Finite Group Databasebeta

← #26217661

Subgroups — #26217661

Order 12032.

2046 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094050C211yesmaximal, characteristic
2C2×#15689591C211yesmaximal, characteristic, complemented
3C2×#15689125C211yesmaximal, characteristic, complemented
4C2×#15689026C211yesmaximal, characteristic, complemented
5#20243740C214yesmaximal, complemented
6#20243733C214yesmaximal, complemented
7#20243109C211yesmaximal, characteristic, complemented
8#20243081C211yesmaximal, characteristic, complemented
9C2×C47×#418C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11C2×#13094050—24no—
12C2×#13094050—24no—
13C2×#13094050C418yescomplemented
14C22×#10625335C2212yes—
15C22×#10625334C2212yes—
16C22×#10625329C2211yescharacteristic
17#15689591—24no—
18#15689591—24no—
19C2×#13093989C2212yescomplemented
20C2×#13093986C2212yescomplemented
21C2×(C22⋊D47)⋊C4—22no—
22C2×#13093981—21no—
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47—22no—
25C22×C4×Dic47C2211yescharacteristic
26C2×C42×D47—21no—
27#15689125—24no—
28C2×#13093949C2212yescomplemented
29C2×#13093946C2212yescomplemented
30#15689026—21no—
31#15689026—21no—
32#15689026C2214yes—
33#15688885C2214yescomplemented
34#15688877C2214yescomplemented
35C23×D4×C47C2211yescharacteristic
36C22×M16×C47C2211yescharacteristic
37C2×#117×C47C2211yescharacteristic
38C47×#418—24no—
39C2×#102×C47C2214yes—
40C2×#10625350—22no—
41C2×#10625350—22no—
42C2×#10625350—22no—
43C2×#10625350C2×C414yes—
44C2×#10625350D414yes—
45C2×#10625350D414yes—
46C22×Dic94C2311yescharacteristic
47C22×D188C2311yescharacteristic
48C22×C22⋊D47—21no—
49C23×Dic47—21no—
50C23×Dic47D412yes—
51C22×C4×D47—21no—
52C22×C4×D47—22no—
53#13094050—232no—
54C2×#10625335—24no—
55C2×#10625335—24no—
56C2×#10625335C2×C418yescomplemented
57C2×#10625334—24no—
58C2×#10625334—24no—
59C2×#10625334C2×C418yescomplemented
60C2×#10625329—22no—
61C2×#10625329—22no—
62C2×#10625329C2×C414yescomplemented
63C22×C47⋊C8C2312yes—
64#13093989—24no—
65#13093989—24no—
66#13093986—24no—
67#13093986—24no—
68(C22⋊D47)⋊C4—216no—
69#13093981—28no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47—22no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47C2312yes—
74C2×Dic47⋊C4—22no—
75C2×C22⋊Dic47—24no—
76C2×C22⋊Dic47—24no—
77C2×C22⋊Dic47—48no—
78C2×(C2×D47)⋊C4—22no—
79C2×C4×Dic47—22no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—22no—
82C2×C4×Dic47D411yescharacteristic
83C2×C4×Dic47D411yescharacteristic
84C2×C4×Dic47C2312yes—
85C42×D47—28no—
86#13093949—24no—
87#13093946—24no—
88C25×C47—21no—
89C22×D4×C47—22no—
90C22×D4×C47—22no—
91C22×D4×C47—22no—
92C22×D4×C47—21no—
93C22×D4×C47—22no—
94C22×D4×C47—22no—
95C22×D4×C47C2×C414yescomplemented
96C22×D4×C47C2312yes—
97C23×C4×C47C2311yescharacteristic
98C2×M16×C47—22no—
99C2×M16×C47—22no—
100C2×M16×C47—22no—
101C22×C8×C47C2312yes—
102#117×C47—22no—
103#117×C47D414yes—
104C2×C4⋊C4×C47C2312yes—
105C2×C22⋊C4×C47—21no—
106C2×C42×C47—21no—
107#102×C47—28no—
108C24×C47—24no—
109C24×C47—22no—
110C24×C47—44no—
111C24×C47—44no—
112C24×C47—42no—
113C24×C47—42no—
114C24×C47C2×D411yescharacteristic
115C23×D47—21no—
116C2×D4×C47—28no—
117C2×D4×C47—28no—
118C2×D4×C47—24no—
119C2×D4×C47—22no—
120C2×D4×C47—22no—
121C2×D4×C47—22no—
122C2×D4×C47—22no—
123C2×D4×C47—22no—
124C2×D4×C47—42no—
125C2×D4×C47—44no—
126C2×D4×C47—42no—
127C2×D4×C47—44no—
128C2×D4×C47C22×C414yes—
129C22×C4×C47—22no—
130C22×C4×C47C22×C412yes—
131C22×C4×C47C2×D412yes—
132C22×C4×C47C2×D412yes—
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D412yes—
135C22×C4×C47#4112yes—
136C22×C4×C47#4112yes—
137C22×C4×C47C2411yescharacteristic
138C2×C22⋊D47—24no—
139C2×C22⋊D47—24no—
140C2×C22⋊D47—24no—
141C22×Dic47—21no—
142C22×Dic47—24no—
143C22×Dic47—24no—
144C22×Dic47—22no—
145C22×Dic47—42no—
146C22×Dic47—44no—
147C22×Dic47—42no—
148C22×Dic47C2×D412yes—
149C22×Dic47C2×D412yes—
150#10625350—28no—
151#10625350—28no—
152#10625350—28no—
153#10625350C22⋊C4116yescomplemented
154C2×D188—21no—
155C2×D188—21no—
156C2×D188—21no—
157C2×D188C22×C412yes—
158C2×D188C2×D412yes—
159C2×D188C2×D412yes—
160C2×C4×D47—24no—
161C2×C4×D47—24no—
162C2×C4×D47—24no—
163C2×C4×D47—28no—
164C2×C4×D47—44no—
165C2×C4×D47—44no—
166C2×Dic94—21no—
167C2×Dic94—21no—
168C2×Dic94—21no—
169C2×Dic94C22×C412yes—
170C2×Dic94C2×D412yes—
171C2×Dic94C2×D412yes—
172M16×C47—44no—
173C2×C8×C47—22no—
174C2×C8×C47—22no—
175C2×C8×C47—22no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47C2×D414yes—
178C22⋊C4×C47—24no—
179C42×C47—24no—
180C22⋊Dic47—48no—
181C22⋊Dic47—48no—
182#10625335—216no—
183#10625334—216no—
184(C2×D47)⋊C4—28no—
185C4⋊Dic47—22no—
186C4⋊Dic47—22no—
187C4⋊Dic47—42no—
188Dic47⋊C4—28no—
189C4×Dic47—28no—
190C4×Dic47—22no—
191C4×Dic47—22no—
192C4×Dic47—22no—
193C4×Dic47—22no—
194#10625329—28no—
195C2×C47⋊C8—22no—
196C2×C47⋊C8—22no—
197C2×C47⋊C8C22×C414yes—
198C23×C47—22no—
199C23×C47—22no—
200C23×C47—24no—
201C23×C47—416no—
202C23×C47—42no—
203C23×C47—42no—
204C23×C47—44no—
205C23×C47—44no—
206C23×C47—48no—
207C23×C47—88no—
208C23×C47—84no—
209C23×C47—84no—
210C23×C47C4×D412yes—
211C23×C47#12012yes—
212C23×C47#12112yes—
213C23×C47C22×D411yescharacteristic
214C22×D47—22no—
215C22×D47—22no—
216C22×D47—22no—
217C22×D47—42no—
218C22×D47—42no—
219D4×C47—24no—
220D4×C47—24no—
221D4×C47—42no—
222D4×C47—42no—
223D4×C47—48no—
224C2×C4×C47—24no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47C2×C22⋊C414yes—
228C2×C4×C47C4×D412yes—
229C2×C4×C47C4×D414yes—
230C2×C4×C47#12012yes—
231C2×C4×C47#12114yes—
232C2×C4×C47#12112yes—
233C2×C4×C47#12314yes—
234C2×C4×C47C23×C411yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C22⋊D47—216no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—48no—
250C2×Dic47—42no—
251C2×Dic47—44no—
252C2×Dic47—84no—
253C2×Dic47AGL(1,ℤ/8)14yescomplemented
254D188—22no—
255D188—22no—
256D188—22no—
257D188C2×C22⋊C414yescomplemented
258C4×D47—216no—
259C4×D47—416no—
260Dic94—22no—
261Dic94—22no—
262Dic94—22no—
263Dic94C2×C22⋊C414yescomplemented
264C8×C47—42no—
265C47⋊C8—24no—
266#20928—471nomaximal, Sylow
267C22×C47—24no—
268C22×C47—24no—
269C22×C47—22no—
270C22×C47—22no—
271C22×C47—48no—
272C22×C47—44no—
273C22×C47—816no—
274C22×C47—84no—
275C22×C47—82no—
276C22×C47—82no—
277C22×C47#38614yes—
278C22×C47C2×C4×D411yescharacteristic
279C22×C47C2×#12011yescharacteristic
280C22×C47C2×#12111yescharacteristic
281C22×C47C2×AGL(1,ℤ/8)12yes—
282C22×C47#57512yes—
283C2×D47—24no—
284C2×D47—44no—
285C2×D47—44no—
286C2×D47—42no—
287C2×D47—42no—
288C4×C47—44no—
289C4×C47#38614yes—
290C4×C47C22×C22⋊C411yescharacteristic
291C4×C47C2×C4×D411yescharacteristic
292C4×C47C2×#12111yescharacteristic
293C4×C47C2×#12311yescharacteristic
294Dic47—24no—
295Dic47—24no—
296Dic47—42no—
297Dic47—82no—
298C22×AGL(1,ℤ/8)—471no—
299C2×C4×#41—471no—
300C2×#417—471no—
301C2×#418D4711yescharacteristic, complemented
302C2×#390—471no—
303#1880—474no—
304#1879—474no—
305#1736—471no—
306#1728—471no—
307C2×C47—24no—
308C2×C47—84no—
309C2×C47C2×#38611yescharacteristic
310C2×C47C4×AGL(1,ℤ/8)12yes—
311C2×C47#300612yes—
312C2×C47#303811yescharacteristic
313C2×C47#304011yescharacteristic
314D47—44no—
315C22×#41—471no—
316C23×D4C2×D4711yescharacteristic
317C2×AGL(1,ℤ/8)—478no—
318C2×AGL(1,ℤ/8)—944no—
319C2×AGL(1,ℤ/8)—944no—
320C22×SD16—472no—
321C22×D8—472no—
322C22×M16—471no—
323C22×M16C2×D4711yescharacteristic
324C4×#41—944no—
325C4×#41—944no—
326C2×C4×Q8—472no—
327C2×C4×D4—472no—
328C2×C4×D4—942no—
329C2×#117—941no—
330C2×#117C2×D4711yescharacteristic
331C22×C4⋊C4—471no—
332C22×C22⋊C4—942no—
333C22×C42—471no—
334C22×C42—941no—
335#418—24no—
336#417—944no—
337C2×#103—472no—
338C2×#102—472no—
339C2×#102C2×D4714yes—
340#390—474no—
341#390—941no—
342#390—941no—
343#340—474no—
344#336—474no—
345C47#2092811yescharacteristic, complemented, Sylow
346C25—21no—
347C2×#41—474no—
348C2×#41—474no—
349C2×#41—474no—
350C2×#41—942no—
351C2×#41—942no—
352C2×#41—942no—
353C22×Q8—471no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—471no—
361C22×D4—941no—
362C22×D4C4×D4714yescomplemented
363C22×D4C22×D4712yes—
364C23×C4—472no—
365C23×C4—942no—
366C23×C4—941no—
367C23×C4—941no—
368C23×C4C22×D4711yescharacteristic
369AGL(1,ℤ/8)—9432no—
370C2×SD16—478no—
371C2×SD16—944no—
372C2×SD16—944no—
373C2×D8—478no—
374C2×D8—944no—
375C2×D8—944no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—474no—
380C2×M16—942no—
381C2×M16—942no—
382C22×C8—472no—
383C22×C8C22×D4712yes—
384C4×Q8—944no—
385C4×Q8—944no—
386C4×D4—9416no—
387C4×D4—944no—
388C4×D4—944no—
389#117—22no—
390#117—948no—
391#117C22⋊D4714yes—
392C2×C4⋊C4—472no—
393C2×C4⋊C4—942no—
394C2×C4⋊C4—942no—
395C2×C4⋊C4—942no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4C22×D4712yes—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—942no—
400C2×C22⋊C4—944no—
401C2×C22⋊C4—944no—
402C2×C22⋊C4—1888no—
403C2×C42—21no—
404C2×C42—471no—
405C2×C42—471no—
406C2×C42—472no—
407C2×C42—948no—
408C2×C42—942no—
409C2×C42—942no—
410C2×C42—942no—
411#103—944no—
412#102—28no—
413#102—944no—
414C24—24no—
415C24—22no—
416C24—44no—
417C24—44no—
418C24—42no—
419C24—42no—
420C24—941no—
421C24D4×D4711yescharacteristic
422#41—4716no—
423#41—948no—
424#41—948no—
425#41—948no—
426C2×Q8—472no—
427C2×Q8—472no—
428C2×Q8—472no—
429C2×Q8—941no—
430C2×Q8—941no—
431C2×Q8—941no—
432C2×D4—28no—
433C2×D4—24no—
434C2×D4—28no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—42no—
443C2×D4—44no—
444C2×D4—472no—
445C2×D4—472no—
446C2×D4—472no—
447C2×D4—944no—
448C2×D4—944no—
449C2×D4—944no—
450C2×D4—941no—
451C2×D4—941no—
452C2×D4—941no—
453C2×D4C2×C4×D4714yes—
454C22×C4—22no—
455C22×C4—472no—
456C22×C4—472no—
457C22×C4—948no—
458C22×C4—944no—
459C22×C4—941no—
460C22×C4—944no—
461C22×C4—944no—
462C22×C4—944no—
463C22×C4—944no—
464C22×C4—942no—
465C22×C4—1884no—
466C22×C4—1884no—
467C22×C4—1882no—
468C22×C4—1884no—
469C22×C4—1882no—
470C22×C4C2×C4×D4712yes—
471C22×C4#1062535012yes—
472C22×C4D4×D4712yes—
473C22×C4D4×D4712yes—
474C22×C4D4×D4711yescharacteristic
475C22×C4#1062535212yes—
476C22×C4C2×C22⋊D4712yes—
477C22×C4C23×D4711yescharacteristic
478SD16—9416no—
479D8—9416no—
480M16—44no—
481M16—948no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—474no—
486C2×C8—942no—
487C2×C8—942no—
488C4⋊C4—22no—
489C4⋊C4—948no—
490C4⋊C4—942no—
491C4⋊C4—942no—
492C4⋊C4—1882no—
493C4⋊C4C2×C22⋊D4714yes—
494C22⋊C4—24no—
495C22⋊C4—948no—
496C22⋊C4—1888no—
497C22⋊C4—1888no—
498C42—24no—
499C42—948no—
500C42—942no—
501C42—942no—
502C42—942no—
503C42—942no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—416no—
508C23—48no—
509C23—42no—
510C23—42no—
511C23—44no—
512C23—44no—
513C23—84no—
514C23—84no—
515C23—88no—
516C23—942no—
517C23—942no—
518C23—942no—
519C23—1882no—
520C23—1882no—
521C23(C22⋊D47)⋊C412yes—
522C23#1309399212yes—
523C23#1309399712yes—
524C23C2×D4×D4711yescharacteristic
525Q8—474no—
526Q8—942no—
527Q8—942no—
528Q8—942no—
529D4—24no—
530D4—24no—
531D4—48no—
532D4—42no—
533D4—42no—
534D4—474no—
535D4—9416no—
536D4—942no—
537D4—942no—
538D4—942no—
539C2×C4—24no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—474no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—9416no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—3764no—
553C2×C4—18816no—
554C2×C4—1888no—
555C2×C4—1882no—
556C2×C4—1884no—
557C2×C4C22⋊C4×D4714yes—
558C2×C4(C22⋊D47)⋊C412yes—
559C2×C4C4×C22⋊D4714yes—
560C2×C4#1309399212yes—
561C2×C4#1309399514yes—
562C2×C4#1309399712yes—
563C2×C4#1309400614yes—
564C2×C4C22×C4×D4711yescharacteristic
565C2×C4C2×D4×D4711yescharacteristic
566C2×C4C2×D4×D4711yescharacteristic
567C2×C4C22×C22⋊D4711yescharacteristic
568C2×C4C2×#1062535211yescharacteristic
569C2×C4C2×#1062535011yescharacteristic
570C8—42no—
571C8—944no—
572C22—24no—
573C22—22no—
574C22—22no—
575C22—24no—
576C22—48no—
577C22—44no—
578C22—816no—
579C22—82no—
580C22—82no—
581C22—84no—
582C22—944no—
583C22—1884no—
584C22—1882no—
585C22—1882no—
586C22—1884no—
587C22#1568899914yes—
588C22C2×(C22⋊D47)⋊C411yescharacteristic
589C22C2×#1309399211yescharacteristic
590C22C2×#1309399711yescharacteristic
591C22AGL(1,ℤ/8)×D4712yes—
592C22#1568991912yes—
593C4—44no—
594C4—944no—
595C4—944no—
596C4—3762no—
597C4—1882no—
598C4#1568899914yes—
599C4C2×C22⋊C4×D4711yescharacteristic
600C4C2×C4×C22⋊D4711yescharacteristic
601C4C2×#1309399511yescharacteristic
602C4C2×#1309400611yescharacteristic
603C2—24no—
604C2—84no—
605C2—1884no—
606C2C2×#1568899911yescharacteristic
607C2#2025219212yes—
608C2#2025263612yes—
609C2#2025286711yescharacteristic
610C2#2025288111yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#418C2
socleC23×C47C22×D4
prime radicalC22×#13094050C2
cosocleC22×C4×C47C24
hypercenterC2×#418D47
hypocenterC47#20928
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#15689591C2semidirect
3. C2×#15689125C2semidirect
4. C2×#15689026C2semidirect
5. #20243740C2semidirect
6. #20243733C2semidirect
7. #20243109C2semidirect
8. #20243081C2semidirect
9. C2×C47×#418C2semidirect
13. C2×#13094050C4semidirect
19. C2×#13093989C22semidirect
20. C2×#13093986C22semidirect
28. C2×#13093949C22semidirect
29. C2×#13093946C22semidirect
33. #15688885C22semidirect
34. #15688877C22semidirect
56. C2×#10625335C2×C4semidirect
59. C2×#10625334C2×C4semidirect
62. C2×#10625329C2×C4semidirect
95. C22×D4×C47C2×C4semidirect
153. #10625350C22⋊C4semidirect
253. C2×Dic47AGL(1,ℤ/8)semidirect
257. D188C2×C22⋊C4semidirect
263. Dic94C2×C22⋊C4semidirect
301. C2×#418D47semidirect
345. C47#20928semidirect
362. C22×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130940502
C2×#156895912
C2×#156891252
C2×#156890262
#202437402
#202437332
#202431092
#202430812
C2×C47×#4182
#2092847