Finite Group Databasebeta

← #26217912

Subgroups — #26217912

Order 12032.

2126 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689598C211yesmaximal, characteristic, complemented
2C22×#13093939C211yesmaximal, characteristic, complemented
3#20245966C212yesmaximal, complemented
4#20243802C214yesmaximal, complemented
5#20243797C214yesmaximal, complemented
6C2×#15688889C212yesmaximal, complemented
7C2×C47×#534C211yesmaximal, characteristic
8#15689598—24no—
9#15689598—22no—
10#15689598C2214yes—
11C2×D4×Dic47—24no—
12C2×#13093983—21no—
13C22×C22⋊Dic47—21no—
14C22×C22⋊Dic47C2212yes—
15C22×C22⋊Dic47C2212yes—
16C2×#13093939—24no—
17C2×#13093939C2214yes—
18#15689003—24no—
19#15689003—24no—
20#15688986C2214yescomplemented
21#15688979C2214yescomplemented
22#15688889C2218yescomplemented
23C23×D4×C47C2211yescharacteristic
24C23×D4×C47C2211yescharacteristic
25C47×#534—24no—
26C47×#534C418yescomplemented
27C2×#123×C47—21no—
28C2×#123×C47C2212yes—
29C2×#121×C47—22no—
30C2×#120×C47—21no—
31C2×#120×C47C2212yes—
32C22×C22⋊C4×C47C2211yescharacteristic
33C23×Dic47—22no—
34C23×Dic47—22no—
35C23×Dic47D414yescomplemented
36D4×Dic47—216no—
37D4×Dic47—216no—
38#13093983—24no—
39#13093983—24no—
40C2×C4⋊Dic47—22no—
41C2×C22⋊Dic47—22no—
42C2×C22⋊Dic47—24no—
43C2×C22⋊Dic47—22no—
44C2×C22⋊Dic47—24no—
45C2×C22⋊Dic47—22no—
46C2×C22⋊Dic47—22no—
47C2×C22⋊Dic47—22no—
48C2×C22⋊Dic47—24no—
49C2×C22⋊Dic47—24no—
50C2×C22⋊Dic47—22no—
51C2×C22⋊Dic47—28no—
52C2×C22⋊Dic47D414yescomplemented
53C2×C22⋊Dic47C2314yes—
54C2×C22⋊Dic47C2314yes—
55C2×C4×Dic47—22no—
56#13093939—28no—
57C47⋊#95—28no—
58C25×C47D411yescharacteristic
59C25×C47C2311yescharacteristic
60C25×C47C2311yescharacteristic
61C22×D4×C47—22no—
62C22×D4×C47—22no—
63C22×D4×C47—24no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—22no—
69C22×D4×C47—24no—
70C22×D4×C47—22no—
71C22×D4×C47C2×C414yes—
72C22×D4×C47C2×C414yescomplemented
73C22×D4×C47D414yes—
74C22×D4×C47D412yes—
75C22×D4×C47C2312yes—
76C23×C4×C47—21no—
77C23×C4×C47D411yescharacteristic
78C23×C4×C47C2311yescharacteristic
79#123×C47—24no—
80#123×C47—28no—
81#123×C47C2×C418yescomplemented
82#121×C47—216no—
83#120×C47—28no—
84#120×C47—24no—
85#120×C47C2×C418yescomplemented
86C2×C4⋊C4×C47—22no—
87C2×C22⋊C4×C47—21no—
88C2×C22⋊C4×C47—22no—
89C2×C22⋊C4×C47—22no—
90C2×C22⋊C4×C47—22no—
91C2×C22⋊C4×C47C2×C414yescomplemented
92C2×C22⋊C4×C47C2312yes—
93C24×C47—21no—
94C24×C47—21no—
95C24×C47—22no—
96C24×C47—21no—
97C24×C47—22no—
98C24×C47—21no—
99C24×C47—22no—
100C24×C47—82no—
101C24×C47—82no—
102C24×C47—82no—
103C24×C47C22⋊C414yescomplemented
104C24×C47C22×C412yes—
105C24×C47C22×C412yescomplemented
106C24×C47C2×D412yes—
107C24×C47C2×D411yescharacteristic
108C24×C47C2×D411yescharacteristic
109C24×C47C2×D412yes—
110C24×C47C2×D412yes—
111C24×C47C2×D412yes—
112C24×C47#4114yes—
113C24×C47C2411yescharacteristic
114C2×D4×C47—28no—
115C2×D4×C47—28no—
116C2×D4×C47—24no—
117C2×D4×C47—28no—
118C2×D4×C47—28no—
119C2×D4×C47—24no—
120C2×D4×C47—24no—
121C2×D4×C47—24no—
122C2×D4×C47—24no—
123C2×D4×C47—24no—
124C2×D4×C47—28no—
125C2×D4×C47—28no—
126C2×D4×C47—28no—
127C2×D4×C47—41no—
128C2×D4×C47—42no—
129C2×D4×C47—41no—
130C2×D4×C47—44no—
131C2×D4×C47—44no—
132C2×D4×C47—42no—
133C2×D4×C47—42no—
134C2×D4×C47—84no—
135C2×D4×C47C22⋊C418yescomplemented
136C2×D4×C47C22×C414yes—
137C2×D4×C47C2×D414yes—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—24no—
147C22×C4×C47—82no—
148C22×C4×C47C22⋊C414yescomplemented
149C22×C4×C47C22×C412yescomplemented
150C22×C4×C47C2×D412yes—
151C22×Dic47—24no—
152C22×Dic47—28no—
153C22×Dic47—24no—
154C22×Dic47—24no—
155C22×Dic47—44no—
156C22×Dic47—84no—
157C22×Dic47—84no—
158C22×Dic47—84no—
159C22×Dic47C2×D418yes—
160C4⋊C4×C47—28no—
161C22⋊C4×C47—24no—
162C22⋊C4×C47—28no—
163C22⋊C4×C47—22no—
164C22⋊C4×C47—28no—
165C22⋊C4×C47C22×C414yescomplemented
166C22⋊Dic47—28no—
167C22⋊Dic47—24no—
168C22⋊Dic47—24no—
169C22⋊Dic47—24no—
170C22⋊Dic47—24no—
171C22⋊Dic47—24no—
172C22⋊Dic47—24no—
173C22⋊Dic47—44no—
174C22⋊Dic47—88no—
175C4⋊Dic47—28no—
176C4×Dic47—28no—
177C23×C47—22no—
178C23×C47—24no—
179C23×C47—22no—
180C23×C47—24no—
181C23×C47—22no—
182C23×C47—24no—
183C23×C47—44no—
184C23×C47—44no—
185C23×C47—42no—
186C23×C47—42no—
187C23×C47—42no—
188C23×C47—44no—
189C23×C47—44no—
190C23×C47—48no—
191C23×C47—44no—
192C23×C47—41no—
193C23×C47—42no—
194C23×C47—41no—
195C23×C47—82no—
196C23×C47—82no—
197C23×C47—82no—
198C23×C47—82no—
199C23×C47—84no—
200C23×C47—84no—
201C23×C47—84no—
202C23×C47—82no—
203C23×C47—84no—
204C23×C47C2×C22⋊C414yes—
205C23×C47C2×C22⋊C412yes—
206C23×C47C2×C22⋊C412yes—
207C23×C47C4×D414yes—
208C23×C47C4×D414yes—
209C23×C47#12011yescharacteristic
210C23×C47#12012yes—
211C23×C47#12011yescharacteristic
212C23×C47#12114yes—
213C23×C47#12114yes—
214C23×C47#12312yes—
215C23×C47#12312yes—
216C23×C47C23×C411yescharacteristic
217C23×C47C22×D412yes—
218C23×C47C22×D411yescharacteristic
219C23×C47C22×D411yescharacteristic
220C23×C47C2×#4112yes—
221D4×C47—28no—
222D4×C47—28no—
223D4×C47—216no—
224D4×C47—44no—
225D4×C47—44no—
226D4×C47—48no—
227D4×C47—88no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—24no—
233C2×C4×C47—22no—
234C2×C4×C47—24no—
235C2×C4×C47—44no—
236C2×C4×C47—41no—
237C2×C4×C47—42no—
238C2×C4×C47—41no—
239C2×C4×C47—84no—
240C2×C4×C47C2×C22⋊C414yes—
241C2×Dic47—28no—
242C2×Dic47—48no—
243C2×Dic47—48no—
244C2×Dic47—48no—
245C2×Dic47—44no—
246C2×Dic47—84no—
247C2×Dic47—88no—
248C2×Dic47—88no—
249#20960—471nomaximal, Sylow
250C22×C47—22no—
251C22×C47—24no—
252C22×C47—24no—
253C22×C47—22no—
254C22×C47—22no—
255C22×C47—24no—
256C22×C47—44no—
257C22×C47—42no—
258C22×C47—42no—
259C22×C47—42no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—42no—
263C22×C47—44no—
264C22×C47—44no—
265C22×C47—44no—
266C22×C47—42no—
267C22×C47—44no—
268C22×C47—48no—
269C22×C47—44no—
270C22×C47—48no—
271C22×C47—44no—
272C22×C47—42no—
273C22×C47—82no—
274C22×C47—84no—
275C22×C47—84no—
276C22×C47—82no—
277C22×C47—82no—
278C22×C47#38612yes—
279C22×C47#38612yes—
280C22×C47#38614yes—
281C22×C47C22×C22⋊C411yescharacteristic
282C22×C47C2×C4×D412yes—
283C22×C47C2×#12011yescharacteristic
284C22×C47C2×#12112yes—
285C22×C47C2×#12311yescharacteristic
286C4×C47—24no—
287C4×C47—44no—
288C4×C47—42no—
289Dic47—48no—
290Dic47—84no—
291C2×#534D4711yescharacteristic
292C2×#518—471no—
293C22×#99—471no—
294#2308—472no—
295#1890—474no—
296#1889—474no—
297C2×#342—472no—
298C2×C47—22no—
299C2×C47—21no—
300C2×C47—22no—
301C2×C47—22no—
302C2×C47—21no—
303C2×C47—22no—
304C2×C47—24no—
305C2×C47—44no—
306C2×C47—82no—
307C2×C47C2×#38611yescharacteristic
308C2×C47#302612yes—
309C23×D4C2×D4711yescharacteristic
310C23×D4C2×D4711yescharacteristic
311#534—24no—
312#534Dic4718yescomplemented
313C2×#123—21no—
314C2×#123C2×D4712yes—
315C2×#121—22no—
316C2×#120—21no—
317C2×#120C2×D4712yes—
318#518—474no—
319#518—944no—
320#518—942no—
321C2×C4×D4—944no—
322C2×#117—941no—
323C22×C22⋊C4—472no—
324C22×C22⋊C4—472no—
325C22×C22⋊C4—941no—
326C22×C22⋊C4C2×D4711yescharacteristic
327C2×#99—474no—
328C2×#99—944no—
329#386—944no—
330#386—944no—
331#381—474no—
332#379—474no—
333#342—478no—
334C47#2096011yescharacteristic, complemented, Sylow
335C25C22⋊D4711yescharacteristic
336C25C22×D4711yescharacteristic
337C25C22×D4711yescharacteristic
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4C2×Dic4714yes—
349C22×D4C2×Dic4714yescomplemented
350C22×D4C22⋊D4714yes—
351C22×D4C22⋊D4712yes—
352C22×D4C22×D4712yes—
353C23×C4—21no—
354C23×C4—474no—
355C23×C4—942no—
356C23×C4—942no—
357C23×C4C22⋊D4711yescharacteristic
358C23×C4C22×D4711yescharacteristic
359#123—24no—
360#123—28no—
361#123C2×Dic4718yescomplemented
362#121—216no—
363#120—28no—
364#120—24no—
365#120C2×Dic4718yescomplemented
366C4×D4—9416no—
367C4×D4—9416no—
368#117—944no—
369#117—944no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—942no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—474no—
377C2×C22⋊C4—474no—
378C2×C22⋊C4—474no—
379C2×C22⋊C4—942no—
380C2×C22⋊C4—944no—
381C2×C22⋊C4—942no—
382C2×C22⋊C4—942no—
383C2×C22⋊C4—942no—
384C2×C22⋊C4—942no—
385C2×C22⋊C4—944no—
386C2×C22⋊C4—944no—
387C2×C22⋊C4—944no—
388C2×C22⋊C4—948no—
389C2×C22⋊C4—942no—
390C2×C22⋊C4C2×Dic4714yescomplemented
391C2×C22⋊C4C22×D4712yes—
392C2×C42—942no—
393#99—948no—
394#95—948no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—82no—
403C24—82no—
404C24—82no—
405C24C22⋊Dic4714yescomplemented
406C24D4×D4712yes—
407C24D4×D4712yes—
408C24#1062535214yes—
409C24C22×Dic4712yes—
410C24C22×Dic4712yescomplemented
411C24C2×C22⋊D4712yes—
412C24C2×C22⋊D4711yescharacteristic
413C24C2×C22⋊D4711yescharacteristic
414C24C2×C22⋊D4712yes—
415C24C23×D4711yescharacteristic
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—24no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—28no—
427C2×D4—28no—
428C2×D4—28no—
429C2×D4—41no—
430C2×D4—42no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—84no—
437C2×D4C22⋊Dic4718yescomplemented
438C2×D4C22×Dic4714yes—
439C2×D4C2×C22⋊D4714yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—82no—
450C22×C4—478no—
451C22×C4—948no—
452C22×C4—944no—
453C22×C4—944no—
454C22×C4—944no—
455C22×C4—3764no—
456C22×C4—3764no—
457C22×C4—3764no—
458C22×C4—1884no—
459C22×C4C22⋊Dic4714yescomplemented
460C22×C4C22×Dic4712yescomplemented
461C22×C4C2×C22⋊D4712yes—
462C4⋊C4—28no—
463C4⋊C4—948no—
464C22⋊C4—24no—
465C22⋊C4—28no—
466C22⋊C4—22no—
467C22⋊C4—28no—
468C22⋊C4—948no—
469C22⋊C4—944no—
470C22⋊C4—944no—
471C22⋊C4—944no—
472C22⋊C4—944no—
473C22⋊C4—944no—
474C22⋊C4—944no—
475C22⋊C4—3768no—
476C22⋊C4—1884no—
477C22⋊C4C22×Dic4714yescomplemented
478C42—948no—
479C23—24no—
480C23—22no—
481C23—24no—
482C23—22no—
483C23—22no—
484C23—24no—
485C23—42no—
486C23—44no—
487C23—44no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—44no—
492C23—48no—
493C23—44no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—82no—
498C23—84no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—84no—
503C23—84no—
504C23—82no—
505C23—84no—
506C23C2×C22⋊Dic4714yes—
507C23C2×C22⋊Dic4712yes—
508C23C2×C22⋊Dic4712yes—
509C23D4×Dic4714yes—
510C23D4×Dic4714yes—
511C23#1309399211yescharacteristic
512C23#1309399212yes—
513C23#1309399211yescharacteristic
514C23#1309399614yes—
515C23#1309399614yes—
516C23#1309400512yes—
517C23#1309400512yes—
518C23C23×Dic4711yescharacteristic
519C23C2×D4×D4712yes—
520C23C22×C22⋊D4711yescharacteristic
521C23C22×C22⋊D4711yescharacteristic
522C23C2×#1062535212yes—
523D4—216no—
524D4—28no—
525D4—28no—
526D4—44no—
527D4—44no—
528D4—48no—
529D4—88no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—44no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—948no—
543C2×C4—3768no—
544C2×C4—3764no—
545C2×C4—3768no—
546C2×C4—1888no—
547C2×C4—1884no—
548C2×C4—1888no—
549C2×C4—1888no—
550C2×C4C2×C22⋊Dic4714yes—
551C22—22no—
552C22—24no—
553C22—22no—
554C22—24no—
555C22—22no—
556C22—24no—
557C22—42no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—41no—
563C22—42no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—42no—
568C22—44no—
569C22—48no—
570C22—44no—
571C22—48no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—84no—
576C22—84no—
577C22—82no—
578C22—82no—
579C22#1568900312yes—
580C22#1568900312yes—
581C22#1568900314yes—
582C22C22×C22⋊Dic4711yescharacteristic
583C22C2×D4×Dic4712yes—
584C22C2×#1309399211yescharacteristic
585C22C2×#1309399612yes—
586C22C2×#1309400511yescharacteristic
587C4—24no—
588C4—44no—
589C4—42no—
590C4—3764no—
591C4—1888no—
592C2—21no—
593C2—22no—
594C2—22no—
595C2—22no—
596C2—21no—
597C2—22no—
598C2—24no—
599C2—44no—
600C2—82no—
601C2C2×#1568900311yescharacteristic
602C2#2025278412yes—
subgroupG/H
centerC22C2×#13093992
commutatorC23×C47C23×C4
FrattiniC24C23×D47
Fitting, prime radicalC2×C47×#534C2
socleC22×C47C2×#120
cosocleC24×C47C24
hypercenterC2×#534D47
hypocenterC47#20960
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C2×#15689598C2semidirect
2. C22×#13093939C2semidirect
3. #20245966C2semidirect
4. #20243802C2semidirect
5. #20243797C2semidirect
6. C2×#15688889C2semidirect
20. #15688986C22semidirect
21. #15688979C22semidirect
22. #15688889C22semidirect
26. C47×#534C4semidirect
35. C23×Dic47D4semidirect
52. C2×C22⋊Dic47D4semidirect
72. C22×D4×C47C2×C4semidirect
81. #123×C47C2×C4semidirect
85. #120×C47C2×C4semidirect
91. C2×C22⋊C4×C47C2×C4semidirect
103. C24×C47C22⋊C4semidirect
105. C24×C47C22×C4semidirect
135. C2×D4×C47C22⋊C4semidirect
148. C22×C4×C47C22⋊C4semidirect
149. C22×C4×C47C22×C4semidirect
165. C22⋊C4×C47C22×C4semidirect
312. #534Dic47semidirect
334. C47#20960semidirect
349. C22×D4C2×Dic47semidirect
361. #123C2×Dic47semidirect
365. #120C2×Dic47semidirect
390. C2×C22⋊C4C2×Dic47semidirect
405. C24C22⋊Dic47semidirect
410. C24C22×Dic47semidirect
437. C2×D4C22⋊Dic47semidirect
459. C22×C4C22⋊Dic47semidirect
460. C22×C4C22×Dic47semidirect
477. C22⋊C4C22×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156895982
C22×#130939392
#202459662
#202438022
#202437972
C2×#156888892
C2×C47×#5342
#2096047