Finite Group Databasebeta

← C139×#9042 #48003638

Subgroups — C139×#9042 #48003638

Order 35584.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C139C211yesmaximal, characteristic
2#2329×C139C211yesmaximal, characteristic, complemented
3#1786×C139C211yesmaximal, characteristic
4C2×#328×C139C211yesmaximal, characteristic, complemented
5#1438×C139C211yesmaximal, characteristic
6#1294×C139C211yesmaximal, characteristic, complemented
7#1280×C139C211yesmaximal, characteristic, complemented
8C23×D4×C139C2211yescharacteristic
9C22×SD16×C139—21no—
10C2×C22⋊Q8×C139C2211yescharacteristic
11C22×C22⋊C4×C139—21no—
12C22×C22⋊C4×C139—21no—
13#450×C139—22no—
14#450×C139C414yescomplemented
15C2×#102×C139—21no—
16C2×#102×C139—21no—
17C2×#102×C139—21no—
18C2×C22⋊C8×C139C2211yescharacteristic
19C2×C22⋊C8×C139C2211yescharacteristic
20#391×C139—21no—
21#389×C139—21no—
22#387×C139—21no—
23#387×C139—21no—
24#385×C139—21no—
25#380×C139C2211yescharacteristic
26C4×C22⋊C4×C139—21no—
27C2×#95×C139C2211yescharacteristic
28C2×#95×C139C2211yescharacteristic
29#328×C139—22no—
30C25×C139—21no—
31C22×Q8×C139D411yescharacteristic
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×C412yes—
40C23×C4×C139—21no—
41C23×C4×C139D411yescharacteristic
42C23×C4×C139D411yescharacteristic
43C23×C4×C139C2311yescharacteristic
44C2×SD16×C139—24no—
45C2×SD16×C139—42no—
46C2×SD16×C139—42no—
47C22×C8×C139—21no—
48C22×C8×C139—21no—
49C22⋊Q8×C139—21no—
50C22⋊Q8×C139—21no—
51C22⋊Q8×C139C2×C412yes—
52C22⋊Q8×C139D412yes—
53C2×C4⋊C4×C139—21no—
54C2×C4⋊C4×C139—21no—
55C2×C4⋊C4×C139—21no—
56C2×C4⋊C4×C139D411yescharacteristic
57C2×C4⋊C4×C139D411yescharacteristic
58C2×C4⋊C4×C139D411yescharacteristic
59C2×C22⋊C4×C139—21no—
60C2×C22⋊C4×C139—21no—
61C2×C22⋊C4×C139—42no—
62C2×C22⋊C4×C139—42no—
63C2×C22⋊C4×C139—42no—
64C2×C22⋊C4×C139—42no—
65C2×C22⋊C4×C139—42no—
66C2×C22⋊C4×C139—42no—
67C2×C42×C139—21no—
68C2×C42×C139—21no—
69#102×C139—24no—
70#102×C139—42no—
71#102×C139—42no—
72C22⋊C8×C139—21no—
73C22⋊C8×C139—21no—
74C22⋊C8×C139—21no—
75C22⋊C8×C139C2×C412yes—
76#95×C139—21no—
77#95×C139—21no—
78#95×C139—21no—
79#95×C139—21no—
80#95×C139—21no—
81#95×C139—21no—
82#95×C139—21no—
83#95×C139—21no—
84#95×C139—21no—
85C24×C139—22no—
86C24×C139—22no—
87C24×C139—22no—
88C24×C139—41no—
89C24×C139—41no—
90C24×C139—41no—
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×C139C2×D411yescharacteristic
101C2×Q8×C139—21no—
102C2×Q8×C139—41no—
103C2×Q8×C139—41no—
104C2×Q8×C139C22⋊C412yescomplemented
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—41no—
112C2×D4×C139—41no—
113C2×D4×C139—41no—
114C2×D4×C139—41no—
115C2×D4×C139—44no—
116C2×D4×C139—44no—
117C2×D4×C139—44no—
118C2×D4×C139—44no—
119C2×D4×C139—41no—
120C2×D4×C139—41no—
121C22×C4×C139—21no—
122C22×C4×C139—21no—
123C22×C4×C139—21no—
124C22×C4×C139—21no—
125C22×C4×C139—22no—
126C22×C4×C139—21no—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—21no—
130C22×C4×C139—21no—
131C22×C4×C139—41no—
132C22×C4×C139—41no—
133C22×C4×C139—41no—
134C22×C4×C139—41no—
135C22×C4×C139—41no—
136C22×C4×C139—41no—
137C22×C4×C139—41no—
138C22×C4×C139—41no—
139C22×C4×C139—41no—
140C22×C4×C139—41no—
141C22×C4×C139—41no—
142C22×C4×C139—41no—
143C22×C4×C139SD1612yescomplemented
144C22×C4×C139C22×C411yescharacteristic
145C22×C4×C139C2×D411yescharacteristic
146C22×C4×C139C2×D411yescharacteristic
147C22×C4×C139C2×D411yescharacteristic
148C22×C4×C139#4111yescharacteristic
149C22×C4×C139#4111yescharacteristic
150SD16×C139—48no—
151C2×C8×C139—22no—
152C2×C8×C139—41no—
153C2×C8×C139—41no—
154C2×C8×C139—41no—
155C2×C8×C139—41no—
156C2×C8×C139—41no—
157C4⋊C4×C139—22no—
158C4⋊C4×C139—22no—
159C4⋊C4×C139—21no—
160C4⋊C4×C139—41no—
161C4⋊C4×C139—41no—
162C4⋊C4×C139—81no—
163C4⋊C4×C139—81no—
164C4⋊C4×C139C22⋊C412yescomplemented
165C22⋊C4×C139—22no—
166C22⋊C4×C139—22no—
167C22⋊C4×C139—48no—
168C22⋊C4×C139—48no—
169C22⋊C4×C139—41no—
170C22⋊C4×C139—41no—
171C42×C139—81no—
172C42×C139—81no—
173C23×C139—21no—
174C23×C139—21no—
175C23×C139—21no—
176C23×C139—21no—
177C23×C139—24no—
178C23×C139—42no—
179C23×C139—42no—
180C23×C139—42no—
181C23×C139—42no—
182C23×C139—42no—
183C23×C139—42no—
184C23×C139—42no—
185C23×C139—42no—
186C23×C139—42no—
187C23×C139—42no—
188C23×C139—42no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—42no—
192C23×C139—42no—
193C23×C139—42no—
194C23×C139—42no—
195C23×C139—42no—
196C23×C139—81no—
197C23×C139—81no—
198C23×C139—81no—
199C23×C139—81no—
200C23×C139—81no—
201C23×C139—81no—
202C23×C139—81no—
203C23×C139—81no—
204C23×C139—81no—
205C23×C139—81no—
206C23×C139—81no—
207C23×C139—81no—
208C23×C139—81no—
209C23×C139—81no—
210C23×C139—81no—
211C23×C139—81no—
212C23×C139C4×D411yescharacteristic
213C23×C139#12011yescharacteristic
214C23×C139#12111yescharacteristic
215C23×C139C2×SD1611yescharacteristic
216C23×C139#13511yescharacteristic
217C23×C139AGL(1,ℤ/8)11yescharacteristic
218C23×C139#13711yescharacteristic
219Q8×C139—42no—
220Q8×C139—81no—
221D4×C139—24no—
222D4×C139—24no—
223D4×C139—42no—
224D4×C139—42no—
225D4×C139—42no—
226D4×C139—42no—
227D4×C139—42no—
228D4×C139—42no—
229C2×C4×C139—21no—
230C2×C4×C139—21no—
231C2×C4×C139—21no—
232C2×C4×C139—21no—
233C2×C4×C139—22no—
234C2×C4×C139—22no—
235C2×C4×C139—22no—
236C2×C4×C139—41no—
237C2×C4×C139—41no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—42no—
247C2×C4×C139—42no—
248C2×C4×C139—42no—
249C2×C4×C139—42no—
250C2×C4×C139—42no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—81no—
261C2×C4×C139—81no—
262C2×C4×C139—81no—
263C2×C4×C139—81no—
264C2×C4×C139—81no—
265C2×C4×C139—81no—
266C2×C4×C139C2×C22⋊C411yescharacteristic
267C2×C4×C139C4×D411yescharacteristic
268C2×C4×C139#12111yescharacteristic
269C2×C4×C139#12311yescharacteristic
270C8×C139—42no—
271C8×C139—81no—
272C22×C139—21no—
273C22×C139—21no—
274C22×C139—21no—
275C22×C139—21no—
276C22×C139—21no—
277C22×C139—21no—
278C22×C139—21no—
279C22×C139—21no—
280C22×C139—21no—
281C22×C139—21no—
282C22×C139—21no—
283C22×C139—21no—
284C22×C139—44no—
285C22×C139—44no—
286C22×C139—44no—
287C22×C139—82no—
288C22×C139—82no—
289C22×C139—82no—
290C22×C139—82no—
291C22×C139—82no—
292C22×C139—82no—
293C22×C139—82no—
294C22×C139—82no—
295C22×C139—82no—
296C22×C139—82no—
297C22×C139—82no—
298C22×C139—82no—
299C22×C139#38611yescharacteristic
300C22×C139C4×SD1611yescharacteristic
301C22×C139#44011yescharacteristic
302C22×C139#44811yescharacteristic
303C22×C139#44911yescharacteristic
304C22×C139#45311yescharacteristic
305C22×C139#45411yescharacteristic
306C22×C139B(4,𝔽2)11yescharacteristic
307C22×C139B(4,𝔽2)11yescharacteristic
308C22×C139#46011yescharacteristic
309C22×C139#46411yescharacteristic
310C4×C139—21no—
311C4×C139—21no—
312C4×C139—21no—
313C4×C139—21no—
314C4×C139—42no—
315C4×C139—42no—
316C4×C139—42no—
317C4×C139—82no—
318C4×C139—81no—
319C4×C139—81no—
320C4×C139—81no—
321C2×C139—21no—
322C2×C139—21no—
323C2×C139—21no—
324C2×C139—21no—
325C2×C139—84no—
326C2×C139#159611yescharacteristic
327C2×C139#159711yescharacteristic
328C2×C139#159911yescharacteristic
329C2×C139#160011yescharacteristic
330C2×C139#188011yescharacteristic
331C2×C139#188311yescharacteristic
332C2×C139#188911yescharacteristic
333#9042C13911yesmaximal, characteristic, direct product factor, Sylow
334C139#904211yescharacteristic, direct product factor, Sylow
335C2×#450C2×C13911yescharacteristic
336#2329C2×C13911yescharacteristic, complemented
337#1786C2×C13911yescharacteristic
338C2×#328C2×C13911yescharacteristic, complemented
339#1438C2×C13911yescharacteristic
340#1294C2×C13911yescharacteristic, complemented
341#1280C2×C13911yescharacteristic, complemented
342C23×D4C22×C13911yescharacteristic
343C22×SD16—21no—
344C2×C22⋊Q8C22×C13911yescharacteristic
345C22×C22⋊C4—21no—
346C22×C22⋊C4—21no—
347#450—22no—
348#450C4×C13914yescomplemented
349C2×#102—21no—
350C2×#102—21no—
351C2×#102—21no—
352C2×C22⋊C8C22×C13911yescharacteristic
353C2×C22⋊C8C22×C13911yescharacteristic
354#391—21no—
355#389—21no—
356#387—21no—
357#387—21no—
358#385—21no—
359#380C22×C13911yescharacteristic
360C4×C22⋊C4—21no—
361C2×#95C22×C13911yescharacteristic
362C2×#95C22×C13911yescharacteristic
363#328—22no—
364C25—21no—
365C22×Q8D4×C13911yescharacteristic
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4C2×C4×C13912yes—
374C23×C4—21no—
375C23×C4D4×C13911yescharacteristic
376C23×C4D4×C13911yescharacteristic
377C23×C4C23×C13911yescharacteristic
378C2×SD16—24no—
379C2×SD16—42no—
380C2×SD16—42no—
381C22×C8—21no—
382C22×C8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8C2×C4×C13912yes—
386C22⋊Q8D4×C13912yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C13911yescharacteristic
391C2×C4⋊C4D4×C13911yescharacteristic
392C2×C4⋊C4D4×C13911yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C42—21no—
402C2×C42—21no—
403#102—24no—
404#102—42no—
405#102—42no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8C2×C4×C13912yes—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24C2×D4×C13911yescharacteristic
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8C22⋊C4×C13912yescomplemented
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—41no—
454C2×D4—41no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4SD16×C13912yescomplemented
478C22×C4C22×C4×C13911yescharacteristic
479C22×C4C2×D4×C13911yescharacteristic
480C22×C4C2×D4×C13911yescharacteristic
481C22×C4C2×D4×C13911yescharacteristic
482C22×C4#41×C13911yescharacteristic
483C22×C4#41×C13911yescharacteristic
484SD16—48no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4C22⋊C4×C13912yescomplemented
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—48no—
502C22⋊C4—48no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—81no—
506C42—81no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23—81no—
546C23C4×D4×C13911yescharacteristic
547C23#120×C13911yescharacteristic
548C23#121×C13911yescharacteristic
549C23C2×SD16×C13911yescharacteristic
550C23#135×C13911yescharacteristic
551C23AGL(1,ℤ/8)×C13911yescharacteristic
552C23#137×C13911yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4C2×C22⋊C4×C13911yescharacteristic
601C2×C4C4×D4×C13911yescharacteristic
602C2×C4#121×C13911yescharacteristic
603C2×C4#123×C13911yescharacteristic
604C8—42no—
605C8—81no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—82no—
631C22—82no—
632C22—82no—
633C22#386×C13911yescharacteristic
634C22C4×SD16×C13911yescharacteristic
635C22#440×C13911yescharacteristic
636C22#448×C13911yescharacteristic
637C22#449×C13911yescharacteristic
638C22#453×C13911yescharacteristic
639C22#454×C13911yescharacteristic
640C22B(4,𝔽2)×C13911yescharacteristic
641C22B(4,𝔽2)×C13911yescharacteristic
642C22#460×C13911yescharacteristic
643C22#464×C13911yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—82no—
652C4—81no—
653C4—81no—
654C4—81no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—84no—
660C2#1596×C13911yescharacteristic
661C2#1597×C13911yescharacteristic
662C2#1599×C13911yescharacteristic
663C2#1600×C13911yescharacteristic
664C2#1880×C13911yescharacteristic
665C2#1883×C13911yescharacteristic
666C2#1889×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC23×D4×C139C22
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. #2329×C139C2semidirect
4. C2×#328×C139C2semidirect
6. #1294×C139C2semidirect
7. #1280×C139C2semidirect
14. #450×C139C4semidirect
104. C2×Q8×C139C22⋊C4semidirect
143. C22×C4×C139SD16semidirect
164. C4⋊C4×C139C22⋊C4semidirect
333. #9042C139direct (N × H)
334. C139#9042direct (N × H)
336. #2329C2×C139semidirect
338. C2×#328C2×C139semidirect
340. #1294C2×C139semidirect
341. #1280C2×C139semidirect
348. #450C4×C139semidirect
438. C2×Q8C22⋊C4×C139semidirect
477. C22×C4SD16×C139semidirect
498. 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×#450×C1392
#2329×C1392
#1786×C1392
C2×#328×C1392
#1438×C1392
#1294×C1392
#1280×C1392
#9042139