Finite Group Databasebeta

← #26187679

Subgroups — #26187679

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#20253425C211yesmaximal, characteristic
2#20252486C211yesmaximal, characteristic
3#20252474C211yesmaximal, characteristic
4#20242282C211yesmaximal, characteristic, complemented
5#20242260C211yesmaximal, characteristic, complemented
6#20242258C211yesmaximal, characteristic, complemented
7#20242236C211yesmaximal, characteristic, complemented
8#20242236C211yesmaximal, characteristic, complemented
9#20242208C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#20242165C211yesmaximal, characteristic
12#20241859C211yesmaximal, characteristic
13#20241781C211yesmaximal, characteristic
14#20241689C211yesmaximal, characteristic
15C47×#1593C211yesmaximal, characteristic, complemented
16#15689677C2211yescharacteristic
17C4×Q8×D47C2211yescharacteristic
18#15689460C411yescharacteristic
19#15689457C411yescharacteristic
20#15689417C411yescharacteristic
21#15689416C411yescharacteristic
22#15689332C411yescharacteristic
23#15689331C411yescharacteristic
24#15689280C411yescharacteristic
25#15689277C411yescharacteristic
26#15689254C2211yescharacteristic
27#15689252—21no—
28#15689251—21no—
29#15689251—21no—
30#15689250C2211yescharacteristic
31Q8×C47⋊C8C2211yescharacteristic
32C8×Dic94C2211yescharacteristic
33C8×Dic94C2211yescharacteristic
34#15689247—21no—
35#15689247C2211yescharacteristic
36C4×Dic188C2211yescharacteristic
37C4×#10625337C2211yescharacteristic
38C4×#10625337C2211yescharacteristic
39#15689185—21no—
40#15689183—21no—
41#15689179C2211yescharacteristic
42#15689178—21no—
43#15689175—21no—
44#15689175C2211yescharacteristic
45#15689174C2211yescharacteristic
46#15689174C2211yescharacteristic
47#15689174C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688855C2211yescharacteristic
52#15688855C2211yescharacteristic
53Q8⋊(C47⋊C8)C2211yescharacteristic
54Q8⋊(C47⋊C8)C2211yescharacteristic
55#15688853C2211yescharacteristic
56#15688853C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C47×#446C2211yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Q8×D47C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×#10625337C2×C411yescharacteristic
71#13094023C2×C411yescharacteristic
72#13094022C2×C411yescharacteristic
73#13094014—21no—
74#13094004C2×C411yescharacteristic
75#13094002—21no—
76#13094000C2×C411yescharacteristic
77Q8×Dic47C2×C411yescharacteristic
78C4×Dic94—21no—
79C4×Dic94—21no—
80C4×Dic94C2311yescharacteristic
81C4×Dic94C2311yescharacteristic
82#13093989—21no—
83#13093989C2×C411yescharacteristic
84#13093981—21no—
85C4⋊C4×D47—21no—
86C4⋊C4×D47C2×C411yescharacteristic
87C42×D47—21no—
88C42×D47C2311yescharacteristic
89#13093958C2×C411yescharacteristic
90#13093957C2×C411yescharacteristic
91#13093957C2×C411yescharacteristic
92C4⋊(C47⋊C8)—21no—
93C4⋊(C47⋊C8)—21no—
94C4⋊(C47⋊C8)C2311yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96Dic47⋊C8—21no—
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8C2×C411yescharacteristic
102Dic47⋊C8C2×C411yescharacteristic
103Dic47⋊C8D411yescharacteristic
104Dic47⋊C8D411yescharacteristic
105#13093949C2×C411yescharacteristic
106#13093949C2×C411yescharacteristic
107#13093948C2×C411yescharacteristic
108#13093948C2×C411yescharacteristic
109#13093947C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111(C2×D47)⋊C8—21no—
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8C2×C411yescharacteristic
115(C2×D47)⋊C8C2×C411yescharacteristic
116(C2×D47)⋊C8D411yescharacteristic
117(C2×D47)⋊C8D411yescharacteristic
118#13093935—21no—
119#13093934—21no—
120#13093934—21no—
121C4×C47⋊C8—21no—
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47—21no—
129C2×Q16×C47C2×C411yescharacteristic
130C4×Q8×C47C2311yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132#107×C47C2×C411yescharacteristic
133C4⋊C8×C47—21no—
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#103×C47C2×C411yescharacteristic
139#97×C47—21no—
140#97×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146Q8×D47—22no—
147Q8×D47—41no—
148C2×C4×D47—21no—
149C2×C4×D47—21no—
150C2×C4×D47C22×C411yescharacteristic
151C2×C4×D47C2×D411yescharacteristic
152C2×C4×D47#4111yescharacteristic
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157Q16×C47—41no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47C22×C411yescharacteristic
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C2×D411yescharacteristic
164C2×C8×C47C2×D411yescharacteristic
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47C22×C411yescharacteristic
168C4⋊C4×C47C22×C411yescharacteristic
169C42×C47—21no—
170C42×C47—21no—
171C42×C47C2411yescharacteristic
172#10625337—22no—
173#10625337—41no—
174(C2×D47)⋊C4—21no—
175(C2×D47)⋊C4—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47C22×C411yescharacteristic
179C4⋊Dic47C22×C411yescharacteristic
180Dic47⋊C4—21no—
181Dic47⋊C4—21no—
182Dic47⋊C4—21no—
183Dic47⋊C4—21no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188C4×Dic47—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47C22×C411yescharacteristic
193C4×Dic47C2×D411yescharacteristic
194C4×Dic47#4111yescharacteristic
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202Dic188—22no—
203C22×D47C4×D411yescharacteristic
204Q8×C47—21no—
205Q8×C47—21no—
206Q8×C47—21no—
207Q8×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
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×Dic47C4×D411yescharacteristic
220C2×Dic47C4×D411yescharacteristic
221C2×Dic47C4×D411yescharacteristic
222C4×D47—21no—
223C4×D47—21no—
224C4×D47—21no—
225C4×D47—21no—
226C4×D47—41no—
227C4×D47—42no—
228C4×D47—42no—
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—41no—
240C8×C47—41no—
241C8×C47—41no—
242C47⋊C8—21no—
243C47⋊C8—21no—
244C47⋊C8—21no—
245C47⋊C8—21no—
246C47⋊C8—41no—
247C47⋊C8—41no—
248C47⋊C8—41no—
249#18032—471nomaximal, Sylow
250C22×C47C2×C4×D411yescharacteristic
251C2×D47—21no—
252C2×D47—21no—
253C2×D47—21no—
254C4×C47—21no—
255C4×C47—41no—
256C4×C47—41no—
257C4×C47—41no—
258C4×C47—41no—
259C4×C47C2×#13111yescharacteristic
260C4×C47#56811yescharacteristic
261C4×C47#57811yescharacteristic
262C4×C47#57811yescharacteristic
263Dic47—22no—
264Dic47—21no—
265Dic47—21no—
266Dic47—21no—
267Dic47—41no—
268Dic47—41no—
269Dic47—41no—
270#3104—471no—
271#2986—471no—
272#2984—471no—
273#1593D4711yescharacteristic, complemented
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#1454—471no—
285C2×C47#293311yescharacteristic
286C2×C47#295011yescharacteristic
287C2×C47#295511yescharacteristic
288D47—41no—
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—941no—
302#446—941no—
303#446—941no—
304#446C2×D4711yescharacteristic
305#446C2×D4711yescharacteristic
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×Q16C2×D4711yescharacteristic
315#433—941no—
316#433—941no—
317#432—471no—
318#432—941no—
319#431—471no—
320#431—471no—
321#431—471no—
322#431—471no—
323#431—941no—
324#335—471no—
325#335—471no—
326#334—471no—
327#334C2×D4711yescharacteristic
328Q8⋊C8—471no—
329Q8⋊C8—471no—
330Q8⋊C8—471no—
331Q8⋊C8—471no—
332Q8⋊C8—471no—
333Q8⋊C8—471no—
334Q8⋊C8C2×D4711yescharacteristic
335Q8⋊C8C2×D4711yescharacteristic
336#322—471no—
337#322—471no—
338#322C2×D4711yescharacteristic
339C82—471no—
340C47#1803211yescharacteristic, complemented, Sylow
341C22×Q8—471no—
342C2×Q16—471no—
343C2×Q16—471no—
344C2×Q16—471no—
345C2×Q16C4×D4711yescharacteristic
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—941no—
357C4×Q8—941no—
358C4×Q8—941no—
359C4×Q8C22×D4711yescharacteristic
360C4×Q8C22×D4711yescharacteristic
361#117—941no—
362C2×C4⋊C4—471no—
363C2×C4⋊C4—941no—
364C2×C42—471no—
365C2×C42—941no—
366#107—471no—
367#107—471no—
368#107—471no—
369#107C4×D4711yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—471no—
373C4⋊C8—471no—
374C4⋊C8—471no—
375C4⋊C8—471no—
376C4⋊C8—471no—
377C4⋊C8—471no—
378C4⋊C8—941no—
379C4⋊C8—941no—
380C4⋊C8—941no—
381C4⋊C8—941no—
382C4⋊C8—941no—
383C4⋊C8—941no—
384C4⋊C8—941no—
385C4⋊C8C22×D4711yescharacteristic
386C4⋊C8C22×D4711yescharacteristic
387#103—471no—
388#103—471no—
389#103—471no—
390#103—471no—
391#103—471no—
392#103—471no—
393#103C4×D4711yescharacteristic
394#103C4×D4711yescharacteristic
395C22⋊C8—471no—
396C22⋊C8—471no—
397C22⋊C8—471no—
398C22⋊C8—471no—
399C22⋊C8—941no—
400C22⋊C8—941no—
401C22⋊C8—941no—
402#97—21no—
403#97—21no—
404#97—941no—
405#97—941no—
406#97—941no—
407C4×C8—471no—
408C4×C8—471no—
409C4×C8—471no—
410C4×C8—941no—
411C4×C8—941no—
412C4×C8—941no—
413C4×C8—941no—
414C4×C8—941no—
415C4×C8C22×D4711yescharacteristic
416C4×C8C22×D4711yescharacteristic
417C4×C8C22×D4711yescharacteristic
418C2×Q8—471no—
419C2×Q8—471no—
420C2×Q8—941no—
421C2×Q8—941no—
422C2×Q8—942no—
423C2×Q8—1881no—
424C2×Q8C2×C4×D4711yescharacteristic
425C2×Q8C2×C4×D4711yescharacteristic
426C22×C4—471no—
427C22×C4—471no—
428C22×C4—471no—
429C22×C4—941no—
430C22×C4—941no—
431Q16—41no—
432Q16—942no—
433Q16—942no—
434Q16—1881no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—471no—
439C2×C8—471no—
440C2×C8—471no—
441C2×C8—471no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8C2×C4×D4711yescharacteristic
446C2×C8C2×C4×D4711yescharacteristic
447C2×C8D4×D4711yescharacteristic
448C2×C8D4×D4711yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
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⋊C4C2×C4×D4711yescharacteristic
464C4⋊C4C2×C4×D4711yescharacteristic
465C22⋊C4—941no—
466C22⋊C4—941no—
467C42—21no—
468C42—21no—
469C42—471no—
470C42—471no—
471C42—471no—
472C42—941no—
473C42—941no—
474C42—941no—
475C42—941no—
476C42C23×D4711yescharacteristic
477C23—471no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—472no—
483Q8—941no—
484Q8—941no—
485Q8—941no—
486Q8—1882no—
487Q8—1882no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—471no—
493C2×C4—471no—
494C2×C4—471no—
495C2×C4—941no—
496C2×C4—941no—
497C2×C4—941no—
498C2×C4—941no—
499C2×C4—941no—
500C2×C4—941no—
501C2×C4—941no—
502C2×C4—941no—
503C2×C4—1881no—
504C2×C4—1882no—
505C2×C4—1882no—
506C2×C4C22×C4×D4711yescharacteristic
507C2×C4C2×D4×D4711yescharacteristic
508C2×C4#41×D4711yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—941no—
517C8—941no—
518C8—941no—
519C8—941no—
520C8—1881no—
521C8—1881no—
522C8—1881no—
523C22—941no—
524C22—941no—
525C22—941no—
526C22C4×D4×D4711yescharacteristic
527C4—21no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—941no—
533C4—941no—
534C4—941no—
535C4—942no—
536C4—1881no—
537C4—1881no—
538C4—1881no—
539C4#131×D4711yescharacteristic
540C4#1568988911yescharacteristic
541C4#1568993911yescharacteristic
542C4#1568993911yescharacteristic
543C2—1881no—
544C2#2025211711yescharacteristic
545C2#2025225311yescharacteristic
546C2#2025228811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1593C2
socleC22×C47C2×C4×D4
prime radicalC22×D47C4×D4
cosocleC42×C47C24
hypercenter#1593D47
hypocenterC47#18032
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1593

Complements

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

NH ≅ G/Ntype
4. #20242282C2semidirect
5. #20242260C2semidirect
6. #20242258C2semidirect
7. #20242236C2semidirect
8. #20242236C2semidirect
9. #20242208C2semidirect
10. #20242192C2semidirect
15. C47×#1593C2semidirect
273. #1593D47semidirect
340. C47#18032semidirect

Maximal subgroups

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

subgroupindex
#202534252
#202524862
#202524742
#202422822
#202422602
#202422582
#202422362
#202422082
#202421922
#202421652
#202418592
#202417812
#202416892
C47×#15932
#1803247