Finite Group Databasebeta

← #26188017

Subgroups — #26188017

Order 12032.

718 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252421C211yesmaximal, characteristic, complemented
2#20252420C211yesmaximal, characteristic, complemented
3C4×D8×D47C211yesmaximal, characteristic
4#20242300C211yesmaximal, characteristic, complemented
5#20242299C211yesmaximal, characteristic, complemented
6#20242219C211yesmaximal, characteristic, complemented
7#20242218C211yesmaximal, characteristic, complemented
8#20242216C211yesmaximal, characteristic, complemented
9#20242210C211yesmaximal, characteristic, complemented
10#20242209C211yesmaximal, characteristic, complemented
11#20242150C211yesmaximal, characteristic, complemented
12#20241829C211yesmaximal, characteristic, complemented
13#20241829C211yesmaximal, characteristic, complemented
14#20241676C211yesmaximal, characteristic, complemented
15C47×#1581C211yesmaximal, characteristic, complemented
16C2×D8×D47C411yescharacteristic
17C4×D4×D47C2211yescharacteristic
18C4×D4×D47C2211yescharacteristic
19C4×D376C2211yescharacteristic
20D8×Dic47C411yescharacteristic
21#15689205C411yescharacteristic
22C4×#10625334C2211yescharacteristic
23C4×#10625334C2211yescharacteristic
24#15689203C411yescharacteristic
25#15689203C411yescharacteristic
26#15689202C2211yescharacteristic, complemented
27#15689201C2211yescharacteristic, complemented
28#15689200C2211yescharacteristic, complemented
29#15689197—21no—
30#15689194—21no—
31#15689192—21no—
32#15689191—21no—
33C8×D188C2211yescharacteristic, complemented
34D4×C47⋊C8C2211yescharacteristic, complemented
35#15689188C2211yescharacteristic, complemented
36#15689179C2211yescharacteristic
37#15689179C2211yescharacteristic
38#15689174C2211yescharacteristic
39#107×D47C411yescharacteristic
40#102×D47C411yescharacteristic
41#102×D47C411yescharacteristic
42#15689086—21no—
43#15689085—21no—
44C2×(C2×D47)⋊C8—21no—
45C22⋊C8×D47—21no—
46C4×#10625324C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic, complemented
49#15688873C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688852C2211yescharacteristic, complemented
52#15688852C2211yescharacteristic, complemented
53D4⋊(C47⋊C8)C2211yescharacteristic, complemented
54D4⋊(C47⋊C8)C2211yescharacteristic, complemented
55#15688850C2211yescharacteristic, complemented
56#15688850C2211yescharacteristic, complemented
57#15688845C2211yescharacteristic, complemented
58#15688845C2211yescharacteristic, complemented
59#15688845C2211yescharacteristic, complemented
60C4×D8×C47C2211yescharacteristic
61C47×#436C2211yescharacteristic, complemented
62C8×D4×C47C2211yescharacteristic, complemented
63C47×#335C2211yescharacteristic, complemented
64C47×D4⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic, complemented
66C47×#322C2211yescharacteristic, complemented
67C2×D4×D47C2×C411yescharacteristic
68C2×D4×D47C2×C411yescharacteristic
69C22×C4×D47—21no—
70C22×C4×D47—21no—
71C2×D376C2×C411yescharacteristic
72C2×#10625334C2×C411yescharacteristic
73C2×#10625334C2×C411yescharacteristic
74D8×D47—24no—
75C2×#10625329—21no—
76C2×#10625324—21no—
77C2×#10625324—21no—
78C2×#10625324—21no—
79C22×C47⋊C8—21no—
80C2×C8×D47—21no—
81C2×C8×D47—21no—
82C2×C8×D47C2×C411yescharacteristic
83C2×C8×D47C2×C411yescharacteristic
84C4×D188C2311yescharacteristic
85C4×D188C2311yescharacteristic
86D4×Dic47C2×C411yescharacteristic
87D4×Dic47C2×C411yescharacteristic
88#13093986C2×C411yescharacteristic
89#13093986C2×C411yescharacteristic
90C4×C22⋊D47—21no—
91C4×C22⋊D47—21no—
92(C22⋊D47)⋊C4—21no—
93(C22⋊D47)⋊C4—21no—
94C4⋊C4×D47C2×C411yescharacteristic
95C4⋊C4×D47C2×C411yescharacteristic
96C22⋊C4×D47—21no—
97C22⋊C4×D47—21no—
98C42×D47C2311yescharacteristic
99#13093958C2×C411yescharacteristic
100#13093957C2×C411yescharacteristic
101#13093957C2×C411yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103C4⋊(C47⋊C8)C2311yescharacteristic
104Dic47⋊C8D411yescharacteristic
105Dic47⋊C8D411yescharacteristic
106#13093946C2×C411yescharacteristic
107#13093946C2×C411yescharacteristic
108#13093945C2×C411yescharacteristic
109#13093945C2×C411yescharacteristic
110#13093944C2×C411yescharacteristic
111#13093944C2×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(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8D411yescharacteristic
121(C2×D47)⋊C8D411yescharacteristic
122#13093934—21no—
123#13093934—21no—
124#13093934—21no—
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C4×C47⋊C8C2311yescharacteristic
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
145C23×D47—21no—
146C23×D47—21no—
147C2×D4×C47C22×C411yescharacteristic
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C2×C22⋊D47—21no—
152C2×C22⋊D47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155D4×D47—22no—
156D4×D47—22no—
157D4×D47—41no—
158D4×D47—41no—
159C2×D188C22×C411yescharacteristic
160C2×D188C22×C411yescharacteristic
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—81no—
168C2×C4×D47—81no—
169C2×C4×D47—81no—
170C2×C4×D47—81no—
171C2×C4×D47C22×C411yescharacteristic
172C2×C4×D47C2×D411yescharacteristic
173C2×C4×D47#4111yescharacteristic
174D8×C47—22no—
175M16×C47—81no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—81no—
180C2×C8×C47C22×C411yescharacteristic
181C2×C8×C47C22×C411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
184C4⋊C4×C47C22×C411yescharacteristic
185C4⋊C4×C47C22×C411yescharacteristic
186C22⋊C4×C47—21no—
187C22⋊C4×C47—21no—
188C42×C47C2411yescharacteristic
189C22⋊Dic47—21no—
190C22⋊Dic47—21no—
191#10625334—22no—
192#10625334M1614yescomplemented
193(C2×D47)⋊C4—21no—
194(C2×D47)⋊C4—21no—
195(C2×D47)⋊C4—21no—
196(C2×D47)⋊C4—21no—
197C4⋊Dic47C22×C411yescharacteristic
198C4⋊Dic47C22×C411yescharacteristic
199Dic47⋊C4—21no—
200Dic47⋊C4—21no—
201C4×Dic47C22×C411yescharacteristic
202C4×Dic47C2×D411yescharacteristic
203C4×Dic47#4111yescharacteristic
204#10625329—81no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—81no—
209C2×C47⋊C8C22×C411yescharacteristic
210C2×C47⋊C8C22×C411yescharacteristic
211C2×C47⋊C8C2×D411yescharacteristic
212C2×C47⋊C8C2×D411yescharacteristic
213D376—22no—
214#10625324—42no—
215#10625324—81no—
216#10625324—81no—
217C8×D47—22no—
218C8×D47—41no—
219C8×D47—81no—
220C8×D47—81no—
221C23×C47—21no—
222C23×C47—21no—
223C22×D47—21no—
224C22×D47—21no—
225C22×D47—42no—
226C22×D47—42no—
227C22×D47—42no—
228C22×D47—42no—
229C22×D47—81no—
230C22×D47—81no—
231C22×D47C4×D411yescharacteristic
232D4×C47—21no—
233D4×C47—21no—
234D4×C47—21no—
235D4×C47C2×M1612yes—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47C23×C411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C22⋊D47—42no—
246C22⋊D47—42no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—81no—
250C2×Dic47—81no—
251C2×Dic47C4×D411yescharacteristic
252C2×Dic47C4×D411yescharacteristic
253C2×Dic47C4×D411yescharacteristic
254D188—21no—
255D188—21no—
256D188—21no—
257D188C2×M1612yes—
258C4×D47—22no—
259C4×D47—21no—
260C4×D47—21no—
261C4×D47—21no—
262C4×D47—21no—
263C4×D47—41no—
264C4×D47—41no—
265C4×D47—41no—
266C4×D47—41no—
267C4×D47—81no—
268C4×D47—81no—
269C4×D47—81no—
270C4×D47—81no—
271C8×C47—21no—
272C8×C47—21no—
273C8×C47—21no—
274C8×C47—21no—
275C8×C47—41no—
276C8×C47—41no—
277C8×C47—41no—
278C47⋊C8—21no—
279C47⋊C8—21no—
280C47⋊C8—21no—
281C47⋊C8—41no—
282C47⋊C8—41no—
283C47⋊C8—41no—
284C47⋊C8C2×M1612yes—
285#18064—471nomaximal, Sylow
286C22×C47—22no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47C2×C4×D411yescharacteristic
293C2×D47—21no—
294C2×D47—21no—
295C2×D47—22no—
296C2×D47—41no—
297C2×D47—41no—
298C2×D47—41no—
299C2×D47—41no—
300C2×D47—41no—
301C2×D47—84no—
302C2×D47—84no—
303C2×D47#44412yes—
304C4×C47—21no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47C22×M1611yescharacteristic
308C4×C47#56811yescharacteristic
309C4×C47#57611yescharacteristic
310C4×C47#57611yescharacteristic
311Dic47—21no—
312Dic47—21no—
313Dic47—21no—
314Dic47—41no—
315Dic47—41no—
316#2974—471no—
317#2974—471no—
318C2×C4×D8—471no—
319#1594—471no—
320#1594—471no—
321#1581—471no—
322#1581—471no—
323#1581—471no—
324#1581D4711yescharacteristic, complemented
325#1580—471no—
326#1580—471no—
327#1568—471no—
328#1490—471no—
329#1490—471no—
330#1451—471no—
331C2×C47—42no—
332C2×C47—81no—
333C2×C47D4×M1611yescharacteristic
334C2×C47#294811yescharacteristic
335C2×C47C2×#44411yescharacteristic
336D47—22no—
337D47—42no—
338D47—81no—
339C22×D8—471no—
340C2×C4×D4—471no—
341C2×C4×D4—471no—
342C4×D8—471no—
343C4×D8—471no—
344C4×D8—471no—
345C4×D8—471no—
346C4×D8—471no—
347C4×D8—471no—
348C4×D8—471no—
349C4×D8C2×D4711yescharacteristic
350#436—471no—
351#436—471no—
352#436—471no—
353#436C2×D4711yescharacteristic, complemented
354#435—941no—
355#435—941no—
356#435—941no—
357#435—941no—
358C8×D4—471no—
359C8×D4—471no—
360C8×D4—471no—
361C8×D4C2×D4711yescharacteristic, complemented
362#432—471no—
363#432—471no—
364#431—471no—
365C2×#107—471no—
366C2×#102—471no—
367C2×#102—471no—
368#407—941no—
369#407—941no—
370C2×C22⋊C8—941no—
371C2×C22⋊C8—941no—
372C4×M16—471no—
373C2×C4×C8—471no—
374#335—471no—
375#335C2×D4711yescharacteristic, complemented
376#334—471no—
377#334—471no—
378D4⋊C8—471no—
379D4⋊C8—471no—
380D4⋊C8—471no—
381D4⋊C8—471no—
382D4⋊C8—471no—
383D4⋊C8—471no—
384D4⋊C8C2×D4711yescharacteristic, complemented
385D4⋊C8C2×D4711yescharacteristic, complemented
386#322—471no—
387#322—471no—
388#322—471no—
389#322C2×D4711yescharacteristic, complemented
390C47#1806411yescharacteristic, complemented, Sylow
391C22×D4—471no—
392C22×D4—471no—
393C23×C4—941no—
394C23×C4—941no—
395C2×D8—471no—
396C2×D8—471no—
397C2×D8—471no—
398C2×D8—944no—
399C2×D8C4×D4711yescharacteristic
400C2×M16—21no—
401C2×M16—941no—
402C2×M16—941no—
403C2×M16—941no—
404C2×M16—941no—
405C22×C8—21no—
406C22×C8—471no—
407C22×C8—471no—
408C22×C8—941no—
409C22×C8—941no—
410C22×C8—941no—
411C4×D4—471no—
412C4×D4—471no—
413C4×D4—471no—
414C4×D4—471no—
415C4×D4—471no—
416C4×D4—471no—
417C4×D4—941no—
418C4×D4—941no—
419C4×D4—941no—
420C4×D4—941no—
421C4×D4C22×D4711yescharacteristic
422C4×D4C22×D4711yescharacteristic
423C2×C4⋊C4—471no—
424C2×C4⋊C4—471no—
425C2×C22⋊C4—941no—
426C2×C22⋊C4—941no—
427C2×C42—471no—
428#107—471no—
429#107—471no—
430#107—471no—
431#107C4×D4711yescharacteristic
432C4⋊C8—471no—
433C4⋊C8—471no—
434C4⋊C8—471no—
435C4⋊C8—471no—
436C4⋊C8C22×D4711yescharacteristic
437C4⋊C8C22×D4711yescharacteristic
438#102—471no—
439#102—471no—
440#102—471no—
441#102—471no—
442#102—471no—
443#102—471no—
444#102C4×D4711yescharacteristic
445#102C4×D4711yescharacteristic
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—471no—
449C22⋊C8—471no—
450C22⋊C8—941no—
451C22⋊C8—941no—
452C22⋊C8—941no—
453C22⋊C8—941no—
454C22⋊C8—941no—
455C22⋊C8—941no—
456C22⋊C8—941no—
457C22⋊C8—941no—
458#97—941no—
459#97—941no—
460#97—941no—
461C4×C8—471no—
462C4×C8—471no—
463C4×C8—471no—
464C4×C8—471no—
465C4×C8—471no—
466C4×C8C22×D4711yescharacteristic
467C4×C8C22×D4711yescharacteristic
468C4×C8C22×D4711yescharacteristic
469C24—941no—
470C24—941no—
471C2×D4—471no—
472C2×D4—471no—
473C2×D4—941no—
474C2×D4—941no—
475C2×D4—942no—
476C2×D4—942no—
477C2×D4—1881no—
478C2×D4—1881no—
479C2×D4C2×C4×D4711yescharacteristic
480C2×D4C2×C4×D4711yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—471no—
484C22×C4—471no—
485C22×C4—471no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4—941no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4—3761no—
495C22×C4—3761no—
496C22×C4—3761no—
497C22×C4—3761no—
498D8—22no—
499D8—474no—
500D8—942no—
501D8—942no—
502M16—81no—
503M16—3761no—
504M16—3761no—
505M16—3761no—
506M16—1882no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—81no—
511C2×C8—471no—
512C2×C8—471no—
513C2×C8—471no—
514C2×C8—471no—
515C2×C8—942no—
516C2×C8—941no—
517C2×C8—941no—
518C2×C8—941no—
519C2×C8—3761no—
520C2×C8—3761no—
521C2×C8—3761no—
522C2×C8—1881no—
523C2×C8C2×C4×D4711yescharacteristic
524C2×C8C2×C4×D4711yescharacteristic
525C2×C8D4×D4711yescharacteristic
526C2×C8D4×D4711yescharacteristic
527C4⋊C4—471no—
528C4⋊C4—471no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C4⋊C4C2×C4×D4711yescharacteristic
532C4⋊C4C2×C4×D4711yescharacteristic
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—941no—
536C22⋊C4—941no—
537C22⋊C4—941no—
538C22⋊C4—941no—
539C22⋊C4—941no—
540C22⋊C4—941no—
541C42—471no—
542C42—471no—
543C42—471no—
544C42C23×D4711yescharacteristic
545C23—21no—
546C23—21no—
547C23—471no—
548C23—941no—
549C23—941no—
550C23—3761no—
551C23—3761no—
552C23—1882no—
553C23—1882no—
554C23—1882no—
555C23—1882no—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—472no—
560D4—941no—
561D4—941no—
562D4—941no—
563D4—1882no—
564D4—1882no—
565D4M16×D4712yes—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—471no—
573C2×C4—471no—
574C2×C4—471no—
575C2×C4—942no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—941no—
579C2×C4—941no—
580C2×C4—941no—
581C2×C4—941no—
582C2×C4—3761no—
583C2×C4—3761no—
584C2×C4—3761no—
585C2×C4—3761no—
586C2×C4—3761no—
587C2×C4—3761no—
588C2×C4—1881no—
589C2×C4—1881no—
590C2×C4—1881no—
591C2×C4—1881no—
592C2×C4C22×C4×D4711yescharacteristic
593C2×C4C2×D4×D4711yescharacteristic
594C2×C4#41×D4711yescharacteristic
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—41no—
600C8—41no—
601C8—41no—
602C8—472no—
603C8—941no—
604C8—941no—
605C8—941no—
606C8—1881no—
607C8—1881no—
608C8—1881no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—472no—
616C22—941no—
617C22—941no—
618C22—942no—
619C22—3764no—
620C22—3764no—
621C22—1881no—
622C22—1881no—
623C22—1881no—
624C22—1881no—
625C22—1881no—
626C22C4×D4×D4711yescharacteristic
627C4—21no—
628C4—41no—
629C4—41no—
630C4—941no—
631C4—941no—
632C4—941no—
633C4—1881no—
634C4—1881no—
635C4C2×M16×D4711yescharacteristic
636C4#1568988811yescharacteristic
637C4#1568992411yescharacteristic
638C4#1568992511yescharacteristic
639C2—42no—
640C2—81no—
641C2—942no—
642C2—3761no—
643C2—1882no—
644C2#2025212111yescharacteristic
645C2#2025223511yescharacteristic
646C2#444×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1581C2
socleC22×C47C2×C4×D4
prime radicalC2×D8×D47C4
cosocleC42×C47C24
hypercenter#1581D47
hypocenterC47#18064
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. #20252421C2semidirect
2. #20252420C2semidirect
4. #20242300C2semidirect
5. #20242299C2semidirect
6. #20242219C2semidirect
7. #20242218C2semidirect
8. #20242216C2semidirect
9. #20242210C2semidirect
10. #20242209C2semidirect
11. #20242150C2semidirect
12. #20241829C2semidirect
13. #20241829C2semidirect
14. #20241676C2semidirect
15. C47×#1581C2semidirect
26. #15689202C22semidirect
27. #15689201C22semidirect
28. #15689200C22semidirect
33. C8×D188C22semidirect
34. D4×C47⋊C8C22semidirect
35. #15689188C22semidirect
48. #15688876C22semidirect
49. #15688873C22semidirect
50. #15688873C22semidirect
51. #15688852C22semidirect
52. #15688852C22semidirect
53. D4⋊(C47⋊C8)C22semidirect
54. D4⋊(C47⋊C8)C22semidirect
55. #15688850C22semidirect
56. #15688850C22semidirect
57. #15688845C22semidirect
58. #15688845C22semidirect
59. #15688845C22semidirect
61. C47×#436C22semidirect
62. C8×D4×C47C22semidirect
63. C47×#335C22semidirect
64. C47×D4⋊C8C22semidirect
65. C47×D4⋊C8C22semidirect
66. C47×#322C22semidirect
192. #10625334M16semidirect
324. #1581D47semidirect
353. #436C2×D47semidirect
361. C8×D4C2×D47semidirect
375. #335C2×D47semidirect
384. D4⋊C8C2×D47semidirect
385. D4⋊C8C2×D47semidirect
389. #322C2×D47semidirect
390. C47#18064semidirect

Maximal subgroups

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

subgroupindex
#202524212
#202524202
C4×D8×D472
#202423002
#202422992
#202422192
#202422182
#202422162
#202422102
#202422092
#202421502
#202418292
#202416762
C47×#15812
#1806447