Finite Group Databasebeta

← C2×#24918640 #36276480

Subgroups — C2×#24918640 #36276480

Order 21248.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128256C211yesmaximal, characteristic, complemented
2C2×#19128233C211yesmaximal, characteristic
3#24918640C2116yesmaximal, direct product factor
4C2×#19128102C212yesmaximal, complemented
5C2×#19128054C212yesmaximal, complemented
6C2×#19128044C212yesmaximal, complemented
7C2×#19128023C212yesmaximal
8C2×#19127997C211yesmaximal, characteristic, complemented
9C2×#19127983C211yesmaximal, characteristic, complemented
10C2×#19127991C211yesmaximal, characteristic, complemented
11C2×#19127753C211yesmaximal, characteristic, complemented
12C2×#474×C83C211yesmaximal, characteristic, complemented
13#19128256—24no—
14#19128256C2218yescomplemented
15C2×#14581792C2211yescharacteristic
16#19128233—24no—
17#19128233C2218yes—
18C2×#14581785—21no—
19C2×#14581783C2212yes—
20C2×#14581783C2211yescharacteristic
21C2×#14581779C2211yescharacteristic
22C2×#14581774—21no—
23C2×#14581772—21no—
24C2×#14581772C2211yescharacteristic
25C2×#14581768—21no—
26C2×#14581763C2211yescharacteristic
27C2×Q8×Dic83—21no—
28C2×C4×Dic166C2211yescharacteristic
29C2×#14581757—21no—
30C2×C4×C22⋊D83—21no—
31C2×#14581751—21no—
32C2×#14581750C2212yes—
33C2×C42×D83C2211yescharacteristic
34#19128102C22116yescomplemented
35#19128054C22116yescomplemented
36#19128044C22116yescomplemented
37#19128023C22116yes—
38#19127997C2218yescomplemented
39#19127991C2218yescomplemented
40#19127983C2218yescomplemented
41#19127753C2218yescomplemented
42C2×#14581726C2212yes—
43C2×#14581723C2212yes—
44C2×#14581723C2212yes—
45C2×C4⋊(C83⋊C8)C2211yescharacteristic
46C2×#14581717C2212yes—
47C2×#14581715C2212yes—
48C2×#14581713C2212yes—
49C2×(C2×D83)⋊C8C2212yes—
50C2×C8×Dic83C2212yes—
51C2×C4⋊Q8×C83C2211yescharacteristic
52C2×C4×D4×C83C2211yescharacteristic
53#474×C83C2218yescomplemented
54C2×#107×C83C2212yes—
55C2×C4⋊C8×C83C2211yescharacteristic
56C2×#102×C83C2212yes—
57C22×Dic166—21no—
58C22×Dic166C2311yescharacteristic
59C22×C22⋊D83—21no—
60C22×C4×D83D411yescharacteristic
61C22×C4×D83D411yescharacteristic
62C22×C4×D83C2311yescharacteristic
63C22×C83⋊C8C2312yes—
64#14581792—22no—
65#14581792C2314yes—
66#14581785—28no—
67#14581783—22no—
68#14581783—24no—
69#14581783C2314yes—
70#14581783C2318yes—
71#14581779—22no—
72#14581779C2314yes—
73#14581774—28no—
74#14581772—28no—
75#14581772—22no—
76#14581772C2314yes—
77#14581768—28no—
78#14581763—22no—
79#14581763C2314yes—
80Q8×Dic83—28no—
81C4×Dic166—22no—
82C4×Dic166C2314yes—
83#14581757—28no—
84C4×C22⋊D83—28no—
85#14581751—28no—
86#14581750—24no—
87#14581750C2318yes—
88C2×C4⋊Dic83—21no—
89C2×C4⋊Dic83—21no—
90C2×C4⋊Dic83—22no—
91C2×C4⋊Dic83—21no—
92C2×C4⋊Dic83C2312yes—
93C2×C4⋊Dic83C2311yescharacteristic
94C2×Dic83⋊C4—21no—
95C2×Dic83⋊C4—22no—
96C2×Dic83⋊C4—21no—
97C2×C22⋊Dic83—21no—
98C2×C22⋊Dic83—21no—
99C2×C22⋊Dic83—21no—
100C2×(C2×D83)⋊C4—22no—
101C2×(C2×D83)⋊C4—21no—
102C2×C4×Dic83—22no—
103C2×C4×Dic83—21no—
104C2×C4×Dic83D411yescharacteristic
105C2×C4×Dic83D411yescharacteristic
106C2×C4×Dic83C2311yescharacteristic
107C42×D83D414yes—
108C42×D83C2314yes—
109#14581726C2318yes—
110#14581723C2318yes—
111#14581723C2318yes—
112C4⋊(C83⋊C8)C2314yes—
113#14581717C2318yes—
114#14581715C2318yes—
115#14581713C2318yes—
116(C2×D83)⋊C8C2318yes—
117C8×Dic83C2318yes—
118C22×Q8×C83—21no—
119C22×D4×C83C2311yescharacteristic
120C23×C4×C83—21no—
121C22×C8×C83C2312yes—
122C4⋊Q8×C83—22no—
123C4⋊Q8×C83C2314yes—
124C4×D4×C83—22no—
125C4×D4×C83C2314yes—
126C2×C4⋊C4×C83—21no—
127C2×C4⋊C4×C83C2311yescharacteristic
128C2×C4⋊C4×C83C2312yes—
129C2×C22⋊C4×C83—21no—
130C2×C42×C83C2311yescharacteristic
131#107×C83C2318yes—
132C4⋊C8×C83C2314yes—
133#102×C83C2318yes—
134C23×D83C2×D411yescharacteristic
135C2×Dic166—22no—
136C2×Dic166—22no—
137C2×Dic166—21no—
138C2×Dic166—24no—
139C2×Dic166—44no—
140C2×Dic166C2412yes—
141C2×C22⋊D83—24no—
142C2×C22⋊D83—44no—
143C22×Dic83—21no—
144C22×Dic83—22no—
145C22×Dic83—21no—
146C22×Dic83C2×D411yescharacteristic
147C22×Dic83C2×D411yescharacteristic
148C22×Dic83C2×D411yescharacteristic
149C2×C4×D83—24no—
150C2×C4×D83—22no—
151C2×C4×D83—22no—
152C2×C4×D83—42no—
153C2×C4×D83C2×D412yes—
154C2×C4×D83C2×D414yes—
155C2×C4×D83C2×D414yes—
156C2×C4×D83C2412yes—
157C2×C83⋊C8—24no—
158C2×C83⋊C8C2414yes—
159C4⋊Dic83—21no—
160C4⋊Dic83—24no—
161C4⋊Dic83—22no—
162C4⋊Dic83—28no—
163C4⋊Dic83—24no—
164C4⋊Dic83—24no—
165C4⋊Dic83C2412yes—
166C4⋊Dic83C2414yes—
167Dic83⋊C4—24no—
168Dic83⋊C4—28no—
169Dic83⋊C4—24no—
170C22⋊Dic83—24no—
171C22⋊Dic83—24no—
172C22⋊Dic83—24no—
173(C2×D83)⋊C4—28no—
174(C2×D83)⋊C4—24no—
175C4×Dic83—24no—
176C4×Dic83—28no—
177C4×Dic83C2×D412yes—
178C4×Dic83C2×D414yes—
179C4×Dic83C2×D414yes—
180C4×Dic83C2412yes—
181C24×C83—21no—
182C2×Q8×C83—24no—
183C2×Q8×C83—44no—
184C2×D4×C83—21no—
185C2×D4×C83—22no—
186C2×D4×C83—22no—
187C2×D4×C83C2412yes—
188C22×C4×C83—21no—
189C22×C4×C83—22no—
190C22×C4×C83—24no—
191C22×C4×C83—44no—
192C22×C4×C83C2×D411yescharacteristic
193C22×C4×C83C2×D411yescharacteristic
194C22×C4×C83C2411yescharacteristic
195C2×C8×C83—24no—
196C2×C8×C83C2414yes—
197C4⋊C4×C83—21no—
198C4⋊C4×C83—24no—
199C4⋊C4×C83—22no—
200C4⋊C4×C83C2412yes—
201C4⋊C4×C83C2414yes—
202C22⋊C4×C83—24no—
203C42×C83C2×D412yes—
204C42×C83C2412yes—
205C23×C83—22no—
206C23×C83—42no—
207C23×C83—42no—
208C23×C83—42no—
209C23×C83C22×D411yescharacteristic
210C22×D83—22no—
211C22×D83—22no—
212C22×D83—22no—
213C22×D83C22×D412yes—
214Q8×C83—48no—
215D4×C83—22no—
216D4×C83—22no—
217D4×C83—42no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—24no—
221C2×C4×C83—42no—
222C2×C4×C83—44no—
223C2×C4×C83—48no—
224C2×C4×C83#13514yes—
225C2×C4×C83C22×D412yes—
226C2×C4×C83C22×D411yescharacteristic
227C2×C4×C83C22×D412yes—
228C2×C4×C832−1+412yes—
229C2×C4×C832−1+412yes—
230C2×C4×C83C2511yescharacteristic
231C22⋊D83—48no—
232C2×Dic83—22no—
233C2×Dic83—22no—
234C2×Dic83—22no—
235C2×Dic83—22no—
236C2×Dic83—24no—
237C2×Dic83—22no—
238C2×Dic83—42no—
239C2×Dic83—42no—
240C2×Dic83—44no—
241C2×Dic83C22×D412yes—
242C2×Dic83C22×D412yes—
243C2×Dic83C22×D412yes—
244C4×D83—24no—
245C4×D83—28no—
246C4×D83—22no—
247C4×D83—22no—
248C4×D83—44no—
249Dic166—22no—
250Dic166—22no—
251Dic166—48no—
252Dic166—42no—
253C8×C83—24no—
254C83⋊C8—24no—
255C22×C83—42no—
256C22×C83—42no—
257C22×C83—42no—
258C22×C83—84no—
259C22×C83#53612yes—
260C22×C83C2×#13512yes—
261C22×C83#57512yes—
262C22×C83C23×D411yescharacteristic
263C2×D83—22no—
264C2×D83—22no—
265C2×D83—22no—
266C2×D83—44no—
267C4×C83—22no—
268C4×C83—42no—
269C4×C83—44no—
270C4×C83#53612yes—
271C4×C83C2×#13514yes—
272C4×C83C2×2−1+411yescharacteristic
273C4×C83C2×2−1+411yescharacteristic
274Dic83—22no—
275Dic83—22no—
276Dic83—22no—
277Dic83—42no—
278Dic83—44no—
279Dic83—42no—
280C2×#3233—831nomaximal, Sylow
281C2×C83—82no—
282C2×C83#323314yescomplemented
283C2×C83C2×#53611yescharacteristic
284C2×C83C22×#13511yescharacteristic
285C2×C83C2×#57511yescharacteristic
286D83—42no—
287C2×#533—831no—
288C2×#529—831no—
289#3233—8316no—
290C2×#499—832no—
291C2×#488—832no—
292C2×#485—832no—
293C2×#482—832no—
294C2×#477—831no—
295C2×#475—831no—
296C2×#476—831no—
297C2×#474D8311yescharacteristic, complemented
298C2×#431—831no—
299C83C2×#323311yescharacteristic, complemented, Sylow
300#533—838no—
301#533—1664no—
302C2×C4⋊Q8—831no—
303C2×C4⋊Q8C2×D8311yescharacteristic
304#529—838no—
305#529—1664no—
306C2×#126—1661no—
307C2×#125—832no—
308C2×#125—831no—
309C2×#124—831no—
310C2×#123—1661no—
311C2×C22⋊Q8—831no—
312C2×C22⋊Q8—1661no—
313C2×C22⋊Q8—1661no—
314C2×#121—831no—
315C2×C4×Q8—831no—
316C2×C4×Q8—1661no—
317C2×C4×Q8—1661no—
318C2×C4×D4—1661no—
319C2×C4×D4C2×D8311yescharacteristic
320C2×#117—832no—
321C2×#117—1661no—
322C22×C42—831no—
323#499—8316no—
324#488—8316no—
325#485—8316no—
326#482—8316no—
327#477—838no—
328#476—838no—
329#475—838no—
330#474C2×D8318yescomplemented
331#431—838no—
332C2×#107—832no—
333C2×#107C2×D8312yes—
334C2×#106—832no—
335C2×#106—832no—
336C2×C4⋊C8—831no—
337C2×C4⋊C8C2×D8311yescharacteristic
338C2×#103—832no—
339C2×#103—832no—
340C2×#102—832no—
341C2×#102C2×D8312yes—
342C2×C22⋊C8—832no—
343C2×C4×C8—832no—
344C22×Q8—21no—
345C22×Q8—831no—
346C22×Q8—1661no—
347C22×D4—1661no—
348C22×D4C22×D8311yescharacteristic
349C23×C4—21no—
350C23×C4—831no—
351C23×C4—831no—
352C23×C4—831no—
353C22×C8—832no—
354C22×C8C22×D8312yes—
355C4⋊Q8—22no—
356C4⋊Q8—834no—
357C4⋊Q8—1662no—
358C4⋊Q8C22×D8314yes—
359#126—1668no—
360#125—834no—
361#125—838no—
362#125—1662no—
363#125—1664no—
364#124—834no—
365#124—1662no—
366#123—1668no—
367C22⋊Q8—834no—
368C22⋊Q8—1662no—
369C22⋊Q8—1668no—
370C22⋊Q8—1668no—
371#121—834no—
372#121—1662no—
373C4×Q8—834no—
374C4×Q8—1668no—
375C4×Q8—1668no—
376C4×Q8—1662no—
377C4×D4—22no—
378C4×D4—1668no—
379C4×D4C22×D8314yes—
380#117—838no—
381#117—1668no—
382#117—1664no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—832no—
385C2×C4⋊C4—831no—
386C2×C4⋊C4—1661no—
387C2×C4⋊C4—1661no—
388C2×C4⋊C4—1661no—
389C2×C4⋊C4—1662no—
390C2×C4⋊C4—1662no—
391C2×C4⋊C4—1661no—
392C2×C4⋊C4—1661no—
393C2×C4⋊C4C22×D8312yes—
394C2×C4⋊C4C22×D8311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—1662no—
397C2×C22⋊C4—1661no—
398C2×C22⋊C4—1661no—
399C2×C22⋊C4—1661no—
400C2×C22⋊C4—1661no—
401C2×C42—831no—
402C2×C42—831no—
403C2×C42—831no—
404C2×C42—834no—
405C2×C42—834no—
406C2×C42—1662no—
407C2×C42—1661no—
408C2×C42C22×D8311yescharacteristic
409#107—838no—
410#107C22×D8318yes—
411#106—838no—
412#106—838no—
413C4⋊C8—834no—
414C4⋊C8C22×D8314yes—
415#103—838no—
416#103—838no—
417#102—838no—
418#102C22×D8318yes—
419C22⋊C8—838no—
420C4×C8—838no—
421C24—21no—
422C24—831no—
423C2×Q8—24no—
424C2×Q8—44no—
425C2×Q8—3324no—
426C2×Q8—832no—
427C2×Q8—1662no—
428C2×Q8—1662no—
429C2×Q8—1661no—
430C2×Q8—1664no—
431C2×D4—21no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—3324no—
435C2×D4—1664no—
436C2×D4C23×D8312yes—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—44no—
441C22×C4—3322no—
442C22×C4—834no—
443C22×C4—831no—
444C22×C4—831no—
445C22×C4—831no—
446C22×C4—832no—
447C22×C4—834no—
448C22×C4—832no—
449C22×C4—1661no—
450C22×C4—1661no—
451C22×C4—1662no—
452C22×C4—1664no—
453C22×C4—1662no—
454C22×C4—1662no—
455C22×C4D4×D8311yescharacteristic
456C22×C4D4×D8311yescharacteristic
457C22×C4C23×D8311yescharacteristic
458C2×C8—24no—
459C2×C8—834no—
460C2×C8—1664no—
461C2×C8C23×D8314yes—
462C4⋊C4—24no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—834no—
466C4⋊C4—832no—
467C4⋊C4—1664no—
468C4⋊C4—1664no—
469C4⋊C4—1664no—
470C4⋊C4—1668no—
471C4⋊C4—1668no—
472C4⋊C4—1662no—
473C4⋊C4—1661no—
474C4⋊C4—1664no—
475C4⋊C4—1664no—
476C4⋊C4C23×D8314yes—
477C4⋊C4C23×D8312yes—
478C22⋊C4—24no—
479C22⋊C4—1668no—
480C22⋊C4—1664no—
481C22⋊C4—1664no—
482C22⋊C4—1664no—
483C22⋊C4—1664no—
484C42—834no—
485C42—834no—
486C42—832no—
487C42—832no—
488C42—1668no—
489C42—1664no—
490C42D4×D8312yes—
491C42C23×D8312yes—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—832no—
497C23—1662no—
498C23—1662no—
499C23—1662no—
500C23C2×D4×D8311yescharacteristic
501Q8—48no—
502Q8—3328no—
503Q8—3322no—
504Q8—1662no—
505Q8—1662no—
506D4—22no—
507D4—22no—
508D4—42no—
509D4—3328no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—48no—
516C2×C4—3324no—
517C2×C4—3322no—
518C2×C4—3324no—
519C2×C4—3322no—
520C2×C4—832no—
521C2×C4—832no—
522C2×C4—832no—
523C2×C4—1662no—
524C2×C4—1662no—
525C2×C4—1664no—
526C2×C4—1662no—
527C2×C4—1662no—
528C2×C4—1662no—
529C2×C4—1668no—
530C2×C4—1664no—
531C2×C4—1662no—
532C2×C4—1662no—
533C2×C4#1458181114yes—
534C2×C4C2×D4×D8312yes—
535C2×C4C2×D4×D8312yes—
536C2×C4C2×D4×D8311yescharacteristic
537C2×C4#1458183912yes—
538C2×C4#1458184012yes—
539C2×C4C24×D8311yescharacteristic
540C8—24no—
541C8—1664no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—84no—
546C22—3324no—
547C22—1662no—
548C22—1662no—
549C22—1662no—
550C22#1912827412yes—
551C22C2×#1458181112yes—
552C22#1912850012yes—
553C22C22×D4×D8311yescharacteristic
554C4—22no—
555C4—42no—
556C4—44no—
557C4—3322no—
558C4—3324no—
559C4—3322no—
560C4—1662no—
561C4—1662no—
562C4—1662no—
563C4#1912827412yes—
564C4C2×#1458181114yes—
565C4C2×#1458183911yescharacteristic
566C4C2×#1458184011yescharacteristic
567C2—82no—
568C2—3322no—
569C2#2491864014yesdirect product factor
570C2C2×#1912827411yescharacteristic
571C2C22×#1458181111yescharacteristic
572C2C2×#1912850011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#474×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581763C22
hypercenterC2×#474D83
hypocenterC83C2×#3233
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#19128256C2semidirect
3. #24918640C2direct (N × H)
4. C2×#19128102C2semidirect
5. C2×#19128054C2semidirect
6. C2×#19128044C2semidirect
8. C2×#19127997C2semidirect
9. C2×#19127983C2semidirect
10. C2×#19127991C2semidirect
11. C2×#19127753C2semidirect
12. C2×#474×C83C2semidirect
14. #19128256C22semidirect
34. #19128102C22semidirect
35. #19128054C22semidirect
36. #19128044C22semidirect
38. #19127997C22semidirect
39. #19127991C22semidirect
40. #19127983C22semidirect
41. #19127753C22semidirect
53. #474×C83C22semidirect
282. C2×C83#3233semidirect
297. C2×#474D83semidirect
299. C83C2×#3233semidirect
330. #474C2×D83semidirect
569. C2#24918640direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282562
C2×#191282332
#249186402
C2×#191281022
C2×#191280542
C2×#191280442
C2×#191280232
C2×#191279972
C2×#191279832
C2×#191279912
C2×#191277532
C2×#474×C832
C2×#323383