Finite Group Databasebeta

← C4×#16839930 #29685887

Subgroups — C4×#16839930 #29685887

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
1C2×#16839930C211yesmaximal, characteristic
2C4×#14519802C212yesmaximal, complemented
3C4×#14519773C211yesmaximal, characteristic, complemented
4#21446217C211yesmaximal, characteristic, complemented
5#21446195C212yesmaximal, complemented
6#21446045C212yesmaximal, complemented
7#21446029C211yesmaximal, characteristic, complemented
8#21445773C211yesmaximal, characteristic, complemented
9C4×#14519704C212yesmaximal, complemented
10C4×#14519694C211yesmaximal, characteristic, complemented
11C4×H(5,𝔽2)×C61C211yesmaximal, characteristic, complemented
12C2×#14519802C2212yes—
13C2×#14519773C2211yescharacteristic
14C2×C4×D244C2211yescharacteristic, complemented
15C2×C4×C22⋊D61—22no—
16#16839930C418yesdirect product factor
17#16839872—22no—
18#16839860—22no—
19C4×#11758201—22no—
20C4×#11758199—22no—
21#16839805C2212yescomplemented
22C2×#14519704C2212yes—
23C2×#14519704C2212yes—
24#16839766C2212yescomplemented
25#16839763C2212yes—
26C2×#14519694C2211yescharacteristic
27C2×#14519694C2211yescharacteristic
28C4×#11758194C2212yescomplemented
29#16839665C2211yescharacteristic
30#16839663C2211yescharacteristic, complemented
31#16839662—22no—
32#16839631C2211yescharacteristic, complemented
33C42×Dic61C2211yescharacteristic, complemented
34#16839531C2212yescomplemented
35#16839521C2212yescomplemented
36#16839521C2212yescomplemented
37C2×H(5,𝔽2)×C61C2211yescharacteristic
38C61×#520—22no—
39C61×#520C2212yes—
40C61×#518—22no—
41C61×#518—22no—
42C61×#518C2211yescharacteristic
43C4×#41×C61—22no—
44C4×#41×C61C2212yes—
45C2×C4×D4×C61—22no—
46C2×C4×D4×C61—22no—
47C2×C4×D4×C61C2211yescharacteristic
48C22×D244C2311yescharacteristic
49C22×C22⋊D61—22no—
50C22×C4×D61—21no—
51#14519802—24no—
52#14519802C2×C418yescomplemented
53C2×#11758201—22no—
54C2×#11758199—22no—
55C2×#11758194C2312yes—
56C2×#11758194C2312yes—
57#14519773—22no—
58#14519773C2×C414yescomplemented
59C4×D244—22no—
60C4×D244—22no—
61C4×C22⋊D61—48no—
62C2×C4⋊Dic61C2311yescharacteristic
63C2×#11758196—22no—
64C2×C22⋊Dic61—22no—
65C2×#11758198—22no—
66C2×#11758198—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61—21no—
69C2×C4×Dic61C2311yescharacteristic
70C2×C4×Dic61C2311yescharacteristic
71#14519710—22no—
72#14519708—22no—
73#14519704—24no—
74#14519704C2×C418yescomplemented
75#14519701—22no—
76#14519698—22no—
77#14519697—22no—
78#14519697—22no—
79#14519694—22no—
80#14519694C2×C414yescomplemented
81#14519688—22no—
82C4×#92418—22no—
83H(5,𝔽2)×C61—24no—
84H(5,𝔽2)×C61—22no—
85H(5,𝔽2)×C61C2×C414yescomplemented
86C2×#41×C61—22no—
87C2×#41×C61C2312yes—
88C22×D4×C61—22no—
89C22×D4×C61—22no—
90C22×D4×C61C2311yescharacteristic
91C23×C4×C61—22no—
92C23×C4×C61D412yes—
93C4×Q8×C61—22no—
94C4×Q8×C61D412yescomplemented
95C4×Q8×C61D412yescomplemented
96C4×D4×C61—24no—
97C4×D4×C61—24no—
98C4×D4×C61—24no—
99C4×D4×C61—24no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C4×D4×C61—24no—
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61—22no—
106C4×D4×C61—22no—
107C4×D4×C61—22no—
108C4×D4×C61D412yescomplemented
109C4×D4×C61D412yescomplemented
110#117×C61—24no—
111#117×C61—22no—
112#117×C61—22no—
113#117×C61C2312yes—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—24no—
119C2×C22⋊C4×C61—22no—
120C2×C22⋊C4×C61D412yes—
121C2×C42×C61—22no—
122C2×C42×C61—22no—
123C2×C42×C61C2311yescharacteristic
124C24×C61—22no—
125C24×C61C2×D412yes—
126C23×D61—21no—
127#41×C61—28no—
128#41×C61—28no—
129#41×C61—22no—
130#41×C61—22no—
131#41×C61C22×C414yes—
132#41×C61#4114yes—
133C2×Q8×C61C2×D412yes—
134C2×D4×C61—24no—
135C2×D4×C61—28no—
136C2×D4×C61—28no—
137C2×D4×C61—28no—
138C2×D4×C61—22no—
139C2×D4×C61—28no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61C22×C412yes—
143C2×D4×C61C2×D412yes—
144C2×D4×C61#4112yes—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—24no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—44no—
155C22×C4×C61—84no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—28no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—44no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C2×D244—22no—
167C2×D244—22no—
168C2×D244—21no—
169C2×D244C22×C412yescomplemented
170C2×C4×D61—44no—
171C2×C4×D61—41no—
172C2×C4×D61—41no—
173C4⋊C4×C61—24no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61C2×D412yes—
178C4⋊C4×C61C2×D412yes—
179C22⋊C4×C61—24no—
180C22⋊C4×C61—24no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—24no—
185C42×C61—24no—
186C42×C61—22no—
187C42×C61—22no—
188C42×C61—22no—
189C42×C61C2×D412yes—
190C42×C61C2×D412yes—
191C22⋊Dic61—44no—
192#11758201—28no—
193#11758199—28no—
194#11758198—44no—
195#11758198—42no—
196C4⋊Dic61—22no—
197#11758196—44no—
198C4×Dic61—24no—
199C4×Dic61—21no—
200C4×Dic61—22no—
201C4×Dic61—42no—
202C4×Dic61C22×C412yescomplemented
203#11758194—22no—
204#11758194—22no—
205#11758194—22no—
206#11758194C22×C414yescomplemented
207C2×#92418—22no—
208C2×#92418—22no—
209C23×C61—28no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—42no—
214C23×C61—42no—
215C23×C61—82no—
216C23×C61—82no—
217C23×C61C4×D414yes—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—41no—
223C22×D61—41no—
224Q8×C61—22no—
225Q8×C61C4×D414yescomplemented
226D4×C61—216no—
227D4×C61—24no—
228D4×C61—24no—
229D4×C61—24no—
230D4×C61—22no—
231D4×C61—24no—
232D4×C61C4×D414yescomplemented
233C2×C4×C61—28no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—41no—
242C2×C4×C61—44no—
243C2×C4×C61—44no—
244C2×C4×C61—42no—
245C2×C4×C61—82no—
246C2×C4×C61—82no—
247C2×C4×C61—82no—
248C2×C4×C61—84no—
249C2×C4×C61—82no—
250C2×C4×C61#12012yes—
251C2×C4×C61#12011yescharacteristic
252C2×C4×C61#12011yescharacteristic
253C2×C4×C61C23×C411yescharacteristic
254C2×C4×C61C22×D412yes—
255C2×C4×C61C2×#4112yes—
256C2×C4×C61C2×#4111yescharacteristic
257C22⋊D61—416no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61—41no—
266D244—24no—
267D244—42no—
268C4×D61—82no—
269C4×D61—82no—
270#92418—24no—
271#92418—42no—
272C4×#453—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—24no—
276C22×C61—24no—
277C22×C61—44no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—82no—
283C22×C61—88no—
284C22×C61C2×C4×D411yescharacteristic
285C22×C61C2×#12011yescharacteristic
286C22×C61#52511yescharacteristic
287C2×D61—44no—
288C2×D61—42no—
289C2×D61—82no—
290C2×D61—81no—
291C2×D61—81no—
292C4×C61—21no—
293C4×C61—22no—
294C4×C61—24no—
295C4×C61—42no—
296C4×C61—42no—
297C4×C61—42no—
298C4×C61#45312yescomplemented
299C4×C61C2×C4×D412yes—
300C4×C61#52512yes—
301Dic61—24no—
302Dic61—42no—
303Dic61—81no—
304C4×H(5,𝔽2)D6111yescharacteristic, complemented
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×#100—611no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—44no—
318C2×C61—44no—
319C2×C61C4×#12011yescharacteristic
320C2×C61C2×#45311yescharacteristic
321C2×C61#301811yescharacteristic
322D61—82no—
323C2×H(5,𝔽2)C2×D6111yescharacteristic
324C2×AGL(1,ℤ/8)—612no—
325C2×#127—611no—
326#520—22no—
327#520C2×D6112yes—
328#518—22no—
329#518—22no—
330#518C2×D6111yescharacteristic
331C4×#41—22no—
332C4×#41C2×D6112yes—
333C2×C4×D4—22no—
334C2×C4×D4—22no—
335C2×C4×D4—611no—
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×#100—611no—
349C2×#100—611no—
350C4×M16—612no—
351#390—611no—
352#390—611no—
353#390—1222no—
354#384—611no—
355C43—611no—
356#343—612no—
357#339—612no—
358#339—612no—
359C61C4×#45311yescharacteristic, complemented, Sylow
360H(5,𝔽2)—24no—
361H(5,𝔽2)—22no—
362H(5,𝔽2)C4×D6114yescomplemented
363C2×#41—22no—
364C2×#41C22×D6112yes—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—611no—
368C22×D4—1222no—
369C22×D4C22×D6111yescharacteristic
370C23×C4—22no—
371C23×C4—1221no—
372C23×C4C22⋊D6112yes—
373AGL(1,ℤ/8)—618no—
374AGL(1,ℤ/8)—1224no—
375C2×SD16—1222no—
376C2×D8—1222no—
377C2×M16—612no—
378C2×M16—612no—
379#127—614no—
380#127—1222no—
381C4×Q8—22no—
382C4×Q8C22⋊D6112yescomplemented
383C4×Q8C22⋊D6112yescomplemented
384C4×D4—24no—
385C4×D4—24no—
386C4×D4—24no—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—24no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—2448no—
399C4×D4C22⋊D6112yescomplemented
400C4×D4C22⋊D6112yescomplemented
401#117—24no—
402#117—22no—
403#117—22no—
404#117C22×D6112yes—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—1222no—
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—1222no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1222no—
416C2×C22⋊C4C22⋊D6112yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—1221no—
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—614no—
433#100—1222no—
434#97—1222no—
435C4×C8—1222no—
436C24—22no—
437C24—1221no—
438C24C2×C22⋊D6112yes—
439#41—28no—
440#41—28no—
441#41—22no—
442#41—22no—
443#41C2×C4×D6114yes—
444#41#1175822214yes—
445C2×Q8C2×C22⋊D6112yes—
446C2×D4—24no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—22no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—612no—
455C2×D4—1228no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1221no—
459C2×D4—2444no—
460C2×D4—2444no—
461C2×D4C2×C4×D6112yes—
462C2×D4#1175822212yes—
463C2×D4C2×C22⋊D6112yes—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—44no—
474C22×C4—84no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—2444no—
479C22×C4—2441no—
480C22×C4—2441no—
481C22×C4C2×C22⋊D6111yescharacteristic
482C22×C4C2×C22⋊D6112yes—
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485SD16—1228no—
486D8—1228no—
487M16—614no—
488M16—1222no—
489M16—1222no—
490M16—1222no—
491C2×C8—1222no—
492C2×C8—1222no—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—1222no—
498C4⋊C4—2444no—
499C4⋊C4C2×C22⋊D6112yes—
500C4⋊C4C2×C22⋊D6112yes—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—24no—
507C22⋊C4—2444no—
508C22⋊C4—2444no—
509C22⋊C4—2442no—
510C42—24no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—612no—
515C42—1224no—
516C42—1221no—
517C42—1222no—
518C42—2442no—
519C42C2×C22⋊D6112yes—
520C42C2×C22⋊D6112yes—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—42no—
526C23—42no—
527C23—82no—
528C23—82no—
529C23—1222no—
530C23—2442no—
531C23—2442no—
532C23—2441no—
533C23—2441no—
534C23C4×C22⋊D6114yes—
535C23C22×C22⋊D6111yescharacteristic
536Q8—22no—
537Q8C4×C22⋊D6114yescomplemented
538D4—216no—
539D4—24no—
540D4—24no—
541D4—24no—
542D4—24no—
543D4—22no—
544D4—1224no—
545D4—24416no—
546D4—2442no—
547D4C4×C22⋊D6114yescomplemented
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—42no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—84no—
564C2×C4—82no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—4882no—
570C2×C4—4882no—
571C2×C4—2442no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4#1451974612yes—
576C2×C4#1451974611yescharacteristic
577C2×C4#1451974611yescharacteristic
578C2×C4C22×C4×D6111yescharacteristic
579C2×C4C22×C22⋊D6112yes—
580C2×C4C2×#1175822212yes—
581C2×C4C2×#1175822211yescharacteristic
582C8—1224no—
583C8—2442no—
584C22—21no—
585C22—21no—
586C22—24no—
587C22—24no—
588C22—44no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—88no—
595C22—4882no—
596C22—4881no—
597C22—4881no—
598C22—2444no—
599C22—2442no—
600C22C2×C4×C22⋊D6111yescharacteristic
601C22C2×#1451974611yescharacteristic
602C22#1684027311yescharacteristic
603C4—21no—
604C4—22no—
605C4—24no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—1224no—
610C4—4881no—
611C4—2442no—
612C4#1683993012yesdirect product factor
613C4C2×C4×C22⋊D6112yes—
614C4#1684027312yes—
615C2—21no—
616C2—21no—
617C2—44no—
618C2—44no—
619C2—4882no—
620C2C4×#1451974611yescharacteristic
621C2C2×#1683993011yescharacteristic
622C2#2145516811yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×H(5,𝔽2)×C61C2
socleC22×C61C2×#120
prime radicalC2×#16839930C2
cosocleC22×C4×C61C24
hypercenterC4×H(5,𝔽2)D61
hypocenterC61C4×#453
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C4×#14519802C2semidirect
3. C4×#14519773C2semidirect
4. #21446217C2semidirect
5. #21446195C2semidirect
6. #21446045C2semidirect
7. #21446029C2semidirect
8. #21445773C2semidirect
9. C4×#14519704C2semidirect
10. C4×#14519694C2semidirect
11. C4×H(5,𝔽2)×C61C2semidirect
14. C2×C4×D244C22semidirect
16. #16839930C4direct (N × H)
21. #16839805C22semidirect
24. #16839766C22semidirect
28. C4×#11758194C22semidirect
30. #16839663C22semidirect
32. #16839631C22semidirect
33. C42×Dic61C22semidirect
34. #16839531C22semidirect
35. #16839521C22semidirect
36. #16839521C22semidirect
52. #14519802C2×C4semidirect
58. #14519773C2×C4semidirect
74. #14519704C2×C4semidirect
80. #14519694C2×C4semidirect
85. H(5,𝔽2)×C61C2×C4semidirect
94. C4×Q8×C61D4semidirect
95. C4×Q8×C61D4semidirect
108. C4×D4×C61D4semidirect
109. C4×D4×C61D4semidirect
169. C2×D244C22×C4semidirect
202. C4×Dic61C22×C4semidirect
206. #11758194C22×C4semidirect
225. Q8×C61C4×D4semidirect
232. D4×C61C4×D4semidirect
298. C4×C61#453semidirect
304. C4×H(5,𝔽2)D61semidirect
359. C61C4×#453semidirect
362. H(5,𝔽2)C4×D61semidirect
382. C4×Q8C22⋊D61semidirect
383. C4×Q8C22⋊D61semidirect
399. C4×D4C22⋊D61semidirect
400. C4×D4C22⋊D61semidirect
537. Q8C4×C22⋊D61semidirect
547. D4C4×C22⋊D61semidirect
612. C4#16839930direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399302
C4×#145198022
C4×#145197732
#214462172
#214461952
#214460452
#214460292
#214457732
C4×#145197042
C4×#145196942
C4×H(5,𝔽2)×C612
C4×#45361