Finite Group Databasebeta

← C2×#21444786 #29652183

Subgroups — C2×#21444786 #29652183

Order 15616.

1480 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840339C211yesmaximal, characteristic
2C2×#16839901C211yesmaximal, characteristic, complemented
3C2×#16839681C211yesmaximal, characteristic, complemented
4#21444786C218yesmaximal, direct product factor
5C2×#16839497C211yesmaximal, characteristic, complemented
6C2×#16839496C211yesmaximal, characteristic, complemented
7C2×#16839487C211yesmaximal, characteristic, complemented
8C2×C61×#448C211yesmaximal, characteristic, complemented
9C22×#11758224—21no—
10C22×#11758201—21no—
11#16840339—22no—
12#16840339—22no—
13#16840339—22no—
14#16840339C2214yes—
15C2×#14519755—21no—
16C2×#14519754—21no—
17C2×#14519751C2211yescharacteristic
18C2×#14519750—21no—
19C2×#14519749—21no—
20C2×#14519749—21no—
21C22×#11758196—21no—
22C22×#11758196C2211yescharacteristic
23#16839901—22no—
24#16839901C2214yescomplemented
25C2×#14519701—21no—
26C2×C22⋊#92418C2211yescharacteristic
27#16839681—22no—
28#16839681C2214yescomplemented
29C2×#14519684—21no—
30C2×#14519684C2211yescharacteristic
31#16839497C2214yescomplemented
32#16839496C2214yescomplemented
33#16839487C2214yescomplemented
34C23×Q8×C61C2211yescharacteristic
35C22×SD16×C61—21no—
36C2×#121×C61C2211yescharacteristic
37C61×#448—22no—
38C61×#448C2214yescomplemented
39C2×#103×C61—21no—
40C2×C22⋊C8×C61C2211yescharacteristic
41C2×#11758224—24no—
42C2×#11758224—24no—
43C2×#11758224—44no—
44C2×#11758224—44no—
45C22×Dic122—21no—
46C22×D244D411yescharacteristic
47C22×C22⋊D61—21no—
48C22×C22⋊D61—21no—
49C22×C22⋊D61—21no—
50C23×Dic61—21no—
51C23×Dic61—21no—
52C23×Dic61D411yescharacteristic
53C23×Dic61D411yescharacteristic
54C22×C4×D61—21no—
55C2×#11758201—24no—
56C2×#11758201—44no—
57C22×#92418—21no—
58#14519755—24no—
59#14519755—24no—
60#14519754—24no—
61#14519754—24no—
62#14519751—21no—
63#14519751—21no—
64#14519751D412yes—
65#14519751C2312yes—
66#14519750—24no—
67#14519750—24no—
68#14519749—24no—
69#14519749—24no—
70#14519749—24no—
71#14519749—24no—
72C2×C4⋊Dic61D411yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—24no—
79C2×#11758196—44no—
80C2×#11758196D412yes—
81C2×#11758196C2312yes—
82C2×C22⋊Dic61—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85#14519701—24no—
86C22⋊#92418—21no—
87C22⋊#92418C2312yes—
88#14519684—21no—
89#14519684—24no—
90#14519684C2312yes—
91C22×Q8×C61—21no—
92C22×Q8×C61—21no—
93C22×Q8×C61—21no—
94C22×Q8×C61—21no—
95C22×Q8×C61—21no—
96C22×Q8×C61—44no—
97C22×Q8×C61C2312yes—
98C22×D4×C61—21no—
99C22×D4×C61D411yescharacteristic
100C23×C4×C61—21no—
101C23×C4×C61C2311yescharacteristic
102C2×SD16×C61—24no—
103C2×SD16×C61—44no—
104C22×C8×C61—21no—
105#121×C61—21no—
106#121×C61—21no—
107#121×C61D412yes—
108#121×C61C2312yes—
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C22⋊C4×C61—21no—
111#103×C61—24no—
112C22⋊C8×C61—21no—
113C22⋊C8×C61C2312yes—
114C24×C61—21no—
115C24×C61C2×D411yescharacteristic
116C23×D61—21no—
117C2×Q8×C61—24no—
118C2×Q8×C61—24no—
119C2×Q8×C61—22no—
120C2×Q8×C61—22no—
121C2×Q8×C61—44no—
122C2×Q8×C61—42no—
123C2×Q8×C61—42no—
124C2×Q8×C61—44no—
125C2×Q8×C61—44no—
126C2×Q8×C61—44no—
127C2×Q8×C61—41no—
128C2×Q8×C61—41no—
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61—21no—
132C2×D4×C61—42no—
133C2×D4×C61—42no—
134C2×D4×C61—42no—
135C2×D4×C61C2×D412yes—
136C22×C4×C61—24no—
137C22×C4×C61—21no—
138C22×C4×C61—22no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61—41no—
142C22×C4×C61—41no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2411yescharacteristic
149C2×C22⋊D61—24no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—24no—
153C2×C22⋊D61—44no—
154C2×C22⋊D61—42no—
155C2×C22⋊D61—42no—
156C2×C22⋊D61—82no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—24no—
161C22×Dic61—24no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—22no—
165C22×Dic61—21no—
166C22×Dic61—44no—
167C22×Dic61—42no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61SD1614yescomplemented
171C22×Dic61C2×D412yes—
172C22×Dic61C2×D412yes—
173#11758224—48no—
174#11758224—416no—
175#11758224—48no—
176C2×D244—21no—
177C2×D244—42no—
178C2×D244C2×D412yes—
179C2×C4×D61—24no—
180C2×C4×D61—44no—
181C2×Dic122—24no—
182C2×Dic122—44no—
183SD16×C61—48no—
184C2×C8×C61—22no—
185C2×C8×C61—42no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61C2×D412yes—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊Dic61—24no—
191#11758201—48no—
192#11758198—24no—
193#11758198—22no—
194#11758198—22no—
195C4⋊Dic61—21no—
196C4⋊Dic61C2×D412yes—
197#11758196—24no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—48no—
203C2×#92418—22no—
204C2×#92418—42no—
205C23×C61—22no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—42no—
211C23×C61#12011yescharacteristic
212C23×C61#12011yescharacteristic
213C23×C61C2×SD1612yes—
214C23×C61AGL(1,ℤ/8)12yes—
215C23×C61C22×D411yescharacteristic
216C22×D61—22no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220Q8×C61—24no—
221Q8×C61—24no—
222Q8×C61—42no—
223Q8×C61—42no—
224Q8×C61—44no—
225Q8×C61—44no—
226D4×C61—42no—
227D4×C61—42no—
228D4×C61—42no—
229D4×C61—44no—
230D4×C61—81no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—24no—
234C2×C4×C61—22no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—42no—
240C2×C4×C61—44no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—44no—
244C2×C4×C61#12011yescharacteristic
245C2×C4×C61#12011yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C22⋊D61—48no—
249C22⋊D61—42no—
250C22⋊D61—42no—
251C22⋊D61—44no—
252C22⋊D61—84no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—48no—
261C2×Dic61—42no—
262C2×Dic61—48no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—81no—
268C2×Dic61C2×SD1614yescomplemented
269D244—42no—
270D244—81no—
271C4×D61—48no—
272Dic122—48no—
273C8×C61—42no—
274#92418—42no—
275C2×#1604—611nomaximal, Sylow
276C22×C61—24no—
277C22×C61—24no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—42no—
283C22×C61—42no—
284C22×C61—42no—
285C22×C61—84no—
286C22×C61#45012yes—
287C22×C61#45012yes—
288C22×C61#45612yes—
289C22×C61B(4,𝔽2)12yes—
290C22×C61C2×#12011yescharacteristic
291C22×C61C22×SD1611yescharacteristic
292C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—84no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—42no—
302C4×C61—44no—
303Dic61—24no—
304Dic61—44no—
305Dic61—42no—
306Dic61—42no—
307C2×#537—611no—
308C2×#448—611no—
309C2×#448D6111yescharacteristic, complemented
310C2×#395—611no—
311#1604—618no—
312C2×#327—611no—
313C2×#327—611no—
314C2×#324—611no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—22no—
318C2×C61—82no—
319C2×C61#160414yescomplemented
320C2×C61C2×#45011yescharacteristic
321C2×C61C2×#45611yescharacteristic
322C2×C61C2×B(4,𝔽2)11yescharacteristic
323D61—82no—
324C22×#41—1221no—
325C23×Q8C2×D6111yescharacteristic
326C22×SD16—21no—
327C22×SD16—1221no—
328#537—614no—
329#537—1222no—
330#537—1222no—
331#537—1222no—
332C2×C22⋊Q8—1221no—
333C2×C22⋊Q8—1221no—
334C2×#121—611no—
335C2×#121—1221no—
336C2×#121—1221no—
337C2×#121—1221no—
338C2×#121C2×D6111yescharacteristic
339C22×C4⋊C4—611no—
340C22×C4⋊C4—1221no—
341#448—22no—
342#448—614no—
343#448—1222no—
344#448C2×D6114yescomplemented
345C2×#103—21no—
346C2×#103—1221no—
347C2×C22⋊C8—611no—
348C2×C22⋊C8C2×D6111yescharacteristic
349#395—614no—
350#395—1222no—
351C2×#95—611no—
352C2×#95—1221no—
353#327—614no—
354#327—614no—
355#324—614no—
356C61C2×#160411yescharacteristic, complemented, Sylow
357C2×#41—1224no—
358C2×#41—1224no—
359C2×#41—2444no—
360C2×#41—2444no—
361C22×Q8—21no—
362C22×Q8—21no—
363C22×Q8—21no—
364C22×Q8—21no—
365C22×Q8—21no—
366C22×Q8—44no—
367C22×Q8—1221no—
368C22×Q8C22×D6112yes—
369C22×D4—21no—
370C22×D4—611no—
371C22×D4—1221no—
372C22×D4—1221no—
373C22×D4—1221no—
374C22×D4C22⋊D6111yescharacteristic
375C23×C4—21no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—1221no—
379C23×C4—1221no—
380C23×C4—1221no—
381C23×C4C22×D6111yescharacteristic
382C2×SD16—24no—
383C2×SD16—44no—
384C2×SD16—1224no—
385C2×SD16—2444no—
386C22×C8—21no—
387C22×C8—1221no—
388C22⋊Q8—1224no—
389C22⋊Q8—1224no—
390C22⋊Q8—1224no—
391C22⋊Q8—1224no—
392#121—21no—
393#121—21no—
394#121—612no—
395#121—612no—
396#121—1224no—
397#121—1224no—
398#121—1224no—
399#121—1224no—
400#121—1224no—
401#121—1224no—
402#121—1221no—
403#121—1221no—
404#121C22⋊D6112yes—
405#121C22×D6112yes—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—612no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1224no—
415C2×C4⋊C4—2444no—
416C2×C4⋊C4C22⋊D6111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421#103—24no—
422#103—1224no—
423C22⋊C8—21no—
424C22⋊C8—612no—
425C22⋊C8—1221no—
426C22⋊C8C22×D6112yes—
427#95—612no—
428#95—1224no—
429#95—1221no—
430C24—21no—
431C24—1221no—
432C24D4×D6111yescharacteristic
433#41—2448no—
434#41—2448no—
435#41—24416no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—44no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—1224no—
449C2×Q8—2444no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—612no—
457C2×D4—1224no—
458C2×D4—1224no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—1221no—
462C2×D4—4882no—
463C2×D4—2442no—
464C2×D4—2444no—
465C2×D4—2442no—
466C2×D4—2442no—
467C2×D4C2×C22⋊D6112yes—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—612no—
476C22×C4—614no—
477C22×C4—612no—
478C22×C4—1224no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1222no—
482C22×C4—1221no—
483C22×C4—1224no—
484C22×C4—1224no—
485C22×C4—1222no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—2444no—
489C22×C4—2444no—
490C22×C4—2442no—
491C22×C4—2442no—
492C22×C4—2442no—
493C22×C4D4×D6111yescharacteristic
494C22×C4D4×D6111yescharacteristic
495C22×C4D4×D6111yescharacteristic
496C22×C4C2×C22⋊D6111yescharacteristic
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C23×D6111yescharacteristic
499SD16—48no—
500SD16—2448no—
501C2×C8—22no—
502C2×C8—42no—
503C2×C8—1222no—
504C2×C8—2442no—
505C4⋊C4—21no—
506C4⋊C4—612no—
507C4⋊C4—1224no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4—2448no—
514C4⋊C4C2×C22⋊D6112yes—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—1224no—
518C22⋊C4—1224no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—1222no—
528C23—2442no—
529C23—2442no—
530C23—2442no—
531C23#1451974511yescharacteristic
532C23#1451974511yescharacteristic
533C23SD16×D6112yes—
534C23#1451980412yes—
535C23C2×D4×D6111yescharacteristic
536Q8—24no—
537Q8—24no—
538Q8—42no—
539Q8—42no—
540Q8—44no—
541Q8—44no—
542Q8—2448no—
543D4—42no—
544D4—42no—
545D4—42no—
546D4—44no—
547D4—81no—
548D4—4881no—
549D4—4884no—
550D4—2442no—
551D4—2448no—
552D4—2442no—
553D4—2442no—
554D4—2444no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—614no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1224no—
572C2×C4—1224no—
573C2×C4—1224no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—4881no—
577C2×C4—2448no—
578C2×C4—2448no—
579C2×C4—2442no—
580C2×C4—2448no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4#1451974511yescharacteristic
586C2×C4#1451974511yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C22×C22⋊D6111yescharacteristic
589C8—42no—
590C8—2442no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—24no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—84no—
601C22—4884no—
602C22—2442no—
603C22—2442no—
604C22—2442no—
605C22#1683991112yes—
606C22#1683991112yes—
607C22#1683994312yes—
608C22#1683994812yes—
609C22C2×#1451974511yescharacteristic
610C22C2×SD16×D6111yescharacteristic
611C22C2×#1451980411yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—44no—
617C4—42no—
618C4—1224no—
619C4—2444no—
620C4—2442no—
621C4—2442no—
622C2—21no—
623C2—21no—
624C2—22no—
625C2—82no—
626C2—4882no—
627C2#2144478614yesdirect product factor
628C2C2×#1683991111yescharacteristic
629C2C2×#1683994311yescharacteristic
630C2C2×#1683994811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#448C2
socleC23×C61#120
prime radicalC2×#16840339C2
hypercenterC2×#448D61
hypocenterC61C2×#1604
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C2×#16839901C2semidirect
3. C2×#16839681C2semidirect
4. #21444786C2direct (N × H)
5. C2×#16839497C2semidirect
6. C2×#16839496C2semidirect
7. C2×#16839487C2semidirect
8. C2×C61×#448C2semidirect
24. #16839901C22semidirect
28. #16839681C22semidirect
31. #16839497C22semidirect
32. #16839496C22semidirect
33. #16839487C22semidirect
38. C61×#448C22semidirect
170. C22×Dic61SD16semidirect
268. C2×Dic61C2×SD16semidirect
309. C2×#448D61semidirect
319. C2×C61#1604semidirect
344. #448C2×D61semidirect
356. C61C2×#1604semidirect
627. C2#21444786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403392
C2×#168399012
C2×#168396812
#214447862
C2×#168394972
C2×#168394962
C2×#168394872
C2×C61×#4482
C2×#160461