Finite Group Databasebeta

← #26186906

Subgroups — #26186906

Order 12032.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253983C211yesmaximal, characteristic
2#20252533C211yesmaximal, characteristic, complemented
3#20252466C211yesmaximal, characteristic, complemented
4#20242301C211yesmaximal, characteristic, complemented
5#20242289C211yesmaximal, characteristic, complemented
6#20242277C211yesmaximal, characteristic, complemented
7#20242272C211yesmaximal, characteristic, complemented
8#20242211C211yesmaximal, characteristic, complemented
9#20242199C211yesmaximal, characteristic, complemented
10#20242187C211yesmaximal, characteristic, complemented
11#20242182C211yesmaximal, characteristic, complemented
12#20241846C211yesmaximal, characteristic, complemented
13#20241838C211yesmaximal, characteristic, complemented
14M16×C47⋊C8C211yesmaximal, characteristic, complemented
15C47×#1569C211yesmaximal, characteristic, complemented
16#15689673C2211yescharacteristic
17#15689657C2211yescharacteristic
18#15689532C411yescharacteristic
19#15689512C411yescharacteristic
20#15689488C411yescharacteristic
21#15689483C411yescharacteristic
22#15689376C411yescharacteristic
23#15689376C411yescharacteristic
24#15689369C411yescharacteristic
25#15689369C411yescharacteristic
26#15689250C2211yescharacteristic
27#15689247C2211yescharacteristic
28C4×#10625325C2211yescharacteristic
29C4×#10625325C2211yescharacteristic
30C4×D376C2211yescharacteristic
31C4×D376C2211yescharacteristic
32#15689200C2211yescharacteristic
33#15689200C2211yescharacteristic
34#15689200C2211yescharacteristic
35#15689199—21no—
36#15689196—21no—
37#15689196—21no—
38#15689192—21no—
39#15689188C2211yescharacteristic
40#15689188C2211yescharacteristic
41#15689188C2211yescharacteristic
42#15689183—21no—
43#15689176C2211yescharacteristic
44#15689148—21no—
45#15689088—21no—
46#15689088—21no—
47C2×C4×C47⋊C8C2211yescharacteristic
48#15688853C2211yescharacteristic
49#15688853C2211yescharacteristic
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688850C2211yescharacteristic
53#15688850C2211yescharacteristic
54#15688850C2211yescharacteristic
55#15688850C2211yescharacteristic
56#15688844C2211yescharacteristic
57#15688844C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#432C2211yescharacteristic
61C47×#423C2211yescharacteristic
62C4×M16×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×#335C2211yescharacteristic
65C47×#334C2211yescharacteristic
66C47×#334C2211yescharacteristic
67C2×#10625350—21no—
68C2×#10625325C2×C411yescharacteristic
69C2×#10625325C2×C411yescharacteristic
70C2×D376C2×C411yescharacteristic
71C2×D376C2×C411yescharacteristic
72C2×#10625324—21no—
73C2×#10625324—21no—
74C2×#10625324—21no—
75C22×C47⋊C8—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47—21no—
79#13094024C2×C411yescharacteristic
80#13094021C2×C411yescharacteristic
81#13094018—21no—
82#13094016C2×C411yescharacteristic
83#13094012—21no—
84#13094012C2×C411yescharacteristic
85#13094007—21no—
86#13094003C2×C411yescharacteristic
87#13093998—21no—
88#13093998C2×C411yescharacteristic
89#13093998C2×C411yescharacteristic
90#13093998C2×C411yescharacteristic
91C4×Dic94C2311yescharacteristic
92C4×D188—21no—
93C4×D188C2311yescharacteristic
94C4×D188C2311yescharacteristic
95C4×D188C2311yescharacteristic
96C4×C22⋊D47—21no—
97#13093981—21no—
98#13093958C2×C411yescharacteristic
99#13093958C2×C411yescharacteristic
100#13093956C2×C411yescharacteristic
101#13093956C2×C411yescharacteristic
102C4⋊(C47⋊C8)D411yescharacteristic
103C4⋊(C47⋊C8)D411yescharacteristic
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106#13093949C2×C411yescharacteristic
107#13093949C2×C411yescharacteristic
108#13093946C2×C411yescharacteristic
109#13093946C2×C411yescharacteristic
110#13093946C2×C411yescharacteristic
111#13093946C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114C22⋊(C47⋊C8)D411yescharacteristic
115C22⋊(C47⋊C8)D411yescharacteristic
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121(C2×D47)⋊C8—21no—
122#13093934—21no—
123C4×C47⋊C8—21no—
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C4×C47⋊C8C2311yescharacteristic
128C8×Dic47—21no—
129C2×M16×C47—21no—
130C2×M16×C47C2×C411yescharacteristic
131C2×M16×C47C2×C411yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C4⋊C8×C47—21no—
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C22⋊C8×C47—21no—
139#97×C47—21no—
140#97×C47C2×C411yescharacteristic
141#97×C47C2×C411yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C2×C22⋊D47—21no—
148C2×C22⋊D47—21no—
149C2×C22⋊D47—21no—
150#10625350—81no—
151#10625350—81no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188C22×C411yescharacteristic
155C2×D188C22×C411yescharacteristic
156C2×D188C22×C411yescharacteristic
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×Dic94—21no—
161C2×Dic94C22×C411yescharacteristic
162M16×C47—22no—
163M16×C47—22no—
164M16×C47—81no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C22×C411yescharacteristic
173C42×C47C22×C411yescharacteristic
174C42×C47C2×D411yescharacteristic
175C42×C47#4111yescharacteristic
176C42×C47C2411yescharacteristic
177C22⋊Dic47—21no—
178(C2×D47)⋊C4—21no—
179(C2×D47)⋊C4—21no—
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189C4⋊Dic47C22×C411yescharacteristic
190C4⋊Dic47C22×C411yescharacteristic
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195C4×Dic47—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—42no—
199C2×C47⋊C8C2×D411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202C2×C47⋊C8C2×D411yescharacteristic
203D376—22no—
204D376—22no—
205#10625325—22no—
206#10625325—22no—
207#10625324—81no—
208#10625324—81no—
209#10625324—81no—
210C8×D47—81no—
211C8×D47—81no—
212C8×D47—81no—
213C23×C47C4×D411yescharacteristic
214C22×D47—21no—
215C22×D47—21no—
216C22×D47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—41no—
222C2×C4×C47C4×D411yescharacteristic
223C2×C4×C47C4×D411yescharacteristic
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C23×C411yescharacteristic
226C2×C4×C47C22×D411yescharacteristic
227C2×C4×C47C2×#4111yescharacteristic
228C22⋊D47—81no—
229C22⋊D47—81no—
230C22⋊D47—81no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236D188—21no—
237D188—21no—
238D188—21no—
239D188—21no—
240D188—21no—
241D188—21no—
242D188—81no—
243D188—81no—
244C4×D47—41no—
245C4×D47—41no—
246C4×D47—41no—
247C4×D47—41no—
248C4×D47—41no—
249C4×D47—41no—
250Dic94—21no—
251Dic94—21no—
252Dic94—81no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47#13112yes—
260C8×C47#13112yes—
261C47⋊C8—22no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—21no—
266C47⋊C8—41no—
267#17968—471nomaximal, Sylow
268C22×C47—21no—
269C22×C47—21no—
270C22×C47—21no—
271C22×C47C2×C4×D411yescharacteristic
272C2×D47—41no—
273C2×D47—41no—
274C2×D47—41no—
275C2×D47—41no—
276C2×D47—41no—
277C2×D47—41no—
278C2×D47—41no—
279C2×D47—41no—
280C2×D47—41no—
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47C2×#13111yescharacteristic
286C4×C47C2×#13111yescharacteristic
287C4×C47#57611yescharacteristic
288C4×C47#57711yescharacteristic
289Dic47—41no—
290Dic47—41no—
291Dic47—41no—
292Dic47—41no—
293Dic47—41no—
294#3171—471no—
295#2993—471no—
296#2981—471no—
297#1594—471no—
298#1592—471no—
299#1590—471no—
300#1589—471no—
301#1580—471no—
302SD16⋊C8—471no—
303C8×SD16—471no—
304C8×D8—471no—
305#1569D4711yescharacteristic, complemented
306#1494—471no—
307#1492—471no—
308C8×M16—471no—
309C2×C47—41no—
310C2×C47#293111yescharacteristic
311C2×C47#294611yescharacteristic
312C2×C47#295611yescharacteristic
313D47—81no—
314D47—81no—
315D47—81no—
316#532—471no—
317#529—471no—
318#501—471no—
319#496—471no—
320#490—471no—
321#489—471no—
322#469—471no—
323#469—471no—
324#468—471no—
325#468—471no—
326#446—471no—
327C8×Q8—471no—
328C4×SD16—471no—
329C4×SD16—471no—
330C4×D8—471no—
331C4×D8—471no—
332#436—471no—
333#436—471no—
334#436—471no—
335#436—941no—
336#435—941no—
337#435—941no—
338#435—941no—
339C8×D4—471no—
340C8×D4—471no—
341C8×D4—471no—
342#433—941no—
343#432C2×D4711yescharacteristic
344#431—471no—
345#424—941no—
346#423C2×D4711yescharacteristic
347#408—941no—
348#408—941no—
349C4×M16C2×D4711yescharacteristic
350C2×C4×C8—471no—
351#335C2×D4711yescharacteristic
352#335C2×D4711yescharacteristic
353#334C2×D4711yescharacteristic
354#334C2×D4711yescharacteristic
355Q8⋊C8—471no—
356Q8⋊C8—471no—
357D4⋊C8—471no—
358D4⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363#322—471no—
364#322—471no—
365C82—471no—
366C82—471no—
367C47#1796811yescharacteristic, complemented, Sylow
368C2×#41—941no—
369C2×SD16—471no—
370C2×SD16—471no—
371C2×D8—471no—
372C2×D8—471no—
373C2×M16—21no—
374C2×M16—941no—
375C2×M16—941no—
376C2×M16—941no—
377C2×M16C4×D4711yescharacteristic
378C2×M16C4×D4711yescharacteristic
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—941no—
382C22×C8—941no—
383C4⋊Q8—471no—
384#127—471no—
385#126—941no—
386#125—471no—
387#124—471no—
388#124—941no—
389#123—941no—
390C22⋊Q8—471no—
391#121—471no—
392#121—471no—
393#121—471no—
394#121—941no—
395C4×Q8—471no—
396C4×D4—471no—
397C4×D4—471no—
398C4×D4—471no—
399C4×D4—941no—
400C4×D4—941no—
401#117—941no—
402C2×C42C22×D4711yescharacteristic
403#107—471no—
404#107—471no—
405#106—471no—
406#106—471no—
407C4⋊C8—21no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8C22×D4711yescharacteristic
413C4⋊C8C22×D4711yescharacteristic
414C4⋊C8C22×D4711yescharacteristic
415C4⋊C8C22×D4711yescharacteristic
416#103—471no—
417#103—471no—
418#102—471no—
419#102—471no—
420#102—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424C22⋊C8—21no—
425C22⋊C8—471no—
426C22⋊C8—471no—
427C22⋊C8—941no—
428C22⋊C8—941no—
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433#97—21no—
434#97—941no—
435#97C4×D4711yescharacteristic
436#97C4×D4711yescharacteristic
437C4×C8—471no—
438C4×C8—471no—
439C4×C8—471no—
440C4×C8—471no—
441C4×C8—941no—
442C4×C8—941no—
443C4×C8C22×D4711yescharacteristic
444C4×C8C22×D4711yescharacteristic
445#41—3761no—
446#41—3761no—
447C2×Q8—471no—
448C2×Q8—941no—
449C2×D4—471no—
450C2×D4—471no—
451C2×D4—471no—
452C2×D4—941no—
453C2×D4—941no—
454C2×D4—941no—
455C2×D4—941no—
456C2×D4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4D4×D4711yescharacteristic
462C22×C4#1062535411yescharacteristic
463SD16—942no—
464SD16—942no—
465D8—942no—
466D8—942no—
467M16—22no—
468M16—22no—
469M16—81no—
470M16—3761no—
471M16—3761no—
472M16—3761no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—471no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—471no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—3761no—
484C2×C8—3761no—
485C2×C8—3761no—
486C2×C8—1882no—
487C2×C8C2×C4×D4711yescharacteristic
488C2×C8C2×C4×D4711yescharacteristic
489C2×C8C2×C4×D4711yescharacteristic
490C2×C8C2×C4×D4711yescharacteristic
491C4⋊C4—471no—
492C4⋊C4—471no—
493C4⋊C4—471no—
494C4⋊C4—471no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C22⋊C4—941no—
501C22⋊C4—941no—
502C22⋊C4—941no—
503C22⋊C4—941no—
504C22⋊C4—941no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C42—941no—
510C42C2×C4×D4711yescharacteristic
511C42D4×D4711yescharacteristic
512C42#1062535411yescharacteristic
513C42C23×D4711yescharacteristic
514C23—941no—
515C23—941no—
516C23—941no—
517C23#1309398611yescharacteristic
518Q8—941no—
519Q8—941no—
520Q8—3761no—
521D4—941no—
522D4—941no—
523D4—941no—
524D4—941no—
525D4—941no—
526D4—941no—
527D4—3761no—
528D4—3761no—
529D4—3761no—
530D4—3761no—
531D4—3761no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—941no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—1881no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4#1309398611yescharacteristic
549C2×C4#1309398611yescharacteristic
550C2×C4#1309398611yescharacteristic
551C2×C4C22×C4×D4711yescharacteristic
552C2×C4C2×D4×D4711yescharacteristic
553C2×C4C2×#1062535411yescharacteristic
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—942no—
561C8—941no—
562C8—941no—
563C8—941no—
564C8—941no—
565C8—1881no—
566C8#1309403212yes—
567C8#1309403212yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—1881no—
572C22—1881no—
573C22—1881no—
574C22—1881no—
575C22—1881no—
576C22—1881no—
577C22—1881no—
578C22—1881no—
579C22—1881no—
580C22C2×#1309398611yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—1881no—
586C4—1881no—
587C4—1881no—
588C4—1881no—
589C4—1881no—
590C4C2×#1309403211yescharacteristic
591C4C2×#1309403211yescharacteristic
592C4#1568992711yescharacteristic
593C4#1568993211yescharacteristic
594C2—41no—
595C2—3761no—
596C2—3761no—
597C2—3761no—
598C2#2025209911yescharacteristic
599C2#2025221811yescharacteristic
600C2#2025229711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1569C2
socleC22×C47C2×C4×D4
prime radical#20253983C2
cosocleC42×C47C24
hypercenter#1569D47
hypocenterC47#17968
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
2. #20252533C2semidirect
3. #20252466C2semidirect
4. #20242301C2semidirect
5. #20242289C2semidirect
6. #20242277C2semidirect
7. #20242272C2semidirect
8. #20242211C2semidirect
9. #20242199C2semidirect
10. #20242187C2semidirect
11. #20242182C2semidirect
12. #20241846C2semidirect
13. #20241838C2semidirect
14. M16×C47⋊C8C2semidirect
15. C47×#1569C2semidirect
305. #1569D47semidirect
367. C47#17968semidirect

Maximal subgroups

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

subgroupindex
#202539832
#202525332
#202524662
#202423012
#202422892
#202422772
#202422722
#202422112
#202421992
#202421872
#202421822
#202418462
#202418382
M16×C47⋊C82
C47×#15692
#1796847