Finite Group Databasebeta

← C139×#9113 #48003709

Subgroups — C139×#9113 #48003709

Order 35584.

1062 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C139C211yesmaximal, characteristic, complemented
2#2847×C139C211yesmaximal, characteristic
3C2×#327×C139C212yesmaximal, complemented
4C22⋊#95×C139C211yesmaximal, characteristic, complemented
5#1294×C139C212yesmaximal, complemented
6C24×C4×C139C2211yescharacteristic
7C23×C8×C139—21no—
8C2×#121×C139C411yescharacteristic, complemented
9C2×#121×C139C411yescharacteristic, complemented
10C2×#121×C139C2211yescharacteristic
11C2×#120×C139—21no—
12C22×C22⋊C4×C139—21no—
13C2×C22⋊C8×C139—21no—
14C2×C22⋊C8×C139—24no—
15C2×C22⋊C8×C139C2212yes—
16#386×C139—21no—
17#386×C139—21no—
18#386×C139—21no—
19#380×C139C411yescharacteristic, complemented
20#380×C139C411yescharacteristic, complemented
21#380×C139C2211yescharacteristic
22C2×#95×C139—21no—
23C2×#95×C139C2212yes—
24#327×C139—24no—
25C25×C139D411yescharacteristic
26C22×D4×C139—21no—
27C22×D4×C139—21no—
28C22×D4×C139—21no—
29C22×D4×C139C2×C411yescharacteristic
30C23×C4×C139—22no—
31C23×C4×C139—22no—
32C23×C4×C139—22no—
33C23×C4×C139—42no—
34C23×C4×C139—42no—
35C23×C4×C139C2×C411yescharacteristic
36C23×C4×C139C2×C411yescharacteristic
37C23×C4×C139D411yescharacteristic
38C23×C4×C139D411yescharacteristic
39C23×C4×C139D411yescharacteristic
40C23×C4×C139C2311yescharacteristic
41C22×C8×C139—24no—
42C22×C8×C139—22no—
43C22×C8×C139—42no—
44C22×C8×C139—42no—
45#121×C139—22no—
46#121×C139—22no—
47#121×C139—42no—
48#121×C139—42no—
49#120×C139—42no—
50#120×C139—42no—
51C2×C4⋊C4×C139C2×C411yescharacteristic
52C2×C4⋊C4×C139C2×C411yescharacteristic
53C2×C4⋊C4×C139C2×C411yescharacteristic
54C2×C22⋊C4×C139—24no—
55C2×C22⋊C4×C139—21no—
56C2×C22⋊C4×C139—21no—
57C2×C22⋊C4×C139—21no—
58C2×C22⋊C4×C139—21no—
59C2×C22⋊C4×C139—21no—
60C2×C22⋊C4×C139—21no—
61C2×C22⋊C4×C139—42no—
62C2×C22⋊C4×C139—42no—
63C22⋊C8×C139—24no—
64C22⋊C8×C139—22no—
65C22⋊C8×C139D414yescomplemented
66#95×C139—21no—
67#95×C139—21no—
68#95×C139—21no—
69#95×C139—22no—
70#95×C139—22no—
71#95×C139—42no—
72C24×C139—22no—
73C24×C139—22no—
74C24×C139—22no—
75C24×C139—22no—
76C24×C139—21no—
77C24×C139—41no—
78C24×C139—41no—
79C24×C139C22⋊C411yescharacteristic
80C24×C139C22⋊C411yescharacteristic
81C24×C139D812yes—
82C24×C139SD1612yes—
83C24×C139C2×D411yescharacteristic
84C2×D4×C139—22no—
85C2×D4×C139—41no—
86C2×D4×C139—41no—
87C2×D4×C139—42no—
88C2×D4×C139—42no—
89C2×D4×C139—42no—
90C2×D4×C139—42no—
91C2×D4×C139—42no—
92C2×D4×C139—42no—
93C2×D4×C139—42no—
94C2×D4×C139—41no—
95C2×D4×C139—41no—
96C2×D4×C139—42no—
97C22×C4×C139—22no—
98C22×C4×C139—22no—
99C22×C4×C139—21no—
100C22×C4×C139—21no—
101C22×C4×C139—22no—
102C22×C4×C139—22no—
103C22×C4×C139—22no—
104C22×C4×C139—22no—
105C22×C4×C139—22no—
106C22×C4×C139—22no—
107C22×C4×C139—21no—
108C22×C4×C139—21no—
109C22×C4×C139—24no—
110C22×C4×C139—21no—
111C22×C4×C139—21no—
112C22×C4×C139—21no—
113C22×C4×C139—41no—
114C22×C4×C139—41no—
115C22×C4×C139—41no—
116C22×C4×C139—41no—
117C22×C4×C139—41no—
118C22×C4×C139—41no—
119C22×C4×C139—41no—
120C22×C4×C139—48no—
121C22×C4×C139—48no—
122C22×C4×C139—42no—
123C22×C4×C139—42no—
124C22×C4×C139—42no—
125C22×C4×C139—42no—
126C22×C4×C139—42no—
127C22×C4×C139—42no—
128C22×C4×C139C22⋊C411yescharacteristic
129C22×C4×C139C22⋊C411yescharacteristic
130C22×C4×C139C22×C411yescharacteristic
131C22×C4×C139C2×D411yescharacteristic
132C22×C4×C139C2×D412yes—
133C22×C4×C139#4112yes—
134C2×C8×C139—24no—
135C2×C8×C139—48no—
136C2×C8×C139—42no—
137C2×C8×C139—42no—
138C4⋊C4×C139—22no—
139C4⋊C4×C139—41no—
140C4⋊C4×C139—41no—
141C22⋊C4×C139—42no—
142C22⋊C4×C139—48no—
143C22⋊C4×C139—42no—
144C22⋊C4×C139—42no—
145C22⋊C4×C139—41no—
146C22⋊C4×C139—41no—
147C22⋊C4×C139—42no—
148C22⋊C4×C139—41no—
149C22⋊C4×C139—41no—
150C23×C139—21no—
151C23×C139—21no—
152C23×C139—21no—
153C23×C139—21no—
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—24no—
167C23×C139—24no—
168C23×C139—42no—
169C23×C139—42no—
170C23×C139—44no—
171C23×C139—44no—
172C23×C139—44no—
173C23×C139—44no—
174C23×C139—41no—
175C23×C139—41no—
176C23×C139—41no—
177C23×C139—41no—
178C23×C139—41no—
179C23×C139—41no—
180C23×C139—41no—
181C23×C139#9912yes—
182C23×C139#10212yes—
183C23×C139#10212yes—
184C23×C139#10412yes—
185C23×C139C2×C22⋊C411yescharacteristic
186C23×C139#12112yes—
187C23×C139C2×D811yescharacteristic
188C23×C139C2×SD1611yescharacteristic
189C23×C139#13512yes—
190D4×C139—82no—
191D4×C139—84no—
192D4×C139—84no—
193D4×C139—82no—
194D4×C139—82no—
195C2×C4×C139—24no—
196C2×C4×C139—24no—
197C2×C4×C139—21no—
198C2×C4×C139—21no—
199C2×C4×C139—21no—
200C2×C4×C139—21no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—21no—
206C2×C4×C139—42no—
207C2×C4×C139—42no—
208C2×C4×C139—44no—
209C2×C4×C139—44no—
210C2×C4×C139—44no—
211C2×C4×C139—42no—
212C2×C4×C139—42no—
213C2×C4×C139—44no—
214C2×C4×C139—44no—
215C2×C4×C139—44no—
216C2×C4×C139—41no—
217C2×C4×C139—41no—
218C2×C4×C139—41no—
219C2×C4×C139—41no—
220C2×C4×C139—41no—
221C2×C4×C139—41no—
222C2×C4×C139—41no—
223C2×C4×C139—41no—
224C2×C4×C139—41no—
225C2×C4×C139—82no—
226C2×C4×C139—82no—
227C2×C4×C139—82no—
228C2×C4×C139—82no—
229C2×C4×C139#9912yes—
230C2×C4×C139C4×D412yes—
231C2×C4×C139#12011yescharacteristic
232C2×C4×C139#12311yescharacteristic
233C8×C139—44no—
234C22×C139—22no—
235C22×C139—22no—
236C22×C139—22no—
237C22×C139—22no—
238C22×C139—22no—
239C22×C139—21no—
240C22×C139—21no—
241C22×C139—22no—
242C22×C139—22no—
243C22×C139—22no—
244C22×C139—22no—
245C22×C139—21no—
246C22×C139—22no—
247C22×C139—21no—
248C22×C139—22no—
249C22×C139—22no—
250C22×C139—22no—
251C22×C139—48no—
252C22×C139—48no—
253C22×C139—41no—
254C22×C139—41no—
255C22×C139—41no—
256C22×C139—41no—
257C22×C139—81no—
258C22×C139—81no—
259C22×C139—81no—
260C22×C139—81no—
261C22×C139—81no—
262C22×C139—81no—
263C22×C139—81no—
264C22×C139#32714yescomplemented
265C22×C139#38611yescharacteristic
266C22×C139C2×#9911yescharacteristic
267C22×C139C2×#9911yescharacteristic
268C22×C139C2×#10211yescharacteristic
269C22×C139#41611yescharacteristic
270C22×C139C2×#10411yescharacteristic
271C22×C139#42111yescharacteristic
272C22×C139#46512yes—
273C22×C139#46612yes—
274C4×C139—21no—
275C4×C139—22no—
276C4×C139—21no—
277C4×C139—22no—
278C4×C139—41no—
279C4×C139—84no—
280C4×C139—81no—
281C4×C139—81no—
282C4×C139—81no—
283C2×C139—22no—
284C2×C139—24no—
285C2×C139—22no—
286C2×C139—42no—
287C2×C139—161no—
288C2×C139C2×#32711yescharacteristic
289C2×C139#150111yescharacteristic
290C2×C139#151611yescharacteristic
291C2×C139#151911yescharacteristic
292C2×C139#187111yescharacteristic
293C2×C139#189311yescharacteristic
294C2×C139#189811yescharacteristic
295#9113C13911yesmaximal, characteristic, direct product factor, Sylow
296C139#911311yescharacteristic, direct product factor, Sylow
297C22×C22⋊C8C2×C13911yescharacteristic, complemented
298#2847C2×C13911yescharacteristic
299C2×#327C2×C13912yescomplemented
300C22⋊#95C2×C13911yescharacteristic, complemented
301#1294C2×C13912yescomplemented
302C24×C4C22×C13911yescharacteristic
303C23×C8—21no—
304C2×#121C4×C13911yescharacteristic, complemented
305C2×#121C4×C13911yescharacteristic, complemented
306C2×#121C22×C13911yescharacteristic
307C2×#120—21no—
308C22×C22⋊C4—21no—
309C2×C22⋊C8—21no—
310C2×C22⋊C8—24no—
311C2×C22⋊C8C22×C13912yes—
312#386—21no—
313#386—21no—
314#386—21no—
315#380C4×C13911yescharacteristic, complemented
316#380C4×C13911yescharacteristic, complemented
317#380C22×C13911yescharacteristic
318C2×#95—21no—
319C2×#95C22×C13912yes—
320#327—24no—
321C25D4×C13911yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C13911yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C2×C4×C13911yescharacteristic
332C23×C4C2×C4×C13911yescharacteristic
333C23×C4D4×C13911yescharacteristic
334C23×C4D4×C13911yescharacteristic
335C23×C4D4×C13911yescharacteristic
336C23×C4C23×C13911yescharacteristic
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—42no—
340C22×C8—42no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×C4×C13911yescharacteristic
348C2×C4⋊C4C2×C4×C13911yescharacteristic
349C2×C4⋊C4C2×C4×C13911yescharacteristic
350C2×C22⋊C4—24no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C22⋊C8—24no—
360C22⋊C8—22no—
361C22⋊C8D4×C13914yescomplemented
362#95—21no—
363#95—21no—
364#95—21no—
365#95—22no—
366#95—22no—
367#95—42no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24C22⋊C4×C13911yescharacteristic
376C24C22⋊C4×C13911yescharacteristic
377C24D8×C13912yes—
378C24SD16×C13912yes—
379C24C2×D4×C13911yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C13911yescharacteristic
425C22×C4C22⋊C4×C13911yescharacteristic
426C22×C4C22×C4×C13911yescharacteristic
427C22×C4C2×D4×C13911yescharacteristic
428C22×C4C2×D4×C13912yes—
429C22×C4#41×C13912yes—
430C2×C8—24no—
431C2×C8—48no—
432C2×C8—42no—
433C2×C8—42no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—48no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—21no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#99×C13912yes—
478C23#102×C13912yes—
479C23#102×C13912yes—
480C23#104×C13912yes—
481C23C2×C22⋊C4×C13911yescharacteristic
482C23#121×C13912yes—
483C23C2×D8×C13911yescharacteristic
484C23C2×SD16×C13911yescharacteristic
485C23#135×C13912yes—
486D4—82no—
487D4—84no—
488D4—82no—
489D4—82no—
490D4—84no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4#99×C13912yes—
526C2×C4C4×D4×C13912yes—
527C2×C4#120×C13911yescharacteristic
528C2×C4#123×C13911yescharacteristic
529C8—44no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—21no—
537C22—22no—
538C22—21no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22#327×C13914yescomplemented
561C22#386×C13911yescharacteristic
562C22C2×#99×C13911yescharacteristic
563C22C2×#99×C13911yescharacteristic
564C22C2×#102×C13911yescharacteristic
565C22#416×C13911yescharacteristic
566C22C2×#104×C13911yescharacteristic
567C22#421×C13911yescharacteristic
568C22#465×C13912yes—
569C22#466×C13912yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—84no—
576C4—81no—
577C4—81no—
578C4—81no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—42no—
583C2—161no—
584C2C2×#327×C13911yescharacteristic
585C2#1501×C13911yescharacteristic
586C2#1516×C13911yescharacteristic
587C2#1519×C13911yescharacteristic
588C2#1871×C13911yescharacteristic
589C2#1893×C13911yescharacteristic
590C2#1898×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radical#2847×C139C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊C8×C139C2semidirect
3. C2×#327×C139C2semidirect
4. C22⋊#95×C139C2semidirect
5. #1294×C139C2semidirect
8. C2×#121×C139C4semidirect
9. C2×#121×C139C4semidirect
19. #380×C139C4semidirect
20. #380×C139C4semidirect
65. C22⋊C8×C139D4semidirect
264. C22×C139#327semidirect
295. #9113C139direct (N × H)
296. C139#9113direct (N × H)
297. C22×C22⋊C8C2×C139semidirect
299. C2×#327C2×C139semidirect
300. C22⋊#95C2×C139semidirect
301. #1294C2×C139semidirect
304. C2×#121C4×C139semidirect
305. C2×#121C4×C139semidirect
315. #380C4×C139semidirect
316. #380C4×C139semidirect
361. C22⋊C8D4×C139semidirect
560. C22#327×C139semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C1392
#2847×C1392
C2×#327×C1392
C22⋊#95×C1392
#1294×C1392
#9113139