Finite Group Databasebeta

← #26226536

Subgroups — #26226536

Order 12032.

1266 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D47C211yesmaximal, characteristic
2C2×#15688980C211yesmaximal, characteristic
3#380×D47C211yesmaximal, characteristic
4#20243583C211yesmaximal, characteristic, complemented
5#20243582C212yesmaximal, complemented
6#20243581C211yesmaximal, characteristic, complemented
7#20243580C211yesmaximal, characteristic, complemented
8#20243579C212yesmaximal, complemented
9#20243412C212yesmaximal, complemented
10#20243410C212yesmaximal, complemented
11C47×#1853C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C22×C8×D47C2212yes—
14C22×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊C4×D47C2211yescharacteristic
16C2×C4⋊C4×D47C2211yescharacteristic
17C22×(C2×D47)⋊C4—21no—
18C2×C22⋊C4×D47—21no—
19C2×#13093956C2212yescomplemented
20C2×#13093955C2212yescomplemented
21C2×#13093955C2212yescomplemented
22C2×C22⋊(C47⋊C8)C2211yescharacteristic
23C2×(C2×D47)⋊C8C2212yes—
24C22⋊C8×D47C418yescomplemented
25#15688983C2211yescharacteristic
26#15688982—21no—
27#15688981—21no—
28#15688980—21no—
29#15688980—21no—
30#15688980C2212yes—
31#15688980C2211yescharacteristic
32#15688980C2212yes—
33#15688980C2211yescharacteristic
34C2×C47⋊#95—21no—
35#95×D47—21no—
36#15688886C2212yescomplemented
37#15688885C2212yescomplemented
38#15688885C2212yescomplemented
39C22×C4⋊C4×C47C2211yescharacteristic
40C2×#106×C47C2212yescomplemented
41C2×C22⋊C8×C47C2211yescharacteristic
42C47×#380C2211yescharacteristic
43C47×#340C2212yescomplemented
44C24×D47D411yescharacteristic
45C23×Dic47—21no—
46C23×Dic47D411yescharacteristic
47C22×C4×D47—21no—
48C22×C4×D47—21no—
49C22×C4×D47—42no—
50C22×C4×D47—42no—
51C22×C4×D47C2×C414yes—
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C22×C4×D47Q814yes—
55C22×C4×D47C2311yescharacteristic
56C22×C4×D47C2311yescharacteristic
57C22×C47⋊C8C2312yes—
58C2×C8×D47—42no—
59C2×C8×D47—42no—
60C2×C8×D47C2×C418yescomplemented
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47—42no—
63C2×C4⋊Dic47C2312yes—
64C2×C4⋊Dic47C2311yescharacteristic
65C2×C4⋊Dic47C2311yescharacteristic
66C2×Dic47⋊C4—21no—
67C2×Dic47⋊C4—21no—
68C4⋊C4×D47—42no—
69C4⋊C4×D47—42no—
70C2×C22⋊Dic47—21no—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4—22no—
73C2×(C2×D47)⋊C4—21no—
74C2×(C2×D47)⋊C4—21no—
75C2×(C2×D47)⋊C4—44no—
76C22⋊C4×D47—44no—
77#13093956—42no—
78#13093955—42no—
79#13093955—42no—
80C22⋊(C47⋊C8)C2×C414yescomplemented
81(C2×D47)⋊C8C2×C418yescomplemented
82C47⋊#95—21no—
83C47⋊#95—21no—
84C47⋊#95—21no—
85C47⋊#95—22no—
86C47⋊#95—22no—
87C23×C4×C47—21no—
88C23×C4×C47C2311yescharacteristic
89C22×C8×C47C2312yes—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—42no—
92C2×C4⋊C4×C47C2312yes—
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C22⋊C4×C47—21no—
96#106×C47—42no—
97C22⋊C8×C47C2×C414yescomplemented
98#95×C47—21no—
99C24×C47C2×D411yescharacteristic
100C23×D47—41no—
101C23×D47—41no—
102C23×D47—41no—
103C23×D47—41no—
104C23×D47C4⋊C414yes—
105C23×D47SD1614yes—
106C23×D47SD1614yes—
107C23×D47C2×D411yescharacteristic
108C23×D47C2×D411yescharacteristic
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—22no—
114C22×C4×C47—42no—
115C22×C4×C47—42no—
116C22×C4×C47—42no—
117C22×C4×C47C22×C412yes—
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×Q812yes—
120C22×C4×C47C2411yescharacteristic
121C22×Dic47—22no—
122C22×Dic47—21no—
123C22×Dic47—21no—
124C22×Dic47—41no—
125C22×Dic47—41no—
126C22×Dic47—42no—
127C22×Dic47—42no—
128C22×Dic47—42no—
129C22×Dic47C4⋊C414yes—
130C22×Dic47C2×D411yescharacteristic
131C22×Dic47C2×D411yescharacteristic
132C2×C4×D47—22no—
133C2×C4×D47—22no—
134C2×C4×D47—22no—
135C2×C4×D47—22no—
136C2×C4×D47—48no—
137C2×C4×D47—48no—
138C2×C4×D47—41no—
139C2×C4×D47—41no—
140C2×C4×D47—41no—
141C2×C4×D47—41no—
142C2×C4×D47—42no—
143C2×C4×D47—42no—
144C2×C4×D47—42no—
145C2×C4×D47—42no—
146C2×C4×D47—42no—
147C2×C4×D47—42no—
148C2×C4×D47C4⋊C414yes—
149C2×C4×D47C4⋊C414yes—
150C2×C4×D47C22×C412yes—
151C2×C4×D47C22×C412yes—
152C2×C4×D47C2×Q812yes—
153C2×C4×D47C2×Q812yes—
154C2×C8×C47—22no—
155C2×C8×C47—22no—
156C2×C8×C47C22×C414yes—
157C4⋊C4×C47—22no—
158C4⋊C4×C47—22no—
159C4⋊C4×C47—22no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—42no—
162C22⋊C4×C47—42no—
163C22⋊Dic47—42no—
164(C2×D47)⋊C4—42no—
165(C2×D47)⋊C4—42no—
166(C2×D47)⋊C4—44no—
167(C2×D47)⋊C4—44no—
168C4⋊Dic47—22no—
169C4⋊Dic47—22no—
170C4⋊Dic47—22no—
171C4⋊Dic47—22no—
172C4⋊Dic47—42no—
173Dic47⋊C4—42no—
174Dic47⋊C4—42no—
175C2×C47⋊C8—22no—
176C2×C47⋊C8—22no—
177C2×C47⋊C8C22×C414yes—
178C8×D47—48no—
179C23×C47—21no—
180C23×C47—21no—
181C23×C47—21no—
182C23×C47—21no—
183C23×C47C2×C4⋊C412yes—
184C23×C47C2×SD1612yes—
185C23×C47C2×SD1612yes—
186C23×C47C22×D411yescharacteristic
187C22×D47—21no—
188C22×D47—21no—
189C22×D47—21no—
190C22×D47—21no—
191C22×D47—21no—
192C22×D47—21no—
193C22×D47—21no—
194C22×D47—21no—
195C22×D47—44no—
196C22×D47—44no—
197C22×D47—44no—
198C22×D47—44no—
199C22×D47—44no—
200C22×D47—44no—
201C22×D47#106116yescomplemented
202C22×D47C2×C4⋊C412yes—
203C22×D47C2×C4⋊C412yes—
204C22×D47C2×SD1612yes—
205C22×D47C2×SD1612yes—
206C22×D47C2×SD1612yes—
207C22×D47C2×SD1612yes—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—24no—
211C2×C4×C47—24no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—42no—
221C2×C4×C47—84no—
222C2×C4×C47C2×C4⋊C412yes—
223C2×C4×C47C23×C411yescharacteristic
224C2×C4×C47C22×Q811yescharacteristic
225C2×C4×C47H(5,𝔽2)12yes—
226C2×C4×C47H(5,𝔽2)12yes—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—44no—
232C2×Dic47—41no—
233C2×Dic47—41no—
234C2×Dic47—42no—
235C2×Dic47—42no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—42no—
241C2×Dic47—84no—
242C2×Dic47C2×C4⋊C412yes—
243C2×Dic47C2×C4⋊C412yes—
244C4×D47—24no—
245C4×D47—24no—
246C4×D47—24no—
247C4×D47—24no—
248C4×D47—44no—
249C4×D47—44no—
250C4×D47—84no—
251C4×D47—84no—
252C8×C47—24no—
253C47⋊C8—24no—
254#21938—471nomaximal, Sylow
255C22×C47—22no—
256C22×C47—22no—
257C22×C47—22no—
258C22×C47—22no—
259C22×C47—22no—
260C22×C47—22no—
261C22×C47C2×#10614yes—
262C22×C47C22×C4⋊C411yescharacteristic
263C22×C47#53411yescharacteristic
264C22×C47#53411yescharacteristic
265C22×C47C22×SD1611yescharacteristic
266C22×C47C22×SD1611yescharacteristic
267C22×C47#57511yescharacteristic
268C22×C47#57511yescharacteristic
269C2×D47—22no—
270C2×D47—22no—
271C2×D47—22no—
272C2×D47—22no—
273C2×D47—22no—
274C2×D47—22no—
275C2×D47—22no—
276C2×D47—22no—
277C2×D47—22no—
278C2×D47—22no—
279C2×D47—22no—
280C2×D47—22no—
281C2×D47—416no—
282C2×D47C2×#10614yes—
283C2×D47C2×#10614yes—
284C4×C47—22no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47—82no—
288C4×C47#51812yes—
289C4×C47#54312yes—
290Dic47—22no—
291Dic47—22no—
292Dic47—81no—
293Dic47—81no—
294Dic47—82no—
295C22×C22⋊C8—471no—
296C2×#380—471no—
297C2×#380—471no—
298#1853—472no—
299#1853—471no—
300#1853—471no—
301#1853—472no—
302#1853—471no—
303#1853D4711yescharacteristic, complemented
304#1807—472no—
305#1807—472no—
306C2×C47—24no—
307C2×C47#231511yescharacteristic
308C2×C47C22×#10611yescharacteristic
309C2×C47#291111yescharacteristic
310C2×C47#318711yescharacteristic
311C2×C47#318711yescharacteristic
312C2×C47#318711yescharacteristic
313C2×C47#318711yescharacteristic
314D47—24no—
315D47—24no—
316C24×C4—471no—
317C23×C8—472no—
318C22×C4⋊C4—471no—
319C22×C4⋊C4—471no—
320C22×C4⋊C4—471no—
321C22×C4⋊C4C2×D4711yescharacteristic
322C22×C22⋊C4—941no—
323C22×C22⋊C4—941no—
324C2×#106—472no—
325C2×#106—472no—
326C2×#106—472no—
327C2×#106C2×D4712yescomplemented
328C2×C22⋊C8—471no—
329C2×C22⋊C8—472no—
330C2×C22⋊C8—478no—
331C2×C22⋊C8C2×D4711yescharacteristic
332#380—471no—
333#380—471no—
334#380—471no—
335#380—472no—
336#380—472no—
337#380—941no—
338#380—941no—
339#380—941no—
340#380—941no—
341#380C2×D4711yescharacteristic
342C2×#95—941no—
343C2×#95—941no—
344#340—472no—
345#340—472no—
346#340—472no—
347#340C2×D4712yescomplemented
348C47#2193811yescharacteristic, complemented, Sylow
349C25—471no—
350C23×C4—21no—
351C23×C4—471no—
352C23×C4—471no—
353C23×C4—471no—
354C23×C4—474no—
355C23×C4—471no—
356C23×C4—471no—
357C23×C4—474no—
358C23×C4—941no—
359C23×C4—941no—
360C23×C4—941no—
361C23×C4—1882no—
362C23×C4—1882no—
363C23×C4C22×D4711yescharacteristic
364C22×C8—472no—
365C22×C8—478no—
366C22×C8—1882no—
367C22×C8—1882no—
368C22×C8C22×D4712yes—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—472no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4—1882no—
378C2×C4⋊C4—1882no—
379C2×C4⋊C4—1882no—
380C2×C4⋊C4C22×D4711yescharacteristic
381C2×C4⋊C4C22×D4711yescharacteristic
382C2×C4⋊C4C22×D4712yes—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—941no—
385C2×C22⋊C4—941no—
386C2×C22⋊C4—942no—
387C2×C22⋊C4—942no—
388C2×C22⋊C4—941no—
389C2×C22⋊C4—1884no—
390C2×C22⋊C4—1884no—
391#106—42no—
392#106—1882no—
393#106—1882no—
394#106—1882no—
395C22⋊C8—474no—
396C22⋊C8—478no—
397C22⋊C8C4×D4714yescomplemented
398#95—21no—
399#95—941no—
400#95—941no—
401#95—942no—
402#95—942no—
403#95—941no—
404C24—471no—
405C24—471no—
406C24—474no—
407C24—474no—
408C24—474no—
409C24—1881no—
410C24—1881no—
411C24—1881no—
412C24—1881no—
413C24D4×D4711yescharacteristic
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—471no—
423C22×C4—471no—
424C22×C4—474no—
425C22×C4—472no—
426C22×C4—472no—
427C22×C4—472no—
428C22×C4—472no—
429C22×C4—474no—
430C22×C4—474no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—942no—
438C22×C4—1888no—
439C22×C4—1888no—
440C22×C4—1881no—
441C22×C4—1881no—
442C22×C4—1881no—
443C22×C4—1881no—
444C22×C4—1882no—
445C22×C4—1882no—
446C22×C4—1882no—
447C22×C4—1882no—
448C22×C4—1882no—
449C22×C4—1882no—
450C22×C4—1881no—
451C22×C4—1881no—
452C22×C4—1882no—
453C22×C4—1882no—
454C22×C4—1882no—
455C22×C4C2×C4×D4712yes—
456C22×C4D4×D4711yescharacteristic
457C22×C4Q8×D4712yes—
458C22×C4C23×D4711yescharacteristic
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—474no—
462C2×C8—942no—
463C2×C8—942no—
464C2×C8—1888no—
465C2×C8C2×C4×D4714yes—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—42no—
471C4⋊C4—942no—
472C4⋊C4—942no—
473C4⋊C4—942no—
474C4⋊C4—942no—
475C4⋊C4—1882no—
476C4⋊C4—1882no—
477C4⋊C4—1882no—
478C22⋊C4—42no—
479C22⋊C4—1882no—
480C22⋊C4—1882no—
481C22⋊C4—1884no—
482C22⋊C4—1884no—
483C22⋊C4—1882no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—472no—
489C23—472no—
490C23—472no—
491C23—472no—
492C23—472no—
493C23—472no—
494C23—4716no—
495C23—941no—
496C23—941no—
497C23—941no—
498C23—941no—
499C23—941no—
500C23—941no—
501C23—941no—
502C23—941no—
503C23—1884no—
504C23—1884no—
505C23—1884no—
506C23—1884no—
507C23—1884no—
508C23—1884no—
509C23C4⋊C4×D4712yes—
510C23SD16×D4712yes—
511C23SD16×D4712yes—
512C23C2×D4×D4711yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—84no—
527C2×C4—472no—
528C2×C4—472no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—941no—
532C2×C4—941no—
533C2×C4—944no—
534C2×C4—944no—
535C2×C4—944no—
536C2×C4—944no—
537C2×C4—3764no—
538C2×C4—3764no—
539C2×C4—3764no—
540C2×C4—1884no—
541C2×C4—1884no—
542C2×C4—1884no—
543C2×C4—1881no—
544C2×C4—1882no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1882no—
549C2×C4—1881no—
550C2×C4—1882no—
551C2×C4—1881no—
552C2×C4C4⋊C4×D4712yes—
553C2×C4C22×C4×D4711yescharacteristic
554C2×C4C2×Q8×D4711yescharacteristic
555C2×C4#1309406912yes—
556C2×C4#1309407012yes—
557C8—24no—
558C8—944no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—474no—
566C22—474no—
567C22—942no—
568C22—942no—
569C22—942no—
570C22—942no—
571C22—942no—
572C22—942no—
573C22—942no—
574C22—942no—
575C22—942no—
576C22—942no—
577C22—942no—
578C22—942no—
579C22—18816no—
580C22#106×D4714yes—
581C22C2×C4⋊C4×D4711yescharacteristic
582C22#1568968311yescharacteristic
583C22#1568968411yescharacteristic
584C22C2×SD16×D4711yescharacteristic
585C22C2×SD16×D4711yescharacteristic
586C22#1568991911yescharacteristic
587C22#1568992211yescharacteristic
588C4—22no—
589C4—82no—
590C4—81no—
591C4—81no—
592C4—942no—
593C4—942no—
594C4—3761no—
595C4—3762no—
596C4—3761no—
597C4#1568959512yes—
598C4#1568974812yes—
599C2—24no—
600C2—944no—
601C2—944no—
602C2#2024599911yescharacteristic
603C2C2×#106×D4711yescharacteristic
604C2#2025197511yescharacteristic
605C2#2025414211yescharacteristic
606C2#2025414311yescharacteristic
607C2#2025414411yescharacteristic
608C2#2025414711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1853C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1853D47
hypocenterC47#21938
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #20243583C2semidirect
5. #20243582C2semidirect
6. #20243581C2semidirect
7. #20243580C2semidirect
8. #20243579C2semidirect
9. #20243412C2semidirect
10. #20243410C2semidirect
11. C47×#1853C2semidirect
19. C2×#13093956C22semidirect
20. C2×#13093955C22semidirect
21. C2×#13093955C22semidirect
24. C22⋊C8×D47C4semidirect
36. #15688886C22semidirect
37. #15688885C22semidirect
38. #15688885C22semidirect
40. C2×#106×C47C22semidirect
43. C47×#340C22semidirect
60. C2×C8×D47C2×C4semidirect
80. C22⋊(C47⋊C8)C2×C4semidirect
81. (C2×D47)⋊C8C2×C4semidirect
97. C22⋊C8×C47C2×C4semidirect
201. C22×D47#106semidirect
303. #1853D47semidirect
327. C2×#106C2×D47semidirect
347. #340C2×D47semidirect
348. C47#21938semidirect
397. C22⋊C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D472
C2×#156889802
#380×D472
#202435832
#202435822
#202435812
#202435802
#202435792
#202434122
#202434102
C47×#18532
#2193847