Finite Group Databasebeta

← #26186152

Subgroups — #26186152

Order 12032.

686 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253417C211yesmaximal, characteristic
2C8×Q8×D47C211yesmaximal, characteristic, complemented
3#20252097C211yesmaximal, characteristic
4#20242233C211yesmaximal, characteristic, complemented
5#20242231C211yesmaximal, characteristic, complemented
6#20242229C211yesmaximal, characteristic, complemented
7#20242191C211yesmaximal, characteristic, complemented
8SD16×C47⋊C8C211yesmaximal, characteristic, complemented
9#20242187C211yesmaximal, characteristic, complemented
10#20242185C211yesmaximal, characteristic, complemented
11#20242157C211yesmaximal, characteristic, complemented
12#20241815C211yesmaximal, characteristic, complemented
13#20241785C211yesmaximal, characteristic
14#20241673C211yesmaximal, characteristic, complemented
15C47×#1583C211yesmaximal, characteristic, complemented
16C2×#13094032—21no—
17#15689670C2211yescharacteristic
18C4×Q8×D47C2211yescharacteristic
19#15689443C411yescharacteristic
20#15689440C411yescharacteristic
21#15689407C411yescharacteristic
22#15689406C411yescharacteristic
23#15689322C411yescharacteristic
24#15689321C411yescharacteristic
25#15689263C411yescharacteristic
26#15689260C411yescharacteristic
27Q8×C47⋊C8C2211yescharacteristic
28C8×Dic94—21no—
29C8×Dic94C2211yescharacteristic
30#15689247—21no—
31#15689247C2211yescharacteristic
32C4×#10625325C2211yescharacteristic
33C4×#10625336C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35#15689202C2211yescharacteristic
36#15689199—21no—
37D4×C47⋊C8C2211yescharacteristic
38#15689188C2211yescharacteristic
39(C22⋊D47)⋊C8—21no—
40#15689174C2211yescharacteristic
41#15689174C2211yescharacteristic
42#15689145C2211yescharacteristic
43C4⋊C8×D47—21no—
44C4⋊C8×D47C2211yescharacteristic
45#15689088—21no—
46C4×C8×D47—21no—
47C4×C8×D47C2211yescharacteristic
48#15688874C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688855C2211yescharacteristic
52Q8⋊(C47⋊C8)C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688852C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688844C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C4×SD16×C47C2211yescharacteristic
62C47×#436C2211yescharacteristic
63C47×#334C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#10625350—21no—
68C2×Q8×D47C2×C411yescharacteristic
69C2×#10625325C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625336C2×C411yescharacteristic
72#13094032—44no—
73C2×#10625324—21no—
74C2×#10625324—21no—
75C22×C47⋊C8—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47D411yescharacteristic
79C2×C8×D47D411yescharacteristic
80#13094023C2×C411yescharacteristic
81#13094020C2×C411yescharacteristic
82#13094010—21no—
83#13093999C2×C411yescharacteristic
84#13093997—21no—
85#13093995C2×C411yescharacteristic
86Q8×Dic47C2×C411yescharacteristic
87C4×Dic94—21no—
88C4×Dic94C2311yescharacteristic
89#13093989—21no—
90#13093989C2×C411yescharacteristic
91C4×D188C2311yescharacteristic
92C4×C22⋊D47—21no—
93C4⋊C4×D47—21no—
94C4⋊C4×D47C2×C411yescharacteristic
95C42×D47—21no—
96C42×D47C2311yescharacteristic
97#13093956C2×C411yescharacteristic
98#13093955C2×C411yescharacteristic
99#13093955C2×C411yescharacteristic
100C4⋊(C47⋊C8)—21no—
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8C2×C411yescharacteristic
109Dic47⋊C8C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093948C2×C411yescharacteristic
112#13093947C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114#13093945C2×C411yescharacteristic
115#13093944C2×C411yescharacteristic
116C22⋊(C47⋊C8)—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8C2×C411yescharacteristic
121(C2×D47)⋊C8C2×C411yescharacteristic
122C4×C47⋊C8—21no—
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47D411yescharacteristic
129C8×Dic47D411yescharacteristic
130C2×SD16×C47C2×C411yescharacteristic
131C2×M16×C47—21no—
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47C2311yescharacteristic
134#106×C47C2×C411yescharacteristic
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138#103×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C2×C22⋊D47—21no—
149C2×C22⋊D47—21no—
150C2×C22⋊D47—21no—
151Q8×D47—22no—
152Q8×D47—22no—
153#10625350—42no—
154#10625350—42no—
155C2×D188—21no—
156C2×D188C22×C411yescharacteristic
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47C22×C411yescharacteristic
161C2×C4×D47C2×D411yescharacteristic
162C2×C4×D47#4111yescharacteristic
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94C22×C411yescharacteristic
166SD16×C47—22no—
167M16×C47—42no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C22×C411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C4⋊C4×C47—21no—
176C4⋊C4×C47C22×C411yescharacteristic
177C4⋊C4×C47C22×C411yescharacteristic
178C22⋊C4×C47—21no—
179C42×C47—21no—
180C42×C47C2411yescharacteristic
181C22⋊Dic47—21no—
182#10625336—22no—
183#10625335—22no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C4×Dic47C22×C411yescharacteristic
197C4×Dic47C2×D411yescharacteristic
198C4×Dic47#4111yescharacteristic
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—42no—
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207#10625325—22no—
208#10625324—42no—
209#10625324—42no—
210C8×D47—22no—
211C8×D47—42no—
212C8×D47—42no—
213C8×D47SD1614yescomplemented
214C23×C47—21no—
215C22×D47—21no—
216C22×D47C4×D411yescharacteristic
217Q8×C47—21no—
218Q8×C47#13112yescomplemented
219D4×C47—21no—
220D4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47C23×C411yescharacteristic
227C2×C4×C47C22×D411yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C22⋊D47—42no—
230C22⋊D47—42no—
231C22⋊D47—42no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47C4×D411yescharacteristic
236C2×Dic47C4×D411yescharacteristic
237C2×Dic47C4×D411yescharacteristic
238D188—21no—
239D188—21no—
240D188—42no—
241C4×D47—24no—
242C4×D47—21no—
243C4×D47—21no—
244C4×D47—41no—
245C4×D47—42no—
246C4×D47—41no—
247C4×D47—41no—
248C4×D47C2×SD1612yes—
249C4×D47#13512yes—
250Dic94—24no—
251Dic94—21no—
252Dic94—42no—
253Dic94#13112yescomplemented
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47C2×SD1612yes—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267C47⋊C8C2×SD1612yes—
268#17901—471nomaximal, Sylow
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47C2×C4×D411yescharacteristic
273C2×D47—21no—
274C2×D47—21no—
275C2×D47—41no—
276C2×D47—41no—
277C2×D47—41no—
278C2×D47C4×SD1612yes—
279C4×C47—22no—
280C4×C47—21no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47C2×#13111yescharacteristic
284C4×C47C2×#13111yescharacteristic
285C4×C47C22×SD1611yescharacteristic
286C4×C47C2×#13511yescharacteristic
287Dic47—21no—
288Dic47—22no—
289Dic47—21no—
290Dic47—41no—
291Dic47—41no—
292Dic47C4×SD1612yes—
293#3103—471no—
294C2×C8×Q8—471no—
295#2931—471no—
296#1583—471no—
297#1583—471no—
298#1583—471no—
299#1583D4711yescharacteristic, complemented
300C8×SD16—471no—
301C8×SD16—471no—
302C8×SD16—471no—
303C8×SD16—471no—
304#1570—471no—
305#1487—471no—
306#1480—471no—
307#1450—471no—
308C2×C47—81no—
309C2×C47#292911yescharacteristic
310C2×C47C2×C4×SD1611yescharacteristic
311C2×C47#295511yescharacteristic
312D47—22no—
313D47—81no—
314C2×#131—941no—
315#532—471no—
316C2×C4×Q8—471no—
317#481—471no—
318#481—471no—
319#475—471no—
320#475—471no—
321#460—471no—
322#460—471no—
323#448—471no—
324#448—471no—
325C8×Q8—471no—
326C8×Q8—471no—
327C8×Q8—471no—
328C8×Q8—941no—
329C8×Q8—941no—
330C8×Q8C2×D4711yescharacteristic
331C4×SD16—471no—
332C4×SD16—471no—
333C4×SD16—471no—
334C4×SD16C2×D4711yescharacteristic
335#436—471no—
336#436—941no—
337#436C2×D4711yescharacteristic
338C8×D4—471no—
339C8×D4—471no—
340C8×D4—941no—
341#431—471no—
342#431—471no—
343#423—471no—
344C2×C4⋊C8—471no—
345C2×C4⋊C8—941no—
346#408—941no—
347C2×C4×C8—471no—
348C2×C4×C8—941no—
349#334—471no—
350#334—471no—
351#334—471no—
352#334C2×D4711yescharacteristic
353Q8⋊C8—471no—
354Q8⋊C8—471no—
355Q8⋊C8—471no—
356Q8⋊C8C2×D4711yescharacteristic
357D4⋊C8—471no—
358D4⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8C2×D4711yescharacteristic
361#322—471no—
362#322C2×D4711yescharacteristic
363C82—471no—
364C82—471no—
365C47#1790111yescharacteristic, complemented, Sylow
366C2×#41—941no—
367C22×Q8—471no—
368C2×SD16—471no—
369C2×SD16—471no—
370C2×SD16—471no—
371C2×SD16C4×D4711yescharacteristic
372#131—1884no—
373C2×M16—21no—
374C2×M16—941no—
375C2×M16—941no—
376C22×C8—471no—
377C22×C8—471no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8—941no—
381C4⋊Q8—471no—
382#127—471no—
383#124—941no—
384#121—471no—
385#121—471no—
386#121—941no—
387C4×Q8—471no—
388C4×Q8—471no—
389C4×Q8—471no—
390C4×Q8—941no—
391C4×Q8—941no—
392C4×Q8C22×D4711yescharacteristic
393C4×D4—471no—
394C4×D4—941no—
395C4×D4C22×D4711yescharacteristic
396C2×C4⋊C4—471no—
397C2×C4⋊C4—941no—
398C2×C42—471no—
399C2×C42—941no—
400#106—471no—
401#106—471no—
402#106—471no—
403#106C4×D4711yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—471no—
406C4⋊C8—471no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—941no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8—941no—
414C4⋊C8—941no—
415C4⋊C8C22×D4711yescharacteristic
416C4⋊C8C22×D4711yescharacteristic
417#103—471no—
418#103—471no—
419#103—471no—
420#103C4×D4711yescharacteristic
421#102—471no—
422#102—471no—
423#102—471no—
424#102C4×D4711yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—471no—
427C22⋊C8—471no—
428C22⋊C8—941no—
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C4×C8—21no—
433C4×C8—471no—
434C4×C8—471no—
435C4×C8—471no—
436C4×C8—471no—
437C4×C8—471no—
438C4×C8—941no—
439C4×C8—941no—
440C4×C8—941no—
441C4×C8C22×D4711yescharacteristic
442C4×C8C22×D4711yescharacteristic
443C4×C8C22×D4711yescharacteristic
444#41—1882no—
445#41—1882no—
446C2×Q8—471no—
447C2×Q8—941no—
448C2×Q8—941no—
449C2×Q8—942no—
450C2×Q8—942no—
451C2×Q8C2×C4×D4711yescharacteristic
452C2×D4—471no—
453C2×D4—941no—
454C2×D4—941no—
455C2×D4—941no—
456C2×D4—941no—
457C2×D4C2×C4×D4711yescharacteristic
458C22×C4—21no—
459C22×C4—471no—
460C22×C4—471no—
461C22×C4—471no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465SD16—22no—
466SD16—942no—
467SD16—942no—
468SD16—942no—
469M16—42no—
470M16—1882no—
471M16—1882no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—471no—
476C2×C8—474no—
477C2×C8—471no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—942no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—1882no—
485C2×C8—1882no—
486C2×C8—1882no—
487C2×C8C2×C4×D4711yescharacteristic
488C2×C8C2×C4×D4711yescharacteristic
489C2×C8D4×D4711yescharacteristic
490C2×C8D4×D4711yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—471no—
493C4⋊C4—471no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4C2×C4×D4711yescharacteristic
500C4⋊C4C2×C4×D4711yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—941no—
503C22⋊C4—941no—
504C22⋊C4—941no—
505C42—21no—
506C42—471no—
507C42—471no—
508C42—471no—
509C42—941no—
510C42—941no—
511C42—941no—
512C42C23×D4711yescharacteristic
513C23—21no—
514C23—471no—
515C23—941no—
516Q8—21no—
517Q8—472no—
518Q8—944no—
519Q8—941no—
520Q8—1882no—
521Q8#1309403212yescomplemented
522D4—21no—
523D4—21no—
524D4—941no—
525D4—941no—
526D4—1882no—
527D4—1882no—
528D4—1882no—
529D4—1882no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—471no—
536C2×C4—472no—
537C2×C4—472no—
538C2×C4—471no—
539C2×C4—471no—
540C2×C4—944no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—1881no—
547C2×C4—1882no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4C22×C4×D4711yescharacteristic
551C2×C4C2×D4×D4711yescharacteristic
552C2×C4#41×D4711yescharacteristic
553C8—21no—
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—472no—
560C8—941no—
561C8—941no—
562C8—941no—
563C8—1881no—
564C8—1881no—
565C8—1881no—
566C8SD16×D4712yes—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—472no—
571C22—941no—
572C22—941no—
573C22—1881no—
574C22—1881no—
575C22—1881no—
576C22C4×D4×D4711yescharacteristic
577C4—21no—
578C4—22no—
579C4—41no—
580C4—41no—
581C4—472no—
582C4—941no—
583C4—941no—
584C4—942no—
585C4—1881no—
586C4—1881no—
587C4#131×D4711yescharacteristic
588C4C2×#1309403211yescharacteristic
589C4C2×SD16×D4711yescharacteristic
590C4#135×D4711yescharacteristic
591C2—81no—
592C2—942no—
593C2—3761no—
594C2#2025207911yescharacteristic
595C2C4×SD16×D4711yescharacteristic
596C2#2025228811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1583C2
socleC22×C47C2×C4×D4
prime radical#15689670C22
cosocleC42×C47C24
hypercenter#1583D47
hypocenterC47#17901
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. C8×Q8×D47C2semidirect
4. #20242233C2semidirect
5. #20242231C2semidirect
6. #20242229C2semidirect
7. #20242191C2semidirect
8. SD16×C47⋊C8C2semidirect
9. #20242187C2semidirect
10. #20242185C2semidirect
11. #20242157C2semidirect
12. #20241815C2semidirect
14. #20241673C2semidirect
15. C47×#1583C2semidirect
213. C8×D47SD16semidirect
218. Q8×C47#131semidirect
253. Dic94#131semidirect
299. #1583D47semidirect
365. C47#17901semidirect
521. Q8#13094032semidirect

Maximal subgroups

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

subgroupindex
#202534172
C8×Q8×D472
#202520972
#202422332
#202422312
#202422292
#202421912
SD16×C47⋊C82
#202421872
#202421852
#202421572
#202418152
#202417852
#202416732
C47×#15832
#1790147