Finite Group Databasebeta

← C4×#19128442 #35567094

Subgroups — C4×#19128442 #35567094

Order 21248.

2568 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128442C211yesmaximal, characteristic
2#24910655C211yesmaximal, characteristic, complemented
3#24910652C211yesmaximal, characteristic, complemented
4#24910639C211yesmaximal, characteristic, complemented
5#24910618C213yesmaximal, complemented
6#24910616C213yesmaximal, complemented
7#24910610C213yesmaximal, complemented
8#24910603C213yesmaximal, complemented
9C4×#14581789C211yesmaximal, characteristic, complemented
10C4×#14581786C211yesmaximal, characteristic, complemented
11C4×#14581777C213yesmaximal, complemented
12C4×#14581767C213yesmaximal, complemented
13C4×#14581765C213yesmaximal, complemented
14C4×#14581762C213yesmaximal, complemented
15C4×#126×C83C211yesmaximal, characteristic, complemented
16C23×C4×D83C2211yescharacteristic
17#19128442C4116yesdirect product factor
18C2×#14581789C2211yescharacteristic
19C2×#14581786C2211yescharacteristic
20C2×#14581777C2213yes—
21C2×#14581767C2213yes—
22C2×#14581765C2213yes—
23C2×#14581762C2213yes—
24C2×C4×D332C2213yes—
25C2×C4×D332C2213yes—
26C2×C4×D332C2213yescomplemented
27C2×C4×C22⋊D83C2213yes—
28C2×C42×D83C2213yescomplemented
29#19127603C2213yes—
30#19127603C2213yescomplemented
31#19127602C2213yes—
32#19127601C2213yes—
33#19127600C2213yescomplemented
34#19127598C2213yescomplemented
35#19127594C2213yes—
36#19127593C2213yes—
37#19127593C2213yescomplemented
38#19127592C2213yes—
39#19127591C2213yes—
40#19127590C2213yes—
41#19127590C2213yescomplemented
42#19127588C2213yescomplemented
43#19127587C2213yescomplemented
44#19127585C2213yescomplemented
45#19127579C2213yes—
46#19127579C2213yes—
47#19127579C2213yes—
48#19127579C2213yes—
49#19127579C2213yescomplemented
50#19127579C2213yescomplemented
51#19127578C2213yes—
52#19127577C2213yes—
53#19127576C2213yes—
54#19127575C2213yes—
55#19127575C2213yes—
56#19127572C2213yescomplemented
57#19127571C2211yescharacteristic, complemented
58#19127569C2211yescharacteristic, complemented
59#19127563C2213yescomplemented
60#19127560C2213yescomplemented
61#19127558C2213yescomplemented
62#19127556C2213yes—
63C4×Dic83⋊C4C2213yescomplemented
64C4×(C2×D83)⋊C4C2213yes—
65C4×(C2×D83)⋊C4C2213yes—
66C4×(C2×D83)⋊C4C2213yescomplemented
67C2×#126×C83C2211yescharacteristic
68#388×C83C2213yes—
69#387×C83C2213yescomplemented
70#383×C83C2211yescharacteristic, complemented
71C4×C4⋊C4×C83C2213yescomplemented
72C4×C22⋊C4×C83C2213yes—
73C43×C83C2211yescharacteristic, complemented
74C24×D83C2311yescharacteristic
75C22×D332C2313yes—
76C22×D332C2313yes—
77C22×D332C2313yes—
78C22×C22⋊D83C2313yes—
79C23×Dic83C2311yescharacteristic
80C22×C4×D83—46no—
81C22×C4×D83C2313yes—
82C22×C4×D83C2311yescharacteristic
83C22×C4×D83C2311yescharacteristic
84C22×C4×D83C2313yes—
85C22×C4×D83C2311yescharacteristic
86C22×C4×D83C2311yescharacteristic
87C22×C4×D83C2313yes—
88#14581789C2×C418yescomplemented
89#14581786C2×C418yescomplemented
90#14581777C2×C4124yescomplemented
91#14581767C2×C4124yescomplemented
92#14581765C2×C4124yescomplemented
93#14581762C2×C4124yescomplemented
94C4×D332—46no—
95C4×D332—46no—
96C4×D332—46no—
97C4×C22⋊D83—46no—
98C2×C4⋊Dic83C2313yes—
99C2×C4⋊Dic83C2313yes—
100C2×C4⋊Dic83C2313yes—
101C2×Dic83⋊C4C2313yes—
102C2×Dic83⋊C4C2313yes—
103C2×Dic83⋊C4C2313yes—
104C2×C22⋊Dic83C2313yes—
105C2×(C2×D83)⋊C4C2313yes—
106C2×(C2×D83)⋊C4C2313yes—
107C2×(C2×D83)⋊C4C2313yes—
108C2×(C2×D83)⋊C4C2313yes—
109C2×(C2×D83)⋊C4C2313yes—
110C2×(C2×D83)⋊C4C2313yes—
111C2×(C2×D83)⋊C4C2313yes—
112C2×(C2×D83)⋊C4C2313yes—
113C2×(C2×D83)⋊C4C2313yes—
114C2×(C2×D83)⋊C4C2313yes—
115C2×(C2×D83)⋊C4C2313yes—
116C2×(C2×D83)⋊C4C2313yes—
117C2×(C2×D83)⋊C4C2313yes—
118C2×C4×Dic83C2313yes—
119C2×C4×Dic83C2313yes—
120C2×C4×Dic83C2313yes—
121C42×D83—46no—
122C83⋊#95C2313yes—
123C83⋊#95C2313yes—
124C83⋊#95C2313yes—
125C83⋊#95C2313yes—
126C83⋊#95C2313yes—
127C83⋊#95C2313yes—
128C83⋊#95C2313yes—
129C83⋊#95C2313yes—
130C23×C4×C83C2311yescharacteristic
131#126×C83C2×C418yescomplemented
132C2×C4⋊C4×C83C2313yes—
133C2×C4⋊C4×C83C2313yes—
134C2×C22⋊C4×C83C2313yes—
135C2×C22⋊C4×C83C2313yes—
136C2×C42×C83C2313yes—
137C2×C42×C83C2313yes—
138C2×C42×C83C2313yes—
139C2×C42×C83C2311yescharacteristic
140#95×C83C2313yes—
141#95×C83C2313yes—
142#95×C83C2313yes—
143#95×C83C2313yes—
144C23×D83—43no—
145C23×D83—43no—
146C23×D83C22×C414yes—
147C23×D83C2413yes—
148C23×D83C2411yescharacteristic
149C23×D83C2411yescharacteristic
150C2×D332—43no—
151C2×D332—43no—
152C2×D332—43no—
153C2×D332—43no—
154C2×D332—43no—
155C2×D332—43no—
156C2×D332C22×C4112yes—
157C2×D332C22×C4112yes—
158C2×D332C22×C4112yescomplemented
159C2×C22⋊D83—43no—
160C2×C22⋊D83—43no—
161C2×C22⋊D83C22×C4112yes—
162C22×Dic83—43no—
163C22×Dic83C2411yescharacteristic
164C22×Dic83C2411yescharacteristic
165C22×Dic83C2413yes—
166C22×Dic83C2413yes—
167C22×Dic83C2413yes—
168C2×C4×D83—26no—
169C2×C4×D83—26no—
170C2×C4×D83—26no—
171C2×C4×D83—26no—
172C2×C4×D83—26no—
173C2×C4×D83—43no—
174C2×C4×D83—43no—
175C2×C4×D83—43no—
176C2×C4×D83—43no—
177C2×C4×D83—43no—
178C2×C4×D83—43no—
179C2×C4×D83—43no—
180C2×C4×D83—416no—
181C2×C4×D83C22×C4112yescomplemented
182C4⋊Dic83—43no—
183C4⋊Dic83—43no—
184C4⋊Dic83—43no—
185Dic83⋊C4—43no—
186Dic83⋊C4—43no—
187Dic83⋊C4C22×C4112yescomplemented
188C22⋊Dic83—43no—
189(C2×D83)⋊C4—43no—
190(C2×D83)⋊C4—43no—
191(C2×D83)⋊C4—43no—
192(C2×D83)⋊C4—43no—
193(C2×D83)⋊C4—43no—
194(C2×D83)⋊C4—43no—
195(C2×D83)⋊C4—43no—
196(C2×D83)⋊C4—43no—
197(C2×D83)⋊C4—43no—
198(C2×D83)⋊C4—43no—
199(C2×D83)⋊C4C22×C4112yes—
200(C2×D83)⋊C4C22×C4112yes—
201(C2×D83)⋊C4C22×C4112yescomplemented
202C4×Dic83—26no—
203C4×Dic83—43no—
204C4×Dic83—43no—
205C24×C83C2411yescharacteristic
206C22×C4×C83—26no—
207C22×C4×C83C2411yescharacteristic
208C22×C4×C83C2413yes—
209C22×C4×C83C2413yes—
210C22×C4×C83C2413yes—
211C22×C4×C83C2413yes—
212C22×C4×C83C2411yescharacteristic
213C4⋊C4×C83—43no—
214C4⋊C4×C83C22×C4112yescomplemented
215C22⋊C4×C83—43no—
216C22⋊C4×C83C22×C4112yes—
217C42×C83—26no—
218C42×C83—26no—
219C42×C83—43no—
220C42×C83C22×C414yescomplemented
221C23×C83—23no—
222C23×C83—23no—
223C23×C83C23×C412yes—
224C23×C83C2511yescharacteristic
225C22×D83—23no—
226C22×D83—23no—
227C22×D83—23no—
228C22×D83—23no—
229C22×D83—23no—
230C22×D83—23no—
231C22×D83—23no—
232C22×D83—23no—
233C22×D83—23no—
234C22×D83—23no—
235C22×D83—412no—
236C22×D83—44no—
237C22×D83—412no—
238C22×D83C23×C412yes—
239C22×D83C23×C412yes—
240C22×D83C23×C416yes—
241C2×C4×C83—23no—
242C2×C4×C83—23no—
243C2×C4×C83—23no—
244C2×C4×C83—23no—
245C2×C4×C83—23no—
246C2×C4×C83—23no—
247C2×C4×C83—23no—
248C2×C4×C83—23no—
249C2×C4×C83—23no—
250C2×C4×C83—23no—
251C2×C4×C83—23no—
252C2×C4×C83—44no—
253C2×C4×C83C23×C416yes—
254C2×C4×C83C23×C416yes—
255C2×C4×C83H(5,𝔽2)16yes—
256C22⋊D83—412no—
257C2×Dic83—23no—
258C2×Dic83—23no—
259C2×Dic83—23no—
260C2×Dic83—23no—
261C2×Dic83—23no—
262C2×Dic83—23no—
263C2×Dic83—23no—
264C2×Dic83—23no—
265C2×Dic83—23no—
266C2×Dic83—23no—
267C2×Dic83—44no—
268C2×Dic83C23×C416yes—
269D332—412no—
270D332—412no—
271D332—412no—
272C4×D83—412no—
273C4×D83—412no—
274C4×D83—44no—
275C4×D83—44no—
276C4×D83—412no—
277C4×D83—44no—
278C4×D83—44no—
279C22×C83—26no—
280C22×C83—41no—
281C22×C83—43no—
282C22×C83C24×C411yescharacteristic
283C22×C83C2×H(5,𝔽2)13yes—
284C22×C83#58513yes—
285C2×D83—26no—
286C2×D83—26no—
287C2×D83—26no—
288C2×D83—26no—
289C2×D83—26no—
290C2×D83—416no—
291C2×D83—41no—
292C2×D83—41no—
293C2×D83—43no—
294C2×D83—43no—
295C2×D83—43no—
296C2×D83—43no—
297C2×D83—43no—
298C2×D83—43no—
299C4×C83—26no—
300C4×C83—26no—
301C4×C83—41no—
302C4×C83—43no—
303C4×C83—43no—
304C4×C83#56014yescomplemented
305Dic83—26no—
306Dic83—41no—
307Dic83—41no—
308Dic83—43no—
309Dic83—43no—
310C4×#560—831nomaximal, Sylow
311C2×C83—42no—
312C2×C83C4×H(5,𝔽2)13yes—
313C2×C83C2×#56011yescharacteristic
314C2×C83#352913yes—
315D83—46no—
316D83—42no—
317D83—42no—
318C2×#560—831no—
319#2383—831no—
320#2383—831no—
321#2380—831no—
322#2377—833no—
323#2377—833no—
324#2376—833no—
325#2375—833no—
326C4×#127—831no—
327C4×#126—831no—
328C4×#126D8311yescharacteristic, complemented
329C4×#123—833no—
330C4×#121—833no—
331C4×#121—833no—
332C4×#120—833no—
333C83C4×#56011yescharacteristic, complemented, Sylow
334C24×C4—831no—
335#560—8316no—
336C2×#127—831no—
337C2×#126—831no—
338C2×#126C2×D8311yescharacteristic
339C2×#123—833no—
340C2×#121—833no—
341C2×#121—833no—
342C2×#120—833no—
343C2×C4×D4—833no—
344C2×C4×D4—833no—
345C2×C4×D4—833no—
346C2×C4×D4—833no—
347C22×C42—833no—
348#390—833no—
349#390—833no—
350#390—833no—
351#390—833no—
352#389—833no—
353#389—833no—
354#388—833no—
355#388—833no—
356#388—833no—
357#388—833no—
358#388—833no—
359#388—833no—
360#388—833no—
361#388C2×D8313yes—
362#387—833no—
363#387—833no—
364#387—833no—
365#387C2×D8313yescomplemented
366#386—833no—
367#386—833no—
368#386—833no—
369#386—833no—
370#386—833no—
371#386—833no—
372#386—833no—
373#386—833no—
374#385—833no—
375#385—833no—
376#385—833no—
377#385—833no—
378#384—831no—
379#383—831no—
380#383C2×D8311yescharacteristic, complemented
381#381—833no—
382#380—833no—
383#380—833no—
384#379—833no—
385C4×C4⋊C4—833no—
386C4×C4⋊C4C2×D8313yescomplemented
387C4×C22⋊C4—833no—
388C4×C22⋊C4—833no—
389C4×C22⋊C4—833no—
390C4×C22⋊C4C2×D8313yes—
391C43C2×D8311yescharacteristic, complemented
392C25—831no—
393C22×D4—833no—
394C22×D4—833no—
395C22×D4—833no—
396C22×D4—833no—
397C23×C4—3326no—
398C23×C4—831no—
399C23×C4—831no—
400C23×C4—831no—
401C23×C4—833no—
402C23×C4—833no—
403C23×C4—833no—
404C23×C4—831no—
405C23×C4—831no—
406C23×C4C22×D8311yescharacteristic
407#127—838no—
408#126—838no—
409#126C4×D8318yescomplemented
410#123—8324no—
411#121—8324no—
412#121—8324no—
413#120—8324no—
414C4×D4—3326no—
415C4×D4—3326no—
416C4×D4—3326no—
417C4×D4—3326no—
418C2×C4⋊C4—833no—
419C2×C4⋊C4—833no—
420C2×C4⋊C4—833no—
421C2×C4⋊C4—833no—
422C2×C4⋊C4—833no—
423C2×C4⋊C4—833no—
424C2×C4⋊C4C22×D8313yes—
425C2×C4⋊C4C22×D8313yes—
426C2×C22⋊C4—833no—
427C2×C22⋊C4—833no—
428C2×C22⋊C4—833no—
429C2×C22⋊C4—833no—
430C2×C22⋊C4—833no—
431C2×C22⋊C4—833no—
432C2×C22⋊C4—833no—
433C2×C22⋊C4—833no—
434C2×C22⋊C4—833no—
435C2×C22⋊C4—833no—
436C2×C22⋊C4—833no—
437C2×C22⋊C4—833no—
438C2×C22⋊C4—833no—
439C2×C22⋊C4—833no—
440C2×C22⋊C4C22×D8313yes—
441C2×C22⋊C4C22×D8313yes—
442C2×C42—3326no—
443C2×C42—833no—
444C2×C42—833no—
445C2×C42—833no—
446C2×C42C22×D8313yes—
447C2×C42C22×D8313yes—
448C2×C42C22×D8313yes—
449C2×C42C22×D8311yescharacteristic
450#95—833no—
451#95—833no—
452#95—833no—
453#95—833no—
454#95—833no—
455#95—833no—
456#95—833no—
457#95—833no—
458#95C22×D8313yes—
459#95C22×D8313yes—
460#95C22×D8313yes—
461#95C22×D8313yes—
462C24—3323no—
463C24—3323no—
464C24—834no—
465C24—831no—
466C24—831no—
467C24—833no—
468C24C23×D8311yescharacteristic
469C2×D4—3323no—
470C2×D4—3323no—
471C2×D4—3323no—
472C2×D4—3323no—
473C2×D4—3323no—
474C2×D4—3323no—
475C2×D4—3323no—
476C2×D4—3323no—
477C2×D4—8312no—
478C2×D4—8312no—
479C2×D4—8312no—
480C2×D4—8312no—
481C22×C4—26no—
482C22×C4—3323no—
483C22×C4—3323no—
484C22×C4—3323no—
485C22×C4—3323no—
486C22×C4—3323no—
487C22×C4—3323no—
488C22×C4—3323no—
489C22×C4—33216no—
490C22×C4—3323no—
491C22×C4—8312no—
492C22×C4—833no—
493C22×C4—833no—
494C22×C4—831no—
495C22×C4—831no—
496C22×C4—833no—
497C22×C4—1666no—
498C22×C4—1666no—
499C22×C4—1666no—
500C22×C4—1666no—
501C22×C4—1666no—
502C22×C4C23×D8313yes—
503C22×C4C23×D8313yes—
504C22×C4C23×D8311yescharacteristic
505C22×C4C23×D8313yes—
506C22×C4C23×D8313yes—
507C22×C4C23×D8311yescharacteristic
508C4⋊C4—43no—
509C4⋊C4—3323no—
510C4⋊C4—3323no—
511C4⋊C4—3323no—
512C4⋊C4—3323no—
513C4⋊C4—3323no—
514C4⋊C4—8312no—
515C4⋊C4C2×C4×D83112yescomplemented
516C22⋊C4—43no—
517C22⋊C4—3323no—
518C22⋊C4—3323no—
519C22⋊C4—3323no—
520C22⋊C4—3323no—
521C22⋊C4—3323no—
522C22⋊C4—3323no—
523C22⋊C4—3323no—
524C22⋊C4—3323no—
525C22⋊C4—3323no—
526C22⋊C4—3323no—
527C22⋊C4—3323no—
528C22⋊C4—8312no—
529C22⋊C4—8312no—
530C22⋊C4—8312no—
531C22⋊C4C2×C4×D83112yes—
532C42—26no—
533C42—26no—
534C42—43no—
535C42—3323no—
536C42—3323no—
537C42—1666no—
538C42C2×C4×D8314yescomplemented
539C23—23no—
540C23—23no—
541C23—33212no—
542C23—3324no—
543C23—33212no—
544C23—832no—
545C23—832no—
546C23—836no—
547C23—1663no—
548C23—1663no—
549C23—1663no—
550C23—1663no—
551C23—1663no—
552C23—1663no—
553C23—1663no—
554C23—1663no—
555C23—1663no—
556C23—1663no—
557C23C22×C4×D8312yes—
558C23C24×D8311yescharacteristic
559D4—33212no—
560D4—33212no—
561D4—33212no—
562D4—33212no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—44no—
575C2×C4—33212no—
576C2×C4—3324no—
577C2×C4—3324no—
578C2×C4—33212no—
579C2×C4—3324no—
580C2×C4—3324no—
581C2×C4—3324no—
582C2×C4—33212no—
583C2×C4—836no—
584C2×C4—1663no—
585C2×C4—1663no—
586C2×C4—1663no—
587C2×C4—1663no—
588C2×C4—1663no—
589C2×C4—1663no—
590C2×C4—1663no—
591C2×C4—1663no—
592C2×C4—1663no—
593C2×C4—1663no—
594C2×C4C22×C4×D8316yes—
595C2×C4C22×C4×D8316yes—
596C2×C4#1458183816yes—
597C22—26no—
598C22—43no—
599C22—41no—
600C22—33216no—
601C22—3323no—
602C22—3323no—
603C22—3323no—
604C22—3323no—
605C22—3323no—
606C22—3321no—
607C22—3321no—
608C22—3323no—
609C22—1666no—
610C22—1666no—
611C22—1666no—
612C22—1666no—
613C22—1666no—
614C22C23×C4×D8311yescharacteristic
615C22C2×#1458183813yes—
616C22#1912853713yes—
617C4—26no—
618C4—26no—
619C4—43no—
620C4—43no—
621C4—41no—
622C4—3323no—
623C4—3321no—
624C4—3321no—
625C4—3323no—
626C4—1666no—
627C4#1912844214yesdirect product factor
628C2—42no—
629C2—3322no—
630C2—3322no—
631C2—3326no—
632C2C4×#1458183813yes—
633C2C2×#1912844211yescharacteristic
634C2#2492160213yes—
subgroupG/H
centerC22×C4C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC4×#126×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#19128442C2
hypercenterC4×#126D83
hypocenterC83C4×#560
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
2. #24910655C2semidirect
3. #24910652C2semidirect
4. #24910639C2semidirect
5. #24910618C2semidirect
6. #24910616C2semidirect
7. #24910610C2semidirect
8. #24910603C2semidirect
9. C4×#14581789C2semidirect
10. C4×#14581786C2semidirect
11. C4×#14581777C2semidirect
12. C4×#14581767C2semidirect
13. C4×#14581765C2semidirect
14. C4×#14581762C2semidirect
15. C4×#126×C83C2semidirect
17. #19128442C4direct (N × H)
26. C2×C4×D332C22semidirect
28. C2×C42×D83C22semidirect
30. #19127603C22semidirect
33. #19127600C22semidirect
34. #19127598C22semidirect
37. #19127593C22semidirect
41. #19127590C22semidirect
42. #19127588C22semidirect
43. #19127587C22semidirect
44. #19127585C22semidirect
49. #19127579C22semidirect
50. #19127579C22semidirect
56. #19127572C22semidirect
57. #19127571C22semidirect
58. #19127569C22semidirect
59. #19127563C22semidirect
60. #19127560C22semidirect
61. #19127558C22semidirect
63. C4×Dic83⋊C4C22semidirect
66. C4×(C2×D83)⋊C4C22semidirect
69. #387×C83C22semidirect
70. #383×C83C22semidirect
71. C4×C4⋊C4×C83C22semidirect
73. C43×C83C22semidirect
88. #14581789C2×C4semidirect
89. #14581786C2×C4semidirect
90. #14581777C2×C4semidirect
91. #14581767C2×C4semidirect
92. #14581765C2×C4semidirect
93. #14581762C2×C4semidirect
131. #126×C83C2×C4semidirect
158. C2×D332C22×C4semidirect
181. C2×C4×D83C22×C4semidirect
187. Dic83⋊C4C22×C4semidirect
201. (C2×D83)⋊C4C22×C4semidirect
214. C4⋊C4×C83C22×C4semidirect
220. C42×C83C22×C4semidirect
304. C4×C83#560semidirect
328. C4×#126D83semidirect
333. C83C4×#560semidirect
365. #387C2×D83semidirect
380. #383C2×D83semidirect
386. C4×C4⋊C4C2×D83semidirect
391. C43C2×D83semidirect
409. #126C4×D83semidirect
515. C4⋊C4C2×C4×D83semidirect
538. C42C2×C4×D83semidirect
627. C4#19128442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284422
#249106552
#249106522
#249106392
#249106182
#249106162
#249106102
#249106032
C4×#145817892
C4×#145817862
C4×#145817772
C4×#145817672
C4×#145817652
C4×#145817622
C4×#126×C832
C4×#56083