Finite Group Databasebeta

← #26252337

Subgroups — #26252337

Order 12032.

1378 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
1C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
2C2×#15689403C211yesmaximal, characteristic, complemented
3C4×#13093995C211yesmaximal, characteristic
4#20244714C212yesmaximal, complemented
5#20244522C212yesmaximal, complemented
6#20244341C211yesmaximal, characteristic, complemented
7#20244339C211yesmaximal, characteristic, complemented
8#20243702C212yesmaximal
9#20243574C212yesmaximal, complemented
10#20243365C211yesmaximal, characteristic, complemented
11C2×C47×#474C211yesmaximal, characteristic, complemented
12C22×Q8×D47—21no—
13C2×#13094024C2211yescharacteristic
14C2×#13094023—21no—
15C2×#13094023C2212yes—
16C2×#13094022—21no—
17C4⋊Q8×D47—24no—
18C4⋊Q8×D47—24no—
19C2×#13093995C2211yescharacteristic
20C2×C4×C22⋊D47—21no—
21C2×C4⋊C4×D47—21no—
22C2×C4⋊C4×D47C2212yes—
23C2×C42×D47C2211yescharacteristic
24#15689403—24no—
25C2×#13093957C2212yes—
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×#13093945C2212yes—
28C2×(C2×D47)⋊C8C2212yes—
29#15689026C2211yescharacteristic
30#15689019C2211yescharacteristic
31#15689011—21no—
32#15688999—21no—
33#15688980C2211yescharacteristic
34C4×C4⋊Dic47C2211yescharacteristic
35C4×C22⋊Dic47—21no—
36#15688886C2212yes—
37#15688886C2212yes—
38#15688885C2212yes—
39#15688885C2212yes—
40#15688877C2212yes—
41C2×C4⋊Q8×C47C2211yescharacteristic
42C2×C4×D4×C47C2211yescharacteristic
43C47×#474—24no—
44C2×#107×C47C2212yes—
45C2×C4⋊C8×C47C2211yescharacteristic
46C2×#102×C47C2212yes—
47C22×Dic94—21no—
48C22×Dic94—22no—
49C2×Q8×D47—28no—
50C2×Q8×D47—44no—
51C2×Q8×D47—44no—
52C22×C22⋊D47—21no—
53C22×C4×D47—22no—
54C22×C4×D47D411yescharacteristic
55C22×C4×D47D411yescharacteristic
56C22×C4×D47C2311yescharacteristic
57C22×C47⋊C8C2312yes—
58#13094024—22no—
59#13094024D414yescomplemented
60#13094023—28no—
61#13094023—24no—
62#13094023—24no—
63#13094022—28no—
64#13093995—22no—
65#13093995Q814yescomplemented
66C4×C22⋊D47—44no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2312yes—
70C2×C4⋊Dic47C2311yescharacteristic
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—21no—
74C4⋊C4×D47—28no—
75C4⋊C4×D47—24no—
76C4⋊C4×D47—24no—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47D411yescharacteristic
83C2×C4×Dic47D411yescharacteristic
84C2×C4×Dic47C2311yescharacteristic
85C42×D47—22no—
86C42×D47—22no—
87#13093957—24no—
88C4⋊(C47⋊C8)—22no—
89#13093945—24no—
90(C2×D47)⋊C8—24no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C22×Q8×C47—21no—
95C22×D4×C47C2311yescharacteristic
96C23×C4×C47—21no—
97C22×C8×C47C2312yes—
98C4⋊Q8×C47—22no—
99C4⋊Q8×C47D414yescomplemented
100C4×D4×C47—22no—
101C4×D4×C47—22no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2312yes—
105C2×C22⋊C4×C47—21no—
106C2×C42×C47C2311yescharacteristic
107#107×C47—24no—
108C4⋊C8×C47—22no—
109#102×C47—24no—
110C24×C47—21no—
111C23×D47C2×D411yescharacteristic
112C2×Q8×C47—24no—
113C2×Q8×C47—42no—
114C2×Q8×C47—42no—
115C2×D4×C47—21no—
116C2×D4×C47—21no—
117C2×D4×C47—21no—
118C2×D4×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47C2×Q812yescomplemented
121C22×C4×C47—22no—
122C22×C4×C47—21no—
123C22×C4×C47—42no—
124C22×C4×C47—42no—
125C22×C4×C47—42no—
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2411yescharacteristic
129C2×C22⋊D47—24no—
130C2×C22⋊D47—42no—
131C2×C22⋊D47—42no—
132C22×Dic47—21no—
133C22×Dic47—22no—
134C22×Dic47—21no—
135C22×Dic47C2×D411yescharacteristic
136C22×Dic47C2×D411yescharacteristic
137C22×Dic47C2×D411yescharacteristic
138Q8×D47—432no—
139C2×C4×D47—22no—
140C2×C4×D47—22no—
141C2×C4×D47—22no—
142C2×C4×D47—22no—
143C2×C4×D47—21no—
144C2×C4×D47—21no—
145C2×C4×D47—21no—
146C2×C4×D47—21no—
147C2×C4×D47—22no—
148C2×C4×D47—28no—
149C2×C4×D47—44no—
150C2×C4×D47—44no—
151C2×C4×D47D814yes—
152C2×C4×D47C2×Q812yes—
153C2×C4×D47#4112yes—
154C2×Dic94—28no—
155C2×Dic94—24no—
156C2×Dic94—44no—
157C2×Dic94—42no—
158C2×Dic94—42no—
159C2×Dic94—44no—
160C2×C8×C47—22no—
161C2×C8×C47—22no—
162C2×C8×C47—22no—
163C4⋊C4×C47—24no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47C2×D414yes—
168C22⋊C4×C47—42no—
169C42×C47C2×D412yes—
170C42×C47C2×D412yes—
171C22⋊Dic47—24no—
172C22⋊Dic47—42no—
173C22⋊Dic47—42no—
174(C2×D47)⋊C4—42no—
175C4⋊Dic47—24no—
176C4⋊Dic47—22no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47C2×D414yes—
181C4⋊Dic47C2×Q812yescomplemented
182Dic47⋊C4—28no—
183Dic47⋊C4—28no—
184Dic47⋊C4—42no—
185C4×Dic47—22no—
186C4×Dic47—22no—
187C4×Dic47—21no—
188C4×Dic47—21no—
189C4×Dic47—42no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C23×C47—22no—
194C23×C47—41no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47C22×D411yescharacteristic
201C22×D47—21no—
202C22×D47—21no—
203C22×D47—21no—
204C22×D47—21no—
205C22×D47C22⋊Q812yes—
206C22×D47C2×D812yes—
207C22×D47#13712yes—
208Q8×C47—48no—
209D4×C47—22no—
210D4×C47—22no—
211D4×C47—41no—
212D4×C47—41no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—24no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—84no—
222C2×C4×C47#12012yes—
223C2×C4×C47#12012yes—
224C2×C4×C47C2×D812yes—
225C2×C4×C47AGL(1,ℤ/8)12yes—
226C2×C4×C47C22×D411yescharacteristic
227C2×C4×C47C22×D411yescharacteristic
228C2×C4×C47C22×Q811yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C2×C4×C472−1+411yescharacteristic
231C2×C4×C472−1+411yescharacteristic
232C22⋊D47—48no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—24no—
240C2×Dic47—22no—
241C2×Dic47—41no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47C22⋊Q812yes—
249C2×Dic47C2×D812yes—
250C2×Dic47#13712yes—
251C4×D47—28no—
252C4×D47—22no—
253C4×D47—22no—
254C4×D47—22no—
255C4×D47—22no—
256C4×D47—28no—
257C4×D47—416no—
258Dic94—416no—
259Dic94—48no—
260C8×C47—42no—
261C47⋊C8—42no—
262#24298—471nomaximal, Sylow
263C22×C47—42no—
264C22×C47—42no—
265C22×C47—42no—
266C22×C47—81no—
267C22×C47—81no—
268C22×C47—81no—
269C22×C47—81no—
270C22×C47C2×#12011yescharacteristic
271C22×C47C2×C22⋊Q811yescharacteristic
272C22×C47#53611yescharacteristic
273C22×C47C22×D811yescharacteristic
274C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C47C2×#13711yescharacteristic
276C22×C47C2×#13711yescharacteristic
277C2×D47—22no—
278C2×D47—22no—
279C2×D47—22no—
280C2×D47—22no—
281C2×D47—22no—
282C2×D47—22no—
283C2×D47#47414yescomplemented
284C4×C47—22no—
285C4×C47—44no—
286C4×C47—81no—
287C4×C47#44714yes—
288C4×C47#54811yescharacteristic
289C4×C47#54811yescharacteristic
290C4×C47D4×Q811yescharacteristic
291C4×C47D4×Q811yescharacteristic
292Dic47—22no—
293Dic47—22no—
294Dic47—22no—
295Dic47—44no—
296Dic47—42no—
297Dic47—81no—
298C22×C4⋊Q8—471no—
299C2×#474—471no—
300C2×#474D4711yescharacteristic, complemented
301C4×#121—471no—
302#2057—472no—
303#2023—472no—
304#1988—471no—
305#1988—471no—
306#1874—472no—
307#1852—472no—
308#1797—471no—
309C2×C47—82no—
310C2×C47#240911yescharacteristic
311C2×C47C2×#44711yescharacteristic
312C2×C47#300411yescharacteristic
313C2×C47C2×#47411yescharacteristic
314C2×C47#307911yescharacteristic
315C2×C47#322611yescharacteristic
316C2×C47#323911yescharacteristic
317D47—24no—
318C23×Q8—941no—
319C2×C4⋊Q8—472no—
320C2×C4⋊Q8—471no—
321C2×C4⋊Q8—941no—
322C2×C4⋊Q8—941no—
323C2×C4⋊Q8—944no—
324C2×C4⋊Q8—944no—
325C2×C4⋊Q8C2×D4711yescharacteristic
326C2×#121—471no—
327C2×C4×D4—941no—
328C2×C4×D4C2×D4711yescharacteristic
329C22×C4⋊C4—472no—
330C22×C4⋊C4—941no—
331C22×C42—471no—
332#474—24no—
333#474—944no—
334C2×#107—472no—
335C2×#107C2×D4712yes—
336C2×C4⋊C8—471no—
337C2×C4⋊C8C2×D4711yescharacteristic
338C2×#102—472no—
339C2×#102C2×D4712yes—
340C2×C22⋊C8—472no—
341#390—471no—
342#389—471no—
343#388—941no—
344#386—941no—
345#380—471no—
346C4×C4⋊C4—471no—
347C4×C22⋊C4—941no—
348#340—472no—
349#340—472no—
350#340—472no—
351#340—472no—
352#336—472no—
353C47#2429811yescharacteristic, complemented, Sylow
354C22×Q8—21no—
355C22×Q8—942no—
356C22×Q8—948no—
357C22×Q8—941no—
358C22×Q8—1884no—
359C22×Q8—1884no—
360C22×D4—941no—
361C22×D4C22×D4711yescharacteristic
362C23×C4—21no—
363C23×C4—471no—
364C23×C4—471no—
365C23×C4—471no—
366C23×C4—942no—
367C22×C8—472no—
368C22×C8C22×D4712yes—
369C4⋊Q8—22no—
370C4⋊Q8—474no—
371C4⋊Q8—944no—
372C4⋊Q8—948no—
373C4⋊Q8—948no—
374C4⋊Q8—944no—
375C4⋊Q8—942no—
376C4⋊Q8C22⋊D4714yescomplemented
377#121—474no—
378#121—942no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—1884no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—472no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—944no—
387C2×C4⋊C4—948no—
388C2×C4⋊C4—942no—
389C2×C4⋊C4—942no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—944no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4C22×D4711yescharacteristic
394C2×C4⋊C4C22×D4712yes—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—941no—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C42—471no—
401C2×C42—471no—
402C2×C42—471no—
403C2×C42—942no—
404C2×C42—942no—
405C2×C42—941no—
406C2×C42C22×D4711yescharacteristic
407#107—24no—
408#107—944no—
409C4⋊C8—22no—
410C4⋊C8—942no—
411#102—24no—
412#102—944no—
413C22⋊C8—944no—
414#95—941no—
415#95—941no—
416#95—941no—
417C24—21no—
418C24—471no—
419C2×Q8—24no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8—948no—
423C2×Q8—944no—
424C2×Q8—1884no—
425C2×Q8—1884no—
426C2×Q8—18832no—
427C2×Q8—1882no—
428C2×Q8—1882no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—944no—
435C2×D4—1882no—
436C2×D4—1882no—
437C2×D4Q8×D4712yescomplemented
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—474no—
447C22×C4—472no—
448C22×C4—472no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—948no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—942no—
461C22×C4—941no—
462C22×C4—1884no—
463C22×C4—1884no—
464C22×C4D4×D4711yescharacteristic
465C22×C4D4×D4711yescharacteristic
466C22×C4C23×D4711yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—942no—
471C2×C8—942no—
472C2×C8—942no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—474no—
478C4⋊C4—472no—
479C4⋊C4—948no—
480C4⋊C4—948no—
481C4⋊C4—944no—
482C4⋊C4—942no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—1882no—
487C4⋊C4C2×C22⋊D4714yes—
488C22⋊C4—42no—
489C22⋊C4—944no—
490C22⋊C4—1882no—
491C22⋊C4—1882no—
492C22⋊C4—1882no—
493C42—942no—
494C42—942no—
495C42—941no—
496C42—941no—
497C42—1882no—
498C42D4×D4712yes—
499C42C2×C22⋊D4712yes—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—472no—
508C23—472no—
509C23—472no—
510C23—941no—
511C23—941no—
512C23—941no—
513C23—941no—
514C23C2×D4×D4711yescharacteristic
515Q8—48no—
516Q8—18816no—
517Q8—1888no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522D4—1888no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—84no—
532C2×C4—472no—
533C2×C4—472no—
534C2×C4—472no—
535C2×C4—948no—
536C2×C4—941no—
537C2×C4—941no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—948no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—944no—
548C2×C4—942no—
549C2×C4—18816no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1881no—
557C2×C4#1309399212yes—
558C2×C4#1309399212yes—
559C2×C4D8×D4712yes—
560C2×C4#1309404812yes—
561C2×C4C2×D4×D4711yescharacteristic
562C2×C4C22×C22⋊D4711yescharacteristic
563C2×C4C2×Q8×D4711yescharacteristic
564C2×C4#41×D4711yescharacteristic
565C2×C4#1309407111yescharacteristic
566C2×C4#1309407211yescharacteristic
567C8—42no—
568C8—1882no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—474no—
577C22—942no—
578C22—942no—
579C22—942no—
580C22—942no—
581C22—942no—
582C22—942no—
583C22C2×#1309399211yescharacteristic
584C22C22⋊Q8×D4711yescharacteristic
585C22#1568969611yescharacteristic
586C22C2×D8×D4711yescharacteristic
587C22C2×#1309404811yescharacteristic
588C22#137×D4711yescharacteristic
589C22#137×D4711yescharacteristic
590C4—22no—
591C4—44no—
592C4—81no—
593C4—942no—
594C4—942no—
595C4—942no—
596C4—3761no—
597C4—1884no—
598C4—1882no—
599C4#1568925514yes—
600C4#1568978011yescharacteristic
601C4#1568978311yescharacteristic
602C4#1568978611yescharacteristic
603C4Q8×C22⋊D4711yescharacteristic
604C2—82no—
605C2—944no—
606C2#2024674911yescharacteristic
607C2C2×#1568925511yescharacteristic
608C2#2025262011yescharacteristic
609C2#474×D4711yescharacteristic
610C2#2025319611yescharacteristic
611C2#2025450811yescharacteristic
612C2#2025461711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#474C2
socleC23×C47C22×D4
prime radicalC2×#13093995C22
hypercenterC2×#474D47
hypocenterC47#24298
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D47C2semidirect
2. C2×#15689403C2semidirect
4. #20244714C2semidirect
5. #20244522C2semidirect
6. #20244341C2semidirect
7. #20244339C2semidirect
9. #20243574C2semidirect
10. #20243365C2semidirect
11. C2×C47×#474C2semidirect
59. #13094024D4semidirect
65. #13093995Q8semidirect
99. C4⋊Q8×C47D4semidirect
120. C2×D4×C47C2×Q8semidirect
181. C4⋊Dic47C2×Q8semidirect
283. C2×D47#474semidirect
300. C2×#474D47semidirect
353. C47#24298semidirect
376. C4⋊Q8C22⋊D47semidirect
437. C2×D4Q8×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D472
C2×#156894032
C4×#130939952
#202447142
#202445222
#202443412
#202443392
#202437022
#202435742
#202433652
C2×C47×#4742
#2429847