Finite Group Databasebeta

← C4×#16839932 #29685891

Subgroups — C4×#16839932 #29685891

Order 15616.

1578 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519822C211yesmaximal, characteristic, complemented
2C2×#16839932C211yesmaximal, characteristic
3C4×#14519805C212yesmaximal, complemented
4C4×#14519773C211yesmaximal, characteristic, complemented
5#21446215C211yesmaximal, characteristic, complemented
6#21446194C212yesmaximal, complemented
7#21446048C212yesmaximal, complemented
8#21446031C211yesmaximal, characteristic, complemented
9#21445775C211yesmaximal, characteristic, complemented
10C4×#14519703C212yesmaximal, complemented
11C4×#100×C61C211yesmaximal, characteristic, complemented
12C2×#14519822C2211yescharacteristic
13C2×#14519805C2212yes—
14C2×#14519773C2211yescharacteristic
15#16840243C2212yes—
16#16840241—22no—
17#16840237C2211yescharacteristic
18#16840235—22no—
19#16840234—22no—
20C4×#11758222C2212yes—
21C4×#11758224—22no—
22C2×C4×D244C2211yescharacteristic, complemented
23C2×C4×C22⋊D61—22no—
24C2×C4×C22⋊D61—22no—
25C4×D4×D61—22no—
26#16839932C418yesdirect product factor
27#16839875—22no—
28#16839864—22no—
29C4×#11758190—22no—
30C4×D488—22no—
31#16839804C2212yescomplemented
32C2×#14519703C2212yes—
33C2×#14519703C2212yes—
34#16839768C2212yescomplemented
35#16839764C2212yes—
36#16839665C2211yescharacteristic
37#16839663C2211yescharacteristic, complemented
38#16839662—22no—
39#16839631C2211yescharacteristic, complemented
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×C414yescomplemented
51C2×#11758222C2312yes—
52C2×#11758224—22no—
53C22×D244C2311yescharacteristic
54C22×C22⋊D61—22no—
55C22×C22⋊D61—22no—
56C2×D4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—21no—
59#14519805—24no—
60#14519805C2×C418yescomplemented
61C2×#11758190—22no—
62C2×D488—22no—
63#14519773—22no—
64#14519773C2×C414yescomplemented
65C4×Dic122D412yescomplemented
66C4×Dic122D412yescomplemented
67#14519742—22no—
68C4×D244—22no—
69C4×D244—22no—
70C4×D244D412yescomplemented
71C4×D244D412yescomplemented
72D4×Dic61—22no—
73D4×Dic61—22no—
74#14519739—22no—
75C4×C22⋊D61—24no—
76C4×C22⋊D61—24no—
77C4×C22⋊D61—22no—
78C4×C22⋊D61—24no—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—48no—
81#14519737—24no—
82#14519737—24no—
83#14519736C2312yes—
84#14519735—22no—
85#14519734—22no—
86#14519733—24no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—22no—
89C2×#11758196—22no—
90C4⋊C4×D61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—21no—
96C22⋊C4×D61—24no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C42×D61—22no—
103#14519711—22no—
104#14519709—22no—
105#14519703—24no—
106#14519703C2×C418yescomplemented
107#14519702—22no—
108#14519699—22no—
109#14519699—22no—
110#14519699—22no—
111C22×D4×C61C2311yescharacteristic
112C23×C4×C61D412yes—
113C2×M16×C61C2312yes—
114C2×M16×C61C2312yes—
115C4×D4×C61—22no—
116C4×D4×C61—22no—
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61D412yes—
119C2×C42×C61C2311yescharacteristic
120#100×C61—22no—
121#100×C61C2×C414yescomplemented
122#97×C61—22no—
123C4×C8×C61—22no—
124C24×C61C2×D412yes—
125C23×D61—22no—
126C23×D61—21no—
127C2×D4×C61—22no—
128C2×D4×C61—22no—
129C2×D4×C61C22×C412yes—
130C2×D4×C61#4112yes—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—44no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C2×C22⋊D61—24no—
139C2×C22⋊D61—28no—
140C2×C22⋊D61—28no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—28no—
143C2×C22⋊D61—44no—
144C2×C22⋊D61—44no—
145C22×Dic61—22no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—21no—
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×D244—22no—
160C2×D244—22no—
161C2×D244—21no—
162C2×D244C22×C412yescomplemented
163C2×D244C2×D412yes—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—24no—
167C2×C4×D61—22no—
168C2×C4×D61—44no—
169C2×C4×D61—41no—
170C2×C4×D61—41no—
171C2×C4×D61—84no—
172C2×Dic122C2×D412yes—
173M16×C61—22no—
174M16×C61—22no—
175M16×C61—22no—
176M16×C61C22×C414yescomplemented
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C4⋊C4×C61—22no—
180C22⋊C4×C61—24no—
181C42×C61C2×D412yes—
182C42×C61C2×D412yes—
183C22⋊Dic61—24no—
184C22⋊Dic61—22no—
185C22⋊Dic61—44no—
186#11758198—24no—
187#11758198—22no—
188#11758198—22no—
189#11758198—44no—
190#11758198—42no—
191C4⋊Dic61—22no—
192C4⋊Dic61C2×D412yes—
193C4⋊Dic61C2×D412yes—
194#11758196—24no—
195#11758196—22no—
196#11758196—22no—
197#11758196—44no—
198C4×Dic61—24no—
199C4×Dic61—24no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—21no—
204C4×Dic61—22no—
205C4×Dic61—42no—
206C4×Dic61C22×C412yescomplemented
207D488—28no—
208#11758190—28no—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—42no—
212C23×C61—42no—
213C23×C61C4×D414yes—
214C23×C61C22×D411yescharacteristic
215C22×D61—22no—
216C22×D61—28no—
217C22×D61—22no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—82no—
223C22×D61—82no—
224D4×C61—24no—
225D4×C61—24no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—41no—
229C2×C4×C61—44no—
230C2×C4×C61—42no—
231C2×C4×C61—82no—
232C2×C4×C61#12012yes—
233C2×C4×C61#12011yescharacteristic
234C2×C4×C61#12011yescharacteristic
235C2×C4×C61C23×C411yescharacteristic
236C2×C4×C61C22×D412yes—
237C2×C4×C61C2×#4112yes—
238C2×C4×C61C2×#4111yescharacteristic
239C22⋊D61—216no—
240C22⋊D61—24no—
241C22⋊D61—24no—
242C22⋊D61—416no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—28no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—42no—
254C2×Dic61—41no—
255C2×Dic61—82no—
256C2×Dic61—82no—
257D244—24no—
258D244—22no—
259D244—42no—
260D244C4×D414yescomplemented
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—44no—
264C4×D61—82no—
265C4×D61—84no—
266C4×D61—82no—
267C4×D61—82no—
268Dic122—22no—
269Dic122C4×D414yescomplemented
270C8×C61—24no—
271C8×C61—42no—
272C4×#453—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—24no—
276C22×C61—44no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—82no—
280C22×C61C2×C4×D411yescharacteristic
281C22×C61C2×#12011yescharacteristic
282C22×C61#52511yescharacteristic
283C2×D61—24no—
284C2×D61—42no—
285C2×D61—42no—
286C2×D61—44no—
287C2×D61—42no—
288C2×D61—88no—
289C2×D61—82no—
290C2×D61—81no—
291C2×D61—81no—
292C4×C61—21no—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61#45312yescomplemented
296C4×C61C2×C4×D412yes—
297C4×C61#52512yes—
298Dic61—24no—
299Dic61—24no—
300Dic61—42no—
301Dic61—42no—
302Dic61—42no—
303Dic61—81no—
304C4×H(5,𝔽2)—611no—
305C2×#453—611no—
306C4×AGL(1,ℤ/8)—612no—
307C4×#127—611no—
308#1887—611no—
309#1883—612no—
310#1859—612no—
311#1856—611no—
312#1792—611no—
313C4×#104—612no—
314C4×#100D6111yescharacteristic, complemented
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—44no—
318C2×C61C4×#12011yescharacteristic
319C2×C61C2×#45311yescharacteristic
320C2×C61#301811yescharacteristic
321D61—44no—
322D61—82no—
323C2×H(5,𝔽2)—611no—
324C2×AGL(1,ℤ/8)—612no—
325C2×#127—611no—
326#520—612no—
327#520—1222no—
328#518—611no—
329#518—1222no—
330#518—1222no—
331C4×#41—612no—
332C4×#41—1222no—
333C2×C4×D4—611no—
334C2×C4×D4—1222no—
335C2×C4×D4—1222no—
336C2×C4×D4—1222no—
337C2×C4×D4C2×D6111yescharacteristic
338#453—618no—
339#442—1222no—
340#440—1222no—
341C4×SD16—1222no—
342C4×D8—1222no—
343#428—612no—
344C2×#104—612no—
345C2×#104—612no—
346#418—612no—
347#417—612no—
348C2×#100C2×D6111yescharacteristic
349C2×#100C2×D6111yescharacteristic
350C4×M16C2×D6112yescomplemented
351#390—611no—
352#390—611no—
353#390—1222no—
354#384—611no—
355C43—611no—
356#343C2×D6112yescomplemented
357#339—612no—
358#339—612no—
359C61C4×#45311yescharacteristic, complemented, Sylow
360H(5,𝔽2)—614no—
361H(5,𝔽2)—1224no—
362H(5,𝔽2)—1222no—
363C2×#41—612no—
364C2×#41—1222no—
365C22×D4—611no—
366C22×D4—1222no—
367C22×D4—1222no—
368C22×D4—1222no—
369C22×D4C22×D6111yescharacteristic
370C23×C4—1222no—
371C23×C4—1221no—
372C23×C4D24412yes—
373AGL(1,ℤ/8)—618no—
374AGL(1,ℤ/8)—1224no—
375C2×SD16—1222no—
376C2×D8—1222no—
377C2×M16C22×D6112yes—
378C2×M16C22×D6112yes—
379#127—614no—
380#127—1222no—
381C4×Q8—612no—
382C4×Q8—612no—
383C4×Q8—1222no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—612no—
387C4×D4—612no—
388C4×D4—1224no—
389C4×D4—1224no—
390C4×D4—1222no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4—1224no—
394C4×D4—1224no—
395C4×D4—1222no—
396C4×D4—1224no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C4×D4—2448no—
401#117—612no—
402#117—1224no—
403#117—1222no—
404#117—1222no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4—1222no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C22⋊C4—1224no—
411C2×C22⋊C4—1222no—
412C2×C22⋊C4—1222no—
413C2×C22⋊C4—1222no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1222no—
416C2×C22⋊C4D24412yes—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—1222no—
420C2×C42—1221no—
421C2×C42—1222no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424#107—1222no—
425#106—1222no—
426#104—618no—
427#104—1224no—
428#103—1222no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#100—22no—
433#100C4×D6114yescomplemented
434#97—22no—
435C4×C8—22no—
436C24—1222no—
437C24—1221no—
438C24C2×D24412yes—
439#41—614no—
440#41—614no—
441#41—1228no—
442#41—1228no—
443#41—1222no—
444#41—1222no—
445C2×Q8—612no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—612no—
449C2×D4—612no—
450C2×D4—1228no—
451C2×D4—1228no—
452C2×D4—1224no—
453C2×D4—1228no—
454C2×D4—1222no—
455C2×D4—1228no—
456C2×D4—1228no—
457C2×D4—1222no—
458C2×D4—1222no—
459C2×D4—1221no—
460C2×D4—2444no—
461C2×D4—2444no—
462C2×D4C2×C4×D6112yes—
463C2×D4#1175822212yes—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—44no—
467C22×C4—1224no—
468C22×C4—1222no—
469C22×C4—1221no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1221no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1221no—
477C22×C4—4884no—
478C22×C4—2444no—
479C22×C4—2441no—
480C22×C4—2441no—
481C22×C4C2×D24411yescharacteristic
482C22×C4C2×D24412yes—
483C22×C4C2×D24411yescharacteristic
484C22×C4C23×D6111yescharacteristic
485SD16—1228no—
486D8—1228no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16C2×C4×D6114yescomplemented
491C2×C8—22no—
492C2×C8—22no—
493C4⋊C4—22no—
494C4⋊C4—612no—
495C4⋊C4—612no—
496C4⋊C4—1224no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—2444no—
501C22⋊C4—24no—
502C22⋊C4—1224no—
503C22⋊C4—1224no—
504C22⋊C4—1222no—
505C22⋊C4—1222no—
506C22⋊C4—1222no—
507C22⋊C4—2444no—
508C22⋊C4—2444no—
509C22⋊C4—2442no—
510C42—612no—
511C42—1224no—
512C42—1224no—
513C42—1222no—
514C42—1221no—
515C42—1222no—
516C42—1222no—
517C42—1222no—
518C42—2442no—
519C42D4×D6112yes—
520C42D4×D6112yes—
521C23—22no—
522C23—22no—
523C23—42no—
524C23—42no—
525C23—1228no—
526C23—1222no—
527C23—1222no—
528C23—4882no—
529C23—4882no—
530C23—2442no—
531C23—2442no—
532C23—2441no—
533C23—2441no—
534C23C4×D24414yes—
535C23C22×D24411yescharacteristic
536Q8—614no—
537Q8—1222no—
538D4—24no—
539D4—24no—
540D4—614no—
541D4—12216no—
542D4—1224no—
543D4—1224no—
544D4—1224no—
545D4—1222no—
546D4—24416no—
547D4—2442no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—82no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1228no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1224no—
560C2×C4—1224no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—4882no—
565C2×C4—4882no—
566C2×C4—4884no—
567C2×C4—4882no—
568C2×C4—4882no—
569C2×C4—4882no—
570C2×C4—2442no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2444no—
575C2×C4#1451974712yes—
576C2×C4#1451974711yescharacteristic
577C2×C4#1451974711yescharacteristic
578C2×C4C22×C4×D6111yescharacteristic
579C2×C4C2×D4×D6112yes—
580C2×C4#41×D6112yes—
581C2×C4C2×#1175822211yescharacteristic
582C8—24no—
583C8—42no—
584C22—21no—
585C22—21no—
586C22—24no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22—82no—
591C22—1224no—
592C22—4882no—
593C22—4888no—
594C22—4881no—
595C22—4881no—
596C22—2444no—
597C22—2442no—
598C22—2442no—
599C22—2442no—
600C22C2×C4×D24411yescharacteristic
601C22C2×#1451974711yescharacteristic
602C22#1684027411yescharacteristic
603C4—21no—
604C4—22no—
605C4—42no—
606C4—1224no—
607C4—1224no—
608C4—4881no—
609C4—2442no—
610C4—2442no—
611C4—2442no—
612C4#1683993212yesdirect product factor
613C4C4×D4×D6112yes—
614C4#1684027112yes—
615C2—21no—
616C2—21no—
617C2—44no—
618C2—4882no—
619C2—2444no—
620C2C4×#1451974711yescharacteristic
621C2C2×#1683993211yescharacteristic
622C2#2145517211yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#100×C61C2
socleC22×C61C2×#120
prime radicalC2×#16839932C2
cosocleC22×C4×C61C24
hypercenterC4×#100D61
hypocenterC61C4×#453
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
1. C4×#14519822C2semidirect
3. C4×#14519805C2semidirect
4. C4×#14519773C2semidirect
5. #21446215C2semidirect
6. #21446194C2semidirect
7. #21446048C2semidirect
8. #21446031C2semidirect
9. #21445775C2semidirect
10. C4×#14519703C2semidirect
11. C4×#100×C61C2semidirect
22. C2×C4×D244C22semidirect
26. #16839932C4direct (N × H)
31. #16839804C22semidirect
34. #16839768C22semidirect
37. #16839663C22semidirect
39. #16839631C22semidirect
40. C42×Dic61C22semidirect
41. #16839523C22semidirect
42. #16839523C22semidirect
46. C4×M16×C61C22semidirect
47. C61×#343C22semidirect
50. #14519822C2×C4semidirect
60. #14519805C2×C4semidirect
64. #14519773C2×C4semidirect
65. C4×Dic122D4semidirect
66. C4×Dic122D4semidirect
70. C4×D244D4semidirect
71. C4×D244D4semidirect
106. #14519703C2×C4semidirect
121. #100×C61C2×C4semidirect
162. C2×D244C22×C4semidirect
176. M16×C61C22×C4semidirect
206. C4×Dic61C22×C4semidirect
260. D244C4×D4semidirect
269. Dic122C4×D4semidirect
295. C4×C61#453semidirect
314. C4×#100D61semidirect
350. C4×M16C2×D61semidirect
356. #343C2×D61semidirect
359. C61C4×#453semidirect
433. #100C4×D61semidirect
490. M16C2×C4×D61semidirect
612. C4#16839932direct (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×#168399322
C4×#145198052
C4×#145197732
#214462152
#214461942
#214460482
#214460312
#214457752
C4×#145197032
C4×#100×C612
C4×#45361