Finite Group Databasebeta

← #26215745

Subgroups — #26215745

Order 12032.

1514 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625352C211yesmaximal, characteristic
2C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
3C2×#15689116C212yesmaximal
4#20245793C211yesmaximal, characteristic, complemented
5#20243402C212yesmaximal, complemented
6#20243396C212yesmaximal, complemented
7#20243394C211yesmaximal, characteristic, complemented
8#20243390C211yesmaximal, characteristic, complemented
9#20243388C211yesmaximal, characteristic, complemented
10#20243103C212yesmaximal, complemented
11C47×#1802C211yesmaximal, characteristic, complemented
12C22×#10625352C2211yescharacteristic
13C22×C8×D47C2212yes—
14C4×#10625352—24no—
15C4×#10625352C418yescomplemented
16C2×C4×Dic94C2211yescharacteristic
17C2×#13093989C2211yescharacteristic
18C2×D4×Dic47C2211yescharacteristic
19C2×C4×C22⋊D47—21no—
20C2×(C22⋊D47)⋊C4—21no—
21C2×#13093982C2212yes—
22C2×#13093982C2211yescharacteristic
23C2×#13093980—21no—
24C22×C4×Dic47—21no—
25C2×C42×D47C2211yescharacteristic
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×Dic47⋊C8C2212yes—
28C4⋊C8×D47—24no—
29#15689116—28no—
30C2×#13093949C2212yes—
31C2×#13093947C2212yes—
32C2×#13093945C2212yes—
33#15688993C2211yescharacteristic
34#15688988C2212yes—
35#15688980—21no—
36#15688980—21no—
37C4⋊C4×Dic47—21no—
38C4⋊C4×Dic47—21no—
39#15688886C2212yes—
40#15688885C2212yes—
41#15688885C2212yes—
42C2×C4×D4×C47C2211yescharacteristic
43C2×C4⋊C8×C47C2211yescharacteristic
44C2×#102×C47C2212yes—
45C47×#384C2211yescharacteristic
46C47×#340C2212yes—
47C2×#10625352—22no—
48C2×#10625352—22no—
49C2×#10625352—22no—
50C2×#10625352C2×C414yes—
51C2×#10625352D414yes—
52C2×#10625352Q814yes—
53C22×Dic94C2311yescharacteristic
54C22×C22⋊D47—21no—
55C23×Dic47—21no—
56C23×Dic47—21no—
57C22×C4×D47D411yescharacteristic
58C22×C4×D47D411yescharacteristic
59C22×C4×D47C2311yescharacteristic
60C22×C47⋊C8C2312yes—
61C2×C8×D47—24no—
62C2×C8×D47—24no—
63C2×C8×D47—24no—
64C4×Dic94—22no—
65C4×Dic94C2×C414yes—
66#13093989—22no—
67#13093989C2×C414yes—
68D4×Dic47—22no—
69D4×Dic47C2×C414yes—
70C4×C22⋊D47—28no—
71(C22⋊D47)⋊C4—28no—
72#13093982—22no—
73#13093982—24no—
74#13093982—24no—
75#13093982C2×C414yes—
76#13093980—28no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47C2312yes—
80C2×C4⋊Dic47C2311yescharacteristic
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×C22⋊Dic47—21no—
84C2×(C2×D47)⋊C4—21no—
85C2×(C2×D47)⋊C4—22no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47—28no—
90C2×C4×Dic47—22no—
91C2×C4×Dic47D411yescharacteristic
92C2×C4×Dic47D411yescharacteristic
93C2×C4×Dic47C2311yescharacteristic
94C42×D47C2×C414yes—
95C42×D47D414yes—
96C4⋊(C47⋊C8)—22no—
97Dic47⋊C8—24no—
98#13093949—24no—
99#13093947—24no—
100#13093945—24no—
101C47⋊#95—22no—
102C47⋊#95—22no—
103C22×D4×C47C2311yescharacteristic
104C23×C4×C47—21no—
105C22×C8×C47C2312yes—
106C4×D4×C47—22no—
107C4×D4×C47C2×C414yes—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47C2312yes—
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C42×C47C2311yescharacteristic
114C4⋊C8×C47—22no—
115#102×C47—24no—
116C24×C47—21no—
117C23×D47C2×D411yescharacteristic
118C2×D4×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47C22×C412yes—
122C2×D4×C47C2×D412yes—
123C2×D4×C47C2×Q812yes—
124C22×C4×C47—21no—
125C22×C4×C47—24no—
126C22×C4×C47—22no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2411yescharacteristic
132C2×C22⋊D47—24no—
133C2×C22⋊D47—24no—
134C2×C22⋊D47—24no—
135C22×Dic47—21no—
136C22×Dic47—24no—
137C22×Dic47—24no—
138C22×Dic47—24no—
139C22×Dic47—21no—
140C22×Dic47—24no—
141C22×Dic47—22no—
142C22×Dic47—42no—
143C22×Dic47—42no—
144C22×Dic47C2×D411yescharacteristic
145C22×Dic47C2×D411yescharacteristic
146C22×Dic47C2×D411yescharacteristic
147#10625352—28no—
148#10625352—28no—
149#10625352—28no—
150#10625352C4⋊C4116yescomplemented
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—41no—
154C2×C4×D47—41no—
155C2×C4×D47C22⋊C414yes—
156C2×C4×D47C22⋊C414yes—
157C2×C4×D47C22×C412yes—
158C2×C4×D47C2×D412yes—
159C2×C4×D47C2×D412yes—
160C2×C4×D47C2×Q812yes—
161C2×C4×D47#4112yes—
162C2×C4×D47#4112yes—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94C22×C412yes—
167C2×Dic94C2×D412yes—
168C2×Dic94C2×Q812yes—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47—22no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—42no—
176C4⋊C4×C47—42no—
177C4⋊C4×C47C22×C412yes—
178C22⋊C4×C47—24no—
179C42×C47C22×C412yes—
180C42×C47C2×D412yes—
181C22⋊Dic47—24no—
182(C2×D47)⋊C4—24no—
183(C2×D47)⋊C4—44no—
184C4⋊Dic47—21no—
185C4⋊Dic47—22no—
186C4⋊Dic47—22no—
187C4⋊Dic47—42no—
188C4⋊Dic47—42no—
189C4⋊Dic47C22×C412yes—
190Dic47⋊C4—24no—
191Dic47⋊C4—24no—
192C4×Dic47—24no—
193C4×Dic47—24no—
194C4×Dic47—24no—
195C4×Dic47—44no—
196C4×Dic47C22⋊C414yes—
197C4×Dic47C22⋊C414yes—
198C4×Dic47C22×C412yes—
199C4×Dic47C2×D412yes—
200C2×C47⋊C8—22no—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—22no—
203C8×D47—48no—
204C23×C47—22no—
205C23×C47—22no—
206C23×C47—22no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47C22×D411yescharacteristic
212C22×D47—21no—
213C22×D47—21no—
214C22×D47—21no—
215C22×D47—21no—
216C22×D47C2×C22⋊C412yes—
217C22×D47#12112yes—
218C22×D47C22⋊Q812yes—
219D4×C47—22no—
220D4×C47—22no—
221D4×C47—22no—
222D4×C47C2×C4⋊C414yes—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—22no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—48no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47C2×C22⋊C412yes—
233C2×C4×C47C2×C22⋊C412yes—
234C2×C4×C47#13512yes—
235C2×C4×C47#13512yes—
236C2×C4×C47C23×C411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C22×Q811yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C22⋊D47—216no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—216no—
251C2×Dic47—22no—
252C2×Dic47—48no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47C2×C22⋊C412yes—
259C2×Dic47C2×C22⋊C412yes—
260C2×Dic47C2×C22⋊C412yes—
261C2×Dic47#12112yes—
262C2×Dic47C22⋊Q812yes—
263C4×D47—28no—
264C4×D47—44no—
265C4×D47C2×C4⋊C414yes—
266C4×D47#11714yes—
267C4×D47#12114yes—
268C4×D47C22⋊Q814yes—
269Dic94—22no—
270Dic94—22no—
271Dic94—22no—
272Dic94C2×C4⋊C414yes—
273C8×C47—42no—
274C47⋊C8—42no—
275#20645—471nomaximal, Sylow
276C22×C47—24no—
277C22×C47—42no—
278C22×C47—42no—
279C22×C47—42no—
280C22×C47—42no—
281C22×C47—42no—
282C22×C47—42no—
283C22×C47C22×C22⋊C411yescharacteristic
284C22×C47C2×#12111yescharacteristic
285C22×C47C2×C22⋊Q811yescharacteristic
286C22×C47C2×#13511yescharacteristic
287C22×C47C2×#13511yescharacteristic
288C22×C47#57511yescharacteristic
289C22×C47#57511yescharacteristic
290C2×D47—22no—
291C2×D47—22no—
292C2×D47—22no—
293C2×D47—22no—
294C2×D47—22no—
295C2×D47—22no—
296C2×D47#38014yes—
297C4×C47—22no—
298C4×C47—42no—
299C4×C47—82no—
300C4×C47#41614yescomplemented
301C4×C47C22×C4⋊C411yescharacteristic
302C4×C47C2×#11711yescharacteristic
303C4×C47C2×#12111yescharacteristic
304C4×C47C2×C22⋊Q811yescharacteristic
305Dic47—22no—
306Dic47—22no—
307Dic47—24no—
308Dic47—42no—
309Dic47—82no—
310Dic47#38014yes—
311C2×C4×#41—471no—
312C22×C4⋊C8—471no—
313C2×#416—472no—
314#2285—471no—
315#1805—472no—
316#1804—472no—
317#1803—471no—
318#1803—471no—
319#1802—471no—
320#1802D4711yescharacteristic, complemented
321#1735—472no—
322C2×C47—44no—
323C2×C47C2×#38011yescharacteristic
324C2×C47C2×#41611yescharacteristic
325C2×C47#289611yescharacteristic
326C2×C47#303511yescharacteristic
327C2×C47#303511yescharacteristic
328C2×C47#307611yescharacteristic
329C2×C47#307611yescharacteristic
330D47—24no—
331C22×#41—471no—
332C23×C8—472no—
333C4×#41—478no—
334C4×#41—944no—
335C2×C4×Q8—471no—
336C2×C4×Q8—471no—
337C2×C4×D4—471no—
338C2×C4×D4—941no—
339C2×C4×D4—941no—
340C2×C4×D4C2×D4711yescharacteristic
341C2×#117—471no—
342C2×#117—472no—
343C2×#117—941no—
344C22×C42—471no—
345C22×C42—941no—
346C2×C4⋊C8—472no—
347C2×C4⋊C8—471no—
348C2×C4⋊C8—944no—
349C2×C4⋊C8C2×D4711yescharacteristic
350#416—948no—
351C2×#103—472no—
352C2×#103—472no—
353C2×#102—472no—
354C2×#102C2×D4712yes—
355#384—471no—
356#384C2×D4711yescharacteristic
357#382—472no—
358#380—941no—
359#380—941no—
360C4×C4⋊C4—941no—
361C4×C4⋊C4—941no—
362#340—472no—
363#340—472no—
364#340—472no—
365#340C2×D4712yes—
366C47#2064511yescharacteristic, complemented, Sylow
367C2×#41—474no—
368C2×#41—474no—
369C2×#41—474no—
370C2×#41—942no—
371C2×#41—942no—
372C2×#41—942no—
373C22×Q8—471no—
374C22×D4—941no—
375C22×D4C22×D4711yescharacteristic
376C23×C4—21no—
377C23×C4—471no—
378C23×C4—471no—
379C23×C4—471no—
380C23×C4—941no—
381C23×C4—941no—
382C22×C8—472no—
383C22×C8—944no—
384C22×C8—944no—
385C22×C8—944no—
386C22×C8C22×D4712yes—
387C4×Q8—474no—
388C4×Q8—474no—
389C4×Q8—942no—
390C4×Q8—942no—
391C4×D4—22no—
392C4×D4—474no—
393C4×D4—942no—
394C4×D4—948no—
395C4×D4—948no—
396C4×D4C4×D4714yes—
397#117—474no—
398#117—948no—
399#117—942no—
400#117—944no—
401#117—944no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—471no—
405C2×C4⋊C4—472no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4—941no—
408C2×C4⋊C4—941no—
409C2×C4⋊C4—941no—
410C2×C4⋊C4C22×D4712yes—
411C2×C4⋊C4C22×D4711yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—941no—
414C2×C22⋊C4—941no—
415C2×C22⋊C4—942no—
416C2×C42—471no—
417C2×C42—471no—
418C2×C42—471no—
419C2×C42—474no—
420C2×C42—474no—
421C2×C42—948no—
422C2×C42—941no—
423C2×C42—941no—
424C2×C42—941no—
425C2×C42—942no—
426C2×C42C22×D4711yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—944no—
429C4⋊C8—942no—
430#103—944no—
431#103—944no—
432#102—24no—
433#102—944no—
434#95—942no—
435#95—942no—
436C24—21no—
437C24—471no—
438#41—4716no—
439#41—948no—
440#41—948no—
441#41—948no—
442C2×Q8—472no—
443C2×Q8—472no—
444C2×Q8—472no—
445C2×Q8—941no—
446C2×Q8—941no—
447C2×Q8—941no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—944no—
452C2×D4—944no—
453C2×D4—944no—
454C2×D4C2×C4×D4712yes—
455C2×D4D4×D4712yes—
456C2×D4Q8×D4712yes—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—471no—
463C22×C4—472no—
464C22×C4—472no—
465C22×C4—472no—
466C22×C4—472no—
467C22×C4—472no—
468C22×C4—472no—
469C22×C4—471no—
470C22×C4—471no—
471C22×C4—474no—
472C22×C4—474no—
473C22×C4—944no—
474C22×C4—944no—
475C22×C4—944no—
476C22×C4—944no—
477C22×C4—941no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—941no—
481C22×C4—942no—
482C22×C4—1881no—
483C22×C4—1881no—
484C22×C4—1882no—
485C22×C4—1882no—
486C22×C4D4×D4711yescharacteristic
487C22×C4D4×D4711yescharacteristic
488C22×C4C23×D4711yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—942no—
493C2×C8—942no—
494C2×C8—942no—
495C2×C8—1888no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—472no—
502C4⋊C4—944no—
503C4⋊C4—944no—
504C4⋊C4—941no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—1882no—
508C4⋊C4—1882no—
509C4⋊C4C2×C4×D4712yes—
510C22⋊C4—24no—
511C22⋊C4—944no—
512C22⋊C4—944no—
513C22⋊C4—1884no—
514C42—474no—
515C42—474no—
516C42—472no—
517C42—472no—
518C42—944no—
519C42—944no—
520C42—944no—
521C42—1884no—
522C42C2×C4×D4712yes—
523C42D4×D4712yes—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—472no—
532C23—472no—
533C23—472no—
534C23—941no—
535C23—941no—
536C23—941no—
537C23—941no—
538C23C2×D4×D4711yescharacteristic
539Q8—474no—
540Q8—942no—
541Q8—942no—
542Q8—942no—
543D4—22no—
544D4—22no—
545D4—22no—
546D4—9416no—
547D4C4⋊C4×D4714yes—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—48no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—472no—
558C2×C4—472no—
559C2×C4—472no—
560C2×C4—474no—
561C2×C4—474no—
562C2×C4—474no—
563C2×C4—474no—
564C2×C4—472no—
565C2×C4—472no—
566C2×C4—9416no—
567C2×C4—942no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—941no—
571C2×C4—941no—
572C2×C4—941no—
573C2×C4—941no—
574C2×C4—948no—
575C2×C4—942no—
576C2×C4—1884no—
577C2×C4—1888no—
578C2×C4—1882no—
579C2×C4—1882no—
580C2×C4—1882no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4C22⋊C4×D4712yes—
584C2×C4C22⋊C4×D4712yes—
585C2×C4#1309404312yes—
586C2×C4#1309404512yes—
587C2×C4C22×C4×D4711yescharacteristic
588C2×C4C2×D4×D4711yescharacteristic
589C2×C4C2×D4×D4711yescharacteristic
590C2×C4C2×Q8×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C8—42no—
594C8—1882no—
595C22—24no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—474no—
603C22—942no—
604C22—942no—
605C22—942no—
606C22—942no—
607C22—942no—
608C22—942no—
609C22C2×C22⋊C4×D4711yescharacteristic
610C22#121×D4711yescharacteristic
611C22C22⋊Q8×D4711yescharacteristic
612C22C2×#1309404311yescharacteristic
613C22C2×#1309404511yescharacteristic
614C22#1568991911yescharacteristic
615C22#1568992211yescharacteristic
616C4—22no—
617C4—42no—
618C4—82no—
619C4—474no—
620C4—942no—
621C4—942no—
622C4—944no—
623C4—3762no—
624C4—1882no—
625C4#1568911614yescomplemented
626C4C2×C4⋊C4×D4711yescharacteristic
627C4#117×D4711yescharacteristic
628C4#121×D4711yescharacteristic
629C4C22⋊Q8×D4711yescharacteristic
630C2—44no—
631C2—944no—
632C2#380×D4711yescharacteristic
633C2C2×#1568911611yescharacteristic
634C2#2025190411yescharacteristic
635C2#2025283611yescharacteristic
636C2#2025284411yescharacteristic
637C2#2025316911yescharacteristic
638C2#2025317711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1802C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
cosocleC22×C4×C47C24
hypercenter#1802D47
hypocenterC47#20645
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D47C2semidirect
4. #20245793C2semidirect
5. #20243402C2semidirect
6. #20243396C2semidirect
7. #20243394C2semidirect
8. #20243390C2semidirect
9. #20243388C2semidirect
10. #20243103C2semidirect
11. C47×#1802C2semidirect
15. C4×#10625352C4semidirect
150. #10625352C4⋊C4semidirect
300. C4×C47#416semidirect
320. #1802D47semidirect
366. C47#20645semidirect
625. C4#15689116semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253522
C2×C4⋊C8×D472
C2×#156891162
#202457932
#202434022
#202433962
#202433942
#202433902
#202433882
#202431032
C47×#18022
#2064547