Finite Group Databasebeta

← C2×#24913395 #35570843

Subgroups — C2×#24913395 #35570843

Order 21248.

3326 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581770C211yesmaximal, characteristic, complemented
2C22×#14581767C211yesmaximal, characteristic
3#24913395C2116yesmaximal, direct product factor
4C2×#19127639C211yesmaximal, characteristic, complemented
5C2×#19127630C212yesmaximal, complemented
6C2×#19127619C211yesmaximal, characteristic, complemented
7C2×#19127618C211yesmaximal, characteristic, complemented
8C2×#19127614C212yesmaximal, complemented
9C2×#19127579C212yesmaximal, complemented
10C2×#19127579C212yesmaximal, complemented
11C2×#95×D83C211yesmaximal, characteristic, complemented
12C2×#400×C83C211yesmaximal, characteristic, complemented
13C23×Dic166C2211yescharacteristic
14C23×D332C2212yes—
15C23×D332C2211yescharacteristic
16C23×C4×D83C2212yes—
17C23×C4×D83C2211yescharacteristic
18C2×#14581770—28no—
19C2×#14581770C2218yescomplemented
20C2×#14581767—28no—
21C2×#14581767C2218yes—
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2212yes—
27C22×(C2×D83)⋊C4C2212yes—
28C22×(C2×D83)⋊C4C2212yes—
29C22×(C2×D83)⋊C4C2212yes—
30C22×(C2×D83)⋊C4C2212yes—
31#19127639C2218yescomplemented
32#19127630C22116yescomplemented
33#19127619C2218yescomplemented
34#19127618C2218yescomplemented
35#19127614C22116yescomplemented
36#19127579C22116yescomplemented
37#19127579C22116yescomplemented
38C2×C83⋊#95C2212yes—
39C2×C83⋊#95C2212yes—
40C2×C83⋊#95C2212yes—
41C2×C83⋊#95C2211yescharacteristic
42#95×D83C2218yescomplemented
43C22×C4⋊C4×C83C2211yescharacteristic
44C22×C4⋊C4×C83C2211yescharacteristic
45#400×C83C2218yescomplemented
46C2×#95×C83C2212yes—
47C2×#95×C83C2212yes—
48C2×#95×C83C2211yescharacteristic
49C24×D83C2312yes—
50C24×D83C2311yescharacteristic
51C22×Dic166—24no—
52C22×Dic166—44no—
53C22×Dic166C2314yes—
54C22×D332—28no—
55C22×D332—28no—
56C22×D332—28no—
57C22×D332—24no—
58C22×D332—44no—
59C22×D332C2318yes—
60C22×D332C2314yes—
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2312yes—
64C23×Dic83C2311yescharacteristic
65C22×C4×D83—28no—
66C22×C4×D83—44no—
67C22×C4×D83—44no—
68C22×C4×D83—44no—
69C22×C4×D83D418yes—
70C22×C4×D83C2318yes—
71C22×C4×D83C2314yes—
72#14581770—232no—
73#14581767—232no—
74C2×Dic83⋊C4—24no—
75C2×Dic83⋊C4—24no—
76C2×Dic83⋊C4C2314yes—
77C2×Dic83⋊C4C2314yes—
78C2×(C2×D83)⋊C4—24no—
79C2×(C2×D83)⋊C4—24no—
80C2×(C2×D83)⋊C4—28no—
81C2×(C2×D83)⋊C4—44no—
82C2×(C2×D83)⋊C4—44no—
83C2×(C2×D83)⋊C4—44no—
84C2×(C2×D83)⋊C4—44no—
85C2×(C2×D83)⋊C4C2314yes—
86C2×(C2×D83)⋊C4C2314yes—
87C2×(C2×D83)⋊C4C2318yes—
88C2×(C2×D83)⋊C4C2318yes—
89C2×(C2×D83)⋊C4C2318yes—
90C2×(C2×D83)⋊C4C2318yes—
91C2×(C2×D83)⋊C4C2318yes—
92C83⋊#95C2318yes—
93C83⋊#95C2318yes—
94C83⋊#95C2318yes—
95C83⋊#95C2314yes—
96C23×C4×C83C2311yescharacteristic
97C23×C4×C83C2311yescharacteristic
98C23×C4×C83C2312yes—
99C23×C4×C83C2312yes—
100C23×C4×C83C2311yescharacteristic
101C2×C4⋊C4×C83—24no—
102C2×C4⋊C4×C83—24no—
103C2×C4⋊C4×C83C2314yes—
104C2×C4⋊C4×C83C2314yes—
105#95×C83C2318yes—
106#95×C83C2318yes—
107#95×C83C2314yes—
108C23×D83—24no—
109C23×D83—22no—
110C23×D83—22no—
111C23×D83—24no—
112C23×D83—24no—
113C23×D83—24no—
114C23×D83—24no—
115C23×D83—24no—
116C23×D83—24no—
117C23×D83—24no—
118C23×D83C2×D414yes—
119C23×D83#4118yes—
120C23×D83C2414yes—
121C23×D83C2412yes—
122C2×Dic166—28no—
123C2×Dic166—48no—
124C2×Dic166—416no—
125C2×D332—216no—
126C2×D332—216no—
127C2×D332—216no—
128C2×D332—28no—
129C2×D332—48no—
130C2×D332—416no—
131C2×D332—432no—
132C22×Dic83—24no—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—24no—
136C22×Dic83—24no—
137C22×Dic83—24no—
138C22×Dic83—24no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83C2×D414yes—
142C22×Dic83C2414yes—
143C22×Dic83C2412yes—
144C22×Dic83C2412yes—
145C22×Dic83C2412yes—
146C2×C4×D83—216no—
147C2×C4×D83—416no—
148C2×C4×D83—48no—
149C2×C4×D83—48no—
150C2×C4×D83—48no—
151C2×C4×D83—432no—
152C2×C4×D83C2×D4116yes—
153Dic83⋊C4—28no—
154Dic83⋊C4—28no—
155(C2×D83)⋊C4—28no—
156(C2×D83)⋊C4—28no—
157(C2×D83)⋊C4—216no—
158(C2×D83)⋊C4—48no—
159(C2×D83)⋊C4—48no—
160(C2×D83)⋊C4—48no—
161(C2×D83)⋊C4—48no—
162C24×C83C2411yescharacteristic
163C22×C4×C83—24no—
164C22×C4×C83—24no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—24no—
168C22×C4×C83—24no—
169C22×C4×C83—24no—
170C22×C4×C83—24no—
171C22×C4×C83—24no—
172C22×C4×C83—24no—
173C22×C4×C83—22no—
174C22×C4×C83—22no—
175C22×C4×C83C2×D414yes—
176C22×C4×C83C2414yes—
177C22×C4×C83C2414yes—
178C22×C4×C83C2412yes—
179C22×C4×C83C2412yes—
180C22×C4×C83C2412yes—
181C4⋊C4×C83—28no—
182C4⋊C4×C83—28no—
183C23×C83C22×D412yes—
184C23×C83C2×#4114yes—
185C23×C83H(5,𝔽2)14yes—
186C23×C83H(5,𝔽2)12yes—
187C23×C832−1+412yes—
188C23×C83C2511yescharacteristic
189C22×D83—28no—
190C22×D83—28no—
191C22×D83—216no—
192C22×D83—216no—
193C22×D83—24no—
194C22×D83—22no—
195C22×D83—22no—
196C22×D83—24no—
197C22×D83—24no—
198C22×D83—24no—
199C22×D83—24no—
200C22×D83—24no—
201C22×D83—24no—
202C22×D83—24no—
203C22×D83—48no—
204C22×D83—48no—
205C22×D83—48no—
206C22×D83—48no—
207C22×D83—48no—
208C22×D83—48no—
209C22×D83—48no—
210C22×D83#124116yes—
211C22×D83C22×D414yes—
212C22×D83C2×#4118yes—
213C2×C4×C83—28no—
214C2×C4×C83—24no—
215C2×C4×C83—22no—
216C2×C4×C83—24no—
217C2×C4×C83—22no—
218C2×C4×C83—24no—
219C2×C4×C83—24no—
220C2×C4×C83—24no—
221C2×C4×C83—22no—
222C2×C4×C83—24no—
223C2×C4×C83—24no—
224C2×C4×C83—24no—
225C2×C4×C83—22no—
226C2×C4×C83—48no—
227C2×C4×C83—44no—
228C2×C4×C83—44no—
229C2×C4×C83—48no—
230C2×C4×C83C22×D414yes—
231C2×Dic83—28no—
232C2×Dic83—24no—
233C2×Dic83—22no—
234C2×Dic83—22no—
235C2×Dic83—24no—
236C2×Dic83—22no—
237C2×Dic83—24no—
238C2×Dic83—24no—
239C2×Dic83—24no—
240C2×Dic83—22no—
241C2×Dic83—44no—
242C2×Dic83—44no—
243C2×Dic83—48no—
244C2×Dic83C22×D414yes—
245D332—416no—
246D332—432no—
247C4×D83—416no—
248C4×D83—432no—
249Dic166—416no—
250C22×C83C2×#12414yes—
251C22×C83#53414yes—
252C22×C83#53714yes—
253C22×C83#53818yes—
254C22×C83#53918yes—
255C22×C83C23×D411yescharacteristic
256C22×C83C22×#4112yes—
257C22×C83C2×H(5,𝔽2)12yes—
258C22×C83C2×H(5,𝔽2)11yescharacteristic
259C22×C83C2×2−1+411yescharacteristic
260C2×D83—232no—
261C2×D83—24no—
262C2×D83—24no—
263C2×D83—28no—
264C2×D83—28no—
265C2×D83—44no—
266C2×D83—44no—
267C2×D83—44no—
268C2×D83—44no—
269C2×D83—44no—
270C2×D83—44no—
271C2×D83—44no—
272C2×D83—816no—
273C2×D83C2×#12418yes—
274C4×C83—24no—
275C4×C83—44no—
276C4×C83—42no—
277C4×C83—42no—
278C4×C83—44no—
279Dic83—24no—
280Dic83—42no—
281Dic83—42no—
282Dic83—44no—
283C2×#2639—831nomaximal, Sylow
284C2×C83#263918yescomplemented
285C2×C83C22×#12411yescharacteristic
286C2×C83C2×#53411yescharacteristic
287C2×C83C2×#53711yescharacteristic
288C2×C83C2×#53812yes—
289C2×C83C2×#53912yes—
290D83—28no—
291D83—84no—
292C22×C22⋊Q8—831no—
293C22×#121—831no—
294#2639—8316no—
295C2×#400—831no—
296C2×#400D8311yescharacteristic, complemented
297C2×#397—832no—
298C2×#394—831no—
299C2×#394—831no—
300C2×#393—832no—
301C2×#386—832no—
302C2×#386—832no—
303C22×#95—831no—
304C83C2×#263911yescharacteristic, complemented, Sylow
305C23×Q8—831no—
306C23×D4—831no—
307C23×D4—832no—
308C24×C4—831no—
309C24×C4—832no—
310C2×C22⋊Q8—838no—
311C2×C22⋊Q8—1668no—
312C2×#121—838no—
313C2×#121—1668no—
314C22×C4⋊C4—831no—
315C22×C4⋊C4—831no—
316C22×C4⋊C4C2×D8311yescharacteristic
317C22×C4⋊C4C2×D8311yescharacteristic
318C22×C22⋊C4—832no—
319C22×C22⋊C4—832no—
320C22×C22⋊C4—832no—
321C22×C22⋊C4—832no—
322C22×C22⋊C4—832no—
323C22×C22⋊C4—831no—
324C22×C22⋊C4—831no—
325#400—838no—
326#400C2×D8318yescomplemented
327#397—8316no—
328#394—838no—
329#394—838no—
330#393—8316no—
331#386—8316no—
332#386—8316no—
333C2×#95—832no—
334C2×#95—832no—
335C2×#95—831no—
336C2×#95—832no—
337C2×#95—838no—
338C2×#95C2×D8312yes—
339C2×#95C2×D8311yescharacteristic
340C2×#95C2×D8312yes—
341C25—831no—
342C25—832no—
343C22×Q8—3324no—
344C22×Q8—834no—
345C22×Q8—1664no—
346C22×D4—3324no—
347C22×D4—834no—
348C22×D4—838no—
349C22×D4—1668no—
350C22×D4—1668no—
351C22×D4—1668no—
352C22×D4—1664no—
353C23×C4—3324no—
354C23×C4—3324no—
355C23×C4—3324no—
356C23×C4—838no—
357C23×C4—834no—
358C23×C4—838no—
359C23×C4—831no—
360C23×C4—831no—
361C23×C4—831no—
362C23×C4—832no—
363C23×C4—1668no—
364C23×C4C22×D8311yescharacteristic
365C23×C4C22×D8311yescharacteristic
366C23×C4C22×D8312yes—
367C23×C4C22×D8312yes—
368C23×C4C22×D8311yescharacteristic
369C22⋊Q8—16632no—
370#121—16632no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—834no—
374C2×C4⋊C4—834no—
375C2×C4⋊C4—1664no—
376C2×C4⋊C4—1664no—
377C2×C4⋊C4C22×D8314yes—
378C2×C4⋊C4C22×D8314yes—
379C2×C22⋊C4—3324no—
380C2×C22⋊C4—3324no—
381C2×C22⋊C4—3324no—
382C2×C22⋊C4—3324no—
383C2×C22⋊C4—838no—
384C2×C22⋊C4—838no—
385C2×C22⋊C4—838no—
386C2×C22⋊C4—838no—
387C2×C22⋊C4—838no—
388C2×C22⋊C4—834no—
389C2×C22⋊C4—834no—
390C2×C22⋊C4—1668no—
391C2×C22⋊C4—1664no—
392C2×C22⋊C4—1664no—
393#95—838no—
394#95—834no—
395#95—838no—
396#95—838no—
397#95C22×D8314yes—
398#95C22×D8318yes—
399#95C22×D8318yes—
400C24—834no—
401C24—838no—
402C24—832no—
403C24—834no—
404C24—1664no—
405C24—1664no—
406C24—1664no—
407C24—1664no—
408C24—1664no—
409C24—1664no—
410C24—1664no—
411C24—1664no—
412C24—1662no—
413C24—1662no—
414C24C23×D8311yescharacteristic
415C2×Q8—3328no—
416C2×Q8—33216no—
417C2×Q8—1668no—
418C2×D4—33216no—
419C2×D4—3328no—
420C2×D4—33232no—
421C2×D4—16616no—
422C2×D4—16616no—
423C2×D4—16616no—
424C2×D4—1668no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—33216no—
438C22×C4—3328no—
439C22×C4—3328no—
440C22×C4—3328no—
441C22×C4—33232no—
442C22×C4—8316no—
443C22×C4—834no—
444C22×C4—832no—
445C22×C4—834no—
446C22×C4—832no—
447C22×C4—832no—
448C22×C4—16616no—
449C22×C4—1662no—
450C22×C4—1662no—
451C22×C4—1664no—
452C22×C4—1662no—
453C22×C4—1664no—
454C22×C4—1664no—
455C22×C4—1664no—
456C22×C4—1662no—
457C22×C4—1664no—
458C22×C4D4×D8314yes—
459C22×C4C23×D8314yes—
460C22×C4C23×D8314yes—
461C22×C4C23×D8312yes—
462C22×C4C23×D8312yes—
463C22×C4C23×D8312yes—
464C4⋊C4—28no—
465C4⋊C4—28no—
466C4⋊C4—1668no—
467C4⋊C4—1668no—
468C22⋊C4—3328no—
469C22⋊C4—3328no—
470C22⋊C4—3328no—
471C22⋊C4—3328no—
472C22⋊C4—16616no—
473C22⋊C4—1668no—
474C22⋊C4—1668no—
475C23—3328no—
476C23—3328no—
477C23—3328no—
478C23—3328no—
479C23—3328no—
480C23—3328no—
481C23—3328no—
482C23—8316no—
483C23—834no—
484C23—838no—
485C23—1664no—
486C23—1664no—
487C23—1664no—
488C23—1664no—
489C23—1664no—
490C23—1664no—
491C23—1664no—
492C23—1668no—
493C23—1664no—
494C23—1662no—
495C23—1662no—
496C23—1668no—
497C23—16616no—
498C23—16616no—
499C23C2×D4×D8312yes—
500C23#41×D8314yes—
501C23#1458183814yes—
502C23#1458183812yes—
503C23#1458184012yes—
504C23C24×D8311yescharacteristic
505Q8—33216no—
506D4—33216no—
507D4—33232no—
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—33216no—
526C2×C4—33232no—
527C2×C4—3324no—
528C2×C4—3324no—
529C2×C4—3328no—
530C2×C4—834no—
531C2×C4—1662no—
532C2×C4—1662no—
533C2×C4—1664no—
534C2×C4—1662no—
535C2×C4—1664no—
536C2×C4—1664no—
537C2×C4—1664no—
538C2×C4—1662no—
539C2×C4—1668no—
540C2×C4—1664no—
541C2×C4C2×D4×D8314yes—
542C22—3324no—
543C22—3324no—
544C22—3324no—
545C22—3324no—
546C22—3324no—
547C22—3324no—
548C22—3324no—
549C22—838no—
550C22—66416no—
551C22—1664no—
552C22—1664no—
553C22—1668no—
554C22—1668no—
555C22—16632no—
556C22#124×D8314yes—
557C22#1912826214yes—
558C22#1912828114yes—
559C22#1912829018yes—
560C22#1912829918yes—
561C22C22×D4×D8311yescharacteristic
562C22C2×#41×D8312yes—
563C22C2×#1458183812yes—
564C22C2×#1458183811yescharacteristic
565C22C2×#1458184011yescharacteristic
566C4—24no—
567C4—44no—
568C4—42no—
569C4—42no—
570C4—44no—
571C4—3322no—
572C4—3322no—
573C4—3324no—
574C4—1664no—
575C2—6644no—
576C2—1668no—
577C2#2491339518yesdirect product factor
578C2C2×#124×D8311yescharacteristic
579C2C2×#1912826211yescharacteristic
580C2C2×#1912828111yescharacteristic
581C2C2×#1912829012yes—
582C2C2×#1912829912yes—
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#400×C83C2
socleC24×C83C24
prime radicalC22×#14581767C2
hypercenterC2×#400D83
hypocenterC83C2×#2639
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#14581770C2semidirect
3. #24913395C2direct (N × H)
4. C2×#19127639C2semidirect
5. C2×#19127630C2semidirect
6. C2×#19127619C2semidirect
7. C2×#19127618C2semidirect
8. C2×#19127614C2semidirect
9. C2×#19127579C2semidirect
10. C2×#19127579C2semidirect
11. C2×#95×D83C2semidirect
12. C2×#400×C83C2semidirect
19. C2×#14581770C22semidirect
31. #19127639C22semidirect
32. #19127630C22semidirect
33. #19127619C22semidirect
34. #19127618C22semidirect
35. #19127614C22semidirect
36. #19127579C22semidirect
37. #19127579C22semidirect
42. #95×D83C22semidirect
45. #400×C83C22semidirect
284. C2×C83#2639semidirect
296. C2×#400D83semidirect
304. C83C2×#2639semidirect
326. #400C2×D83semidirect
577. C2#24913395direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817702
C22×#145817672
#249133952
C2×#191276392
C2×#191276302
C2×#191276192
C2×#191276182
C2×#191276142
C2×#191275792
C2×#95×D832
C2×#400×C832
C2×#263983