Finite Group Databasebeta

← #26186243

Subgroups — #26186243

Order 12032.

720 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253433C211yesmaximal, characteristic
2#20252360C211yesmaximal, characteristic, complemented
3C8×D4×D47C211yesmaximal, characteristic, complemented
4#20242255C211yesmaximal, characteristic, complemented
5#20242253C211yesmaximal, characteristic, complemented
6#20242244C211yesmaximal, characteristic, complemented
7#20242242C211yesmaximal, characteristic, complemented
8C8×#10625325C211yesmaximal, characteristic, complemented
9C8×#10625335C211yesmaximal, characteristic, complemented
10C8×#10625334C211yesmaximal, characteristic, complemented
11#20242172C211yesmaximal, characteristic, complemented
12#20241829C211yesmaximal, characteristic, complemented
13#20241798C211yesmaximal, characteristic, complemented
14C8×#10625324C211yesmaximal, characteristic, complemented
15C8×D8×C47C211yesmaximal, characteristic, complemented
16C22×C8×D47—21no—
17#15689655C2211yescharacteristic
18C4×D4×D47C2211yescharacteristic
19#15689460C411yescharacteristic
20#15689440C411yescharacteristic
21#15689426C411yescharacteristic
22#15689425C411yescharacteristic
23#15689337C411yescharacteristic
24#15689336C411yescharacteristic
25#15689275C411yescharacteristic
26#15689255C411yescharacteristic
27#15689250C2211yescharacteristic, complemented
28C8×Dic94C2211yescharacteristic, complemented
29C4×#10625325C2211yescharacteristic
30C4×#10625335C2211yescharacteristic
31C4×#10625334C2211yescharacteristic
32#15689201C2211yescharacteristic, complemented
33#15689197—21no—
34C8×D188C2211yescharacteristic
35D4×C47⋊C8C2211yescharacteristic
36#15689188C2211yescharacteristic
37C8×C22⋊D47—21no—
38C8×C22⋊D47—21no—
39(C22⋊D47)⋊C8—21no—
40#15689181—21no—
41#15689179C2211yescharacteristic
42#15689174C2211yescharacteristic
43C4⋊C8×D47C2211yescharacteristic
44C22⋊C8×D47—21no—
45#15689078—21no—
46C4×#10625324C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688875C2211yescharacteristic, complemented
49#15688874C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688855C2211yescharacteristic, complemented
52#15688853C2211yescharacteristic, complemented
53#15688852C2211yescharacteristic
54D4⋊(C47⋊C8)C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic, complemented
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic, complemented
58#15688844C2211yescharacteristic, complemented
59C8×C47⋊C8C2211yescharacteristic, complemented
60C4×D8×C47C2211yescharacteristic
61C8×D4×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic, complemented
63C47×#335C2211yescharacteristic, complemented
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic, complemented
66C82×C47C2211yescharacteristic, complemented
67C2×D4×D47C2×C411yescharacteristic
68C22×C4×D47—21no—
69C2×#10625325C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625329—21no—
73C2×#10625324—21no—
74C22×C47⋊C8—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47—44no—
79C2×C8×D47D411yescharacteristic
80C2×C8×D47D411yescharacteristic
81#13094017—21no—
82#13094015C2×C411yescharacteristic
83#13094011C2×C411yescharacteristic
84#13094006—21no—
85#13094004C2×C411yescharacteristic
86#13093995C2×C411yescharacteristic
87C4×Dic94C2311yescharacteristic
88C4×D188C2311yescharacteristic
89D4×Dic47C2×C411yescharacteristic
90#13093986C2×C411yescharacteristic
91C4×C22⋊D47—21no—
92C4×C22⋊D47—21no—
93(C22⋊D47)⋊C4—21no—
94#13093983—21no—
95C4⋊C4×D47C2×C411yescharacteristic
96C22⋊C4×D47—21no—
97C42×D47C2311yescharacteristic
98#13093957C2×C411yescharacteristic
99#13093956C2×C411yescharacteristic
100#13093955C2×C411yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8C2×C411yescharacteristic
107Dic47⋊C8C2×C411yescharacteristic
108#13093949C2×C411yescharacteristic
109#13093947C2×C411yescharacteristic
110#13093946C2×C411yescharacteristic
111#13093945C2×C411yescharacteristic
112#13093945C2×C411yescharacteristic
113#13093944C2×C411yescharacteristic
114C22⋊(C47⋊C8)—21no—
115C22⋊(C47⋊C8)—21no—
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8C2×C411yescharacteristic
120(C2×D47)⋊C8C2×C411yescharacteristic
121#13093934—21no—
122#13093934—21no—
123#13093934—21no—
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C8×Dic47—21no—
128C8×Dic47D411yescharacteristic
129C8×Dic47D411yescharacteristic
130C2×D8×C47C2×C411yescharacteristic
131C22×C8×C47—21no—
132C22×C8×C47—21no—
133C4×D4×C47C2311yescharacteristic
134C4×D4×C47C2311yescharacteristic
135#107×C47C2×C411yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138#102×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47—21no—
141C22⋊C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C23×D47—21no—
146C2×D4×C47C22×C411yescharacteristic
147C2×D4×C47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C2×C22⋊D47—21no—
151C2×C22⋊D47—21no—
152C22×Dic47—21no—
153D4×D47—22no—
154D4×D47—22no—
155C2×D188C22×C411yescharacteristic
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—42no—
160C2×C4×D47—42no—
161C2×C4×D47C22×C411yescharacteristic
162C2×C4×D47C2×D411yescharacteristic
163C2×C4×D47#4111yescharacteristic
164C2×Dic94C22×C411yescharacteristic
165D8×C47—22no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—42no—
170C2×C8×C47—42no—
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C22×C411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C4⋊C4×C47C22×C411yescharacteristic
176C4⋊C4×C47C22×C411yescharacteristic
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C42×C47C2411yescharacteristic
180C22⋊Dic47—21no—
181C22⋊Dic47—21no—
182C22⋊Dic47—21no—
183C22⋊Dic47—21no—
184#10625335—22no—
185#10625334—22no—
186(C2×D47)⋊C4—21no—
187(C2×D47)⋊C4—21no—
188(C2×D47)⋊C4—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47C22×C411yescharacteristic
192C4⋊Dic47C22×C411yescharacteristic
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196C4×Dic47—21no—
197C4×Dic47C22×C411yescharacteristic
198C4×Dic47C2×D411yescharacteristic
199C4×Dic47#4111yescharacteristic
200#10625329—42no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—42no—
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209#10625325—22no—
210#10625324—24no—
211C8×D47—22no—
212C8×D47—41no—
213C8×D47—42no—
214C8×D47—42no—
215C8×D47—42no—
216C23×C47—21no—
217C23×C47—21no—
218C22×D47—24no—
219C22×D47—21no—
220C22×D47—42no—
221C22×D47—42no—
222C22×D47C4×D411yescharacteristic
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—21no—
226D4×C47#13112yes—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47C23×C411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C22⋊D47—24no—
237C22⋊D47—42no—
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—42no—
242C2×Dic47C4×D411yescharacteristic
243C2×Dic47C4×D411yescharacteristic
244C2×Dic47C4×D411yescharacteristic
245D188—21no—
246D188#13112yes—
247C4×D47—22no—
248C4×D47—21no—
249C4×D47—21no—
250C4×D47—21no—
251C4×D47—21no—
252C4×D47—42no—
253C4×D47—42no—
254C4×D47—41no—
255C4×D47—41no—
256Dic94—21no—
257Dic94—21no—
258C8×C47—22no—
259C8×C47—21no—
260C8×C47—21no—
261C8×C47—21no—
262C8×C47—41no—
263C8×C47—41no—
264C8×C47AGL(1,ℤ/8)12yes—
265C47⋊C8—22no—
266C47⋊C8—21no—
267C47⋊C8—21no—
268C47⋊C8—21no—
269C47⋊C8—21no—
270C47⋊C8—41no—
271C47⋊C8—41no—
272#17910—471nomaximal, Sylow
273C22×C47—22no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47C2×C4×D411yescharacteristic
280C2×D47—21no—
281C2×D47—21no—
282C2×D47—22no—
283C2×D47—48no—
284C2×D47—41no—
285C2×D47—41no—
286C2×D47#44312yes—
287C4×C47—21no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47C2×#13111yescharacteristic
291C4×C47C2×#13111yescharacteristic
292C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C47#57511yescharacteristic
294Dic47—21no—
295Dic47—21no—
296Dic47—21no—
297Dic47—41no—
298Dic47—41no—
299Dic47—41no—
300#3105—471no—
301#2966—471no—
302C2×C8×D4—471no—
303#1586—471no—
304#1586—471no—
305#1585—471no—
306#1585—471no—
307C8×SD16—471no—
308C8×SD16—471no—
309C8×D8—471no—
310C8×D8D4711yescharacteristic, complemented
311#1573—471no—
312#1490—471no—
313#1483—471no—
314C8×M16—471no—
315C2×C47—42no—
316C2×C47—81no—
317C2×C47#292911yescharacteristic
318C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
319C2×C47C2×#44311yescharacteristic
320D47—22no—
321D47—42no—
322C23×C8—941no—
323#529—471no—
324C2×C4×D4—471no—
325#484—471no—
326#481—471no—
327#478—471no—
328#478—471no—
329#463—471no—
330#463—471no—
331#450—471no—
332#447—471no—
333#446—471no—
334C8×Q8—471no—
335C4×SD16—471no—
336C4×SD16—471no—
337C4×D8—471no—
338C4×D8C2×D4711yescharacteristic
339#436—471no—
340#435—941no—
341C8×D4—471no—
342C8×D4—471no—
343C8×D4—471no—
344C8×D4—941no—
345C8×D4—941no—
346C8×D4—941no—
347C8×D4C2×D4711yescharacteristic
348C8×D4C2×D4711yescharacteristic, complemented
349#433—941no—
350#432—471no—
351#431—471no—
352C2×C4⋊C8—471no—
353C2×C22⋊C8—941no—
354#405—941no—
355C4×M16—471no—
356C2×C4×C8—471no—
357#335—471no—
358#335C2×D4711yescharacteristic, complemented
359#334—471no—
360#334—471no—
361Q8⋊C8—471no—
362Q8⋊C8—471no—
363D4⋊C8—471no—
364D4⋊C8—471no—
365D4⋊C8—471no—
366D4⋊C8—471no—
367D4⋊C8C2×D4711yescharacteristic
368D4⋊C8C2×D4711yescharacteristic, complemented
369#322—471no—
370#322—471no—
371C82—471no—
372C82C2×D4711yescharacteristic, complemented
373C47#1791011yescharacteristic, complemented, Sylow
374C22×D4—471no—
375C23×C4—941no—
376C2×SD16—471no—
377C2×SD16—471no—
378C2×D8—471no—
379C2×D8C4×D4711yescharacteristic
380C2×M16—941no—
381C2×M16—941no—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—471no—
385C22×C8—471no—
386C22×C8—941no—
387C22×C8—941no—
388C22×C8—941no—
389C22×C8—941no—
390C22×C8—1884no—
391#126—941no—
392#125—471no—
393#124—471no—
394#123—941no—
395C22⋊Q8—471no—
396#121—471no—
397C4×Q8—471no—
398C4×D4—471no—
399C4×D4—471no—
400C4×D4—471no—
401C4×D4—941no—
402C4×D4—941no—
403C4×D4—941no—
404C4×D4C22×D4711yescharacteristic
405C4×D4C22×D4711yescharacteristic
406#117—941no—
407C2×C4⋊C4—471no—
408C2×C22⋊C4—941no—
409C2×C42—471no—
410#107—471no—
411#107C4×D4711yescharacteristic
412#106—471no—
413#106—471no—
414C4⋊C8—471no—
415C4⋊C8—471no—
416C4⋊C8—471no—
417C4⋊C8—471no—
418C4⋊C8—941no—
419C4⋊C8—941no—
420C4⋊C8—941no—
421C4⋊C8C22×D4711yescharacteristic
422C4⋊C8C22×D4711yescharacteristic
423#103—471no—
424#103—471no—
425#102—471no—
426#102—471no—
427#102—471no—
428#102—471no—
429#102C4×D4711yescharacteristic
430#102C4×D4711yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—471no—
434C22⋊C8—471no—
435C22⋊C8—941no—
436C22⋊C8—941no—
437C22⋊C8—941no—
438C22⋊C8—941no—
439C22⋊C8—941no—
440#97—941no—
441#97—941no—
442#97—941no—
443C4×C8—471no—
444C4×C8—471no—
445C4×C8—471no—
446C4×C8—471no—
447C4×C8—471no—
448C4×C8—941no—
449C4×C8C22×D4711yescharacteristic
450C4×C8C22×D4711yescharacteristic
451C4×C8C22×D4711yescharacteristic
452C24—941no—
453C2×Q8—471no—
454C2×D4—471no—
455C2×D4—941no—
456C2×D4—942no—
457C2×D4—942no—
458C2×D4—941no—
459C2×D4C2×C4×D4711yescharacteristic
460C2×D4C2×C4×D4711yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—471no—
464C22×C4—471no—
465C22×C4—471no—
466C22×C4—941no—
467C22×C4—941no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—1882no—
471C22×C4—1882no—
472SD16—942no—
473SD16—942no—
474D8—22no—
475D8—942no—
476M16—944no—
477M16—1882no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8—471no—
484C2×C8—471no—
485C2×C8—471no—
486C2×C8—471no—
487C2×C8—941no—
488C2×C8—942no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—1881no—
492C2×C8—1882no—
493C2×C8—1882no—
494C2×C8—1882no—
495C2×C8—1882no—
496C2×C8C2×C4×D4711yescharacteristic
497C2×C8C2×C4×D4711yescharacteristic
498C2×C8D4×D4711yescharacteristic
499C2×C8D4×D4711yescharacteristic
500C4⋊C4—471no—
501C4⋊C4—471no—
502C4⋊C4—941no—
503C4⋊C4—941no—
504C4⋊C4—941no—
505C4⋊C4—941no—
506C4⋊C4—941no—
507C4⋊C4C2×C4×D4711yescharacteristic
508C4⋊C4C2×C4×D4711yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—941no—
512C22⋊C4—941no—
513C22⋊C4—941no—
514C22⋊C4—941no—
515C22⋊C4—941no—
516C22⋊C4—941no—
517C22⋊C4—941no—
518C42—471no—
519C42—471no—
520C42—471no—
521C42—941no—
522C42C23×D4711yescharacteristic
523C23—21no—
524C23—21no—
525C23—471no—
526C23—944no—
527C23—941no—
528C23—1882no—
529C23—1882no—
530Q8—941no—
531Q8—941no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—472no—
536D4—944no—
537D4—941no—
538D4—1882no—
539D4#1309403012yes—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—471no—
547C2×C4—471no—
548C2×C4—471no—
549C2×C4—942no—
550C2×C4—941no—
551C2×C4—941no—
552C2×C4—941no—
553C2×C4—941no—
554C2×C4—941no—
555C2×C4—941no—
556C2×C4—941no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4C22×C4×D4711yescharacteristic
563C2×C4C2×D4×D4711yescharacteristic
564C2×C4#41×D4711yescharacteristic
565C8—22no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—942no—
572C8—941no—
573C8—941no—
574C8—941no—
575C8—941no—
576C8—1881no—
577C8—1881no—
578C8#1309404812yes—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—472no—
586C22—941no—
587C22—941no—
588C22—942no—
589C22—1888no—
590C22—1881no—
591C22—1881no—
592C22C4×D4×D4711yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—941no—
597C4—941no—
598C4—941no—
599C4—1881no—
600C4—1881no—
601C4—1881no—
602C4#131×D4711yescharacteristic
603C4C2×#1309403011yescharacteristic
604C4C2×#1309404811yescharacteristic
605C4#1568992011yescharacteristic
606C2—42no—
607C2—81no—
608C2—942no—
609C2—1882no—
610C2#2025207711yescharacteristic
611C2C4×#1309404811yescharacteristic
612C2#443×D4711yescharacteristic
subgroupG/H
centerC2×C8D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC8×D8×C47C2
socleC22×C47C2×C4×D4
prime radical#15689255C4
cosocleC42×C47C24
hypercenterC8×D8D47
hypocenterC47#17910
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #20252360C2semidirect
3. C8×D4×D47C2semidirect
4. #20242255C2semidirect
5. #20242253C2semidirect
6. #20242244C2semidirect
7. #20242242C2semidirect
8. C8×#10625325C2semidirect
9. C8×#10625335C2semidirect
10. C8×#10625334C2semidirect
11. #20242172C2semidirect
12. #20241829C2semidirect
13. #20241798C2semidirect
14. C8×#10625324C2semidirect
15. C8×D8×C47C2semidirect
27. #15689250C22semidirect
28. C8×Dic94C22semidirect
32. #15689201C22semidirect
48. #15688875C22semidirect
49. #15688874C22semidirect
50. #15688873C22semidirect
51. #15688855C22semidirect
52. #15688853C22semidirect
55. D4⋊(C47⋊C8)C22semidirect
57. #15688845C22semidirect
58. #15688844C22semidirect
59. C8×C47⋊C8C22semidirect
62. C8×D4×C47C22semidirect
63. C47×#335C22semidirect
65. C47×D4⋊C8C22semidirect
66. C82×C47C22semidirect
310. C8×D8D47semidirect
348. C8×D4C2×D47semidirect
358. #335C2×D47semidirect
368. D4⋊C8C2×D47semidirect
372. C82C2×D47semidirect
373. C47#17910semidirect

Maximal subgroups

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

subgroupindex
#202534332
#202523602
C8×D4×D472
#202422552
#202422532
#202422442
#202422422
C8×#106253252
C8×#106253352
C8×#106253342
#202421722
#202418292
#202417982
C8×#106253242
C8×D8×C472
#1791047