Finite Group Databasebeta

← C2×#24907693 #35405263

Subgroups — C2×#24907693 #35405263

Order 21248.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128181C211yesmaximal, characteristic
2C22×#14581718C211yesmaximal, characteristic
3C2×#19127700C211yesmaximal, characteristic
4C2×#19127566C211yesmaximal, characteristic, complemented
5#24907693C218yesmaximal, direct product factor
6C2×#19127469C211yesmaximal, characteristic, complemented
7C2×#19127460C211yesmaximal, characteristic, complemented
8C2×#428×C83C211yesmaximal, characteristic, complemented
9C22×#13050590C2211yescharacteristic
10C22×#13050574C2211yescharacteristic
11#19128181—22no—
12#19128181—22no—
13#19128181—22no—
14#19128181C2214yes—
15C2×C4×Dic166—21no—
16C2×C4×D332—21no—
17C2×(C22⋊D83)⋊C4—22no—
18C2×#14581750—21no—
19C22×C4⋊Dic83C2211yescharacteristic
20C2×C4⋊C4×D83—21no—
21C22×C4×Dic83C2211yescharacteristic
22C2×#14581718C418yescomplemented
23C2×#14581718C2214yes—
24#19127700—22no—
25#19127700C2214yes—
26C2×#14581715—21no—
27C2×#14581712—21no—
28#19127566—22no—
29#19127566C2214yescomplemented
30C2×C83⋊#95—22no—
31#19127469C2214yescomplemented
32#19127460C2214yescomplemented
33C22×M16×C83C2211yescharacteristic
34C2×#117×C83C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic
36#428×C83—22no—
37#428×C83C2214yescomplemented
38C2×#107×C83—21no—
39C2×#106×C83—21no—
40C2×#13050590—21no—
41C2×#13050590—21no—
42C2×#13050590—22no—
43C2×#13050590—22no—
44C2×#13050590C2×C414yes—
45C2×#13050590D412yes—
46C2×#13050590Q814yes—
47C2×#13050590C2312yes—
48C22×Dic166D411yescharacteristic
49C22×D332D411yescharacteristic
50C22×C22⋊D83—21no—
51C23×Dic83—21no—
52C23×Dic83D412yes—
53C22×C4×D83—22no—
54C22×C4×D83—21no—
55C2×#13050574—21no—
56C2×#13050574—22no—
57C2×#13050574—22no—
58C2×#13050574C2312yes—
59C22×C83⋊C8—21no—
60C4×Dic166—24no—
61C4×Dic166—24no—
62C4×D332—24no—
63C4×D332—24no—
64(C22⋊D83)⋊C4—28no—
65(C22⋊D83)⋊C4—28no—
66#14581750—24no—
67#14581750—24no—
68C2×C4⋊Dic83—21no—
69C2×C4⋊Dic83—21no—
70C2×C4⋊Dic83—21no—
71C2×C4⋊Dic83—21no—
72C2×C4⋊Dic83D412yes—
73C2×C4⋊Dic83C2312yes—
74C2×Dic83⋊C4—22no—
75C4⋊C4×D83—24no—
76C4⋊C4×D83—24no—
77C2×(C2×D83)⋊C4—22no—
78C2×C4×Dic83—22no—
79C2×C4×Dic83—21no—
80C2×C4×Dic83—22no—
81C2×C4×Dic83C2×C414yescomplemented
82C2×C4×Dic83C2312yes—
83#14581718C2×C4116yescomplemented
84#14581715—24no—
85#14581712—24no—
86C83⋊#95—28no—
87C23×C4×C83—21no—
88C23×C4×C83C2311yescharacteristic
89C2×M16×C83—21no—
90C2×M16×C83—22no—
91C2×M16×C83C2×C414yescomplemented
92C2×M16×C83C2312yes—
93C22×C8×C83—21no—
94#117×C83—21no—
95#117×C83—21no—
96#117×C83D412yes—
97#117×C83C2312yes—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83—21no—
102C2×C4⋊C4×C83—21no—
103C2×C4⋊C4×C83D411yescharacteristic
104C2×C4⋊C4×C83D411yescharacteristic
105C2×C4⋊C4×C83C2312yes—
106C2×C22⋊C4×C83—21no—
107C2×C42×C83—21no—
108#107×C83—24no—
109#106×C83—24no—
110C23×D83—21no—
111#13050590—24no—
112#13050590—24no—
113#13050590—24no—
114#13050590—24no—
115#13050590—24no—
116#13050590—22no—
117#13050590—22no—
118#13050590C4⋊C418yes—
119#13050590C22×C414yes—
120#13050590C2×Q814yes—
121C2×Dic166—21no—
122C2×Dic166—22no—
123C2×Dic166C4⋊C414yes—
124C2×Dic166C2×D412yes—
125C2×D332—21no—
126C2×D332—22no—
127C2×D332C4⋊C414yes—
128C2×D332C2×D412yes—
129C2×C22⋊D83—24no—
130C2×C22⋊D83—22no—
131C2×C22⋊D83—24no—
132C2×C22⋊D83—22no—
133C22×Dic83—21no—
134C22×Dic83—24no—
135C22×Dic83—22no—
136C22×Dic83—22no—
137C22×Dic83—22no—
138C22×Dic83—42no—
139C22×Dic83—42no—
140C22×Dic83—44no—
141C22×Dic83C2×D414yes—
142C2×C4×D83—24no—
143C2×C4×D83—22no—
144C2×C4×D83—24no—
145C2×C4×D83—22no—
146C2×C4×D83—28no—
147C2×C4×D83—84no—
148#13050574—22no—
149#13050574—22no—
150#13050574—42no—
151C2×C83⋊C8—22no—
152C2×C83⋊C8—42no—
153C4⋊Dic83—22no—
154C4⋊Dic83—22no—
155C4⋊Dic83—22no—
156C4⋊Dic83—22no—
157Dic83⋊C4—28no—
158(C2×D83)⋊C4—28no—
159C4×Dic83—28no—
160C4×Dic83—24no—
161C4×Dic83—22no—
162C4×Dic83C22×C414yescomplemented
163C24×C83C2×D411yescharacteristic
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—22no—
167C22×C4×C83—44no—
168C22×C4×C83—41no—
169C22×C4×C83—41no—
170C22×C4×C83C22×C412yes—
171C22×C4×C83C2×D411yescharacteristic
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×Q812yes—
177C22×C4×C83#4112yes—
178C22×C4×C83#4112yes—
179C22×C4×C83C2411yescharacteristic
180M16×C83—24no—
181M16×C83—22no—
182M16×C83C22×C414yescomplemented
183C2×C8×C83—24no—
184C2×C8×C83—22no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—22no—
188C4⋊C4×C83—22no—
189C4⋊C4×C83—41no—
190C4⋊C4×C83—41no—
191C4⋊C4×C83C2×D412yes—
192C4⋊C4×C83C2×D412yes—
193C22⋊C4×C83—22no—
194C22⋊C4×C83—22no—
195C42×C83—22no—
196C42×C83—22no—
197C23×C83—22no—
198C23×C83—22no—
199C23×C83C4×D412yes—
200C23×C83#12011yescharacteristic
201C23×C83#12011yescharacteristic
202C23×C83C22⋊Q812yes—
203C23×C83C22×D411yescharacteristic
204C22×D83—22no—
205C22×D83—24no—
206C22×D83—42no—
207C22×D83—42no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
210C2×C4×C83—42no—
211C2×C4×C83—42no—
212C2×C4×C83—44no—
213C2×C4×C83—42no—
214C2×C4×C83—82no—
215C2×C4×C83—82no—
216C2×C4×C83C2×C4⋊C412yes—
217C2×C4×C83C2×C4⋊C412yes—
218C2×C4×C83C4×D412yes—
219C2×C4×C83C4×D412yes—
220C2×C4×C83C4×D412yes—
221C2×C4×C83#12011yescharacteristic
222C2×C4×C83#12011yescharacteristic
223C2×C4×C83C22⋊Q812yes—
224C2×C4×C83C22⋊Q812yes—
225C2×C4×C83C22⋊Q812yes—
226C2×C4×C83#12312yes—
227C2×C4×C83#12312yes—
228C2×C4×C83C23×C411yescharacteristic
229C2×C4×C83C22×D411yescharacteristic
230C2×C4×C83C22×D411yescharacteristic
231C2×C4×C83C22×Q811yescharacteristic
232C2×C4×C83C2×#4111yescharacteristic
233C2×C4×C83C2×#4111yescharacteristic
234C22⋊D83—24no—
235C22⋊D83—24no—
236C22⋊D83—28no—
237C2×Dic83—22no—
238C2×Dic83—24no—
239C2×Dic83—24no—
240C2×Dic83—24no—
241C2×Dic83—48no—
242C2×Dic83—42no—
243C2×Dic83—42no—
244C2×Dic83—44no—
245C2×Dic83—44no—
246C2×Dic83—82no—
247D332—22no—
248D332—24no—
249D332C2×C4⋊C414yes—
250C4×D83—24no—
251C4×D83—24no—
252C4×D83—28no—
253C4×D83—88no—
254Dic166—22no—
255Dic166—24no—
256Dic166C2×C4⋊C414yes—
257C8×C83—24no—
258C83⋊C8—42no—
259C22×C83—24no—
260C22×C83—24no—
261C22×C83—21no—
262C22×C83—21no—
263C22×C83—21no—
264C22×C83—21no—
265C22×C83#38512yes—
266C22×C83#38512yes—
267C22×C83#45412yes—
268C22×C83#45512yes—
269C22×C83C2×C4×D411yescharacteristic
270C22×C83C2×#12011yescharacteristic
271C22×C83C2×C22⋊Q811yescharacteristic
272C2×D83—24no—
273C2×D83—48no—
274C2×D83—42no—
275C2×D83—42no—
276C4×C83—42no—
277C4×C83—42no—
278C4×C83—82no—
279C4×C83#38512yes—
280C4×C83#38512yes—
281C4×C83C22×C4⋊C411yescharacteristic
282C4×C83C2×C4×D411yescharacteristic
283C4×C83C2×C22⋊Q811yescharacteristic
284C4×C83C2×#12311yescharacteristic
285Dic83—24no—
286Dic83—44no—
287Dic83—44no—
288C2×#1860—831nomaximal, Sylow
289C2×C83—21no—
290C2×C83—21no—
291C2×C83—22no—
292C2×C83#186014yescomplemented
293C2×C83C2×#38511yescharacteristic
294C2×C83C2×#45511yescharacteristic
295C2×C83C2×#45411yescharacteristic
296D83—44no—
297C2×#520—831no—
298C2×#428D8311yescharacteristic, complemented
299C22×#104—831no—
300C2×#417—831no—
301C2×#382—831no—
302#1860—838no—
303C2×#343—831no—
304C2×#339—831no—
305C83C2×#186011yescharacteristic, complemented, Sylow
306C22×#41—831no—
307C22×M16—831no—
308C22×M16C2×D8311yescharacteristic
309#520—834no—
310#520—1662no—
311#520—1662no—
312#520—1662no—
313C2×C4×Q8—1661no—
314C2×C4×D4—1661no—
315C2×C4×D4—1662no—
316C2×#117—1661no—
317C2×#117C2×D8311yescharacteristic
318C22×C4⋊C4—831no—
319C22×C4⋊C4—1661no—
320C22×C4⋊C4C2×D8311yescharacteristic
321C22×C42—831no—
322#428—22no—
323#428C2×D8314yescomplemented
324C2×#107—21no—
325C2×#106—21no—
326C2×#104—838no—
327C2×#104—834no—
328#417—834no—
329#417—1662no—
330C2×#103—1661no—
331C2×#102—1661no—
332#382—834no—
333#382—1662no—
334C2×#95—1662no—
335#343—834no—
336#339—834no—
337C2×#41—834no—
338C2×#41—832no—
339C2×#41—834no—
340C2×#41—832no—
341C2×#41—1661no—
342C2×#41—1661no—
343C2×#41—1662no—
344C2×#41—1662no—
345C22×Q8—831no—
346C22×D4—831no—
347C22×D4—1661no—
348C23×C4—21no—
349C23×C4—832no—
350C23×C4—1662no—
351C23×C4—1661no—
352C23×C4—1661no—
353C23×C4C22×D8311yescharacteristic
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—832no—
357C2×M16—1662no—
358C2×M16—1662no—
359C2×M16—1661no—
360C2×M16C4×D8314yescomplemented
361C2×M16C22×D8312yes—
362C22×C8—21no—
363C22×C8—1661no—
364C4×Q8—1664no—
365C4×Q8—1664no—
366C4×D4—1664no—
367C4×D4—1664no—
368C4×D4—1668no—
369C4×D4—1668no—
370#117—21no—
371#117—21no—
372#117—1664no—
373#117—1664no—
374#117C22⋊D8312yes—
375#117C22×D8312yes—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—832no—
382C2×C4⋊C4—832no—
383C2×C4⋊C4—1664no—
384C2×C4⋊C4—1662no—
385C2×C4⋊C4—1661no—
386C2×C4⋊C4—1661no—
387C2×C4⋊C4—1661no—
388C2×C4⋊C4—1661no—
389C2×C4⋊C4—1664no—
390C2×C4⋊C4C22⋊D8311yescharacteristic
391C2×C4⋊C4C22⋊D8311yescharacteristic
392C2×C4⋊C4C22×D8312yes—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—1662no—
395C2×C42—21no—
396C2×C42—834no—
397C2×C42—832no—
398C2×C42—1662no—
399C2×C42—1661no—
400C2×C42—1662no—
401#107—24no—
402#106—24no—
403#104—8316no—
404#103—1664no—
405#102—1664no—
406#95—1668no—
407C24—1661no—
408C24D4×D8311yescharacteristic
409#41—834no—
410#41—834no—
411#41—838no—
412#41—1664no—
413#41—1664no—
414#41—1664no—
415#41—1662no—
416#41—1662no—
417#41—1664no—
418#41—1664no—
419C2×Q8—832no—
420C2×Q8—834no—
421C2×Q8—1661no—
422C2×Q8—1662no—
423C2×D4—832no—
424C2×D4—834no—
425C2×D4—1662no—
426C2×D4—1664no—
427C2×D4—1662no—
428C2×D4—1664no—
429C2×D4—1661no—
430C2×D4—1662no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—3322no—
438C22×C4—3322no—
439C22×C4—3324no—
440C22×C4—834no—
441C22×C4—6644no—
442C22×C4—1668no—
443C22×C4—1662no—
444C22×C4—1662no—
445C22×C4—1664no—
446C22×C4—1662no—
447C22×C4—1661no—
448C22×C4—1662no—
449C22×C4—1664no—
450C22×C4—1662no—
451C22×C4—1664no—
452C22×C4C2×C4×D8312yes—
453C22×C4D4×D8311yescharacteristic
454C22×C4D4×D8311yescharacteristic
455C22×C4D4×D8311yescharacteristic
456C22×C4C2×C22⋊D8311yescharacteristic
457C22×C4C2×C22⋊D8311yescharacteristic
458C22×C4Q8×D8312yes—
459C22×C4#1305059012yes—
460C22×C4#1305059112yes—
461C22×C4C23×D8311yescharacteristic
462M16—22no—
463M16—24no—
464M16—3322no—
465M16—1662no—
466M16—1662no—
467M16C2×C4×D8314yescomplemented
468C2×C8—22no—
469C2×C8—24no—
470C2×C8—3322no—
471C2×C8—1662no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—1668no—
479C4⋊C4—1662no—
480C4⋊C4—1662no—
481C4⋊C4—1662no—
482C4⋊C4—1662no—
483C4⋊C4C2×C22⋊D8312yes—
484C4⋊C4C2×C22⋊D8312yes—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—1668no—
488C42—22no—
489C42—22no—
490C42—834no—
491C42—1668no—
492C42—1662no—
493C42—1664no—
494C23—22no—
495C23—22no—
496C23—3322no—
497C23—3322no—
498C23—1664no—
499C23—1662no—
500C23#1458175412yes—
501C23#1458176011yescharacteristic
502C23#1458176011yescharacteristic
503C23#1458177012yes—
504C23C2×D4×D8311yescharacteristic
505Q8—834no—
506Q8—1664no—
507Q8—1662no—
508D4—834no—
509D4—1668no—
510D4—1664no—
511D4—1664no—
512D4—1664no—
513D4—1662no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—3322no—
523C2×C4—3322no—
524C2×C4—3328no—
525C2×C4—3324no—
526C2×C4—3324no—
527C2×C4—6648no—
528C2×C4—6642no—
529C2×C4—1664no—
530C2×C4—1664no—
531C2×C4—1664no—
532C2×C4—1662no—
533C2×C4—1668no—
534C2×C4—1664no—
535C2×C4—1664no—
536C2×C4C4⋊C4×D8312yes—
537C2×C4C4⋊C4×D8312yes—
538C2×C4C4×C22⋊D8312yes—
539C2×C4C4×C22⋊D8312yes—
540C2×C4#1458175412yes—
541C2×C4#1458176011yescharacteristic
542C2×C4#1458176011yescharacteristic
543C2×C4#1458176812yes—
544C2×C4#1458176812yes—
545C2×C4#1458177012yes—
546C2×C4#1458177712yes—
547C2×C4#1458177712yes—
548C2×C4C22×C4×D8311yescharacteristic
549C2×C4C2×D4×D8311yescharacteristic
550C2×C4C22×C22⋊D8311yescharacteristic
551C2×C4C2×Q8×D8311yescharacteristic
552C2×C4C2×#1305059011yescharacteristic
553C2×C4C2×#1305059111yescharacteristic
554C8—24no—
555C8—3322no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—3322no—
563C22—3322no—
564C22—3328no—
565C22—1664no—
566C22#1912757212yes—
567C22#1912757212yes—
568C22#1912787212yes—
569C22#1912787712yes—
570C22C2×#1458175411yescharacteristic
571C22C2×#1458176011yescharacteristic
572C22C2×#1458177011yescharacteristic
573C4—42no—
574C4—42no—
575C4—82no—
576C4—3324no—
577C4—3324no—
578C4—1664no—
579C4#1912757212yes—
580C4#1912757212yes—
581C4C2×C4⋊C4×D8311yescharacteristic
582C4C2×C4×C22⋊D8311yescharacteristic
583C4C2×#1458176811yescharacteristic
584C4C2×#1458177711yescharacteristic
585C2—21no—
586C2—22no—
587C2—21no—
588C2—3324no—
589C2#2490769314yesdirect product factor
590C2C2×#1912757211yescharacteristic
591C2C2×#1912787711yescharacteristic
592C2C2×#1912787211yescharacteristic
subgroupG/H
centerC23#14581760
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#428×C83C2
socleC23×C83#120
prime radicalC22×#13050590C22
cosocleC22×C4×C83C24
hypercenterC2×#428D83
hypocenterC83C2×#1860
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C2×#19127566C2semidirect
5. #24907693C2direct (N × H)
6. C2×#19127469C2semidirect
7. C2×#19127460C2semidirect
8. C2×#428×C83C2semidirect
22. C2×#14581718C4semidirect
29. #19127566C22semidirect
31. #19127469C22semidirect
32. #19127460C22semidirect
37. #428×C83C22semidirect
81. C2×C4×Dic83C2×C4semidirect
83. #14581718C2×C4semidirect
91. C2×M16×C83C2×C4semidirect
162. C4×Dic83C22×C4semidirect
182. M16×C83C22×C4semidirect
292. C2×C83#1860semidirect
298. C2×#428D83semidirect
305. C83C2×#1860semidirect
323. #428C2×D83semidirect
360. C2×M16C4×D83semidirect
467. M16C2×C4×D83semidirect
589. C2#24907693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191281812
C22×#145817182
C2×#191277002
C2×#191275662
#249076932
C2×#191274692
C2×#191274602
C2×#428×C832
C2×#186083