Finite Group Databasebeta

← C2×#21446943 #29707243

Subgroups — C2×#21446943 #29707243

Order 15616.

3986 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519745C212yesmaximal, complemented
2C22×#14519692C212yesmaximal, complemented
3C2×#16839617C211yesmaximal, characteristic, complemented
4#21446943C218yesmaximal, direct product factor
5C2×#16839529C211yesmaximal, characteristic, complemented
6C2×C61×#534C211yesmaximal, characteristic, complemented
7C25×D61C2211yescharacteristic
8C23×C22⋊D61—22no—
9C2×#14519745—28no—
10C2×#14519745—24no—
11C2×#14519745—28no—
12C2×#14519745C2218yescomplemented
13C22×C22⋊Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2212yes—
15C22×#11758198—22no—
16C22×#11758198—22no—
17C2×#14519692—28no—
18C2×#14519692C2218yescomplemented
19#16839617—22no—
20#16839617C2214yescomplemented
21#16839529C2214yescomplemented
22C23×D4×C61C2212yes—
23C61×#534—24no—
24C61×#534—22no—
25C61×#534C2214yescomplemented
26C2×#123×C61—22no—
27C2×#121×C61—22no—
28C2×#120×C61—22no—
29C22×C22⋊C4×C61C2211yescharacteristic
30C24×D61—21no—
31C24×D61—22no—
32C24×D61—24no—
33C24×D61—22no—
34C24×D61—21no—
35C24×D61—22no—
36C24×D61—48no—
37C24×D61D414yescomplemented
38C24×D61C2312yes—
39C22×C22⋊D61—216no—
40C22×C22⋊D61—28no—
41C22×C22⋊D61—416no—
42C23×Dic61—22no—
43C23×Dic61—21no—
44#14519745—232no—
45#14519745—216no—
46#14519745—216no—
47C2×C22⋊Dic61—24no—
48C2×C22⋊Dic61—22no—
49C2×C22⋊Dic61—24no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61D418yescomplemented
52C2×C22⋊Dic61C2312yes—
53C2×C22⋊Dic61C2314yes—
54C2×#11758198—216no—
55C2×#11758198—28no—
56C2×#11758198—28no—
57C2×#11758198—48no—
58#14519692—216no—
59C25×C61D412yescomplemented
60C25×C61C2311yescharacteristic
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—24no—
64C22×D4×C61—24no—
65C22×D4×C61—24no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—24no—
69C22×D4×C61—22no—
70C22×D4×C61D414yescomplemented
71C22×D4×C61C2314yes—
72C23×C4×C61D412yescomplemented
73C23×C4×C61D412yescomplemented
74#123×C61—28no—
75#123×C61—28no—
76#121×C61—28no—
77#121×C61—28no—
78#120×C61—28no—
79#120×C61—28no—
80C2×C4⋊C4×C61—22no—
81C2×C22⋊C4×C61—24no—
82C2×C22⋊C4×C61—22no—
83C2×C22⋊C4×C61—22no—
84C2×C22⋊C4×C61D412yescomplemented
85C2×C22⋊C4×C61C2312yes—
86C24×C61—24no—
87C24×C61—22no—
88C24×C61—22no—
89C24×C61—24no—
90C24×C61—44no—
91C24×C61—48no—
92C24×C61C2×D412yes—
93C24×C61C2×D411yescharacteristic
94C24×C61C2×D412yes—
95C24×C61C2×D412yes—
96C24×C61C2×D414yes—
97C24×C61C2×D411yescharacteristic
98C24×C61C2×D414yescomplemented
99C24×C61#4112yes—
100C24×C61C2411yescharacteristic
101C23×D61—216no—
102C23×D61—28no—
103C23×D61—28no—
104C23×D61—24no—
105C23×D61—24no—
106C23×D61—22no—
107C23×D61—28no—
108C23×D61—24no—
109C23×D61—24no—
110C23×D61—22no—
111C23×D61—416no—
112C23×D61—48no—
113C23×D61—48no—
114C23×D61—416no—
115C23×D61—432no—
116C23×D61—416no—
117C23×D61—44no—
118C23×D61—48no—
119C23×D61—42no—
120C23×D61—41no—
121C23×D61—41no—
122C23×D61—44no—
123C23×D61—44no—
124C23×D61—42no—
125C23×D61—42no—
126C23×D61C2×D414yescomplemented
127C2×D4×C61—24no—
128C2×D4×C61—24no—
129C2×D4×C61—28no—
130C2×D4×C61—28no—
131C2×D4×C61—24no—
132C2×D4×C61—24no—
133C2×D4×C61—24no—
134C2×D4×C61—24no—
135C2×D4×C61—24no—
136C2×D4×C61—24no—
137C2×D4×C61—28no—
138C2×D4×C61—44no—
139C2×D4×C61—44no—
140C2×D4×C61—44no—
141C2×D4×C61—44no—
142C2×D4×C61—44no—
143C2×D4×C61—44no—
144C2×D4×C61—44no—
145C2×D4×C61—44no—
146C2×D4×C61—84no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—24no—
151C22×C4×C61—24no—
152C22×C4×C61—22no—
153C22×C4×C61—44no—
154C22×C4×C61C2×D414yescomplemented
155C22×C4×C61C2×D414yescomplemented
156C2×C22⋊D61—232no—
157C2×C22⋊D61—432no—
158C2×C22⋊D61—464no—
159C22×Dic61—28no—
160C22×Dic61—24no—
161C22×Dic61—22no—
162C22×Dic61—48no—
163C22×Dic61—44no—
164C22×Dic61—42no—
165C4⋊C4×C61—28no—
166C22⋊C4×C61—216no—
167C22⋊C4×C61—24no—
168C22⋊C4×C61—24no—
169C22⋊Dic61—28no—
170C22⋊Dic61—24no—
171C22⋊Dic61—24no—
172C22⋊Dic61—42no—
173C22⋊Dic61C2×D418yescomplemented
174#11758198—232no—
175#11758198—416no—
176C23×C61—24no—
177C23×C61—28no—
178C23×C61—24no—
179C23×C61—24no—
180C23×C61—24no—
181C23×C61—42no—
182C23×C61—44no—
183C23×C61—44no—
184C23×C61—48no—
185C23×C61—44no—
186C23×C61—42no—
187C23×C61—48no—
188C23×C61—416no—
189C23×C61—44no—
190C23×C61—44no—
191C23×C61—48no—
192C23×C61—84no—
193C23×C61—88no—
194C23×C61#12014yes—
195C23×C61#12012yes—
196C23×C61#12011yescharacteristic
197C23×C61#12014yes—
198C23×C61#12011yescharacteristic
199C23×C61#12112yes—
200C23×C61#12114yes—
201C23×C61#12112yes—
202C23×C61#12114yes—
203C23×C61#12712yes—
204C23×C61#12712yes—
205C23×C61C22×D412yes—
206C23×C61C22×D411yescharacteristic
207C23×C61C22×D411yescharacteristic
208C23×C61C22×D412yes—
209C23×C61C2×#4111yescharacteristic
210C22×D61—28no—
211C22×D61—216no—
212C22×D61—232no—
213C22×D61—216no—
214C22×D61—28no—
215C22×D61—24no—
216C22×D61—48no—
217C22×D61—432no—
218C22×D61—416no—
219C22×D61—416no—
220C22×D61—48no—
221C22×D61—44no—
222C22×D61—48no—
223C22×D61—48no—
224C22×D61—416no—
225C22×D61—416no—
226C22×D61—416no—
227C22×D61—48no—
228C22×D61—432no—
229C22×D61—432no—
230C22×D61—416no—
231C22×D61—42no—
232C22×D61—44no—
233C22×D61—42no—
234C22×D61—48no—
235C22×D61—44no—
236C22×D61—44no—
237C22×D61—48no—
238D4×C61—44no—
239D4×C61—44no—
240D4×C61—44no—
241D4×C61—44no—
242D4×C61—48no—
243D4×C61—48no—
244D4×C61—88no—
245C2×C4×C61—24no—
246C2×C4×C61—24no—
247C2×C4×C61—24no—
248C2×C4×C61—24no—
249C2×C4×C61—44no—
250C2×C4×C61—44no—
251C2×C4×C61—44no—
252C2×C4×C61—44no—
253C2×C4×C61—82no—
254C22⋊D61—464no—
255C2×Dic61—28no—
256C2×Dic61—48no—
257C2×Dic61—416no—
258C2×Dic61—44no—
259C2×Dic61—42no—
260C2×Dic61—84no—
261C2×#2021—611nomaximal, Sylow
262C22×C61—22no—
263C22×C61—24no—
264C22×C61—22no—
265C22×C61—24no—
266C22×C61—28no—
267C22×C61—24no—
268C22×C61—24no—
269C22×C61—28no—
270C22×C61—44no—
271C22×C61—42no—
272C22×C61—44no—
273C22×C61—42no—
274C22×C61—41no—
275C22×C61—42no—
276C22×C61—41no—
277C22×C61—48no—
278C22×C61—44no—
279C22×C61—48no—
280C22×C61—84no—
281C22×C61—88no—
282C22×C61—88no—
283C22×C61#39214yes—
284C22×C61#39212yes—
285C22×C61#39212yes—
286C22×C61B(4,𝔽2)14yes—
287C22×C61C2×#12012yes—
288C22×C61C2×#12011yescharacteristic
289C22×C61C2×#12111yescharacteristic
290C22×C61C2×#12112yes—
291C22×C61C2×#12711yescharacteristic
292C2×D61—216no—
293C2×D61—28no—
294C2×D61—48no—
295C2×D61—48no—
296C2×D61—44no—
297C2×D61—416no—
298C2×D61—432no—
299C2×D61—416no—
300C2×D61—44no—
301C2×D61—48no—
302C2×D61—416no—
303C4×C61—44no—
304C4×C61—44no—
305Dic61—48no—
306Dic61—82no—
307C2×#534D6111yescharacteristic, complemented
308C22×#120—612no—
309C22×#99—612no—
310C2×#379—611no—
311#2021—618no—
312C2×#342—611no—
313C2×C61—22no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61—22no—
317C2×C61—24no—
318C2×C61—22no—
319C2×C61—84no—
320C2×C61#202114yescomplemented
321C2×C61C2×#39211yescharacteristic
322C2×C61C2×B(4,𝔽2)12yes—
323D61—48no—
324C26—611no—
325C23×D4—1222no—
326C23×D4C2×D6112yes—
327#534—24no—
328#534—22no—
329#534C2×D6114yescomplemented
330C2×#123—22no—
331C2×#121—22no—
332C2×#120—22no—
333C2×#120—618no—
334C2×#120—1228no—
335C2×#120—1228no—
336C2×#120—1224no—
337C22×C22⋊C4—612no—
338C22×C22⋊C4—611no—
339C22×C22⋊C4—1222no—
340C22×C22⋊C4—1222no—
341C22×C22⋊C4C2×D6111yescharacteristic
342C2×#99—618no—
343C2×#99—1228no—
344#379—614no—
345#379—1222no—
346#342—614no—
347C61C2×#202111yescharacteristic, complemented, Sylow
348C25—614no—
349C25—612no—
350C25—1221no—
351C25—1222no—
352C25—1224no—
353C25—1222no—
354C25—1222no—
355C25—1221no—
356C25—2448no—
357C25C22⋊D6112yescomplemented
358C25C22×D6111yescharacteristic
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—12216no—
369C22×D4—1228no—
370C22×D4—24416no—
371C22×D4C22⋊D6114yescomplemented
372C22×D4C22×D6114yes—
373C23×C4—1222no—
374C23×C4—1221no—
375C23×C4C22⋊D6112yescomplemented
376C23×C4C22⋊D6112yescomplemented
377#123—28no—
378#123—28no—
379#121—28no—
380#121—28no—
381#120—28no—
382#120—28no—
383#120—12216no—
384#120—12216no—
385#120—12232no—
386C2×C4⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—618no—
391C2×C22⋊C4—614no—
392C2×C22⋊C4—612no—
393C2×C22⋊C4—12216no—
394C2×C22⋊C4—1224no—
395C2×C22⋊C4—1222no—
396C2×C22⋊C4—1228no—
397C2×C22⋊C4—1224no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1228no—
400C2×C22⋊C4—2448no—
401C2×C22⋊C4C22⋊D6112yescomplemented
402C2×C22⋊C4C22×D6112yes—
403#99—12216no—
404C24—24no—
405C24—22no—
406C24—22no—
407C24—24no—
408C24—44no—
409C24—48no—
410C24—614no—
411C24—1228no—
412C24—12216no—
413C24—1222no—
414C24—1224no—
415C24—1228no—
416C24—1224no—
417C24—1224no—
418C24—1222no—
419C24—1228no—
420C24—1224no—
421C24—2444no—
422C24—2448no—
423C24—24416no—
424C24—2448no—
425C24—24432no—
426C24—24416no—
427C24—2448no—
428C24—24416no—
429C24—2442no—
430C24—2441no—
431C24—2441no—
432C24—2444no—
433C24—2444no—
434C24—2442no—
435C24—2442no—
436C24D4×D6112yes—
437C24D4×D6114yes—
438C24#1175822412yes—
439C24C2×C22⋊D6112yes—
440C24C2×C22⋊D6111yescharacteristic
441C24C2×C22⋊D6112yes—
442C24C2×C22⋊D6111yescharacteristic
443C24C2×C22⋊D6114yescomplemented
444C24C23×D6111yescharacteristic
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—28no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—84no—
465C2×D4—12232no—
466C2×D4—24432no—
467C2×D4—24464no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—44no—
475C22×C4—1224no—
476C22×C4—1228no—
477C22×C4—1222no—
478C22×C4—2444no—
479C22×C4—2442no—
480C22×C4—2448no—
481C22×C4C2×C22⋊D6114yescomplemented
482C22×C4C2×C22⋊D6114yescomplemented
483C4⋊C4—28no—
484C22⋊C4—216no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—618no—
488C22⋊C4—12232no—
489C22⋊C4—1224no—
490C22⋊C4—1228no—
491C22⋊C4—1224no—
492C22⋊C4—24416no—
493C22⋊C4—2442no—
494C23—24no—
495C23—28no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—48no—
500C23—44no—
501C23—44no—
502C23—42no—
503C23—44no—
504C23—42no—
505C23—48no—
506C23—416no—
507C23—48no—
508C23—44no—
509C23—44no—
510C23—84no—
511C23—88no—
512C23—1228no—
513C23—12232no—
514C23—12216no—
515C23—12216no—
516C23—1228no—
517C23—1224no—
518C23—24416no—
519C23—24416no—
520C23—24432no—
521C23—2448no—
522C23—2444no—
523C23—2448no—
524C23—2448no—
525C23—24416no—
526C23—2448no—
527C23—24416no—
528C23—2448no—
529C23—24432no—
530C23—24416no—
531C23—24432no—
532C23—24416no—
533C23—2448no—
534C23—2442no—
535C23—2444no—
536C23—2442no—
537C23—2448no—
538C23—2444no—
539C23—2444no—
540C23#1451974514yes—
541C23#1451974514yes—
542C23#1451974612yes—
543C23#1451974611yescharacteristic
544C23#1451974611yescharacteristic
545C23#1451974812yes—
546C23#1451974812yes—
547C23#1451974914yes—
548C23#1451974914yes—
549C23#1451977312yes—
550C23#1451977312yes—
551C23C2×D4×D6111yescharacteristic
552C23C2×D4×D6112yes—
553C23C22×C22⋊D6112yes—
554C23C22×C22⋊D6111yescharacteristic
555C23C2×#1175822411yescharacteristic
556D4—44no—
557D4—44no—
558D4—44no—
559D4—44no—
560D4—48no—
561D4—48no—
562D4—88no—
563D4—24464no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—82no—
573C2×C4—1228no—
574C2×C4—4884no—
575C2×C4—2444no—
576C2×C4—2442no—
577C2×C4—24416no—
578C2×C4—2448no—
579C22—24no—
580C22—28no—
581C22—28no—
582C22—24no—
583C22—22no—
584C22—22no—
585C22—24no—
586C22—24no—
587C22—42no—
588C22—41no—
589C22—41no—
590C22—44no—
591C22—42no—
592C22—44no—
593C22—42no—
594C22—48no—
595C22—44no—
596C22—48no—
597C22—84no—
598C22—88no—
599C22—88no—
600C22—12216no—
601C22—1228no—
602C22—2448no—
603C22—2448no—
604C22—24416no—
605C22—24432no—
606C22—2444no—
607C22—24416no—
608C22—24416no—
609C22—2444no—
610C22—2448no—
611C22#1683967014yes—
612C22#1683967012yes—
613C22#1683967012yes—
614C22#1683994914yes—
615C22C2×#1451974512yes—
616C22C2×#1451974611yescharacteristic
617C22C2×#1451974811yescharacteristic
618C22C2×#1451974912yes—
619C22C2×#1451977311yescharacteristic
620C4—44no—
621C4—44no—
622C4—4882no—
623C4—2448no—
624C2—21no—
625C2—22no—
626C2—22no—
627C2—24no—
628C2—21no—
629C2—22no—
630C2—84no—
631C2—2448no—
632C2#2144694314yesdirect product factor
633C2C2×#1683967011yescharacteristic
634C2C2×#1683994912yes—
subgroupG/H
centerC23#14519746
commutator, cosocleC24×C61C24
FrattiniC24C23×D61
FittingC2×C61×#534C2
socleC23×C61#120
hypercenterC2×#534D61
hypocenterC61C2×#2021
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C22×#14519745C2semidirect
2. C22×#14519692C2semidirect
3. C2×#16839617C2semidirect
4. #21446943C2direct (N × H)
5. C2×#16839529C2semidirect
6. C2×C61×#534C2semidirect
12. C2×#14519745C22semidirect
18. C2×#14519692C22semidirect
20. #16839617C22semidirect
21. #16839529C22semidirect
25. C61×#534C22semidirect
37. C24×D61D4semidirect
51. C2×C22⋊Dic61D4semidirect
59. C25×C61D4semidirect
70. C22×D4×C61D4semidirect
72. C23×C4×C61D4semidirect
73. C23×C4×C61D4semidirect
84. C2×C22⋊C4×C61D4semidirect
98. C24×C61C2×D4semidirect
126. C23×D61C2×D4semidirect
154. C22×C4×C61C2×D4semidirect
155. C22×C4×C61C2×D4semidirect
173. C22⋊Dic61C2×D4semidirect
307. C2×#534D61semidirect
320. C2×C61#2021semidirect
329. #534C2×D61semidirect
347. C61C2×#2021semidirect
357. C25C22⋊D61semidirect
371. C22×D4C22⋊D61semidirect
375. C23×C4C22⋊D61semidirect
376. C23×C4C22⋊D61semidirect
401. C2×C22⋊C4C22⋊D61semidirect
443. C24C2×C22⋊D61semidirect
481. C22×C4C2×C22⋊D61semidirect
482. C22×C4C2×C22⋊D61semidirect
632. C2#21446943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197452
C22×#145196922
C2×#168396172
#214469432
C2×#168395292
C2×C61×#5342
C2×#202161