Finite Group Databasebeta

← C4×#19128083 #35412846

Subgroups — C4×#19128083 #35412846

Order 21248.

1150 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×#19128083C211yesmaximal, characteristic
2C2×C4×#13050580C211yesmaximal, characteristic, complemented
3C2×C4×#13050577C211yesmaximal, characteristic, complemented
4C2×C4×#13050578C211yesmaximal, characteristic, complemented
5C2×C4×#13050575C211yesmaximal, characteristic
6C4×#14581780C211yesmaximal, characteristic, complemented
7#24908328C211yesmaximal, characteristic
8#24908323C211yesmaximal, characteristic, complemented
9#24908320C211yesmaximal, characteristic, complemented
10#24908316C211yesmaximal, characteristic, complemented
11#24908275C211yesmaximal, characteristic, complemented
12#24908272C211yesmaximal, characteristic, complemented
13#24907625C211yesmaximal, characteristic, complemented
14C42×C83⋊C8C211yesmaximal, characteristic, complemented
15C4×#124×C83C211yesmaximal, characteristic, complemented
16C22×#13050580C2211yescharacteristic
17C22×#13050578C2211yescharacteristic
18C22×#13050577C2211yescharacteristic
19C22×#13050575C2211yescharacteristic
20C2×#14581780C2211yescharacteristic
21C2×C4×Dic166C2211yescharacteristic
22C2×C4×D332C2211yescharacteristic
23#19128083C418yesdirect product factor
24C4×#13050580—24no—
25C4×#13050577—24no—
26C4×#13050578—24no—
27C4×#13050575—24no—
28C2×#14581725C2211yescharacteristic
29C2×#14581725C2211yescharacteristic
30C2×#14581723C2211yescharacteristic
31C2×#14581723C2211yescharacteristic
32C2×#14581716C2211yescharacteristic
33C2×#14581716C2211yescharacteristic
34C2×#14581715C2211yescharacteristic
35C2×#14581715C2211yescharacteristic
36C2×#14581713C2211yescharacteristic
37C2×#14581713C2211yescharacteristic
38C2×#14581712C2211yescharacteristic
39C2×#14581712C2211yescharacteristic
40C2×C4×C83⋊C8C2211yescharacteristic
41C2×C4×C83⋊C8C2211yescharacteristic
42C2×C4×C83⋊C8C2211yescharacteristic
43C2×C4×C83⋊C8C2211yescharacteristic
44C2×C4×C83⋊C8C2211yescharacteristic
45C2×C4×C83⋊C8C2211yescharacteristic
46#19127607C2211yescharacteristic
47#19127603C2211yescharacteristic
48#19127592—22no—
49#19127567C2211yescharacteristic
50C4×(C2×D83)⋊C4—22no—
51C2×#124×C83C2211yescharacteristic
52C2×C4×Q8×C83C2211yescharacteristic
53C2×C4×D4×C83C2211yescharacteristic
54#391×C83C2211yescharacteristic
55#390×C83C2211yescharacteristic
56#388×C83—22no—
57#382×C83C2211yescharacteristic
58C4×C22⋊C4×C83—22no—
59C43×C83C2211yescharacteristic
60C22×Dic166C2311yescharacteristic
61C22×D332C2311yescharacteristic
62C22×C4×D83—21no—
63C2×#13050580—22no—
64C2×#13050580—22no—
65C2×#13050580C2×C414yescomplemented
66C2×#13050578—22no—
67C2×#13050578—22no—
68C2×#13050578C2×C414yescomplemented
69C2×#13050577—22no—
70C2×#13050577—22no—
71C2×#13050577C2×C414yescomplemented
72C2×#13050575—22no—
73C2×#13050575—22no—
74C2×#13050575C2×C414yes—
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77C22×C83⋊C8C2311yescharacteristic
78C22×C83⋊C8C2311yescharacteristic
79#14581780—22no—
80#14581780C2×C414yescomplemented
81C4×Dic166—22no—
82C4×Dic166—22no—
83C4×D332—22no—
84C4×D332—22no—
85C2×C4⋊Dic83C2311yescharacteristic
86C2×C4⋊Dic83C2311yescharacteristic
87C2×Dic83⋊C4—21no—
88C2×(C2×D83)⋊C4—22no—
89C2×(C2×D83)⋊C4—21no—
90C2×(C2×D83)⋊C4—22no—
91C2×C4×Dic83—21no—
92#14581725—22no—
93#14581725—22no—
94#14581723—22no—
95#14581723—22no—
96#14581716—22no—
97#14581716—22no—
98#14581715—22no—
99#14581715—22no—
100#14581713—22no—
101#14581713—22no—
102#14581712—22no—
103#14581712—22no—
104C4×C83⋊C8—22no—
105C4×C83⋊C8—22no—
106C4×C83⋊C8—22no—
107C4×C83⋊C8C2×C414yescomplemented
108C4×C83⋊C8D414yes—
109C4×C83⋊C8D414yes—
110C83⋊#95—22no—
111C83⋊#95—22no—
112C22×Q8×C83C2311yescharacteristic
113C22×D4×C83C2311yescharacteristic
114C23×C4×C83—21no—
115#124×C83—22no—
116#124×C83C2×C414yescomplemented
117C4×Q8×C83—22no—
118C4×Q8×C83—22no—
119C4×D4×C83—22no—
120C4×D4×C83—22no—
121C2×C4⋊C4×C83—21no—
122C2×C4⋊C4×C83C2311yescharacteristic
123C2×C4⋊C4×C83C2311yescharacteristic
124C2×C22⋊C4×C83—22no—
125C2×C22⋊C4×C83—21no—
126C2×C22⋊C4×C83—22no—
127C2×C42×C83—21no—
128C2×C42×C83D412yes—
129C2×C42×C83D412yes—
130C2×C42×C83C2311yescharacteristic
131C2×C42×C83C2311yescharacteristic
132C2×C42×C83C2311yescharacteristic
133#95×C83—22no—
134#95×C83—22no—
135C23×D83—21no—
136C2×Dic166—21no—
137C2×Dic166—21no—
138C2×Dic166—21no—
139C2×Dic166—21no—
140C2×Dic166—21no—
141C2×Dic166C22×C412yes—
142C2×D332—21no—
143C2×D332—21no—
144C2×D332—21no—
145C2×D332—21no—
146C2×D332—21no—
147C2×D332C22×C412yes—
148C22×Dic83—21no—
149C22×Dic83—21no—
150C22×Dic83—21no—
151C2×C4×D83—42no—
152C2×C4×D83—44no—
153#13050580—28no—
154#13050578—28no—
155#13050577—28no—
156#13050575—28no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8C22×C412yes—
162C2×C83⋊C8C22×C412yes—
163C2×C83⋊C8C2×D412yes—
164C2×C83⋊C8C2×D412yes—
165C2×C83⋊C8C2×D412yes—
166C2×C83⋊C8C2×D412yes—
167C2×C83⋊C8#4112yes—
168C2×C83⋊C8#4112yes—
169C4⋊Dic83—21no—
170C4⋊Dic83—21no—
171C4⋊Dic83—21no—
172C4⋊Dic83—21no—
173Dic83⋊C4—42no—
174(C2×D83)⋊C4—28no—
175(C2×D83)⋊C4—42no—
176(C2×D83)⋊C4—44no—
177C4×Dic83—42no—
178C24×C83—21no—
179C2×Q8×C83—21no—
180C2×Q8×C83—21no—
181C2×Q8×C83—21no—
182C2×Q8×C83—21no—
183C2×Q8×C83—21no—
184C2×Q8×C83C22×C412yes—
185C2×D4×C83—21no—
186C2×D4×C83—21no—
187C2×D4×C83—21no—
188C2×D4×C83—21no—
189C2×D4×C83—21no—
190C2×D4×C83C22×C412yes—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—42no—
195C22×C4×C83—44no—
196C22×C4×C83C2×D412yes—
197C22×C4×C83C2×D411yescharacteristic
198C22×C4×C83C2×D412yes—
199C22×C4×C83C2×D411yescharacteristic
200C22×C4×C83C2411yescharacteristic
201C4⋊C4×C83—21no—
202C4⋊C4×C83—21no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83—21no—
205C4⋊C4×C83—42no—
206C22⋊C4×C83—28no—
207C22⋊C4×C83—42no—
208C22⋊C4×C83—44no—
209C42×C83—24no—
210C42×C83—24no—
211C42×C83—21no—
212C42×C83—21no—
213C42×C83—42no—
214C42×C83C22×C412yes—
215C42×C83C2×D412yes—
216C42×C83C2×D412yes—
217C42×C83#4112yes—
218C23×C83—22no—
219C23×C83—41no—
220C23×C83—41no—
221C23×C83—42no—
222C23×C83—42no—
223C23×C83C22×D411yescharacteristic
224C22×D83—22no—
225C22×D83—41no—
226C22×D83—41no—
227C22×D83—42no—
228C22×D83—42no—
229Q8×C83—22no—
230Q8×C83—22no—
231Q8×C83—41no—
232Q8×C83—41no—
233D4×C83—22no—
234D4×C83—22no—
235D4×C83—41no—
236D4×C83—41no—
237C2×C4×C83—22no—
238C2×C4×C83—22no—
239C2×C4×C83—22no—
240C2×C4×C83—22no—
241C2×C4×C83—22no—
242C2×C4×C83—22no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83—41no—
247C2×C4×C83—42no—
248C2×C4×C83—42no—
249C2×C4×C83—84no—
250C2×C4×C83C4×D414yes—
251C2×C4×C83#12712yes—
252C2×C4×C83#12712yes—
253C2×C4×C83#13514yes—
254C2×C4×C83#13514yes—
255C2×C4×C83C23×C411yescharacteristic
256C2×C4×C83C22×D411yescharacteristic
257C2×C4×C83C22×D411yescharacteristic
258C2×C4×C83C2×#4111yescharacteristic
259C2×C4×C83C2×#4111yescharacteristic
260C2×C4×C83C2×#4111yescharacteristic
261C2×Dic83—22no—
262C2×Dic83—41no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265C2×Dic83—41no—
266C2×Dic83—42no—
267C2×Dic83—42no—
268D332—22no—
269D332—22no—
270D332—41no—
271D332—41no—
272C4×D83—84no—
273Dic166—22no—
274Dic166—22no—
275Dic166—41no—
276Dic166—41no—
277C83⋊C8—22no—
278C83⋊C8—22no—
279C83⋊C8C4×D414yes—
280C83⋊C8C4×D414yes—
281C22×C83—42no—
282C22×C83—44no—
283C22×C83—81no—
284C22×C83—81no—
285C22×C83—82no—
286C22×C83C2×C4×D411yescharacteristic
287C22×C83C2×#12711yescharacteristic
288C22×C83#53211yescharacteristic
289C22×C83C2×#13512yes—
290C22×C83C2×#13512yes—
291C2×D83—42no—
292C2×D83—44no—
293C2×D83—81no—
294C2×D83—81no—
295C2×D83—82no—
296C4×C83—22no—
297C4×C83—24no—
298C4×C83—24no—
299C4×C83—42no—
300C4×C83—81no—
301C4×C83—81no—
302C4×C83#49514yescomplemented
303C4×C83C2×C4×D411yescharacteristic
304C4×C83C2×C4×D411yescharacteristic
305C4×C83#53211yescharacteristic
306C4×C83#53211yescharacteristic
307Dic83—42no—
308Dic83—81no—
309Dic83—81no—
310C4×#495—831nomaximal, Sylow
311C2×C83—82no—
312C2×C83C4×#12711yescharacteristic
313C2×C83C4×#13512yes—
314C2×C83C2×#49511yescharacteristic
315C2×C83#314711yescharacteristic
316C2×C83#316812yes—
317D83—82no—
318C2×#495—831no—
319C2×C4×Q16—831no—
320C2×C4×SD16—831no—
321C2×C4×SD16—831no—
322C2×C4×D8—831no—
323C4×#124—831no—
324C4×#124D8311yescharacteristic, complemented
325#1970—831no—
326#1969—831no—
327#1968—831no—
328#1968—831no—
329#1958—831no—
330#1958—831no—
331#1846—831no—
332C42×C8—831no—
333C83C4×#49511yescharacteristic, complemented, Sylow
334C22×Q16—831no—
335C22×SD16—831no—
336C22×SD16—831no—
337C22×D8—831no—
338C2×#124—831no—
339C2×#124C2×D8311yescharacteristic
340C2×C4×Q8—831no—
341C2×C4×Q8C2×D8311yescharacteristic
342C2×C4×D4—831no—
343C2×C4×D4C2×D8311yescharacteristic
344#495—838no—
345C4×Q16—1664no—
346C4×SD16—1664no—
347C4×SD16—1664no—
348C4×D8—1664no—
349C2×#107—831no—
350C2×#107—831no—
351C2×#106—831no—
352C2×#106—831no—
353C2×#103—831no—
354C2×#103—831no—
355C2×#103—831no—
356C2×#103—831no—
357C2×#102—831no—
358C2×#102—831no—
359C2×#102—831no—
360C2×#102—831no—
361C2×C4×C8—831no—
362C2×C4×C8—831no—
363C2×C4×C8—831no—
364C2×C4×C8—831no—
365C2×C4×C8—831no—
366C2×C4×C8—831no—
367#391—831no—
368#391C2×D8311yescharacteristic
369#390—831no—
370#390C2×D8311yescharacteristic
371#388—22no—
372#388—1662no—
373#382—831no—
374#382C2×D8311yescharacteristic
375C4×C22⋊C4—22no—
376C4×C22⋊C4—1662no—
377C43C2×D8311yescharacteristic
378C22×Q8—831no—
379C22×Q8C22×D8311yescharacteristic
380C22×D4—831no—
381C22×D4C22×D8311yescharacteristic
382C23×C4—21no—
383C23×C4—1661no—
384C2×Q16—834no—
385C2×Q16—1662no—
386C2×Q16—1662no—
387C2×SD16—834no—
388C2×SD16—834no—
389C2×SD16—1662no—
390C2×SD16—1662no—
391C2×SD16—1662no—
392C2×SD16—1662no—
393C2×D8—834no—
394C2×D8—1662no—
395C2×D8—1662no—
396C22×C8—831no—
397C22×C8—831no—
398C22×C8—831no—
399C22×C8—831no—
400#124—22no—
401#124—834no—
402#124—1662no—
403#124C4×D8314yescomplemented
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—1662no—
407C4×Q8—1662no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—1662no—
411C4×D4—1662no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—831no—
414C2×C4⋊C4—831no—
415C2×C4⋊C4—1661no—
416C2×C4⋊C4C22×D8311yescharacteristic
417C2×C4⋊C4C22×D8311yescharacteristic
418C2×C22⋊C4—22no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—1661no—
422C2×C22⋊C4—1662no—
423C2×C22⋊C4—1662no—
424C2×C42—21no—
425C2×C42—1661no—
426C2×C42C22⋊D8312yes—
427C2×C42C22⋊D8312yes—
428C2×C42C22×D8311yescharacteristic
429C2×C42C22×D8311yescharacteristic
430C2×C42C22×D8311yescharacteristic
431#107—1662no—
432#107—1662no—
433#106—1662no—
434#106—1662no—
435#103—1662no—
436#103—1662no—
437#103—1662no—
438#103—1662no—
439#102—1662no—
440#102—1662no—
441#102—1662no—
442#102—1662no—
443C4×C8—834no—
444C4×C8—834no—
445C4×C8—834no—
446C4×C8—1662no—
447C4×C8—1662no—
448C4×C8—1662no—
449#95—22no—
450#95—22no—
451#95—1662no—
452#95—1662no—
453C24—21no—
454C24—1661no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—832no—
461C2×Q8—1661no—
462C2×Q8—1661no—
463C2×Q8—1661no—
464C2×Q8—1661no—
465C2×Q8—1661no—
466C2×Q8C2×C4×D8312yes—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—832no—
473C2×D4—1661no—
474C2×D4—1661no—
475C2×D4—1661no—
476C2×D4—1661no—
477C2×D4—1661no—
478C2×D4C2×C4×D8312yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—44no—
484C22×C4—3322no—
485C22×C4—3324no—
486C22×C4—1661no—
487C22×C4—1661no—
488C22×C4—1661no—
489C22×C4C2×C22⋊D8311yescharacteristic
490C22×C4C2×C22⋊D8312yes—
491C22×C4C2×C22⋊D8312yes—
492C22×C4C2×C22⋊D8311yescharacteristic
493C22×C4C23×D8311yescharacteristic
494Q16—1668no—
495SD16—1668no—
496SD16—1668no—
497D8—1668no—
498C2×C8—832no—
499C2×C8—832no—
500C2×C8—832no—
501C2×C8—832no—
502C2×C8—832no—
503C2×C8—832no—
504C2×C8—832no—
505C2×C8—832no—
506C2×C8—1661no—
507C2×C8—1661no—
508C2×C8—1661no—
509C2×C8—1661no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—3322no—
516C4⋊C4—1661no—
517C4⋊C4—1661no—
518C4⋊C4—1661no—
519C4⋊C4—1661no—
520C22⋊C4—28no—
521C22⋊C4—42no—
522C22⋊C4—44no—
523C22⋊C4—3322no—
524C22⋊C4—3324no—
525C22⋊C4—1668no—
526C42—24no—
527C42—24no—
528C42—21no—
529C42—21no—
530C42—42no—
531C42—3322no—
532C42C2×C4×D8312yes—
533C42D4×D8312yes—
534C42D4×D8312yes—
535C42#1305059012yes—
536C23—22no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23—3322no—
542C23—3322no—
543C23—3321no—
544C23—3321no—
545C23—1662no—
546C23C22×C22⋊D8311yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—41no—
550Q8—41no—
551Q8—3321no—
552Q8—3321no—
553Q8—1662no—
554Q8—1662no—
555D4—22no—
556D4—22no—
557D4—41no—
558D4—41no—
559D4—3321no—
560D4—3321no—
561D4—1662no—
562D4—1662no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—3321no—
577C2×C4—3321no—
578C2×C4—3322no—
579C2×C4—3322no—
580C2×C4—3321no—
581C2×C4—3321no—
582C2×C4—6644no—
583C2×C4—1662no—
584C2×C4C4×C22⋊D8314yes—
585C2×C4#1458178812yes—
586C2×C4#1458178812yes—
587C2×C4#1458181214yes—
588C2×C4#1458181214yes—
589C2×C4C22×C4×D8311yescharacteristic
590C2×C4C2×D4×D8311yescharacteristic
591C2×C4C2×D4×D8311yescharacteristic
592C2×C4#41×D8311yescharacteristic
593C2×C4#41×D8311yescharacteristic
594C2×C4C2×#1305059011yescharacteristic
595C8—834no—
596C8—834no—
597C8—1662no—
598C8—1662no—
599C22—44no—
600C22—42no—
601C22—82no—
602C22—81no—
603C22—81no—
604C22—3324no—
605C22—3322no—
606C22—6642no—
607C22—6641no—
608C22—6641no—
609C22C2×C4×C22⋊D8311yescharacteristic
610C22C2×#1458178811yescharacteristic
611C22#1912824711yescharacteristic
612C22C2×#1458181212yes—
613C22C2×#1458181212yes—
614C4—24no—
615C4—24no—
616C4—22no—
617C4—42no—
618C4—81no—
619C4—81no—
620C4—3322no—
621C4—6641no—
622C4—6641no—
623C4#1912808314yesdirect product factor
624C4C4×D4×D8311yescharacteristic
625C4C4×D4×D8311yescharacteristic
626C4#1912824811yescharacteristic
627C4#1912824811yescharacteristic
628C2—82no—
629C2—6642no—
630C2C4×#1458178811yescharacteristic
631C2C4×#1458181212yes—
632C2C2×#1912808311yescharacteristic
633C2#2491788911yescharacteristic
634C2#2491802712yes—
subgroupG/H
centerC22×C4C2×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×#124×C83C2
socleC23×C83C22×D4
prime radicalC22×#13050575C22
cosocleC22×C4×C83C24
hypercenterC4×#124D83
hypocenterC83C4×#495
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. C2×C4×#13050580C2semidirect
3. C2×C4×#13050577C2semidirect
4. C2×C4×#13050578C2semidirect
6. C4×#14581780C2semidirect
8. #24908323C2semidirect
9. #24908320C2semidirect
10. #24908316C2semidirect
11. #24908275C2semidirect
12. #24908272C2semidirect
13. #24907625C2semidirect
14. C42×C83⋊C8C2semidirect
15. C4×#124×C83C2semidirect
23. #19128083C4direct (N × H)
65. C2×#13050580C2×C4semidirect
68. C2×#13050578C2×C4semidirect
71. C2×#13050577C2×C4semidirect
80. #14581780C2×C4semidirect
107. C4×C83⋊C8C2×C4semidirect
116. #124×C83C2×C4semidirect
302. C4×C83#495semidirect
324. C4×#124D83semidirect
333. C83C4×#495semidirect
403. #124C4×D83semidirect
623. C4#19128083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191280832
C2×C4×#130505802
C2×C4×#130505772
C2×C4×#130505782
C2×C4×#130505752
C4×#145817802
#249083282
#249083232
#249083202
#249083162
#249082752
#249082722
#249076252
C42×C83⋊C82
C4×#124×C832
C4×#49583