Finite Group Databasebeta

← C139×#9041 #48003637

Subgroups — C139×#9041 #48003637

Order 35584.

1050 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C139C211yesmaximal, characteristic
2#2325×C139C211yesmaximal, characteristic, complemented
3#1786×C139C211yesmaximal, characteristic, complemented
4C2×#327×C139C211yesmaximal, characteristic, complemented
5#1438×C139C211yesmaximal, characteristic, complemented
6#1294×C139C211yesmaximal, characteristic, complemented
7#1280×C139C211yesmaximal, characteristic, complemented
8C23×D4×C139C2211yescharacteristic
9C22×D8×C139—21no—
10C2×#121×C139C2211yescharacteristic
11C2×C4×D4×C139—21no—
12C22×C22⋊C4×C139—21no—
13C22×C22⋊C4×C139—21no—
14#447×C139—22no—
15#447×C139C414yescomplemented
16C2×#102×C139—21no—
17C2×#102×C139—21no—
18C2×#102×C139—21no—
19C2×C22⋊C8×C139C2211yescharacteristic
20C2×C22⋊C8×C139C2211yescharacteristic
21#388×C139—21no—
22#387×C139—21no—
23#386×C139—21no—
24#386×C139—21no—
25#385×C139—21no—
26#380×C139C2211yescharacteristic
27C2×#95×C139C2211yescharacteristic
28C2×#95×C139C2211yescharacteristic
29#327×C139—22no—
30C25×C139—21no—
31C22×D4×C139—21no—
32C22×D4×C139—21no—
33C22×D4×C139—21no—
34C22×D4×C139—21no—
35C22×D4×C139—21no—
36C22×D4×C139—21no—
37C22×D4×C139—42no—
38C22×D4×C139—42no—
39C22×D4×C139C2×C412yescomplemented
40C22×D4×C139D411yescharacteristic
41C23×C4×C139—21no—
42C23×C4×C139—21no—
43C23×C4×C139D411yescharacteristic
44C23×C4×C139D411yescharacteristic
45C23×C4×C139C2311yescharacteristic
46C2×D8×C139—24no—
47C2×D8×C139—42no—
48C2×D8×C139—42no—
49C22×C8×C139—21no—
50C22×C8×C139—21no—
51#121×C139—21no—
52#121×C139—21no—
53#121×C139C2×C412yes—
54#121×C139D412yes—
55C4×D4×C139—42no—
56C4×D4×C139—42no—
57C2×C4⋊C4×C139—21no—
58C2×C4⋊C4×C139D411yescharacteristic
59C2×C4⋊C4×C139D411yescharacteristic
60C2×C4⋊C4×C139D411yescharacteristic
61C2×C22⋊C4×C139—21no—
62C2×C22⋊C4×C139—21no—
63C2×C22⋊C4×C139—21no—
64C2×C22⋊C4×C139—21no—
65C2×C22⋊C4×C139—21no—
66C2×C22⋊C4×C139—42no—
67C2×C22⋊C4×C139—42no—
68C2×C22⋊C4×C139—42no—
69C2×C22⋊C4×C139—42no—
70C2×C22⋊C4×C139—42no—
71C2×C22⋊C4×C139—42no—
72C2×C42×C139—21no—
73#102×C139—24no—
74#102×C139—42no—
75#102×C139—42no—
76C22⋊C8×C139—21no—
77C22⋊C8×C139—21no—
78C22⋊C8×C139—21no—
79C22⋊C8×C139C2×C412yescomplemented
80#95×C139—21no—
81#95×C139—21no—
82#95×C139—21no—
83#95×C139—21no—
84#95×C139—21no—
85#95×C139—21no—
86#95×C139—21no—
87C24×C139—22no—
88C24×C139—22no—
89C24×C139—22no—
90C24×C139—21no—
91C24×C139—41no—
92C24×C139—41no—
93C24×C139—41no—
94C24×C139—41no—
95C24×C139—41no—
96C24×C139—41no—
97C24×C139—41no—
98C24×C139—41no—
99C24×C139—41no—
100C24×C139—41no—
101C24×C139—41no—
102C24×C139—41no—
103C24×C139C2×D411yescharacteristic
104C2×D4×C139—22no—
105C2×D4×C139—22no—
106C2×D4×C139—22no—
107C2×D4×C139—22no—
108C2×D4×C139—22no—
109C2×D4×C139—22no—
110C2×D4×C139—22no—
111C2×D4×C139—22no—
112C2×D4×C139—21no—
113C2×D4×C139—41no—
114C2×D4×C139—41no—
115C2×D4×C139—41no—
116C2×D4×C139—41no—
117C2×D4×C139—41no—
118C2×D4×C139—41no—
119C2×D4×C139—44no—
120C2×D4×C139—44no—
121C2×D4×C139—44no—
122C2×D4×C139—44no—
123C2×D4×C139—41no—
124C2×D4×C139—41no—
125C2×D4×C139—41no—
126C2×D4×C139—41no—
127C2×D4×C139—41no—
128C2×D4×C139—41no—
129C2×D4×C139C22⋊C412yescomplemented
130C22×C4×C139—21no—
131C22×C4×C139—21no—
132C22×C4×C139—21no—
133C22×C4×C139—22no—
134C22×C4×C139—21no—
135C22×C4×C139—21no—
136C22×C4×C139—21no—
137C22×C4×C139—21no—
138C22×C4×C139—21no—
139C22×C4×C139—41no—
140C22×C4×C139—41no—
141C22×C4×C139—42no—
142C22×C4×C139—41no—
143C22×C4×C139—41no—
144C22×C4×C139—41no—
145C22×C4×C139—41no—
146C22×C4×C139—41no—
147C22×C4×C139—41no—
148C22×C4×C139—41no—
149C22×C4×C139—41no—
150C22×C4×C139—41no—
151C22×C4×C139—41no—
152C22×C4×C139—81no—
153C22×C4×C139—81no—
154C22×C4×C139D812yescomplemented
155C22×C4×C139C22×C411yescharacteristic
156C22×C4×C139C2×D411yescharacteristic
157C22×C4×C139C2×D411yescharacteristic
158C22×C4×C139C2×D411yescharacteristic
159C22×C4×C139#4111yescharacteristic
160C22×C4×C139#4111yescharacteristic
161D8×C139—48no—
162C2×C8×C139—22no—
163C2×C8×C139—41no—
164C2×C8×C139—41no—
165C2×C8×C139—41no—
166C2×C8×C139—41no—
167C2×C8×C139—41no—
168C4⋊C4×C139—21no—
169C4⋊C4×C139—41no—
170C4⋊C4×C139—41no—
171C4⋊C4×C139—42no—
172C4⋊C4×C139C22⋊C412yescomplemented
173C22⋊C4×C139—22no—
174C22⋊C4×C139—22no—
175C22⋊C4×C139—42no—
176C22⋊C4×C139—48no—
177C22⋊C4×C139—48no—
178C22⋊C4×C139—41no—
179C22⋊C4×C139—41no—
180C22⋊C4×C139—81no—
181C22⋊C4×C139—81no—
182C42×C139—42no—
183C23×C139—21no—
184C23×C139—21no—
185C23×C139—21no—
186C23×C139—21no—
187C23×C139—24no—
188C23×C139—22no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—42no—
192C23×C139—42no—
193C23×C139—42no—
194C23×C139—42no—
195C23×C139—42no—
196C23×C139—42no—
197C23×C139—42no—
198C23×C139—42no—
199C23×C139—42no—
200C23×C139—42no—
201C23×C139—42no—
202C23×C139—42no—
203C23×C139—42no—
204C23×C139—42no—
205C23×C139—41no—
206C23×C139—41no—
207C23×C139—41no—
208C23×C139—41no—
209C23×C139—41no—
210C23×C139—41no—
211C23×C139—42no—
212C23×C139—42no—
213C23×C139—81no—
214C23×C139—81no—
215C23×C139—81no—
216C23×C139—81no—
217C23×C139—81no—
218C23×C139—81no—
219C23×C139—81no—
220C23×C139—81no—
221C23×C139—81no—
222C23×C139—81no—
223C23×C139—81no—
224C23×C139—81no—
225C23×C139—81no—
226C23×C139—81no—
227C23×C139—81no—
228C23×C139—81no—
229C23×C139C4×D411yescharacteristic
230C23×C139#12011yescharacteristic
231C23×C139#12111yescharacteristic
232C23×C139C2×D811yescharacteristic
233C23×C139#13511yescharacteristic
234C23×C139AGL(1,ℤ/8)11yescharacteristic
235C23×C139AGL(1,ℤ/8)11yescharacteristic
236D4×C139—24no—
237D4×C139—24no—
238D4×C139—42no—
239D4×C139—42no—
240D4×C139—42no—
241D4×C139—42no—
242D4×C139—42no—
243D4×C139—42no—
244D4×C139—42no—
245D4×C139—42no—
246D4×C139—42no—
247D4×C139—42no—
248D4×C139—42no—
249D4×C139—81no—
250C2×C4×C139—21no—
251C2×C4×C139—21no—
252C2×C4×C139—21no—
253C2×C4×C139—21no—
254C2×C4×C139—22no—
255C2×C4×C139—22no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—41no—
263C2×C4×C139—41no—
264C2×C4×C139—42no—
265C2×C4×C139—42no—
266C2×C4×C139—42no—
267C2×C4×C139—42no—
268C2×C4×C139—42no—
269C2×C4×C139—41no—
270C2×C4×C139—41no—
271C2×C4×C139—41no—
272C2×C4×C139—41no—
273C2×C4×C139—41no—
274C2×C4×C139—41no—
275C2×C4×C139—41no—
276C2×C4×C139—41no—
277C2×C4×C139—41no—
278C2×C4×C139—81no—
279C2×C4×C139—84no—
280C2×C4×C139—81no—
281C2×C4×C139—81no—
282C2×C4×C139—81no—
283C2×C4×C139—81no—
284C2×C4×C139—81no—
285C2×C4×C139C2×C22⋊C411yescharacteristic
286C2×C4×C139C4×D411yescharacteristic
287C2×C4×C139#12111yescharacteristic
288C2×C4×C139#12311yescharacteristic
289C8×C139—42no—
290C8×C139—81no—
291C22×C139—21no—
292C22×C139—21no—
293C22×C139—21no—
294C22×C139—21no—
295C22×C139—21no—
296C22×C139—21no—
297C22×C139—21no—
298C22×C139—21no—
299C22×C139—21no—
300C22×C139—21no—
301C22×C139—21no—
302C22×C139—21no—
303C22×C139—44no—
304C22×C139—44no—
305C22×C139—42no—
306C22×C139—42no—
307C22×C139—44no—
308C22×C139—42no—
309C22×C139—82no—
310C22×C139—82no—
311C22×C139—82no—
312C22×C139—82no—
313C22×C139—82no—
314C22×C139—82no—
315C22×C139—81no—
316C22×C139—82no—
317C22×C139—81no—
318C22×C139—82no—
319C22×C139—81no—
320C22×C139—82no—
321C22×C139—81no—
322C22×C139—82no—
323C22×C139—82no—
324C22×C139—82no—
325C22×C139#38611yescharacteristic
326C22×C139C4×D811yescharacteristic
327C22×C139#44211yescharacteristic
328C22×C139#44711yescharacteristic
329C22×C139#44911yescharacteristic
330C22×C139#45311yescharacteristic
331C22×C139#45411yescharacteristic
332C22×C139B(4,𝔽2)11yescharacteristic
333C22×C139B(4,𝔽2)11yescharacteristic
334C22×C139#45911yescharacteristic
335C22×C139#46311yescharacteristic
336C4×C139—21no—
337C4×C139—21no—
338C4×C139—21no—
339C4×C139—21no—
340C4×C139—42no—
341C4×C139—42no—
342C4×C139—82no—
343C4×C139—81no—
344C4×C139—81no—
345C4×C139—81no—
346C2×C139—21no—
347C2×C139—21no—
348C2×C139—21no—
349C2×C139—21no—
350C2×C139—82no—
351C2×C139—84no—
352C2×C139#159511yescharacteristic
353C2×C139#159711yescharacteristic
354C2×C139#159811yescharacteristic
355C2×C139#160011yescharacteristic
356C2×C139#187911yescharacteristic
357C2×C139#188311yescharacteristic
358C2×C139#188911yescharacteristic
359#9041C13911yesmaximal, characteristic, direct product factor, Sylow
360C139#904111yescharacteristic, direct product factor, Sylow
361C2×#447C2×C13911yescharacteristic
362#2325C2×C13911yescharacteristic, complemented
363#1786C2×C13911yescharacteristic, complemented
364C2×#327C2×C13911yescharacteristic, complemented
365#1438C2×C13911yescharacteristic, complemented
366#1294C2×C13911yescharacteristic, complemented
367#1280C2×C13911yescharacteristic, complemented
368C23×D4C22×C13911yescharacteristic
369C22×D8—21no—
370C2×#121C22×C13911yescharacteristic
371C2×C4×D4—21no—
372C22×C22⋊C4—21no—
373C22×C22⋊C4—21no—
374#447—22no—
375#447C4×C13914yescomplemented
376C2×#102—21no—
377C2×#102—21no—
378C2×#102—21no—
379C2×C22⋊C8C22×C13911yescharacteristic
380C2×C22⋊C8C22×C13911yescharacteristic
381#388—21no—
382#387—21no—
383#386—21no—
384#386—21no—
385#385—21no—
386#380C22×C13911yescharacteristic
387C2×#95C22×C13911yescharacteristic
388C2×#95C22×C13911yescharacteristic
389#327—22no—
390C25—21no—
391C22×D4—21no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—42no—
398C22×D4—42no—
399C22×D4C2×C4×C13912yescomplemented
400C22×D4D4×C13911yescharacteristic
401C23×C4—21no—
402C23×C4—21no—
403C23×C4D4×C13911yescharacteristic
404C23×C4D4×C13911yescharacteristic
405C23×C4C23×C13911yescharacteristic
406C2×D8—24no—
407C2×D8—42no—
408C2×D8—42no—
409C22×C8—21no—
410C22×C8—21no—
411#121—21no—
412#121—21no—
413#121C2×C4×C13912yes—
414#121D4×C13912yes—
415C4×D4—42no—
416C4×D4—42no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4D4×C13911yescharacteristic
419C2×C4⋊C4D4×C13911yescharacteristic
420C2×C4⋊C4D4×C13911yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C42—21no—
433#102—24no—
434#102—42no—
435#102—42no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8C2×C4×C13912yescomplemented
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24—41no—
463C24C2×D4×C13911yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4C22⋊C4×C13912yescomplemented
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4D8×C13912yescomplemented
515C22×C4C22×C4×C13911yescharacteristic
516C22×C4C2×D4×C13911yescharacteristic
517C22×C4C2×D4×C13911yescharacteristic
518C22×C4C2×D4×C13911yescharacteristic
519C22×C4#41×C13911yescharacteristic
520C22×C4#41×C13911yescharacteristic
521D8—48no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—42no—
532C4⋊C4C22⋊C4×C13912yescomplemented
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—42no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C42—42no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—24no—
548C23—22no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—81no—
574C23—81no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23C4×D4×C13911yescharacteristic
590C23#120×C13911yescharacteristic
591C23#121×C13911yescharacteristic
592C23C2×D8×C13911yescharacteristic
593C23#135×C13911yescharacteristic
594C23AGL(1,ℤ/8)×C13911yescharacteristic
595C23AGL(1,ℤ/8)×C13911yescharacteristic
596D4—24no—
597D4—24no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—42no—
608D4—42no—
609D4—81no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—81no—
639C2×C4—84no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4C2×C22⋊C4×C13911yescharacteristic
646C2×C4C4×D4×C13911yescharacteristic
647C2×C4#121×C13911yescharacteristic
648C2×C4#123×C13911yescharacteristic
649C8—42no—
650C8—81no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—44no—
664C22—44no—
665C22—42no—
666C22—42no—
667C22—44no—
668C22—42no—
669C22—82no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—81no—
676C22—82no—
677C22—82no—
678C22—81no—
679C22—82no—
680C22—81no—
681C22—82no—
682C22—81no—
683C22—82no—
684C22—82no—
685C22#386×C13911yescharacteristic
686C22C4×D8×C13911yescharacteristic
687C22#442×C13911yescharacteristic
688C22#447×C13911yescharacteristic
689C22#449×C13911yescharacteristic
690C22#453×C13911yescharacteristic
691C22#454×C13911yescharacteristic
692C22B(4,𝔽2)×C13911yescharacteristic
693C22B(4,𝔽2)×C13911yescharacteristic
694C22#459×C13911yescharacteristic
695C22#463×C13911yescharacteristic
696C4—21no—
697C4—21no—
698C4—21no—
699C4—21no—
700C4—42no—
701C4—42no—
702C4—82no—
703C4—81no—
704C4—81no—
705C4—81no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—21no—
710C2—84no—
711C2—82no—
712C2#1595×C13911yescharacteristic
713C2#1597×C13911yescharacteristic
714C2#1598×C13911yescharacteristic
715C2#1600×C13911yescharacteristic
716C2#1879×C13911yescharacteristic
717C2#1883×C13911yescharacteristic
718C2#1889×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#447×C139C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2325×C139C2semidirect
3. #1786×C139C2semidirect
4. C2×#327×C139C2semidirect
5. #1438×C139C2semidirect
6. #1294×C139C2semidirect
7. #1280×C139C2semidirect
15. #447×C139C4semidirect
39. C22×D4×C139C2×C4semidirect
79. C22⋊C8×C139C2×C4semidirect
129. C2×D4×C139C22⋊C4semidirect
154. C22×C4×C139D8semidirect
172. C4⋊C4×C139C22⋊C4semidirect
359. #9041C139direct (N × H)
360. C139#9041direct (N × H)
362. #2325C2×C139semidirect
363. #1786C2×C139semidirect
364. C2×#327C2×C139semidirect
365. #1438C2×C139semidirect
366. #1294C2×C139semidirect
367. #1280C2×C139semidirect
375. #447C4×C139semidirect
399. C22×D4C2×C4×C139semidirect
439. C22⋊C8C2×C4×C139semidirect
489. C2×D4C22⋊C4×C139semidirect
514. C22×C4D8×C139semidirect
532. C4⋊C4C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1392
#2325×C1392
#1786×C1392
C2×#327×C1392
#1438×C1392
#1294×C1392
#1280×C1392
#9041139