Finite Group Databasebeta

← #26244429

Subgroups — #26244429

Order 12032.

1520 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689673C211yesmaximal, characteristic, complemented
2C2×C4×#10625334C212yesmaximal, complemented
3#20244716C211yesmaximal, characteristic, complemented
4#20244622C211yesmaximal, characteristic, complemented
5#20244570C212yesmaximal, complemented
6#20244524C211yesmaximal, characteristic, complemented
7#20244458C211yesmaximal, characteristic, complemented
8#20244384C212yesmaximal, complemented
9C4×#13093944C212yesmaximal, complemented
10C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
11C4×#121×C47C211yesmaximal, characteristic, complemented
12C22×#10625350—21no—
13C22×#10625334C2212yes—
14#15689673—28no—
15C2×#13094024C2211yescharacteristic
16C2×#13094021C2211yescharacteristic
17C2×#13094012—21no—
18C2×#13093998—21no—
19C2×#13093998C2212yes—
20C2×C4×D188—21no—
21C2×C4×D188C2212yes—
22C4×#10625334—28no—
23C2×#13093957C2212yes—
24C2×#13093945C2212yes—
25C2×#13093944C2212yes—
26C2×#13093944C2212yes—
27C2×#13093944C2212yes—
28C2×C22⋊(C47⋊C8)C2212yes—
29C2×C4×C47⋊C8C2212yes—
30#15688885C2212yes—
31#15688885C2212yes—
32#15688878C2211yescharacteristic
33#15688878C2211yescharacteristic
34C2×#121×C47C2211yescharacteristic
35C2×C4×D4×C47—21no—
36C2×C4×D4×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C47×#390C2211yescharacteristic
39C47×#389C2211yescharacteristic
40C47×#388—21no—
41C47×#386—21no—
42C47×#380C2211yescharacteristic
43C4×C4⋊C4×C47C2211yescharacteristic
44C4×C22⋊C4×C47—21no—
45C2×#10625350—28no—
46C2×#10625350—44no—
47C2×#10625350—44no—
48C22×Dic94—21no—
49C22×D188—21no—
50C22×D188—21no—
51C22×D188C2312yes—
52C22×C22⋊D47—22no—
53C22×C4×D47—22no—
54C2×#10625334—24no—
55C2×#10625334—24no—
56C2×#10625334—24no—
57C22×C47⋊C8C2312yes—
58C22×C47⋊C8C2312yes—
59#13094024—24no—
60#13094021—24no—
61#13094012—28no—
62#13093998—28no—
63#13093998—24no—
64#13093998—24no—
65C4×D188—28no—
66C4×D188—24no—
67C4×D188D418yescomplemented
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47C2312yes—
70C2×(C2×D47)⋊C4—22no—
71C2×(C2×D47)⋊C4—22no—
72#13093957—24no—
73#13093945—24no—
74#13093944—24no—
75#13093944—24no—
76#13093944—24no—
77C22⋊(C47⋊C8)—24no—
78C4×C47⋊C8—24no—
79C22×D4×C47—21no—
80C22×D4×C47C2311yescharacteristic
81C23×C4×C47—21no—
82C23×C4×C47D411yescharacteristic
83C23×C4×C47D411yescharacteristic
84C23×C4×C47C2311yescharacteristic
85#121×C47—22no—
86#121×C47—22no—
87C4×D4×C47—24no—
88C4×D4×C47—44no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C4⋊C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47C2311yescharacteristic
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C22⋊C4×C47—21no—
97C2×C22⋊C4×C47—21no—
98C2×C42×C47—24no—
99C2×C42×C47—21no—
100C2×C42×C47D411yescharacteristic
101C2×C42×C47D411yescharacteristic
102C2×C42×C47C2311yescharacteristic
103C2×C42×C47C2311yescharacteristic
104#95×C47—21no—
105#95×C47—21no—
106#95×C47—21no—
107C24×C47—21no—
108C24×C47C2×D411yescharacteristic
109C23×D47—22no—
110C2×D4×C47—24no—
111C2×D4×C47—22no—
112C2×D4×C47—22no—
113C2×D4×C47—21no—
114C2×D4×C47—42no—
115C2×D4×C47—42no—
116C2×D4×C47#4112yescomplemented
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—22no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—41no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47—42no—
132C22×C4×C47D814yescomplemented
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C2×C22⋊D47—28no—
140C2×C22⋊D47—44no—
141C2×C22⋊D47—44no—
142C22×Dic47—22no—
143#10625350—432no—
144C2×D188—22no—
145C2×D188—22no—
146C2×D188—22no—
147C2×D188—22no—
148C2×D188—24no—
149C2×D188—24no—
150C2×D188—22no—
151C2×D188—42no—
152C2×D188—42no—
153C2×D188—42no—
154C2×D188—42no—
155C2×D188C2×D414yes—
156C2×C4×D47—28no—
157C2×C4×D47—44no—
158C2×C4×D47—44no—
159C2×Dic94—24no—
160C2×Dic94—42no—
161C2×Dic94—42no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—42no—
166C4⋊C4×C47#4112yescomplemented
167C22⋊C4×C47—24no—
168C22⋊C4×C47—42no—
169C22⋊C4×C47—42no—
170C22⋊C4×C47—42no—
171C22⋊C4×C47—42no—
172C42×C47—22no—
173C42×C47—22no—
174C42×C47—22no—
175C42×C47—42no—
176C42×C47C2×D414yes—
177#10625334—216no—
178(C2×D47)⋊C4—28no—
179(C2×D47)⋊C4—28no—
180C4⋊Dic47—24no—
181C4⋊Dic47—22no—
182C4⋊Dic47C2×D414yes—
183C2×C47⋊C8—22no—
184C2×C47⋊C8—22no—
185C2×C47⋊C8—22no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8#4114yescomplemented
189C23×C47—21no—
190C23×C47—21no—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—22no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47C2×D812yes—
203C23×C47C22×D411yescharacteristic
204C22×D47—24no—
205C22×D47—42no—
206C22×D47—42no—
207C22×D47—42no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47—42no—
211D4×C47—24no—
212D4×C47—48no—
213D4×C47—42no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—28no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—22no—
224C2×C4×C47—21no—
225C2×C4×C47—44no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—84no—
237C2×C4×C47#12012yes—
238C2×C4×C47#12012yes—
239C2×C4×C47C2×D812yes—
240C2×C4×C47C2×D812yes—
241C2×C4×C47#13512yes—
242C2×C4×C47AGL(1,ℤ/8)12yes—
243C2×C4×C47C22×D412yes—
244C2×C4×C47C2×#4112yes—
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C22⋊D47—416no—
248C2×Dic47—24no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251D188—24no—
252D188—24no—
253D188—48no—
254D188—48no—
255D188—42no—
256D188—42no—
257C4×D47—416no—
258Dic94—48no—
259C47⋊C8—24no—
260C47⋊C8—42no—
261#23567—471nomaximal, Sylow
262C22×C47—22no—
263C22×C47—22no—
264C22×C47—22no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—42no—
270C22×C47—42no—
271C22×C47—42no—
272C22×C47—81no—
273C22×C47—81no—
274C22×C47—81no—
275C22×C47—81no—
276C22×C47C2×#12011yescharacteristic
277C22×C47#52511yescharacteristic
278C22×C47#53211yescharacteristic
279C22×C47C22×D811yescharacteristic
280C22×C47C2×#13511yescharacteristic
281C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C47#57511yescharacteristic
283C2×D47—44no—
284C2×D47—44no—
285C2×D47—44no—
286C2×D47—82no—
287C2×D47—82no—
288C2×D47—82no—
289C2×D47—82no—
290C4×C47—22no—
291C4×C47—22no—
292C4×C47—22no—
293C4×C47—42no—
294C4×C47—41no—
295C4×C47—81no—
296C4×C47—81no—
297C4×C47#44714yes—
298C4×C47#52512yes—
299C4×C47#53212yes—
300Dic47—44no—
301C2×#532—471no—
302C2×C4×D8—472no—
303C4×#121D4711yescharacteristic, complemented
304#2057—471no—
305#2041—471no—
306#2033—472no—
307#2023—471no—
308#2011—471no—
309#1999—472no—
310C4×#102—472no—
311C4×C22⋊C8—471no—
312C2×C47—42no—
313C2×C47—82no—
314C2×C47#238811yescharacteristic
315C2×C47C2×#44711yescharacteristic
316C2×C47#300211yescharacteristic
317C2×C47#310011yescharacteristic
318C2×C47#310611yescharacteristic
319C2×C47#316911yescharacteristic
320C2×C47#317111yescharacteristic
321D47—84no—
322C22×#41—941no—
323C22×D8—472no—
324#532—948no—
325C2×C4⋊Q8—471no—
326C2×#127—471no—
327C2×#124—941no—
328C2×#121—472no—
329C2×#121—941no—
330C2×#121C2×D4711yescharacteristic
331C2×C4×D4—21no—
332C2×C4×D4—472no—
333C2×C4×D4—941no—
334C2×C4×D4C2×D4711yescharacteristic
335C22×C42C2×D4711yescharacteristic
336C4×D8—948no—
337C2×#107—472no—
338C2×#102—472no—
339C2×#102—472no—
340C2×#102—472no—
341C2×#102—472no—
342C2×C22⋊C8—472no—
343C2×C4×C8—472no—
344#390C2×D4711yescharacteristic
345#389C2×D4711yescharacteristic
346#388—21no—
347#386—21no—
348#380C2×D4711yescharacteristic
349C4×C4⋊C4C2×D4711yescharacteristic
350C4×C22⋊C4—21no—
351#340—472no—
352#340—472no—
353#336—471no—
354#336—471no—
355C47#2356711yescharacteristic, complemented, Sylow
356C2×#41—948no—
357C2×#41—1884no—
358C2×#41—1884no—
359C22×Q8—941no—
360C22×D4—21no—
361C22×D4—472no—
362C22×D4—942no—
363C22×D4—941no—
364C22×D4—941no—
365C22×D4C22×D4711yescharacteristic
366C23×C4—21no—
367C23×C4—942no—
368C23×C4C22⋊D4711yescharacteristic
369C23×C4C22⋊D4711yescharacteristic
370C23×C4C22×D4711yescharacteristic
371C2×D8—944no—
372C2×D8—944no—
373C2×D8—944no—
374C22×C8—472no—
375C22×C8—472no—
376C4⋊Q8—944no—
377#127—944no—
378#124—948no—
379#121—22no—
380#121—22no—
381#121—944no—
382#121—944no—
383#121—948no—
384C4×D4—24no—
385C4×D4—44no—
386C4×D4—478no—
387C4×D4—948no—
388C4×D4—944no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—472no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4C22×D4711yescharacteristic
393C2×C4⋊C4C22×D4711yescharacteristic
394C2×C4⋊C4C22×D4711yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—942no—
401C2×C22⋊C4—942no—
402C2×C42—24no—
403C2×C42—21no—
404C2×C42C22⋊D4711yescharacteristic
405C2×C42C22⋊D4711yescharacteristic
406C2×C42C22×D4711yescharacteristic
407C2×C42C22×D4711yescharacteristic
408#107—944no—
409#102—944no—
410#102—944no—
411#102—944no—
412#102—944no—
413C22⋊C8—944no—
414C4×C8—944no—
415#95—21no—
416#95—21no—
417#95—21no—
418C24—21no—
419C24—942no—
420C24C2×C22⋊D4711yescharacteristic
421#41—18832no—
422C2×Q8—944no—
423C2×Q8—1882no—
424C2×Q8—1882no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—474no—
432C2×D4—944no—
433C2×D4—944no—
434C2×D4—948no—
435C2×D4—942no—
436C2×D4—942no—
437C2×D4—942no—
438C2×D4—942no—
439C2×D4—942no—
440C2×D4—1882no—
441C2×D4—1882no—
442C2×D4—1884no—
443C2×D4—1884no—
444C2×D4—1882no—
445C2×D4—1882no—
446C2×D4#1062535012yescomplemented
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—942no—
463C22×C4—948no—
464C22×C4—1884no—
465C22×C4—1884no—
466C22×C4#1062533414yescomplemented
467C22×C4C2×C22⋊D4711yescharacteristic
468C22×C4C2×C22⋊D4711yescharacteristic
469C22×C4C2×C22⋊D4711yescharacteristic
470C22×C4C2×C22⋊D4711yescharacteristic
471C22×C4C2×C22⋊D4711yescharacteristic
472C22×C4C23×D4711yescharacteristic
473D8—9416no—
474C2×C8—474no—
475C2×C8—942no—
476C2×C8—942no—
477C2×C8—942no—
478C2×C8—942no—
479C2×C8—942no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—42no—
484C4⋊C4—474no—
485C4⋊C4—944no—
486C4⋊C4—942no—
487C4⋊C4#1062535012yescomplemented
488C22⋊C4—24no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—948no—
494C22⋊C4—948no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—42no—
499C42D4×D4714yes—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—944no—
514C23—1882no—
515C23—1882no—
516C23—1882no—
517C23—1882no—
518C23—1882no—
519C23—1882no—
520C23C2×#1062533412yes—
521C23C22×C22⋊D4711yescharacteristic
522Q8—1888no—
523D4—24no—
524D4—48no—
525D4—42no—
526D4—944no—
527D4—944no—
528D4—1888no—
529D4—1888no—
530D4—18816no—
531D4—1882no—
532D4—1882no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—28no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—44no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4—944no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—18816no—
560C2×C4#1309399212yes—
561C2×C4#1309399212yes—
562C2×C4C2×#1062533412yes—
563C2×C4C2×#1062533412yes—
564C2×C4#1309404412yes—
565C2×C4#1309404912yes—
566C2×C4C2×D4×D4712yes—
567C2×C4#41×D4712yes—
568C2×C4C2×#1062535011yescharacteristic
569C2×C4C2×#1062535011yescharacteristic
570C8—944no—
571C8—1882no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—3762no—
587C22—3762no—
588C22—3762no—
589C22—3762no—
590C22—1884no—
591C22—1884no—
592C22—1884no—
593C22C2×#1309399211yescharacteristic
594C22#1568963411yescharacteristic
595C22#1568966911yescharacteristic
596C22C22×#1062533411yescharacteristic
597C22C2×#1309404411yescharacteristic
598C22C2×#1309404911yescharacteristic
599C22#1568992111yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—41no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—1884no—
608C4#1568925614yes—
609C4#1568963212yes—
610C4#1568967012yes—
611C2—42no—
612C2—82no—
613C2—3764no—
614C2#2024660311yescharacteristic
615C2C2×#1568925611yescharacteristic
616C2#2025260411yescharacteristic
617C2#2025338811yescharacteristic
618C2#2025344811yescharacteristic
619C2#2025396311yescharacteristic
620C2#2025398411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC4×#121×C47C2
socleC23×C47C22×D4
hypercenterC4×#121D47
hypocenterC47#23567
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#15689673C2semidirect
2. C2×C4×#10625334C2semidirect
3. #20244716C2semidirect
4. #20244622C2semidirect
5. #20244570C2semidirect
6. #20244524C2semidirect
7. #20244458C2semidirect
8. #20244384C2semidirect
9. C4×#13093944C2semidirect
10. C4×C22⋊(C47⋊C8)C2semidirect
11. C4×#121×C47C2semidirect
67. C4×D188D4semidirect
116. C2×D4×C47#41semidirect
132. C22×C4×C47D8semidirect
166. C4⋊C4×C47#41semidirect
188. C2×C47⋊C8#41semidirect
303. C4×#121D47semidirect
355. C47#23567semidirect
446. C2×D4#10625350semidirect
466. C22×C4#10625334semidirect
487. C4⋊C4#10625350semidirect

Maximal subgroups

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

subgroupindex
C2×#156896732
C2×C4×#106253342
#202447162
#202446222
#202445702
#202445242
#202444582
#202443842
C4×#130939442
C4×C22⋊(C47⋊C8)2
C4×#121×C472
#2356747