Finite Group Databasebeta

← C139×#9083 #48003679

Subgroups — C139×#9083 #48003679

Order 35584.

1100 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#407×C139C211yesmaximal, characteristic, complemented
2C2×#386×C139C211yesmaximal, characteristic
3#1779×C139C211yesmaximal, characteristic, complemented
4C2×#323×C139C212yesmaximal, complemented
5#1280×C139C212yesmaximal, complemented
6C23×D4×C139C411yescharacteristic
7C24×C4×C139C2211yescharacteristic
8C22×M16×C139—21no—
9C22×C22⋊C4×C139C411yescharacteristic
10C22×C22⋊C4×C139C411yescharacteristic
11C22×C22⋊C4×C139C2211yescharacteristic
12#407×C139—24no—
13C2×C22⋊C8×C139—21no—
14C2×C22⋊C8×C139—21no—
15C2×C22⋊C8×C139—21no—
16C2×C22⋊C8×C139C2212yes—
17C2×C22⋊C8×C139C2212yes—
18#386×C139—21no—
19#386×C139—21no—
20#386×C139—21no—
21#386×C139—21no—
22C2×#95×C139C411yescharacteristic
23C2×#95×C139C2211yescharacteristic
24#323×C139—24no—
25C25×C139C2×C411yescharacteristic
26C25×C139C2×C411yescharacteristic
27C22×D4×C139—21no—
28C22×D4×C139—21no—
29C22×D4×C139—22no—
30C22×D4×C139—22no—
31C22×D4×C139—42no—
32C22×D4×C139—42no—
33C23×C4×C139—22no—
34C23×C4×C139—22no—
35C23×C4×C139—42no—
36C23×C4×C139—42no—
37C23×C4×C139C2×C411yescharacteristic
38C23×C4×C139C2×C411yescharacteristic
39C23×C4×C139C2×C411yescharacteristic
40C23×C4×C139C2×C411yescharacteristic
41C23×C4×C139D411yescharacteristic
42C23×C4×C139D411yescharacteristic
43C23×C4×C139D411yescharacteristic
44C23×C4×C139D411yescharacteristic
45C23×C4×C139C2311yescharacteristic
46C2×M16×C139—24no—
47C2×M16×C139—42no—
48C2×M16×C139—42no—
49C22×C8×C139—22no—
50C22×C8×C139—22no—
51C2×C22⋊C4×C139—21no—
52C2×C22⋊C4×C139—21no—
53C2×C22⋊C4×C139—21no—
54C2×C22⋊C4×C139—21no—
55C2×C22⋊C4×C139—22no—
56C2×C22⋊C4×C139—21no—
57C2×C22⋊C4×C139—21no—
58C2×C22⋊C4×C139—22no—
59C2×C22⋊C4×C139—42no—
60C2×C22⋊C4×C139—42no—
61C22⋊C8×C139—24no—
62C22⋊C8×C139—22no—
63C22⋊C8×C139—22no—
64C22⋊C8×C139—22no—
65C22⋊C8×C139—42no—
66C22⋊C8×C139—42no—
67C22⋊C8×C139D414yescomplemented
68#95×C139—21no—
69#95×C139—21no—
70#95×C139—21no—
71#95×C139—21no—
72C24×C139—22no—
73C24×C139—22no—
74C24×C139—21no—
75C24×C139—21no—
76C24×C139—21no—
77C24×C139—22no—
78C24×C139—21no—
79C24×C139—22no—
80C24×C139—22no—
81C24×C139—22no—
82C24×C139—41no—
83C24×C139—41no—
84C24×C139—41no—
85C24×C139—41no—
86C24×C139—41no—
87C24×C139—41no—
88C24×C139C22⋊C411yescharacteristic
89C24×C139C22⋊C411yescharacteristic
90C24×C139M1612yescomplemented
91C24×C139C22×C411yescharacteristic
92C2×D4×C139—24no—
93C2×D4×C139—24no—
94C2×D4×C139—48no—
95C2×D4×C139—42no—
96C2×D4×C139—42no—
97C2×D4×C139—48no—
98C2×D4×C139—42no—
99C2×D4×C139—42no—
100C22×C4×C139—22no—
101C22×C4×C139—22no—
102C22×C4×C139—21no—
103C22×C4×C139—21no—
104C22×C4×C139—22no—
105C22×C4×C139—21no—
106C22×C4×C139—22no—
107C22×C4×C139—21no—
108C22×C4×C139—22no—
109C22×C4×C139—22no—
110C22×C4×C139—21no—
111C22×C4×C139—22no—
112C22×C4×C139—22no—
113C22×C4×C139—21no—
114C22×C4×C139—21no—
115C22×C4×C139—21no—
116C22×C4×C139—22no—
117C22×C4×C139—22no—
118C22×C4×C139—41no—
119C22×C4×C139—41no—
120C22×C4×C139—41no—
121C22×C4×C139—41no—
122C22×C4×C139—41no—
123C22×C4×C139—41no—
124C22×C4×C139—41no—
125C22×C4×C139—48no—
126C22×C4×C139—48no—
127C22×C4×C139—41no—
128C22×C4×C139—41no—
129C22×C4×C139—41no—
130C22×C4×C139—41no—
131C22×C4×C139—41no—
132C22×C4×C139—41no—
133C22×C4×C139C22⋊C411yescharacteristic
134C22×C4×C139C22⋊C411yescharacteristic
135C22×C4×C139M1612yescomplemented
136C22×C4×C139C2×D411yescharacteristic
137C22×C4×C139C2×D411yescharacteristic
138C22×C4×C139C2×D412yes—
139C22×C4×C139#4112yes—
140M16×C139—48no—
141C2×C8×C139—24no—
142C2×C8×C139—42no—
143C2×C8×C139—42no—
144C2×C8×C139—42no—
145C2×C8×C139—42no—
146C2×C8×C139—42no—
147C22⋊C4×C139—42no—
148C22⋊C4×C139—42no—
149C22⋊C4×C139—42no—
150C22⋊C4×C139—42no—
151C22⋊C4×C139—41no—
152C22⋊C4×C139—42no—
153C22⋊C4×C139—41no—
154C23×C139—21no—
155C23×C139—21no—
156C23×C139—21no—
157C23×C139—21no—
158C23×C139—24no—
159C23×C139—24no—
160C23×C139—21no—
161C23×C139—21no—
162C23×C139—21no—
163C23×C139—21no—
164C23×C139—21no—
165C23×C139—21no—
166C23×C139—21no—
167C23×C139—21no—
168C23×C139—21no—
169C23×C139—21no—
170C23×C139—21no—
171C23×C139—21no—
172C23×C139—22no—
173C23×C139—24no—
174C23×C139—44no—
175C23×C139—44no—
176C23×C139—44no—
177C23×C139—44no—
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—41no—
187C23×C139—41no—
188C23×C139—41no—
189C23×C139—41no—
190C23×C139—41no—
191C23×C139—41no—
192C23×C139—42no—
193C23×C139—82no—
194C23×C139—82no—
195C23×C139—82no—
196C23×C139—82no—
197C23×C139#9912yes—
198C23×C139#10012yes—
199C23×C139C2×C22⋊C411yescharacteristic
200C23×C139C4×D412yes—
201C23×C139C2×M1611yescharacteristic
202C23×C139C2×M1611yescharacteristic
203C23×C139#13112yes—
204D4×C139—48no—
205D4×C139—48no—
206C2×C4×C139—24no—
207C2×C4×C139—24no—
208C2×C4×C139—21no—
209C2×C4×C139—21no—
210C2×C4×C139—21no—
211C2×C4×C139—21no—
212C2×C4×C139—21no—
213C2×C4×C139—21no—
214C2×C4×C139—21no—
215C2×C4×C139—22no—
216C2×C4×C139—21no—
217C2×C4×C139—21no—
218C2×C4×C139—42no—
219C2×C4×C139—42no—
220C2×C4×C139—44no—
221C2×C4×C139—44no—
222C2×C4×C139—44no—
223C2×C4×C139—42no—
224C2×C4×C139—42no—
225C2×C4×C139—42no—
226C2×C4×C139—41no—
227C2×C4×C139—41no—
228C2×C4×C139—42no—
229C2×C4×C139—41no—
230C2×C4×C139—41no—
231C2×C4×C139—41no—
232C2×C4×C139—41no—
233C2×C4×C139—41no—
234C2×C4×C139—41no—
235C2×C4×C139—82no—
236C2×C4×C139—82no—
237C2×C4×C139#9912yes—
238C2×C4×C139#12011yescharacteristic
239C2×C4×C139#12112yes—
240C2×C4×C139#12311yescharacteristic
241C8×C139—44no—
242C8×C139—82no—
243C22×C139—22no—
244C22×C139—22no—
245C22×C139—21no—
246C22×C139—21no—
247C22×C139—21no—
248C22×C139—21no—
249C22×C139—22no—
250C22×C139—22no—
251C22×C139—22no—
252C22×C139—22no—
253C22×C139—22no—
254C22×C139—22no—
255C22×C139—22no—
256C22×C139—22no—
257C22×C139—48no—
258C22×C139—48no—
259C22×C139—41no—
260C22×C139—41no—
261C22×C139—41no—
262C22×C139—41no—
263C22×C139—41no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139—41no—
267C22×C139—42no—
268C22×C139—42no—
269C22×C139—42no—
270C22×C139—84no—
271C22×C139—84no—
272C22×C139—81no—
273C22×C139—81no—
274C22×C139—81no—
275C22×C139—81no—
276C22×C139#38611yescharacteristic
277C22×C139#40711yescharacteristic
278C22×C139#40811yescharacteristic
279C22×C139C2×#9911yescharacteristic
280C22×C139C2×#9911yescharacteristic
281C22×C139C2×#10011yescharacteristic
282C22×C139#41311yescharacteristic
283C22×C139#43512yes—
284C22×C139#43612yes—
285C4×C139—21no—
286C4×C139—22no—
287C4×C139—22no—
288C4×C139—21no—
289C4×C139—41no—
290C4×C139—42no—
291C4×C139—81no—
292C4×C139—81no—
293C2×C139—22no—
294C2×C139—22no—
295C2×C139—42no—
296C2×C139—42no—
297C2×C139—82no—
298C2×C139#146211yescharacteristic
299C2×C139#146511yescharacteristic
300C2×C139#146811yescharacteristic
301C2×C139#147111yescharacteristic
302C2×C139#187011yescharacteristic
303C2×C139#189811yescharacteristic
304C2×C139#190011yescharacteristic
305#9083C13911yesmaximal, characteristic, direct product factor, Sylow
306C139#908311yescharacteristic, direct product factor, Sylow
307C2×#407C2×C13911yescharacteristic, complemented
308C2×#386C2×C13911yescharacteristic
309#1779C2×C13911yescharacteristic, complemented
310C2×#323C2×C13912yescomplemented
311#1280C2×C13912yescomplemented
312C23×D4C4×C13911yescharacteristic
313C24×C4C22×C13911yescharacteristic
314C22×M16—21no—
315C22×C22⋊C4C4×C13911yescharacteristic
316C22×C22⋊C4C4×C13911yescharacteristic
317C22×C22⋊C4C22×C13911yescharacteristic
318#407—24no—
319C2×C22⋊C8—21no—
320C2×C22⋊C8—21no—
321C2×C22⋊C8—21no—
322C2×C22⋊C8C22×C13912yes—
323C2×C22⋊C8C22×C13912yes—
324#386—21no—
325#386—21no—
326#386—21no—
327#386—21no—
328C2×#95C4×C13911yescharacteristic
329C2×#95C22×C13911yescharacteristic
330#323—24no—
331C25C2×C4×C13911yescharacteristic
332C25C2×C4×C13911yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4C2×C4×C13911yescharacteristic
344C23×C4C2×C4×C13911yescharacteristic
345C23×C4C2×C4×C13911yescharacteristic
346C23×C4C2×C4×C13911yescharacteristic
347C23×C4D4×C13911yescharacteristic
348C23×C4D4×C13911yescharacteristic
349C23×C4D4×C13911yescharacteristic
350C23×C4D4×C13911yescharacteristic
351C23×C4C23×C13911yescharacteristic
352C2×M16—24no—
353C2×M16—42no—
354C2×M16—42no—
355C22×C8—22no—
356C22×C8—22no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C22⋊C8—24no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8D4×C13914yescomplemented
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—22no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24C22⋊C4×C13911yescharacteristic
395C24C22⋊C4×C13911yescharacteristic
396C24M16×C13912yescomplemented
397C24C22×C4×C13911yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—48no—
404C2×D4—42no—
405C2×D4—42no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C13911yescharacteristic
440C22×C4C22⋊C4×C13911yescharacteristic
441C22×C4M16×C13912yescomplemented
442C22×C4C2×D4×C13911yescharacteristic
443C22×C4C2×D4×C13911yescharacteristic
444C22×C4C2×D4×C13912yes—
445C22×C4#41×C13912yes—
446M16—48no—
447C2×C8—24no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—24no—
465C23—24no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—24no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—42no—
498C23—41no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—82no—
503C23#99×C13912yes—
504C23#100×C13912yes—
505C23C2×C22⋊C4×C13911yescharacteristic
506C23C4×D4×C13912yes—
507C23C2×M16×C13911yescharacteristic
508C23C2×M16×C13911yescharacteristic
509C23#131×C13912yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#99×C13912yes—
544C2×C4#120×C13911yescharacteristic
545C2×C4#121×C13912yes—
546C2×C4#123×C13911yescharacteristic
547C8—44no—
548C8—82no—
549C22—22no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—48no—
564C22—48no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—84no—
577C22—84no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22#386×C13911yescharacteristic
583C22#407×C13911yescharacteristic
584C22#408×C13911yescharacteristic
585C22C2×#99×C13911yescharacteristic
586C22C2×#99×C13911yescharacteristic
587C22C2×#100×C13911yescharacteristic
588C22#413×C13911yescharacteristic
589C22#435×C13912yes—
590C22#436×C13912yes—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—42no—
602C2—42no—
603C2—82no—
604C2#1462×C13911yescharacteristic
605C2#1465×C13911yescharacteristic
606C2#1468×C13911yescharacteristic
607C2#1471×C13911yescharacteristic
608C2#1870×C13911yescharacteristic
609C2#1898×C13911yescharacteristic
610C2#1900×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC24C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC23×D4×C139C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#407×C139C2semidirect
3. #1779×C139C2semidirect
4. C2×#323×C139C2semidirect
5. #1280×C139C2semidirect
67. C22⋊C8×C139D4semidirect
90. C24×C139M16semidirect
135. C22×C4×C139M16semidirect
305. #9083C139direct (N × H)
306. C139#9083direct (N × H)
307. C2×#407C2×C139semidirect
309. #1779C2×C139semidirect
310. C2×#323C2×C139semidirect
311. #1280C2×C139semidirect
373. C22⋊C8D4×C139semidirect
396. C24M16×C139semidirect
441. C22×C4M16×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#407×C1392
C2×#386×C1392
#1779×C1392
C2×#323×C1392
#1280×C1392
#9083139