Finite Group Databasebeta

← #26185973

Subgroups — #26185973

Order 12032.

626 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252470C211yesmaximal, characteristic
2#20252467C211yesmaximal, characteristic
3C4×Q16×D47C211yesmaximal, characteristic
4#20242261C211yesmaximal, characteristic, complemented
5#20242260C211yesmaximal, characteristic, complemented
6#20242258C211yesmaximal, characteristic, complemented
7#20242241C211yesmaximal, characteristic, complemented
8#20242238C211yesmaximal, characteristic, complemented
9#20242236C211yesmaximal, characteristic, complemented
10#20242235C211yesmaximal, characteristic, complemented
11#20242133C211yesmaximal, characteristic
12#20241781C211yesmaximal, characteristic
13#20241781C211yesmaximal, characteristic
14#20241679C211yesmaximal, characteristic
15C47×#1587C211yesmaximal, characteristic, complemented
16C2×Q16×D47C411yescharacteristic
17C4×Q8×D47C2211yescharacteristic
18C4×Q8×D47C2211yescharacteristic
19#15689254C2211yescharacteristic
20#15689253C2211yescharacteristic
21#15689252—21no—
22#15689251—21no—
23#15689250C2211yescharacteristic
24Q8×C47⋊C8C2211yescharacteristic
25C8×Dic94—21no—
26C8×Dic94C2211yescharacteristic
27#15689247—21no—
28#15689247C2211yescharacteristic
29C4×Dic188C2211yescharacteristic
30Q16×Dic47C411yescharacteristic
31#15689217C411yescharacteristic
32C4×#10625337C2211yescharacteristic
33C4×#10625337C2211yescharacteristic
34#15689215C411yescharacteristic
35#15689215C411yescharacteristic
36#15689179—21no—
37#15689178—21no—
38#15689175—21no—
39#15689175C2211yescharacteristic
40#15689175C2211yescharacteristic
41#15689174—21no—
42#15689174C2211yescharacteristic
43#15689174C2211yescharacteristic
44#107×D47C411yescharacteristic
45#103×D47C411yescharacteristic
46#103×D47C411yescharacteristic
47C4×C8×D47C2211yescharacteristic
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#15688845C2211yescharacteristic
59#15688844C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Q8×D47C2×C411yescharacteristic
68C2×Q8×D47C2×C411yescharacteristic
69C2×Dic188C2×C411yescharacteristic
70C2×#10625337C2×C411yescharacteristic
71C2×#10625337C2×C411yescharacteristic
72Q16×D47—24no—
73C2×C8×D47C2×C411yescharacteristic
74C2×C8×D47C2×C411yescharacteristic
75Q8×Dic47C2×C411yescharacteristic
76Q8×Dic47C2×C411yescharacteristic
77C4×Dic94—21no—
78C4×Dic94—21no—
79C4×Dic94C2311yescharacteristic
80C4×Dic94C2311yescharacteristic
81#13093989—21no—
82#13093989—21no—
83#13093989C2×C411yescharacteristic
84#13093989C2×C411yescharacteristic
85C4⋊C4×D47—21no—
86C4⋊C4×D47—21no—
87C4⋊C4×D47C2×C411yescharacteristic
88C4⋊C4×D47C2×C411yescharacteristic
89C42×D47—21no—
90C42×D47—21no—
91C42×D47C2311yescharacteristic
92#13093958C2×C411yescharacteristic
93#13093957C2×C411yescharacteristic
94#13093957C2×C411yescharacteristic
95C4⋊(C47⋊C8)—21no—
96C4⋊(C47⋊C8)—21no—
97C4⋊(C47⋊C8)C2311yescharacteristic
98C4⋊(C47⋊C8)C2311yescharacteristic
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8D411yescharacteristic
105Dic47⋊C8D411yescharacteristic
106#13093949C2×C411yescharacteristic
107#13093949C2×C411yescharacteristic
108#13093948C2×C411yescharacteristic
109#13093948C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111#13093947C2×C411yescharacteristic
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8D411yescharacteristic
116(C2×D47)⋊C8D411yescharacteristic
117#13093935—21no—
118#13093934—21no—
119#13093934—21no—
120C4×C47⋊C8—21no—
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47C2×C411yescharacteristic
129C8×Dic47C2×C411yescharacteristic
130C2×Q16×C47C2×C411yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132C4×Q8×C47C2311yescharacteristic
133#107×C47C2×C411yescharacteristic
134C4⋊C8×C47—21no—
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138#103×C47C2×C411yescharacteristic
139#103×C47C2×C411yescharacteristic
140#97×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146C2×Q8×C47C22×C411yescharacteristic
147Q8×D47—22no—
148Q8×D47—22no—
149Q8×D47—22no—
150Q8×D47M1614yes—
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47C22×C411yescharacteristic
156C2×C4×D47C2×D411yescharacteristic
157C2×C4×D47#4111yescharacteristic
158C2×Dic94—21no—
159C2×Dic94—21no—
160C2×Dic94C22×C411yescharacteristic
161C2×Dic94C22×C411yescharacteristic
162Q16×C47—22no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47C22×C411yescharacteristic
167C2×C8×C47C22×C411yescharacteristic
168C2×C8×C47C2×D411yescharacteristic
169C2×C8×C47C2×D411yescharacteristic
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47C22×C411yescharacteristic
173C4⋊C4×C47C22×C411yescharacteristic
174C42×C47—21no—
175C42×C47—21no—
176C42×C47C2411yescharacteristic
177#10625337—22no—
178#10625337—22no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
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—
194C4×Dic47—21no—
195C4×Dic47C22×C411yescharacteristic
196C4×Dic47C2×D411yescharacteristic
197C4×Dic47#4111yescharacteristic
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205Dic188—22no—
206C8×D47—22no—
207C8×D47—22no—
208C22×D47C4×D411yescharacteristic
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47C2×M1612yes—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47C23×C411yescharacteristic
218C2×C4×C47C22×D411yescharacteristic
219C2×C4×C47C2×#4111yescharacteristic
220C2×Dic47—21no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47C4×D411yescharacteristic
225C2×Dic47C4×D411yescharacteristic
226C2×Dic47C4×D411yescharacteristic
227C4×D47—24no—
228C4×D47—21no—
229C4×D47—21no—
230C4×D47—41no—
231C4×D47—42no—
232C4×D47—81no—
233C4×D47—81no—
234C4×D47C2×M1612yes—
235C4×D47#13112yes—
236Dic94—21no—
237Dic94—24no—
238Dic94—21no—
239Dic94—21no—
240Dic94—42no—
241Dic94C2×M1612yes—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256#17880—471nomaximal, Sylow
257C22×C47C2×C4×D411yescharacteristic
258C2×D47—21no—
259C2×D47—21no—
260C2×D47#43512yes—
261C4×C47—22no—
262C4×C47—21no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47C22×M1611yescharacteristic
267C4×C47C2×#13111yescharacteristic
268C4×C47#57811yescharacteristic
269C4×C47#57811yescharacteristic
270Dic47—22no—
271Dic47—21no—
272Dic47—21no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276Dic47#43512yes—
277#2983—471no—
278#2982—471no—
279C2×C4×Q16—471no—
280#1587—471no—
281#1587—471no—
282#1587—471no—
283#1587D4711yescharacteristic, complemented
284#1584—471no—
285#1584—471no—
286#1584—471no—
287#1584—471no—
288#1564—471no—
289#1479—471no—
290#1479—471no—
291#1452—471no—
292C2×C47C2×#43511yescharacteristic
293C2×C47#295011yescharacteristic
294C2×C47#295711yescharacteristic
295D47—22no—
296C22×Q16—471no—
297C2×C4×Q8—471no—
298C2×C4×Q8—471no—
299#446—471no—
300#446—471no—
301#446—471no—
302#446—941no—
303#446—941no—
304#446C2×D4711yescharacteristic
305C8×Q8—471no—
306C8×Q8—471no—
307C8×Q8—471no—
308C8×Q8—941no—
309C8×Q8—941no—
310C8×Q8C2×D4711yescharacteristic
311C4×Q16—471no—
312C4×Q16—471no—
313C4×Q16—471no—
314C4×Q16—471no—
315C4×Q16—471no—
316C4×Q16—471no—
317C4×Q16—471no—
318C4×Q16C2×D4711yescharacteristic
319#432—941no—
320#432—941no—
321#431—471no—
322#431—471no—
323#431—471no—
324#431—471no—
325#431—941no—
326#431—941no—
327C2×#107—471no—
328C2×#103—471no—
329C2×#103—471no—
330C2×C4×C8—471no—
331#335—471no—
332#335—471no—
333#334—471no—
334#334C2×D4711yescharacteristic
335Q8⋊C8—471no—
336Q8⋊C8—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8C2×D4711yescharacteristic
342Q8⋊C8C2×D4711yescharacteristic
343#322—471no—
344#322—471no—
345#322—471no—
346#322C2×D4711yescharacteristic
347C47#1788011yescharacteristic, complemented, Sylow
348C22×Q8—471no—
349C22×Q8—471no—
350C2×Q16—471no—
351C2×Q16—471no—
352C2×Q16—471no—
353C2×Q16—944no—
354C2×Q16C4×D4711yescharacteristic
355C22×C8—471no—
356C22×C8—471no—
357C4×Q8—471no—
358C4×Q8—471no—
359C4×Q8—471no—
360C4×Q8—471no—
361C4×Q8—471no—
362C4×Q8—471no—
363C4×Q8—941no—
364C4×Q8—941no—
365C4×Q8—941no—
366C4×Q8—941no—
367C4×Q8C22×D4711yescharacteristic
368C4×Q8C22×D4711yescharacteristic
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—941no—
372C2×C4⋊C4—941no—
373C2×C42—471no—
374C2×C42—941no—
375C2×C42—941no—
376#107—471no—
377#107—471no—
378#107—471no—
379#107C4×D4711yescharacteristic
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—471no—
383C4⋊C8—471no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—941no—
387C4⋊C8—941no—
388C4⋊C8—941no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8C22×D4711yescharacteristic
394C4⋊C8C22×D4711yescharacteristic
395#103—471no—
396#103—471no—
397#103—471no—
398#103—471no—
399#103—471no—
400#103—471no—
401#103C4×D4711yescharacteristic
402#103C4×D4711yescharacteristic
403C22⋊C8—471no—
404C22⋊C8—471no—
405C22⋊C8—941no—
406C22⋊C8—941no—
407C22⋊C8—941no—
408#97—21no—
409#97—941no—
410#97—941no—
411#97—941no—
412C4×C8—21no—
413C4×C8—471no—
414C4×C8—471no—
415C4×C8—471no—
416C4×C8—471no—
417C4×C8—471no—
418C4×C8—941no—
419C4×C8—941no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8C22×D4711yescharacteristic
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426C2×Q8—474no—
427C2×Q8—471no—
428C2×Q8—471no—
429C2×Q8—941no—
430C2×Q8—941no—
431C2×Q8—942no—
432C2×Q8—942no—
433C2×Q8—942no—
434C2×Q8C2×C4×D4711yescharacteristic
435C2×Q8C2×C4×D4711yescharacteristic
436C22×C4—471no—
437C22×C4—471no—
438C22×C4—471no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443Q16—22no—
444Q16—942no—
445Q16—942no—
446Q16—942no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—942no—
455C2×C8—942no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8C2×C4×D4711yescharacteristic
460C2×C8C2×C4×D4711yescharacteristic
461C2×C8D4×D4711yescharacteristic
462C2×C8D4×D4711yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—471no—
466C4⋊C4—471no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4C2×C4×D4711yescharacteristic
476C4⋊C4C2×C4×D4711yescharacteristic
477C42—21no—
478C42—21no—
479C42—471no—
480C42—471no—
481C42—471no—
482C42—941no—
483C42—941no—
484C42—941no—
485C42—941no—
486C42—941no—
487C42—941no—
488C42C23×D4711yescharacteristic
489C23—471no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—472no—
494Q8—944no—
495Q8—941no—
496Q8—941no—
497Q8—941no—
498Q8—1882no—
499Q8M16×D4712yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—471no—
505C2×C4—472no—
506C2×C4—472no—
507C2×C4—471no—
508C2×C4—471no—
509C2×C4—944no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—3761no—
517C2×C4—3761no—
518C2×C4—1881no—
519C2×C4—1882no—
520C2×C4C22×C4×D4711yescharacteristic
521C2×C4C2×D4×D4711yescharacteristic
522C2×C4#41×D4711yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—941no—
531C8—941no—
532C8—941no—
533C8—941no—
534C8—1881no—
535C8—1881no—
536C8—1881no—
537C22—472no—
538C22—941no—
539C22—941no—
540C22C4×D4×D4711yescharacteristic
541C4—21no—
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—472no—
547C4—941no—
548C4—941no—
549C4—942no—
550C4—1881no—
551C4—1881no—
552C4—1881no—
553C4C2×M16×D4711yescharacteristic
554C4#131×D4711yescharacteristic
555C4#1568993911yescharacteristic
556C4#1568993911yescharacteristic
557C2—942no—
558C2#435×D4711yescharacteristic
559C2#2025225311yescharacteristic
560C2#2025230011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1587C2
socleC22×C47C2×C4×D4
prime radicalC22×D47C4×D4
cosocleC42×C47C24
hypercenter#1587D47
hypocenterC47#17880
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #20242261C2semidirect
5. #20242260C2semidirect
6. #20242258C2semidirect
7. #20242241C2semidirect
8. #20242238C2semidirect
9. #20242236C2semidirect
10. #20242235C2semidirect
15. C47×#1587C2semidirect
283. #1587D47semidirect
347. C47#17880semidirect

Maximal subgroups

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

subgroupindex
#202524702
#202524672
C4×Q16×D472
#202422612
#202422602
#202422582
#202422412
#202422382
#202422362
#202422352
#202421332
#202417812
#202416792
C47×#15872
#1788047