Finite Group Databasebeta

← C139×#10960 #48005556

Subgroups — C139×#10960 #48005556

Order 35584.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C139C212yesmaximal
2C2×#386×C139C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
4C2×#342×C139C212yesmaximal, complemented
5C22⋊#95×C139C211yesmaximal, characteristic, complemented
6C23×D4×C139C2211yescharacteristic
7C24×C4×C139C2211yescharacteristic
8C22×C22⋊C4×C139C412yescomplemented
9C22×C22⋊C4×C139C2211yescharacteristic
10C22×C22⋊C4×C139C2212yes—
11C22×C22⋊C4×C139C2212yes—
12C22×C42×C139—21no—
13C2×#99×C139—24no—
14C2×#99×C139—24no—
15C2×#99×C139C418yescomplemented
16#386×C139—21no—
17#386×C139—22no—
18#386×C139—21no—
19C4×C22⋊C4×C139—24no—
20C2×#95×C139—21no—
21C2×#95×C139—22no—
22C2×#95×C139C412yescomplemented
23#342×C139—24no—
24C25×C139C2×C411yescharacteristic
25C25×C139C2311yescharacteristic
26C22×D4×C139—22no—
27C22×D4×C139—22no—
28C22×D4×C139—21no—
29C22×D4×C139—21no—
30C22×D4×C139—22no—
31C22×D4×C139—22no—
32C22×D4×C139—22no—
33C22×D4×C139C2×C414yes—
34C23×C4×C139—22no—
35C23×C4×C139—22no—
36C23×C4×C139—22no—
37C23×C4×C139—22no—
38C23×C4×C139—44no—
39C23×C4×C139C2×C411yescharacteristic
40C23×C4×C139C2×C412yes—
41C23×C4×C139C2×C412yes—
42C23×C4×C139D411yescharacteristic
43C23×C4×C139D412yes—
44C23×C4×C139D411yescharacteristic
45C2×C22⋊C4×C139—22no—
46C2×C22⋊C4×C139—22no—
47C2×C22⋊C4×C139—22no—
48C2×C22⋊C4×C139—22no—
49C2×C22⋊C4×C139—22no—
50C2×C22⋊C4×C139—22no—
51C2×C22⋊C4×C139—22no—
52C2×C22⋊C4×C139—22no—
53C2×C22⋊C4×C139—21no—
54C2×C22⋊C4×C139—21no—
55C2×C22⋊C4×C139—22no—
56C2×C22⋊C4×C139—22no—
57C2×C22⋊C4×C139—22no—
58C2×C22⋊C4×C139—22no—
59C2×C22⋊C4×C139—44no—
60C2×C22⋊C4×C139C2×C414yes—
61C2×C22⋊C4×C139C2×C414yes—
62C2×C22⋊C4×C139D414yes—
63C2×C22⋊C4×C139D414yes—
64C2×C42×C139—24no—
65C2×C42×C139—44no—
66#99×C139—216no—
67#95×C139—24no—
68#95×C139—22no—
69#95×C139—22no—
70#95×C139—44no—
71C24×C139—21no—
72C24×C139—21no—
73C24×C139—22no—
74C24×C139—22no—
75C24×C139—42no—
76C24×C139—42no—
77C24×C139—42no—
78C24×C139—42no—
79C24×C139C4212yescomplemented
80C24×C139C22×C411yescharacteristic
81C24×C139C22×C412yes—
82C24×C139C2×D411yescharacteristic
83C24×C139C2×D411yescharacteristic
84C24×C139C2×D412yes—
85C24×C139C2×D412yes—
86C24×C139#4112yes—
87C24×C139#4112yes—
88C24×C139#4112yes—
89C2×D4×C139—24no—
90C2×D4×C139—24no—
91C2×D4×C139—24no—
92C2×D4×C139—24no—
93C2×D4×C139—24no—
94C2×D4×C139—24no—
95C2×D4×C139—41no—
96C2×D4×C139—42no—
97C2×D4×C139—42no—
98C2×D4×C139—42no—
99C2×D4×C139—41no—
100C2×D4×C139—42no—
101C2×D4×C139—42no—
102C2×D4×C139—41no—
103C2×D4×C139—42no—
104C2×D4×C139—41no—
105C22×C4×C139—21no—
106C22×C4×C139—21no—
107C22×C4×C139—24no—
108C22×C4×C139—21no—
109C22×C4×C139—21no—
110C22×C4×C139—24no—
111C22×C4×C139—24no—
112C22×C4×C139—22no—
113C22×C4×C139—22no—
114C22×C4×C139—21no—
115C22×C4×C139—24no—
116C22×C4×C139—24no—
117C22×C4×C139—24no—
118C22×C4×C139—21no—
119C22×C4×C139—24no—
120C22×C4×C139—24no—
121C22×C4×C139—22no—
122C22×C4×C139—24no—
123C22×C4×C139—24no—
124C22×C4×C139—42no—
125C22×C4×C139—42no—
126C22×C4×C139—42no—
127C22×C4×C139—48no—
128C22×C4×C139—48no—
129C22×C4×C139—44no—
130C22×C4×C139—44no—
131C22×C4×C139—44no—
132C22×C4×C139—44no—
133C22×C4×C139—42no—
134C22×C4×C139—42no—
135C22×C4×C139—42no—
136C22×C4×C139—42no—
137C22×C4×C139C4212yescomplemented
138C22×C4×C139C22⋊C412yes—
139C22×C4×C139C22⋊C412yes—
140C22⋊C4×C139—24no—
141C22⋊C4×C139—24no—
142C22⋊C4×C139—24no—
143C22⋊C4×C139—24no—
144C22⋊C4×C139—24no—
145C22⋊C4×C139—44no—
146C22⋊C4×C139—42no—
147C22⋊C4×C139—42no—
148C22⋊C4×C139—42no—
149C22⋊C4×C139—41no—
150C22⋊C4×C139—41no—
151C22⋊C4×C139—44no—
152C22⋊C4×C139C22⋊C418yescomplemented
153C42×C139—48no—
154C23×C139—22no—
155C23×C139—22no—
156C23×C139—22no—
157C23×C139—22no—
158C23×C139—22no—
159C23×C139—22no—
160C23×C139—22no—
161C23×C139—24no—
162C23×C139—42no—
163C23×C139—42no—
164C23×C139—44no—
165C23×C139—42no—
166C23×C139—44no—
167C23×C139—42no—
168C23×C139—44no—
169C23×C139—44no—
170C23×C139—44no—
171C23×C139—44no—
172C23×C139—41no—
173C23×C139—42no—
174C23×C139—41no—
175C23×C139—42no—
176C23×C139—42no—
177C23×C139—82no—
178C23×C139—82no—
179C23×C139—84no—
180C23×C139C2×C4211yescharacteristic
181C23×C139C2×C22⋊C412yes—
182C23×C139C2×C22⋊C411yescharacteristic
183C23×C139#11711yescharacteristic
184C23×C139#11712yes—
185C23×C139C4×D412yes—
186C23×C139C4×D412yes—
187C23×C139C4×D412yes—
188C23×C139C4×D412yes—
189C23×C139C4×D412yes—
190C23×C139C4×D412yes—
191C23×C139#12011yescharacteristic
192C23×C139#12112yes—
193C23×C139#12112yes—
194C23×C139#12112yes—
195C23×C139#12311yescharacteristic
196C23×C139#12312yes—
197C23×C139#12411yescharacteristic
198C23×C139#12412yes—
199C23×C139#12612yes—
200C23×C139#12711yescharacteristic
201D4×C139—44no—
202D4×C139—44no—
203D4×C139—44no—
204D4×C139—44no—
205C2×C4×C139—24no—
206C2×C4×C139—24no—
207C2×C4×C139—22no—
208C2×C4×C139—22no—
209C2×C4×C139—24no—
210C2×C4×C139—22no—
211C2×C4×C139—28no—
212C2×C4×C139—22no—
213C2×C4×C139—22no—
214C2×C4×C139—22no—
215C2×C4×C139—48no—
216C2×C4×C139—48no—
217C2×C4×C139—44no—
218C2×C4×C139—44no—
219C2×C4×C139—48no—
220C2×C4×C139—48no—
221C2×C4×C139—42no—
222C2×C4×C139—42no—
223C2×C4×C139—41no—
224C2×C4×C139—42no—
225C2×C4×C139—41no—
226C2×C4×C139—48no—
227C2×C4×C139—44no—
228C2×C4×C139—42no—
229C2×C4×C139—42no—
230C2×C4×C139—42no—
231C2×C4×C139—82no—
232C2×C4×C139—82no—
233C2×C4×C139—84no—
234C2×C4×C139—84no—
235C2×C4×C139#9914yescomplemented
236C22×C139—21no—
237C22×C139—21no—
238C22×C139—22no—
239C22×C139—22no—
240C22×C139—21no—
241C22×C139—22no—
242C22×C139—22no—
243C22×C139—21no—
244C22×C139—24no—
245C22×C139—22no—
246C22×C139—24no—
247C22×C139—22no—
248C22×C139—24no—
249C22×C139—24no—
250C22×C139—22no—
251C22×C139—22no—
252C22×C139—42no—
253C22×C139—42no—
254C22×C139—42no—
255C22×C139—42no—
256C22×C139—42no—
257C22×C139—42no—
258C22×C139—42no—
259C22×C139—42no—
260C22×C139—42no—
261C22×C139—44no—
262C22×C139—84no—
263C22×C139—84no—
264C22×C139—81no—
265C22×C139—81no—
266C22×C139—82no—
267C22×C139C4×C22⋊C412yes—
268C22×C139C4×C22⋊C411yescharacteristic
269C22×C139#38612yes—
270C22×C139#38611yescharacteristic
271C22×C139#38812yes—
272C22×C139#38812yes—
273C22×C139#38812yes—
274C22×C139#39012yes—
275C22×C139#39011yescharacteristic
276C22×C139C2×#9912yes—
277C22×C139#41012yes—
278C4×C139—24no—
279C4×C139—48no—
280C4×C139—42no—
281C4×C139—42no—
282C4×C139—84no—
283C4×C139—82no—
284C2×C139—22no—
285C2×C139—22no—
286C2×C139—22no—
287C2×C139—22no—
288C2×C139—22no—
289C2×C139—22no—
290C2×C139—82no—
291C2×C139#143711yescharacteristic
292C2×C139C4×#9912yes—
293C2×C139#189811yescharacteristic
294C2×C139#189911yescharacteristic
295C2×C139#196412yes—
296#10960C13911yesmaximal, characteristic, direct product factor, Sylow
297C139#1096011yescharacteristic, direct product factor, Sylow
298C22×#99C2×C13912yes—
299C2×#386C2×C13911yescharacteristic
300C2×C4×C22⋊C4C2×C13911yescharacteristic, complemented
301C2×#342C2×C13912yescomplemented
302C22⋊#95C2×C13911yescharacteristic, complemented
303C23×D4C22×C13911yescharacteristic
304C24×C4C22×C13911yescharacteristic
305C22×C22⋊C4C4×C13912yescomplemented
306C22×C22⋊C4C22×C13911yescharacteristic
307C22×C22⋊C4C22×C13912yes—
308C22×C22⋊C4C22×C13912yes—
309C22×C42—21no—
310C2×#99—24no—
311C2×#99—24no—
312C2×#99C4×C13918yescomplemented
313#386—21no—
314#386—22no—
315#386—21no—
316C4×C22⋊C4—24no—
317C2×#95—21no—
318C2×#95—22no—
319C2×#95C4×C13912yescomplemented
320#342—24no—
321C25C2×C4×C13911yescharacteristic
322C25C23×C13911yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4C2×C4×C13914yes—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—44no—
336C23×C4C2×C4×C13911yescharacteristic
337C23×C4C2×C4×C13912yes—
338C23×C4C2×C4×C13912yes—
339C23×C4D4×C13911yescharacteristic
340C23×C4D4×C13912yes—
341C23×C4D4×C13911yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×C4×C13914yes—
358C2×C22⋊C4C2×C4×C13914yes—
359C2×C22⋊C4D4×C13914yes—
360C2×C22⋊C4D4×C13914yes—
361C2×C42—24no—
362C2×C42—44no—
363#99—216no—
364#95—24no—
365#95—22no—
366#95—22no—
367#95—44no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—22no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24C42×C13912yescomplemented
377C24C22×C4×C13911yescharacteristic
378C24C22×C4×C13912yes—
379C24C2×D4×C13911yescharacteristic
380C24C2×D4×C13911yescharacteristic
381C24C2×D4×C13912yes—
382C24C2×D4×C13912yes—
383C24#41×C13912yes—
384C24#41×C13912yes—
385C24#41×C13912yes—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—41no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—41no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C42×C13912yescomplemented
435C22×C4C22⋊C4×C13912yes—
436C22×C4C22⋊C4×C13912yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—44no—
449C22⋊C4C22⋊C4×C13918yescomplemented
450C42—48no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—42no—
463C23—44no—
464C23—44no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—82no—
475C23—82no—
476C23—84no—
477C23C2×C42×C13911yescharacteristic
478C23C2×C22⋊C4×C13912yes—
479C23C2×C22⋊C4×C13911yescharacteristic
480C23#117×C13911yescharacteristic
481C23#117×C13912yes—
482C23C4×D4×C13912yes—
483C23C4×D4×C13912yes—
484C23C4×D4×C13912yes—
485C23C4×D4×C13912yes—
486C23C4×D4×C13912yes—
487C23C4×D4×C13912yes—
488C23#120×C13911yescharacteristic
489C23#121×C13912yes—
490C23#121×C13912yes—
491C23#121×C13912yes—
492C23#123×C13911yescharacteristic
493C23#123×C13912yes—
494C23#124×C13911yescharacteristic
495C23#124×C13912yes—
496C23#126×C13912yes—
497C23#127×C13911yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—28no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—48no—
518C2×C4—44no—
519C2×C4—48no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—48no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4#99×C13914yescomplemented
533C22—24no—
534C22—24no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—22no—
543C22—22no—
544C22—21no—
545C22—24no—
546C22—22no—
547C22—24no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—42no—
559C22—84no—
560C22—84no—
561C22—81no—
562C22—81no—
563C22—82no—
564C22C4×C22⋊C4×C13912yes—
565C22C4×C22⋊C4×C13911yescharacteristic
566C22#386×C13912yes—
567C22#386×C13911yescharacteristic
568C22#388×C13912yes—
569C22#388×C13912yes—
570C22#388×C13912yes—
571C22#390×C13912yes—
572C22#390×C13911yescharacteristic
573C22C2×#99×C13912yes—
574C22#410×C13912yes—
575C4—24no—
576C4—48no—
577C4—42no—
578C4—42no—
579C4—84no—
580C4—82no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2#1437×C13911yescharacteristic
589C2C4×#99×C13912yes—
590C2#1898×C13911yescharacteristic
591C2#1899×C13911yescharacteristic
592C2#1964×C13912yes—
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC23C2×C42×C139
Frattini, cosocleC25C23×C139
prime radicalC23×D4×C139C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C139C2semidirect
4. C2×#342×C139C2semidirect
5. C22⋊#95×C139C2semidirect
8. C22×C22⋊C4×C139C4semidirect
15. C2×#99×C139C4semidirect
22. C2×#95×C139C4semidirect
79. C24×C139C42semidirect
137. C22×C4×C139C42semidirect
152. C22⋊C4×C139C22⋊C4semidirect
235. C2×C4×C139#99semidirect
296. #10960C139direct (N × H)
297. C139#10960direct (N × H)
300. C2×C4×C22⋊C4C2×C139semidirect
301. C2×#342C2×C139semidirect
302. C22⋊#95C2×C139semidirect
305. C22×C22⋊C4C4×C139semidirect
312. C2×#99C4×C139semidirect
319. C2×#95C4×C139semidirect
376. C24C42×C139semidirect
434. C22×C4C42×C139semidirect
449. C22⋊C4C22⋊C4×C139semidirect
532. C2×C4#99×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C1392
C2×#386×C1392
C2×C4×C22⋊C4×C1392
C2×#342×C1392
C22⋊#95×C1392
#10960139