Finite Group Databasebeta

← #26187417

Subgroups — #26187417

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253460C211yesmaximal, characteristic
2#20252405C211yesmaximal, characteristic
3#20252331C211yesmaximal, characteristic, complemented
4#20242289C211yesmaximal, characteristic, complemented
5#20242277C211yesmaximal, characteristic, complemented
6#20242265C211yesmaximal, characteristic, complemented
7#20242258C211yesmaximal, characteristic, complemented
8#20242237C211yesmaximal, characteristic, complemented
9#20242230C211yesmaximal, characteristic, complemented
10#20242206C211yesmaximal, characteristic, complemented
11#20242194C211yesmaximal, characteristic, complemented
12#20241860C211yesmaximal, characteristic, complemented
13#20241773C211yesmaximal, characteristic
14#20241683C211yesmaximal, characteristic, complemented
15C47×#1573C211yesmaximal, characteristic, complemented
16#15689680C2211yescharacteristic
17C4×#10625350C2211yescharacteristic
18#15689465C411yescharacteristic
19#15689465C411yescharacteristic
20#15689409C411yescharacteristic
21#15689404C411yescharacteristic
22#15689334C411yescharacteristic
23#15689329C411yescharacteristic
24#15689287C411yescharacteristic
25#15689287C411yescharacteristic
26#15689252—21no—
27#15689252—21no—
28#15689250C2211yescharacteristic
29#15689250C2211yescharacteristic
30#15689247C2211yescharacteristic
31#15689247C2211yescharacteristic
32#15689247C2211yescharacteristic
33#15689247C2211yescharacteristic
34C4×Dic188C2211yescharacteristic
35C4×Dic188C2211yescharacteristic
36C4×#10625325C2211yescharacteristic
37C4×#10625325C2211yescharacteristic
38#15689200C2211yescharacteristic
39#15689200C2211yescharacteristic
40#15689198—21no—
41#15689198—21no—
42#15689178—21no—
43#15689176C2211yescharacteristic
44#15689149—21no—
45#15689078—21no—
46C4×#10625329C2211yescharacteristic
47#15689075—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×#432C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C2×C4⋊C8×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×#335C2211yescharacteristic
65C47×#334C2211yescharacteristic
66C47×#334C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×Dic188C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×#10625325C2×C411yescharacteristic
72C2×#10625329D411yescharacteristic
73C2×#10625329D411yescharacteristic
74C2×#10625324—21no—
75C2×#10625324—21no—
76#13094024C2×C411yescharacteristic
77#13094024C2×C411yescharacteristic
78#13094016—21no—
79#13094003—21no—
80#13094003C2×C411yescharacteristic
81#13094003C2×C411yescharacteristic
82C4×Dic94—21no—
83C4×Dic94C2×C411yescharacteristic
84C4×Dic94C2311yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×Dic94C2311yescharacteristic
87C4×D188C2×C411yescharacteristic
88C4×D188C2311yescharacteristic
89C4×C22⋊D47—21no—
90C4×C22⋊D47—21no—
91#13093983—21no—
92#13093983C2×C411yescharacteristic
93#13093981—21no—
94C42×D47—21no—
95#13093958C2×C411yescharacteristic
96#13093958C2×C411yescharacteristic
97#13093956C2×C411yescharacteristic
98#13093956C2×C411yescharacteristic
99C4⋊(C47⋊C8)—21no—
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—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8—21no—
117#13093935D411yescharacteristic
118#13093935D411yescharacteristic
119#13093934—21no—
120#13093934—21no—
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47—21no—
129C22×C8×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
141#97×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C2×C22⋊D47—21no—
148#10625350—22no—
149#10625350—41no—
150C2×D188C22×C411yescharacteristic
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×Dic94—21no—
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—42no—
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—
172C22⋊Dic47—21no—
173C22⋊Dic47—21no—
174(C2×D47)⋊C4—21no—
175(C2×D47)⋊C4—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47C22×C411yescharacteristic
180C4⋊Dic47C22×C411yescharacteristic
181C4⋊Dic47C22×C411yescharacteristic
182C4⋊Dic47C22×C411yescharacteristic
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—
194#10625329—22no—
195#10625329—41no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C2×D411yescharacteristic
199C2×C47⋊C8C2×D411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202Dic188—22no—
203Dic188—22no—
204#10625325—41no—
205#10625325—41no—
206#10625324—42no—
207#10625324—42no—
208C23×C47C4×D411yescharacteristic
209C22×D47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—41no—
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C4×D411yescharacteristic
218C2×C4×C47C23×C411yescharacteristic
219C2×C4×C47C22×D411yescharacteristic
220C2×C4×C47C2×#4111yescharacteristic
221C22⋊D47—42no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229D188—21no—
230D188—21no—
231C4×D47—42no—
232C4×D47—41no—
233C4×D47—41no—
234C4×D47—81no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94—21no—
239Dic94—21no—
240Dic94—81no—
241Dic94#13112yes—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255C47⋊C8#13712yes—
256#18013—471nomaximal, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47C2×C4×D411yescharacteristic
261C2×D47—41no—
262C2×D47—41no—
263C2×D47—41no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47C2×#13111yescharacteristic
269C4×C47#56811yescharacteristic
270C4×C47C2×#13711yescharacteristic
271C4×C47#57511yescharacteristic
272Dic47—22no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277Dic47—41no—
278Dic47—41no—
279#3107—471no—
280#2971—471no—
281#2962—471no—
282#1592—471no—
283#1590—471no—
284#1588—471no—
285#1587—471no—
286#1584—471no—
287#1583—471no—
288#1579—471no—
289C8×Q16—471no—
290#1573D4711yescharacteristic, complemented
291#1497—471no—
292#1477—471no—
293#1453—471no—
294C2×C47—41no—
295C2×C47#293311yescharacteristic
296C2×C47C4×#13711yescharacteristic
297C2×C47#295711yescharacteristic
298D47—81no—
299#533—471no—
300C4×#41—471no—
301#485—471no—
302#485—471no—
303#475—471no—
304#474—471no—
305#462—471no—
306#461—471no—
307#452—471no—
308#452—471no—
309#446—471no—
310#446—471no—
311#446—941no—
312#446—941no—
313C8×Q8—471no—
314C8×Q8—471no—
315C8×Q8—471no—
316C8×Q8—471no—
317C4×Q16—471no—
318C4×Q16—471no—
319C4×SD16—471no—
320C4×SD16—471no—
321#436—471no—
322#436—471no—
323#436—941no—
324#436—941no—
325#432—941no—
326#432C2×D4711yescharacteristic
327#431—471no—
328#431C2×D4711yescharacteristic
329#424—941no—
330C2×C4⋊C8C2×D4711yescharacteristic
331#405—941no—
332C4×M16—471no—
333C4×M16—941no—
334#335C2×D4711yescharacteristic
335#335C2×D4711yescharacteristic
336#334C2×D4711yescharacteristic
337#334C2×D4711yescharacteristic
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342Q8⋊C8—471no—
343Q8⋊C8—471no—
344D4⋊C8—471no—
345D4⋊C8—471no—
346#322—471no—
347#322—471no—
348#322—471no—
349C82—471no—
350C47#1801311yescharacteristic, complemented, Sylow
351C2×#41—471no—
352C2×Q16—471no—
353C2×Q16—471no—
354C2×SD16—471no—
355C2×SD16—471no—
356C2×M16—471no—
357C2×M16—471no—
358C2×M16—941no—
359C2×M16—941no—
360C22×C8—21no—
361C4⋊Q8—471no—
362C4⋊Q8—471no—
363#125—941no—
364C22⋊Q8—471no—
365C22⋊Q8—471no—
366C22⋊Q8—941no—
367C4×Q8—471no—
368C4×Q8—471no—
369C4×Q8—471no—
370C4×Q8—471no—
371C4×Q8—941no—
372C4×D4—471no—
373C4×D4—471no—
374C4×D4—941no—
375C4×D4—941no—
376#117—471no—
377#117—941no—
378#117—941no—
379C2×C42—941no—
380C2×C42C22×D4711yescharacteristic
381#107—471no—
382#107—471no—
383#106—471no—
384#106—471no—
385C4⋊C8—21no—
386C4⋊C8—941no—
387C4⋊C8—941no—
388C4⋊C8—941no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8C4×D4711yescharacteristic
394C4⋊C8C4×D4711yescharacteristic
395C4⋊C8C22×D4711yescharacteristic
396C4⋊C8C22×D4711yescharacteristic
397C4⋊C8C22×D4711yescharacteristic
398C4⋊C8C22×D4711yescharacteristic
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#103—471no—
405#102—471no—
406#102—471no—
407C22⋊C8—21no—
408C22⋊C8—941no—
409C22⋊C8—941no—
410C22⋊C8—941no—
411C22⋊C8C4×D4711yescharacteristic
412C22⋊C8C4×D4711yescharacteristic
413#97—21no—
414#97—471no—
415#97—471no—
416#97—941no—
417#97—941no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8—941no—
425C4×C8—941no—
426C4×C8C22×D4711yescharacteristic
427C4×C8C22×D4711yescharacteristic
428#41—942no—
429#41—1881no—
430C2×Q8—471no—
431C2×Q8—471no—
432C2×Q8—471no—
433C2×Q8—941no—
434C2×D4—471no—
435C2×D4—941no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4C2×C4×D4711yescharacteristic
440C22×C4D4×D4711yescharacteristic
441C22×C4#1062535411yescharacteristic
442Q16—942no—
443Q16—942no—
444SD16—1881no—
445SD16—1881no—
446M16—942no—
447M16—1882no—
448M16—1882no—
449M16—1881no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—941no—
460C2×C8—941no—
461C2×C8C2×C4×D4711yescharacteristic
462C2×C8C2×C4×D4711yescharacteristic
463C2×C8C2×C4×D4711yescharacteristic
464C2×C8C2×C4×D4711yescharacteristic
465C4⋊C4—471no—
466C4⋊C4—471no—
467C4⋊C4—471no—
468C4⋊C4—471no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C22⋊C4—941no—
482C22⋊C4—941no—
483C42—941no—
484C42—941no—
485C42—941no—
486C42—941no—
487C42—941no—
488C42C2×C4×D4711yescharacteristic
489C42D4×D4711yescharacteristic
490C42#1062535411yescharacteristic
491C42C23×D4711yescharacteristic
492C23—941no—
493C23#1309398611yescharacteristic
494Q8—472no—
495Q8—941no—
496Q8—941no—
497Q8—941no—
498Q8—941no—
499Q8—941no—
500Q8—3761no—
501D4—941no—
502D4—941no—
503D4—1882no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—3761no—
517C2×C4—1882no—
518C2×C4—1881no—
519C2×C4—1881no—
520C2×C4#1309398611yescharacteristic
521C2×C4#1309398611yescharacteristic
522C2×C4#1309398611yescharacteristic
523C2×C4C22×C4×D4711yescharacteristic
524C2×C4C2×D4×D4711yescharacteristic
525C2×C4C2×#1062535411yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—472no—
535C8—941no—
536C8—941no—
537C8—941no—
538C8—1881no—
539C8—1881no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—1881no—
544C22—1881no—
545C22—1881no—
546C22C2×#1309398611yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—942no—
552C4—1881no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4—1881no—
557C4—1881no—
558C4#131×D4711yescharacteristic
559C4#1568988811yescharacteristic
560C4#137×D4711yescharacteristic
561C4#1568991911yescharacteristic
562C2—41no—
563C2—3761no—
564C2#2025211211yescharacteristic
565C2#2025220611yescharacteristic
566C2#2025230411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1573C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C2×C4
cosocleC42×C47C24
hypercenter#1573D47
hypocenterC47#18013
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #20252331C2semidirect
4. #20242289C2semidirect
5. #20242277C2semidirect
6. #20242265C2semidirect
7. #20242258C2semidirect
8. #20242237C2semidirect
9. #20242230C2semidirect
10. #20242206C2semidirect
11. #20242194C2semidirect
12. #20241860C2semidirect
14. #20241683C2semidirect
15. C47×#1573C2semidirect
290. #1573D47semidirect
350. C47#18013semidirect

Maximal subgroups

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

subgroupindex
#202534602
#202524052
#202523312
#202422892
#202422772
#202422652
#202422582
#202422372
#202422302
#202422062
#202421942
#202418602
#202417732
#202416832
C47×#15732
#1801347