Finite Group Databasebeta

← C2×#24911742 #35573326

Subgroups — C2×#24911742 #35573326

Order 21248.

4382 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D83)⋊C4C211yesmaximal, characteristic
2C22×C22⋊C4×D83C211yesmaximal, characteristic
3#24911742C2116yesmaximal, direct product factor
4C2×#19127630C212yesmaximal, complemented
5C2×#19127628C212yesmaximal, complemented
6C2×#19127576C211yesmaximal, characteristic, complemented
7C2×#19127575C212yesmaximal, complemented
8C2×#19127573C211yesmaximal, characteristic, complemented
9C2×#19127564C211yesmaximal, characteristic, complemented
10C2×#19127563C212yesmaximal, complemented
11C2×#19127556C211yesmaximal, characteristic
12C2×#381×C83C211yesmaximal, characteristic, complemented
13C25×D83C2211yescharacteristic
14C24×Dic83C2211yescharacteristic
15C23×C4×D83C2211yescharacteristic
16C23×C4×D83C2211yescharacteristic
17C22×C4⋊Dic83C2212yescomplemented
18C22×Dic83⋊C4C2212yescomplemented
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×(C2×D83)⋊C4—28no—
22C22×(C2×D83)⋊C4C2212yes—
23C22×(C2×D83)⋊C4C2212yes—
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2212yes—
27C22×(C2×D83)⋊C4C2218yes—
28C22×(C2×D83)⋊C4C2212yes—
29C2×C22⋊C4×D83—28no—
30C2×C22⋊C4×D83C2218yes—
31#19127630C22116yescomplemented
32#19127628C22116yescomplemented
33#19127576C2218yescomplemented
34#19127575C22116yescomplemented
35#19127573C2218yescomplemented
36#19127564C2218yescomplemented
37#19127563C22116yescomplemented
38#19127556C2218yes—
39C2×C83⋊#95C2212yescomplemented
40C2×C83⋊#95C2212yescomplemented
41C2×C83⋊#95C2212yescomplemented
42C2×C83⋊#95C2212yescomplemented
43C24×C4×C83C2211yescharacteristic
44C22×C22⋊C4×C83C2211yescharacteristic
45C22×C22⋊C4×C83C2211yescharacteristic
46#381×C83C2218yescomplemented
47C2×#95×C83C2212yescomplemented
48C2×#95×C83C2212yescomplemented
49C24×D83—28no—
50C24×D83—24no—
51C24×D83—24no—
52C24×D83—44no—
53C24×D83D418yes—
54C24×D83C2311yescharacteristic
55C24×D83C2314yes—
56C24×D83C2311yescharacteristic
57C23×Dic83—24no—
58C23×Dic83—44no—
59C23×Dic83C2312yes—
60C23×Dic83C2312yes—
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2314yes—
64C22×C4×D83—24no—
65C22×C4×D83—24no—
66C22×C4×D83—28no—
67C22×C4×D83—44no—
68C22×C4×D83C2314yes—
69C22×C4×D83C2314yes—
70C2×C4⋊Dic83—44no—
71C2×C4⋊Dic83C2318yescomplemented
72C2×Dic83⋊C4—44no—
73C2×Dic83⋊C4C2318yescomplemented
74C2×C22⋊Dic83—24no—
75C2×C22⋊Dic83—24no—
76C2×C22⋊Dic83C2314yes—
77C2×C22⋊Dic83C2314yes—
78C2×(C2×D83)⋊C4—24no—
79C2×(C2×D83)⋊C4—24no—
80C2×(C2×D83)⋊C4—28no—
81C2×(C2×D83)⋊C4—232no—
82C2×(C2×D83)⋊C4—28no—
83C2×(C2×D83)⋊C4—28no—
84C2×(C2×D83)⋊C4—44no—
85C2×(C2×D83)⋊C4C2318yes—
86C2×(C2×D83)⋊C4C2318yes—
87C2×(C2×D83)⋊C4C2314yes—
88C2×(C2×D83)⋊C4C2318yes—
89C2×(C2×D83)⋊C4C2314yes—
90C2×(C2×D83)⋊C4C2318yes—
91C22⋊C4×D83—232no—
92C83⋊#95C2318yescomplemented
93C83⋊#95C2318yescomplemented
94C83⋊#95C2318yescomplemented
95C83⋊#95C2318yescomplemented
96C25×C83C2311yescharacteristic
97C23×C4×C83—24no—
98C23×C4×C83—24no—
99C23×C4×C83—24no—
100C23×C4×C83C2314yes—
101C23×C4×C83C2312yes—
102C23×C4×C83C2311yescharacteristic
103C23×C4×C83C2311yescharacteristic
104C23×C4×C83C2312yes—
105C2×C22⋊C4×C83—24no—
106C2×C22⋊C4×C83—24no—
107C2×C22⋊C4×C83C2314yes—
108C2×C22⋊C4×C83C2314yes—
109#95×C83C2318yescomplemented
110#95×C83C2318yescomplemented
111C23×D83—22no—
112C23×D83—22no—
113C23×D83—24no—
114C23×D83—232no—
115C23×D83—24no—
116C23×D83—28no—
117C23×D83—22no—
118C23×D83—28no—
119C23×D83—22no—
120C23×D83—24no—
121C23×D83—232no—
122C23×D83—216no—
123C23×D83—416no—
124C23×D83—48no—
125C23×D83—432no—
126C23×D83—432no—
127C23×D83C2×D414yes—
128C23×D83C2×D4116yes—
129C23×D83C2×D414yes—
130C23×D83#4118yes—
131C23×D83C2412yes—
132C23×D83C2412yes—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—28no—
136C22×Dic83—24no—
137C22×Dic83—24no—
138C22×Dic83—24no—
139C22×Dic83—24no—
140C22×Dic83—24no—
141C22×Dic83—24no—
142C22×Dic83—24no—
143C22×Dic83—24no—
144C22×Dic83—48no—
145C22×Dic83—416no—
146C22×Dic83C2412yes—
147C22×Dic83C2412yes—
148C22×Dic83C2414yes—
149C22×Dic83C2414yes—
150C2×C4×D83—28no—
151C2×C4×D83—28no—
152C2×C4×D83—216no—
153C2×C4×D83—48no—
154C2×C4×D83—416no—
155C2×C4×D83—416no—
156C4⋊Dic83—48no—
157Dic83⋊C4—48no—
158C22⋊Dic83—28no—
159C22⋊Dic83—28no—
160(C2×D83)⋊C4—28no—
161(C2×D83)⋊C4—28no—
162(C2×D83)⋊C4—216no—
163(C2×D83)⋊C4—216no—
164(C2×D83)⋊C4—216no—
165(C2×D83)⋊C4—48no—
166C24×C83—24no—
167C24×C83—24no—
168C24×C83C2×D414yes—
169C24×C83#4114yes—
170C24×C83#4114yes—
171C24×C83C2412yes—
172C24×C83C2411yescharacteristic
173C22×C4×C83—22no—
174C22×C4×C83—22no—
175C22×C4×C83—28no—
176C22×C4×C83—24no—
177C22×C4×C83—24no—
178C22×C4×C83—24no—
179C22×C4×C83—28no—
180C22×C4×C83—24no—
181C22×C4×C83—28no—
182C22×C4×C83—24no—
183C22×C4×C83—24no—
184C22×C4×C83—24no—
185C22×C4×C83—24no—
186C22×C4×C83—416no—
187C22×C4×C83C2412yes—
188C22×C4×C83C2412yes—
189C22×C4×C83C2414yes—
190C22×C4×C83C2414yes—
191C22⋊C4×C83—28no—
192C22⋊C4×C83—28no—
193C23×C83—28no—
194C23×C83—28no—
195C23×C83—216no—
196C23×C83—216no—
197C23×C83—24no—
198C23×C83—24no—
199C23×C83#123116yes—
200C23×C83C22×D414yes—
201C23×C83C22×D412yes—
202C23×C83C2×#4114yes—
203C23×C83C2×#4114yes—
204C23×C83C2×#4112yes—
205C23×C83C2×#4114yes—
206C23×C83C2×#4112yes—
207C23×C83H(5,𝔽2)14yes—
208C23×C83C2511yescharacteristic
209C22×D83—28no—
210C22×D83—28no—
211C22×D83—216no—
212C22×D83—216no—
213C22×D83—22no—
214C22×D83—22no—
215C22×D83—24no—
216C22×D83—28no—
217C22×D83—232no—
218C22×D83—28no—
219C22×D83—28no—
220C22×D83—24no—
221C22×D83—22no—
222C22×D83—22no—
223C22×D83—24no—
224C22×D83—232no—
225C22×D83—416no—
226C22×D83—432no—
227C22×D83—432no—
228C22×D83—4128no—
229C22×D83—48no—
230C22×D83—48no—
231C22×D83#123116yes—
232C22×D83C22×D414yes—
233C22×D83C22×D414yes—
234C22×D83C2×#4118yes—
235C2×C4×C83—22no—
236C2×C4×C83—22no—
237C2×C4×C83—24no—
238C2×C4×C83—24no—
239C2×C4×C83—24no—
240C2×C4×C83—24no—
241C2×C4×C83—24no—
242C2×C4×C83—24no—
243C2×C4×C83—24no—
244C2×C4×C83—24no—
245C2×C4×C83—416no—
246C2×C4×C83—48no—
247C2×C4×C83—44no—
248C2×C4×C83—44no—
249C2×C4×C83—48no—
250C2×Dic83—24no—
251C2×Dic83—22no—
252C2×Dic83—22no—
253C2×Dic83—24no—
254C2×Dic83—24no—
255C2×Dic83—24no—
256C2×Dic83—24no—
257C2×Dic83—24no—
258C2×Dic83—24no—
259C2×Dic83—24no—
260C2×Dic83—416no—
261C2×Dic83—44no—
262C2×Dic83—44no—
263C2×Dic83—48no—
264C2×Dic83—48no—
265C4×D83—416no—
266C4×D83—416no—
267C22×C83—24no—
268C22×C83—24no—
269C22×C83—28no—
270C22×C83—28no—
271C22×C83—232no—
272C22×C83C2×#12314yes—
273C22×C83C2×#12318yes—
274C22×C83C2×#12314yes—
275C22×C83#53414yes—
276C22×C83#55118yes—
277C22×C83#55118yes—
278C22×C83C23×D411yescharacteristic
279C22×C83C22×#4112yes—
280C22×C83C22×#4111yescharacteristic
281C22×C83C22×#4111yescharacteristic
282C22×C83C2×H(5,𝔽2)12yes—
283C2×D83—24no—
284C2×D83—24no—
285C2×D83—28no—
286C2×D83—28no—
287C2×D83—232no—
288C2×D83—24no—
289C2×D83—24no—
290C2×D83—24no—
291C2×D83—464no—
292C2×D83—44no—
293C2×D83—44no—
294C2×D83—416no—
295C2×D83C2×#12318yes—
296C4×C83—42no—
297C4×C83—44no—
298C4×C83—42no—
299C4×C83—44no—
300Dic83—42no—
301Dic83—42no—
302Dic83—44no—
303Dic83—44no—
304C2×#2483—831nomaximal, Sylow
305C2×C83—28no—
306C2×C83#248318yescomplemented
307C2×C83C22×#12311yescharacteristic
308C2×C83C22×#12311yescharacteristic
309C2×C83C2×#53411yescharacteristic
310C2×C83C2×#55112yes—
311C2×C83C2×#55112yes—
312D83—28no—
313D83—44no—
314C23×C22⋊C4—831no—
315C23×C22⋊C4—831no—
316#2483—8316no—
317C2×#397—832no—
318C2×#397—832no—
319C2×#385—832no—
320C2×#385—831no—
321C2×#385—831no—
322C2×#381—832no—
323C2×#381—831no—
324C2×#381D8311yescharacteristic, complemented
325C2×#379—831no—
326C83C2×#248311yescharacteristic, complemented, Sylow
327C26—831no—
328C24×C4—831no—
329C24×C4—831no—
330C24×C4—831no—
331C24×C4C2×D8311yescharacteristic
332C22×C4⋊C4—832no—
333C22×C4⋊C4—832no—
334C22×C22⋊C4—832no—
335C22×C22⋊C4—831no—
336C22×C22⋊C4—831no—
337C22×C22⋊C4—832no—
338C22×C22⋊C4—831no—
339C22×C22⋊C4—831no—
340C22×C22⋊C4—838no—
341C22×C22⋊C4—832no—
342C22×C22⋊C4—832no—
343C22×C22⋊C4—838no—
344C22×C22⋊C4—1668no—
345C22×C22⋊C4—1668no—
346C22×C22⋊C4C2×D8311yescharacteristic
347C22×C22⋊C4C2×D8311yescharacteristic
348#397—8316no—
349#397—8316no—
350#385—838no—
351#385—838no—
352#385—8316no—
353#381—838no—
354#381—8316no—
355#381C2×D8318yescomplemented
356#379—838no—
357C2×#95—832no—
358C2×#95—832no—
359C2×#95—832no—
360C2×#95—832no—
361C2×#95C2×D8312yescomplemented
362C2×#95C2×D8312yescomplemented
363C25—3324no—
364C25—838no—
365C25—834no—
366C25—831no—
367C25—831no—
368C25—1668no—
369C25—1664no—
370C25—1664no—
371C25C22×D8311yescharacteristic
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—3324no—
376C23×C4—3324no—
377C23×C4—834no—
378C23×C4—834no—
379C23×C4—832no—
380C23×C4—831no—
381C23×C4—832no—
382C23×C4—831no—
383C23×C4—834no—
384C23×C4—1664no—
385C23×C4—1664no—
386C23×C4—1668no—
387C23×C4—1664no—
388C23×C4C22×D8314yes—
389C23×C4C22×D8312yes—
390C23×C4C22×D8312yes—
391C23×C4C22×D8311yescharacteristic
392C23×C4C22×D8311yescharacteristic
393C2×C4⋊C4—3324no—
394C2×C4⋊C4—3324no—
395C2×C4⋊C4—838no—
396C2×C4⋊C4—838no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—3324no—
400C2×C22⋊C4—838no—
401C2×C22⋊C4—834no—
402C2×C22⋊C4—834no—
403C2×C22⋊C4—838no—
404C2×C22⋊C4—834no—
405C2×C22⋊C4—838no—
406C2×C22⋊C4—834no—
407C2×C22⋊C4—838no—
408C2×C22⋊C4—16632no—
409C2×C22⋊C4—1664no—
410C2×C22⋊C4—1664no—
411C2×C22⋊C4—16632no—
412C2×C22⋊C4—1668no—
413C2×C22⋊C4—1668no—
414C2×C22⋊C4—1668no—
415C2×C22⋊C4—1664no—
416C2×C22⋊C4—1664no—
417C2×C22⋊C4C22×D8314yes—
418C2×C22⋊C4C22×D8314yes—
419#95—838no—
420#95—838no—
421#95—838no—
422#95—838no—
423#95C22×D8318yescomplemented
424#95C22×D8318yescomplemented
425C24—24no—
426C24—24no—
427C24—33232no—
428C24—33232no—
429C24—33216no—
430C24—3328no—
431C24—8316no—
432C24—834no—
433C24—838no—
434C24—832no—
435C24—834no—
436C24—832no—
437C24—16632no—
438C24—16616no—
439C24—16632no—
440C24—1664no—
441C24—1668no—
442C24—1662no—
443C24—1668no—
444C24—1662no—
445C24—1664no—
446C24—1662no—
447C24—1662no—
448C24—1664no—
449C24D4×D8314yes—
450C24#1305058914yes—
451C24#1305059014yes—
452C24C23×D8312yes—
453C24C23×D8311yescharacteristic
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—24no—
463C22×C4—28no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—416no—
468C22×C4—3328no—
469C22×C4—33216no—
470C22×C4—33216no—
471C22×C4—33216no—
472C22×C4—3328no—
473C22×C4—832no—
474C22×C4—834no—
475C22×C4—832no—
476C22×C4—834no—
477C22×C4—1668no—
478C22×C4—1668no—
479C22×C4—16616no—
480C22×C4—1668no—
481C22×C4—1662no—
482C22×C4—1664no—
483C22×C4—1662no—
484C22×C4—1664no—
485C22×C4—1664no—
486C22×C4—1664no—
487C22×C4—1664no—
488C22×C4—1664no—
489C22×C4—1664no—
490C22×C4—1664no—
491C22×C4C23×D8314yes—
492C22×C4C23×D8312yes—
493C22×C4C23×D8314yes—
494C22×C4C23×D8312yes—
495C4⋊C4—3328no—
496C4⋊C4—3328no—
497C22⋊C4—28no—
498C22⋊C4—28no—
499C22⋊C4—3328no—
500C22⋊C4—1668no—
501C22⋊C4—1668no—
502C22⋊C4—16616no—
503C22⋊C4—16616no—
504C22⋊C4—16616no—
505C22⋊C4—1668no—
506C22⋊C4—1668no—
507C23—216no—
508C23—216no—
509C23—28no—
510C23—28no—
511C23—24no—
512C23—24no—
513C23—33232no—
514C23—332128no—
515C23—33232no—
516C23—33216no—
517C23—3328no—
518C23—3328no—
519C23—8316no—
520C23—834no—
521C23—838no—
522C23—834no—
523C23—16632no—
524C23—1668no—
525C23—16632no—
526C23—1668no—
527C23—1668no—
528C23—1664no—
529C23—1662no—
530C23—1662no—
531C23—1664no—
532C23—16616no—
533C23—16616no—
534C23—1668no—
535C23—1668no—
536C23—1662no—
537C23—1662no—
538C23—1664no—
539C23#14581774116yes—
540C23C2×D4×D8314yes—
541C23C2×D4×D8312yes—
542C23#41×D8314yes—
543C23C2×#1305058914yes—
544C23C2×#1305058912yes—
545C23C2×#1305059014yes—
546C23C2×#1305059012yes—
547C23#1458183814yes—
548C23C24×D8311yescharacteristic
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—416no—
562C2×C4—48no—
563C2×C4—44no—
564C2×C4—33216no—
565C2×C4—33216no—
566C2×C4—33216no—
567C2×C4—3328no—
568C2×C4—3324no—
569C2×C4—3324no—
570C2×C4—3328no—
571C2×C4—1662no—
572C2×C4—1664no—
573C2×C4—1662no—
574C2×C4—1664no—
575C2×C4—1664no—
576C2×C4—1664no—
577C2×C4—1664no—
578C2×C4—1664no—
579C2×C4—1664no—
580C2×C4—1664no—
581C22—24no—
582C22—28no—
583C22—232no—
584C22—28no—
585C22—24no—
586C22—33264no—
587C22—3324no—
588C22—33216no—
589C22—3324no—
590C22—838no—
591C22—1664no—
592C22—1664no—
593C22—1664no—
594C22—1664no—
595C22—1668no—
596C22—16632no—
597C22—1668no—
598C22—1664no—
599C22#123×D8314yes—
600C22C2×#1458177418yes—
601C22C2×#1458177414yes—
602C22#1912826214yes—
603C22#1912837418yes—
604C22#1912837518yes—
605C22C22×D4×D8311yescharacteristic
606C22C2×#41×D8312yes—
607C22C22×#1305058911yescharacteristic
608C22C22×#1305059011yescharacteristic
609C22C2×#1458183812yes—
610C4—42no—
611C4—44no—
612C4—44no—
613C4—42no—
614C4—3322no—
615C4—3324no—
616C4—3322no—
617C4—3324no—
618C2—28no—
619C2—3324no—
620C2—1668no—
621C2#2491174218yesdirect product factor
622C2C2×#123×D8311yescharacteristic
623C2C22×#1458177411yescharacteristic
624C2C2×#1912826211yescharacteristic
625C2C2×#1912837412yes—
626C2C2×#1912837512yes—
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#381×C83C2
socleC24×C83C24
prime radicalC25×D83C22
hypercenterC2×#381D83
hypocenterC83C2×#2483
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #24911742C2direct (N × H)
4. C2×#19127630C2semidirect
5. C2×#19127628C2semidirect
6. C2×#19127576C2semidirect
7. C2×#19127575C2semidirect
8. C2×#19127573C2semidirect
9. C2×#19127564C2semidirect
10. C2×#19127563C2semidirect
12. C2×#381×C83C2semidirect
17. C22×C4⋊Dic83C22semidirect
18. C22×Dic83⋊C4C22semidirect
31. #19127630C22semidirect
32. #19127628C22semidirect
33. #19127576C22semidirect
34. #19127575C22semidirect
35. #19127573C22semidirect
36. #19127564C22semidirect
37. #19127563C22semidirect
39. C2×C83⋊#95C22semidirect
40. C2×C83⋊#95C22semidirect
41. C2×C83⋊#95C22semidirect
42. C2×C83⋊#95C22semidirect
46. #381×C83C22semidirect
47. C2×#95×C83C22semidirect
48. C2×#95×C83C22semidirect
71. C2×C4⋊Dic83C23semidirect
73. C2×Dic83⋊C4C23semidirect
92. C83⋊#95C23semidirect
93. C83⋊#95C23semidirect
94. C83⋊#95C23semidirect
95. C83⋊#95C23semidirect
109. #95×C83C23semidirect
110. #95×C83C23semidirect
306. C2×C83#2483semidirect
324. C2×#381D83semidirect
326. C83C2×#2483semidirect
355. #381C2×D83semidirect
361. C2×#95C2×D83semidirect
362. C2×#95C2×D83semidirect
423. #95C22×D83semidirect
424. #95C22×D83semidirect
621. C2#24911742direct (N × H)

Maximal subgroups

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

subgroupindex
C23×(C2×D83)⋊C42
C22×C22⋊C4×D832
#249117422
C2×#191276302
C2×#191276282
C2×#191275762
C2×#191275752
C2×#191275732
C2×#191275642
C2×#191275632
C2×#191275562
C2×#381×C832
C2×#248383