Finite Group Databasebeta

← C4×#19127580 #35325552

Subgroups — C4×#19127580 #35325552

Order 21248.

3366 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D83C211yesmaximal, characteristic
2C2×#19127580C212yesmaximal
3C2×C4×(C2×D83)⋊C4C212yesmaximal, complemented
4C2×C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
5#24905701C212yesmaximal, complemented
6#24905696C212yesmaximal, complemented
7#24905686C212yesmaximal, complemented
8C4×C83⋊#95C212yesmaximal, complemented
9C23×C42×C83C211yesmaximal, characteristic, complemented
10C23×C22⋊D83C2211yescharacteristic
11C23×C4×D83C2211yescharacteristic
12C2×C4×C22⋊D83—24no—
13C2×C4×C22⋊D83—24no—
14C2×C4×C22⋊D83C418yescomplemented
15C22×Dic83⋊C4C2211yescharacteristic
16C22×C22⋊Dic83C2211yescharacteristic
17C22×C22⋊Dic83C2212yes—
18C22×(C2×D83)⋊C4C2211yescharacteristic
19C22×(C2×D83)⋊C4C2214yes—
20C22×C4×Dic83C2212yes—
21C22×C4×Dic83C2211yescharacteristic
22#19127580C4116yesdirect product factor
23C4×(C2×D83)⋊C4—28no—
24C4×C22⋊Dic83—24no—
25C2×C83⋊#95C2214yes—
26C2×C83⋊#95C2214yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2214yes—
29C24×C4×C83C2212yes—
30C24×C4×C83C2211yescharacteristic
31C22×C42×C83—24no—
32C22×C42×C83—28no—
33C22×C42×C83C2212yes—
34C22×C42×C83C2212yes—
35C24×D83C2311yescharacteristic
36C22×C22⋊D83—22no—
37C22×C22⋊D83—22no—
38C22×C22⋊D83—24no—
39C22×C22⋊D83C2×C418yes—
40C22×C22⋊D83C2×C414yes—
41C23×Dic83C2314yes—
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2311yescharacteristic
44C23×Dic83C2311yescharacteristic
45C22×C4×D83—22no—
46C22×C4×D83—22no—
47C22×C4×D83—24no—
48C22×C4×D83—24no—
49C22×C4×D83C2×C414yescomplemented
50C4×C22⋊D83—232no—
51C2×Dic83⋊C4—22no—
52C2×Dic83⋊C4—22no—
53C2×Dic83⋊C4C2×C414yescomplemented
54C2×C22⋊Dic83—22no—
55C2×C22⋊Dic83—22no—
56C2×C22⋊Dic83—24no—
57C2×C22⋊Dic83—24no—
58C2×C22⋊Dic83C2×C414yes—
59C2×C22⋊Dic83C2×C418yescomplemented
60C2×(C2×D83)⋊C4—22no—
61C2×(C2×D83)⋊C4—22no—
62C2×(C2×D83)⋊C4—28no—
63C2×(C2×D83)⋊C4—28no—
64C2×(C2×D83)⋊C4C2×C4116yescomplemented
65C2×(C2×D83)⋊C4C2×C414yescomplemented
66C2×C4×Dic83—22no—
67C2×C4×Dic83—22no—
68C2×C4×Dic83—24no—
69C2×C4×Dic83—24no—
70C2×C4×Dic83—24no—
71C2×C4×Dic83C2×C414yescomplemented
72C83⋊#95—24no—
73C83⋊#95—28no—
74C83⋊#95—28no—
75C83⋊#95C2×C4116yescomplemented
76C25×C83C2311yescharacteristic
77C23×C4×C83—24no—
78C23×C4×C83—24no—
79C23×C4×C83—28no—
80C23×C4×C83—24no—
81C23×C4×C83—28no—
82C23×C4×C83—24no—
83C23×C4×C83C2×C414yes—
84C23×C4×C83C2×C418yescomplemented
85C23×C4×C83D414yes—
86C23×C4×C83D414yes—
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2314yes—
89C23×C4×C83C2311yescharacteristic
90C2×C42×C83—232no—
91C2×C42×C83—24no—
92C2×C42×C83—28no—
93C2×C42×C83—24no—
94C2×C42×C83—24no—
95C2×C42×C83D418yescomplemented
96C23×D83—21no—
97C23×D83—21no—
98C23×D83—22no—
99C23×D83—22no—
100C23×D83—22no—
101C23×D83—24no—
102C23×D83C22×C412yes—
103C23×D83C22×C414yes—
104C2×C22⋊D83—28no—
105C2×C22⋊D83—28no—
106C2×C22⋊D83—216no—
107C2×C22⋊D83—216no—
108C2×C22⋊D83C42116yescomplemented
109C22×Dic83—21no—
110C22×Dic83—21no—
111C22×Dic83—22no—
112C22×Dic83—22no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—24no—
116C22×Dic83—24no—
117C22×Dic83—21no—
118C22×Dic83—21no—
119C22×Dic83—22no—
120C22×Dic83—24no—
121C22×Dic83—24no—
122C22×Dic83—24no—
123C22×Dic83—24no—
124C22×Dic83—24no—
125C22×Dic83C22×C412yes—
126C22×Dic83C22×C418yes—
127C22×Dic83C22×C412yes—
128C22×Dic83C22×C414yes—
129C22×Dic83C22×C412yes—
130C2×C4×D83—28no—
131C2×C4×D83—216no—
132C2×C4×D83—44no—
133C2×C4×D83—48no—
134C2×C4×D83—44no—
135Dic83⋊C4—28no—
136C22⋊Dic83—28no—
137C22⋊Dic83—216no—
138(C2×D83)⋊C4—28no—
139(C2×D83)⋊C4—232no—
140C4×Dic83—28no—
141C4×Dic83—48no—
142C24×C83—22no—
143C24×C83—22no—
144C24×C83—24no—
145C24×C83C22×C412yes—
146C24×C83C22×C414yes—
147C24×C83C2×D412yes—
148C24×C83C2×D412yes—
149C24×C83#4114yes—
150C24×C83C2411yescharacteristic
151C22×C4×C83—216no—
152C22×C4×C83—232no—
153C22×C4×C83—216no—
154C22×C4×C83—216no—
155C22×C4×C83—22no—
156C22×C4×C83—24no—
157C22×C4×C83—24no—
158C22×C4×C83—22no—
159C22×C4×C83—24no—
160C22×C4×C83—24no—
161C22×C4×C83—216no—
162C22×C4×C83—232no—
163C22×C4×C83—28no—
164C22×C4×C83—216no—
165C22×C4×C83—28no—
166C22×C4×C83C22⋊C4116yescomplemented
167C22×C4×C83C22×C412yes—
168C22×C4×C83C22×C418yes—
169C22×C4×C83C22×C412yes—
170C22×C4×C83C2×D412yes—
171C22×C4×C83C2×D418yes—
172C22×C4×C83C2×D412yes—
173C22×C4×C83C2×D414yes—
174C22×C4×C83C2×D412yes—
175C22×C4×C83C2×D412yes—
176C22×C4×C83#4118yes—
177C22×C4×C83#4114yes—
178C42×C83—216no—
179C42×C83—216no—
180C23×C83—24no—
181C23×C83—28no—
182C23×C83—24no—
183C23×C83—28no—
184C23×C83—22no—
185C23×C83—24no—
186C23×C83—22no—
187C23×C83—24no—
188C23×C83—28no—
189C23×C83—28no—
190C23×C83—24no—
191C23×C83C2×C4214yes—
192C23×C83C2×C22⋊C414yes—
193C23×C83#11714yes—
194C23×C83C4×D418yes—
195C23×C83C4×D418yes—
196C23×C83C23×C411yescharacteristic
197C23×C83C23×C412yes—
198C23×C83C22×D411yescharacteristic
199C23×C83C22×D412yes—
200C23×C83C22×D411yescharacteristic
201C23×C83C2×#4112yes—
202C23×C83C2×#4112yes—
203C23×C83C2×#4114yes—
204C22×D83—22no—
205C22×D83—22no—
206C22×D83—28no—
207C22×D83—24no—
208C22×D83—24no—
209C22×D83—24no—
210C22×D83—24no—
211C22×D83—28no—
212C22×D83—41no—
213C22×D83—42no—
214C22×D83—41no—
215C22×D83—44no—
216C22×D83—42no—
217C22×D83—44no—
218C22×D83—42no—
219C22×D83C2×C4214yescomplemented
220C2×C4×C83—264no—
221C2×C4×C83—24no—
222C2×C4×C83—28no—
223C2×C4×C83—28no—
224C2×C4×C83—22no—
225C2×C4×C83—28no—
226C2×C4×C83—24no—
227C2×C4×C83—22no—
228C2×C4×C83—28no—
229C2×C4×C83—28no—
230C2×C4×C83—28no—
231C2×C4×C83—232no—
232C2×C4×C83C2×C22⋊C414yes—
233C2×C4×C83C2×C22⋊C414yes—
234C2×C4×C83C4×D418yes—
235C2×C4×C83C4×D4116yescomplemented
236C2×C4×C83#12014yes—
237C2×C4×C83#12118yes—
238C2×C4×C83#12314yes—
239C22⋊D83—232no—
240C2×Dic83—22no—
241C2×Dic83—22no—
242C2×Dic83—24no—
243C2×Dic83—24no—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—28no—
247C2×Dic83—28no—
248C2×Dic83—24no—
249C2×Dic83—24no—
250C2×Dic83—28no—
251C2×Dic83—41no—
252C2×Dic83—44no—
253C2×Dic83—42no—
254C2×Dic83—41no—
255C2×Dic83—42no—
256C2×Dic83—44no—
257C2×Dic83—44no—
258C2×Dic83—42no—
259C2×Dic83—44no—
260C2×Dic83C2×C4214yescomplemented
261C4×D83—416no—
262C22×C83—28no—
263C22×C83—24no—
264C22×C83—28no—
265C22×C83—24no—
266C22×C83—28no—
267C22×C83—216no—
268C22×C83—28no—
269C22×C83C4×C22⋊C418yescomplemented
270C22×C83C22×C4211yescharacteristic
271C22×C83C22×C22⋊C411yescharacteristic
272C22×C83C2×#11711yescharacteristic
273C22×C83C2×C4×D412yes—
274C22×C83C2×C4×D412yes—
275C22×C83C2×C4×D414yes—
276C22×C83C2×C4×D412yes—
277C22×C83C4×#4112yes—
278C22×C83C4×#4114yes—
279C22×C83C2×#12011yescharacteristic
280C22×C83C2×#12112yes—
281C22×C83C2×#12311yescharacteristic
282C22×C83#52514yes—
283C22×C83#52512yes—
284C22×C83#52914yes—
285C22×C83#53212yes—
286C2×D83—24no—
287C2×D83—28no—
288C2×D83—42no—
289C2×D83—44no—
290C2×D83—42no—
291C2×D83—44no—
292C2×D83—48no—
293C2×D83—44no—
294C4×C83—24no—
295C4×C83—216no—
296C4×C83#38618yescomplemented
297Dic83—24no—
298Dic83—42no—
299Dic83—42no—
300Dic83—48no—
301C4×#386—831nomaximal, Sylow
302C2×C83—28no—
303C2×C83C2×C4×C22⋊C411yescharacteristic
304C2×C83C42×D412yes—
305C2×C83C2×#38611yescharacteristic
306C2×C83#229012yes—
307C2×C83#229711yescharacteristic
308C2×C83C4×#12012yes—
309C2×C83C4×#12114yes—
310C2×C83C4×#12312yes—
311D83—44no—
312C22×C4×D4—831no—
313C23×C42D8311yescharacteristic, complemented
314C2×#386—832no—
315C2×C4×C22⋊C4—832no—
316C2×C4×C22⋊C4—831no—
317#1437—832no—
318#1436—832no—
319C22⋊#95—832no—
320C4×#95—832no—
321C83C4×#38611yescharacteristic, complemented, Sylow
322C23×D4—831no—
323C24×C4—831no—
324C24×C4C2×D8312yes—
325C24×C4C2×D8311yescharacteristic
326C2×C4×D4—838no—
327C2×C4×D4—1664no—
328C2×C4×D4—1664no—
329C22×C4⋊C4—831no—
330C22×C22⋊C4—831no—
331C22×C22⋊C4—832no—
332C22×C22⋊C4—831no—
333C22×C22⋊C4—834no—
334C22×C42—24no—
335C22×C42—28no—
336C22×C42—831no—
337C22×C42—832no—
338C22×C42C2×D8312yes—
339C22×C42C2×D8312yes—
340#386—8316no—
341C4×C22⋊C4—1664no—
342C4×C22⋊C4—1668no—
343C2×#95—834no—
344C2×#95—834no—
345C2×#95—834no—
346C2×#95—832no—
347C25—831no—
348C25C22×D8311yescharacteristic
349C22×D4—834no—
350C22×D4—838no—
351C22×D4—1662no—
352C22×D4—1662no—
353C22×D4—1664no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—28no—
357C23×C4—24no—
358C23×C4—28no—
359C23×C4—24no—
360C23×C4—831no—
361C23×C4—834no—
362C23×C4—831no—
363C23×C4—831no—
364C23×C4—834no—
365C23×C4—1662no—
366C23×C4—1664no—
367C23×C4—1662no—
368C23×C4—1664no—
369C23×C4C4×D8314yes—
370C23×C4C4×D8318yescomplemented
371C23×C4D33214yes—
372C23×C4C22⋊D8314yes—
373C23×C4C22×D8311yescharacteristic
374C23×C4C22×D8314yes—
375C23×C4C22×D8311yescharacteristic
376C4×D4—16632no—
377C2×C4⋊C4—834no—
378C2×C4⋊C4—1662no—
379C2×C4⋊C4—1662no—
380C2×C22⋊C4—834no—
381C2×C22⋊C4—838no—
382C2×C22⋊C4—834no—
383C2×C22⋊C4—8316no—
384C2×C22⋊C4—1662no—
385C2×C22⋊C4—1662no—
386C2×C22⋊C4—1664no—
387C2×C22⋊C4—1664no—
388C2×C22⋊C4—1662no—
389C2×C22⋊C4—1668no—
390C2×C22⋊C4—1662no—
391C2×C22⋊C4—1668no—
392C2×C42—232no—
393C2×C42—24no—
394C2×C42—28no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—834no—
398C2×C42—1664no—
399C2×C42—1664no—
400C2×C42—1664no—
401C2×C42—1662no—
402C2×C42—1662no—
403C2×C42C22⋊D8318yescomplemented
404#95—8316no—
405#95—1668no—
406#95—1664no—
407#95—1668no—
408C24—22no—
409C24—22no—
410C24—24no—
411C24—834no—
412C24—832no—
413C24—1662no—
414C24—1661no—
415C24—1661no—
416C24—1664no—
417C24—1662no—
418C24—1662no—
419C24C2×C4×D8312yes—
420C24C2×C4×D8314yes—
421C24C2×C22⋊D8312yes—
422C24C2×D33212yes—
423C24#1305059014yes—
424C24C23×D8311yescharacteristic
425C2×D4—8316no—
426C2×D4—1668no—
427C2×D4—1668no—
428C2×D4—16616no—
429C2×D4—16616no—
430C22×C4—216no—
431C22×C4—232no—
432C22×C4—216no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—216no—
440C22×C4—28no—
441C22×C4—216no—
442C22×C4—28no—
443C22×C4—216no—
444C22×C4—232no—
445C22×C4—3324no—
446C22×C4—3328no—
447C22×C4—3324no—
448C22×C4—834no—
449C22×C4—832no—
450C22×C4—838no—
451C22×C4—832no—
452C22×C4—832no—
453C22×C4—1662no—
454C22×C4—1664no—
455C22×C4—1661no—
456C22×C4—1661no—
457C22×C4—1664no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4—1664no—
461C22×C4—1664no—
462C22×C4—1664no—
463C22×C4—1664no—
464C22×C4—1664no—
465C22×C4—1662no—
466C22×C4—1668no—
467C22×C4—16616no—
468C22×C4—1661no—
469C22×C4—1661no—
470C22×C4—1662no—
471C22×C4(C2×D83)⋊C4116yescomplemented
472C22×C4C2×C4×D8312yes—
473C22×C4C2×C4×D8318yes—
474C22×C4C2×C4×D8312yes—
475C22×C4C2×C22⋊D8312yes—
476C22×C4C2×C22⋊D8318yes—
477C22×C4C2×C22⋊D8314yes—
478C22×C4C2×C22⋊D8312yes—
479C22×C4C2×D33212yes—
480C22×C4C2×D33212yes—
481C22×C4#1305059018yes—
482C22×C4#1305059014yes—
483C4⋊C4—1668no—
484C22⋊C4—1668no—
485C22⋊C4—16616no—
486C22⋊C4—1668no—
487C22⋊C4—16632no—
488C42—216no—
489C42—216no—
490C42—3328no—
491C42—1668no—
492C23—24no—
493C23—28no—
494C23—24no—
495C23—28no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—24no—
500C23—28no—
501C23—28no—
502C23—24no—
503C23—3321no—
504C23—3322no—
505C23—3321no—
506C23—3324no—
507C23—3322no—
508C23—3324no—
509C23—3322no—
510C23—834no—
511C23—1662no—
512C23—1662no—
513C23—1668no—
514C23—1664no—
515C23—1664no—
516C23—1664no—
517C23—1664no—
518C23—1668no—
519C23C42×D8314yes—
520C23C2×(C2×D83)⋊C414yes—
521C23#1458174914yes—
522C23C4×C22⋊D8318yes—
523C23C4×D33218yes—
524C23C22×C4×D8311yescharacteristic
525C23C22×C4×D8312yes—
526C23C22×C22⋊D8311yescharacteristic
527C23C22×C22⋊D8312yes—
528C23C22×D33211yescharacteristic
529C23C2×#1305059012yes—
530C23C2×#1305059012yes—
531C23C2×#1305059014yes—
532D4—16632no—
533C2×C4—264no—
534C2×C4—24no—
535C2×C4—28no—
536C2×C4—28no—
537C2×C4—22no—
538C2×C4—28no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—28no—
542C2×C4—28no—
543C2×C4—28no—
544C2×C4—232no—
545C2×C4—3321no—
546C2×C4—3324no—
547C2×C4—3322no—
548C2×C4—3321no—
549C2×C4—3322no—
550C2×C4—3324no—
551C2×C4—3324no—
552C2×C4—3322no—
553C2×C4—3324no—
554C2×C4—33216no—
555C2×C4—834no—
556C2×C4—1662no—
557C2×C4—1662no—
558C2×C4—1668no—
559C2×C4—1664no—
560C2×C4—1668no—
561C2×C4—1664no—
562C2×C4—1668no—
563C2×C4—1662no—
564C2×C4—1662no—
565C2×C4—1664no—
566C2×C4—1664no—
567C2×C4C2×(C2×D83)⋊C414yes—
568C2×C4C2×(C2×D83)⋊C414yes—
569C2×C4C4×C22⋊D8318yes—
570C2×C4C4×C22⋊D83116yescomplemented
571C2×C4#1458176114yes—
572C2×C4#1458176618yes—
573C2×C4#1458177514yes—
574C22—24no—
575C22—28no—
576C22—24no—
577C22—28no—
578C22—216no—
579C22—28no—
580C22—28no—
581C22—3322no—
582C22—3324no—
583C22—3322no—
584C22—3324no—
585C22—3328no—
586C22—3324no—
587C22—1664no—
588C22—1668no—
589C22C4×(C2×D83)⋊C418yescomplemented
590C22C2×C42×D8311yescharacteristic
591C22C22×(C2×D83)⋊C411yescharacteristic
592C22C2×#1458174911yescharacteristic
593C22C2×C4×C22⋊D8312yes—
594C22C2×C4×C22⋊D8314yes—
595C22C2×C4×C22⋊D8312yes—
596C22C2×C4×D33212yes—
597C22C4×#1305059012yes—
598C22C4×#1305059014yes—
599C22C2×#1458176111yescharacteristic
600C22C2×#1458176612yes—
601C22C2×#1458177511yescharacteristic
602C22#1912821214yes—
603C22#1912821212yes—
604C22#1912823514yes—
605C22#1912825112yes—
606C4—24no—
607C4—216no—
608C4—3322no—
609C4—3322no—
610C4—3328no—
611C4—1664no—
612C4#1912758018yesdirect product factor
613C2—28no—
614C2—3324no—
615C2C2×C4×(C2×D83)⋊C411yescharacteristic
616C2C42×C22⋊D8312yes—
617C2C2×#1912758011yescharacteristic
618C2#2490990612yes—
619C2#2490995311yescharacteristic
620C2C4×#1458176112yes—
621C2C4×#1458176614yes—
622C2C4×#1458177512yes—
subgroupG/H
centerC23×C4C22×D83
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC23×C42×C83C2
socle, cosocleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC23×C42D83
hypocenterC83C4×#386
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C23×C42

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D83)⋊C4C2semidirect
4. C2×C4×C22⋊Dic83C2semidirect
5. #24905701C2semidirect
6. #24905696C2semidirect
7. #24905686C2semidirect
8. C4×C83⋊#95C2semidirect
9. C23×C42×C83C2semidirect
14. C2×C4×C22⋊D83C4semidirect
22. #19127580C4direct (N × H)
49. C22×C4×D83C2×C4semidirect
53. C2×Dic83⋊C4C2×C4semidirect
59. C2×C22⋊Dic83C2×C4semidirect
64. C2×(C2×D83)⋊C4C2×C4semidirect
65. C2×(C2×D83)⋊C4C2×C4semidirect
71. C2×C4×Dic83C2×C4semidirect
75. C83⋊#95C2×C4semidirect
84. C23×C4×C83C2×C4semidirect
95. C2×C42×C83D4semidirect
108. C2×C22⋊D83C42semidirect
166. C22×C4×C83C22⋊C4semidirect
219. C22×D83C2×C42semidirect
235. C2×C4×C83C4×D4semidirect
260. C2×Dic83C2×C42semidirect
269. C22×C83C4×C22⋊C4semidirect
296. C4×C83#386semidirect
313. C23×C42D83semidirect
321. C83C4×#386semidirect
370. C23×C4C4×D83semidirect
403. C2×C42C22⋊D83semidirect
471. C22×C4(C2×D83)⋊C4semidirect
570. C2×C4C4×C22⋊D83semidirect
589. C22C4×(C2×D83)⋊C4semidirect
612. C4#19127580direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D832
C2×#191275802
C2×C4×(C2×D83)⋊C42
C2×C4×C22⋊Dic832
#249057012
#249056962
#249056862
C4×C83⋊#952
C23×C42×C832
C4×#38683