Finite Group Databasebeta

← #26220925

Subgroups — #26220925

Order 12032.

1338 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689748C211yesmaximal, characteristic
2#20246001C211yesmaximal, characteristic
3#20245740C211yesmaximal, characteristic
4#20244374C211yesmaximal, characteristic, complemented
5#20244373C211yesmaximal, characteristic, complemented
6#20244372C211yesmaximal, characteristic, complemented
7#20244371C214yesmaximal, complemented
8#342×D47C214yesmaximal
9C47×#1996C211yesmaximal, characteristic, complemented
10#15689748—22no—
11#15689748—22no—
12#15689748—22no—
13#15689748—22no—
14C2×#13094004C412yescomplemented
15C2×#13094003C2211yescharacteristic
16C2×#13094002C412yescomplemented
17C2×#13094002C412yescomplemented
18C2×#13094001C2212yes—
19C2×#13094000C412yescomplemented
20C22×(C2×D47)⋊C4C2211yescharacteristic
21C2×C22⋊C4×D47C2212yes—
22C2×C22⋊C4×D47C2212yes—
23C2×C22⋊C4×D47C2212yes—
24#15688997—22no—
25#15688994—22no—
26#15688983C2211yescharacteristic
27#15688981C2212yes—
28C22⋊C4×Dic47C2212yes—
29C4×(C2×D47)⋊C4—22no—
30C4×C22⋊Dic47C2211yescharacteristic
31#15688970—22no—
32#15688890C2214yes—
33#15688889C2214yes—
34#15688889C2214yes—
35C2×C22⋊Q8×C47C2211yescharacteristic
36C47×#380C2211yescharacteristic
37C4×C22⋊C4×C47C2211yescharacteristic
38C47×#342C2214yes—
39C24×D47C2311yescharacteristic
40C22×Dic94C2×C412yescomplemented
41C22×Dic94C2×C411yescharacteristic, complemented
42C23×Dic47C2311yescharacteristic
43C22×C4×D47—22no—
44C22×C4×D47—22no—
45C22×C4×D47C2×C412yes—
46C22×C4×D47C2×C412yes—
47#13094004—24no—
48#13094004—24no—
49#13094003—21no—
50#13094003—21no—
51#13094003—21no—
52#13094003—21no—
53#13094002—24no—
54#13094002—24no—
55#13094002—24no—
56#13094002—24no—
57#13094001—24no—
58#13094001—24no—
59#13094000—24no—
60#13094000—24no—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47C2×C412yescomplemented
63C2×C4⋊Dic47C2×C411yescharacteristic, complemented
64C2×Dic47⋊C4—22no—
65C2×Dic47⋊C4C2×C412yescomplemented
66C2×Dic47⋊C4C2×C412yescomplemented
67C2×Dic47⋊C4C2×C412yescomplemented
68C2×C22⋊Dic47C2312yes—
69C2×C22⋊Dic47C2312yes—
70C2×C22⋊Dic47C2312yes—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4—22no—
73C2×(C2×D47)⋊C4C2×C412yes—
74C2×(C2×D47)⋊C4C2×C412yes—
75C2×(C2×D47)⋊C4C2×C412yes—
76C2×(C2×D47)⋊C4C2×C412yes—
77C2×(C2×D47)⋊C4D412yes—
78C2×(C2×D47)⋊C4D412yes—
79C2×(C2×D47)⋊C4D412yes—
80C2×(C2×D47)⋊C4D412yes—
81C22⋊C4×D47—24no—
82C22⋊C4×D47—24no—
83C22⋊C4×D47—24no—
84C22⋊C4×D47—28no—
85C22⋊C4×D47Q818yescomplemented
86C2×C4×Dic47—21no—
87C2×C4×Dic47—22no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—22no—
91C47⋊#95—22no—
92C22×Q8×C47C2×C411yescharacteristic, complemented
93C23×C4×C47C2311yescharacteristic
94C22⋊Q8×C47—21no—
95C22⋊Q8×C47—21no—
96C22⋊Q8×C47—21no—
97C22⋊Q8×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
100C2×C4⋊C4×C47C2×C412yescomplemented
101C2×C22⋊C4×C47C2312yes—
102C2×C22⋊C4×C47C2312yes—
103C2×C22⋊C4×C47C2312yes—
104C2×C42×C47—21no—
105#95×C47—21no—
106#95×C47—21no—
107C24×C47C2411yescharacteristic
108C23×D47—81no—
109C23×D47—81no—
110C23×D47C22×C412yes—
111C23×D47C2×D412yes—
112C23×D47C2×D412yes—
113C23×D47C2×Q814yes—
114C23×D47#4114yes—
115C2×Q8×C47—21no—
116C2×Q8×C47—21no—
117C2×Q8×C47—81no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—81no—
121C22×C4×C47C22×C412yes—
122C22×C4×C47C22×C412yes—
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×Dic47—22no—
130C22×Dic47—22no—
131C22×Dic47—81no—
132C22×Dic47C22×C412yes—
133C22×Dic47C22×C412yes—
134C22×Dic47C22×C412yes—
135C22×Dic47C2×D412yes—
136C22×Dic47C2×D412yes—
137C2×C4×D47—24no—
138C2×C4×D47—24no—
139C2×C4×D47—28no—
140C2×C4×D47—44no—
141C2×C4×D47—82no—
142C2×C4×D47—82no—
143C2×C4×D47—82no—
144C2×C4×D47—82no—
145C2×C4×D47—82no—
146C2×C4×D47—82no—
147C2×Dic94—21no—
148C2×Dic94—21no—
149C2×Dic94—24no—
150C2×Dic94—82no—
151C2×Dic94—81no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—81no—
157C22⋊C4×C47—22no—
158C22⋊C4×C47—22no—
159C22⋊C4×C47—22no—
160C22⋊C4×C47—24no—
161C22⋊C4×C47C2×Q814yes—
162C42×C47—81no—
163C22⋊Dic47—22no—
164C22⋊Dic47—22no—
165C22⋊Dic47—22no—
166C22⋊Dic47—24no—
167C22⋊Dic47C2×Q814yes—
168(C2×D47)⋊C4—24no—
169(C2×D47)⋊C4—24no—
170(C2×D47)⋊C4—28no—
171(C2×D47)⋊C4—44no—
172(C2×D47)⋊C4C22⋊C414yes—
173(C2×D47)⋊C4C22⋊C414yes—
174(C2×D47)⋊C4C22⋊C414yes—
175(C2×D47)⋊C4C22⋊C414yes—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—24no—
179C4⋊Dic47—81no—
180Dic47⋊C4—22no—
181Dic47⋊C4—22no—
182Dic47⋊C4—24no—
183Dic47⋊C4—24no—
184Dic47⋊C4—82no—
185C4×Dic47—82no—
186C4×Dic47—81no—
187C23×C47—41no—
188C23×C47—41no—
189C23×C47C23×C411yescharacteristic
190C23×C47C22×D411yescharacteristic
191C23×C47C22×D411yescharacteristic
192C23×C47C22×Q812yes—
193C23×C47C2×#4112yes—
194C22×D47—42no—
195C22×D47—42no—
196C22×D47—42no—
197C22×D47—42no—
198C22×D47—42no—
199C22×D47—42no—
200C22×D47—84no—
201C22×D47—84no—
202C22×D47C2×C22⋊C414yes—
203C22×D47C4×Q818yes—
204C22×D47C22⋊Q814yes—
205C22×D47C22⋊Q814yes—
206C22×D47#12414yes—
207C22×D47C4⋊Q814yes—
208Q8×C47—81no—
209Q8×C47—81no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—24no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C2×C22⋊C411yescharacteristic
228C2×C4×C47C2×C22⋊C411yescharacteristic
229C2×C4×C47C2×C22⋊C411yescharacteristic
230C2×Dic47—22no—
231C2×Dic47—22no—
232C2×Dic47—24no—
233C2×Dic47—42no—
234C2×Dic47—42no—
235C2×Dic47—42no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47C2×C22⋊C414yes—
244C4×D47—84no—
245C4×D47—84no—
246C4×D47—88no—
247C4×D47—88no—
248Dic94—84no—
249Dic94—81no—
250Dic94—81no—
251#21333—471nomaximal, Sylow
252C22×C47—21no—
253C22×C47—21no—
254C22×C47—21no—
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—21no—
258C22×C47—42no—
259C22×C47—42no—
260C22×C47C22×C22⋊C411yescharacteristic
261C22×C47C2×C4×Q812yes—
262C22×C47C2×C22⋊Q812yes—
263C22×C47C2×#12411yescharacteristic
264C22×C47C2×C4⋊Q811yescharacteristic
265C2×D47—24no—
266C2×D47—24no—
267C2×D47—44no—
268C2×D47—44no—
269C2×D47—48no—
270C2×D47—44no—
271C2×D47—44no—
272C2×D47#39118yes—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—21no—
276C4×C47—21no—
277C4×C47—44no—
278C4×C47—42no—
279C4×C47—42no—
280C4×C47—82no—
281Dic47—24no—
282Dic47—44no—
283Dic47—42no—
284Dic47—42no—
285Dic47—82no—
286C2×#543—471no—
287#2315—471no—
288#2273—471no—
289#1996—471no—
290#1996—471no—
291#1996—474no—
292#1996—471no—
293#1996D4711yescharacteristic, complemented
294C2×#342—474no—
295C2×C47—22no—
296C2×C47—21no—
297C2×C47—22no—
298C2×C47—21no—
299C2×C47C2×#39111yescharacteristic
300C2×C47#288311yescharacteristic
301C2×C47#288311yescharacteristic
302D47—28no—
303#543—942no—
304#543—942no—
305#543—942no—
306#543—942no—
307C2×C22⋊Q8—472no—
308C2×C22⋊Q8—471no—
309C2×C22⋊Q8—472no—
310C2×C22⋊Q8—472no—
311C2×C22⋊Q8—472no—
312C2×C22⋊Q8—472no—
313C2×C22⋊Q8C2×D4711yescharacteristic
314C22×C22⋊C4—471no—
315C22×C22⋊C4—472no—
316C22×C22⋊C4—472no—
317C22×C22⋊C4—472no—
318#385—942no—
319#385—942no—
320#380—471no—
321#380—472no—
322#380C2×D4711yescharacteristic
323C4×C22⋊C4—471no—
324C4×C22⋊C4—472no—
325C4×C22⋊C4—942no—
326C4×C22⋊C4—942no—
327C4×C22⋊C4C2×D4711yescharacteristic
328#342—474no—
329#342—474no—
330#342—474no—
331#342C2×D4714yes—
332C47#2133311yescharacteristic, complemented, Sylow
333C25—471no—
334C22×Q8—472no—
335C22×Q8—471no—
336C22×Q8C4×D4711yescharacteristic, complemented
337C23×C4—471no—
338C23×C4—472no—
339C23×C4—472no—
340C23×C4—942no—
341C23×C4—942no—
342C23×C4C22×D4711yescharacteristic
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—944no—
348C22⋊Q8—944no—
349C22⋊Q8—944no—
350C22⋊Q8—944no—
351C22⋊Q8—944no—
352C22⋊Q8—944no—
353C22⋊Q8—944no—
354C22⋊Q8—944no—
355C22⋊Q8—944no—
356C22⋊Q8—944no—
357C22⋊Q8—941no—
358C22⋊Q8—941no—
359C22⋊Q8—941no—
360C22⋊Q8—941no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—472no—
363C2×C4⋊C4—472no—
364C2×C4⋊C4—472no—
365C2×C4⋊C4—472no—
366C2×C4⋊C4—471no—
367C2×C4⋊C4—942no—
368C2×C4⋊C4—941no—
369C2×C4⋊C4C4×D4712yescomplemented
370C2×C4⋊C4C4×D4711yescharacteristic, complemented
371C2×C22⋊C4—472no—
372C2×C22⋊C4—472no—
373C2×C22⋊C4—472no—
374C2×C22⋊C4—472no—
375C2×C22⋊C4—472no—
376C2×C22⋊C4—472no—
377C2×C22⋊C4—472no—
378C2×C22⋊C4—478no—
379C2×C22⋊C4—472no—
380C2×C22⋊C4—472no—
381C2×C22⋊C4—472no—
382C2×C22⋊C4—472no—
383C2×C22⋊C4—944no—
384C2×C22⋊C4—944no—
385C2×C22⋊C4—944no—
386C2×C22⋊C4—948no—
387C2×C22⋊C4—942no—
388C2×C22⋊C4—942no—
389C2×C22⋊C4C22×D4712yes—
390C2×C22⋊C4C22×D4712yes—
391C2×C22⋊C4C22×D4712yes—
392C2×C42—21no—
393C2×C42—942no—
394C2×C42—941no—
395#95—21no—
396#95—21no—
397#95—942no—
398#95—942no—
399#95—941no—
400#95—941no—
401C24—474no—
402C24—474no—
403C24—472no—
404C24—472no—
405C24—472no—
406C24—3761no—
407C24—3761no—
408C24C23×D4711yescharacteristic
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—81no—
412C2×Q8—944no—
413C2×Q8—941no—
414C2×Q8—941no—
415C2×Q8—3761no—
416C2×Q8—3762no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—81no—
420C22×C4—472no—
421C22×C4—472no—
422C22×C4—472no—
423C22×C4—472no—
424C22×C4—472no—
425C22×C4—948no—
426C22×C4—944no—
427C22×C4—944no—
428C22×C4—942no—
429C22×C4—942no—
430C22×C4—3762no—
431C22×C4—3762no—
432C22×C4—3762no—
433C22×C4—3762no—
434C22×C4—3762no—
435C22×C4—3762no—
436C22×C4—3761no—
437C22×C4—1884no—
438C22×C4C2×C4×D4712yes—
439C22×C4C2×C4×D4712yes—
440C22×C4C2×C4×D4711yescharacteristic
441C22×C4C2×C4×D4711yescharacteristic
442C22×C4D4×D4711yescharacteristic
443C22×C4D4×D4711yescharacteristic
444C22×C4D4×D4711yescharacteristic
445C22×C4D4×D4711yescharacteristic
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—81no—
451C4⋊C4—944no—
452C4⋊C4—944no—
453C4⋊C4—944no—
454C4⋊C4—942no—
455C4⋊C4—942no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—3762no—
459C4⋊C4—3761no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—24no—
464C22⋊C4—474no—
465C22⋊C4—474no—
466C22⋊C4—474no—
467C22⋊C4—474no—
468C22⋊C4—474no—
469C22⋊C4—948no—
470C22⋊C4—944no—
471C22⋊C4—944no—
472C22⋊C4—942no—
473C22⋊C4—942no—
474C22⋊C4—942no—
475C22⋊C4—944no—
476C22⋊C4—1884no—
477C22⋊C4Q8×D4714yes—
478C42—81no—
479C42—3761no—
480C42—3762no—
481C23—41no—
482C23—41no—
483C23—474no—
484C23—478no—
485C23—474no—
486C23—474no—
487C23—474no—
488C23—474no—
489C23—3764no—
490C23—3764no—
491C23—1882no—
492C23—1882no—
493C23—1882no—
494C23—1882no—
495C23—1882no—
496C23—1882no—
497C23C22×C4×D4711yescharacteristic
498C23C2×D4×D4711yescharacteristic
499C23C2×D4×D4711yescharacteristic
500C23C2×Q8×D4712yes—
501C23#41×D4712yes—
502Q8—81no—
503Q8—81no—
504Q8—3761no—
505Q8—3761no—
506Q8—3764no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—474no—
524C2×C4—942no—
525C2×C4—942no—
526C2×C4—944no—
527C2×C4—3764no—
528C2×C4—3764no—
529C2×C4—3768no—
530C2×C4—3768no—
531C2×C4—1882no—
532C2×C4—1882no—
533C2×C4—1882no—
534C2×C4—1882no—
535C2×C4—1882no—
536C2×C4—1882no—
537C2×C4—1882no—
538C2×C4—1882no—
539C2×C4—1882no—
540C2×C4—1882no—
541C2×C4C22⋊C4×D4711yescharacteristic
542C2×C4C22⋊C4×D4711yescharacteristic
543C2×C4C22⋊C4×D4711yescharacteristic
544C2×C4C22⋊C4×D4711yescharacteristic
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—42no—
552C22—42no—
553C22—478no—
554C22—944no—
555C22—944no—
556C22—1884no—
557C22—1884no—
558C22—1884no—
559C22—1888no—
560C22—1884no—
561C22C2×C22⋊C4×D4711yescharacteristic
562C22C4×Q8×D4712yes—
563C22C22⋊Q8×D4712yes—
564C22#124×D4711yescharacteristic
565C22C4⋊Q8×D4711yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—44no—
571C4—42no—
572C4—42no—
573C4—82no—
574C4—944no—
575C4—3762no—
576C4—1884no—
577C4—1882no—
578C4—1882no—
579C2—22no—
580C2—21no—
581C2—22no—
582C2—21no—
583C2—948no—
584C2#391×D4711yescharacteristic
585C2#2025184611yescharacteristic
586C2#2025184711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1996C2
socleC22×C47C22×C22⋊C4
prime radicalC24×D47C23
cosocleC24×C47C24
hypercenter#1996D47
hypocenterC47#21333
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
4. #20244374C2semidirect
5. #20244373C2semidirect
6. #20244372C2semidirect
7. #20244371C2semidirect
9. C47×#1996C2semidirect
14. C2×#13094004C4semidirect
16. C2×#13094002C4semidirect
17. C2×#13094002C4semidirect
19. C2×#13094000C4semidirect
40. C22×Dic94C2×C4semidirect
41. C22×Dic94C2×C4semidirect
62. C2×C4⋊Dic47C2×C4semidirect
63. C2×C4⋊Dic47C2×C4semidirect
65. C2×Dic47⋊C4C2×C4semidirect
66. C2×Dic47⋊C4C2×C4semidirect
67. C2×Dic47⋊C4C2×C4semidirect
85. C22⋊C4×D47Q8semidirect
92. C22×Q8×C47C2×C4semidirect
99. C2×C4⋊C4×C47C2×C4semidirect
100. C2×C4⋊C4×C47C2×C4semidirect
293. #1996D47semidirect
332. C47#21333semidirect
336. C22×Q8C4×D47semidirect
369. C2×C4⋊C4C4×D47semidirect
370. C2×C4⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156897482
#202460012
#202457402
#202443742
#202443732
#202443722
#202443712
#342×D472
C47×#19962
#2133347