Finite Group Databasebeta

← #26186391

Subgroups — #26186391

Order 12032.

678 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253386C211yesmaximal, characteristic
2#20252462C211yesmaximal, characteristic, complemented
3#20252409C211yesmaximal, characteristic, complemented
4#20242255C211yesmaximal, characteristic, complemented
5#20242249C211yesmaximal, characteristic, complemented
6#20242218C211yesmaximal, characteristic, complemented
7#20242216C211yesmaximal, characteristic, complemented
8#20242210C211yesmaximal, characteristic, complemented
9#20242210C211yesmaximal, characteristic, complemented
10C8×D376C211yesmaximal, characteristic, complemented
11#20242167C211yesmaximal, characteristic, complemented
12#20241829C211yesmaximal, characteristic, complemented
13#20241803C211yesmaximal, characteristic, complemented
14#20241682C211yesmaximal, characteristic, complemented
15C8×D8×C47C211yesmaximal, characteristic, complemented
16#15689670C2211yescharacteristic
17C4×D4×D47C2211yescharacteristic
18#15689438C411yescharacteristic
19#15689435C411yescharacteristic
20#15689402C411yescharacteristic
21#15689401C411yescharacteristic
22#15689317C411yescharacteristic
23#15689316C411yescharacteristic
24#15689258C411yescharacteristic
25#15689255C411yescharacteristic
26C4×D376C2211yescharacteristic
27C4×#10625334C2211yescharacteristic
28C4×#10625334C2211yescharacteristic
29#15689201C2211yescharacteristic, complemented
30#15689200C2211yescharacteristic, complemented
31#15689197—21no—
32#15689194—21no—
33C8×D188C2211yescharacteristic
34C8×D188C2211yescharacteristic, complemented
35D4×C47⋊C8C2211yescharacteristic
36#15689188C2211yescharacteristic
37C8×C22⋊D47—21no—
38(C22⋊D47)⋊C8—21no—
39#15689179C2211yescharacteristic
40#15689175C2211yescharacteristic
41#15689174C2211yescharacteristic
42#15689174C2211yescharacteristic
43#15689089—21no—
44#15689088—21no—
45C2×(C2×D47)⋊C8—21no—
46C22⋊C8×D47—21no—
47C4×#10625324C2211yescharacteristic
48#15688876C2211yescharacteristic, complemented
49#15688873C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688852C2211yescharacteristic
52#15688852C2211yescharacteristic, complemented
53D4⋊(C47⋊C8)C2211yescharacteristic
54D4⋊(C47⋊C8)C2211yescharacteristic, complemented
55#15688850C2211yescharacteristic
56#15688850C2211yescharacteristic, complemented
57#15688845C2211yescharacteristic, complemented
58#15688845C2211yescharacteristic, complemented
59#15688844C2211yescharacteristic, complemented
60C4×D8×C47C2211yescharacteristic
61C8×D4×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic, complemented
63C47×#335C2211yescharacteristic, complemented
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic, complemented
66C82×C47C2211yescharacteristic, complemented
67C2×#10625350—21no—
68C2×D4×D47C2×C411yescharacteristic
69C22×C4×D47—21no—
70C2×D376C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625334C2×C411yescharacteristic
73C2×#10625329—21no—
74C2×#10625324—21no—
75C2×#10625324—21no—
76C22×C47⋊C8—21no—
77C2×C8×D47—21no—
78C2×C8×D47—21no—
79C2×C8×D47—21no—
80#13094023C2×C411yescharacteristic
81#13094020C2×C411yescharacteristic
82#13094010—21no—
83#13093999C2×C411yescharacteristic
84#13093997—21no—
85#13093995C2×C411yescharacteristic
86C4×D188C2311yescharacteristic
87C4×D188C2311yescharacteristic
88D4×Dic47C2×C411yescharacteristic
89#13093986C2×C411yescharacteristic
90C4×C22⋊D47—21no—
91C4×C22⋊D47—21no—
92(C22⋊D47)⋊C4—21no—
93C4⋊C4×D47C2×C411yescharacteristic
94C22⋊C4×D47—21no—
95C42×D47C2311yescharacteristic
96#13093958C2×C411yescharacteristic
97#13093957C2×C411yescharacteristic
98#13093957C2×C411yescharacteristic
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101Dic47⋊C8C2×C411yescharacteristic
102Dic47⋊C8C2×C411yescharacteristic
103Dic47⋊C8D411yescharacteristic
104Dic47⋊C8D411yescharacteristic
105#13093946C2×C411yescharacteristic
106#13093946C2×C411yescharacteristic
107#13093945C2×C411yescharacteristic
108#13093945C2×C411yescharacteristic
109#13093944C2×C411yescharacteristic
110#13093944C2×C411yescharacteristic
111C22⋊(C47⋊C8)—21no—
112C22⋊(C47⋊C8)—21no—
113(C2×D47)⋊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)⋊C8C2×C411yescharacteristic
120(C2×D47)⋊C8C2×C411yescharacteristic
121(C2×D47)⋊C8D411yescharacteristic
122(C2×D47)⋊C8D411yescharacteristic
123#13093934—21no—
124#13093934—21no—
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C4×C47⋊C8C2311yescharacteristic
128C8×Dic47—21no—
129C2×D8×C47C2×C411yescharacteristic
130C22×C8×C47—21no—
131C22×C8×C47—21no—
132C4×D4×C47C2311yescharacteristic
133C4×D4×C47C2311yescharacteristic
134#107×C47C2×C411yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#102×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C23×D47—21no—
145C2×D4×C47C22×C411yescharacteristic
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C2×C22⋊D47—21no—
150C2×C22⋊D47—21no—
151C2×C22⋊D47—21no—
152C2×C22⋊D47—21no—
153C22×Dic47—21no—
154D4×D47—22no—
155D4×D47—22no—
156#10625350—81no—
157#10625350—81no—
158C2×D188—21no—
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—81no—
166C2×C4×D47—81no—
167C2×C4×D47C22×C411yescharacteristic
168C2×C4×D47C2×D411yescharacteristic
169C2×C4×D47#4111yescharacteristic
170C2×Dic94—21no—
171D8×C47—22no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—81no—
176C2×C8×C47—81no—
177C2×C8×C47C22×C411yescharacteristic
178C2×C8×C47C22×C411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C4⋊C4×C47C22×C411yescharacteristic
182C4⋊C4×C47C22×C411yescharacteristic
183C22⋊C4×C47—21no—
184C22⋊C4×C47—21no—
185C42×C47C2411yescharacteristic
186C22⋊Dic47—21no—
187C22⋊Dic47—21no—
188#10625334—22no—
189#10625334—22no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192(C2×D47)⋊C4—21no—
193(C2×D47)⋊C4—21no—
194C4⋊Dic47C22×C411yescharacteristic
195C4⋊Dic47C22×C411yescharacteristic
196Dic47⋊C4—21no—
197Dic47⋊C4—21no—
198C4×Dic47C22×C411yescharacteristic
199C4×Dic47C2×D411yescharacteristic
200C4×Dic47#4111yescharacteristic
201#10625329—81no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—81no—
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209C2×C47⋊C8C2×D411yescharacteristic
210D376—22no—
211#10625324—42no—
212#10625324—81no—
213C8×D47—81no—
214C8×D47—81no—
215C8×D47—81no—
216C23×C47—21no—
217C23×C47—21no—
218C22×D47—21no—
219C22×D47—24no—
220C22×D47—21no—
221C22×D47—81no—
222C22×D47—81no—
223C22×D47C4×D411yescharacteristic
224D4×C47—21no—
225D4×C47—21no—
226D4×C47—21no—
227D4×C47#13112yes—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47C23×C411yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C22⋊D47—24no—
238C22⋊D47—81no—
239C22⋊D47—81no—
240C22⋊D47—81no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—81no—
244C2×Dic47C4×D411yescharacteristic
245C2×Dic47C4×D411yescharacteristic
246C2×Dic47C4×D411yescharacteristic
247D188—21no—
248D188—21no—
249D188—21no—
250D188—81no—
251D188#13112yes—
252C4×D47—21no—
253C4×D47—21no—
254C4×D47—21no—
255C4×D47—21no—
256C4×D47—41no—
257C4×D47—41no—
258C4×D47—41no—
259C4×D47—41no—
260C4×D47—41no—
261C4×D47—81no—
262C4×D47—81no—
263Dic94—81no—
264C8×C47—22no—
265C8×C47—21no—
266C8×C47—21no—
267C8×C47—21no—
268C8×C47—21no—
269C8×C47—41no—
270C8×C47—41no—
271C47⋊C8—21no—
272C47⋊C8—21no—
273C47⋊C8—21no—
274C47⋊C8—21no—
275C47⋊C8—41no—
276C47⋊C8—41no—
277C47⋊C8—41no—
278#17922—471nomaximal, Sylow
279C22×C47—22no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47C2×C4×D411yescharacteristic
286C2×D47—21no—
287C2×D47—22no—
288C2×D47—21no—
289C2×D47—21no—
290C2×D47—41no—
291C2×D47—41no—
292C2×D47—41no—
293C2×D47—41no—
294C2×D47—41no—
295C2×D47—84no—
296C4×C47—21no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47C2×#13111yescharacteristic
300C4×C47C2×#13111yescharacteristic
301C4×C47#57611yescharacteristic
302C4×C47#57611yescharacteristic
303Dic47—21no—
304Dic47—21no—
305Dic47—21no—
306Dic47—41no—
307Dic47—41no—
308#3100—471no—
309#2981—471no—
310#2972—471no—
311#1586—471no—
312#1586—471no—
313#1581—471no—
314#1581—471no—
315#1580—471no—
316#1580—471no—
317C8×D8—471no—
318C8×D8D4711yescharacteristic, complemented
319#1572—471no—
320#1490—471no—
321#1484—471no—
322#1453—471no—
323C2×C47—42no—
324C2×C47—81no—
325C2×C47#292911yescharacteristic
326C2×C47#294811yescharacteristic
327C2×C47#295611yescharacteristic
328D47—41no—
329D47—42no—
330D47—81no—
331#532—471no—
332C2×C4×D4—471no—
333#480—471no—
334#480—471no—
335#474—471no—
336#474—471no—
337#459—471no—
338#459—471no—
339#447—471no—
340#447—471no—
341C4×D8—471no—
342C4×D8—471no—
343C4×D8—471no—
344C4×D8C2×D4711yescharacteristic
345#436—471no—
346#436—471no—
347#435—941no—
348#435—941no—
349C8×D4—471no—
350C8×D4—471no—
351C8×D4—471no—
352C8×D4—471no—
353C8×D4—941no—
354C8×D4—941no—
355C8×D4C2×D4711yescharacteristic
356C8×D4C2×D4711yescharacteristic, complemented
357#432—471no—
358#431—471no—
359#431—471no—
360#431—471no—
361#408—941no—
362#408—941no—
363C2×C22⋊C8—941no—
364C2×C22⋊C8—941no—
365C4×M16—471no—
366#335—471no—
367#335C2×D4711yescharacteristic, complemented
368#334—471no—
369#334—471no—
370D4⋊C8—471no—
371D4⋊C8—471no—
372D4⋊C8—471no—
373D4⋊C8—471no—
374D4⋊C8—471no—
375D4⋊C8—471no—
376D4⋊C8C2×D4711yescharacteristic
377D4⋊C8C2×D4711yescharacteristic, complemented
378#322—471no—
379#322—471no—
380#322—471no—
381C82C2×D4711yescharacteristic, complemented
382C47#1792211yescharacteristic, complemented, Sylow
383C2×#41—941no—
384C22×D4—471no—
385C23×C4—941no—
386C2×D8—471no—
387C2×D8—471no—
388C2×D8—471no—
389C2×D8C4×D4711yescharacteristic
390C2×M16—941no—
391C2×M16—941no—
392C2×M16—941no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—941no—
396C22×C8—941no—
397C22×C8—941no—
398C22×C8—941no—
399C4⋊Q8—471no—
400#127—471no—
401#124—941no—
402#121—471no—
403#121—471no—
404#121—941no—
405C4×D4—471no—
406C4×D4—471no—
407C4×D4—471no—
408C4×D4—471no—
409C4×D4—941no—
410C4×D4—941no—
411C4×D4—941no—
412C4×D4C22×D4711yescharacteristic
413C4×D4C22×D4711yescharacteristic
414C2×C4⋊C4—471no—
415C2×C22⋊C4—941no—
416C2×C42—471no—
417#107—471no—
418#107—471no—
419#107—471no—
420#107C4×D4711yescharacteristic
421C4⋊C8—471no—
422C4⋊C8—471no—
423C4⋊C8—471no—
424C4⋊C8—471no—
425C4⋊C8—471no—
426C4⋊C8—471no—
427C4⋊C8C22×D4711yescharacteristic
428C4⋊C8C22×D4711yescharacteristic
429#102—471no—
430#102—471no—
431#102—471no—
432#102—471no—
433#102—471no—
434#102—471no—
435#102C4×D4711yescharacteristic
436#102C4×D4711yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—471no—
440C22⋊C8—471no—
441C22⋊C8—471no—
442C22⋊C8—471no—
443C22⋊C8—941no—
444C22⋊C8—941no—
445C22⋊C8—941no—
446C22⋊C8—941no—
447C22⋊C8—941no—
448C22⋊C8—941no—
449C22⋊C8—941no—
450C22⋊C8—941no—
451#97—941no—
452#97—941no—
453C4×C8—471no—
454C4×C8—471no—
455C4×C8—471no—
456C4×C8—941no—
457C4×C8C22×D4711yescharacteristic
458C4×C8C22×D4711yescharacteristic
459C4×C8C22×D4711yescharacteristic
460C24—941no—
461#41—3761no—
462#41—3761no—
463C2×Q8—941no—
464C2×D4—471no—
465C2×D4—471no—
466C2×D4—941no—
467C2×D4—941no—
468C2×D4—941no—
469C2×D4—941no—
470C2×D4—942no—
471C2×D4—942no—
472C2×D4—941no—
473C2×D4C2×C4×D4711yescharacteristic
474C2×D4C2×C4×D4711yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—471no—
478C22×C4—471no—
479C22×C4—471no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4—941no—
485C22×C4—3761no—
486C22×C4—3761no—
487D8—22no—
488D8—942no—
489D8—942no—
490D8—942no—
491M16—3761no—
492M16—3761no—
493M16—1882no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—81no—
498C2×C8—81no—
499C2×C8—471no—
500C2×C8—471no—
501C2×C8—471no—
502C2×C8—471no—
503C2×C8—941no—
504C2×C8—941no—
505C2×C8—941no—
506C2×C8—3761no—
507C2×C8—3761no—
508C2×C8—3761no—
509C2×C8—3761no—
510C2×C8C2×C4×D4711yescharacteristic
511C2×C8C2×C4×D4711yescharacteristic
512C2×C8D4×D4711yescharacteristic
513C2×C8D4×D4711yescharacteristic
514C4⋊C4—471no—
515C4⋊C4—471no—
516C4⋊C4—941no—
517C4⋊C4—941no—
518C4⋊C4C2×C4×D4711yescharacteristic
519C4⋊C4C2×C4×D4711yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—941no—
523C22⋊C4—941no—
524C22⋊C4—941no—
525C22⋊C4—941no—
526C22⋊C4—941no—
527C22⋊C4—941no—
528C42—471no—
529C42—471no—
530C42—471no—
531C42C23×D4711yescharacteristic
532C23—21no—
533C23—21no—
534C23—471no—
535C23—944no—
536C23—941no—
537C23—941no—
538C23—3761no—
539C23—3761no—
540Q8—3761no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—472no—
545D4—944no—
546D4—941no—
547D4—941no—
548D4—941no—
549D4—3761no—
550D4—3761no—
551D4—3761no—
552D4—3761no—
553D4#1309403012yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—471no—
561C2×C4—471no—
562C2×C4—471no—
563C2×C4—941no—
564C2×C4—941no—
565C2×C4—941no—
566C2×C4—941no—
567C2×C4—941no—
568C2×C4—941no—
569C2×C4—3761no—
570C2×C4—3761no—
571C2×C4—3761no—
572C2×C4—1881no—
573C2×C4—1881no—
574C2×C4—1881no—
575C2×C4—1881no—
576C2×C4—1881no—
577C2×C4C22×C4×D4711yescharacteristic
578C2×C4C2×D4×D4711yescharacteristic
579C2×C4#41×D4711yescharacteristic
580C8—22no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—941no—
588C8—941no—
589C8—941no—
590C8—941no—
591C8—1881no—
592C8—1881no—
593C8—1881no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—941no—
601C22—941no—
602C22—941no—
603C22—942no—
604C22—3764no—
605C22—1881no—
606C22—1881no—
607C22—1881no—
608C22—1881no—
609C22—1881no—
610C22C4×D4×D4711yescharacteristic
611C4—21no—
612C4—41no—
613C4—41no—
614C4—941no—
615C4—941no—
616C4—941no—
617C4—1881no—
618C4—1881no—
619C4#131×D4711yescharacteristic
620C4C2×#1309403011yescharacteristic
621C4#1568992411yescharacteristic
622C4#1568992511yescharacteristic
623C2—42no—
624C2—81no—
625C2—3761no—
626C2—1881no—
627C2—1882no—
628C2#2025207711yescharacteristic
629C2#2025223511yescharacteristic
630C2#2025229311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC8×D8×C47C2
socleC22×C47C2×C4×D4
prime radical#20253386C2
cosocleC42×C47C24
hypercenterC8×D8D47
hypocenterC47#17922
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #20252462C2semidirect
3. #20252409C2semidirect
4. #20242255C2semidirect
5. #20242249C2semidirect
6. #20242218C2semidirect
7. #20242216C2semidirect
8. #20242210C2semidirect
9. #20242210C2semidirect
10. C8×D376C2semidirect
11. #20242167C2semidirect
12. #20241829C2semidirect
13. #20241803C2semidirect
14. #20241682C2semidirect
15. C8×D8×C47C2semidirect
29. #15689201C22semidirect
30. #15689200C22semidirect
34. C8×D188C22semidirect
48. #15688876C22semidirect
49. #15688873C22semidirect
50. #15688873C22semidirect
52. #15688852C22semidirect
54. D4⋊(C47⋊C8)C22semidirect
56. #15688850C22semidirect
57. #15688845C22semidirect
58. #15688845C22semidirect
59. #15688844C22semidirect
62. C8×D4×C47C22semidirect
63. C47×#335C22semidirect
65. C47×D4⋊C8C22semidirect
66. C82×C47C22semidirect
318. C8×D8D47semidirect
356. C8×D4C2×D47semidirect
367. #335C2×D47semidirect
377. D4⋊C8C2×D47semidirect
381. C82C2×D47semidirect
382. C47#17922semidirect

Maximal subgroups

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

subgroupindex
#202533862
#202524622
#202524092
#202422552
#202422492
#202422182
#202422162
#202422102
C8×D3762
#202421672
#202418292
#202418032
#202416822
C8×D8×C472
#1792247