Finite Group Databasebeta

← #26187490

Subgroups — #26187490

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253457C211yesmaximal, characteristic
2#20252519C211yesmaximal, characteristic
3#20252488C211yesmaximal, characteristic, complemented
4#20242280C211yesmaximal, characteristic, complemented
5#20242275C211yesmaximal, characteristic, complemented
6#20242266C211yesmaximal, characteristic, complemented
7#20242265C211yesmaximal, characteristic, complemented
8#20242260C211yesmaximal, characteristic, complemented
9#20242259C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#20242178C211yesmaximal, characteristic, complemented
12#20241841C211yesmaximal, characteristic, complemented
13#20241769C211yesmaximal, characteristic
14#20241670C211yesmaximal, characteristic, complemented
15C8×Q16×C47C211yesmaximal, characteristic, complemented
16#15689677C2211yescharacteristic
17C4×#10625354C2211yescharacteristic
18#15689466C411yescharacteristic
19#15689462C411yescharacteristic
20#15689406C411yescharacteristic
21#15689402C411yescharacteristic
22#15689331C411yescharacteristic
23#15689327C411yescharacteristic
24#15689288C411yescharacteristic
25#15689284C411yescharacteristic
26#15689254C2211yescharacteristic
27#15689253C2211yescharacteristic
28#15689252—21no—
29Q8×C47⋊C8C2211yescharacteristic
30C8×Dic94—21no—
31#15689247C2211yescharacteristic
32C4×#10625337C2211yescharacteristic
33C4×#10625325C2211yescharacteristic
34C4×#10625336C2211yescharacteristic
35#15689202—21no—
36#15689202C2211yescharacteristic
37#15689200—21no—
38#15689200C2211yescharacteristic
39#15689183—21no—
40#15689182—21no—
41#15689175C2211yescharacteristic
42#15689174—21no—
43#15689174C2211yescharacteristic
44#15689174C2211yescharacteristic
45#15689145—21no—
46#15689145C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688874C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688855C2211yescharacteristic
52Q8⋊(C47⋊C8)C2211yescharacteristic
53Q8⋊(C47⋊C8)C2211yescharacteristic
54#15688853C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688845C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#10625354C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625325C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625324—21no—
72C2×#10625324—21no—
73C2×#10625324—21no—
74C2×C8×D47—21no—
75#13094023C2×C411yescharacteristic
76#13094022C2×C411yescharacteristic
77#13094014—21no—
78#13094004C2×C411yescharacteristic
79#13094002—21no—
80#13094000C2×C411yescharacteristic
81Q8×Dic47C2×C411yescharacteristic
82C4×Dic94—21no—
83C4×Dic94C2311yescharacteristic
84C4×D188—21no—
85C4×D188C2311yescharacteristic
86#13093986—21no—
87#13093986C2×C411yescharacteristic
88#13093982—21no—
89#13093982C2×C411yescharacteristic
90#13093981—21no—
91C42×D47—21no—
92C42×D47C2311yescharacteristic
93#13093957C2×C411yescharacteristic
94#13093956C2×C411yescharacteristic
95#13093955C2×C411yescharacteristic
96C4⋊(C47⋊C8)—21no—
97C4⋊(C47⋊C8)—21no—
98C4⋊(C47⋊C8)C2311yescharacteristic
99C4⋊(C47⋊C8)C2311yescharacteristic
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8C2×C411yescharacteristic
104Dic47⋊C8C2×C411yescharacteristic
105Dic47⋊C8D411yescharacteristic
106Dic47⋊C8D411yescharacteristic
107#13093949C2×C411yescharacteristic
108#13093948C2×C411yescharacteristic
109#13093948C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111#13093946C2×C411yescharacteristic
112#13093944C2×C411yescharacteristic
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8C2×C411yescharacteristic
117(C2×D47)⋊C8C2×C411yescharacteristic
118(C2×D47)⋊C8D411yescharacteristic
119(C2×D47)⋊C8D411yescharacteristic
120#13093935—21no—
121#13093934—21no—
122C4×C47⋊C8—21no—
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
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
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146#10625354—22no—
147#10625354—41no—
148C2×D188—21no—
149C2×D188C22×C411yescharacteristic
150C2×C4×D47—21no—
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47C22×C411yescharacteristic
154C2×C4×D47C2×D411yescharacteristic
155C2×C4×D47#4111yescharacteristic
156C2×Dic94—21no—
157C2×Dic94C22×C411yescharacteristic
158Q16×C47—22no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C2×D411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47C22×C411yescharacteristic
169C4⋊C4×C47C22×C411yescharacteristic
170C42×C47—21no—
171C42×C47—21no—
172C42×C47C2411yescharacteristic
173#10625337—22no—
174#10625336—41no—
175(C2×D47)⋊C4—21no—
176(C2×D47)⋊C4—21no—
177(C2×D47)⋊C4—21no—
178(C2×D47)⋊C4—21no—
179(C2×D47)⋊C4—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47C22×C411yescharacteristic
183C4⋊Dic47C22×C411yescharacteristic
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×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
202#10625325—41no—
203#10625324—81no—
204#10625324—81no—
205#10625324—81no—
206C8×D47—24no—
207C22×D47—21no—
208C22×D47C4×D411yescharacteristic
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47#13112yes—
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×Dic47C4×D411yescharacteristic
224C2×Dic47C4×D411yescharacteristic
225C2×Dic47C4×D411yescharacteristic
226D188—21no—
227D188—21no—
228D188—42no—
229C4×D47—21no—
230C4×D47—21no—
231C4×D47—21no—
232C4×D47—21no—
233C4×D47—22no—
234C4×D47—42no—
235C4×D47—41no—
236C4×D47—41no—
237C4×D47—42no—
238Dic94—21no—
239Dic94—21no—
240Dic94—42no—
241C8×C47—22no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—41no—
247C8×C47—41no—
248C47⋊C8—22no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#18019—471nomaximal, Sylow
256C22×C47C2×C4×D411yescharacteristic
257C2×D47—21no—
258C2×D47—21no—
259C2×D47—21no—
260C2×D47—41no—
261C2×D47—41no—
262C2×D47—41no—
263C4×C47—22no—
264C4×C47—21no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47C2×#13111yescharacteristic
269C4×C47#56811yescharacteristic
270C4×C47#57711yescharacteristic
271C4×C47#57811yescharacteristic
272Dic47—21no—
273Dic47—21no—
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277Dic47#44312yes—
278#3107—471no—
279#2991—471no—
280#2986—471no—
281#1590—471no—
282#1590—471no—
283#1588—471no—
284#1588—471no—
285#1587—471no—
286#1587—471no—
287C8×Q16—471no—
288C8×Q16D4711yescharacteristic, complemented
289#1574—471no—
290#1493—471no—
291#1476—471no—
292#1450—471no—
293C2×C47#293311yescharacteristic
294C2×C47#294711yescharacteristic
295C2×C47C2×#44311yescharacteristic
296D47—41no—
297D47—81no—
298#533—471no—
299C4×#41—471no—
300#485—471no—
301#485—471no—
302#475—471no—
303#474—471no—
304#462—471no—
305#461—471no—
306#452—471no—
307#452—471no—
308#446—471no—
309#446—471no—
310#446—941no—
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8—941no—
314C8×Q8C2×D4711yescharacteristic
315C8×Q8C2×D4711yescharacteristic
316C4×Q16—471no—
317C4×Q16C2×D4711yescharacteristic
318C4×SD16—471no—
319C4×SD16—471no—
320#436—471no—
321#436—471no—
322#436—941no—
323#436—941no—
324#433—941no—
325#433—941no—
326#431—471no—
327#431—471no—
328#431—471no—
329#431—941no—
330#423—471no—
331#423—941no—
332C2×C4×C8—471no—
333#335—471no—
334#335C2×D4711yescharacteristic
335#334—471no—
336#334—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8C2×D4711yescharacteristic
342Q8⋊C8C2×D4711yescharacteristic
343D4⋊C8—471no—
344D4⋊C8—471no—
345#322—471no—
346#322—471no—
347C82—471no—
348C82C2×D4711yescharacteristic
349C47#1801911yescharacteristic, complemented, Sylow
350C2×#41—471no—
351C2×Q16—471no—
352C2×Q16C4×D4711yescharacteristic
353C2×SD16—471no—
354C2×SD16—471no—
355C2×M16—941no—
356C2×M16—941no—
357C2×M16—941no—
358C22×C8—941no—
359C4⋊Q8—471no—
360C4⋊Q8—471no—
361#125—941no—
362C22⋊Q8—471no—
363C22⋊Q8—471no—
364C22⋊Q8—941no—
365C4×Q8—471no—
366C4×Q8—471no—
367C4×Q8—941no—
368C4×Q8C22×D4711yescharacteristic
369C4×Q8C22×D4711yescharacteristic
370C4×D4—471no—
371C4×D4—471no—
372C4×D4—941no—
373C4×D4—941no—
374#117—471no—
375#117—941no—
376#117—941no—
377C2×C42—471no—
378C2×C42—941no—
379#107—471no—
380#107C4×D4711yescharacteristic
381#106—471no—
382#106—471no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—471no—
390C4⋊C8—471no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C4⋊C8—941no—
396C4⋊C8C22×D4711yescharacteristic
397C4⋊C8C22×D4711yescharacteristic
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103C4×D4711yescharacteristic
403#103C4×D4711yescharacteristic
404#102—471no—
405#102—471no—
406C22⋊C8—471no—
407C22⋊C8—471no—
408C22⋊C8—471no—
409C22⋊C8—471no—
410C22⋊C8—941no—
411C22⋊C8—941no—
412C22⋊C8—941no—
413#97—941no—
414#97—941no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—471no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426C4×C8C22×D4711yescharacteristic
427#41—942no—
428#41—1881no—
429C2×Q8—471no—
430C2×Q8—941no—
431C2×Q8C2×C4×D4711yescharacteristic
432C2×Q8C2×C4×D4711yescharacteristic
433C2×D4—471no—
434C2×D4—941no—
435C22×C4—471no—
436C22×C4—471no—
437C22×C4—471no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441Q16—22no—
442Q16—942no—
443SD16—1881no—
444SD16—1881no—
445M16—3761no—
446M16—3761no—
447M16—3761no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—471no—
455C2×C8—944no—
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⋊C4C2×C4×D4711yescharacteristic
475C4⋊C4C2×C4×D4711yescharacteristic
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—21no—
482C42—21no—
483C42—471no—
484C42—471no—
485C42—471no—
486C42—941no—
487C42—941no—
488C42—941no—
489C42C23×D4711yescharacteristic
490C23—471no—
491C23—941no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—941no—
496Q8—941no—
497Q8—1882no—
498Q8#1309403012yes—
499D4—941no—
500D4—941no—
501D4—1882no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—471no—
507C2×C4—471no—
508C2×C4—471no—
509C2×C4—942no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—1882no—
518C2×C4—1882no—
519C2×C4—1881no—
520C2×C4—1881no—
521C2×C4C22×C4×D4711yescharacteristic
522C2×C4C2×D4×D4711yescharacteristic
523C2×C4#41×D4711yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—942no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—941no—
536C8—1881no—
537C8—1881no—
538C22—941no—
539C22—941no—
540C22—941no—
541C22—1881no—
542C22—1881no—
543C22—1881no—
544C22C4×D4×D4711yescharacteristic
545C4—21no—
546C4—22no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—472no—
551C4—941no—
552C4—941no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4C2×#1309403011yescharacteristic
557C4#1568988811yescharacteristic
558C4#1568993011yescharacteristic
559C4#1568993611yescharacteristic
560C2—3761no—
561C2—1881no—
562C2#2025210811yescharacteristic
563C2#2025222611yescharacteristic
564C2#443×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC8×Q16×C47C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625354C2×C4
cosocleC42×C47C24
hypercenterC8×Q16D47
hypocenterC47#18019
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
3. #20252488C2semidirect
4. #20242280C2semidirect
5. #20242275C2semidirect
6. #20242266C2semidirect
7. #20242265C2semidirect
8. #20242260C2semidirect
9. #20242259C2semidirect
10. #20242192C2semidirect
11. #20242178C2semidirect
12. #20241841C2semidirect
14. #20241670C2semidirect
15. C8×Q16×C47C2semidirect
288. C8×Q16D47semidirect
349. C47#18019semidirect

Maximal subgroups

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

subgroupindex
#202534572
#202525192
#202524882
#202422802
#202422752
#202422662
#202422652
#202422602
#202422592
#202421922
#202421782
#202418412
#202417692
#202416702
C8×Q16×C472
#1801947