Finite Group Databasebeta

← #26186351

Subgroups — #26186351

Order 12032.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253470C211yesmaximal, characteristic
2#20252533C211yesmaximal, characteristic
3#20252468C211yesmaximal, characteristic, complemented
4#20242265C211yesmaximal, characteristic, complemented
5#20242258C211yesmaximal, characteristic, complemented
6#20242237C211yesmaximal, characteristic, complemented
7#20242230C211yesmaximal, characteristic, complemented
8#20242206C211yesmaximal, characteristic, complemented
9#20242199C211yesmaximal, characteristic, complemented
10#20242194C211yesmaximal, characteristic, complemented
11#20242187C211yesmaximal, characteristic, complemented
12#20241816C211yesmaximal, characteristic, complemented
13#20241794C211yesmaximal, characteristic
14#20241688C211yesmaximal, characteristic, complemented
15C47×#1574C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18#15689454C411yescharacteristic
19#15689437C411yescharacteristic
20#15689431C411yescharacteristic
21#15689431C411yescharacteristic
22#15689346C411yescharacteristic
23#15689346C411yescharacteristic
24#15689281C411yescharacteristic
25#15689264C411yescharacteristic
26#15689250C2211yescharacteristic
27C8×Dic94—21no—
28C8×Dic94—21no—
29#15689247C2211yescharacteristic
30#15689247C2211yescharacteristic
31#15689247C2211yescharacteristic
32#15689247C2211yescharacteristic
33#15689247C2211yescharacteristic
34C4×Dic188C2211yescharacteristic
35C4×Dic188C2211yescharacteristic
36C4×#10625325C2211yescharacteristic
37C4×#10625325C2211yescharacteristic
38#15689200C2211yescharacteristic
39#15689199—21no—
40#15689192—21no—
41#15689188C2211yescharacteristic
42#15689183—21no—
43#15689176C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689173—21no—
46#15689173—21no—
47#15689148—21no—
48#15688853C2211yescharacteristic
49#15688853C2211yescharacteristic
50#15688853C2211yescharacteristic
51#15688853C2211yescharacteristic
52#15688853C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688850C2211yescharacteristic
55#15688850C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#431C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#423C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×#335C2211yescharacteristic
65C47×#334C2211yescharacteristic
66C47×#334C2211yescharacteristic
67C22×Dic94C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×Dic188C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×#10625325C2×C411yescharacteristic
72C2×#10625324—21no—
73C2×C8×D47—21no—
74#13094018—21no—
75#13094016C2×C411yescharacteristic
76#13094012C2×C411yescharacteristic
77#13094007—21no—
78#13094003C2×C411yescharacteristic
79#13093998C2×C411yescharacteristic
80C4×Dic94—21no—
81C4×Dic94—21no—
82C4×Dic94C2×C411yescharacteristic
83C4×Dic94C2×C411yescharacteristic
84C4×Dic94C2311yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×Dic94C2311yescharacteristic
87C4×D188C2311yescharacteristic
88C4×C22⋊D47—21no—
89#13093981—21no—
90C2×C4⋊Dic47C2×C411yescharacteristic
91C2×Dic47⋊C4—21no—
92C2×C4×Dic47—21no—
93#13093958C2×C411yescharacteristic
94#13093958C2×C411yescharacteristic
95#13093956C2×C411yescharacteristic
96#13093956C2×C411yescharacteristic
97C4⋊(C47⋊C8)—21no—
98C4⋊(C47⋊C8)D411yescharacteristic
99C4⋊(C47⋊C8)D411yescharacteristic
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106#13093949C2×C411yescharacteristic
107#13093949C2×C411yescharacteristic
108#13093949C2×C411yescharacteristic
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093949C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114C22⋊(C47⋊C8)—21no—
115C22⋊(C47⋊C8)D411yescharacteristic
116C22⋊(C47⋊C8)D411yescharacteristic
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119#13093934—21no—
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47—21no—
129C2×M16×C47—21no—
130C2×C42×C47C2311yescharacteristic
131C4⋊C8×C47—21no—
132C4⋊C8×C47C2×C411yescharacteristic
133C4⋊C8×C47C2×C411yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C22⋊C8×C47—21no—
139C22⋊C8×C47C2×C411yescharacteristic
140C22⋊C8×C47C2×C411yescharacteristic
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C2×C22⋊D47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C2×D188C22×C411yescharacteristic
151C2×C4×D47—21no—
152C2×Dic94—21no—
153C2×Dic94—22no—
154C2×Dic94—22no—
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158M16×C47—81no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C22×C411yescharacteristic
166C2×C8×C47C22×C411yescharacteristic
167C42×C47C22×C411yescharacteristic
168C42×C47C2×D411yescharacteristic
169C42×C47#4111yescharacteristic
170C42×C47C2411yescharacteristic
171C22⋊Dic47—21no—
172(C2×D47)⋊C4—21no—
173(C2×D47)⋊C4—21no—
174(C2×D47)⋊C4—21no—
175(C2×D47)⋊C4—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47C22×C411yescharacteristic
178C4⋊Dic47C22×C411yescharacteristic
179C4⋊Dic47C22×C411yescharacteristic
180C4⋊Dic47C22×C411yescharacteristic
181Dic47⋊C4—21no—
182Dic47⋊C4—21no—
183Dic47⋊C4—21no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8C2×D411yescharacteristic
197C2×C47⋊C8C2×D411yescharacteristic
198C2×C47⋊C8C2×D411yescharacteristic
199C2×C47⋊C8C2×D411yescharacteristic
200Dic188—22no—
201Dic188—22no—
202#10625325—22no—
203#10625325—22no—
204#10625324—81no—
205C8×D47—81no—
206C23×C47C4×D411yescharacteristic
207C22×D47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—41no—
213C2×C4×C47C4×D411yescharacteristic
214C2×C4×C47C4×D411yescharacteristic
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C23×C411yescharacteristic
217C2×C4×C47C22×D411yescharacteristic
218C2×C4×C47C2×#4111yescharacteristic
219C22⋊D47—81no—
220C2×Dic47—24no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—81no—
229D188—21no—
230D188—21no—
231C4×D47—41no—
232C4×D47—41no—
233Dic94—24no—
234Dic94—21no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94#13112yes—
239Dic94#13112yes—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—41no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254#17919—471nomaximal, Sylow
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—21no—
258C22×C47C2×C4×D411yescharacteristic
259C2×D47—41no—
260C2×D47—41no—
261C2×D47—41no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47C2×#13111yescharacteristic
267C4×C47C2×#13111yescharacteristic
268C4×C47#57711yescharacteristic
269C4×C47#57811yescharacteristic
270Dic47—22no—
271Dic47—22no—
272Dic47—41no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277#3108—471no—
278#2993—471no—
279#2982—471no—
280#1588—471no—
281#1587—471no—
282#1584—471no—
283#1583—471no—
284#1579—471no—
285SD16⋊C8—471no—
286C8×Q16—471no—
287C8×SD16—471no—
288#1574D4711yescharacteristic, complemented
289#1487—471no—
290#1482—471no—
291#1454—471no—
292C2×C47—41no—
293C2×C47#292911yescharacteristic
294C2×C47#294711yescharacteristic
295C2×C47#295711yescharacteristic
296D47—81no—
297#529—471no—
298C2×C4×Q8—471no—
299#483—471no—
300#480—471no—
301#479—471no—
302#479—471no—
303#464—471no—
304#464—471no—
305#451—471no—
306#448—471no—
307#446—471no—
308C8×Q8—471no—
309C8×Q8—471no—
310C8×Q8—471no—
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8—941no—
314C8×Q8—941no—
315C4×Q16—471no—
316C4×Q16—471no—
317C4×SD16—471no—
318C4×SD16—471no—
319#436—471no—
320#436—941no—
321#435—941no—
322C8×D4—471no—
323#433—941no—
324#431—471no—
325#431—471no—
326#431—941no—
327#431—941no—
328#431C2×D4711yescharacteristic
329#431C2×D4711yescharacteristic
330#424—941no—
331#423C2×D4711yescharacteristic
332#335C2×D4711yescharacteristic
333#335C2×D4711yescharacteristic
334#334C2×D4711yescharacteristic
335#334C2×D4711yescharacteristic
336Q8⋊C8—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342D4⋊C8—471no—
343D4⋊C8—471no—
344#322—471no—
345#322—471no—
346#322—471no—
347C82—471no—
348C47#1791911yescharacteristic, complemented, Sylow
349C22×Q8—471no—
350C2×Q16—471no—
351C2×Q16—471no—
352C2×SD16—471no—
353C2×SD16—471no—
354C2×M16—21no—
355C2×M16—941no—
356C22×C8—941no—
357#126—941no—
358#125—471no—
359#124—471no—
360#123—941no—
361C22⋊Q8—471no—
362#121—471no—
363C4×Q8—471no—
364C4×Q8—471no—
365C4×Q8—471no—
366C4×Q8—471no—
367C4×Q8—471no—
368C4×Q8—941no—
369C4×Q8—941no—
370C4×D4—471no—
371C4×D4—941no—
372#117—941no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—941no—
375C2×C42—941no—
376C2×C42C22×D4711yescharacteristic
377#107—471no—
378#107—471no—
379#106—471no—
380#106—471no—
381C4⋊C8—21no—
382C4⋊C8—471no—
383C4⋊C8—471no—
384C4⋊C8—941no—
385C4⋊C8—941no—
386C4⋊C8—941no—
387C4⋊C8—941no—
388C4⋊C8—941no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8C4×D4711yescharacteristic
392C4⋊C8C4×D4711yescharacteristic
393C4⋊C8C22×D4711yescharacteristic
394C4⋊C8C22×D4711yescharacteristic
395C4⋊C8C22×D4711yescharacteristic
396C4⋊C8C22×D4711yescharacteristic
397#103—471no—
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#102—471no—
404#102—471no—
405C22⋊C8—21no—
406C22⋊C8—471no—
407C22⋊C8—471no—
408C22⋊C8—941no—
409C22⋊C8—941no—
410C22⋊C8—941no—
411C22⋊C8C4×D4711yescharacteristic
412C22⋊C8C4×D4711yescharacteristic
413#97—941no—
414C4×C8—21no—
415C4×C8—471no—
416C4×C8—471no—
417C4×C8—471no—
418C4×C8—471no—
419C4×C8—941no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426C2×Q8—471no—
427C2×Q8—471no—
428C2×Q8—471no—
429C2×Q8—942no—
430C2×Q8—942no—
431C2×Q8—941no—
432C2×D4—471no—
433C2×D4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4C2×C4×D4711yescharacteristic
438C22×C4D4×D4711yescharacteristic
439C22×C4#1062535411yescharacteristic
440Q16—942no—
441Q16—942no—
442SD16—942no—
443SD16—942no—
444M16—81no—
445M16—3761no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—941no—
455C2×C8—941no—
456C2×C8—3761no—
457C2×C8C2×C4×D4711yescharacteristic
458C2×C8C2×C4×D4711yescharacteristic
459C2×C8C2×C4×D4711yescharacteristic
460C2×C8C2×C4×D4711yescharacteristic
461C4⋊C4—471no—
462C4⋊C4—471no—
463C4⋊C4—471no—
464C4⋊C4—471no—
465C4⋊C4—941no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C22⋊C4—941no—
475C22⋊C4—941no—
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C42—941no—
480C42—941no—
481C42—941no—
482C42—941no—
483C42—941no—
484C42C2×C4×D4711yescharacteristic
485C42D4×D4711yescharacteristic
486C42#1062535411yescharacteristic
487C42C23×D4711yescharacteristic
488C23—941no—
489C23#1309398611yescharacteristic
490Q8—472no—
491Q8—472no—
492Q8—944no—
493Q8—941no—
494Q8—941no—
495Q8—941no—
496Q8—941no—
497D4—941no—
498D4—941no—
499D4—3761no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—944no—
506C2×C4—941no—
507C2×C4—941no—
508C2×C4—941no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—3761no—
514C2×C4—1881no—
515C2×C4—1881no—
516C2×C4#1309398611yescharacteristic
517C2×C4#1309398611yescharacteristic
518C2×C4#1309398611yescharacteristic
519C2×C4C22×C4×D4711yescharacteristic
520C2×C4C2×D4×D4711yescharacteristic
521C2×C4C2×#1062535411yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—941no—
531C8—941no—
532C8—941no—
533C8—941no—
534C8—1881no—
535C8—1881no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—1881no—
540C22—1881no—
541C22—1881no—
542C22C2×#1309398611yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—942no—
548C4—942no—
549C4—1881no—
550C4—1881no—
551C4—1881no—
552C4—1881no—
553C4—1881no—
554C4#131×D4711yescharacteristic
555C4#131×D4711yescharacteristic
556C4#1568993311yescharacteristic
557C4#1568993911yescharacteristic
558C2—41no—
559C2—3761no—
560C2#2025208111yescharacteristic
561C2#2025222911yescharacteristic
562C2#2025230411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1574C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenter#1574D47
hypocenterC47#17919
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
3. #20252468C2semidirect
4. #20242265C2semidirect
5. #20242258C2semidirect
6. #20242237C2semidirect
7. #20242230C2semidirect
8. #20242206C2semidirect
9. #20242199C2semidirect
10. #20242194C2semidirect
11. #20242187C2semidirect
12. #20241816C2semidirect
14. #20241688C2semidirect
15. C47×#1574C2semidirect
288. #1574D47semidirect
348. C47#17919semidirect

Maximal subgroups

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

subgroupindex
#202534702
#202525332
#202524682
#202422652
#202422582
#202422372
#202422302
#202422062
#202421992
#202421942
#202421872
#202418162
#202417942
#202416882
C47×#15742
#1791947