Finite Group Databasebeta

← C4×#16839939 #29685896

Subgroups — C4×#16839939 #29685896

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×#16839939C211yesmaximal, characteristic
3C4×#14519808C212yesmaximal, complemented
4#21446208C211yesmaximal, characteristic, complemented
5#21446191C212yesmaximal, complemented
6#21446051C212yesmaximal, complemented
7#21446028C211yesmaximal, characteristic, complemented
8#21445772C211yesmaximal, characteristic
9C4×#14519705C212yesmaximal, complemented
10C4×#14519694C211yesmaximal, characteristic, complemented
11C4×#124×C61C211yesmaximal, characteristic, complemented
12C2×#14519822C2211yescharacteristic
13C2×#14519808C2212yes—
14#16840243C2212yes—
15#16840241—22no—
16#16840237C2211yescharacteristic
17#16840235—22no—
18#16840234—22no—
19C4×#11758222C2212yes—
20C4×#11758224—22no—
21C2×C4×C22⋊D61—22no—
22C4×D4×D61—22no—
23#16839939C418yesdirect product factor
24#16839867—22no—
25#16839860—22no—
26C4×#11758202—22no—
27C4×#11758201—22no—
28#16839802C2212yescomplemented
29C2×#14519705C2212yes—
30C2×#14519705C2212yes—
31#16839771C2212yescomplemented
32#16839761C2212yes—
33C2×#14519694C2211yescharacteristic
34C2×#14519694C2211yescharacteristic
35C4×#11758194C2212yescomplemented
36#16839531C2212yescomplemented
37#16839522C2212yescomplemented
38#16839522C2212yescomplemented
39C2×#124×C61C2211yescharacteristic
40C2×C4×Q8×C61C2211yescharacteristic, complemented
41C2×C4×D4×C61C2211yescharacteristic
42C61×#391C2211yescharacteristic, complemented
43C61×#390C2211yescharacteristic
44C61×#388—22no—
45C61×#382C2211yescharacteristic, complemented
46C4×C22⋊C4×C61—22no—
47C43×C61C2211yescharacteristic, complemented
48#14519822—22no—
49#14519822—24no—
50#14519822C2×C414yes—
51C2×#11758222C2312yes—
52C2×#11758224—22no—
53C22×C22⋊D61—22no—
54C2×D4×D61—22no—
55C22×C4×D61—22no—
56#14519808—24no—
57#14519808C2×C418yescomplemented
58C2×#11758202—22no—
59C2×#11758201—22no—
60C2×#11758194C2312yes—
61C2×#11758194C2312yes—
62C4×Dic122D412yes—
63C4×Dic122D412yes—
64#14519742—22no—
65C4×D244D412yes—
66C4×D244D412yes—
67D4×Dic61—22no—
68D4×Dic61—22no—
69#14519739—22no—
70C4×C22⋊D61—24no—
71C4×C22⋊D61—24no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—24no—
74C4×C22⋊D61—22no—
75#14519737—24no—
76#14519737—24no—
77#14519736C2312yes—
78#14519735—22no—
79#14519734—22no—
80#14519733—24no—
81C2×#11758196—22no—
82C4⋊C4×D61—22no—
83C2×C22⋊Dic61—22no—
84C2×#11758198—22no—
85C22⋊C4×D61—24no—
86C2×C4×Dic61—22no—
87C42×D61—22no—
88#14519710—22no—
89#14519708—22no—
90#14519705—24no—
91#14519705C2×C418yescomplemented
92#14519701—22no—
93#14519701—22no—
94#14519700—22no—
95#14519697—22no—
96#14519694—22no—
97#14519694C2×C414yescomplemented
98#14519688—22no—
99C4×#92418—22no—
100C22×Q8×C61C2311yescharacteristic
101C22×D4×C61C2311yescharacteristic
102C23×C4×C61D412yes—
103#124×C61—22no—
104#124×C61C2×C414yescomplemented
105C4×Q8×C61—22no—
106C4×Q8×C61—22no—
107C4×D4×C61—22no—
108C4×D4×C61—22no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61D412yes—
115C2×C42×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61—21no—
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121#95×C61—22no—
122#95×C61—22no—
123C24×C61C2×D412yes—
124C23×D61—22no—
125C2×Q8×C61—21no—
126C2×Q8×C61—22no—
127C2×Q8×C61—22no—
128C2×Q8×C61C22×C412yescomplemented
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61C22×C412yes—
132C2×D4×C61#4112yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—44no—
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D412yes—
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C2×C22⋊D61—24no—
145C2×C22⋊D61—28no—
146C2×C22⋊D61—28no—
147C2×C22⋊D61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151#11758224—28no—
152#11758224—28no—
153D4×D61—28no—
154D4×D61—28no—
155#11758222—22no—
156#11758222—22no—
157#11758222C22×C414yes—
158#11758222#4114yes—
159C2×D244C2×D412yes—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—24no—
163C2×C4×D61—22no—
164C2×C4×D61—84no—
165C2×Dic122C2×D412yes—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—42no—
169C22⋊C4×C61—28no—
170C22⋊C4×C61—24no—
171C22⋊C4×C61—44no—
172C42×C61—21no—
173C42×C61—22no—
174C42×C61—42no—
175C42×C61—42no—
176C42×C61—41no—
177C42×C61—41no—
178C42×C61C22×C412yescomplemented
179C42×C61C2×D412yes—
180C42×C61C2×D412yes—
181C22⋊Dic61—24no—
182C22⋊Dic61—22no—
183#11758202—28no—
184#11758201—28no—
185#11758198—24no—
186#11758198—22no—
187#11758198—22no—
188C4⋊Dic61C2×D412yes—
189C4⋊Dic61C2×D412yes—
190#11758196—24no—
191#11758196—22no—
192#11758196—22no—
193C4×Dic61—24no—
194C4×Dic61—22no—
195C4×Dic61—22no—
196C4×Dic61—22no—
197#11758194—22no—
198#11758194—22no—
199#11758194—22no—
200#11758194C22×C414yescomplemented
201C2×#92418—22no—
202C2×#92418—22no—
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—
213Q8×C61—24no—
214Q8×C61—42no—
215D4×C61—24no—
216D4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—44no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—41no—
233C2×C4×C61—82no—
234C2×C4×C61#12012yes—
235C2×C4×C61#12011yescharacteristic
236C2×C4×C61#12011yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C2×C4×C61C22×D412yes—
239C2×C4×C61C2×#4112yes—
240C2×C4×C61C2×#4111yescharacteristic
241C22⋊D61—216no—
242C22⋊D61—24no—
243C22⋊D61—24no—
244C2×Dic61—28no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—82no—
249C2×Dic61—82no—
250D244—22no—
251D244C4×D414yes—
252C4×D61—24no—
253C4×D61—24no—
254C4×D61—44no—
255C4×D61—82no—
256C4×D61—84no—
257Dic122—22no—
258Dic122C4×D414yes—
259#92418—24no—
260#92418—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—42no—
280C4×C61—42no—
281C4×C61—42no—
282C4×C61—81no—
283C4×C61#45512yescomplemented
284C4×C61C2×C4×D412yes—
285C4×C61#52512yes—
286Dic61—24no—
287Dic61—42no—
288Dic61—42no—
289C4×H(5,𝔽2)—611no—
290C2×#455—611no—
291C4×#137—612no—
292C4×#124D6111yescharacteristic, complemented
293#1885—611no—
294#1882—612no—
295#1860—612no—
296#1856—611no—
297#1792—611no—
298C4×#104—612no—
299C4×#100—611no—
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×#124C2×D6111yescharacteristic
310#520—612no—
311#520—1222no—
312#518—611no—
313#518—1222no—
314#518—1222no—
315C4×#41—612no—
316C4×#41—1222no—
317C2×C4×Q8C2×D6111yescharacteristic, complemented
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×#100—611no—
332C2×#100—611no—
333C4×M16—612no—
334#391C2×D6111yescharacteristic, complemented
335#390C2×D6111yescharacteristic
336#388—22no—
337#382C2×D6111yescharacteristic, complemented
338C4×C22⋊C4—22no—
339C43C2×D6111yescharacteristic, complemented
340#343—612no—
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×Q8C22×D6111yescharacteristic
350C22×D4—1222no—
351C22×D4—1222no—
352C22×D4C22×D6111yescharacteristic
353C23×C4—1222no—
354C23×C4C22⋊D6112yes—
355#137—618no—
356#137—1224no—
357C2×Q16—1222no—
358C2×SD16—1222no—
359C2×M16—612no—
360C2×M16—612no—
361#124—22no—
362#124C4×D6114yescomplemented
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8—612no—
366C4×Q8—612no—
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—21no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4C22×D6111yescharacteristic
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—1224no—
394C2×C22⋊C4—1222no—
395C2×C22⋊C4—1222no—
396C2×C22⋊C4C22⋊D6112yes—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—1222no—
401C2×C42—1222no—
402C2×C42C22×D6111yescharacteristic
403C2×C42C22×D6111yescharacteristic
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—614no—
414#100—1222no—
415#97—1222no—
416C4×C8—1222no—
417#95—22no—
418#95—22no—
419C24—1222no—
420C24C2×C22⋊D6112yes—
421#41—614no—
422#41—614no—
423#41—1228no—
424#41—1228no—
425#41—1222no—
426#41—1222no—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—612no—
431C2×Q8C2×C4×D6112yescomplemented
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—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—44no—
450C22×C4—1224no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—4884no—
458C22×C4C2×C22⋊D6111yescharacteristic
459C22×C4C2×C22⋊D6112yes—
460C22×C4C2×C22⋊D6111yescharacteristic
461C22×C4C23×D6111yescharacteristic
462Q16—1228no—
463SD16—1228no—
464M16—614no—
465M16—1222no—
466M16—1222no—
467M16—1222no—
468C2×C8—1222no—
469C2×C8—1222no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—42no—
473C4⋊C4—612no—
474C4⋊C4—612no—
475C4⋊C4—1224no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C22⋊C4—28no—
479C22⋊C4—24no—
480C22⋊C4—44no—
481C22⋊C4—1224no—
482C22⋊C4—1224no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C22⋊C4—1222no—
486C42—21no—
487C42—22no—
488C42—42no—
489C42—42no—
490C42—41no—
491C42—41no—
492C42—1224no—
493C42—1222no—
494C42—1222no—
495C42—1222no—
496C42C2×C4×D6112yescomplemented
497C42D4×D6112yes—
498C42D4×D6112yes—
499C23—22no—
500C23—22no—
501C23—42no—
502C23—42no—
503C23—1228no—
504C23—1222no—
505C23—4882no—
506C23—4882no—
507C23C4×C22⋊D6114yes—
508C23C22×C22⋊D6111yescharacteristic
509Q8—24no—
510Q8—42no—
511Q8—614no—
512Q8—1222no—
513D4—24no—
514D4—24no—
515D4—614no—
516D4—12216no—
517D4—1224no—
518D4—1224no—
519D4—1222no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—1228no—
538C2×C4—1222no—
539C2×C4—1224no—
540C2×C4—1224no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—4882no—
544C2×C4—4884no—
545C2×C4—4882no—
546C2×C4—4882no—
547C2×C4—2444no—
548C2×C4#1451974511yescharacteristic
549C2×C4#1451974512yes—
550C2×C4#1451974511yescharacteristic
551C2×C4C22×C4×D6111yescharacteristic
552C2×C4C2×D4×D6112yes—
553C2×C4#41×D6112yes—
554C2×C4C2×#1175822211yescharacteristic
555C8—1224no—
556C8—2442no—
557C22—21no—
558C22—21no—
559C22—24no—
560C22—44no—
561C22—42no—
562C22—42no—
563C22—82no—
564C22—1224no—
565C22—4888no—
566C22—2442no—
567C22—2442no—
568C22C2×C4×C22⋊D6111yescharacteristic
569C22C2×#1451974511yescharacteristic
570C22#1684026911yescharacteristic
571C4—21no—
572C4—22no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—42no—
577C4—81no—
578C4—1224no—
579C4—2442no—
580C4—2442no—
581C4#1683993912yesdirect product factor
582C4C4×D4×D6112yes—
583C4#1684027112yes—
584C2—21no—
585C2—21no—
586C2—44no—
587C2—2444no—
588C2C4×#1451974511yescharacteristic
589C2C2×#1683993911yescharacteristic
590C2#2145516711yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#124×C61C2
socleC22×C61C2×#120
prime radicalC2×#14519822C22
cosocleC22×C4×C61C24
hypercenterC4×#124D61
hypocenterC61C4×#455
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
3. C4×#14519808C2semidirect
4. #21446208C2semidirect
5. #21446191C2semidirect
6. #21446051C2semidirect
7. #21446028C2semidirect
9. C4×#14519705C2semidirect
10. C4×#14519694C2semidirect
11. C4×#124×C61C2semidirect
23. #16839939C4direct (N × H)
28. #16839802C22semidirect
31. #16839771C22semidirect
35. C4×#11758194C22semidirect
36. #16839531C22semidirect
37. #16839522C22semidirect
38. #16839522C22semidirect
40. C2×C4×Q8×C61C22semidirect
42. C61×#391C22semidirect
45. C61×#382C22semidirect
47. C43×C61C22semidirect
57. #14519808C2×C4semidirect
91. #14519705C2×C4semidirect
97. #14519694C2×C4semidirect
104. #124×C61C2×C4semidirect
128. C2×Q8×C61C22×C4semidirect
178. C42×C61C22×C4semidirect
200. #11758194C22×C4semidirect
283. C4×C61#455semidirect
292. C4×#124D61semidirect
317. C2×C4×Q8C2×D61semidirect
334. #391C2×D61semidirect
337. #382C2×D61semidirect
339. C43C2×D61semidirect
343. C61C4×#455semidirect
362. #124C4×D61semidirect
431. C2×Q8C2×C4×D61semidirect
496. C42C2×C4×D61semidirect
581. C4#16839939direct (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×#168399392
C4×#145198082
#214462082
#214461912
#214460512
#214460282
#214457722
C4×#145197052
C4×#145196942
C4×#124×C612
C4×#45561