Finite Group Databasebeta

← C2×#24910702 #35570625

Subgroups — C2×#24910702 #35570625

Order 21248.

4134 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic83C211yesmaximal, characteristic, complemented
2C22×(C22⋊D83)⋊C4C212yesmaximal, complemented
3C22×#14581750C211yesmaximal, characteristic, complemented
4#24910702C2116yesmaximal, direct product factor
5C2×#19127631C211yesmaximal, characteristic, complemented
6C2×#19127628C211yesmaximal, characteristic, complemented
7C2×#19127624C212yesmaximal, complemented
8C2×#19127616C212yesmaximal, complemented
9C2×#19127609C211yesmaximal, characteristic
10C2×#19127552C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic83C212yesmaximal, complemented
12C2×#394×C83C211yesmaximal, characteristic, complemented
13C23×C22⋊D83C2212yes—
14C24×Dic83C2212yes—
15C23×C4×D83C2211yescharacteristic
16C2×D4×Dic83—28no—
17C2×D4×Dic83C2218yescomplemented
18C2×(C22⋊D83)⋊C4—216no—
19C2×(C22⋊D83)⋊C4C22116yescomplemented
20C2×#14581750—28no—
21C2×#14581750C2218yescomplemented
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C4⋊Dic83C2211yescharacteristic
24C22×Dic83⋊C4C2212yes—
25C22×Dic83⋊C4C2212yes—
26C22×C22⋊Dic83C2212yes—
27C22×C22⋊Dic83C2212yes—
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2212yes—
31C22×C4×Dic83C2211yescharacteristic
32C22×C4×Dic83C2212yes—
33C22×C4×Dic83C2211yescharacteristic
34#19127631C2218yescomplemented
35#19127628C2218yescomplemented
36#19127624C22116yescomplemented
37#19127616C22116yescomplemented
38#19127609C2218yes—
39#19127552C2218yescomplemented
40C22⋊C4×Dic83C22116yescomplemented
41C2×C83⋊#95C2211yescharacteristic
42C2×C83⋊#95C2212yes—
43C2×C83⋊#95C2212yes—
44C23×D4×C83C2211yescharacteristic
45C22×C4⋊C4×C83C2211yescharacteristic
46C22×C22⋊C4×C83C2212yes—
47C22×C22⋊C4×C83C2212yes—
48#394×C83C2218yescomplemented
49C2×#95×C83C2211yescharacteristic
50C24×D83C2311yescharacteristic
51C22×C22⋊D83—28no—
52C22×C22⋊D83—28no—
53C22×C22⋊D83—28no—
54C22×C22⋊D83C2318yes—
55C23×Dic83—28no—
56C23×Dic83—28no—
57C23×Dic83—28no—
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2312yes—
60C23×Dic83C2318yes—
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2312yes—
63C23×Dic83C2311yescharacteristic
64C22×C4×D83—24no—
65C22×C4×D83—24no—
66C22×C4×D83D418yescomplemented
67C22×C4×D83C2314yes—
68D4×Dic83—232no—
69(C22⋊D83)⋊C4—264no—
70#14581750—232no—
71C2×C4⋊Dic83—24no—
72C2×C4⋊Dic83—24no—
73C2×C4⋊Dic83C2314yes—
74C2×C4⋊Dic83C2314yes—
75C2×Dic83⋊C4—28no—
76C2×Dic83⋊C4—28no—
77C2×Dic83⋊C4C2318yes—
78C2×Dic83⋊C4C2318yes—
79C2×C22⋊Dic83—28no—
80C2×C22⋊Dic83—28no—
81C2×C22⋊Dic83C2318yes—
82C2×C22⋊Dic83C2318yes—
83C2×(C2×D83)⋊C4—28no—
84C2×(C2×D83)⋊C4—24no—
85C2×(C2×D83)⋊C4—24no—
86C2×(C2×D83)⋊C4C2314yes—
87C2×(C2×D83)⋊C4C2314yes—
88C2×(C2×D83)⋊C4C2318yes—
89C2×C4×Dic83—24no—
90C2×C4×Dic83—28no—
91C2×C4×Dic83D418yescomplemented
92C2×C4×Dic83C2318yes—
93C2×C4×Dic83C2314yes—
94C2×C4×Dic83C2314yes—
95C83⋊#95C2314yes—
96C83⋊#95C2318yes—
97C83⋊#95C2318yes—
98C25×C83C2312yes—
99C22×D4×C83—28no—
100C22×D4×C83—24no—
101C22×D4×C83C2314yes—
102C23×C4×C83C2311yescharacteristic
103C23×C4×C83C2312yes—
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2311yescharacteristic
106C2×C4⋊C4×C83—24no—
107C2×C4⋊C4×C83C2314yes—
108C2×C22⋊C4×C83—28no—
109C2×C22⋊C4×C83—28no—
110C2×C22⋊C4×C83C2318yes—
111C2×C22⋊C4×C83C2318yes—
112#95×C83C2314yes—
113C23×D83—22no—
114C23×D83—22no—
115C23×D83—24no—
116C23×D83—24no—
117C23×D83C2×D414yes—
118C23×D83C2412yes—
119C2×C22⋊D83—264no—
120C2×C22⋊D83—216no—
121C2×C22⋊D83—216no—
122C2×C22⋊D83—216no—
123C22×Dic83—24no—
124C22×Dic83—24no—
125C22×Dic83—24no—
126C22×Dic83—24no—
127C22×Dic83—24no—
128C22×Dic83—22no—
129C22×Dic83—24no—
130C22×Dic83—24no—
131C22×Dic83—216no—
132C22×Dic83—216no—
133C22×Dic83—216no—
134C22×Dic83—432no—
135C22×Dic83C2×D414yes—
136C22×Dic83C2×D414yes—
137C22×Dic83C2×D414yes—
138C22×Dic83#4118yes—
139C22×Dic83#4114yes—
140C22×Dic83C2414yes—
141C22×Dic83C2412yes—
142C22×Dic83C2412yes—
143C22×Dic83C2414yes—
144C22×Dic83C2412yes—
145C2×C4×D83—232no—
146C2×C4×D83—28no—
147C2×C4×D83—28no—
148C2×C4×D83C2×D4116yescomplemented
149C4⋊Dic83—28no—
150C4⋊Dic83—28no—
151Dic83⋊C4—216no—
152Dic83⋊C4—216no—
153C22⋊Dic83—216no—
154C22⋊Dic83—216no—
155(C2×D83)⋊C4—216no—
156(C2×D83)⋊C4—28no—
157(C2×D83)⋊C4—28no—
158C4×Dic83—28no—
159C4×Dic83—216no—
160C4×Dic83C2×D4116yescomplemented
161C24×C83—24no—
162C24×C83—24no—
163C24×C83—24no—
164C24×C83—24no—
165C24×C83—24no—
166C24×C83—24no—
167C24×C83#4118yes—
168C24×C83C2414yes—
169C24×C83C2411yescharacteristic
170C2×D4×C83—232no—
171C2×D4×C83—216no—
172C2×D4×C83—28no—
173C22×C4×C83—22no—
174C22×C4×C83—22no—
175C22×C4×C83—24no—
176C22×C4×C83—24no—
177C22×C4×C83—22no—
178C22×C4×C83—24no—
179C22×C4×C83—24no—
180C22×C4×C83—24no—
181C22×C4×C83C2×D414yes—
182C22×C4×C83C2×D414yes—
183C22×C4×C83C2414yes—
184C22×C4×C83C2412yes—
185C22×C4×C83C2412yes—
186C22×C4×C83C2412yes—
187C4⋊C4×C83—28no—
188C22⋊C4×C83—216no—
189C22⋊C4×C83—216no—
190C23×C83—216no—
191C23×C83—216no—
192C23×C83—216no—
193C23×C83—24no—
194C23×C83—24no—
195C23×C83—24no—
196C23×C83—24no—
197C23×C83—24no—
198C23×C83—24no—
199C23×C83—48no—
200C23×C83—48no—
201C23×C83—48no—
202C23×C83—48no—
203C23×C83C22×D412yes—
204C23×C83C22×D412yes—
205C23×C83C2×#4112yes—
206C23×C83C2×#4114yes—
207C23×C83C2×#4118yes—
208C23×C83C2×#4114yes—
209C23×C83C2511yescharacteristic
210C22×D83—28no—
211C22×D83—216no—
212C22×D83—22no—
213C22×D83—22no—
214C22×D83—24no—
215C22×D83—24no—
216C22×D83—44no—
217C22×D83—48no—
218C22×D83—44no—
219C22×D83C22×D414yes—
220D4×C83—232no—
221C2×C4×C83—28no—
222C2×C4×C83—28no—
223C2×C4×C83—22no—
224C2×C4×C83—24no—
225C2×C4×C83—22no—
226C2×C4×C83—24no—
227C2×C4×C83—22no—
228C2×C4×C83—24no—
229C2×C4×C83—24no—
230C2×C4×C83—24no—
231C2×C4×C83—44no—
232C2×C4×C83—48no—
233C2×C4×C83C22×D414yes—
234C2×C4×C83C22×D414yes—
235C22⋊D83—264no—
236C2×Dic83—216no—
237C2×Dic83—28no—
238C2×Dic83—24no—
239C2×Dic83—24no—
240C2×Dic83—24no—
241C2×Dic83—22no—
242C2×Dic83—24no—
243C2×Dic83—24no—
244C2×Dic83—24no—
245C2×Dic83—24no—
246C2×Dic83—48no—
247C2×Dic83—44no—
248C2×Dic83—432no—
249C2×Dic83#121116yes—
250C2×Dic83C22×D414yes—
251C2×Dic83C22×D414yes—
252C2×Dic83C22×D414yes—
253C2×Dic83C2×#4118yes—
254C2×Dic83C2×#4114yes—
255C4×D83—232no—
256C22×C83—28no—
257C22×C83—28no—
258C22×C83—28no—
259C22×C83—432no—
260C22×C83—44no—
261C22×C83—44no—
262C22×C83—44no—
263C22×C83—44no—
264C22×C83C2×#12114yes—
265C22×C83#52514yes—
266C22×C83#52518yes—
267C22×C83#52918yes—
268C22×C83#53214yes—
269C22×C83C23×D411yescharacteristic
270C22×C83C23×D411yescharacteristic
271C22×C83C22×#4111yescharacteristic
272C22×C83C22×#4112yes—
273C22×C83C22×#4112yes—
274C2×D83—24no—
275C2×D83—28no—
276C2×D83—416no—
277C2×D83—42no—
278C2×D83—44no—
279C2×D83—42no—
280C4×C83—24no—
281C4×C83—24no—
282C4×C83—42no—
283C4×C83—44no—
284Dic83—28no—
285Dic83—24no—
286Dic83—44no—
287Dic83—42no—
288Dic83C2×#12118yes—
289C2×#2392—831nomaximal, Sylow
290C2×C83—48no—
291C2×C83#239218yescomplemented
292C2×C83C22×#12111yescharacteristic
293C2×C83C2×#52511yescharacteristic
294C2×C83C2×#52512yes—
295C2×C83C2×#52912yes—
296C2×C83C2×#53211yescharacteristic
297D83—44no—
298C22×C4×D4—831no—
299C22×C4×D4—832no—
300C22×#117—831no—
301#2392—8316no—
302C2×#398—831no—
303C2×#397—831no—
304C2×#396—832no—
305C2×#394—832no—
306C2×#394D8311yescharacteristic, complemented
307C2×#392—831no—
308C2×C4×C4⋊C4—831no—
309C2×C4×C22⋊C4—832no—
310C83C2×#239211yescharacteristic, complemented, Sylow
311C23×D4—832no—
312C23×D4C2×D8311yescharacteristic
313C24×C4—831no—
314C24×C4—832no—
315C2×C4×D4—838no—
316C2×C4×D4—8316no—
317C2×C4×D4—1668no—
318C2×C4×D4—16616no—
319C2×#117—838no—
320C2×#117—1668no—
321C22×C4⋊C4—832no—
322C22×C4⋊C4—831no—
323C22×C4⋊C4—832no—
324C22×C4⋊C4—831no—
325C22×C4⋊C4C2×D8311yescharacteristic
326C22×C22⋊C4—832no—
327C22×C22⋊C4—832no—
328C22×C22⋊C4—831no—
329C22×C22⋊C4—831no—
330C22×C22⋊C4—832no—
331C22×C22⋊C4C2×D8312yes—
332C22×C22⋊C4C2×D8312yes—
333C22×C42—831no—
334C22×C42—831no—
335C22×C42—832no—
336#398—838no—
337#397—838no—
338#396—8316no—
339#394—8316no—
340#394C2×D8318yescomplemented
341#392—838no—
342C4×C4⋊C4—838no—
343C4×C22⋊C4—8316no—
344C2×#95—831no—
345C2×#95—832no—
346C2×#95—832no—
347C2×#95C2×D8311yescharacteristic
348C25—831no—
349C25C22×D8312yes—
350C22×D4—28no—
351C22×D4—24no—
352C22×D4—838no—
353C22×D4—1668no—
354C22×D4—1668no—
355C22×D4—1668no—
356C22×D4C22×D8314yes—
357C23×C4—831no—
358C23×C4—831no—
359C23×C4—832no—
360C23×C4—838no—
361C23×C4—834no—
362C23×C4—838no—
363C23×C4—831no—
364C23×C4—832no—
365C23×C4—1664no—
366C23×C4—1664no—
367C23×C4—1668no—
368C23×C4—1668no—
369C23×C4—1668no—
370C23×C4C22×D8312yes—
371C23×C4C22×D8311yescharacteristic
372C23×C4C22×D8311yescharacteristic
373C23×C4C22×D8311yescharacteristic
374C4×D4—16632no—
375C4×D4—16664no—
376#117—16632no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—834no—
379C2×C4⋊C4—838no—
380C2×C4⋊C4—834no—
381C2×C4⋊C4—838no—
382C2×C4⋊C4—1664no—
383C2×C4⋊C4—1668no—
384C2×C4⋊C4—1668no—
385C2×C4⋊C4—1664no—
386C2×C4⋊C4C22×D8314yes—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—838no—
390C2×C22⋊C4—838no—
391C2×C22⋊C4—834no—
392C2×C22⋊C4—834no—
393C2×C22⋊C4—838no—
394C2×C22⋊C4—1664no—
395C2×C22⋊C4—1668no—
396C2×C22⋊C4—1668no—
397C2×C22⋊C4—1668no—
398C2×C22⋊C4—1664no—
399C2×C22⋊C4C22×D8318yes—
400C2×C22⋊C4C22×D8318yes—
401C2×C42—838no—
402C2×C42—834no—
403C2×C42—834no—
404C2×C42—838no—
405C2×C42—1664no—
406C2×C42—1668no—
407#95—838no—
408#95—838no—
409#95—834no—
410#95C22×D8314yes—
411C24—24no—
412C24—24no—
413C24—24no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—834no—
418C24—832no—
419C24—1662no—
420C24—1662no—
421C24—1664no—
422C24—1664no—
423C24#1305058918yes—
424C24C23×D8314yes—
425C24C23×D8311yescharacteristic
426C2×D4—232no—
427C2×D4—216no—
428C2×D4—28no—
429C2×D4—16616no—
430C2×D4—16616no—
431C2×D4—16664no—
432C2×D4—16616no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—33232no—
442C22×C4—834no—
443C22×C4—834no—
444C22×C4—834no—
445C22×C4—832no—
446C22×C4—834no—
447C22×C4—838no—
448C22×C4—834no—
449C22×C4—832no—
450C22×C4—8316no—
451C22×C4—832no—
452C22×C4—834no—
453C22×C4—1668no—
454C22×C4—16632no—
455C22×C4—1668no—
456C22×C4—16616no—
457C22×C4—16616no—
458C22×C4—16616no—
459C22×C4—1662no—
460C22×C4—1664no—
461C22×C4—1664no—
462C22×C4—1664no—
463C22×C4—1664no—
464C22×C4—1664no—
465C22×C4—1664no—
466C22×C4—1664no—
467C22×C4D4×D8314yes—
468C22×C4D4×D8314yes—
469C22×C4C23×D8312yes—
470C22×C4C23×D8314yes—
471C22×C4C23×D8312yes—
472C22×C4C23×D8312yes—
473C4⋊C4—28no—
474C4⋊C4—1668no—
475C4⋊C4—16616no—
476C4⋊C4—16616no—
477C4⋊C4—1668no—
478C22⋊C4—216no—
479C22⋊C4—216no—
480C22⋊C4—1668no—
481C22⋊C4—16616no—
482C22⋊C4—16616no—
483C22⋊C4—16616no—
484C22⋊C4—1668no—
485C42—8316no—
486C42—1668no—
487C42—16616no—
488C23—216no—
489C23—216no—
490C23—216no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—48no—
498C23—48no—
499C23—48no—
500C23—48no—
501C23—3324no—
502C23—3328no—
503C23—3324no—
504C23—834no—
505C23—1668no—
506C23—16616no—
507C23—1662no—
508C23—1662no—
509C23—1664no—
510C23—1664no—
511C23C2×D4×D8312yes—
512C23C2×D4×D8312yes—
513C23#41×D8312yes—
514C23#41×D8314yes—
515C23C2×#1305058918yes—
516C23C2×#1305058914yes—
517C23C24×D8311yescharacteristic
518D4—232no—
519D4—16664no—
520C2×C4—28no—
521C2×C4—28no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—44no—
531C2×C4—48no—
532C2×C4—3328no—
533C2×C4—3324no—
534C2×C4—33232no—
535C2×C4—8316no—
536C2×C4—834no—
537C2×C4—834no—
538C2×C4—834no—
539C2×C4—834no—
540C2×C4—838no—
541C2×C4—16632no—
542C2×C4—1662no—
543C2×C4—1664no—
544C2×C4—1664no—
545C2×C4—1664no—
546C2×C4—1664no—
547C2×C4—16616no—
548C2×C4—1668no—
549C2×C4—1664no—
550C2×C4—1664no—
551C2×C4—1664no—
552C2×C4C2×D4×D8314yes—
553C2×C4C2×D4×D8314yes—
554C22—28no—
555C22—28no—
556C22—28no—
557C22—44no—
558C22—432no—
559C22—44no—
560C22—44no—
561C22—44no—
562C22—33216no—
563C22—3322no—
564C22—3324no—
565C22—3322no—
566C22—1664no—
567C22—1668no—
568C22#121×D8314yes—
569C22#1912820714yes—
570C22#1912821118yes—
571C22#1912822818yes—
572C22#1912825014yes—
573C22C22×D4×D8311yescharacteristic
574C22C22×D4×D8311yescharacteristic
575C22C2×#41×D8311yescharacteristic
576C22C2×#41×D8312yes—
577C22C22×#1305058912yes—
578C4—24no—
579C4—24no—
580C4—42no—
581C4—44no—
582C4—3324no—
583C4—3322no—
584C4—838no—
585C4—1668no—
586C4—1664no—
587C2—48no—
588C2—3324no—
589C2#2491070218yesdirect product factor
590C2C2×#121×D8311yescharacteristic
591C2C2×#1912820711yescharacteristic
592C2C2×#1912821112yes—
593C2C2×#1912822812yes—
594C2C2×#1912825011yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#394×C83C2
socleC24×C83C24
prime radicalC2×#19127609C2
hypercenterC2×#394D83
hypocenterC83C2×#2392
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic83C2semidirect
2. C22×(C22⋊D83)⋊C4C2semidirect
3. C22×#14581750C2semidirect
4. #24910702C2direct (N × H)
5. C2×#19127631C2semidirect
6. C2×#19127628C2semidirect
7. C2×#19127624C2semidirect
8. C2×#19127616C2semidirect
10. C2×#19127552C2semidirect
11. C2×C22⋊C4×Dic83C2semidirect
12. C2×#394×C83C2semidirect
17. C2×D4×Dic83C22semidirect
19. C2×(C22⋊D83)⋊C4C22semidirect
21. C2×#14581750C22semidirect
34. #19127631C22semidirect
35. #19127628C22semidirect
36. #19127624C22semidirect
37. #19127616C22semidirect
39. #19127552C22semidirect
40. C22⋊C4×Dic83C22semidirect
48. #394×C83C22semidirect
66. C22×C4×D83D4semidirect
91. C2×C4×Dic83D4semidirect
148. C2×C4×D83C2×D4semidirect
160. C4×Dic83C2×D4semidirect
291. C2×C83#2392semidirect
306. C2×#394D83semidirect
310. C83C2×#2392semidirect
340. #394C2×D83semidirect
589. C2#24910702direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic832
C22×(C22⋊D83)⋊C42
C22×#145817502
#249107022
C2×#191276312
C2×#191276282
C2×#191276242
C2×#191276162
C2×#191276092
C2×#191275522
C2×C22⋊C4×Dic832
C2×#394×C832
C2×#239283