Finite Group Databasebeta

← #26186337

Subgroups — #26186337

Order 12032.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253439C211yesmaximal, characteristic
2#20252540C211yesmaximal, characteristic, complemented
3#20252409C211yesmaximal, characteristic, complemented
4#20242254C211yesmaximal, characteristic, complemented
5#20242222C211yesmaximal, characteristic, complemented
6#20242217C211yesmaximal, characteristic, complemented
7#20242209C211yesmaximal, characteristic, complemented
8#20242203C211yesmaximal, characteristic, complemented
9SD16×C47⋊C8C211yesmaximal, characteristic, complemented
10#20242182C211yesmaximal, characteristic, complemented
11#20242178C211yesmaximal, characteristic, complemented
12#20241811C211yesmaximal, characteristic, complemented
13#20241795C211yesmaximal, characteristic, complemented
14#20241689C211yesmaximal, characteristic, complemented
15C47×#1585C211yesmaximal, characteristic, complemented
16#15689660C2211yescharacteristic
17C4×D4×D47C2211yescharacteristic
18#15689457C411yescharacteristic
19#15689443C411yescharacteristic
20#15689422C411yescharacteristic
21#15689421C411yescharacteristic
22#15689341C411yescharacteristic
23#15689340C411yescharacteristic
24#15689272C411yescharacteristic
25#15689258C411yescharacteristic
26Q8×C47⋊C8C2211yescharacteristic, complemented
27C4×#10625336C2211yescharacteristic
28C4×D376C2211yescharacteristic
29C4×#10625334C2211yescharacteristic
30#15689202C2211yescharacteristic, complemented
31#15689200—21no—
32#15689196—21no—
33C8×D188C2211yescharacteristic
34D4×C47⋊C8C2211yescharacteristic
35#15689188C2211yescharacteristic
36#15689188C2211yescharacteristic, complemented
37C8×C22⋊D47—21no—
38(C22⋊D47)⋊C8—21no—
39#15689185—21no—
40#15689175C2211yescharacteristic
41#15689174C2211yescharacteristic
42#15689174C2211yescharacteristic
43#15689174C2211yescharacteristic
44#15689148—21no—
45#15689145C2211yescharacteristic
46C2×(C2×D47)⋊C8—21no—
47C22⋊C8×D47—21no—
48#15688875C2211yescharacteristic, complemented
49#15688874C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
52#15688852C2211yescharacteristic
53#15688852C2211yescharacteristic, complemented
54D4⋊(C47⋊C8)C2211yescharacteristic
55#15688850C2211yescharacteristic
56#15688850C2211yescharacteristic, complemented
57#15688845C2211yescharacteristic, complemented
58#15688844C2211yescharacteristic, complemented
59C8×C47⋊C8C2211yescharacteristic, complemented
60C47×#446C2211yescharacteristic, complemented
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic, complemented
67C2×D4×D47C2×C411yescharacteristic
68C22×C4×D47—21no—
69C2×#10625336C2×C411yescharacteristic
70C2×D376C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625324—21no—
73C2×#10625324—21no—
74C22×C47⋊C8—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78#13094019—21no—
79#13094015C2×C411yescharacteristic
80#13094013C2×C411yescharacteristic
81#13094009—21no—
82#13094000C2×C411yescharacteristic
83#13093999C2×C411yescharacteristic
84C4×D188—21no—
85C4×D188C2311yescharacteristic
86C4×D188C2311yescharacteristic
87D4×Dic47C2×C411yescharacteristic
88#13093986C2×C411yescharacteristic
89C4×C22⋊D47—21no—
90(C22⋊D47)⋊C4—21no—
91#13093981—21no—
92C4⋊C4×D47C2×C411yescharacteristic
93C22⋊C4×D47—21no—
94C42×D47C2311yescharacteristic
95#13093958C2×C411yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093955C2×C411yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8C2×C411yescharacteristic
104Dic47⋊C8C2×C411yescharacteristic
105Dic47⋊C8D411yescharacteristic
106Dic47⋊C8D411yescharacteristic
107#13093948C2×C411yescharacteristic
108#13093946C2×C411yescharacteristic
109#13093946C2×C411yescharacteristic
110#13093945C2×C411yescharacteristic
111#13093944C2×C411yescharacteristic
112#13093944C2×C411yescharacteristic
113C22⋊(C47⋊C8)—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊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
122(C2×D47)⋊C8D411yescharacteristic
123(C2×D47)⋊C8D411yescharacteristic
124C4×C47⋊C8—21no—
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C4×C47⋊C8C2311yescharacteristic
128C8×Dic47—21no—
129C2×SD16×C47C2×C411yescharacteristic
130C22×C8×C47—21no—
131C4×Q8×C47C2311yescharacteristic
132C4×D4×C47C2311yescharacteristic
133#106×C47C2×C411yescharacteristic
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139C22⋊C8×C47—21no—
140#97×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C23×D47—21no—
145C2×Q8×C47C22×C411yescharacteristic
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C2×C22⋊D47—21no—
149C22×Dic47—21no—
150D4×D47—22no—
151D4×D47—22no—
152C2×D188—21no—
153C2×D188C22×C411yescharacteristic
154C2×D188C22×C411yescharacteristic
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—81no—
160C2×C4×D47—81no—
161C2×C4×D47C22×C411yescharacteristic
162C2×C4×D47C2×D411yescharacteristic
163C2×C4×D47#4111yescharacteristic
164SD16×C47—22no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—81no—
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C4⋊C4×C47—21no—
174C4⋊C4×C47C22×C411yescharacteristic
175C4⋊C4×C47C22×C411yescharacteristic
176C22⋊C4×C47—21no—
177C42×C47—21no—
178C42×C47C2411yescharacteristic
179C22⋊Dic47—21no—
180#10625336—22no—
181#10625334—22no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—21no—
187(C2×D47)⋊C4—21no—
188(C2×D47)⋊C4—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47C22×C411yescharacteristic
191C4⋊Dic47C22×C411yescharacteristic
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195C4×Dic47C22×C411yescharacteristic
196C4×Dic47C2×D411yescharacteristic
197C4×Dic47#4111yescharacteristic
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—81no—
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206D376—22no—
207#10625324—81no—
208#10625324—81no—
209C8×D47—81no—
210C8×D47—81no—
211C8×D47—81no—
212C23×C47—21no—
213C22×D47—21no—
214C22×D47—24no—
215C22×D47—21no—
216C22×D47—81no—
217C22×D47—81no—
218C22×D47C4×D411yescharacteristic
219Q8×C47—21no—
220Q8×C47—21no—
221D4×C47—21no—
222D4×C47#13112yes—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C22×D411yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C22⋊D47—24no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—81no—
235C2×Dic47C4×D411yescharacteristic
236C2×Dic47C4×D411yescharacteristic
237C2×Dic47C4×D411yescharacteristic
238D188—21no—
239D188—21no—
240D188—21no—
241D188—81no—
242D188#13112yes—
243C4×D47—21no—
244C4×D47—21no—
245C4×D47—21no—
246C4×D47—21no—
247C4×D47—41no—
248C4×D47—41no—
249C4×D47—41no—
250C4×D47—41no—
251C4×D47—41no—
252C4×D47—81no—
253C4×D47—81no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—21no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268#17918—471nomaximal, Sylow
269C22×C47—22no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47C2×C4×D411yescharacteristic
273C2×D47—21no—
274C2×D47—22no—
275C2×D47—21no—
276C2×D47—21no—
277C2×D47—41no—
278C2×D47—41no—
279C2×D47—41no—
280C2×D47—41no—
281C2×D47—41no—
282C2×D47—84no—
283C4×C47—21no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47C2×#13111yescharacteristic
288C4×C47C2×#13111yescharacteristic
289C4×C47#57611yescharacteristic
290C4×C47#57711yescharacteristic
291Dic47—21no—
292Dic47—21no—
293Dic47—21no—
294Dic47—41no—
295Dic47—41no—
296#3105—471no—
297#2993—471no—
298#2972—471no—
299#1586—471no—
300#1585D4711yescharacteristic, complemented
301#1582—471no—
302#1581—471no—
303#1580—471no—
304SD16⋊C8—471no—
305C8×SD16—471no—
306C8×D8—471no—
307#1574—471no—
308#1486—471no—
309#1482—471no—
310#1454—471no—
311C2×C47—42no—
312C2×C47#292911yescharacteristic
313C2×C47#294611yescharacteristic
314C2×C47#295711yescharacteristic
315D47—41no—
316D47—42no—
317D47—81no—
318#529—471no—
319C2×C4×D4—471no—
320#484—471no—
321#481—471no—
322#478—471no—
323#478—471no—
324#463—471no—
325#463—471no—
326#450—471no—
327#447—471no—
328#446C2×D4711yescharacteristic, complemented
329C8×Q8—471no—
330C4×SD16—471no—
331C4×SD16C2×D4711yescharacteristic
332C4×D8—471no—
333C4×D8—471no—
334#436—471no—
335#436—941no—
336#435—941no—
337C8×D4—471no—
338C8×D4—471no—
339C8×D4—471no—
340C8×D4—471no—
341C8×D4—941no—
342C8×D4—941no—
343C8×D4C2×D4711yescharacteristic
344#433—941no—
345#431—471no—
346#431—471no—
347#431—471no—
348#431—471no—
349#424—941no—
350#423—471no—
351C2×C22⋊C8—941no—
352C2×C22⋊C8—941no—
353#335—471no—
354#335C2×D4711yescharacteristic, complemented
355#334—471no—
356#334—471no—
357Q8⋊C8—471no—
358Q8⋊C8C2×D4711yescharacteristic, complemented
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363D4⋊C8—471no—
364D4⋊C8C2×D4711yescharacteristic
365#322—471no—
366#322—471no—
367#322C2×D4711yescharacteristic, complemented
368C82—471no—
369C47#1791811yescharacteristic, complemented, Sylow
370C22×D4—471no—
371C23×C4—941no—
372C2×SD16—471no—
373C2×SD16C4×D4711yescharacteristic
374C2×D8—471no—
375C2×D8—471no—
376C2×M16—941no—
377C2×M16—941no—
378C22×C8—21no—
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—941no—
382C22×C8—941no—
383#126—941no—
384#125—471no—
385#124—471no—
386#123—941no—
387C22⋊Q8—471no—
388#121—471no—
389C4×Q8C22×D4711yescharacteristic
390C4×D4—471no—
391C4×D4—471no—
392C4×D4—471no—
393C4×D4—471no—
394C4×D4—941no—
395C4×D4—941no—
396C4×D4—941no—
397C4×D4C22×D4711yescharacteristic
398#117—941no—
399C2×C4⋊C4—471no—
400C2×C22⋊C4—941no—
401C2×C42—471no—
402#107—471no—
403#107—471no—
404#106—471no—
405#106C4×D4711yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—471no—
411C4⋊C8—471no—
412C4⋊C8—471no—
413C4⋊C8—941no—
414C4⋊C8—941no—
415C4⋊C8—941no—
416C4⋊C8C22×D4711yescharacteristic
417C4⋊C8C22×D4711yescharacteristic
418#103—471no—
419#103C4×D4711yescharacteristic
420#102—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424#102—471no—
425#102C4×D4711yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—471no—
428C22⋊C8—471no—
429C22⋊C8—471no—
430C22⋊C8—471no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8—941no—
436C22⋊C8—941no—
437C22⋊C8—941no—
438#97—21no—
439C4×C8—471no—
440C4×C8—471no—
441C4×C8—471no—
442C4×C8—941no—
443C4×C8—941no—
444C4×C8C22×D4711yescharacteristic
445C4×C8C22×D4711yescharacteristic
446C4×C8C22×D4711yescharacteristic
447C24—941no—
448C2×Q8C2×C4×D4711yescharacteristic
449C2×D4—471no—
450C2×D4—471no—
451C2×D4—941no—
452C2×D4—941no—
453C2×D4—942no—
454C2×D4—942no—
455C2×D4C2×C4×D4711yescharacteristic
456C22×C4—21no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4—471no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—3761no—
466C22×C4—3761no—
467SD16—22no—
468SD16—942no—
469D8—942no—
470D8—942no—
471M16—3761no—
472M16—3761no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—471no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—471no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—3761no—
485C2×C8—3761no—
486C2×C8—3761no—
487C2×C8—3761no—
488C2×C8C2×C4×D4711yescharacteristic
489C2×C8C2×C4×D4711yescharacteristic
490C2×C8D4×D4711yescharacteristic
491C2×C8D4×D4711yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—471no—
494C4⋊C4—471no—
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—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C22⋊C4—941no—
510C42—21no—
511C42—471no—
512C42—471no—
513C42—471no—
514C42C23×D4711yescharacteristic
515C23—21no—
516C23—471no—
517C23—944no—
518C23—941no—
519C23—941no—
520C23—3761no—
521C23—3761no—
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—472no—
526D4—944no—
527D4—941no—
528D4—941no—
529D4—941no—
530D4—3761no—
531D4#1309403212yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—471no—
538C2×C4—471no—
539C2×C4—471no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—3761no—
547C2×C4—3761no—
548C2×C4—3761no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4C22×C4×D4711yescharacteristic
555C2×C4C2×D4×D4711yescharacteristic
556C2×C4#41×D4711yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—941no—
565C8—941no—
566C8—941no—
567C8—941no—
568C8—1881no—
569C8—1881no—
570C8—1881no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—941no—
575C22—941no—
576C22—941no—
577C22—942no—
578C22—3764no—
579C22—1881no—
580C22—1881no—
581C22—1881no—
582C22—1881no—
583C22—1881no—
584C22C4×D4×D4711yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—941no—
590C4—941no—
591C4—941no—
592C4—1881no—
593C4—1881no—
594C4#131×D4711yescharacteristic
595C4C2×#1309403211yescharacteristic
596C4#1568992711yescharacteristic
597C4#1568993211yescharacteristic
598C2—42no—
599C2—3761no—
600C2—1881no—
601C2—1882no—
602C2#2025207911yescharacteristic
603C2#2025221911yescharacteristic
604C2#2025230011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1585C2
socleC22×C47C2×C4×D4
prime radical#15689258C4
cosocleC42×C47C24
hypercenter#1585D47
hypocenterC47#17918
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
2. #20252540C2semidirect
3. #20252409C2semidirect
4. #20242254C2semidirect
5. #20242222C2semidirect
6. #20242217C2semidirect
7. #20242209C2semidirect
8. #20242203C2semidirect
9. SD16×C47⋊C8C2semidirect
10. #20242182C2semidirect
11. #20242178C2semidirect
12. #20241811C2semidirect
13. #20241795C2semidirect
14. #20241689C2semidirect
15. C47×#1585C2semidirect
26. Q8×C47⋊C8C22semidirect
30. #15689202C22semidirect
36. #15689188C22semidirect
48. #15688875C22semidirect
49. #15688874C22semidirect
50. #15688873C22semidirect
51. Q8⋊(C47⋊C8)C22semidirect
53. #15688852C22semidirect
56. #15688850C22semidirect
57. #15688845C22semidirect
58. #15688844C22semidirect
59. C8×C47⋊C8C22semidirect
60. C47×#446C22semidirect
63. C47×#335C22semidirect
64. C47×Q8⋊C8C22semidirect
66. C47×#322C22semidirect
300. #1585D47semidirect
328. #446C2×D47semidirect
354. #335C2×D47semidirect
358. Q8⋊C8C2×D47semidirect
367. #322C2×D47semidirect
369. C47#17918semidirect

Maximal subgroups

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

subgroupindex
#202534392
#202525402
#202524092
#202422542
#202422222
#202422172
#202422092
#202422032
SD16×C47⋊C82
#202421822
#202421782
#202418112
#202417952
#202416892
C47×#15852
#1791847