Finite Group Databasebeta

← #26223675

Subgroups — #26223675

Order 12032.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253299C211yesmaximal, characteristic
2#20252089C211yesmaximal, characteristic
3#20251804C211yesmaximal, characteristic, complemented
4#20244039C211yesmaximal, characteristic, complemented
5#20244038C211yesmaximal, characteristic, complemented
6#20243986C211yesmaximal, characteristic, complemented
7#20243985C211yesmaximal, characteristic, complemented
8#20243687C211yesmaximal, characteristic
9#20243594C211yesmaximal, characteristic, complemented
10#20243486C211yesmaximal, characteristic, complemented
11#20243272C211yesmaximal, characteristic, complemented
12#20243268C211yesmaximal, characteristic, complemented
13#20243223C211yesmaximal, characteristic, complemented
14#20243173C211yesmaximal, characteristic, complemented
15C47×#1765C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C2×M16×D47C2211yescharacteristic
18#15689630C2211yescharacteristic
19#117×D47C2211yescharacteristic
20#15689463C411yescharacteristic, complemented
21#15689462C411yescharacteristic, complemented
22#15689457C411yescharacteristic, complemented
23#15689452C411yescharacteristic, complemented
24#15689446C411yescharacteristic, complemented
25#15689445C411yescharacteristic, complemented
26#15689440C411yescharacteristic, complemented
27#15689435C411yescharacteristic, complemented
28#15689199—21no—
29#15689199—21no—
30#15689194—21no—
31#15689194—21no—
32C2×#13093960C2211yescharacteristic
33C2×#13093959C2211yescharacteristic
34#15689161C2211yescharacteristic
35#15689159C2211yescharacteristic
36#15689151C2211yescharacteristic
37C2×#13093951C2211yescharacteristic
38#15689119C2211yescharacteristic
39#15689090C2211yescharacteristic
40#15689086C2211yescharacteristic
41C2×(C2×D47)⋊C8C2211yescharacteristic
42#15689081C2211yescharacteristic
43#15689080—21no—
44#15689079C2211yescharacteristic
45#15689078C2211yescharacteristic
46#15689078C2211yescharacteristic
47#15689077—21no—
48#15689075—21no—
49C4×#10625324—21no—
50C2×C8×Dic47C2211yescharacteristic
51C4×(C2×D47)⋊C4C2211yescharacteristic
52#15688887C2211yescharacteristic
53#15688884C2211yescharacteristic
54#15688884C2211yescharacteristic
55#15688883C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688882C2211yescharacteristic
58#15688878C2211yescharacteristic
59#15688877C2211yescharacteristic
60C2×#131×C47C2211yescharacteristic
61C2×#104×C47C2211yescharacteristic
62C47×#416C2211yescharacteristic
63C47×#405C2211yescharacteristic
64C2×#97×C47C2211yescharacteristic
65C47×#341C2211yescharacteristic
66C47×#339C2211yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625329C2311yescharacteristic
69C2×#10625329C2311yescharacteristic
70C2×#10625324—21no—
71C2×#10625324—22no—
72C2×#10625324—22no—
73C2×#10625324D411yescharacteristic
74C2×#10625324D411yescharacteristic
75C2×#10625324D411yescharacteristic
76C2×#10625324D411yescharacteristic
77M16×D47—22no—
78M16×D47—22no—
79C22×C47⋊C8C2311yescharacteristic
80C22×C47⋊C8C2311yescharacteristic
81C2×C8×D47—21no—
82#13094005—21no—
83#13094000C2×C411yescharacteristic
84#13094000C2×C411yescharacteristic
85#13093995C2×C411yescharacteristic
86#13093995C2×C411yescharacteristic
87#13093992—21no—
88C4×C22⋊D47—21no—
89C4×C22⋊D47—21no—
90#13093983C2311yescharacteristic
91#13093983C2311yescharacteristic
92#13093982C2×C411yescharacteristic
93#13093982C2×C411yescharacteristic
94#13093981—21no—
95#13093980—21no—
96C4⋊C4×D47C2×C411yescharacteristic
97C4⋊C4×D47C2×C411yescharacteristic
98C2×(C2×D47)⋊C4—21no—
99C22⋊C4×D47—21no—
100C2×C4×Dic47C2311yescharacteristic
101C42×D47—21no—
102#13093960—22no—
103#13093959—22no—
104#13093958C2×C411yescharacteristic
105#13093958C2×C411yescharacteristic
106#13093957C2×C411yescharacteristic
107#13093957C2×C411yescharacteristic
108#13093956C2×C411yescharacteristic
109#13093956C2×C411yescharacteristic
110#13093955C2×C411yescharacteristic
111#13093955C2×C411yescharacteristic
112Dic47⋊C8—21no—
113Dic47⋊C8—21no—
114#13093951—22no—
115#13093948C2×C411yescharacteristic
116#13093948C2×C411yescharacteristic
117#13093945C2×C411yescharacteristic
118#13093945C2×C411yescharacteristic
119C22⋊(C47⋊C8)—21no—
120C22⋊(C47⋊C8)—21no—
121(C2×D47)⋊C8—21no—
122(C2×D47)⋊C8—21no—
123(C2×D47)⋊C8C2×C411yescharacteristic
124(C2×D47)⋊C8C2×C411yescharacteristic
125(C2×D47)⋊C8C2×C411yescharacteristic
126(C2×D47)⋊C8C2×C411yescharacteristic
127#13093935—21no—
128#13093934—21no—
129#13093934—21no—
130#13093934—21no—
131C4×C47⋊C8—21no—
132C8×Dic47—21no—
133C8×Dic47—21no—
134C8×Dic47—22no—
135C8×Dic47—21no—
136C47⋊#95—21no—
137C2×#41×C47C2311yescharacteristic
138#131×C47—22no—
139#131×C47—22no—
140C2×M16×C47—21no—
141C2×M16×C47C2311yescharacteristic
142C2×M16×C47C2311yescharacteristic
143C22×C8×C47—21no—
144C22×C8×C47C2311yescharacteristic
145C22×C8×C47C2311yescharacteristic
146#117×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148#104×C47—22no—
149#103×C47C2×C411yescharacteristic
150#103×C47C2×C411yescharacteristic
151#102×C47C2×C411yescharacteristic
152#102×C47C2×C411yescharacteristic
153#97×C47—21no—
154#97×C47—22no—
155C4×C8×C47—21no—
156C23×D47#4111yescharacteristic
157#41×C47—21no—
158#41×C47—21no—
159#41×C47—21no—
160#41×C47—21no—
161C2×Q8×C47C22×C411yescharacteristic
162C2×D4×C47—21no—
163C2×D4×C47C22×C411yescharacteristic
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47C2411yescharacteristic
167C2×C22⋊D47—21no—
168C2×C22⋊D47—21no—
169C22×Dic47—21no—
170C22×Dic47#4111yescharacteristic
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47C22×C411yescharacteristic
178C2×C4×D47C22×C411yescharacteristic
179C2×C4×D47C2×D411yescharacteristic
180C2×C4×D47C2×D411yescharacteristic
181M16×C47—21no—
182M16×C47—21no—
183M16×C47—21no—
184M16×C47—42no—
185M16×C47#4112yes—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—42no—
191C2×C8×C47C22×C411yescharacteristic
192C2×C8×C47C22×C411yescharacteristic
193C2×C8×C47C2×D411yescharacteristic
194C2×C8×C47C2×D411yescharacteristic
195C2×C8×C47#4112yes—
196C2×C8×C47#4112yes—
197C4⋊C4×C47C22×C411yescharacteristic
198C4⋊C4×C47C22×C411yescharacteristic
199C22⋊C4×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C22⋊Dic47—21no—
204C22⋊Dic47—21no—
205C22⋊Dic47—21no—
206C22⋊Dic47—21no—
207(C2×D47)⋊C4—21no—
208(C2×D47)⋊C4—21no—
209(C2×D47)⋊C4—21no—
210(C2×D47)⋊C4—21no—
211(C2×D47)⋊C4—42no—
212C4⋊Dic47C22×C411yescharacteristic
213C4⋊Dic47C22×C411yescharacteristic
214C4⋊Dic47C22×C411yescharacteristic
215C4⋊Dic47C22×C411yescharacteristic
216Dic47⋊C4—21no—
217Dic47⋊C4—21no—
218Dic47⋊C4—21no—
219Dic47⋊C4—21no—
220C4×Dic47—21no—
221C4×Dic47—21no—
222C4×Dic47—21no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226#10625329—21no—
227#10625329—21no—
228#10625329—21no—
229#10625329#4112yes—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8C22×C411yescharacteristic
237C2×C47⋊C8C22×C411yescharacteristic
238C2×C47⋊C8C2×D411yescharacteristic
239C2×C47⋊C8C2×D411yescharacteristic
240#10625324—24no—
241#10625324—22no—
242#10625324—22no—
243#10625324—22no—
244#10625324—22no—
245C8×D47—24no—
246C23×C47—21no—
247C23×C47C2×#4111yescharacteristic
248C22×D47—21no—
249C22×D47—21no—
250C22×D47—41no—
251C22×D47—41no—
252C22×D47C4×D411yescharacteristic
253C22×D47C4×D411yescharacteristic
254Q8×C47—21no—
255Q8×C47—21no—
256D4×C47—21no—
257D4×C47—21no—
258D4×C47—41no—
259D4×C47—41no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47C23×C411yescharacteristic
269C2×C4×C47C22×D411yescharacteristic
270C2×C4×C47C2×#4111yescharacteristic
271C2×C4×C47C2×#4111yescharacteristic
272C2×C4×C47C2×#4111yescharacteristic
273C2×C4×C47C2×#4111yescharacteristic
274C22⋊D47—81no—
275C22⋊D47—81no—
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—22no—
279C2×Dic47—21no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—41no—
284C2×Dic47—41no—
285C2×Dic47C4×D411yescharacteristic
286C2×Dic47C4×D411yescharacteristic
287C4×D47—21no—
288C4×D47—21no—
289C4×D47—21no—
290C4×D47—21no—
291C4×D47—21no—
292C4×D47—21no—
293C4×D47—21no—
294C4×D47—21no—
295C4×D47—81no—
296C4×D47—81no—
297C8×C47—21no—
298C8×C47—21no—
299C8×C47—22no—
300C8×C47—41no—
301C8×C47#12312yes—
302C8×C47#12312yes—
303C47⋊C8—21no—
304C47⋊C8—21no—
305C47⋊C8—21no—
306C47⋊C8—21no—
307C47⋊C8—22no—
308C47⋊C8—41no—
309#21594—471nomaximal, Sylow
310C22×C47—21no—
311C22×C47—21no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47—41no—
315C22×C47C2×C4×D411yescharacteristic
316C22×C47#52911yescharacteristic
317C22×C47#52911yescharacteristic
318C2×D47—21no—
319C2×D47—21no—
320C2×D47—21no—
321C2×D47—21no—
322C2×D47—21no—
323C2×D47—21no—
324C2×D47—81no—
325C2×D47—81no—
326C4×C47—41no—
327C4×C47—41no—
328C4×C47—41no—
329C4×C47—81no—
330C4×C47C4×#4111yescharacteristic
331C4×C47C4×#4111yescharacteristic
332C4×C47C2×#12311yescharacteristic
333C4×C47#52511yescharacteristic
334Dic47—21no—
335Dic47—21no—
336Dic47—42no—
337Dic47—41no—
338Dic47—41no—
339Dic47—41no—
340Dic47—41no—
341#3091—471no—
342#2930—471no—
343#2873—471no—
344#1929—471no—
345#1929—471no—
346#1922—471no—
347#1922—471no—
348#1871—471no—
349#1855—471no—
350#1826—471no—
351#1773—471no—
352#1772—471no—
353#1765D4711yescharacteristic, complemented
354#1764—471no—
355#1753—471no—
356C2×C47—21no—
357C2×C47—21no—
358C2×C47—81no—
359C2×C47C4×#12311yescharacteristic
360C2×C47#295611yescharacteristic
361C2×C47#295711yescharacteristic
362D47—41no—
363D47—41no—
364C2×#131C2×D4711yescharacteristic
365C22×M16—471no—
366C22×M16—471no—
367#525—471no—
368C2×#117—471no—
369#485—471no—
370#485—471no—
371#484—471no—
372#483—471no—
373#482—471no—
374#482—471no—
375#481—471no—
376#480—471no—
377#436—941no—
378#436—941no—
379#435—941no—
380#435—941no—
381C2×#108—471no—
382C2×#108—471no—
383#427—471no—
384#427—471no—
385#424—471no—
386C2×#104—471no—
387C2×#104C2×D4711yescharacteristic
388#416—471no—
389#416C2×D4711yescharacteristic
390#408—471no—
391#407—471no—
392C2×C22⋊C8—471no—
393#405—471no—
394#405—471no—
395#405—471no—
396#405—471no—
397#405—941no—
398#405—941no—
399#405C2×D4711yescharacteristic
400C4×M16—941no—
401C4×M16—941no—
402C2×#97C2×D4711yescharacteristic
403C2×C4×C8—471no—
404C4×C22⋊C4—471no—
405#341—471no—
406#341C2×D4711yescharacteristic
407#339—471no—
408#339—471no—
409#339—471no—
410#339—471no—
411#339—471no—
412#339C2×D4711yescharacteristic
413#336—471no—
414#336—471no—
415C47#2159411yescharacteristic, complemented, Sylow
416C2×#41C22×D4711yescharacteristic
417C23×C4—471no—
418#131—22no—
419#131—22no—
420C2×M16—21no—
421C2×M16—471no—
422C2×M16—471no—
423C2×M16—471no—
424C2×M16—471no—
425C2×M16—471no—
426C2×M16—471no—
427C2×M16—941no—
428C2×M16—942no—
429C2×M16—942no—
430C2×M16—942no—
431C2×M16—942no—
432C2×M16C22×D4711yescharacteristic
433C2×M16C22×D4711yescharacteristic
434C22×C8—21no—
435C22×C8—471no—
436C22×C8—471no—
437C22×C8—941no—
438C22×C8C22×D4711yescharacteristic
439C22×C8C22×D4711yescharacteristic
440#123—941no—
441C22⋊Q8—471no—
442C22⋊Q8—471no—
443#121—471no—
444#121—471no—
445#120—941no—
446C4×D4—941no—
447C4×D4—941no—
448#117—471no—
449#117—471no—
450#117—471no—
451#117—471no—
452#117—941no—
453#117—941no—
454#117C22×D4711yescharacteristic
455C2×C4⋊C4—471no—
456C2×C4⋊C4—471no—
457C2×C22⋊C4—941no—
458C2×C22⋊C4—941no—
459C2×C42—471no—
460C2×C42—941no—
461C2×C42C22×D4711yescharacteristic
462#108—942no—
463#108—942no—
464#107—471no—
465#107—471no—
466#107—471no—
467#107—471no—
468#106—471no—
469#106—471no—
470#106—471no—
471#106—471no—
472C4⋊C8—941no—
473C4⋊C8—941no—
474#104—22no—
475#104—942no—
476#103—471no—
477#103—471no—
478#103C4×D4711yescharacteristic
479#103C4×D4711yescharacteristic
480#102—471no—
481#102—471no—
482#102C4×D4711yescharacteristic
483#102C4×D4711yescharacteristic
484C22⋊C8—471no—
485C22⋊C8—471no—
486C22⋊C8—471no—
487C22⋊C8—471no—
488C22⋊C8—941no—
489C22⋊C8—941no—
490C22⋊C8—941no—
491C22⋊C8—941no—
492#97—21no—
493#97—22no—
494#97—941no—
495#97—941no—
496#97—941no—
497#97—941no—
498C4×C8—21no—
499C4×C8—941no—
500C4×C8—941no—
501C4×C8—942no—
502C4×C8—941no—
503C4×C8—941no—
504#95—941no—
505C24—471no—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C2×C4×D4711yescharacteristic
511C2×D4—21no—
512C2×D4—941no—
513C2×D4—941no—
514C2×D4C2×C4×D4711yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—471no—
518C22×C4—471no—
519C22×C4—471no—
520C22×C4—471no—
521C22×C4—471no—
522C22×C4—941no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—941no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—941no—
529C22×C4C23×D4711yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—42no—
534M16—472no—
535M16—944no—
536M16—941no—
537M16—942no—
538M16—942no—
539M16—942no—
540M16—942no—
541M16—941no—
542M16—941no—
543M16#1062535012yes—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—42no—
549C2×C8—471no—
550C2×C8—471no—
551C2×C8—471no—
552C2×C8—471no—
553C2×C8—944no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8—941no—
557C2×C8—941no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8C2×C4×D4711yescharacteristic
561C2×C8C2×C4×D4711yescharacteristic
562C2×C8#1062535012yes—
563C2×C8D4×D4711yescharacteristic
564C2×C8D4×D4711yescharacteristic
565C2×C8#1062535212yes—
566C4⋊C4—471no—
567C4⋊C4—471no—
568C4⋊C4—471no—
569C4⋊C4—471no—
570C4⋊C4—941no—
571C4⋊C4—941no—
572C4⋊C4—941no—
573C4⋊C4—941no—
574C4⋊C4C2×C4×D4711yescharacteristic
575C4⋊C4C2×C4×D4711yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—941no—
578C22⋊C4—941no—
579C22⋊C4—941no—
580C22⋊C4—941no—
581C22⋊C4—941no—
582C22⋊C4—941no—
583C22⋊C4—941no—
584C22⋊C4—941no—
585C22⋊C4—1882no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—941no—
590C42—941no—
591C42—941no—
592C42—941no—
593C42—941no—
594C42—941no—
595C23—21no—
596C23—471no—
597C23—471no—
598C23—941no—
599C23—941no—
600C23—1881no—
601C23—1881no—
602C23#41×D4711yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—3761no—
610D4—3761no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—471no—
620C2×C4—471no—
621C2×C4—941no—
622C2×C4—941no—
623C2×C4—941no—
624C2×C4—941no—
625C2×C4—941no—
626C2×C4—941no—
627C2×C4—941no—
628C2×C4—941no—
629C2×C4—941no—
630C2×C4—941no—
631C2×C4—942no—
632C2×C4—941no—
633C2×C4—941no—
634C2×C4—941no—
635C2×C4—941no—
636C2×C4—3761no—
637C2×C4—3761no—
638C2×C4—1881no—
639C2×C4—1881no—
640C2×C4C22×C4×D4711yescharacteristic
641C2×C4C2×D4×D4711yescharacteristic
642C2×C4#41×D4711yescharacteristic
643C2×C4C2×#1062535211yescharacteristic
644C2×C4C2×#1062535011yescharacteristic
645C2×C4C2×#1062535011yescharacteristic
646C8—21no—
647C8—21no—
648C8—22no—
649C8—41no—
650C8—941no—
651C8—941no—
652C8—941no—
653C8—941no—
654C8—942no—
655C8—1881no—
656C8#1309400612yes—
657C8#1309400612yes—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—941no—
664C22—941no—
665C22—941no—
666C22—941no—
667C22—941no—
668C22—941no—
669C22—3761no—
670C22—3761no—
671C22C4×D4×D4711yescharacteristic
672C22#1568965111yescharacteristic
673C22#1568965511yescharacteristic
674C4—41no—
675C4—41no—
676C4—41no—
677C4—81no—
678C4—941no—
679C4—941no—
680C4—1882no—
681C4—1881no—
682C4—1881no—
683C4—1881no—
684C4—1881no—
685C4C4×#1062535211yescharacteristic
686C4C4×#1062535011yescharacteristic
687C4C2×#1309400611yescharacteristic
688C4#1568963211yescharacteristic
689C2—21no—
690C2—21no—
691C2—81no—
692C2—1881no—
693C2—1881no—
694C2C4×#1309400611yescharacteristic
695C2#2025229611yescharacteristic
696C2#2025230211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1765C2
socleC22×C47C2×C4×D4
prime radical#15689630C22
cosocleC22×C4×C47C24
hypercenter#1765D47
hypocenterC47#21594
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
3. #20251804C2semidirect
4. #20244039C2semidirect
5. #20244038C2semidirect
6. #20243986C2semidirect
7. #20243985C2semidirect
9. #20243594C2semidirect
10. #20243486C2semidirect
11. #20243272C2semidirect
12. #20243268C2semidirect
13. #20243223C2semidirect
14. #20243173C2semidirect
15. C47×#1765C2semidirect
20. #15689463C4semidirect
21. #15689462C4semidirect
22. #15689457C4semidirect
23. #15689452C4semidirect
24. #15689446C4semidirect
25. #15689445C4semidirect
26. #15689440C4semidirect
27. #15689435C4semidirect
353. #1765D47semidirect
415. C47#21594semidirect

Maximal subgroups

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

subgroupindex
#202532992
#202520892
#202518042
#202440392
#202440382
#202439862
#202439852
#202436872
#202435942
#202434862
#202432722
#202432682
#202432232
#202431732
C47×#17652
#2159447