Finite Group Databasebeta

← C4×#16839942 #29685902

Subgroups — C4×#16839942 #29685902

Order 15616.

1442 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519822C211yesmaximal, characteristic
2C2×#16839942C211yesmaximal, characteristic
3C4×#14519810C212yesmaximal, complemented
4C4×#14519764C211yesmaximal, characteristic, complemented
5#21446205C211yesmaximal, characteristic, complemented
6#21446187C212yesmaximal, complemented
7#21446055C212yesmaximal, complemented
8#21446031C211yesmaximal, characteristic, complemented
9#21445775C211yesmaximal, characteristic
10C4×#14519703C212yesmaximal, complemented
11C4×#100×C61C211yesmaximal, characteristic, complemented
12C2×#14519822C2211yescharacteristic
13C2×#14519810C2212yes—
14C2×#14519764C2211yescharacteristic
15#16840243C2212yes—
16#16840241—22no—
17#16840237C2211yescharacteristic
18#16840235—22no—
19#16840234—22no—
20C4×#11758222C2212yes—
21C4×#11758224—22no—
22C2×C4×Dic122C2211yescharacteristic, complemented
23C2×C4×C22⋊D61—22no—
24C4×D4×D61—22no—
25#16839942C418yesdirect product factor
26#16839870—22no—
27#16839864—22no—
28C4×Dic244—22no—
29C4×#11758190—22no—
30#16839804C2212yescomplemented
31C2×#14519703C2212yes—
32C2×#14519703C2212yes—
33#16839772C2212yescomplemented
34#16839764C2212yes—
35#16839667C2211yescharacteristic, complemented
36#16839665C2211yescharacteristic
37#16839656—22no—
38#16839627C2211yescharacteristic, complemented
39C4×C22⋊Dic61—22no—
40C42×Dic61C2211yescharacteristic, complemented
41#16839523C2212yescomplemented
42#16839523C2212yescomplemented
43C2×C4×D4×C61C2211yescharacteristic
44C2×#100×C61C2211yescharacteristic
45C2×#100×C61C2211yescharacteristic
46C4×M16×C61C2212yescomplemented
47C61×#343C2212yescomplemented
48#14519822—22no—
49#14519822—24no—
50#14519822C2×C414yes—
51C2×#11758222C2312yes—
52C2×#11758224—22no—
53C22×Dic122C2311yescharacteristic
54C22×C22⋊D61—22no—
55C2×D4×D61—22no—
56C22×C4×D61—22no—
57#14519810—24no—
58#14519810C2×C418yescomplemented
59C2×Dic244—22no—
60C2×#11758190—22no—
61#14519764—22no—
62#14519764C2×C414yescomplemented
63C4×Dic122—22no—
64C4×Dic122—22no—
65C4×Dic122D412yes—
66C4×Dic122D412yes—
67#14519742—22no—
68C4×D244D412yes—
69C4×D244D412yes—
70D4×Dic61—22no—
71D4×Dic61—22no—
72#14519739—22no—
73C4×C22⋊D61—24no—
74C4×C22⋊D61—24no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—24no—
77C4×C22⋊D61—22no—
78#14519737—24no—
79#14519737—24no—
80#14519736C2312yes—
81#14519735—22no—
82#14519734—22no—
83#14519733—24no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—22no—
86C2×#11758196—21no—
87C4⋊C4×D61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×#11758198—22no—
92C22⋊C4×D61—24no—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C42×D61—22no—
100#14519711—22no—
101#14519709—22no—
102#14519703—24no—
103#14519703C2×C418yescomplemented
104#14519702—22no—
105#14519702—22no—
106#14519702—22no—
107#14519699—22no—
108#14519684—22no—
109#14519684—22no—
110C22×D4×C61C2311yescharacteristic
111C23×C4×C61D412yes—
112C2×M16×C61C2312yes—
113C2×M16×C61C2312yes—
114C4×D4×C61—22no—
115C4×D4×C61—22no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61D412yes—
118C2×C42×C61C2311yescharacteristic
119#100×C61—22no—
120#100×C61C2×C414yescomplemented
121#97×C61—22no—
122C4×C8×C61—22no—
123C24×C61C2×D412yes—
124C23×D61—22no—
125C2×D4×C61—22no—
126C2×D4×C61—22no—
127C2×D4×C61C22×C412yes—
128C2×D4×C61#4112yes—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—44no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C2×C22⋊D61—24no—
137C2×C22⋊D61—28no—
138C2×C22⋊D61—28no—
139C2×C22⋊D61—22no—
140C22×Dic61—22no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—21no—
147#11758224—28no—
148#11758224—28no—
149D4×D61—28no—
150D4×D61—28no—
151#11758222—22no—
152#11758222—22no—
153#11758222C22×C414yes—
154#11758222#4114yes—
155C2×D244C2×D412yes—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—24no—
159C2×C4×D61—22no—
160C2×C4×D61—84no—
161C2×Dic122—22no—
162C2×Dic122—22no—
163C2×Dic122—21no—
164C2×Dic122C22×C412yescomplemented
165C2×Dic122C2×D412yes—
166M16×C61—22no—
167M16×C61—22no—
168M16×C61—22no—
169M16×C61C22×C414yescomplemented
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C4⋊C4×C61—22no—
173C22⋊C4×C61—24no—
174C42×C61C2×D412yes—
175C42×C61C2×D412yes—
176C22⋊Dic61—24no—
177C22⋊Dic61—28no—
178C22⋊Dic61—22no—
179C22⋊Dic61—44no—
180#11758198—24no—
181#11758198—22no—
182#11758198—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61C2×D412yes—
185C4⋊Dic61C2×D412yes—
186#11758196—24no—
187#11758196—22no—
188#11758196—22no—
189#11758196—42no—
190C4×Dic61—24no—
191C4×Dic61—22no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61—21no—
195C4×Dic61—22no—
196C4×Dic61—42no—
197C4×Dic61—42no—
198C4×Dic61—41no—
199C4×Dic61—41no—
200C4×Dic61C22×C412yescomplemented
201Dic244—28no—
202#11758190—28no—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61C4×D414yes—
208C23×C61C22×D411yescharacteristic
209C22×D61—22no—
210C22×D61—28no—
211C22×D61—82no—
212C22×D61—82no—
213D4×C61—24no—
214D4×C61—24no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—41no—
218C2×C4×C61—44no—
219C2×C4×C61—42no—
220C2×C4×C61—82no—
221C2×C4×C61#12012yes—
222C2×C4×C61#12011yescharacteristic
223C2×C4×C61#12011yescharacteristic
224C2×C4×C61C23×C411yescharacteristic
225C2×C4×C61C22×D412yes—
226C2×C4×C61C2×#4112yes—
227C2×C4×C61C2×#4111yescharacteristic
228C22⋊D61—216no—
229C22⋊D61—24no—
230C22⋊D61—24no—
231C2×Dic61—28no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—42no—
245C2×Dic61—41no—
246C2×Dic61—82no—
247C2×Dic61—82no—
248D244—22no—
249D244C4×D414yes—
250C4×D61—24no—
251C4×D61—24no—
252C4×D61—44no—
253C4×D61—82no—
254C4×D61—84no—
255Dic122—22no—
256Dic122—24no—
257Dic122—42no—
258Dic122C4×D414yes—
259C8×C61—24no—
260C8×C61—42no—
261C4×#455—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—24no—
265C22×C61—44no—
266C22×C61—42no—
267C22×C61—42no—
268C22×C61—82no—
269C22×C61C2×C4×D411yescharacteristic
270C22×C61C2×#12011yescharacteristic
271C22×C61#52511yescharacteristic
272C2×D61—24no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—88no—
276C4×C61—21no—
277C4×C61—22no—
278C4×C61—42no—
279C4×C61#45512yescomplemented
280C4×C61C2×C4×D412yes—
281C4×C61#52512yes—
282Dic61—24no—
283Dic61—42no—
284Dic61—42no—
285Dic61—42no—
286Dic61—42no—
287Dic61—42no—
288Dic61—81no—
289C4×H(5,𝔽2)—611no—
290C2×#455—611no—
291C4×#137—612no—
292C4×#124—611no—
293#1885—611no—
294#1882—612no—
295#1860—612no—
296#1856—611no—
297#1792—611no—
298C4×#104—612no—
299C4×#100D6111yescharacteristic, complemented
300C2×C61—21no—
301C2×C61—21no—
302C2×C61—44no—
303C2×C61C4×#12011yescharacteristic
304C2×C61C2×#45511yescharacteristic
305C2×C61#301811yescharacteristic
306D61—44no—
307C2×H(5,𝔽2)—611no—
308C2×#137—612no—
309C2×#124—611no—
310#520—612no—
311#520—1222no—
312#518—611no—
313#518—1222no—
314#518—1222no—
315C4×#41—612no—
316C4×#41—1222no—
317C2×C4×Q8—611no—
318C2×C4×D4—1222no—
319C2×C4×D4—1222no—
320C2×C4×D4C2×D6111yescharacteristic
321#455—618no—
322#441—1222no—
323#440—1222no—
324C4×Q16—1222no—
325C4×SD16—1222no—
326#428—612no—
327C2×#104—612no—
328C2×#104—612no—
329#419—612no—
330#417—612no—
331C2×#100C2×D6111yescharacteristic
332C2×#100C2×D6111yescharacteristic
333C4×M16C2×D6112yescomplemented
334#391—611no—
335#390—611no—
336#388—1222no—
337#382—611no—
338C4×C22⋊C4—1222no—
339C43—611no—
340#343C2×D6112yescomplemented
341#339—612no—
342#339—612no—
343C61C4×#45511yescharacteristic, complemented, Sylow
344H(5,𝔽2)—614no—
345H(5,𝔽2)—1224no—
346H(5,𝔽2)—1222no—
347C2×#41—612no—
348C2×#41—1222no—
349C22×Q8—611no—
350C22×D4—1222no—
351C22×D4—1222no—
352C22×D4C22×D6111yescharacteristic
353C23×C4—1222no—
354C23×C4D24412yes—
355#137—618no—
356#137—1224no—
357C2×Q16—1222no—
358C2×SD16—1222no—
359C2×M16C22×D6112yes—
360C2×M16C22×D6112yes—
361#124—614no—
362#124—1222no—
363C4×Q8—612no—
364C4×Q8—612no—
365C4×Q8—1222no—
366C4×Q8—1222no—
367C4×Q8—1222no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—612no—
371C4×D4—612no—
372C4×D4—1224no—
373C4×D4—1224no—
374C4×D4—1222no—
375C4×D4—1222no—
376C4×D4—1222no—
377C4×D4—1224no—
378C4×D4—1224no—
379C4×D4—1222no—
380C4×D4—1224no—
381C4×D4—1222no—
382#117—612no—
383#117—1224no—
384#117—1222no—
385#117—1222no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C22⋊C4—1224no—
392C2×C22⋊C4—1222no—
393C2×C22⋊C4—1222no—
394C2×C22⋊C4—1222no—
395C2×C22⋊C4—1222no—
396C2×C22⋊C4D24412yes—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—1222no—
400C2×C42—1222no—
401C2×C42—1221no—
402C2×C42—1221no—
403C2×C42—1221no—
404C2×C42C22×D6111yescharacteristic
405#107—1222no—
406#106—1222no—
407#104—618no—
408#104—1224no—
409#103—1222no—
410#103—1222no—
411#103—1222no—
412#102—1222no—
413#100—22no—
414#100C4×D6114yescomplemented
415#97—22no—
416C4×C8—22no—
417#95—1222no—
418#95—1222no—
419C24—1222no—
420C24C2×D24412yes—
421#41—614no—
422#41—614no—
423#41—1228no—
424#41—1228no—
425#41—1222no—
426#41—1222no—
427C2×Q8—612no—
428C2×Q8—612no—
429C2×Q8—1221no—
430C2×Q8—1222no—
431C2×Q8—1222no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—612no—
435C2×D4—1228no—
436C2×D4—1228no—
437C2×D4—1224no—
438C2×D4—1228no—
439C2×D4—1222no—
440C2×D4—1228no—
441C2×D4C2×C4×D6112yes—
442C2×D4#1175822212yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—44no—
446C22×C4—1224no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1221no—
457C22×C4—4884no—
458C22×C4C2×D24411yescharacteristic
459C22×C4C2×D24412yes—
460C22×C4C2×D24411yescharacteristic
461C22×C4C23×D6111yescharacteristic
462Q16—1228no—
463SD16—1228no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16C2×C4×D6114yescomplemented
468C2×C8—22no—
469C2×C8—22no—
470C4⋊C4—22no—
471C4⋊C4—612no—
472C4⋊C4—612no—
473C4⋊C4—1224no—
474C4⋊C4—1222no—
475C4⋊C4—1222no—
476C4⋊C4—1222no—
477C4⋊C4—2442no—
478C22⋊C4—24no—
479C22⋊C4—1224no—
480C22⋊C4—1224no—
481C22⋊C4—1222no—
482C22⋊C4—1228no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C22⋊C4—2444no—
486C42—612no—
487C42—1224no—
488C42—1222no—
489C42—1221no—
490C42—1222no—
491C42—1222no—
492C42—1222no—
493C42—2442no—
494C42—2442no—
495C42—2441no—
496C42—2441no—
497C42D4×D6112yes—
498C42D4×D6112yes—
499C23—22no—
500C23—22no—
501C23—42no—
502C23—42no—
503C23—1228no—
504C23—1222no—
505C23—4882no—
506C23—4882no—
507C23C4×D24414yes—
508C23C22×D24411yescharacteristic
509Q8—614no—
510Q8—1222no—
511Q8—1224no—
512Q8—2442no—
513D4—24no—
514D4—24no—
515D4—614no—
516D4—12216no—
517D4—1224no—
518D4—1224no—
519D4—1222no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—1228no—
527C2×C4—1222no—
528C2×C4—1224no—
529C2×C4—1224no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—4882no—
536C2×C4—4884no—
537C2×C4—4882no—
538C2×C4—4882no—
539C2×C4—2442no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2444no—
548C2×C4#1451974712yes—
549C2×C4#1451974711yescharacteristic
550C2×C4#1451974711yescharacteristic
551C2×C4C22×C4×D6111yescharacteristic
552C2×C4C2×D4×D6112yes—
553C2×C4#41×D6112yes—
554C2×C4C2×#1175822211yescharacteristic
555C8—24no—
556C8—42no—
557C22—21no—
558C22—21no—
559C22—24no—
560C22—44no—
561C22—42no—
562C22—42no—
563C22—82no—
564C22—1224no—
565C22—4888no—
566C22—2442no—
567C22—2442no—
568C22C2×C4×D24411yescharacteristic
569C22C2×#1451974711yescharacteristic
570C22#1684027411yescharacteristic
571C4—21no—
572C4—22no—
573C4—42no—
574C4—1224no—
575C4—4881no—
576C4—2442no—
577C4—2442no—
578C4—2442no—
579C4—2442no—
580C4—2442no—
581C4#1683994212yesdirect product factor
582C4C4×D4×D6112yes—
583C4#1684027112yes—
584C2—21no—
585C2—21no—
586C2—44no—
587C2—2444no—
588C2C4×#1451974711yescharacteristic
589C2C2×#1683994211yescharacteristic
590C2#2145517211yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#100×C61C2
socleC22×C61C2×#120
prime radicalC2×#14519822C22
cosocleC22×C4×C61C24
hypercenterC4×#100D61
hypocenterC61C4×#455
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. C4×#14519810C2semidirect
4. C4×#14519764C2semidirect
5. #21446205C2semidirect
6. #21446187C2semidirect
7. #21446055C2semidirect
8. #21446031C2semidirect
10. C4×#14519703C2semidirect
11. C4×#100×C61C2semidirect
22. C2×C4×Dic122C22semidirect
25. #16839942C4direct (N × H)
30. #16839804C22semidirect
33. #16839772C22semidirect
35. #16839667C22semidirect
38. #16839627C22semidirect
40. C42×Dic61C22semidirect
41. #16839523C22semidirect
42. #16839523C22semidirect
46. C4×M16×C61C22semidirect
47. C61×#343C22semidirect
58. #14519810C2×C4semidirect
62. #14519764C2×C4semidirect
103. #14519703C2×C4semidirect
120. #100×C61C2×C4semidirect
164. C2×Dic122C22×C4semidirect
169. M16×C61C22×C4semidirect
200. C4×Dic61C22×C4semidirect
279. C4×C61#455semidirect
299. C4×#100D61semidirect
333. C4×M16C2×D61semidirect
340. #343C2×D61semidirect
343. C61C4×#455semidirect
414. #100C4×D61semidirect
467. M16C2×C4×D61semidirect
581. C4#16839942direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#145198222
C2×#168399422
C4×#145198102
C4×#145197642
#214462052
#214461872
#214460552
#214460312
#214457752
C4×#145197032
C4×#100×C612
C4×#45561