Finite Group Databasebeta

← C4×#16839940 #29685898

Subgroups — C4×#16839940 #29685898

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
1C2×#16839940C211yesmaximal, characteristic
2C4×#14519807C212yesmaximal, complemented
3C4×#14519764C211yesmaximal, characteristic, complemented
4#21446207C211yesmaximal, characteristic, complemented
5#21446188C212yesmaximal, complemented
6#21446052C212yesmaximal, complemented
7#21446029C211yesmaximal, characteristic, complemented
8#21445773C211yesmaximal, characteristic
9C4×#14519704C212yesmaximal, complemented
10C4×#14519694C211yesmaximal, characteristic, complemented
11C4×H(5,𝔽2)×C61C211yesmaximal, characteristic
12C2×#14519807C2212yes—
13C2×#14519764C2211yescharacteristic
14C2×C4×Dic122C2211yescharacteristic, complemented
15#16839940C418yesdirect product factor
16#16839867—22no—
17#16839862—22no—
18C4×#11758202—22no—
19C4×#11758200—22no—
20#16839805C2212yescomplemented
21C2×#14519704C2212yes—
22C2×#14519704C2212yes—
23#16839770C2212yescomplemented
24#16839763C2212yes—
25C2×#14519694C2211yescharacteristic
26C2×#14519694C2211yescharacteristic
27C4×#11758194C2212yescomplemented
28#16839667C2211yescharacteristic, complemented
29#16839665C2211yescharacteristic
30#16839656—22no—
31#16839627C2211yescharacteristic, complemented
32C4×C22⋊Dic61—22no—
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×Dic122C2311yescharacteristic
49#14519807—24no—
50#14519807C2×C418yescomplemented
51C2×#11758202—22no—
52C2×#11758200—22no—
53C2×#11758194C2312yes—
54C2×#11758194C2312yes—
55#14519764—22no—
56#14519764C2×C414yescomplemented
57C4×Dic122—22no—
58C4×Dic122—22no—
59C2×C4⋊Dic61C2311yescharacteristic
60C2×#11758196—21no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—22no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61C2311yescharacteristic
67C2×C4×Dic61C2311yescharacteristic
68#14519710—22no—
69#14519708—22no—
70#14519704—24no—
71#14519704C2×C418yescomplemented
72#14519701—22no—
73#14519700—22no—
74#14519700—22no—
75#14519698—22no—
76#14519694—22no—
77#14519694C2×C414yescomplemented
78#14519688—22no—
79C4×#92418—22no—
80#14519684—22no—
81#14519684—22no—
82H(5,𝔽2)×C61—24no—
83H(5,𝔽2)×C61—22no—
84H(5,𝔽2)×C61C2×C414yes—
85C2×#41×C61—22no—
86C2×#41×C61C2312yes—
87C22×D4×C61—22no—
88C22×D4×C61—22no—
89C22×D4×C61C2311yescharacteristic
90C23×C4×C61—22no—
91C23×C4×C61D412yes—
92C4×Q8×C61—22no—
93C4×Q8×C61D412yes—
94C4×Q8×C61D412yes—
95C4×D4×C61—24no—
96C4×D4×C61—24no—
97C4×D4×C61—24no—
98C4×D4×C61—24no—
99C4×D4×C61—22no—
100C4×D4×C61—22no—
101C4×D4×C61—24no—
102C4×D4×C61—22no—
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61—22no—
106C4×D4×C61—22no—
107C4×D4×C61D412yes—
108C4×D4×C61D412yes—
109#117×C61—24no—
110#117×C61—22no—
111#117×C61—22no—
112#117×C61C2312yes—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—24no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61D412yes—
120C2×C42×C61—22no—
121C2×C42×C61—22no—
122C2×C42×C61C2311yescharacteristic
123C24×C61—22no—
124C24×C61C2×D412yes—
125#41×C61—28no—
126#41×C61—28no—
127#41×C61—22no—
128#41×C61—22no—
129#41×C61C22×C414yes—
130#41×C61#4114yes—
131C2×Q8×C61C2×D412yes—
132C2×D4×C61—24no—
133C2×D4×C61—28no—
134C2×D4×C61—28no—
135C2×D4×C61—28no—
136C2×D4×C61—22no—
137C2×D4×C61—28no—
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61C22×C412yes—
141C2×D4×C61C2×D412yes—
142C2×D4×C61#4112yes—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—24no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—44no—
153C22×C4×C61—84no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C2×Dic122—22no—
163C2×Dic122—22no—
164C2×Dic122—21no—
165C2×Dic122C22×C412yescomplemented
166C4⋊C4×C61—24no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61C2×D412yes—
171C4⋊C4×C61C2×D412yes—
172C22⋊C4×C61—24no—
173C22⋊C4×C61—24no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—24no—
178C42×C61—24no—
179C42×C61—22no—
180C42×C61—22no—
181C42×C61—22no—
182C42×C61C2×D412yes—
183C42×C61C2×D412yes—
184C22⋊Dic61—28no—
185C22⋊Dic61—44no—
186#11758202—28no—
187#11758200—28no—
188C4⋊Dic61—22no—
189#11758196—42no—
190C4×Dic61—21no—
191C4×Dic61—22no—
192C4×Dic61—42no—
193C4×Dic61—42no—
194C4×Dic61—41no—
195C4×Dic61—41no—
196C4×Dic61C22×C412yescomplemented
197#11758194—22no—
198#11758194—22no—
199#11758194—22no—
200#11758194C22×C414yescomplemented
201C2×#92418—22no—
202C2×#92418—22no—
203C23×C61—28no—
204C23×C61—22no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—82no—
210C23×C61—82no—
211C23×C61C4×D414yes—
212C23×C61C22×D411yescharacteristic
213Q8×C61—22no—
214Q8×C61C4×D414yes—
215D4×C61—216no—
216D4×C61—24no—
217D4×C61—24no—
218D4×C61—24no—
219D4×C61—22no—
220D4×C61—24no—
221D4×C61C4×D414yes—
222C2×C4×C61—28no—
223C2×C4×C61—22no—
224C2×C4×C61—24no—
225C2×C4×C61—24no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—41no—
231C2×C4×C61—44no—
232C2×C4×C61—44no—
233C2×C4×C61—42no—
234C2×C4×C61—82no—
235C2×C4×C61—82no—
236C2×C4×C61—82no—
237C2×C4×C61—84no—
238C2×C4×C61—82no—
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12012yes—
241C2×C4×C61#12011yescharacteristic
242C2×C4×C61C23×C411yescharacteristic
243C2×C4×C61C22×D412yes—
244C2×C4×C61C2×#4112yes—
245C2×C4×C61C2×#4111yescharacteristic
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—42no—
256C2×Dic61—41no—
257Dic122—24no—
258Dic122—42no—
259#92418—24no—
260#92418—42no—
261C4×#455—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—24no—
265C22×C61—24no—
266C22×C61—44no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—82no—
272C22×C61—88no—
273C22×C61C2×C4×D411yescharacteristic
274C22×C61C2×#12011yescharacteristic
275C22×C61#52511yescharacteristic
276C4×C61—21no—
277C4×C61—22no—
278C4×C61—24no—
279C4×C61—42no—
280C4×C61—42no—
281C4×C61—42no—
282C4×C61#45512yescomplemented
283C4×C61C2×C4×D412yes—
284C4×C61#52512yes—
285Dic61—42no—
286Dic61—42no—
287Dic61—42no—
288Dic61—81no—
289C4×H(5,𝔽2)D6111yescharacteristic
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×#100—611no—
300C2×C61—21no—
301C2×C61—21no—
302C2×C61—44no—
303C2×C61—44no—
304C2×C61C4×#12011yescharacteristic
305C2×C61C2×#45511yescharacteristic
306C2×C61#301811yescharacteristic
307C2×H(5,𝔽2)C2×D6111yescharacteristic
308C2×#137—612no—
309C2×#124—611no—
310#520—22no—
311#520C2×D6112yes—
312#518—22no—
313#518—22no—
314#518C2×D6111yescharacteristic
315C4×#41—22no—
316C4×#41C2×D6112yes—
317C2×C4×Q8—611no—
318C2×C4×D4—22no—
319C2×C4×D4—22no—
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#391—611no—
335#390—611no—
336#388—1222no—
337#382—611no—
338C4×C22⋊C4—1222no—
339C43—611no—
340#343—612no—
341#339—612no—
342#339—612no—
343C61C4×#45511yescharacteristic, complemented, Sylow
344H(5,𝔽2)—24no—
345H(5,𝔽2)—22no—
346H(5,𝔽2)C4×D6114yes—
347C2×#41—22no—
348C2×#41C22×D6112yes—
349C22×Q8—611no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4C22×D6111yescharacteristic
353C23×C4—22no—
354C23×C4C22⋊D6112yes—
355#137—618no—
356#137—1224no—
357C2×Q16—1222no—
358C2×SD16—1222no—
359C2×M16—612no—
360C2×M16—612no—
361#124—614no—
362#124—1222no—
363C4×Q8—22no—
364C4×Q8—1222no—
365C4×Q8—1222no—
366C4×Q8C22⋊D6112yes—
367C4×Q8C22⋊D6112yes—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—24no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—24no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4C22⋊D6112yes—
381C4×D4C22⋊D6112yes—
382#117—24no—
383#117—22no—
384#117—22no—
385#117C22×D6112yes—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—1222no—
395C2×C22⋊C4—1222no—
396C2×C22⋊C4C22⋊D6112yes—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—611no—
400C2×C42—611no—
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—614no—
414#100—1222no—
415#97—1222no—
416C4×C8—1222no—
417#95—1222no—
418#95—1222no—
419C24—22no—
420C24C2×C22⋊D6112yes—
421#41—28no—
422#41—28no—
423#41—22no—
424#41—22no—
425#41C2×C4×D6114yes—
426#41#1175822214yes—
427C2×Q8—612no—
428C2×Q8—1221no—
429C2×Q8—1222no—
430C2×Q8—1222no—
431C2×Q8C2×C22⋊D6112yes—
432C2×D4—24no—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—22no—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4C2×C4×D6112yes—
441C2×D4#1175822212yes—
442C2×D4C2×C22⋊D6112yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—44no—
453C22×C4—84no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
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—24no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—1222no—
475C4⋊C4—2442no—
476C4⋊C4C2×C22⋊D6112yes—
477C4⋊C4C2×C22⋊D6112yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—24no—
484C22⋊C4—1228no—
485C22⋊C4—2444no—
486C42—24no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—612no—
491C42—1221no—
492C42—1222no—
493C42—2442no—
494C42—2442no—
495C42—2441no—
496C42—2441no—
497C42C2×C22⋊D6112yes—
498C42C2×C22⋊D6112yes—
499C23—28no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—42no—
504C23—42no—
505C23—82no—
506C23—82no—
507C23C4×C22⋊D6114yes—
508C23C22×C22⋊D6111yescharacteristic
509Q8—22no—
510Q8—1224no—
511Q8—2442no—
512Q8C4×C22⋊D6114yes—
513D4—216no—
514D4—24no—
515D4—24no—
516D4—24no—
517D4—24no—
518D4—22no—
519D4C4×C22⋊D6114yes—
520C2×C4—28no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—84no—
536C2×C4—82no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—2442no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4#1451974612yes—
549C2×C4#1451974611yescharacteristic
550C2×C4#1451974611yescharacteristic
551C2×C4C22×C4×D6111yescharacteristic
552C2×C4C22×C22⋊D6112yes—
553C2×C4C2×#1175822212yes—
554C2×C4C2×#1175822211yescharacteristic
555C8—1224no—
556C8—2442no—
557C22—21no—
558C22—21no—
559C22—24no—
560C22—24no—
561C22—44no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—82no—
567C22—88no—
568C22C2×C4×C22⋊D6111yescharacteristic
569C22C2×#1451974611yescharacteristic
570C22#1684027311yescharacteristic
571C4—21no—
572C4—22no—
573C4—24no—
574C4—42no—
575C4—42no—
576C4—42no—
577C4—4881no—
578C4—2442no—
579C4—2442no—
580C4—2442no—
581C4#1683994012yesdirect product factor
582C4C2×C4×C22⋊D6112yes—
583C4#1684027312yes—
584C2—21no—
585C2—21no—
586C2—44no—
587C2—44no—
588C2C4×#1451974611yescharacteristic
589C2C2×#1683994011yescharacteristic
590C2#2145516811yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×H(5,𝔽2)×C61C2
socleC22×C61C2×#120
prime radicalC2×H(5,𝔽2)×C61C22
cosocleC22×C4×C61C24
hypercenterC4×H(5,𝔽2)D61
hypocenterC61C4×#455
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×#14519807C2semidirect
3. C4×#14519764C2semidirect
4. #21446207C2semidirect
5. #21446188C2semidirect
6. #21446052C2semidirect
7. #21446029C2semidirect
9. C4×#14519704C2semidirect
10. C4×#14519694C2semidirect
14. C2×C4×Dic122C22semidirect
15. #16839940C4direct (N × H)
20. #16839805C22semidirect
23. #16839770C22semidirect
27. C4×#11758194C22semidirect
28. #16839667C22semidirect
31. #16839627C22semidirect
33. C42×Dic61C22semidirect
34. #16839531C22semidirect
35. #16839521C22semidirect
36. #16839521C22semidirect
50. #14519807C2×C4semidirect
56. #14519764C2×C4semidirect
71. #14519704C2×C4semidirect
77. #14519694C2×C4semidirect
165. C2×Dic122C22×C4semidirect
196. C4×Dic61C22×C4semidirect
200. #11758194C22×C4semidirect
282. C4×C61#455semidirect
343. C61C4×#455semidirect
581. C4#16839940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399402
C4×#145198072
C4×#145197642
#214462072
#214461882
#214460522
#214460292
#214457732
C4×#145197042
C4×#145196942
C4×H(5,𝔽2)×C612
C4×#45561