Finite Group Databasebeta

← #26185946

Subgroups — #26185946

Order 12032.

726 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252426C211yesmaximal, characteristic, complemented
2#20252409C211yesmaximal, characteristic, complemented
3C4×D8×D47C211yesmaximal, characteristic
4#20242254C211yesmaximal, characteristic, complemented
5#20242253C211yesmaximal, characteristic, complemented
6#20242251C211yesmaximal, characteristic, complemented
7#20242220C211yesmaximal, characteristic, complemented
8#20242217C211yesmaximal, characteristic, complemented
9#20242215C211yesmaximal, characteristic, complemented
10#20242214C211yesmaximal, characteristic, complemented
11#20242133C211yesmaximal, characteristic, complemented
12#20241777C211yesmaximal, characteristic, complemented
13#20241777C211yesmaximal, characteristic, complemented
14#20241679C211yesmaximal, characteristic, complemented
15C47×#1586C211yesmaximal, 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#15689199—21no—
30#15689198—21no—
31C8×D188C2211yescharacteristic, complemented
32D4×C47⋊C8C2211yescharacteristic, complemented
33#15689188C2211yescharacteristic, complemented
34C8×C22⋊D47—21no—
35(C22⋊D47)⋊C8—21no—
36#15689175C2211yescharacteristic
37#15689175C2211yescharacteristic
38#15689174C2211yescharacteristic
39#15689174C2211yescharacteristic
40#107×D47C411yescharacteristic
41#102×D47C411yescharacteristic
42#102×D47C411yescharacteristic
43#15689086—21no—
44#15689085—21no—
45C2×(C2×D47)⋊C8—21no—
46C22⋊C8×D47—21no—
47C4×C8×D47C2211yescharacteristic
48#15688875C2211yescharacteristic, complemented
49#15688875C2211yescharacteristic, complemented
50#15688874C2211yescharacteristic, 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#15688844C2211yescharacteristic, complemented
60C4×D8×C47C2211yescharacteristic
61C47×#436C2211yescharacteristic, complemented
62C8×D4×C47C2211yescharacteristic, complemented
63C47×#334C2211yescharacteristic, 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—
78C22×C47⋊C8—21no—
79C2×C8×D47—21no—
80C2×C8×D47—21no—
81C2×C8×D47C2×C411yescharacteristic
82C2×C8×D47C2×C411yescharacteristic
83C4×D188C2311yescharacteristic
84C4×D188C2311yescharacteristic
85D4×Dic47C2×C411yescharacteristic
86D4×Dic47C2×C411yescharacteristic
87#13093986C2×C411yescharacteristic
88#13093986C2×C411yescharacteristic
89C4×C22⋊D47—21no—
90C4×C22⋊D47—21no—
91(C22⋊D47)⋊C4—21no—
92(C22⋊D47)⋊C4—21no—
93C4⋊C4×D47C2×C411yescharacteristic
94C4⋊C4×D47C2×C411yescharacteristic
95C22⋊C4×D47—21no—
96C22⋊C4×D47—21no—
97C42×D47C2311yescharacteristic
98#13093958C2×C411yescharacteristic
99#13093957C2×C411yescharacteristic
100#13093957C2×C411yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
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)⋊C8—21no—
121(C2×D47)⋊C8D411yescharacteristic
122(C2×D47)⋊C8D411yescharacteristic
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
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—22no—
158D4×D47M1614yescomplemented
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#10625334—22no—
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—81no—
215#10625324—81no—
216C8×D47—22no—
217C8×D47—22no—
218C8×D47—81no—
219C8×D47—81no—
220C23×C47—21no—
221C23×C47—21no—
222C22×D47—21no—
223C22×D47—24no—
224C22×D47—21no—
225C22×D47—42no—
226C22×D47—81no—
227C22×D47—81no—
228C22×D47—81no—
229C22×D47—81no—
230C22×D47C4×D411yescharacteristic
231D4×C47—21no—
232D4×C47—21no—
233D4×C47—21no—
234D4×C47C2×M1612yes—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47C23×C411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C22⋊D47—24no—
245C22⋊D47—42no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—81no—
249C2×Dic47—81no—
250C2×Dic47C4×D411yescharacteristic
251C2×Dic47C4×D411yescharacteristic
252C2×Dic47C4×D411yescharacteristic
253D188—21no—
254D188—21no—
255D188—21no—
256D188C2×M1612yes—
257C4×D47—21no—
258C4×D47—21no—
259C4×D47—41no—
260C4×D47—41no—
261C4×D47—41no—
262C4×D47—41no—
263C4×D47—41no—
264C4×D47—81no—
265C4×D47—81no—
266C4×D47—81no—
267C4×D47—81no—
268C4×D47C2×M1612yes—
269C4×D47#13112yes—
270C8×C47—21no—
271C8×C47—21no—
272C8×C47—21no—
273C8×C47—21no—
274C8×C47—41no—
275C8×C47—41no—
276C8×C47—41no—
277C47⋊C8—21no—
278C47⋊C8—21no—
279C47⋊C8—21no—
280C47⋊C8—21no—
281C47⋊C8—41no—
282C47⋊C8—41no—
283C47⋊C8—41no—
284#17877—471nomaximal, Sylow
285C22×C47—22no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47C2×C4×D411yescharacteristic
292C2×D47—21no—
293C2×D47—21no—
294C2×D47—22no—
295C2×D47—41no—
296C2×D47—41no—
297C2×D47—41no—
298C2×D47—41no—
299C2×D47—41no—
300C2×D47—84no—
301C2×D47—84no—
302C2×D47#43512yes—
303C4×C47—21no—
304C4×C47—41no—
305C4×C47—41no—
306C4×C47C22×M1611yescharacteristic
307C4×C47C2×#13111yescharacteristic
308C4×C47#57611yescharacteristic
309C4×C47#57611yescharacteristic
310Dic47—21no—
311Dic47—21no—
312Dic47—41no—
313Dic47—41no—
314Dic47#43512yes—
315#2975—471no—
316#2972—471no—
317C2×C4×D8—471no—
318#1586—471no—
319#1586—471no—
320#1586—471no—
321#1586D4711yescharacteristic, complemented
322#1581—471no—
323#1581—471no—
324#1581—471no—
325#1581—471no—
326#1564—471no—
327#1478—471no—
328#1478—471no—
329#1452—471no—
330C2×C47—42no—
331C2×C47—81no—
332C2×C47C2×#43511yescharacteristic
333C2×C47#294811yescharacteristic
334C2×C47#295711yescharacteristic
335D47—22no—
336D47—42no—
337D47—81no—
338C22×D8—471no—
339C2×C4×D4—471no—
340C2×C4×D4—471no—
341C4×D8—471no—
342C4×D8—471no—
343C4×D8—471no—
344C4×D8—471no—
345C4×D8—471no—
346C4×D8—471no—
347C4×D8—471no—
348C4×D8C2×D4711yescharacteristic
349#436—471no—
350#436—471no—
351#436—471no—
352#436—941no—
353#436—941no—
354#436C2×D4711yescharacteristic, complemented
355C8×D4—471no—
356C8×D4—471no—
357C8×D4—471no—
358C8×D4—941no—
359C8×D4—941no—
360C8×D4C2×D4711yescharacteristic, complemented
361#431—471no—
362#431—471no—
363#431—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—
372C2×C4×C8—471no—
373#335—471no—
374#335—471no—
375#334—471no—
376#334C2×D4711yescharacteristic, complemented
377D4⋊C8—471no—
378D4⋊C8—471no—
379D4⋊C8—471no—
380D4⋊C8—471no—
381D4⋊C8—471no—
382D4⋊C8—471no—
383D4⋊C8C2×D4711yescharacteristic, complemented
384D4⋊C8C2×D4711yescharacteristic, complemented
385#322—471no—
386#322—471no—
387#322—471no—
388#322C2×D4711yescharacteristic, complemented
389C47#1787711yescharacteristic, complemented, Sylow
390C22×D4—471no—
391C22×D4—471no—
392C23×C4—941no—
393C23×C4—941no—
394C2×D8—471no—
395C2×D8—471no—
396C2×D8—471no—
397C2×D8—944no—
398C2×D8C4×D4711yescharacteristic
399C2×M16—21no—
400C2×M16—941no—
401C2×M16—941no—
402C2×M16—941no—
403C22×C8—21no—
404C22×C8—471no—
405C22×C8—471no—
406C22×C8—941no—
407C22×C8—941no—
408C22×C8—941no—
409C4×D4—471no—
410C4×D4—471no—
411C4×D4—471no—
412C4×D4—471no—
413C4×D4—471no—
414C4×D4—471no—
415C4×D4—941no—
416C4×D4—941no—
417C4×D4—941no—
418C4×D4—941no—
419C4×D4C22×D4711yescharacteristic
420C4×D4C22×D4711yescharacteristic
421C2×C4⋊C4—471no—
422C2×C4⋊C4—471no—
423C2×C22⋊C4—941no—
424C2×C22⋊C4—941no—
425C2×C42—471no—
426#107—471no—
427#107—471no—
428#107—471no—
429#107C4×D4711yescharacteristic
430C4⋊C8—471no—
431C4⋊C8—471no—
432C4⋊C8—471no—
433C4⋊C8—471no—
434C4⋊C8—941no—
435C4⋊C8C22×D4711yescharacteristic
436C4⋊C8C22×D4711yescharacteristic
437#102—471no—
438#102—471no—
439#102—471no—
440#102—471no—
441#102—471no—
442#102—471no—
443#102C4×D4711yescharacteristic
444#102C4×D4711yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—471no—
448C22⋊C8—471no—
449C22⋊C8—941no—
450C22⋊C8—941no—
451C22⋊C8—941no—
452C22⋊C8—941no—
453C22⋊C8—941no—
454C22⋊C8—941no—
455C22⋊C8—941no—
456C22⋊C8—941no—
457C22⋊C8—941no—
458C4×C8—471no—
459C4×C8—471no—
460C4×C8—471no—
461C4×C8—471no—
462C4×C8—471no—
463C4×C8—941no—
464C4×C8—941no—
465C4×C8C22×D4711yescharacteristic
466C4×C8C22×D4711yescharacteristic
467C4×C8C22×D4711yescharacteristic
468C24—941no—
469C24—941no—
470C2×D4—474no—
471C2×D4—471no—
472C2×D4—471no—
473C2×D4—942no—
474C2×D4—942no—
475C2×D4—942no—
476C2×D4—941no—
477C2×D4—941no—
478C2×D4C2×C4×D4711yescharacteristic
479C2×D4C2×C4×D4711yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—471no—
483C22×C4—471no—
484C22×C4—471no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4—941no—
492C22×C4—941no—
493C22×C4—3761no—
494C22×C4—3761no—
495C22×C4—3761no—
496C22×C4—3761no—
497D8—22no—
498D8—942no—
499D8—942no—
500D8—942no—
501M16—81no—
502M16—3761no—
503M16—3761no—
504M16—3761no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—471no—
510C2×C8—471no—
511C2×C8—471no—
512C2×C8—471no—
513C2×C8—942no—
514C2×C8—942no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8—941no—
518C2×C8—3761no—
519C2×C8—3761no—
520C2×C8—3761no—
521C2×C8C2×C4×D4711yescharacteristic
522C2×C8C2×C4×D4711yescharacteristic
523C2×C8D4×D4711yescharacteristic
524C2×C8D4×D4711yescharacteristic
525C4⋊C4—471no—
526C4⋊C4—471no—
527C4⋊C4—941no—
528C4⋊C4—941no—
529C4⋊C4C2×C4×D4711yescharacteristic
530C4⋊C4C2×C4×D4711yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—941no—
534C22⋊C4—941no—
535C22⋊C4—941no—
536C22⋊C4—941no—
537C22⋊C4—941no—
538C22⋊C4—941no—
539C42—471no—
540C42—471no—
541C42—471no—
542C42C23×D4711yescharacteristic
543C23—21no—
544C23—21no—
545C23—471no—
546C23—944no—
547C23—941no—
548C23—941no—
549C23—3761no—
550C23—3761no—
551C23—3761no—
552C23—3761no—
553C23—1882no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—472no—
558D4—944no—
559D4—941no—
560D4—941no—
561D4—941no—
562D4—1882no—
563D4M16×D4712yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—471no—
571C2×C4—472no—
572C2×C4—472no—
573C2×C4—471no—
574C2×C4—471no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—941no—
579C2×C4—3761no—
580C2×C4—3761no—
581C2×C4—3761no—
582C2×C4—3761no—
583C2×C4—3761no—
584C2×C4—3761no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4—1881no—
588C2×C4—1881no—
589C2×C4—1881no—
590C2×C4C22×C4×D4711yescharacteristic
591C2×C4C2×D4×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—941no—
601C8—941no—
602C8—941no—
603C8—941no—
604C8—1881no—
605C8—1881no—
606C8—1881no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—472no—
614C22—941no—
615C22—941no—
616C22—942no—
617C22—3764no—
618C22—3764no—
619C22—1881no—
620C22—1881no—
621C22—1881no—
622C22—1881no—
623C22—1881no—
624C22C4×D4×D4711yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—472no—
629C4—941no—
630C4—941no—
631C4—1881no—
632C4—1881no—
633C4C2×M16×D4711yescharacteristic
634C4#131×D4711yescharacteristic
635C4#1568992711yescharacteristic
636C4#1568992711yescharacteristic
637C2—42no—
638C2—81no—
639C2—942no—
640C2—3761no—
641C2—1882no—
642C2#435×D4711yescharacteristic
643C2#2025223711yescharacteristic
644C2#2025230011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1586C2
socleC22×C47C2×C4×D4
prime radicalC2×D8×D47C4
cosocleC42×C47C24
hypercenter#1586D47
hypocenterC47#17877
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
1. #20252426C2semidirect
2. #20252409C2semidirect
4. #20242254C2semidirect
5. #20242253C2semidirect
6. #20242251C2semidirect
7. #20242220C2semidirect
8. #20242217C2semidirect
9. #20242215C2semidirect
10. #20242214C2semidirect
11. #20242133C2semidirect
12. #20241777C2semidirect
13. #20241777C2semidirect
14. #20241679C2semidirect
15. C47×#1586C2semidirect
26. #15689202C22semidirect
27. #15689201C22semidirect
28. #15689200C22semidirect
31. C8×D188C22semidirect
32. D4×C47⋊C8C22semidirect
33. #15689188C22semidirect
48. #15688875C22semidirect
49. #15688875C22semidirect
50. #15688874C22semidirect
51. #15688852C22semidirect
52. #15688852C22semidirect
53. D4⋊(C47⋊C8)C22semidirect
54. D4⋊(C47⋊C8)C22semidirect
55. #15688850C22semidirect
56. #15688850C22semidirect
57. #15688845C22semidirect
58. #15688845C22semidirect
59. #15688844C22semidirect
61. C47×#436C22semidirect
62. C8×D4×C47C22semidirect
63. C47×#334C22semidirect
64. C47×D4⋊C8C22semidirect
65. C47×D4⋊C8C22semidirect
66. C47×#322C22semidirect
158. D4×D47M16semidirect
321. #1586D47semidirect
354. #436C2×D47semidirect
360. C8×D4C2×D47semidirect
376. #334C2×D47semidirect
383. D4⋊C8C2×D47semidirect
384. D4⋊C8C2×D47semidirect
388. #322C2×D47semidirect
389. C47#17877semidirect

Maximal subgroups

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

subgroupindex
#202524262
#202524092
C4×D8×D472
#202422542
#202422532
#202422512
#202422202
#202422172
#202422152
#202422142
#202421332
#202417772
#202416792
C47×#15862
#1787747