Finite Group Databasebeta

← #26187726

Subgroups — #26187726

Order 12032.

654 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252404C211yesmaximal, characteristic, complemented
2#20252396C211yesmaximal, characteristic, complemented
3C4×#13094043C211yesmaximal, characteristic
4#20242281C211yesmaximal, characteristic, complemented
5#20242276C211yesmaximal, characteristic, complemented
6#20242240C211yesmaximal, characteristic, complemented
7#20242237C211yesmaximal, characteristic, complemented
8#20242218C211yesmaximal, characteristic, complemented
9#20242191C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242150C211yesmaximal, characteristic, complemented
12#20241819C211yesmaximal, characteristic, complemented
13#20241819C211yesmaximal, characteristic, complemented
14#20241667C211yesmaximal, characteristic, complemented
15C47×#1581C211yesmaximal, characteristic, complemented
16C2×#13094043C411yescharacteristic
17C4×#10625352C2211yescharacteristic
18C4×#10625352C2211yescharacteristic
19#15689253C2211yescharacteristic
20#15689250C2211yescharacteristic
21C8×Dic94C2211yescharacteristic
22#15689247C2211yescharacteristic
23C4×Dic188C2211yescharacteristic
24#15689217C411yescharacteristic
25#15689214C411yescharacteristic
26#15689214C411yescharacteristic
27C4×#10625335C2211yescharacteristic
28C4×#10625335C2211yescharacteristic
29D8×Dic47C411yescharacteristic
30#15689201C2211yescharacteristic
31#15689199—21no—
32#15689198—21no—
33#15689194—21no—
34#15689191—21no—
35D4×C47⋊C8C2211yescharacteristic
36#15689179C2211yescharacteristic
37#15689179C2211yescharacteristic
38#15689177—21no—
39#15689177—21no—
40#15689174C2211yescharacteristic
41#15689160C411yescharacteristic
42#15689116C411yescharacteristic
43#15689116C411yescharacteristic
44M16×Dic47—21no—
45C4×#10625324C2211yescharacteristic
46C2×#13093934—21no—
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688855C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688853C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56D4⋊(C47⋊C8)C2211yescharacteristic
57#15688845C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C4×D8×C47C2211yescharacteristic
61C47×#436C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#10625352C2×C411yescharacteristic
68C2×#10625352C2×C411yescharacteristic
69#13094043—24no—
70C2×Dic188C2×C411yescharacteristic
71C2×#10625335C2×C411yescharacteristic
72C2×#10625335C2×C411yescharacteristic
73C2×#10625329—21no—
74C2×#10625324D411yescharacteristic
75C2×#10625324D411yescharacteristic
76C22×C47⋊C8—21no—
77C2×C8×D47C2×C411yescharacteristic
78C2×C8×D47C2×C411yescharacteristic
79C4×Dic94C2311yescharacteristic
80C4×Dic94C2311yescharacteristic
81#13093989C2×C411yescharacteristic
82#13093989C2×C411yescharacteristic
83D4×Dic47C2×C411yescharacteristic
84D4×Dic47C2×C411yescharacteristic
85C4×C22⋊D47—21no—
86C4×C22⋊D47—21no—
87(C22⋊D47)⋊C4—21no—
88(C22⋊D47)⋊C4—21no—
89#13093982C2×C411yescharacteristic
90#13093982C2×C411yescharacteristic
91#13093980—21no—
92#13093980—21no—
93C2×C4×Dic47—21no—
94C2×C4×Dic47—21no—
95C42×D47C2311yescharacteristic
96#13093958C2×C411yescharacteristic
97#13093955C2×C411yescharacteristic
98#13093955C2×C411yescharacteristic
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106#13093949C2×C411yescharacteristic
107#13093949C2×C411yescharacteristic
108#13093947C2×C411yescharacteristic
109#13093947C2×C411yescharacteristic
110#13093945C2×C411yescharacteristic
111#13093945C2×C411yescharacteristic
112C22⋊(C47⋊C8)—21no—
113C22⋊(C47⋊C8)—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8—21no—
117#13093934—21no—
118#13093934—21no—
119#13093934—21no—
120#13093934—21no—
121#13093934D411yescharacteristic
122#13093934D411yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47C2×C411yescharacteristic
129C8×Dic47C2×C411yescharacteristic
130C2×D8×C47C2×C411yescharacteristic
131C2×M16×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
145C2×D4×C47C22×C411yescharacteristic
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C2×C22⋊D47—21no—
150C2×C22⋊D47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155#10625352—22no—
156#10625352—22no—
157#10625352—41no—
158#10625352—41no—
159C2×C4×D47C22×C411yescharacteristic
160C2×C4×D47C2×D411yescharacteristic
161C2×C4×D47#4111yescharacteristic
162C2×Dic94C22×C411yescharacteristic
163C2×Dic94C22×C411yescharacteristic
164D8×C47—22no—
165M16×C47—42no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—42no—
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C4⋊C4×C47C22×C411yescharacteristic
176C22⋊C4×C47—21no—
177C22⋊C4×C47—21no—
178C42×C47C2411yescharacteristic
179C22⋊Dic47—21no—
180C22⋊Dic47—21no—
181#10625335—22no—
182#10625335M1614yescomplemented
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185C4⋊Dic47C22×C411yescharacteristic
186C4⋊Dic47C22×C411yescharacteristic
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—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
209Dic188—22no—
210#10625324—22no—
211#10625324—22no—
212C8×D47—22no—
213C8×D47—41no—
214C23×C47—21no—
215C23×C47—21no—
216C22×D47C4×D411yescharacteristic
217D4×C47—21no—
218D4×C47—21no—
219D4×C47—21no—
220D4×C47C2×M1612yes—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47C23×C411yescharacteristic
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C22⋊D47—42no—
231C22⋊D47—42no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—81no—
239C2×Dic47—81no—
240C2×Dic47C4×D411yescharacteristic
241C2×Dic47C4×D411yescharacteristic
242C2×Dic47C4×D411yescharacteristic
243C4×D47—21no—
244C4×D47—21no—
245C4×D47—21no—
246C4×D47—21no—
247C4×D47—41no—
248Dic94—21no—
249Dic94—21no—
250Dic94—21no—
251Dic94C2×M1612yes—
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47#13512yescomplemented
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—41no—
262C47⋊C8—41no—
263C47⋊C8—41no—
264C47⋊C8C2×M1612yes—
265C47⋊C8#13512yescomplemented
266#18037—471nomaximal, Sylow
267C22×C47—22no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47C2×C4×D411yescharacteristic
274C2×D47—21no—
275C2×D47—21no—
276C2×D47—21no—
277C4×C47—21no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47C22×M1611yescharacteristic
281C4×C47#56811yescharacteristic
282C4×C47C2×#13511yescharacteristic
283C4×C47C2×#13511yescharacteristic
284Dic47—22no—
285Dic47—21no—
286Dic47—21no—
287Dic47—21no—
288Dic47—41no—
289Dic47—41no—
290Dic47—41no—
291#2971—471no—
292#2970—471no—
293C4×#135—471no—
294#1590—471no—
295#1590—471no—
296#1584—471no—
297#1584—471no—
298#1581—471no—
299#1581D4711yescharacteristic, complemented
300C8×SD16—471no—
301C8×SD16—471no—
302#1568—471no—
303#1488—471no—
304#1488—471no—
305C8×M16—471no—
306C2×C47—42no—
307C2×C47—81no—
308C2×C47D4×M1611yescharacteristic
309C2×C47C4×#13511yescharacteristic
310C2×C47#295711yescharacteristic
311D47—41no—
312C2×#135—471no—
313C4×#41—471no—
314C4×#41—471no—
315#446—471no—
316#446—471no—
317C8×Q8—471no—
318C8×Q8—471no—
319C4×Q16—471no—
320C4×Q16—471no—
321C4×SD16—471no—
322C4×SD16—471no—
323C4×SD16—471no—
324C4×SD16—471no—
325C4×D8—471no—
326C4×D8C2×D4711yescharacteristic
327#436—471no—
328#436—941no—
329#436—941no—
330#436C2×D4711yescharacteristic
331#435—941no—
332#435—941no—
333C8×D4—471no—
334C8×D4C2×D4711yescharacteristic
335#432—471no—
336#432—471no—
337#432—941no—
338#432—941no—
339#431—471no—
340#427—471no—
341#416—471no—
342#416—471no—
343C4×M16—471no—
344C4×M16—941no—
345C2×#97—941no—
346C2×C4×C8—471no—
347#335—471no—
348#335C2×D4711yescharacteristic
349#334—471no—
350#334—471no—
351Q8⋊C8—471no—
352Q8⋊C8—471no—
353Q8⋊C8—471no—
354Q8⋊C8—471no—
355D4⋊C8—471no—
356D4⋊C8—471no—
357D4⋊C8C2×D4711yescharacteristic
358D4⋊C8C2×D4711yescharacteristic
359#322—471no—
360#322C2×D4711yescharacteristic
361C82—471no—
362C82—471no—
363C47#1803711yescharacteristic, complemented, Sylow
364C2×#41—471no—
365C2×#41—471no—
366#135—944no—
367C2×Q16—471no—
368C2×SD16—471no—
369C2×SD16—471no—
370C2×D8C4×D4711yescharacteristic
371C2×M16—21no—
372C2×M16—471no—
373C2×M16—471no—
374C2×M16—941no—
375C22×C8—21no—
376C22×C8—471no—
377C22×C8—471no—
378C22×C8—941no—
379C4×Q8—471no—
380C4×Q8—471no—
381C4×Q8—471no—
382C4×Q8—471no—
383C4×D4—471no—
384C4×D4—471no—
385C4×D4—941no—
386C4×D4—941no—
387C4×D4—941no—
388C4×D4—941no—
389C4×D4C22×D4711yescharacteristic
390C4×D4C22×D4711yescharacteristic
391#117—471no—
392#117—471no—
393#117—941no—
394#117—941no—
395C2×C42—471no—
396C2×C42—941no—
397C2×C42—941no—
398#107—471no—
399#107C4×D4711yescharacteristic
400#106—471no—
401#106—471no—
402C4⋊C8—471no—
403C4⋊C8—471no—
404C4⋊C8—941no—
405C4⋊C8—941no—
406C4⋊C8—941no—
407C4⋊C8—941no—
408C4⋊C8—941no—
409C4⋊C8C22×D4711yescharacteristic
410C4⋊C8C22×D4711yescharacteristic
411#103—471no—
412#103—471no—
413#103—471no—
414#103—471no—
415#102—471no—
416#102—471no—
417#102C4×D4711yescharacteristic
418#102C4×D4711yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—941no—
422C22⋊C8—941no—
423C22⋊C8—941no—
424C22⋊C8—941no—
425C22⋊C8—941no—
426#97—471no—
427#97—471no—
428#97—941no—
429#97—941no—
430#97—941no—
431#97—941no—
432C4×C8—471no—
433C4×C8—471no—
434C4×C8—471no—
435C4×C8—471no—
436C4×C8—471no—
437C4×C8—941no—
438C4×C8—941no—
439C4×C8C22×D4711yescharacteristic
440C4×C8C22×D4711yescharacteristic
441C4×C8C22×D4711yescharacteristic
442#41—942no—
443#41—942no—
444#41—1881no—
445#41—1881no—
446C2×Q8—471no—
447C2×Q8—471no—
448C2×D4—941no—
449C2×D4—941no—
450C2×D4C2×C4×D4711yescharacteristic
451C2×D4C2×C4×D4711yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—471no—
455C22×C4—471no—
456C22×C4—471no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461Q16—942no—
462SD16—474no—
463SD16—942no—
464D8—22no—
465M16—42no—
466M16—942no—
467M16—942no—
468M16—1882no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—471no—
474C2×C8—471no—
475C2×C8—471no—
476C2×C8—471no—
477C2×C8—942no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—1881no—
482C2×C8—1882no—
483C2×C8C2×C4×D4711yescharacteristic
484C2×C8C2×C4×D4711yescharacteristic
485C2×C8D4×D4711yescharacteristic
486C2×C8D4×D4711yescharacteristic
487C4⋊C4—471no—
488C4⋊C4—471no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4C2×C4×D4711yescharacteristic
494C4⋊C4C2×C4×D4711yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—941no—
498C22⋊C4—941no—
499C22⋊C4—941no—
500C22⋊C4—941no—
501C42—471no—
502C42—471no—
503C42—471no—
504C42—941no—
505C42—941no—
506C42—941no—
507C42—941no—
508C42—941no—
509C42—941no—
510C42C23×D4711yescharacteristic
511C23—21no—
512C23—21no—
513C23—471no—
514Q8—472no—
515Q8—941no—
516Q8—941no—
517Q8—941no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—1882no—
522D4—1882no—
523D4M16×D4712yes—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—471no—
531C2×C4—471no—
532C2×C4—471no—
533C2×C4—941no—
534C2×C4—941no—
535C2×C4—941no—
536C2×C4—941no—
537C2×C4—941no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—3761no—
542C2×C4—3761no—
543C2×C4—1881no—
544C2×C4—1882no—
545C2×C4—1882no—
546C2×C4C22×C4×D4711yescharacteristic
547C2×C4C2×D4×D4711yescharacteristic
548C2×C4#41×D4711yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—472no—
556C8—472no—
557C8—941no—
558C8—941no—
559C8—1881no—
560C8—1881no—
561C8—1881no—
562C8#1309404312yescomplemented
563C22—22no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—941no—
570C22—941no—
571C22—941no—
572C22C4×D4×D4711yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—941no—
577C4—941no—
578C4—942no—
579C4—941no—
580C4—1881no—
581C4—1881no—
582C4—1881no—
583C4C2×M16×D4711yescharacteristic
584C4#1568988811yescharacteristic
585C4#135×D4711yescharacteristic
586C4C2×#1309404311yescharacteristic
587C2—42no—
588C2—81no—
589C2—1881no—
590C2#2025212111yescharacteristic
591C2C4×#1309404311yescharacteristic
592C2#2025230211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1581C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094043C4
cosocleC42×C47C24
hypercenter#1581D47
hypocenterC47#18037
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
1. #20252404C2semidirect
2. #20252396C2semidirect
4. #20242281C2semidirect
5. #20242276C2semidirect
6. #20242240C2semidirect
7. #20242237C2semidirect
8. #20242218C2semidirect
9. #20242191C2semidirect
10. C8×#10625335C2semidirect
11. #20242150C2semidirect
12. #20241819C2semidirect
13. #20241819C2semidirect
14. #20241667C2semidirect
15. C47×#1581C2semidirect
182. #10625335M16semidirect
258. C8×C47#135semidirect
265. C47⋊C8#135semidirect
299. #1581D47semidirect
363. C47#18037semidirect
562. C8#13094043semidirect

Maximal subgroups

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

subgroupindex
#202524042
#202523962
C4×#130940432
#202422812
#202422762
#202422402
#202422372
#202422182
#202421912
C8×#106253352
#202421502
#202418192
#202416672
C47×#15812
#1803747