Finite Group Databasebeta

← #26185980

Subgroups — #26185980

Order 12032.

660 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#20252503C211yesmaximal, characteristic, complemented
2#20252495C211yesmaximal, characteristic, complemented
3C4×#13094043C211yesmaximal, characteristic
4#20242269C211yesmaximal, characteristic, complemented
5#20242264C211yesmaximal, characteristic, complemented
6#20242245C211yesmaximal, characteristic, complemented
7#20242242C211yesmaximal, characteristic, complemented
8#20242240C211yesmaximal, characteristic, complemented
9#20242237C211yesmaximal, characteristic, complemented
10#20242218C211yesmaximal, characteristic, complemented
11#335×D47C211yesmaximal, characteristic, complemented
12#20241772C211yesmaximal, characteristic, complemented
13#20241772C211yesmaximal, characteristic, complemented
14#20241679C211yesmaximal, 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#15689197—21no—
32#15689192—21no—
33D4×C47⋊C8C2211yescharacteristic
34C8×C22⋊D47—21no—
35(C22⋊D47)⋊C8—21no—
36#15689177—21no—
37#15689174C2211yescharacteristic
38#15689174C2211yescharacteristic
39#15689173—21no—
40#15689160C411yescharacteristic
41#15689146—21no—
42C2×Dic47⋊C8—21no—
43C4⋊C8×D47C2211yescharacteristic
44C4⋊C8×D47C2211yescharacteristic
45#15689116C411yescharacteristic
46#15689116C411yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688875C2211yescharacteristic
51#15688855C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688853C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56D4⋊(C47⋊C8)C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688845C2211yescharacteristic
59#15688844C2211yescharacteristic
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—
74C22×C47⋊C8—21no—
75C2×C8×D47—21no—
76C2×C8×D47—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—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8D411yescharacteristic
109Dic47⋊C8D411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093949C2×C411yescharacteristic
112#13093947C2×C411yescharacteristic
113#13093947C2×C411yescharacteristic
114#13093945C2×C411yescharacteristic
115#13093945C2×C411yescharacteristic
116C22⋊(C47⋊C8)—21no—
117C22⋊(C47⋊C8)—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8D411yescharacteristic
120(C2×D47)⋊C8D411yescharacteristic
121#13093934—21no—
122#13093934—21no—
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—22no—
158#10625352M1614yescomplemented
159C2×C4×D47C22×C411yescharacteristic
160C2×C4×D47C2×D411yescharacteristic
161C2×C4×D47#4111yescharacteristic
162C2×Dic94C22×C411yescharacteristic
163C2×Dic94C22×C411yescharacteristic
164D8×C47—22no—
165M16×C47—81no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—81no—
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#10625335—22no—
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—81no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—81no—
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209Dic188—22no—
210C8×D47—22no—
211C8×D47—22no—
212C8×D47—81no—
213C8×D47—81no—
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—24no—
231C22⋊D47—42no—
232C2×Dic47—21no—
233C2×Dic47—24no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
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—41no—
246C4×D47C2×M1612yes—
247C4×D47#13112yes—
248Dic94—21no—
249Dic94—21no—
250Dic94—21no—
251Dic94C2×M1612yes—
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47—41no—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—41no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266#17881—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#43512yes—
277C4×C47—21no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47C22×M1611yescharacteristic
281C4×C47C2×#13111yescharacteristic
282C4×C47#57611yescharacteristic
283C4×C47#57811yescharacteristic
284Dic47—22no—
285Dic47—21no—
286Dic47—21no—
287Dic47—41no—
288Dic47—41no—
289Dic47—41no—
290Dic47#43512yes—
291#2989—471no—
292#2988—471no—
293C4×#135—471no—
294#1588—471no—
295#1588—471no—
296#1585—471no—
297#1585—471no—
298#1584—471no—
299#1584—471no—
300#1581—471no—
301#1581D4711yescharacteristic, complemented
302C2×#335—471no—
303#1477—471no—
304#1477—471no—
305#1452—471no—
306C2×C47—42no—
307C2×C47—81no—
308C2×C47C2×#43511yescharacteristic
309C2×C47#295111yescharacteristic
310C2×C47#295711yescharacteristic
311D47—22no—
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#436C2×D4711yescharacteristic
329#435—941no—
330#435—941no—
331C8×D4—471no—
332C8×D4—941no—
333C8×D4—941no—
334C8×D4C2×D4711yescharacteristic
335#432—941no—
336#431—471no—
337#431—471no—
338#431—941no—
339#427—471no—
340#423—941no—
341C2×C4⋊C8—471no—
342C2×C4⋊C8—471no—
343C2×C4⋊C8—941no—
344#416—471no—
345#416—471no—
346C2×C4×C8—471no—
347#335—471no—
348#335—471no—
349#335—471no—
350#335C2×D4711yescharacteristic
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#322—471no—
361#322—471no—
362#322C2×D4711yescharacteristic
363C47#1788111yescharacteristic, 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—941no—
373C22×C8—21no—
374C22×C8—471no—
375C22×C8—471no—
376C22×C8—941no—
377C22×C8—941no—
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—471no—
405C4⋊C8—471no—
406C4⋊C8—941no—
407C4⋊C8—941no—
408C4⋊C8—941no—
409C4⋊C8—941no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8C22×D4711yescharacteristic
414C4⋊C8C22×D4711yescharacteristic
415#103—471no—
416#103—471no—
417#103—471no—
418#103—471no—
419#102—471no—
420#102—471no—
421#102C4×D4711yescharacteristic
422#102C4×D4711yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—471no—
426C22⋊C8—471no—
427C22⋊C8—941no—
428C22⋊C8—941no—
429C22⋊C8—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—474no—
443#41—942no—
444#41—942no—
445#41—942no—
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—942no—
463SD16—942no—
464D8—22no—
465M16—81no—
466M16—3761no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—471no—
472C2×C8—471no—
473C2×C8—471no—
474C2×C8—471no—
475C2×C8—942no—
476C2×C8—942no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—3761no—
481C2×C8—3761no—
482C2×C8—3761no—
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—944no—
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—472no—
532C2×C4—472no—
533C2×C4—471no—
534C2×C4—471no—
535C2×C4—944no—
536C2×C4—941no—
537C2×C4—941no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—3761no—
543C2×C4—3761no—
544C2×C4—1881no—
545C2×C4—1882no—
546C2×C4C22×C4×D4711yescharacteristic
547C2×C4C2×D4×D4711yescharacteristic
548C2×C4#41×D4711yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—941no—
557C8—941no—
558C8—941no—
559C8—941no—
560C8—1881no—
561C8—1881no—
562C8—1881no—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—472no—
570C22—941no—
571C22—941no—
572C22C4×D4×D4711yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—472no—
577C4—941no—
578C4—941no—
579C4—942no—
580C4—1881no—
581C4—1881no—
582C4—1881no—
583C4C2×M16×D4711yescharacteristic
584C4#131×D4711yescharacteristic
585C4#1568992411yescharacteristic
586C4#1568993711yescharacteristic
587C2—42no—
588C2—81no—
589C2—942no—
590C2#435×D4711yescharacteristic
591C2#2025225811yescharacteristic
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#17881
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. #20252503C2semidirect
2. #20252495C2semidirect
4. #20242269C2semidirect
5. #20242264C2semidirect
6. #20242245C2semidirect
7. #20242242C2semidirect
8. #20242240C2semidirect
9. #20242237C2semidirect
10. #20242218C2semidirect
11. #335×D47C2semidirect
12. #20241772C2semidirect
13. #20241772C2semidirect
14. #20241679C2semidirect
15. C47×#1581C2semidirect
158. #10625352M16semidirect
301. #1581D47semidirect
363. C47#17881semidirect

Maximal subgroups

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

subgroupindex
#202525032
#202524952
C4×#130940432
#202422692
#202422642
#202422452
#202422422
#202422402
#202422372
#202422182
#335×D472
#202417722
#202416792
C47×#15812
#1788147