Finite Group Databasebeta

← #26186796

Subgroups — #26186796

Order 12032.

682 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253944C211yesmaximal, characteristic
2#20252317C211yesmaximal, characteristic, complemented
3#20252095C211yesmaximal, characteristic
4#20242281C211yesmaximal, characteristic, complemented
5#20242279C211yesmaximal, characteristic, complemented
6#20242277C211yesmaximal, characteristic, complemented
7#20242275C211yesmaximal, characteristic, complemented
8C8×#10625325C211yesmaximal, characteristic, complemented
9C8×#10625336C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242142C211yesmaximal, characteristic, complemented
12#20241841C211yesmaximal, characteristic, complemented
13#20241837C211yesmaximal, characteristic
14C82×D47C211yesmaximal, characteristic, complemented
15C8×SD16×C47C211yesmaximal, characteristic, complemented
16C2×#13094030—21no—
17#15689677C2211yescharacteristic
18#15689670C2211yescharacteristic
19#15689520C411yescharacteristic
20#15689494C411yescharacteristic
21#15689472C411yescharacteristic
22#15689468C411yescharacteristic
23#15689355C411yescharacteristic
24#15689353C411yescharacteristic
25#15689351C411yescharacteristic
26#15689349C411yescharacteristic
27#15689254C2211yescharacteristic
28#15689252—21no—
29#15689250C2211yescharacteristic
30C8×Dic94—21no—
31C8×Dic94C2211yescharacteristic
32C4×#10625325C2211yescharacteristic
33C4×#10625336C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35#15689201C2211yescharacteristic
36#15689200C2211yescharacteristic
37#15689198—21no—
38C8×D188C2211yescharacteristic
39C8×C22⋊D47—21no—
40#15689148—21no—
41#15689145C2211yescharacteristic
42#15689145C2211yescharacteristic
43#15689088—21no—
44#15689077—21no—
45C4×C8×D47C2211yescharacteristic
46C4×C8×D47C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688874C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688855C2211yescharacteristic
52Q8⋊(C47⋊C8)C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688852C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56#15688850C2211yescharacteristic
57C8×C47⋊C8C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#10625350—21no—
68C2×#10625325C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71#13094030—44no—
72C2×#10625329—21no—
73C2×#10625324—21no—
74C2×#10625324—21no—
75C2×#10625324—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47C2×C411yescharacteristic
79C2×C8×D47C2×C411yescharacteristic
80C2×C8×D47D411yescharacteristic
81C2×C8×D47D411yescharacteristic
82#13094023C2×C411yescharacteristic
83#13094023C2×C411yescharacteristic
84#13094022C2×C411yescharacteristic
85#13094020C2×C411yescharacteristic
86#13094014—21no—
87#13094010—21no—
88#13094004C2×C411yescharacteristic
89#13094002—21no—
90#13094000C2×C411yescharacteristic
91#13093999C2×C411yescharacteristic
92#13093997—21no—
93#13093995C2×C411yescharacteristic
94C4×Dic94—21no—
95C4×Dic94C2311yescharacteristic
96C4×D188C2311yescharacteristic
97C4×C22⋊D47—21no—
98#13093981—21no—
99C42×D47C2311yescharacteristic
100#13093956C2×C411yescharacteristic
101#13093955C2×C411yescharacteristic
102#13093955C2×C411yescharacteristic
103C4⋊(C47⋊C8)—21no—
104C4⋊(C47⋊C8)C2311yescharacteristic
105C4⋊(C47⋊C8)C2311yescharacteristic
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109Dic47⋊C8—21no—
110#13093949C2×C411yescharacteristic
111#13093948C2×C411yescharacteristic
112#13093947C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114#13093945C2×C411yescharacteristic
115#13093944C2×C411yescharacteristic
116C22⋊(C47⋊C8)—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119#13093935—21no—
120#13093934—21no—
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C8×Dic47—21no—
126C8×Dic47C2×C411yescharacteristic
127C8×Dic47C2×C411yescharacteristic
128C8×Dic47D411yescharacteristic
129C8×Dic47D411yescharacteristic
130C2×SD16×C47C2×C411yescharacteristic
131C22×C8×C47—21no—
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47C2311yescharacteristic
134#106×C47C2×C411yescharacteristic
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138#103×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C2×C22⋊D47—21no—
149C2×C22⋊D47—21no—
150C2×C22⋊D47—21no—
151#10625350—42no—
152#10625350—42no—
153C2×D188—21no—
154C2×D188C22×C411yescharacteristic
155C2×C4×D47—21no—
156C2×C4×D47C22×C411yescharacteristic
157C2×C4×D47C2×D411yescharacteristic
158C2×C4×D47#4111yescharacteristic
159C2×Dic94—21no—
160C2×Dic94—21no—
161C2×Dic94C22×C411yescharacteristic
162SD16×C47—22no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—42no—
167C2×C8×C47C22×C411yescharacteristic
168C2×C8×C47C22×C411yescharacteristic
169C2×C8×C47C2×D411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C4⋊C4×C47—21no—
172C4⋊C4×C47C22×C411yescharacteristic
173C4⋊C4×C47C22×C411yescharacteristic
174C22⋊C4×C47—21no—
175C42×C47—21no—
176C42×C47C2411yescharacteristic
177C22⋊Dic47—21no—
178#10625336—22no—
179#10625335—22no—
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47C22×C411yescharacteristic
186C4⋊Dic47C22×C411yescharacteristic
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193C4×Dic47—21no—
194C4×Dic47C22×C411yescharacteristic
195C4×Dic47C2×D411yescharacteristic
196C4×Dic47#4111yescharacteristic
197#10625329—42no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205#10625325—22no—
206#10625324—42no—
207#10625324—42no—
208#10625324—42no—
209C8×D47—24no—
210C8×D47—22no—
211C8×D47—22no—
212C8×D47—22no—
213C8×D47—42no—
214C8×D47SD1614yescomplemented
215C23×C47—21no—
216C22×D47—21no—
217C22×D47C4×D411yescharacteristic
218Q8×C47—21no—
219Q8×C47—21no—
220D4×C47—21no—
221D4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47C23×C411yescharacteristic
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C22⋊D47—42no—
231C22⋊D47—42no—
232C22⋊D47—42no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47C4×D411yescharacteristic
237C2×Dic47C4×D411yescharacteristic
238C2×Dic47C4×D411yescharacteristic
239D188—21no—
240D188—21no—
241D188—42no—
242C4×D47—21no—
243C4×D47—21no—
244C4×D47—22no—
245C4×D47—41no—
246C4×D47—41no—
247C4×D47C2×SD1612yes—
248C4×D47#13512yes—
249Dic94—21no—
250Dic94—21no—
251Dic94—42no—
252Dic94—42no—
253C8×C47—22no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47#13112yescomplemented
259C8×C47C2×SD1612yes—
260C47⋊C8—22no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—41no—
264C47⋊C8—41no—
265C47⋊C8#13112yescomplemented
266C47⋊C8C2×SD1612yes—
267#17957—471nomaximal, Sylow
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47C2×C4×D411yescharacteristic
272C2×D47—21no—
273C2×D47—21no—
274C2×D47—41no—
275C2×D47—41no—
276C2×D47—41no—
277C2×D47C4×SD1612yes—
278C4×C47—21no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—41no—
282C4×C47C2×#13111yescharacteristic
283C4×C47C2×#13111yescharacteristic
284C4×C47C22×SD1611yescharacteristic
285C4×C47C2×#13511yescharacteristic
286Dic47—21no—
287Dic47—41no—
288Dic47—41no—
289Dic47—41no—
290Dic47C4×SD1612yes—
291Dic47#44312yes—
292#3167—471no—
293#2960—471no—
294#2931—471no—
295#1590—471no—
296#1590—471no—
297#1590—471no—
298#1590—471no—
299C8×SD16—471no—
300C8×SD16—471no—
301C8×SD16—471no—
302C8×SD16D4711yescharacteristic, complemented
303#1566—471no—
304#1493—471no—
305#1492—471no—
306C2×C82—471no—
307C2×C47—81no—
308C2×C47#293111yescharacteristic
309C2×C47C2×C4×SD1611yescharacteristic
310C2×C47C2×#44311yescharacteristic
311D47—22no—
312D47—81no—
313C2×#131—941no—
314#533—471no—
315#532—471no—
316#498—471no—
317#492—471no—
318#487—471no—
319#486—471no—
320#465—471no—
321#465—471no—
322#465—471no—
323#465—471no—
324#446—471no—
325#446—471no—
326#446—941no—
327C8×Q8—471no—
328C8×Q8—941no—
329C8×Q8C2×D4711yescharacteristic
330C4×SD16—471no—
331C4×SD16—471no—
332C4×SD16—471no—
333C4×SD16C2×D4711yescharacteristic
334#436—471no—
335#436—471no—
336#436—941no—
337C8×D4—471no—
338C8×D4—941no—
339C8×D4C2×D4711yescharacteristic
340#424—941no—
341#423—471no—
342#423—471no—
343#408—941no—
344#405—941no—
345C2×C4×C8—471no—
346C2×C4×C8—471no—
347C2×C4×C8—471no—
348#334—471no—
349#334—471no—
350#334—471no—
351#334C2×D4711yescharacteristic
352Q8⋊C8—471no—
353Q8⋊C8—471no—
354Q8⋊C8—471no—
355Q8⋊C8C2×D4711yescharacteristic
356D4⋊C8—471no—
357D4⋊C8—471no—
358D4⋊C8—471no—
359D4⋊C8C2×D4711yescharacteristic
360C82—471no—
361C82—471no—
362C82—471no—
363C82C2×D4711yescharacteristic
364C47#1795711yescharacteristic, complemented, Sylow
365C2×#41—941no—
366C2×SD16—471no—
367C2×SD16—471no—
368C2×SD16—471no—
369C2×SD16C4×D4711yescharacteristic
370#131—1884no—
371C2×M16—941no—
372C2×M16—941no—
373C2×M16—941no—
374C2×M16—941no—
375C22×C8—21no—
376C22×C8—471no—
377C22×C8—471no—
378C22×C8—471no—
379C22×C8—471no—
380C22×C8—941no—
381C22×C8—941no—
382C4⋊Q8—471no—
383C4⋊Q8—471no—
384C4⋊Q8—471no—
385#127—471no—
386#125—941no—
387#124—941no—
388C22⋊Q8—471no—
389C22⋊Q8—471no—
390C22⋊Q8—941no—
391#121—471no—
392#121—471no—
393#121—941no—
394C4×Q8—471no—
395C4×Q8—941no—
396C4×Q8C22×D4711yescharacteristic
397C4×D4—471no—
398C4×D4—941no—
399C4×D4C22×D4711yescharacteristic
400#117—941no—
401C2×C42—471no—
402#106—471no—
403#106—471no—
404#106—471no—
405#106C4×D4711yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—941no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8—941no—
414C4⋊C8C22×D4711yescharacteristic
415C4⋊C8C22×D4711yescharacteristic
416#103—471no—
417#103—471no—
418#103—471no—
419#103C4×D4711yescharacteristic
420#102—471no—
421#102—471no—
422#102—471no—
423#102C4×D4711yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—941no—
426C22⋊C8—941no—
427C22⋊C8—941no—
428#97—941no—
429#97—941no—
430C4×C8—21no—
431C4×C8—471no—
432C4×C8—471no—
433C4×C8—471no—
434C4×C8—471no—
435C4×C8—471no—
436C4×C8—471no—
437C4×C8—471no—
438C4×C8—941no—
439C4×C8—941no—
440C4×C8C22×D4711yescharacteristic
441C4×C8C22×D4711yescharacteristic
442C4×C8C22×D4711yescharacteristic
443#41—1882no—
444#41—1882no—
445C2×Q8—471no—
446C2×Q8—941no—
447C2×Q8—941no—
448C2×Q8C2×C4×D4711yescharacteristic
449C2×D4—471no—
450C2×D4—941no—
451C2×D4—941no—
452C2×D4—941no—
453C2×D4—941no—
454C2×D4C2×C4×D4711yescharacteristic
455C22×C4—21no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4—941no—
460SD16—22no—
461SD16—942no—
462SD16—942no—
463SD16—942no—
464M16—1882no—
465M16—1882no—
466M16—1882no—
467M16—1882no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—471no—
473C2×C8—471no—
474C2×C8—474no—
475C2×C8—471no—
476C2×C8—471no—
477C2×C8—942no—
478C2×C8—942no—
479C2×C8—944no—
480C2×C8—941no—
481C2×C8—942no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—1882no—
485C2×C8C2×C4×D4711yescharacteristic
486C2×C8C2×C4×D4711yescharacteristic
487C2×C8D4×D4711yescharacteristic
488C2×C8D4×D4711yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—471no—
491C4⋊C4—471no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4C2×C4×D4711yescharacteristic
500C4⋊C4C2×C4×D4711yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—941no—
503C22⋊C4—941no—
504C22⋊C4—941no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C42—21no—
508C42—471no—
509C42—471no—
510C42—471no—
511C42—941no—
512C42C23×D4711yescharacteristic
513C23—21no—
514C23—471no—
515C23—941no—
516Q8—21no—
517Q8—21no—
518Q8—941no—
519Q8—941no—
520Q8—1882no—
521Q8—1882no—
522D4—21no—
523D4—21no—
524D4—941no—
525D4—941no—
526D4—1882no—
527D4—1882no—
528D4—1882no—
529D4—1882no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—471no—
536C2×C4—471no—
537C2×C4—472no—
538C2×C4—472no—
539C2×C4—471no—
540C2×C4—942no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4C22×C4×D4711yescharacteristic
549C2×C4C2×D4×D4711yescharacteristic
550C2×C4#41×D4711yescharacteristic
551C8—22no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—472no—
557C8—472no—
558C8—942no—
559C8—941no—
560C8—941no—
561C8—1881no—
562C8—1881no—
563C8#1309403012yescomplemented
564C8SD16×D4712yes—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—472no—
569C22—941no—
570C22—941no—
571C22—1881no—
572C22—1881no—
573C22—1881no—
574C22C4×D4×D4711yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—472no—
580C4—472no—
581C4—941no—
582C4—1881no—
583C4—1881no—
584C4—1881no—
585C4#131×D4711yescharacteristic
586C4C2×#1309403011yescharacteristic
587C4C2×SD16×D4711yescharacteristic
588C4#135×D4711yescharacteristic
589C2—81no—
590C2—942no—
591C2—3761no—
592C2#2025209511yescharacteristic
593C2C4×SD16×D4711yescharacteristic
594C2#443×D4711yescharacteristic
subgroupG/H
centerC2×C8D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC8×SD16×C47C2
socleC22×C47C2×C4×D4
prime radical#15689670C22
cosocleC42×C47C24
hypercenterC8×SD16D47
hypocenterC47#17957
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
2. #20252317C2semidirect
4. #20242281C2semidirect
5. #20242279C2semidirect
6. #20242277C2semidirect
7. #20242275C2semidirect
8. C8×#10625325C2semidirect
9. C8×#10625336C2semidirect
10. C8×#10625335C2semidirect
11. #20242142C2semidirect
12. #20241841C2semidirect
14. C82×D47C2semidirect
15. C8×SD16×C47C2semidirect
214. C8×D47SD16semidirect
258. C8×C47#131semidirect
265. C47⋊C8#131semidirect
302. C8×SD16D47semidirect
364. C47#17957semidirect
563. C8#13094030semidirect

Maximal subgroups

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

subgroupindex
#202539442
#202523172
#202520952
#202422812
#202422792
#202422772
#202422752
C8×#106253252
C8×#106253362
C8×#106253352
#202421422
#202418412
#202418372
C82×D472
C8×SD16×C472
#1795747