Finite Group Databasebeta

← #26182191

Subgroups — #26182191

Order 12032.

1210 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689602C211yesmaximal, characteristic
2#20252414C212yesmaximal, complemented
3#20241730C212yesmaximal, complemented
4#20241723C212yesmaximal, complemented
5#20241719C212yesmaximal, complemented
6#20241716C212yesmaximal, complemented
7#20241706C211yesmaximal, characteristic, complemented
8C2×#15688848C212yesmaximal, complemented
9C47×#1459C211yesmaximal, characteristic, complemented
10C22×#10625352C411yescharacteristic
11#15689602—24no—
12#15689602—24no—
13C2×C4×Dic94C411yescharacteristic
14C2×#13093989C2211yescharacteristic
15C2×D4×Dic47C411yescharacteristic
16C2×C4×C22⋊D47C411yescharacteristic
17C2×C4×C22⋊D47C2211yescharacteristic
18C2×(C22⋊D47)⋊C4C411yescharacteristic
19C2×(C22⋊D47)⋊C4C2211yescharacteristic
20C2×#13093981C411yescharacteristic
21C2×#13093980C411yescharacteristic
22C2×#13093980C2211yescharacteristic
23C22×Dic47⋊C4C411yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C2×C4⋊C4×D47C2211yescharacteristic
26#15689194—24no—
27#15689191—24no—
28#15689177C2214yes—
29#15689085C2214yes—
30C2×C22⋊(C47⋊C8)C2212yes—
31#15688849C2212yes—
32#15688848C2214yes—
33#15688848C2214yes—
34#15688847C2212yes—
35C2×C4×D4×C47C2211yescharacteristic
36C2×C22⋊C8×C47C2212yes—
37C47×#324C2212yes—
38C47×#323C2212yes—
39C2×#10625352—24no—
40C2×#10625352—24no—
41C2×#10625352—24no—
42C22×Dic94C2×C411yescharacteristic
43C22×C22⋊D47C2×C411yescharacteristic
44C22×C22⋊D47C2×C411yescharacteristic
45C23×Dic47C2×C411yescharacteristic
46C23×Dic47C2×C411yescharacteristic
47C23×Dic47C2×C411yescharacteristic
48C23×Dic47C2×C411yescharacteristic
49C22×C4×D47C2×C411yescharacteristic
50C22×C4×D47C2×C411yescharacteristic
51C22×C4×D47C2311yescharacteristic
52C2×#10625324—24no—
53C22×C47⋊C8—22no—
54C4×Dic94—22no—
55C4×Dic94—22no—
56#13093989—24no—
57D4×Dic47—24no—
58C4×C22⋊D47—22no—
59C4×C22⋊D47—22no—
60C4×C22⋊D47D414yes—
61C4×C22⋊D47D414yes—
62(C22⋊D47)⋊C4—24no—
63(C22⋊D47)⋊C4—24no—
64#13093981—22no—
65#13093981—22no—
66#13093980—24no—
67#13093980—24no—
68C2×C4⋊Dic47C2×C411yescharacteristic
69C2×Dic47⋊C4—22no—
70C2×Dic47⋊C4—22no—
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4C2×C411yescharacteristic
74C2×Dic47⋊C4C2×C411yescharacteristic
75C2×Dic47⋊C4C2×C411yescharacteristic
76C2×Dic47⋊C4C2×C411yescharacteristic
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2311yescharacteristic
80C2×Dic47⋊C4C2311yescharacteristic
81C4⋊C4×D47—24no—
82C2×C22⋊Dic47C2×C411yescharacteristic
83C2×C22⋊Dic47C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C2×(C2×D47)⋊C4C2×C411yescharacteristic
86C2×C4×Dic47C2×C411yescharacteristic
87C2×C4×Dic47C2×C411yescharacteristic
88C2×C4×Dic47C2×C411yescharacteristic
89C2×C4×Dic47C2×C411yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91Dic47⋊C8—24no—
92C22⋊(C47⋊C8)—22no—
93C22⋊(C47⋊C8)C2314yes—
94(C2×D47)⋊C8—24no—
95#13093934—24no—
96C22×D4×C47C2×C411yescharacteristic
97C23×C4×C47C2×C411yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C22×C8×C47—22no—
100C4×D4×C47—22no—
101C4×D4×C47—22no—
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C22⋊C4×C47C2×C411yescharacteristic
104C2×C22⋊C4×C47C2311yescharacteristic
105C2×C42×C47C2×C411yescharacteristic
106C22⋊C8×C47—22no—
107C22⋊C8×C47C2314yes—
108C24×C47C22×C411yescharacteristic
109C24×C47C22×C411yescharacteristic
110C23×D47C22×C411yescharacteristic
111C2×D4×C47—22no—
112C2×D4×C47—22no—
113C2×D4×C47M1614yescomplemented
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—81no—
117C22×C4×C47—81no—
118C22×C4×C47C22×C411yescharacteristic
119C22×C4×C47C22×C411yescharacteristic
120C22×C4×C47C22×C411yescharacteristic
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C2×D412yes—
123C22×C4×C47C2×D412yes—
124C22×C4×C47C2411yescharacteristic
125C2×C22⋊D47—22no—
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47—22no—
130C2×C22⋊D47C22⋊C414yes—
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—81no—
139C22×Dic47—81no—
140C22×Dic47M1614yescomplemented
141C22×Dic47C22×C411yescharacteristic
142C22×Dic47C22×C411yescharacteristic
143C22×Dic47C22×C411yescharacteristic
144C22×Dic47C22×C411yescharacteristic
145C22×Dic47C22×C411yescharacteristic
146C22×Dic47C22×C411yescharacteristic
147C22×Dic47C22×C411yescharacteristic
148#10625352—232no—
149C2×C4×D47—22no—
150C2×C4×D47—22no—
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—81no—
154C2×C4×D47—81no—
155C2×C4×D47C2×D414yes—
156C2×Dic94—22no—
157C2×Dic94—22no—
158C2×Dic94—22no—
159C2×C8×C47—24no—
160C2×C8×C47—82no—
161C4⋊C4×C47—22no—
162C22⋊C4×C47—22no—
163C22⋊C4×C47—22no—
164C42×C47—21no—
165C42×C47—21no—
166C22⋊Dic47—22no—
167C22⋊Dic47C22⋊C414yes—
168(C2×D47)⋊C4—22no—
169(C2×D47)⋊C4C22⋊C412yes—
170(C2×D47)⋊C4C22⋊C412yes—
171C4⋊Dic47—22no—
172Dic47⋊C4—21no—
173Dic47⋊C4—21no—
174Dic47⋊C4—21no—
175Dic47⋊C4—21no—
176Dic47⋊C4—22no—
177Dic47⋊C4—22no—
178Dic47⋊C4—22no—
179Dic47⋊C4—22no—
180Dic47⋊C4—22no—
181Dic47⋊C4C22⋊C412yes—
182Dic47⋊C4C22⋊C412yes—
183C4×Dic47—22no—
184C4×Dic47—22no—
185C4×Dic47—22no—
186C4×Dic47—22no—
187C4×Dic47C2×D414yes—
188C2×C47⋊C8—24no—
189C2×C47⋊C8—82no—
190#10625324—84no—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47—41no—
194C23×C47—41no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47C2×C22⋊C412yes—
198C23×C47C2×M1612yes—
199C23×C47C2×M1612yes—
200C23×C47C2×M1612yes—
201C23×C47C23×C411yescharacteristic
202C22×D47—21no—
203C22×D47—21no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47C2×C22⋊C412yes—
207D4×C47—28no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—81no—
219C2×C4×C47—81no—
220C2×C4×C47C2×C22⋊C411yescharacteristic
221C2×C4×C47C2×C22⋊C411yescharacteristic
222C2×C4×C47C2×M1612yes—
223C2×C4×C47C22×D412yes—
224C22⋊D47—28no—
225C22⋊D47—28no—
226C2×Dic47—28no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—28no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—82no—
241C2×Dic47—82no—
242C2×Dic47C2×C22⋊C412yes—
243C2×Dic47C2×C22⋊C412yes—
244C2×Dic47C2×C22⋊C412yes—
245C2×Dic47C2×M1612yes—
246C2×Dic47C2×M1612yes—
247C4×D47—28no—
248C4×D47—44no—
249C4×D47—82no—
250Dic94—28no—
251C8×C47—44no—
252C47⋊C8—44no—
253#17368—471nomaximal, Sylow
254C22×C47—21no—
255C22×C47—22no—
256C22×C47—21no—
257C22×C47—22no—
258C22×C47—22no—
259C22×C47—42no—
260C22×C47—42no—
261C22×C47—42no—
262C22×C47—42no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47#40714yes—
266C22×C47C22×C22⋊C411yescharacteristic
267C22×C47C22×M1611yescharacteristic
268C22×C47C22×M1611yescharacteristic
269C2×D47—22no—
270C2×D47—22no—
271C2×D47—22no—
272C2×D47—42no—
273C2×D47—42no—
274C4×C47—22no—
275C4×C47—22no—
276C4×C47—21no—
277C4×C47—21no—
278C4×C47—41no—
279C4×C47—41no—
280Dic47—22no—
281Dic47—22no—
282Dic47—22no—
283Dic47—22no—
284Dic47—22no—
285Dic47—41no—
286Dic47—41no—
287C2×#520—471no—
288#2973—472no—
289#1467—472no—
290#1465—472no—
291#1464—472no—
292#1463—472no—
293#1459—471no—
294#1459D4711yescharacteristic, complemented
295C2×#324—472no—
296C2×C47—21no—
297C2×C47—21no—
298C2×C47—24no—
299C2×C47—42no—
300C2×C47C2×#40711yescharacteristic
301C2×C47#288311yescharacteristic
302C2×C47#288911yescharacteristic
303D47—42no—
304C22×#41—471no—
305#520—944no—
306#520—944no—
307C2×C4×Q8—471no—
308C2×C4×Q8—471no—
309C2×C4×D4—471no—
310C2×C4×D4—471no—
311C2×C4×D4—471no—
312C2×C4×D4—471no—
313C2×C4×D4—471no—
314C2×C4×D4C2×D4711yescharacteristic
315C2×#117—471no—
316C2×#117—471no—
317C2×#117—471no—
318C22×C4⋊C4—471no—
319C22×C4⋊C4—471no—
320C22×C4⋊C4—471no—
321#435—944no—
322#435—944no—
323#432—474no—
324#407—474no—
325C2×C22⋊C8—472no—
326C2×C22⋊C8C2×D4712yes—
327#324—472no—
328#324—474no—
329#324—474no—
330#324C2×D4712yes—
331#323—472no—
332#323C2×D4712yes—
333C47#1736811yescharacteristic, complemented, Sylow
334C2×#41—944no—
335C2×#41—944no—
336C2×#41—944no—
337C22×Q8—471no—
338C22×D4—471no—
339C22×D4—471no—
340C22×D4C4×D4711yescharacteristic
341C23×C4—471no—
342C23×C4—471no—
343C23×C4—471no—
344C23×C4—471no—
345C23×C4—471no—
346C23×C4—471no—
347C23×C4—471no—
348C23×C4C4×D4711yescharacteristic
349C23×C4C22×D4711yescharacteristic
350C2×M16—944no—
351C22×C8—22no—
352C22×C8—942no—
353C4×Q8—942no—
354C4×Q8—942no—
355C4×Q8—944no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—474no—
359C4×D4—474no—
360C4×D4—944no—
361C4×D4—944no—
362C4×D4—942no—
363C4×D4—942no—
364C4×D4—944no—
365#117—942no—
366#117—942no—
367#117—944no—
368#117—944no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—471no—
377C2×C4⋊C4—471no—
378C2×C4⋊C4—944no—
379C2×C4⋊C4—942no—
380C2×C4⋊C4—942no—
381C2×C4⋊C4—942no—
382C2×C4⋊C4—942no—
383C2×C4⋊C4C22×D4711yescharacteristic
384C2×C22⋊C4—471no—
385C2×C22⋊C4—471no—
386C2×C22⋊C4—471no—
387C2×C22⋊C4—471no—
388C2×C22⋊C4C4×D4711yescharacteristic
389C2×C22⋊C4C22×D4711yescharacteristic
390C2×C42—471no—
391C2×C42—471no—
392C2×C42—471no—
393C2×C42—471no—
394C2×C42—471no—
395C2×C42C4×D4711yescharacteristic
396C4⋊C8—944no—
397C22⋊C8—22no—
398C22⋊C8—474no—
399C22⋊C8—944no—
400C22⋊C8—942no—
401C22⋊C8C22×D4714yes—
402#97—944no—
403C24—471no—
404C24C2×C4×D4711yescharacteristic
405C24C2×C4×D4711yescharacteristic
406#41—9432no—
407C2×Q8—942no—
408C2×Q8—942no—
409C2×Q8—942no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—474no—
413C2×D4—942no—
414C2×D4—942no—
415C2×D4—942no—
416C2×D4—942no—
417C2×D4—942no—
418C2×D4#1062532414yescomplemented
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—474no—
424C22×C4—471no—
425C22×C4—471no—
426C22×C4—471no—
427C22×C4—471no—
428C22×C4—471no—
429C22×C4—474no—
430C22×C4—471no—
431C22×C4—471no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4—942no—
439C22×C4—942no—
440C22×C4—942no—
441C22×C4—942no—
442C22×C4—942no—
443C22×C4—3761no—
444C22×C4—3761no—
445C22×C4—3761no—
446C22×C4—3761no—
447C22×C4C2×C4×D4711yescharacteristic
448C22×C4C2×C4×D4711yescharacteristic
449C22×C4C2×C4×D4711yescharacteristic
450C22×C4C2×C4×D4711yescharacteristic
451C22×C4D4×D4712yes—
452C22×C4D4×D4712yes—
453C22×C4C23×D4711yescharacteristic
454M16—3764no—
455C2×C8—24no—
456C2×C8—82no—
457C2×C8—944no—
458C2×C8—3762no—
459C4⋊C4—22no—
460C4⋊C4—472no—
461C4⋊C4—472no—
462C4⋊C4—942no—
463C4⋊C4—942no—
464C4⋊C4—942no—
465C4⋊C4—942no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—942no—
471C4⋊C4—942no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—474no—
475C22⋊C4—472no—
476C22⋊C4—472no—
477C22⋊C4—942no—
478C22⋊C4—942no—
479C42—21no—
480C42—21no—
481C42—474no—
482C42—942no—
483C42—942no—
484C42—942no—
485C42—942no—
486C23—21no—
487C23—21no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—472no—
493C23—941no—
494C23—941no—
495C23—1881no—
496C23—1881no—
497C23C22⋊C4×D4712yes—
498C23M16×D4712yes—
499C23C2×#1062532412yes—
500C23C2×#1062532412yes—
501C23C22×C4×D4711yescharacteristic
502Q8—948no—
503D4—28no—
504D4—948no—
505D4—948no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—472no—
519C2×C4—472no—
520C2×C4—472no—
521C2×C4—472no—
522C2×C4—472no—
523C2×C4—948no—
524C2×C4—948no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—948no—
528C2×C4—941no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—941no—
532C2×C4—941no—
533C2×C4—941no—
534C2×C4—3762no—
535C2×C4—3762no—
536C2×C4—3762no—
537C2×C4—1884no—
538C2×C4—1881no—
539C2×C4—1881no—
540C2×C4—1881no—
541C2×C4—1881no—
542C2×C4C22⋊C4×D4711yescharacteristic
543C2×C4C22⋊C4×D4711yescharacteristic
544C2×C4C2×#1062532412yes—
545C2×C4C2×D4×D4712yes—
546C8—44no—
547C8—1884no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—22no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—41no—
558C22—41no—
559C22—942no—
560C22—942no—
561C22—942no—
562C22—1882no—
563C22—1882no—
564C22#1568908514yes—
565C22C2×C22⋊C4×D4711yescharacteristic
566C22C2×M16×D4711yescharacteristic
567C22C22×#1062532411yescharacteristic
568C4—22no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—942no—
575C4—942no—
576C4—942no—
577C4—942no—
578C4—942no—
579C4—1881no—
580C4—1881no—
581C2—21no—
582C2—21no—
583C2—24no—
584C2—42no—
585C2—1882no—
586C2C2×#1568908511yescharacteristic
587C2#2025184611yescharacteristic
588C2#2025186911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1459C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#10625352C4
cosocleC22×C4×C47C24
hypercenter#1459D47
hypocenterC47#17368
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #20252414C2semidirect
3. #20241730C2semidirect
4. #20241723C2semidirect
5. #20241719C2semidirect
6. #20241716C2semidirect
7. #20241706C2semidirect
8. C2×#15688848C2semidirect
9. C47×#1459C2semidirect
113. C2×D4×C47M16semidirect
140. C22×Dic47M16semidirect
294. #1459D47semidirect
333. C47#17368semidirect
418. C2×D4#10625324semidirect

Maximal subgroups

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

subgroupindex
C2×#156896022
#202524142
#202417302
#202417232
#202417192
#202417162
#202417062
C2×#156888482
C47×#14592
#1736847