Finite Group Databasebeta

← C4×#19127627 #35326228

Subgroups — C4×#19127627 #35326228

Order 21248.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127627C211yesmaximal, characteristic
2C2×C4×(C2×D83)⋊C4C212yesmaximal
3C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
4#24905731C211yesmaximal, characteristic, complemented
5#24905724C212yesmaximal, complemented
6#24905722C211yesmaximal, characteristic, complemented
7#24905711C212yesmaximal
8#24905705C211yesmaximal, characteristic
9C4×C83⋊#95C212yesmaximal, complemented
10C4×C83⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
12C23×C4×D83C2211yescharacteristic
13C22×(C2×D83)⋊C4C2212yes—
14C22×(C2×D83)⋊C4C2211yescharacteristic
15C22×(C2×D83)⋊C4C2211yescharacteristic
16C22×(C2×D83)⋊C4C2212yes—
17C22×C4×Dic83C2211yescharacteristic
18C22×C4×Dic83C2212yes—
19#19127627C418yesdirect product factor
20C4×(C2×D83)⋊C4—24no—
21C4×(C2×D83)⋊C4—28no—
22C2×C83⋊#95C2211yescharacteristic
23C2×C83⋊#95C2212yes—
24C2×C83⋊#95C2211yescharacteristic
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2212yes—
33C22×C4⋊C4×C83C2211yescharacteristic
34C22×C4⋊C4×C83C2211yescharacteristic
35C22×C42×C83C2212yes—
36C22×C42×C83C2211yescharacteristic
37C4×C4⋊C4×C83—24no—
38C2×#95×C83C2212yes—
39C24×D83C2311yescharacteristic
40C23×Dic83C2311yescharacteristic
41C23×Dic83C2312yes—
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2312yes—
44C23×Dic83C2311yescharacteristic
45C22×C4×D83—22no—
46C22×C4×D83—22no—
47C22×C4×D83—24no—
48C22×C4×D83—24no—
49C22×C4×D83D414yes—
50C2×(C2×D83)⋊C4—24no—
51C2×(C2×D83)⋊C4—24no—
52C2×(C2×D83)⋊C4—22no—
53C2×(C2×D83)⋊C4—24no—
54C2×(C2×D83)⋊C4—24no—
55C2×(C2×D83)⋊C4—22no—
56C2×(C2×D83)⋊C4—22no—
57C2×(C2×D83)⋊C4—22no—
58C2×(C2×D83)⋊C4—24no—
59C2×(C2×D83)⋊C4—22no—
60C2×(C2×D83)⋊C4C2×C418yes—
61C2×(C2×D83)⋊C4C2×C414yes—
62C2×C4×Dic83—24no—
63C2×C4×Dic83—22no—
64C2×C4×Dic83—24no—
65C2×C4×Dic83—24no—
66C2×C4×Dic83—24no—
67C83⋊#95—24no—
68C83⋊#95—24no—
69C83⋊#95—24no—
70C83⋊#95—24no—
71C83⋊#95—24no—
72C83⋊#95—22no—
73C83⋊#95—22no—
74C83⋊#95—24no—
75C83⋊#95—22no—
76C83⋊#95C2×C418yescomplemented
77C83⋊#95C2×C414yescomplemented
78C23×C4×C83C2312yes—
79C23×C4×C83C2311yescharacteristic
80C23×C4×C83C2312yes—
81C23×C4×C83C2311yescharacteristic
82C23×C4×C83C2311yescharacteristic
83C2×C4⋊C4×C83—22no—
84C2×C4⋊C4×C83—22no—
85C2×C4⋊C4×C83—24no—
86C2×C4⋊C4×C83—22no—
87C2×C4⋊C4×C83C2×C414yescomplemented
88C2×C42×C83—24no—
89C2×C42×C83—24no—
90C2×C42×C83—24no—
91C2×C42×C83—24no—
92C2×C42×C83D414yes—
93#95×C83—24no—
94C23×D83—21no—
95C23×D83—21no—
96C23×D83—22no—
97C23×D83—22no—
98C23×D83—22no—
99C23×D83—21no—
100C23×D83—21no—
101C23×D83—22no—
102C23×D83C22×C412yes—
103C23×D83C2×D412yes—
104C23×D83#4112yes—
105C22×Dic83—21no—
106C22×Dic83—22no—
107C22×Dic83—22no—
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—21no—
111C22×Dic83—22no—
112C22×Dic83—22no—
113C22×Dic83—22no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—22no—
118C22×Dic83—22no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—22no—
123C22×Dic83—22no—
124C22×Dic83—22no—
125C22×Dic83—22no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—22no—
129C22×Dic83C22×C414yes—
130C22×Dic83C22×C412yes—
131C22×Dic83C2×D412yes—
132C22×Dic83#4112yes—
133C22×Dic83#4114yes—
134C2×C4×D83—28no—
135C2×C4×D83—216no—
136C2×C4×D83—44no—
137C2×C4×D83—44no—
138C2×C4×D83—48no—
139(C2×D83)⋊C4—28no—
140(C2×D83)⋊C4—216no—
141(C2×D83)⋊C4—216no—
142(C2×D83)⋊C4—28no—
143C4×Dic83—48no—
144C4×Dic83—44no—
145C24×C83C2411yescharacteristic
146C22×C4×C83—22no—
147C22×C4×C83—22no—
148C22×C4×C83—22no—
149C22×C4×C83—22no—
150C22×C4×C83—22no—
151C22×C4×C83—22no—
152C22×C4×C83—22no—
153C22×C4×C83—22no—
154C22×C4×C83—22no—
155C22×C4×C83—22no—
156C22×C4×C83—22no—
157C22×C4×C83—22no—
158C22×C4×C83—22no—
159C22×C4×C83—22no—
160C22×C4×C83—22no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—22no—
164C22×C4×C83C22×C414yes—
165C22×C4×C83C22×C412yes—
166C22×C4×C83C2×D412yes—
167C22×C4×C83C2×D412yes—
168C22×C4×C83C2×D412yes—
169C22×C4×C83C2×D412yes—
170C22×C4×C83#4112yes—
171C22×C4×C83#4114yes—
172C22×C4×C83#4112yes—
173C22×C4×C83#4114yes—
174C22×C4×C83#4114yes—
175C4⋊C4×C83—28no—
176C4⋊C4×C83—28no—
177C42×C83—28no—
178C42×C83—48no—
179C23×C83C23×C411yescharacteristic
180C23×C83C22×D411yescharacteristic
181C23×C83C22×D411yescharacteristic
182C23×C83C2×#4111yescharacteristic
183C23×C83C2×#4111yescharacteristic
184C23×C83C2×#4112yes—
185C23×C83C2×#4111yescharacteristic
186C23×C83C2×#4111yescharacteristic
187C23×C83C2×#4112yes—
188C23×C83C2×#4112yes—
189C23×C83C2×#4112yes—
190C22×D83—22no—
191C22×D83—22no—
192C22×D83—24no—
193C22×D83—24no—
194C22×D83—22no—
195C22×D83—24no—
196C22×D83—24no—
197C22×D83—22no—
198C22×D83—24no—
199C22×D83—22no—
200C22×D83—24no—
201C22×D83—22no—
202C22×D83—41no—
203C22×D83—41no—
204C22×D83—41no—
205C22×D83—42no—
206C22×D83—42no—
207C22×D83—42no—
208C22×D83—42no—
209C22×D83—42no—
210C22×D83—42no—
211C22×D83—41no—
212C22×D83C4×D414yes—
213C2×C4×C83—24no—
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—24no—
217C2×C4×C83—24no—
218C2×C4×C83—24no—
219C2×C4×C83—24no—
220C2×C4×C83—22no—
221C2×C4×C83—24no—
222C2×C4×C83—22no—
223C2×C4×C83—24no—
224C2×C4×C83—24no—
225C2×C4×C83—22no—
226C2×C4×C83—42no—
227C2×C4×C83—42no—
228C2×C4×C83—42no—
229C2×C4×C83—42no—
230C2×C4×C83—42no—
231C2×C4×C83—42no—
232C2×C4×C83—42no—
233C2×C4×C83—42no—
234C2×C4×C83—42no—
235C2×C4×C83—42no—
236C2×C4×C83C4×D414yes—
237C2×C4×C83#12114yes—
238C2×C4×C83#12314yes—
239C2×C4×C83#12318yes—
240C2×C4×C83#12414yes—
241C2×C4×C83#12618yes—
242C2×Dic83—24no—
243C2×Dic83—22no—
244C2×Dic83—24no—
245C2×Dic83—24no—
246C2×Dic83—24no—
247C2×Dic83—22no—
248C2×Dic83—24no—
249C2×Dic83—22no—
250C2×Dic83—24no—
251C2×Dic83—24no—
252C2×Dic83—24no—
253C2×Dic83—24no—
254C2×Dic83—42no—
255C2×Dic83—42no—
256C2×Dic83—41no—
257C2×Dic83—42no—
258C2×Dic83—41no—
259C2×Dic83—41no—
260C2×Dic83—41no—
261C2×Dic83—41no—
262C2×Dic83—42no—
263C2×Dic83—42no—
264C2×Dic83—42no—
265C2×Dic83—42no—
266C2×Dic83—42no—
267C2×Dic83—42no—
268C2×Dic83—42no—
269C2×Dic83—41no—
270C2×Dic83—42no—
271C4×D83—416no—
272C22×C83C2×C4×D411yescharacteristic
273C22×C83C2×C4×D411yescharacteristic
274C22×C83C4×#4111yescharacteristic
275C22×C83C4×#4112yes—
276C22×C83C4×#4112yes—
277C22×C83C2×#12111yescharacteristic
278C22×C83C2×#12311yescharacteristic
279C22×C83C2×#12312yes—
280C22×C83#52511yescharacteristic
281C22×C83#52512yes—
282C22×C83#52511yescharacteristic
283C22×C83C2×#12411yescharacteristic
284C22×C83C2×#12612yes—
285C22×C83#52912yes—
286C22×C83#52912yes—
287C22×C83#52912yes—
288C22×C83#52911yescharacteristic
289C22×C83#52912yes—
290C22×C83#52912yes—
291C22×C83#52912yes—
292C22×C83#52912yes—
293C22×C83#53211yescharacteristic
294C22×C83#53211yescharacteristic
295C2×D83—24no—
296C2×D83—28no—
297C2×D83—44no—
298C2×D83—42no—
299C2×D83—42no—
300C2×D83—42no—
301C2×D83—44no—
302C2×D83—42no—
303C2×D83—44no—
304C2×D83—42no—
305C2×D83—42no—
306C4×C83—24no—
307C4×C83—44no—
308C4×C83—42no—
309C4×C83—44no—
310C4×C83#39718yescomplemented
311Dic83—42no—
312Dic83—44no—
313Dic83—42no—
314Dic83—44no—
315Dic83—42no—
316C4×#397—831nomaximal, Sylow
317C2×C83C4×#12111yescharacteristic
318C2×C83C4×#12311yescharacteristic
319C2×C83C4×#12312yes—
320C2×C83C4×#12411yescharacteristic
321C2×C83C4×#12612yes—
322C2×C83C2×#39711yescharacteristic
323C2×C83#239211yescharacteristic
324C2×C83#239511yescharacteristic
325C2×C83#239512yes—
326C2×C83#239811yescharacteristic
327C2×C83#240112yes—
328D83—44no—
329C2×#397—831no—
330C2×C4×C4⋊C4D8311yescharacteristic, complemented
331C2×C4×C22⋊C4—831no—
332C2×C4×C22⋊C4—832no—
333#1445—831no—
334#1443—832no—
335#1442—831no—
336#1440—832no—
337#1439—831no—
338C4×#95—831no—
339C4×#95—832no—
340C83C4×#39711yescharacteristic, complemented, Sylow
341C24×C4—831no—
342C22×C4⋊C4C2×D8311yescharacteristic
343C22×C4⋊C4C2×D8311yescharacteristic
344C22×C22⋊C4—831no—
345C22×C22⋊C4—832no—
346C22×C22⋊C4—832no—
347C22×C22⋊C4—831no—
348C22×C42—832no—
349C22×C42—831no—
350C22×C42C2×D8312yes—
351C22×C42C2×D8311yescharacteristic
352#397—838no—
353C4×C4⋊C4—24no—
354C4×C22⋊C4—1668no—
355C4×C22⋊C4—1664no—
356C2×#95—831no—
357C2×#95—832no—
358C2×#95—832no—
359C2×#95—831no—
360C2×#95—832no—
361C2×#95—832no—
362C2×#95—832no—
363C2×#95—832no—
364C2×#95—831no—
365C2×#95—831no—
366C2×#95—832no—
367C2×#95C2×D8312yes—
368C25—831no—
369C23×C4—832no—
370C23×C4—831no—
371C23×C4—832no—
372C23×C4—831no—
373C23×C4—831no—
374C23×C4—834no—
375C23×C4—1662no—
376C23×C4—1662no—
377C23×C4—1664no—
378C23×C4—1664no—
379C23×C4C22×D8312yes—
380C23×C4C22×D8311yescharacteristic
381C23×C4C22×D8312yes—
382C23×C4C22×D8311yescharacteristic
383C23×C4C22×D8311yescharacteristic
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4C4×D8314yescomplemented
389C2×C22⋊C4—838no—
390C2×C22⋊C4—834no—
391C2×C22⋊C4—1664no—
392C2×C22⋊C4—1662no—
393C2×C22⋊C4—1664no—
394C2×C22⋊C4—1664no—
395C2×C22⋊C4—1664no—
396C2×C22⋊C4—1662no—
397C2×C22⋊C4—1662no—
398C2×C22⋊C4—1662no—
399C2×C22⋊C4—1664no—
400C2×C22⋊C4—1662no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—1664no—
406C2×C42—1662no—
407C2×C42—1664no—
408C2×C42—1664no—
409C2×C42—1664no—
410C2×C42C22⋊D8314yes—
411#95—24no—
412#95—838no—
413#95—834no—
414#95—1664no—
415#95—1664no—
416#95—1664no—
417#95—1664no—
418#95—1664no—
419#95—1662no—
420#95—1662no—
421#95—1664no—
422#95—1662no—
423C24—832no—
424C24—832no—
425C24—832no—
426C24—1661no—
427C24—1661no—
428C24—1662no—
429C24—1661no—
430C24—1662no—
431C24—1661no—
432C24—1662no—
433C24—1662no—
434C24C23×D8311yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—3324no—
454C22×C4—3324no—
455C22×C4—3328no—
456C22×C4—834no—
457C22×C4—832no—
458C22×C4—832no—
459C22×C4—832no—
460C22×C4—834no—
461C22×C4—1662no—
462C22×C4—1662no—
463C22×C4—1661no—
464C22×C4—1661no—
465C22×C4—1661no—
466C22×C4—1662no—
467C22×C4—1662no—
468C22×C4—1662no—
469C22×C4—1662no—
470C22×C4—1661no—
471C22×C4—1661no—
472C22×C4—1662no—
473C22×C4—1662no—
474C22×C4—1662no—
475C22×C4—1662no—
476C22×C4—1662no—
477C22×C4—1662no—
478C22×C4—1661no—
479C22×C4—1662no—
480C22×C4—1662no—
481C22×C4—1662no—
482C22×C4—1662no—
483C22×C4—1662no—
484C22×C4—1662no—
485C22×C4—1668no—
486C22×C4—16616no—
487C22×C4C2×C4×D8314yes—
488C22×C4C2×C4×D8312yes—
489C22×C4D4×D8312yes—
490C22×C4C2×C22⋊D8312yes—
491C22×C4C2×C22⋊D8312yes—
492C22×C4C2×C22⋊D8312yes—
493C22×C4#1305058912yes—
494C22×C4#1305059014yes—
495C22×C4#1305059012yes—
496C22×C4#1305059014yes—
497C22×C4#1305059114yes—
498C4⋊C4—28no—
499C4⋊C4—28no—
500C22⋊C4—16616no—
501C22⋊C4—1668no—
502C22⋊C4—16616no—
503C22⋊C4—1668no—
504C42—28no—
505C42—48no—
506C42—3328no—
507C42—3324no—
508C23—3321no—
509C23—3321no—
510C23—3321no—
511C23—3322no—
512C23—3322no—
513C23—3322no—
514C23—3322no—
515C23—3322no—
516C23—3322no—
517C23—3321no—
518C23—834no—
519C23—1662no—
520C23—1662no—
521C23—1664no—
522C23—1664no—
523C23—1662no—
524C23—1664no—
525C23—1662no—
526C23—1664no—
527C23—1664no—
528C23—1662no—
529C23—1664no—
530C23—1662no—
531C23C22×C4×D8311yescharacteristic
532C23C2×D4×D8311yescharacteristic
533C23C22×C22⋊D8311yescharacteristic
534C23#41×D8311yescharacteristic
535C23#41×D8311yescharacteristic
536C23#41×D8312yes—
537C23C2×#1305058911yescharacteristic
538C23C2×#1305059011yescharacteristic
539C23C2×#1305059012yes—
540C23C2×#1305059012yes—
541C23C2×#1305059112yes—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—3321no—
566C2×C4—3322no—
567C2×C4—3322no—
568C2×C4—3322no—
569C2×C4—3321no—
570C2×C4—3321no—
571C2×C4—3321no—
572C2×C4—3321no—
573C2×C4—3322no—
574C2×C4—3322no—
575C2×C4—3322no—
576C2×C4—3322no—
577C2×C4—3322no—
578C2×C4—3322no—
579C2×C4—3322no—
580C2×C4—3321no—
581C2×C4—3322no—
582C2×C4—33216no—
583C2×C4—1664no—
584C2×C4—1662no—
585C2×C4—1664no—
586C2×C4—1664no—
587C2×C4—1664no—
588C2×C4—1662no—
589C2×C4—1664no—
590C2×C4—1662no—
591C2×C4—1664no—
592C2×C4—1664no—
593C2×C4—1664no—
594C2×C4—1664no—
595C2×C4C4×C22⋊D8314yes—
596C2×C4#1458176314yes—
597C2×C4#1458177514yes—
598C2×C4#1458177718yes—
599C2×C4#1458178114yes—
600C2×C4#1458178718yes—
601C22—3322no—
602C22—3322no—
603C22—3322no—
604C22—3324no—
605C22—3322no—
606C22—3322no—
607C22—3324no—
608C22—3322no—
609C22—3324no—
610C22—1664no—
611C22—1668no—
612C22C4×D4×D8311yescharacteristic
613C22C2×C4×C22⋊D8311yescharacteristic
614C22C4×#1305058911yescharacteristic
615C22C4×#1305059012yes—
616C22C4×#1305059112yes—
617C22C2×#1458176311yescharacteristic
618C22C2×#1458177511yescharacteristic
619C22C2×#1458177712yes—
620C22#1912820811yescharacteristic
621C22#1912821012yes—
622C22#1912821211yescharacteristic
623C22C2×#1458178111yescharacteristic
624C22C2×#1458178712yes—
625C22#1912822912yes—
626C22#1912822912yes—
627C22#1912823112yes—
628C22#1912823311yescharacteristic
629C22#1912823512yes—
630C22#1912823812yes—
631C22#1912823812yes—
632C22#1912823812yes—
633C22#1912824711yescharacteristic
634C22#1912824811yescharacteristic
635C4—24no—
636C4—44no—
637C4—42no—
638C4—44no—
639C4—3322no—
640C4—3324no—
641C4—3322no—
642C4—3324no—
643C4—3322no—
644C4#1912762718yesdirect product factor
645C2—3324no—
646C2C4×#1458176311yescharacteristic
647C2C4×#1458177511yescharacteristic
648C2C4×#1458177712yes—
649C2C4×#1458178111yescharacteristic
650C2C4×#1458178712yes—
651C2C2×#1912762711yescharacteristic
652C2#2491070111yescharacteristic
653C2#2491072011yescharacteristic
654C2#2491072612yes—
655C2#2491074611yescharacteristic
656C2#2491076412yes—
subgroupG/H
centerC23×C4C22×D83
commutatorC23×C83C23×C4
FrattiniC24C23×D83
FittingC2×C4×C4⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C4×#397
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #24905731C2semidirect
5. #24905724C2semidirect
6. #24905722C2semidirect
9. C4×C83⋊#95C2semidirect
10. C4×C83⋊#95C2semidirect
11. C2×C4×C4⋊C4×C83C2semidirect
19. #19127627C4direct (N × H)
76. C83⋊#95C2×C4semidirect
77. C83⋊#95C2×C4semidirect
87. C2×C4⋊C4×C83C2×C4semidirect
310. C4×C83#397semidirect
330. C2×C4×C4⋊C4D83semidirect
340. C83C4×#397semidirect
388. C2×C4⋊C4C4×D83semidirect
644. C4#19127627direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191276272
C2×C4×(C2×D83)⋊C42
#249057312
#249057242
#249057222
#249057112
#249057052
C4×C83⋊#952
C2×C4×C4⋊C4×C832
C4×#39783