Finite Group Databasebeta

← C139×#9914 #48004510

Subgroups — C139×#9914 #48004510

Order 35584.

1356 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C139C211yesmaximal, characteristic, complemented
2#2617×C139C211yesmaximal, characteristic, complemented
3C2×#392×C139C211yesmaximal, characteristic, complemented
4#1786×C139C211yesmaximal, characteristic, complemented
5C2×#327×C139C211yesmaximal, characteristic, complemented
6C2×#323×C139C211yesmaximal, characteristic, complemented
7#1294×C139C211yesmaximal, characteristic, complemented
8C23×D4×C139—21no—
9C23×D4×C139C2211yescharacteristic
10C22×D8×C139—21no—
11C2×#121×C139C2211yescharacteristic
12C2×#120×C139—21no—
13C22×C22⋊C4×C139—21no—
14C22×C22⋊C4×C139C2211yescharacteristic
15#447×C139—22no—
16#447×C139—22no—
17C2×#102×C139—21no—
18C2×#102×C139—22no—
19C2×C22⋊C8×C139C2211yescharacteristic
20C2×C22⋊C8×C139C2211yescharacteristic
21#397×C139—21no—
22#394×C139—22no—
23#392×C139—21no—
24#392×C139—22no—
25#392×C139—22no—
26#386×C139—21no—
27#380×C139C2211yescharacteristic
28C2×#95×C139C2211yescharacteristic
29#327×C139—22no—
30#323×C139—22no—
31C25×C139—21no—
32C25×C139D411yescharacteristic
33C22×D4×C139—24no—
34C22×D4×C139—21no—
35C22×D4×C139—22no—
36C22×D4×C139—21no—
37C22×D4×C139—21no—
38C22×D4×C139—21no—
39C22×D4×C139—21no—
40C22×D4×C139—21no—
41C22×D4×C139—44no—
42C22×D4×C139—44no—
43C22×D4×C139—44no—
44C22×D4×C139—42no—
45C22×D4×C139—42no—
46C22×D4×C139D412yescomplemented
47C22×D4×C139D411yescharacteristic, complemented
48C23×C4×C139—21no—
49C23×C4×C139D411yescharacteristic
50C23×C4×C139C2311yescharacteristic
51C2×D8×C139—24no—
52C2×D8×C139—44no—
53C22×C8×C139—21no—
54C22×C8×C139—21no—
55#121×C139—21no—
56#121×C139—21no—
57#121×C139—21no—
58#121×C139—21no—
59#120×C139—42no—
60#120×C139—42no—
61C2×C4⋊C4×C139D411yescharacteristic, complemented
62C2×C4⋊C4×C139D412yescomplemented
63C2×C22⋊C4×C139—22no—
64C2×C22⋊C4×C139—24no—
65C2×C22⋊C4×C139—21no—
66C2×C22⋊C4×C139—21no—
67C2×C22⋊C4×C139—21no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—21no—
70C2×C22⋊C4×C139—21no—
71C2×C22⋊C4×C139—21no—
72C2×C22⋊C4×C139—21no—
73C2×C22⋊C4×C139—22no—
74C2×C22⋊C4×C139—44no—
75#102×C139—24no—
76#102×C139—44no—
77C22⋊C8×C139—21no—
78C22⋊C8×C139—21no—
79C22⋊C8×C139—21no—
80C22⋊C8×C139D412yescomplemented
81#95×C139—22no—
82#95×C139—21no—
83#95×C139—21no—
84#95×C139D412yescomplemented
85C24×C139—24no—
86C24×C139—21no—
87C24×C139—22no—
88C24×C139—21no—
89C24×C139—21no—
90C24×C139—21no—
91C24×C139—21no—
92C24×C139—21no—
93C24×C139—21no—
94C24×C139—42no—
95C24×C139—42no—
96C24×C139—42no—
97C24×C139—42no—
98C24×C139—42no—
99C24×C139—41no—
100C24×C139—41no—
101C24×C139—41no—
102C24×C139—41no—
103C24×C139—41no—
104C24×C139—41no—
105C24×C139D812yescomplemented
106C24×C139C2×D411yescharacteristic
107C2×D4×C139—24no—
108C2×D4×C139—24no—
109C2×D4×C139—22no—
110C2×D4×C139—21no—
111C2×D4×C139—22no—
112C2×D4×C139—21no—
113C2×D4×C139—42no—
114C2×D4×C139—42no—
115C2×D4×C139—48no—
116C2×D4×C139—42no—
117C2×D4×C139—44no—
118C2×D4×C139—44no—
119C2×D4×C139—44no—
120C2×D4×C139—44no—
121C2×D4×C139—48no—
122C2×D4×C139—48no—
123C2×D4×C139—416no—
124C2×D4×C139—416no—
125C2×D4×C139—44no—
126C2×D4×C139—41no—
127C2×D4×C139—41no—
128C2×D4×C139—41no—
129C2×D4×C139—41no—
130C2×D4×C139—41no—
131C2×D4×C139—41no—
132C2×D4×C139—41no—
133C2×D4×C139—41no—
134C2×D4×C139—82no—
135C2×D4×C139—82no—
136C22×C4×C139—24no—
137C22×C4×C139—22no—
138C22×C4×C139—21no—
139C22×C4×C139—21no—
140C22×C4×C139—21no—
141C22×C4×C139—22no—
142C22×C4×C139—21no—
143C22×C4×C139—42no—
144C22×C4×C139—42no—
145C22×C4×C139—41no—
146C22×C4×C139—41no—
147C22×C4×C139—42no—
148C22×C4×C139C2×D411yescharacteristic
149C22×C4×C139C2×D411yescharacteristic
150C22×C4×C139C2×D411yescharacteristic
151C22×C4×C139C2×D411yescharacteristic
152C22×C4×C139C2×D411yescharacteristic
153C22×C4×C139#4111yescharacteristic
154D8×C139—48no—
155C2×C8×C139—22no—
156C2×C8×C139—42no—
157C2×C8×C139—42no—
158C2×C8×C139—41no—
159C4⋊C4×C139—21no—
160C4⋊C4×C139—21no—
161C4⋊C4×C139—42no—
162C22⋊C4×C139—48no—
163C22⋊C4×C139—44no—
164C22⋊C4×C139—41no—
165C22⋊C4×C139—41no—
166C22⋊C4×C139—41no—
167C22⋊C4×C139—41no—
168C22⋊C4×C139—41no—
169C22⋊C4×C139—41no—
170C22⋊C4×C139—41no—
171C22⋊C4×C139—41no—
172C22⋊C4×C139—82no—
173C23×C139—22no—
174C23×C139—22no—
175C23×C139—24no—
176C23×C139—22no—
177C23×C139—22no—
178C23×C139—22no—
179C23×C139—44no—
180C23×C139—42no—
181C23×C139—44no—
182C23×C139—44no—
183C23×C139—44no—
184C23×C139—42no—
185C23×C139—42no—
186C23×C139—42no—
187C23×C139—42no—
188C23×C139—44no—
189C23×C139—44no—
190C23×C139—44no—
191C23×C139—41no—
192C23×C139—42no—
193C23×C139—42no—
194C23×C139—41no—
195C23×C139—41no—
196C23×C139—42no—
197C23×C139—42no—
198C23×C139—44no—
199C23×C139—42no—
200C23×C139—41no—
201C23×C139—41no—
202C23×C139—41no—
203C23×C139—41no—
204C23×C139—42no—
205C23×C139—42no—
206C23×C139—82no—
207C23×C139—82no—
208C23×C139—81no—
209C23×C139—81no—
210C23×C139—82no—
211C23×C139—82no—
212C23×C139—82no—
213C23×C139—82no—
214C23×C139—82no—
215C23×C139—81no—
216C23×C139—81no—
217C23×C139—82no—
218C23×C139—81no—
219C23×C139—81no—
220C23×C139#12011yescharacteristic
221C23×C139#12011yescharacteristic
222C23×C139#12111yescharacteristic
223C23×C139C2×D811yescharacteristic
224C23×C139#13511yescharacteristic
225C23×C139AGL(1,ℤ/8)11yescharacteristic
226C23×C139AGL(1,ℤ/8)11yescharacteristic
227D4×C139—24no—
228D4×C139—24no—
229D4×C139—42no—
230D4×C139—44no—
231D4×C139—42no—
232D4×C139—44no—
233D4×C139—42no—
234D4×C139—432no—
235D4×C139—81no—
236D4×C139—88no—
237D4×C139—81no—
238D4×C139—81no—
239D4×C139—81no—
240D4×C139—81no—
241C2×C4×C139—22no—
242C2×C4×C139—22no—
243C2×C4×C139—24no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—44no—
249C2×C4×C139—44no—
250C2×C4×C139—42no—
251C2×C4×C139—42no—
252C2×C4×C139—42no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—42no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—42no—
259C2×C4×C139—42no—
260C2×C4×C139—42no—
261C2×C4×C139—81no—
262C2×C4×C139#12011yescharacteristic
263C2×C4×C139#12111yescharacteristic
264C2×C4×C139#12111yescharacteristic
265C2×C4×C139#12711yescharacteristic
266C8×C139—42no—
267C8×C139—81no—
268C22×C139—22no—
269C22×C139—22no—
270C22×C139—22no—
271C22×C139—22no—
272C22×C139—21no—
273C22×C139—21no—
274C22×C139—21no—
275C22×C139—21no—
276C22×C139—44no—
277C22×C139—44no—
278C22×C139—44no—
279C22×C139—44no—
280C22×C139—42no—
281C22×C139—44no—
282C22×C139—82no—
283C22×C139—82no—
284C22×C139—82no—
285C22×C139—82no—
286C22×C139—84no—
287C22×C139—82no—
288C22×C139—84no—
289C22×C139—84no—
290C22×C139—82no—
291C22×C139—84no—
292C22×C139—82no—
293C22×C139—81no—
294C22×C139—82no—
295C22×C139—81no—
296C22×C139—82no—
297C22×C139—82no—
298C22×C139—81no—
299C22×C139—81no—
300C22×C139—81no—
301C22×C139#39211yescharacteristic
302C22×C139#44711yescharacteristic
303C22×C139#44711yescharacteristic
304C22×C139#44911yescharacteristic
305C22×C139#44911yescharacteristic
306C22×C139#45312yes—
307C22×C139B(4,𝔽2)12yes—
308C22×C139#46611yescharacteristic
309C22×C139#46911yescharacteristic
310C4×C139—21no—
311C4×C139—21no—
312C4×C139—21no—
313C4×C139—21no—
314C4×C139—44no—
315C4×C139—82no—
316C4×C139—81no—
317C4×C139—81no—
318C2×C139—21no—
319C2×C139—21no—
320C2×C139—21no—
321C2×C139—21no—
322C2×C139—82no—
323C2×C139—84no—
324C2×C139—161no—
325C2×C139#159512yes—
326C2×C139#160012yes—
327C2×C139#199911yescharacteristic
328C2×C139#200211yescharacteristic
329C2×C139#202111yescharacteristic
330#9914C13911yesmaximal, characteristic, direct product factor, Sylow
331C139#991411yescharacteristic, direct product factor, Sylow
332C2×#447C2×C13911yescharacteristic, complemented
333#2617C2×C13911yescharacteristic, complemented
334C2×#392C2×C13911yescharacteristic, complemented
335#1786C2×C13911yescharacteristic, complemented
336C2×#327C2×C13911yescharacteristic, complemented
337C2×#323C2×C13911yescharacteristic, complemented
338#1294C2×C13911yescharacteristic, complemented
339C23×D4—21no—
340C23×D4C22×C13911yescharacteristic
341C22×D8—21no—
342C2×#121C22×C13911yescharacteristic
343C2×#120—21no—
344C22×C22⋊C4—21no—
345C22×C22⋊C4C22×C13911yescharacteristic
346#447—22no—
347#447—22no—
348C2×#102—21no—
349C2×#102—22no—
350C2×C22⋊C8C22×C13911yescharacteristic
351C2×C22⋊C8C22×C13911yescharacteristic
352#397—21no—
353#394—22no—
354#392—21no—
355#392—22no—
356#392—22no—
357#386—21no—
358#380C22×C13911yescharacteristic
359C2×#95C22×C13911yescharacteristic
360#327—22no—
361#323—22no—
362C25—21no—
363C25D4×C13911yescharacteristic
364C22×D4—24no—
365C22×D4—21no—
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4D4×C13911yescharacteristic, complemented
378C22×D4D4×C13912yescomplemented
379C23×C4—21no—
380C23×C4D4×C13911yescharacteristic
381C23×C4C23×C13911yescharacteristic
382C2×D8—24no—
383C2×D8—44no—
384C22×C8—21no—
385C22×C8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#120—42no—
391#120—42no—
392C2×C4⋊C4D4×C13911yescharacteristic, complemented
393C2×C4⋊C4D4×C13912yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—44no—
406#102—24no—
407#102—44no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C13912yescomplemented
412#95—22no—
413#95—21no—
414#95—21no—
415#95D4×C13912yescomplemented
416C24—24no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24D8×C13912yescomplemented
437C24C2×D4×C13911yescharacteristic
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—48no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—82no—
466C2×D4—82no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4C2×D4×C13911yescharacteristic
480C22×C4C2×D4×C13911yescharacteristic
481C22×C4C2×D4×C13911yescharacteristic
482C22×C4C2×D4×C13911yescharacteristic
483C22×C4C2×D4×C13911yescharacteristic
484C22×C4#41×C13911yescharacteristic
485D8—48no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—41no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—44no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—44no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—44no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—42no—
536C23—41no—
537C23—82no—
538C23—81no—
539C23—81no—
540C23—82no—
541C23—82no—
542C23—82no—
543C23—82no—
544C23—82no—
545C23—82no—
546C23—81no—
547C23—81no—
548C23—82no—
549C23—81no—
550C23—81no—
551C23#120×C13911yescharacteristic
552C23#120×C13911yescharacteristic
553C23#121×C13911yescharacteristic
554C23C2×D8×C13911yescharacteristic
555C23#135×C13911yescharacteristic
556C23AGL(1,ℤ/8)×C13911yescharacteristic
557C23AGL(1,ℤ/8)×C13911yescharacteristic
558D4—24no—
559D4—24no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—432no—
566D4—81no—
567D4—88no—
568D4—81no—
569D4—81no—
570D4—81no—
571D4—81no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—81no—
593C2×C4#120×C13911yescharacteristic
594C2×C4#121×C13911yescharacteristic
595C2×C4#121×C13911yescharacteristic
596C2×C4#127×C13911yescharacteristic
597C8—42no—
598C8—81no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—42no—
611C22—44no—
612C22—44no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—84no—
618C22—82no—
619C22—84no—
620C22—82no—
621C22—81no—
622C22—82no—
623C22—81no—
624C22—84no—
625C22—82no—
626C22—84no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—82no—
631C22—82no—
632C22#392×C13911yescharacteristic
633C22#447×C13911yescharacteristic
634C22#447×C13911yescharacteristic
635C22#449×C13911yescharacteristic
636C22#449×C13911yescharacteristic
637C22#453×C13912yes—
638C22B(4,𝔽2)×C13912yes—
639C22#466×C13911yescharacteristic
640C22#469×C13911yescharacteristic
641C4—21no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—44no—
646C4—81no—
647C4—81no—
648C4—82no—
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—82no—
654C2—84no—
655C2—161no—
656C2#1595×C13912yes—
657C2#1600×C13912yes—
658C2#1999×C13911yescharacteristic
659C2#2002×C13911yescharacteristic
660C2#2021×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutator, Frattini, cosocleC23×C4C23×C139
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#447×C139C2semidirect
2. #2617×C139C2semidirect
3. C2×#392×C139C2semidirect
4. #1786×C139C2semidirect
5. C2×#327×C139C2semidirect
6. C2×#323×C139C2semidirect
7. #1294×C139C2semidirect
46. C22×D4×C139D4semidirect
47. C22×D4×C139D4semidirect
61. C2×C4⋊C4×C139D4semidirect
62. C2×C4⋊C4×C139D4semidirect
80. C22⋊C8×C139D4semidirect
84. #95×C139D4semidirect
105. C24×C139D8semidirect
330. #9914C139direct (N × H)
331. C139#9914direct (N × H)
332. C2×#447C2×C139semidirect
333. #2617C2×C139semidirect
334. C2×#392C2×C139semidirect
335. #1786C2×C139semidirect
336. C2×#327C2×C139semidirect
337. C2×#323C2×C139semidirect
338. #1294C2×C139semidirect
377. C22×D4D4×C139semidirect
378. C22×D4D4×C139semidirect
392. C2×C4⋊C4D4×C139semidirect
393. C2×C4⋊C4D4×C139semidirect
411. C22⋊C8D4×C139semidirect
415. #95D4×C139semidirect
436. C24D8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1392
#2617×C1392
C2×#392×C1392
#1786×C1392
C2×#327×C1392
C2×#323×C1392
#1294×C1392
#9914139