Finite Group Databasebeta

← #26187676

Subgroups — #26187676

Order 12032.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253428C211yesmaximal, characteristic
2#20252489C211yesmaximal, characteristic
3#20252475C211yesmaximal, characteristic
4#20242298C211yesmaximal, characteristic, complemented
5#20242286C211yesmaximal, characteristic, complemented
6#20242261C211yesmaximal, characteristic, complemented
7#20242261C211yesmaximal, characteristic, complemented
8#20242240C211yesmaximal, characteristic, complemented
9#20242240C211yesmaximal, characteristic, complemented
10#20242208C211yesmaximal, characteristic, complemented
11C8×Dic188C211yesmaximal, characteristic, complemented
12#20242168C211yesmaximal, characteristic
13#20241862C211yesmaximal, characteristic
14#20241784C211yesmaximal, characteristic
15C47×#1454C211yesmaximal, characteristic
16#15689680C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18#15689459C411yescharacteristic
19#15689459C411yescharacteristic
20#15689419C411yescharacteristic
21#15689419C411yescharacteristic
22#15689334C411yescharacteristic
23#15689334C411yescharacteristic
24#15689281C411yescharacteristic
25#15689281C411yescharacteristic
26#15689253C2211yescharacteristic
27#15689253C2211yescharacteristic
28#15689253C2211yescharacteristic
29#15689253C2211yescharacteristic
30#15689252—21no—
31#15689252—21no—
32#15689250—21no—
33C8×Dic94C2211yescharacteristic
34C8×Dic94C2211yescharacteristic
35C8×Dic94C2211yescharacteristic
36C8×Dic94C2211yescharacteristic
37#15689247—21no—
38C4×Dic188C2211yescharacteristic
39C4×Dic188C2211yescharacteristic
40C4×Dic188C2211yescharacteristic
41C4×Dic188C2211yescharacteristic
42#15689181—21no—
43#15689181—21no—
44#15689180C2211yescharacteristic
45#15689177—21no—
46#15689176C2211yescharacteristic
47#15689173—21no—
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688874C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688855C2211yescharacteristic
57#15688855C2211yescharacteristic
58#15688855C2211yescharacteristic
59#15688855C2211yescharacteristic
60C47×#431C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C47×#322C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C22×Dic94C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×Dic188C2×C411yescharacteristic
70C2×Dic188C2×C411yescharacteristic
71C2×Dic188C2×C411yescharacteristic
72#13094024C2×C411yescharacteristic
73#13094024C2×C411yescharacteristic
74#13094016—21no—
75#13094003—21no—
76#13094003C2×C411yescharacteristic
77#13094003C2×C411yescharacteristic
78C4×Dic94—21no—
79C4×Dic94—21no—
80C4×Dic94—21no—
81C4×Dic94C2×C411yescharacteristic
82C4×Dic94C2×C411yescharacteristic
83C4×Dic94C2311yescharacteristic
84C4×Dic94C2311yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×Dic94C2311yescharacteristic
87#13093983—21no—
88C2×C4⋊Dic47C2×C411yescharacteristic
89C2×Dic47⋊C4—21no—
90C2×C4×Dic47—21no—
91#13093958C2×C411yescharacteristic
92#13093958C2×C411yescharacteristic
93#13093958C2×C411yescharacteristic
94#13093958C2×C411yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97C4⋊(C47⋊C8)C2311yescharacteristic
98C4⋊(C47⋊C8)C2311yescharacteristic
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107#13093949C2×C411yescharacteristic
108#13093949C2×C411yescharacteristic
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093949C2×C411yescharacteristic
112#13093949C2×C411yescharacteristic
113#13093949C2×C411yescharacteristic
114#13093949C2×C411yescharacteristic
115C22⋊(C47⋊C8)—21no—
116C22⋊(C47⋊C8)—21no—
117#13093935—21no—
118#13093934—21no—
119#13093934—21no—
120#13093934—21no—
121#13093934—21no—
122C4×C47⋊C8—21no—
123C8×Dic47—21no—
124C8×Dic47—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C2×C42×C47C2311yescharacteristic
128C4⋊C8×C47—21no—
129C4⋊C8×C47C2×C411yescharacteristic
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47D411yescharacteristic
133C22⋊C8×C47—21no—
134C22⋊C8×C47C2×C411yescharacteristic
135C22⋊C8×C47C2×C411yescharacteristic
136C22⋊C8×C47D411yescharacteristic
137C22⋊C8×C47D411yescharacteristic
138C4×C8×C47C2311yescharacteristic
139C4×C8×C47C2311yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C22×Dic47—21no—
148C22×Dic47—21no—
149C2×Dic94—22no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—41no—
153C2×Dic94C22×C411yescharacteristic
154C2×Dic94C22×C411yescharacteristic
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47C22×C411yescharacteristic
160C2×C8×C47C22×C411yescharacteristic
161C2×C8×C47C22×C411yescharacteristic
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C2×D411yescharacteristic
164C2×C8×C47C2×D411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C42×C47C22×C411yescharacteristic
168C42×C47C2×D411yescharacteristic
169C42×C47#4111yescharacteristic
170C42×C47C2411yescharacteristic
171C22⋊Dic47—21no—
172C22⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—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—
194C4×Dic47—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199Dic188—22no—
200Dic188—22no—
201Dic188—41no—
202Dic188—41no—
203C23×C47C4×D411yescharacteristic
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—41no—
209C2×C4×C47C4×D411yescharacteristic
210C2×C4×C47C4×D411yescharacteristic
211C2×C4×C47C4×D411yescharacteristic
212C2×C4×C47C23×C411yescharacteristic
213C2×C4×C47C22×D411yescharacteristic
214C2×C4×C47C2×#4111yescharacteristic
215C2×Dic47—21no—
216C2×Dic47—21no—
217C2×Dic47—21no—
218C2×Dic47—21no—
219C2×Dic47—21no—
220C2×Dic47—21no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—42no—
224C2×Dic47—42no—
225Dic94—21no—
226Dic94—21no—
227Dic94—21no—
228Dic94—21no—
229Dic94—21no—
230Dic94—21no—
231Dic94—21no—
232Dic94—42no—
233Dic94—42no—
234Dic94#13112yes—
235C8×C47—21no—
236C8×C47—21no—
237C8×C47—21no—
238C8×C47—21no—
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—41no—
244C8×C47—41no—
245C47⋊C8—41no—
246C47⋊C8—41no—
247C47⋊C8—41no—
248C47⋊C8—41no—
249#18032—471nomaximal, Sylow
250C22×C47—21no—
251C22×C47—21no—
252C22×C47—21no—
253C22×C47C2×C4×D411yescharacteristic
254C4×C47—21no—
255C4×C47—21no—
256C4×C47—21no—
257C4×C47—21no—
258C4×C47C2×#13111yescharacteristic
259C4×C47#56811yescharacteristic
260C4×C47#57811yescharacteristic
261C4×C47#57811yescharacteristic
262Dic47—22no—
263Dic47—41no—
264Dic47—41no—
265Dic47—41no—
266Dic47—41no—
267Dic47—41no—
268Dic47—41no—
269Dic47—41no—
270#3104—471no—
271#2986—471no—
272#2984—471no—
273#1593—471no—
274#1591—471no—
275#1587—471no—
276#1587—471no—
277#1584—471no—
278#1584—471no—
279#1579—471no—
280C8×Q16—471no—
281#1572—471no—
282#1497—471no—
283#1479—471no—
284#1454D4711yescharacteristic
285C2×C47—41no—
286C2×C47#293311yescharacteristic
287C2×C47#295011yescharacteristic
288C2×C47#295511yescharacteristic
289#533—471no—
290C2×C4×Q8—471no—
291#484—471no—
292#484—471no—
293#477—471no—
294#477—471no—
295#462—471no—
296#462—471no—
297#451—471no—
298#451—471no—
299#446—471no—
300#446—471no—
301#446—471no—
302#446—471no—
303#446—941no—
304#446—941no—
305#446—941no—
306C8×Q8—471no—
307C8×Q8—471no—
308C8×Q8—471no—
309C8×Q8—471no—
310C8×Q8—941no—
311C4×Q16—471no—
312C4×Q16—471no—
313C4×Q16—471no—
314C4×Q16—471no—
315#433—941no—
316#433—941no—
317#432—471no—
318#432—941no—
319#431—471no—
320#431—941no—
321#431C2×D4711yescharacteristic
322#431C2×D4711yescharacteristic
323#431C2×D4711yescharacteristic
324#335—471no—
325#335—471no—
326#334—471no—
327#334—471no—
328Q8⋊C8—471no—
329Q8⋊C8—471no—
330Q8⋊C8—471no—
331Q8⋊C8—471no—
332Q8⋊C8—471no—
333Q8⋊C8—471no—
334Q8⋊C8—471no—
335Q8⋊C8—471no—
336#322C2×D4711yescharacteristic
337#322C2×D4711yescharacteristic
338#322C2×D4711yescharacteristic
339C82C2×D4711yescharacteristic
340C47#1803211yescharacteristic, complemented, Sylow
341C22×Q8—471no—
342C2×Q16—471no—
343C2×Q16—471no—
344C2×Q16—471no—
345C2×Q16—471no—
346C4⋊Q8—471no—
347C4⋊Q8—471no—
348#125—941no—
349C22⋊Q8—471no—
350C22⋊Q8—471no—
351C22⋊Q8—941no—
352C4×Q8—471no—
353C4×Q8—471no—
354C4×Q8—471no—
355C4×Q8—471no—
356C4×Q8—471no—
357C4×Q8—471no—
358C4×Q8—941no—
359C4×Q8—941no—
360C4×Q8—941no—
361#117—941no—
362C2×C4⋊C4—471no—
363C2×C4⋊C4—941no—
364C2×C42—941no—
365C2×C42C22×D4711yescharacteristic
366#107—471no—
367#107—471no—
368#107—471no—
369#107—471no—
370C4⋊C8—21no—
371C4⋊C8—471no—
372C4⋊C8—471no—
373C4⋊C8—471no—
374C4⋊C8—471no—
375C4⋊C8—941no—
376C4⋊C8—941no—
377C4⋊C8—941no—
378C4⋊C8—941no—
379C4⋊C8—941no—
380C4⋊C8—941no—
381C4⋊C8—941no—
382C4⋊C8—941no—
383C4⋊C8C4×D4711yescharacteristic
384C4⋊C8C4×D4711yescharacteristic
385C4⋊C8D18811yescharacteristic
386C4⋊C8D18811yescharacteristic
387#103—471no—
388#103—471no—
389#103—471no—
390#103—471no—
391#103—471no—
392#103—471no—
393#103—471no—
394#103—471no—
395C22⋊C8—21no—
396C22⋊C8—941no—
397C22⋊C8—941no—
398C22⋊C8C4×D4711yescharacteristic
399C22⋊C8C4×D4711yescharacteristic
400C22⋊C8D18811yescharacteristic
401C22⋊C8D18811yescharacteristic
402#97—941no—
403#97—941no—
404#97—941no—
405#97—941no—
406#97—941no—
407C4×C8—941no—
408C4×C8—941no—
409C4×C8—941no—
410C4×C8—941no—
411C4×C8—941no—
412C4×C8C22×D4711yescharacteristic
413C4×C8C22×D4711yescharacteristic
414C4×C8C22×D4711yescharacteristic
415C4×C8C22×D4711yescharacteristic
416C4×C8C22×D4711yescharacteristic
417C4×C8C22×D4711yescharacteristic
418C2×Q8—471no—
419C2×Q8—471no—
420C2×Q8—471no—
421C2×Q8—471no—
422C2×Q8—942no—
423C2×Q8—941no—
424C2×Q8—941no—
425C2×Q8—1881no—
426C22×C4—941no—
427C22×C4—941no—
428C22×C4C2×C4×D4711yescharacteristic
429C22×C4C2×D18811yescharacteristic
430C22×C4#1062535011yescharacteristic
431Q16—942no—
432Q16—942no—
433Q16—1881no—
434Q16—1881no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—941no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8—941no—
441C2×C8C2×C4×D4711yescharacteristic
442C2×C8C2×C4×D4711yescharacteristic
443C2×C8C2×C4×D4711yescharacteristic
444C2×C8C2×C4×D4711yescharacteristic
445C2×C8C2×D18811yescharacteristic
446C2×C8C2×D18811yescharacteristic
447C2×C8C2×D18811yescharacteristic
448C2×C8C2×D18811yescharacteristic
449C4⋊C4—471no—
450C4⋊C4—471no—
451C4⋊C4—471no—
452C4⋊C4—471no—
453C4⋊C4—941no—
454C4⋊C4—941no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C22⋊C4—941no—
466C22⋊C4—941no—
467C42—941no—
468C42—941no—
469C42—941no—
470C42—941no—
471C42—941no—
472C42—941no—
473C42C2×C4×D4711yescharacteristic
474C42C2×D18811yescharacteristic
475C42#1062535011yescharacteristic
476C42C23×D4711yescharacteristic
477C23C4×D18811yescharacteristic
478Q8—472no—
479Q8—941no—
480Q8—941no—
481Q8—941no—
482Q8—941no—
483Q8—941no—
484Q8—941no—
485Q8—941no—
486Q8—1882no—
487Q8—1882no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—941no—
494C2×C4—941no—
495C2×C4—941no—
496C2×C4—941no—
497C2×C4—941no—
498C2×C4—941no—
499C2×C4—941no—
500C2×C4—941no—
501C2×C4—1882no—
502C2×C4—1882no—
503C2×C4C4×D18811yescharacteristic
504C2×C4C4×D18811yescharacteristic
505C2×C4C4×D18811yescharacteristic
506C2×C4C22×C4×D4711yescharacteristic
507C2×C4C22×D18811yescharacteristic
508C2×C4C2×#1062535011yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—1881no—
520C8—1881no—
521C8—1881no—
522C8—1881no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×C4×D18811yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—942no—
532C4—1881no—
533C4—1881no—
534C4—1881no—
535C4—1881no—
536C4—1881no—
537C4—1881no—
538C4—1881no—
539C4#131×D4711yescharacteristic
540C4#1568988811yescharacteristic
541C4#1568994011yescharacteristic
542C4#1568994011yescharacteristic
543C2—41no—
544C2#2025211611yescharacteristic
545C2#2025225711yescharacteristic
546C2#2025229211yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1454C2
socleC22×C47C2×C4×D4
prime radicalC23×C47C4×D4
cosocleC42×C47C24
hypercenter#1454D47
hypocenterC47#18032
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
4. #20242298C2semidirect
5. #20242286C2semidirect
6. #20242261C2semidirect
7. #20242261C2semidirect
8. #20242240C2semidirect
9. #20242240C2semidirect
10. #20242208C2semidirect
11. C8×Dic188C2semidirect
340. C47#18032semidirect

Maximal subgroups

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

subgroupindex
#202534282
#202524892
#202524752
#202422982
#202422862
#202422612
#202422402
#202422082
C8×Dic1882
#202421682
#202418622
#202417842
C47×#14542
#1803247