Finite Group Databasebeta

← C2×#20243618 #26217137

Subgroups — C2×#20243618 #26217137

Order 12032.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689603C211yesmaximal, characteristic
2C22×#13093950C211yesmaximal, characteristic
3C2×#15689122C211yesmaximal, characteristic
4C2×#15688988C211yesmaximal, characteristic, complemented
5#20243618C218yesmaximal, direct product factor
6C2×#15688891C211yesmaximal, characteristic, complemented
7C2×#15688882C211yesmaximal, characteristic, complemented
8C2×C47×#428C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689603—22no—
12#15689603—22no—
13#15689603—22no—
14#15689603C2214yes—
15C2×C4×Dic94—21no—
16C2×C4×D188—21no—
17C2×(C22⋊D47)⋊C4—22no—
18C2×#13093982—21no—
19C22×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊C4×D47—21no—
21C22×C4×Dic47C2211yescharacteristic
22C2×#13093950C418yescomplemented
23C2×#13093950C2214yes—
24#15689122—22no—
25#15689122C2214yes—
26C2×#13093947—21no—
27C2×#13093944—21no—
28#15688988—22no—
29#15688988C2214yescomplemented
30C2×C47⋊#95—22no—
31#15688891C2214yescomplemented
32#15688882C2214yescomplemented
33C22×M16×C47C2211yescharacteristic
34C2×#117×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C47×#428—22no—
37C47×#428C2214yescomplemented
38C2×#107×C47—21no—
39C2×#106×C47—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—22no—
43C2×#10625350—22no—
44C2×#10625350C2×C414yes—
45C2×#10625350D412yes—
46C2×#10625350Q814yes—
47C2×#10625350C2312yes—
48C22×Dic94D411yescharacteristic
49C22×D188D411yescharacteristic
50C22×C22⋊D47—21no—
51C23×Dic47—21no—
52C23×Dic47D412yes—
53C22×C4×D47—21no—
54C22×C4×D47—22no—
55C2×#10625329—21no—
56C2×#10625329—22no—
57C2×#10625329—22no—
58C2×#10625329C2312yes—
59C22×C47⋊C8—21no—
60C4×Dic94—24no—
61C4×Dic94—24no—
62C4×D188—24no—
63C4×D188—24no—
64(C22⋊D47)⋊C4—28no—
65(C22⋊D47)⋊C4—28no—
66#13093982—24no—
67#13093982—24no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47D412yes—
73C2×C4⋊Dic47C2312yes—
74C2×Dic47⋊C4—22no—
75C4⋊C4×D47—24no—
76C4⋊C4×D47—24no—
77C2×(C2×D47)⋊C4—22no—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47C2×C414yescomplemented
82C2×C4×Dic47C2312yes—
83#13093950C2×C4116yescomplemented
84#13093947—24no—
85#13093944—24no—
86C47⋊#95—28no—
87C23×C4×C47—21no—
88C23×C4×C47C2311yescharacteristic
89C2×M16×C47—21no—
90C2×M16×C47—22no—
91C2×M16×C47C2×C414yescomplemented
92C2×M16×C47C2312yes—
93C22×C8×C47—21no—
94#117×C47—21no—
95#117×C47—21no—
96#117×C47D412yes—
97#117×C47C2312yes—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47D411yescharacteristic
104C2×C4⋊C4×C47D411yescharacteristic
105C2×C4⋊C4×C47C2312yes—
106C2×C22⋊C4×C47—21no—
107C2×C42×C47—21no—
108#107×C47—24no—
109#106×C47—24no—
110C24×C47C2×D411yescharacteristic
111C23×D47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—44no—
116C22×C4×C47—41no—
117C22×C4×C47—41no—
118C22×C4×C47C22×C412yes—
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×Q812yes—
125C22×C4×C47#4112yes—
126C22×C4×C47#4112yes—
127C22×C4×C47C2411yescharacteristic
128C2×C22⋊D47—24no—
129C2×C22⋊D47—22no—
130C2×C22⋊D47—24no—
131C2×C22⋊D47—22no—
132C22×Dic47—21no—
133C22×Dic47—24no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—42no—
138C22×Dic47—42no—
139C22×Dic47—44no—
140C22×Dic47C2×D414yes—
141#10625350—24no—
142#10625350—24no—
143#10625350—24no—
144#10625350—24no—
145#10625350—24no—
146#10625350—22no—
147#10625350—22no—
148#10625350C4⋊C418yes—
149#10625350C22×C414yes—
150#10625350C2×Q814yes—
151C2×D188—21no—
152C2×D188—22no—
153C2×D188C4⋊C414yes—
154C2×D188C2×D412yes—
155C2×C4×D47—24no—
156C2×C4×D47—22no—
157C2×C4×D47—24no—
158C2×C4×D47—22no—
159C2×C4×D47—28no—
160C2×C4×D47—84no—
161C2×Dic94—21no—
162C2×Dic94—22no—
163C2×Dic94C4⋊C414yes—
164C2×Dic94C2×D412yes—
165M16×C47—24no—
166M16×C47—22no—
167M16×C47C22×C414yescomplemented
168C2×C8×C47—24no—
169C2×C8×C47—22no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—41no—
175C4⋊C4×C47—41no—
176C4⋊C4×C47C2×D412yes—
177C4⋊C4×C47C2×D412yes—
178C22⋊C4×C47—22no—
179C22⋊C4×C47—22no—
180C42×C47—22no—
181C42×C47—22no—
182(C2×D47)⋊C4—28no—
183C4⋊Dic47—22no—
184C4⋊Dic47—22no—
185C4⋊Dic47—22no—
186C4⋊Dic47—22no—
187Dic47⋊C4—28no—
188C4×Dic47—28no—
189C4×Dic47—24no—
190C4×Dic47—22no—
191C4×Dic47C22×C414yescomplemented
192#10625329—22no—
193#10625329—22no—
194#10625329—42no—
195C2×C47⋊C8—22no—
196C2×C47⋊C8—42no—
197C23×C47—22no—
198C23×C47—22no—
199C23×C47C4×D412yes—
200C23×C47#12011yescharacteristic
201C23×C47#12011yescharacteristic
202C23×C47C22⋊Q812yes—
203C23×C47C22×D411yescharacteristic
204C22×D47—22no—
205C22×D47—24no—
206C22×D47—42no—
207C22×D47—42no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—44no—
213C2×C4×C47—42no—
214C2×C4×C47—82no—
215C2×C4×C47—82no—
216C2×C4×C47C2×C4⋊C412yes—
217C2×C4×C47C2×C4⋊C412yes—
218C2×C4×C47C4×D412yes—
219C2×C4×C47C4×D412yes—
220C2×C4×C47C4×D412yes—
221C2×C4×C47#12011yescharacteristic
222C2×C4×C47#12011yescharacteristic
223C2×C4×C47C22⋊Q812yes—
224C2×C4×C47C22⋊Q812yes—
225C2×C4×C47C22⋊Q812yes—
226C2×C4×C47#12312yes—
227C2×C4×C47#12312yes—
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C22×D411yescharacteristic
230C2×C4×C47C22×D411yescharacteristic
231C2×C4×C47C22×Q811yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C22⋊D47—24no—
235C22⋊D47—24no—
236C22⋊D47—28no—
237C2×Dic47—22no—
238C2×Dic47—24no—
239C2×Dic47—24no—
240C2×Dic47—24no—
241C2×Dic47—48no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—44no—
245C2×Dic47—44no—
246C2×Dic47—82no—
247D188—22no—
248D188—24no—
249D188C2×C4⋊C414yes—
250C4×D47—24no—
251C4×D47—24no—
252C4×D47—28no—
253C4×D47—88no—
254Dic94—22no—
255Dic94—24no—
256Dic94C2×C4⋊C414yes—
257C8×C47—24no—
258C47⋊C8—42no—
259C2×#1860—471nomaximal, Sylow
260C22×C47—24no—
261C22×C47—24no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—21no—
265C22×C47—21no—
266C22×C47#38512yes—
267C22×C47#38512yes—
268C22×C47#45412yes—
269C22×C47#45512yes—
270C22×C47C2×C4×D411yescharacteristic
271C22×C47C2×#12011yescharacteristic
272C22×C47C2×C22⋊Q811yescharacteristic
273C2×D47—24no—
274C2×D47—48no—
275C2×D47—42no—
276C2×D47—42no—
277C4×C47—42no—
278C4×C47—42no—
279C4×C47—82no—
280C4×C47#38512yes—
281C4×C47#38512yes—
282C4×C47C22×C4⋊C411yescharacteristic
283C4×C47C2×C4×D411yescharacteristic
284C4×C47C2×C22⋊Q811yescharacteristic
285C4×C47C2×#12311yescharacteristic
286Dic47—24no—
287Dic47—44no—
288Dic47—44no—
289C2×#520—471no—
290C2×#428D4711yescharacteristic, complemented
291C22×#104—471no—
292C2×#417—471no—
293C2×#382—471no—
294#1860—478no—
295C2×#343—471no—
296C2×#339—471no—
297C2×C47—21no—
298C2×C47—21no—
299C2×C47—22no—
300C2×C47#186014yescomplemented
301C2×C47C2×#38511yescharacteristic
302C2×C47C2×#45511yescharacteristic
303C2×C47C2×#45411yescharacteristic
304D47—44no—
305C22×#41—471no—
306C22×M16—471no—
307C22×M16C2×D4711yescharacteristic
308#520—474no—
309#520—942no—
310#520—942no—
311#520—942no—
312C2×C4×Q8—941no—
313C2×C4×D4—941no—
314C2×C4×D4—942no—
315C2×#117—941no—
316C2×#117C2×D4711yescharacteristic
317C22×C4⋊C4—471no—
318C22×C4⋊C4—941no—
319C22×C4⋊C4C2×D4711yescharacteristic
320C22×C42—471no—
321#428—22no—
322#428C2×D4714yescomplemented
323C2×#107—21no—
324C2×#106—21no—
325C2×#104—478no—
326C2×#104—474no—
327#417—474no—
328#417—942no—
329C2×#103—941no—
330C2×#102—941no—
331#382—474no—
332#382—942no—
333C2×#95—942no—
334#343—474no—
335#339—474no—
336C47C2×#186011yescharacteristic, complemented, Sylow
337C2×#41—474no—
338C2×#41—472no—
339C2×#41—474no—
340C2×#41—472no—
341C2×#41—942no—
342C2×#41—941no—
343C2×#41—942no—
344C2×#41—941no—
345C22×Q8—471no—
346C22×D4—471no—
347C22×D4—941no—
348C23×C4—21no—
349C23×C4—472no—
350C23×C4—942no—
351C23×C4—941no—
352C23×C4—941no—
353C23×C4C22×D4711yescharacteristic
354C2×M16—22no—
355C2×M16—21no—
356C2×M16—472no—
357C2×M16—941no—
358C2×M16—942no—
359C2×M16—942no—
360C2×M16C4×D4714yescomplemented
361C2×M16C22×D4712yes—
362C22×C8—21no—
363C22×C8—941no—
364C4×Q8—944no—
365C4×Q8—944no—
366C4×D4—944no—
367C4×D4—944no—
368C4×D4—948no—
369C4×D4—948no—
370#117—21no—
371#117—21no—
372#117—944no—
373#117—944no—
374#117C22⋊D4712yes—
375#117C22×D4712yes—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—472no—
382C2×C4⋊C4—472no—
383C2×C4⋊C4—944no—
384C2×C4⋊C4—942no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—941no—
389C2×C4⋊C4—944no—
390C2×C4⋊C4C22⋊D4711yescharacteristic
391C2×C4⋊C4C22⋊D4711yescharacteristic
392C2×C4⋊C4C22×D4712yes—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—942no—
395C2×C42—21no—
396C2×C42—474no—
397C2×C42—472no—
398C2×C42—942no—
399C2×C42—941no—
400C2×C42—942no—
401#107—24no—
402#106—24no—
403#104—4716no—
404#103—944no—
405#102—944no—
406#95—948no—
407C24—941no—
408C24D4×D4711yescharacteristic
409#41—478no—
410#41—474no—
411#41—474no—
412#41—944no—
413#41—944no—
414#41—944no—
415#41—944no—
416#41—944no—
417#41—942no—
418#41—942no—
419C2×Q8—474no—
420C2×Q8—472no—
421C2×Q8—941no—
422C2×Q8—942no—
423C2×D4—474no—
424C2×D4—472no—
425C2×D4—944no—
426C2×D4—942no—
427C2×D4—944no—
428C2×D4—942no—
429C2×D4—941no—
430C2×D4—942no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—474no—
438C22×C4—948no—
439C22×C4—941no—
440C22×C4—944no—
441C22×C4—942no—
442C22×C4—944no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—944no—
446C22×C4—942no—
447C22×C4—942no—
448C22×C4—3764no—
449C22×C4—1884no—
450C22×C4—1882no—
451C22×C4—1882no—
452C22×C4C2×C4×D4712yes—
453C22×C4#1062535012yes—
454C22×C4D4×D4711yescharacteristic
455C22×C4D4×D4711yescharacteristic
456C22×C4D4×D4711yescharacteristic
457C22×C4Q8×D4712yes—
458C22×C4#1062535412yes—
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C23×D4711yescharacteristic
462M16—24no—
463M16—22no—
464M16—942no—
465M16—942no—
466M16—1882no—
467M16C2×C4×D4714yescomplemented
468C2×C8—24no—
469C2×C8—22no—
470C2×C8—942no—
471C2×C8—1882no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—948no—
479C4⋊C4—942no—
480C4⋊C4—942no—
481C4⋊C4—942no—
482C4⋊C4—942no—
483C4⋊C4C2×C22⋊D4712yes—
484C4⋊C4C2×C22⋊D4712yes—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—948no—
488C42—22no—
489C42—22no—
490C42—474no—
491C42—948no—
492C42—944no—
493C42—942no—
494C23—22no—
495C23—22no—
496C23—944no—
497C23—942no—
498C23—1882no—
499C23—1882no—
500C23#1309398612yes—
501C23#1309399211yescharacteristic
502C23#1309399211yescharacteristic
503C23#1309400212yes—
504C23C2×D4×D4711yescharacteristic
505Q8—474no—
506Q8—944no—
507Q8—942no—
508D4—474no—
509D4—948no—
510D4—944no—
511D4—944no—
512D4—944no—
513D4—942no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—944no—
523C2×C4—942no—
524C2×C4—948no—
525C2×C4—944no—
526C2×C4—944no—
527C2×C4—944no—
528C2×C4—944no—
529C2×C4—3768no—
530C2×C4—3762no—
531C2×C4—1882no—
532C2×C4—1882no—
533C2×C4—1888no—
534C2×C4—1884no—
535C2×C4—1884no—
536C2×C4C4⋊C4×D4712yes—
537C2×C4C4⋊C4×D4712yes—
538C2×C4C4×C22⋊D4712yes—
539C2×C4C4×C22⋊D4712yes—
540C2×C4#1309398612yes—
541C2×C4#1309399211yescharacteristic
542C2×C4#1309399211yescharacteristic
543C2×C4#1309400012yes—
544C2×C4#1309400012yes—
545C2×C4#1309400212yes—
546C2×C4#1309400912yes—
547C2×C4#1309400912yes—
548C2×C4C22×C4×D4711yescharacteristic
549C2×C4C2×D4×D4711yescharacteristic
550C2×C4C22×C22⋊D4711yescharacteristic
551C2×C4C2×Q8×D4711yescharacteristic
552C2×C4C2×#1062535011yescharacteristic
553C2×C4C2×#1062535411yescharacteristic
554C8—24no—
555C8—1882no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—944no—
563C22—1882no—
564C22—1882no—
565C22—1888no—
566C22#1568899412yes—
567C22#1568899412yes—
568C22#1568929412yes—
569C22#1568929912yes—
570C22C2×#1309398611yescharacteristic
571C22C2×#1309399211yescharacteristic
572C22C2×#1309400211yescharacteristic
573C4—42no—
574C4—42no—
575C4—82no—
576C4—944no—
577C4—1884no—
578C4—1884no—
579C4#1568899412yes—
580C4#1568899412yes—
581C4C2×C4⋊C4×D4711yescharacteristic
582C4C2×C4×C22⋊D4711yescharacteristic
583C4C2×#1309400011yescharacteristic
584C4C2×#1309400911yescharacteristic
585C2—21no—
586C2—22no—
587C2—21no—
588C2—1884no—
589C2#2024361814yesdirect product factor
590C2C2×#1568899411yescharacteristic
591C2C2×#1568929911yescharacteristic
592C2C2×#1568929411yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#428C2
socleC23×C47#120
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#428D47
hypocenterC47C2×#1860
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C2×#15688988C2semidirect
5. #20243618C2direct (N × H)
6. C2×#15688891C2semidirect
7. C2×#15688882C2semidirect
8. C2×C47×#428C2semidirect
22. C2×#13093950C4semidirect
29. #15688988C22semidirect
31. #15688891C22semidirect
32. #15688882C22semidirect
37. C47×#428C22semidirect
81. C2×C4×Dic47C2×C4semidirect
83. #13093950C2×C4semidirect
91. C2×M16×C47C2×C4semidirect
167. M16×C47C22×C4semidirect
191. C4×Dic47C22×C4semidirect
290. C2×#428D47semidirect
300. C2×C47#1860semidirect
322. #428C2×D47semidirect
336. C47C2×#1860semidirect
360. C2×M16C4×D47semidirect
467. M16C2×C4×D47semidirect
589. C2#20243618direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896032
C22×#130939502
C2×#156891222
C2×#156889882
#202436182
C2×#156888912
C2×#156888822
C2×C47×#4282
C2×#186047