no—
503Q8—16616no—
504Q8—1664no—
505Q8—1664no—
506Q8—1664no—
507D4—3328no—
508D4—3322no—
509D4—1664no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—44no—
523C2×C4—3328no—
524C2×C4—3321no—
525C2×C4—3322no—
526C2×C4—3321no—
527C2×C4—3322no—
528C2×C4—3321no—
529C2×C4—3321no—
530C2×C4—3321no—
531C2×C4—3321no—
532C2×C4—3321no—
533C2×C4—3321no—
534C2×C4—6644no—
535C2×C4—1662no—
536C2×C4—1664no—
537C2×C4—16616no—
538C2×C4—1664no—
539C2×C4—1664no—
540C2×C4—1664no—
541C2×C4C4×D33212yes—
542C2×C4#1458176212yes—
543C2×C4#1458176212yes—
544C2×C4C2×#1305057912yes—
545C2×C4C2×#1305057912yes—
546C2×C4#1458182512yes—
547C2×C4C22×C4×D8311yescharacteristic
548C2×C4C2×D4×D8312yes—
549C2×C4#41×D8312yes—
550C2×C4C2×#1305059011yescharacteristic
551C8—24no—
552C8—42no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—3322no—
560C22—3322no—
561C22—3322no—
562C22—6641no—
563C22—6641no—
564C22—6641no—
565C22—6641no—
566C22C4×#1305057914yescomplemented
567C22C2×C4×D33211yescharacteristic
568C22C2×#1458176211yescharacteristic
569C22#1912821311yescharacteristic
570C22C22×#1305057911yescharacteristic
571C22C2×#1458181411yescharacteristic
572C22C2×#1458182511yescharacteristic
573C22#1912850111yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—3324no—
579C4—3322no—
580C4—6641no—
581C4—6641no—
582C4—1668no—
583C4#1912784214yesdirect product factor
584C4C4×D4×D8312yes—
585C4#1912821012yes—
586C2—24no—
587C2—6642no—
588C2C4×#1458176211yescharacteristic
589C2C2×C4×#1305057911yescharacteristic
590C2C4×#1458182511yescharacteristic
591C2C2×#1912784211yescharacteristic
592C2#2491668511yescharacteristic
593C2#2491749511yescharacteristic
594C2#2491754511yescharacteristic
subgroupG/H
centerC22×C4C2×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×C22⋊C8×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581766C22
cosocleC22×C4×C83C24
hypercenterC4×C22⋊C8D83
hypocenterC83C4×#448
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic166C2semidirect
3. C2×C4×#13050579C2semidirect
5. #24907817C2semidirect
7. #24907734C2semidirect
8. #24907658C2semidirect
9. #24907399C2semidirect
10. C4×#14581717C2semidirect
11. C4×C22⋊C8×C83C2semidirect
25. #19127842C4direct (N × H)
50. C22×Dic166C2×C4semidirect
59. C2×#13050579C2×C4semidirect
67. C4×Dic166D4semidirect
92. #14581717C2×C4semidirect
108. C22⋊C8×C83C2×C4semidirect
170. C22×C4×C83SD16semidirect
252. Dic166C4×D4semidirect
261. C22×C83C4×SD16semidirect
280. C4×C83#448semidirect
308. C4×C22⋊C8D83semidirect
309. C83C4×#448semidirect
403. C22⋊C8C4×D83semidirect
449. C22×C4#13050579semidirect
566. C22C4×#13050579semidirect
583. C4#19127842direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic1662
C2×#191278422
C2×C4×#130505792
C4×#145817662
#249078172
#249077782
#249077342
#249076582
#249073992
C4×#145817172
C4×C22⋊C8×C832
C4×#44883