Finite Group Databasebeta

← C139×#10745 #48005341

Subgroups — C139×#10745 #48005341

Order 35584.

1794 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C139C211yesmaximal, characteristic
2C22×#99×C139C211yesmaximal, characteristic
3C2×#386×C139C211yesmaximal, characteristic
4C2×#342×C139C212yesmaximal, complemented
5C22⋊#95×C139C212yesmaximal, complemented
6C23×D4×C139C2211yescharacteristic
7C24×C4×C139C2211yescharacteristic
8#518×C139—22no—
9#518×C139—24no—
10#518×C139C414yescomplemented
11C2×C4×D4×C139—24no—
12C2×#117×C139—21no—
13C22×C22⋊C4×C139—21no—
14C22×C22⋊C4×C139—21no—
15C22×C22⋊C4×C139C2211yescharacteristic
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2212yes—
18C2×#99×C139—22no—
19C2×#99×C139—22no—
20C2×#99×C139C414yescomplemented
21#386×C139—22no—
22#386×C139C414yescomplemented
23C2×#95×C139—21no—
24C2×#95×C139—24no—
25#342×C139—24no—
26C25×C139D411yescharacteristic
27C25×C139C2311yescharacteristic
28C22×D4×C139—22no—
29C22×D4×C139—22no—
30C22×D4×C139—22no—
31C22×D4×C139—22no—
32C22×D4×C139C2×C412yes—
33C22×D4×C139C2×C412yes—
34C22×D4×C139C2×C412yes—
35C22×D4×C139D412yes—
36C22×D4×C139D412yes—
37C22×D4×C139Q812yes—
38C23×C4×C139—21no—
39C23×C4×C139—22no—
40C23×C4×C139—22no—
41C23×C4×C139—21no—
42C23×C4×C139—22no—
43C23×C4×C139—21no—
44C23×C4×C139—22no—
45C23×C4×C139—44no—
46C23×C4×C139C2×C412yescomplemented
47C23×C4×C139D411yescharacteristic
48C23×C4×C139D414yes—
49C4×D4×C139—216no—
50C4×D4×C139—216no—
51#117×C139—24no—
52#117×C139—24no—
53C2×C4⋊C4×C139—22no—
54C2×C22⋊C4×C139—22no—
55C2×C22⋊C4×C139—24no—
56C2×C22⋊C4×C139—24no—
57C2×C22⋊C4×C139—22no—
58C2×C22⋊C4×C139—22no—
59C2×C22⋊C4×C139—22no—
60C2×C22⋊C4×C139—22no—
61C2×C22⋊C4×C139—22no—
62C2×C22⋊C4×C139—22no—
63C2×C22⋊C4×C139—22no—
64C2×C22⋊C4×C139—22no—
65C2×C22⋊C4×C139—22no—
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139—24no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—22no—
70C2×C22⋊C4×C139—44no—
71C2×C22⋊C4×C139C2×C414yes—
72C2×C22⋊C4×C139C2×C414yescomplemented
73C2×C22⋊C4×C139C2×C412yescomplemented
74C2×C22⋊C4×C139D414yes—
75C2×C42×C139—22no—
76#99×C139—28no—
77#95×C139—24no—
78#95×C139—48no—
79C24×C139—21no—
80C24×C139—21no—
81C24×C139—21no—
82C24×C139—21no—
83C24×C139—42no—
84C24×C139—42no—
85C24×C139—42no—
86C24×C139—42no—
87C24×C139C22⋊C412yes—
88C24×C139C22⋊C412yes—
89C24×C139C4⋊C412yes—
90C24×C139C22×C411yescharacteristic
91C24×C139C22×C411yescharacteristic
92C24×C139C22×C411yescharacteristic
93C24×C139C2×D411yescharacteristic
94C24×C139C2×D412yes—
95C24×C139C2×D411yescharacteristic
96C24×C139C2×D411yescharacteristic
97C24×C139C2×D412yes—
98C24×C139C2×Q811yescharacteristic
99C24×C139#4112yes—
100C24×C139#4112yes—
101C2×D4×C139—24no—
102C2×D4×C139—24no—
103C2×D4×C139—24no—
104C2×D4×C139—24no—
105C2×D4×C139—24no—
106C2×D4×C139—24no—
107C2×D4×C139—24no—
108C2×D4×C139—24no—
109C2×D4×C139—24no—
110C2×D4×C139—24no—
111C2×D4×C139—24no—
112C2×D4×C139—24no—
113C2×D4×C139C4214yes—
114C2×D4×C139C22⋊C414yes—
115C2×D4×C139C4⋊C414yes—
116C2×D4×C139C4⋊C414yes—
117C22×C4×C139—21no—
118C22×C4×C139—21no—
119C22×C4×C139—21no—
120C22×C4×C139—21no—
121C22×C4×C139—28no—
122C22×C4×C139—24no—
123C22×C4×C139—22no—
124C22×C4×C139—24no—
125C22×C4×C139—24no—
126C22×C4×C139—28no—
127C22×C4×C139—24no—
128C22×C4×C139—22no—
129C22×C4×C139—24no—
130C22×C4×C139—44no—
131C22×C4×C139—44no—
132C22×C4×C139—48no—
133C22×C4×C139—44no—
134C22×C4×C139—42no—
135C22×C4×C139—41no—
136C22×C4×C139—42no—
137C22×C4×C139—41no—
138C22×C4×C139—44no—
139C22×C4×C139—44no—
140C22×C4×C139—44no—
141C22×C4×C139—42no—
142C22×C4×C139—44no—
143C22×C4×C139—42no—
144C22×C4×C139—41no—
145C22×C4×C139—42no—
146C22×C4×C139—42no—
147C22×C4×C139—41no—
148C22×C4×C139—82no—
149C22×C4×C139—82no—
150C22×C4×C139C22⋊C412yes—
151C22×C4×C139C22⋊C412yes—
152C22×C4×C139C22⋊C418yescomplemented
153C22×C4×C139C4⋊C412yes—
154C4⋊C4×C139—28no—
155C22⋊C4×C139—28no—
156C22⋊C4×C139—24no—
157C22⋊C4×C139—24no—
158C22⋊C4×C139—24no—
159C22⋊C4×C139—24no—
160C22⋊C4×C139—24no—
161C22⋊C4×C139—24no—
162C22⋊C4×C139—24no—
163C22⋊C4×C139—48no—
164C22⋊C4×C139—42no—
165C22⋊C4×C139—42no—
166C22⋊C4×C139—42no—
167C42×C139—28no—
168C23×C139—24no—
169C23×C139—22no—
170C23×C139—24no—
171C23×C139—22no—
172C23×C139—22no—
173C23×C139—22no—
174C23×C139—22no—
175C23×C139—22no—
176C23×C139—22no—
177C23×C139—22no—
178C23×C139—41no—
179C23×C139—41no—
180C23×C139—42no—
181C23×C139—42no—
182C23×C139—41no—
183C23×C139—42no—
184C23×C139—41no—
185C23×C139—44no—
186C23×C139—42no—
187C23×C139—42no—
188C23×C139—44no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—42no—
192C23×C139—44no—
193C23×C139—44no—
194C23×C139—42no—
195C23×C139—42no—
196C23×C139—82no—
197C23×C139—81no—
198C23×C139—81no—
199C23×C139—82no—
200C23×C139#9514yescomplemented
201C23×C139C2×C4211yescharacteristic
202C23×C139C2×C22⋊C411yescharacteristic
203C23×C139C2×C22⋊C411yescharacteristic
204C23×C139C2×C22⋊C412yes—
205C23×C139C2×C22⋊C411yescharacteristic
206C23×C139C2×C4⋊C411yescharacteristic
207C23×C139C2×C4⋊C411yescharacteristic
208C23×C139C2×C4⋊C411yescharacteristic
209C23×C139#11712yes—
210C23×C139C4×D412yes—
211C23×C139C4×D412yes—
212C23×C139C4×D412yes—
213C23×C139C4×D412yes—
214C23×C139#12011yescharacteristic
215C23×C139#12012yes—
216C23×C139#12011yescharacteristic
217C23×C139#12112yes—
218C23×C139#12112yes—
219C23×C139C22⋊Q812yes—
220C23×C139C22⋊Q812yes—
221C23×C139#12311yescharacteristic
222C23×C139#12311yescharacteristic
223C23×C139#12312yes—
224D4×C139—28no—
225D4×C139—28no—
226D4×C139—28no—
227D4×C139—28no—
228C2×C4×C139—22no—
229C2×C4×C139—22no—
230C2×C4×C139—22no—
231C2×C4×C139—22no—
232C2×C4×C139—22no—
233C2×C4×C139—22no—
234C2×C4×C139—24no—
235C2×C4×C139—28no—
236C2×C4×C139—28no—
237C2×C4×C139—42no—
238C2×C4×C139—44no—
239C2×C4×C139—48no—
240C2×C4×C139—44no—
241C2×C4×C139—42no—
242C2×C4×C139—44no—
243C2×C4×C139—44no—
244C2×C4×C139—44no—
245C2×C4×C139—48no—
246C2×C4×C139—42no—
247C2×C4×C139—48no—
248C2×C4×C139—42no—
249C2×C4×C139—42no—
250C2×C4×C139—44no—
251C2×C4×C139—84no—
252C2×C4×C139—88no—
253C2×C4×C139—82no—
254C2×C4×C139—82no—
255C2×C4×C139—82no—
256C2×C4×C139—84no—
257C2×C4×C139—82no—
258C2×C4×C139#9514yescomplemented
259C22×C139—24no—
260C22×C139—22no—
261C22×C139—22no—
262C22×C139—24no—
263C22×C139—21no—
264C22×C139—22no—
265C22×C139—22no—
266C22×C139—21no—
267C22×C139—21no—
268C22×C139—22no—
269C22×C139—21no—
270C22×C139—22no—
271C22×C139—24no—
272C22×C139—24no—
273C22×C139—22no—
274C22×C139—22no—
275C22×C139—24no—
276C22×C139—41no—
277C22×C139—41no—
278C22×C139—41no—
279C22×C139—41no—
280C22×C139—42no—
281C22×C139—42no—
282C22×C139—42no—
283C22×C139—42no—
284C22×C139—42no—
285C22×C139—42no—
286C22×C139—44no—
287C22×C139—44no—
288C22×C139—42no—
289C22×C139—42no—
290C22×C139—44no—
291C22×C139—82no—
292C22×C139—82no—
293C22×C139—82no—
294C22×C139C2×#9511yescharacteristic
295C22×C139C4×C22⋊C412yes—
296C22×C139#37911yescharacteristic
297C22×C139#38012yes—
298C22×C139#38111yescharacteristic
299C22×C139#38511yescharacteristic
300C22×C139#38512yes—
301C22×C139#38511yescharacteristic
302C22×C139#38611yescharacteristic
303C22×C139#38612yes—
304C22×C139#38611yescharacteristic
305C22×C139B(4,𝔽2)12yes—
306C22×C139#45812yes—
307C4×C139—24no—
308C4×C139—44no—
309C4×C139—48no—
310C4×C139—82no—
311C4×C139—84no—
312C2×C139—21no—
313C2×C139—22no—
314C2×C139—21no—
315C2×C139—21no—
316C2×C139—21no—
317C2×C139—22no—
318C2×C139—22no—
319C2×C139—22no—
320C2×C139—44no—
321C2×C139C22⋊#9511yescharacteristic
322C2×C139#179012yes—
323C2×C139#186712yes—
324C2×C139#188911yescharacteristic
325C2×C139#189011yescharacteristic
326#10745C13911yesmaximal, characteristic, direct product factor, Sylow
327C139#1074511yescharacteristic, direct product factor, Sylow
328C2×#518C2×C13911yescharacteristic
329C22×#99C2×C13911yescharacteristic
330C2×#386C2×C13911yescharacteristic
331C2×#342C2×C13912yescomplemented
332C22⋊#95C2×C13912yescomplemented
333C23×D4C22×C13911yescharacteristic
334C24×C4C22×C13911yescharacteristic
335#518—22no—
336#518—24no—
337#518C4×C13914yescomplemented
338C2×C4×D4—24no—
339C2×#117—21no—
340C22×C22⋊C4—21no—
341C22×C22⋊C4—21no—
342C22×C22⋊C4C22×C13912yes—
343C22×C22⋊C4C22×C13911yescharacteristic
344C22×C22⋊C4C22×C13912yes—
345C2×#99—22no—
346C2×#99—22no—
347C2×#99C4×C13914yescomplemented
348#386—22no—
349#386C4×C13914yescomplemented
350C2×#95—21no—
351C2×#95—24no—
352#342—24no—
353C25D4×C13911yescharacteristic
354C25C23×C13911yescharacteristic
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4C2×C4×C13912yes—
360C22×D4C2×C4×C13912yes—
361C22×D4C2×C4×C13912yes—
362C22×D4D4×C13912yes—
363C22×D4D4×C13912yes—
364C22×D4Q8×C13912yes—
365C23×C4—21no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—21no—
369C23×C4—22no—
370C23×C4—21no—
371C23×C4—22no—
372C23×C4—44no—
373C23×C4C2×C4×C13912yescomplemented
374C23×C4D4×C13911yescharacteristic
375C23×C4D4×C13914yes—
376C4×D4—216no—
377C4×D4—216no—
378#117—24no—
379#117—24no—
380C2×C4⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×C4×C13914yes—
399C2×C22⋊C4C2×C4×C13912yescomplemented
400C2×C22⋊C4C2×C4×C13914yescomplemented
401C2×C22⋊C4D4×C13914yes—
402C2×C42—22no—
403#99—28no—
404#95—24no—
405#95—48no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24C22⋊C4×C13912yes—
415C24C22⋊C4×C13912yes—
416C24C4⋊C4×C13912yes—
417C24C22×C4×C13911yescharacteristic
418C24C22×C4×C13911yescharacteristic
419C24C22×C4×C13911yescharacteristic
420C24C2×D4×C13911yescharacteristic
421C24C2×D4×C13912yes—
422C24C2×D4×C13911yescharacteristic
423C24C2×D4×C13911yescharacteristic
424C24C2×D4×C13912yes—
425C24C2×Q8×C13911yescharacteristic
426C24#41×C13912yes—
427C24#41×C13912yes—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4C42×C13914yes—
441C2×D4C22⋊C4×C13914yes—
442C2×D4C4⋊C4×C13914yes—
443C2×D4C4⋊C4×C13914yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—82no—
476C22×C4—82no—
477C22×C4C22⋊C4×C13912yes—
478C22×C4C22⋊C4×C13912yes—
479C22×C4C22⋊C4×C13918yescomplemented
480C22×C4C4⋊C4×C13912yes—
481C4⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—48no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C42—28no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—41no—
511C23—44no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—44no—
519C23—42no—
520C23—44no—
521C23—42no—
522C23—42no—
523C23—82no—
524C23—82no—
525C23—81no—
526C23—81no—
527C23#95×C13914yescomplemented
528C23C2×C42×C13911yescharacteristic
529C23C2×C22⋊C4×C13911yescharacteristic
530C23C2×C22⋊C4×C13911yescharacteristic
531C23C2×C22⋊C4×C13912yes—
532C23C2×C22⋊C4×C13911yescharacteristic
533C23C2×C4⋊C4×C13911yescharacteristic
534C23C2×C4⋊C4×C13911yescharacteristic
535C23C2×C4⋊C4×C13911yescharacteristic
536C23#117×C13912yes—
537C23C4×D4×C13912yes—
538C23C4×D4×C13912yes—
539C23C4×D4×C13912yes—
540C23C4×D4×C13912yes—
541C23#120×C13911yescharacteristic
542C23#120×C13912yes—
543C23#120×C13911yescharacteristic
544C23#121×C13912yes—
545C23#121×C13912yes—
546C23C22⋊Q8×C13912yes—
547C23C22⋊Q8×C13912yes—
548C23#123×C13911yescharacteristic
549C23#123×C13911yescharacteristic
550C23#123×C13912yes—
551D4—28no—
552D4—28no—
553D4—28no—
554D4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—28no—
563C2×C4—28no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—48no—
573C2×C4—42no—
574C2×C4—48no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—84no—
579C2×C4—88no—
580C2×C4—84no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—82no—
585C2×C4#95×C13914yescomplemented
586C22—24no—
587C22—24no—
588C22—22no—
589C22—22no—
590C22—24no—
591C22—22no—
592C22—22no—
593C22—24no—
594C22—21no—
595C22—22no—
596C22—22no—
597C22—21no—
598C22—21no—
599C22—22no—
600C22—21no—
601C22—22no—
602C22—24no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—82no—
619C22—82no—
620C22—82no—
621C22C2×#95×C13911yescharacteristic
622C22C4×C22⋊C4×C13912yes—
623C22#379×C13911yescharacteristic
624C22#380×C13912yes—
625C22#381×C13911yescharacteristic
626C22#385×C13911yescharacteristic
627C22#385×C13912yes—
628C22#385×C13911yescharacteristic
629C22#386×C13911yescharacteristic
630C22#386×C13912yes—
631C22#386×C13911yescharacteristic
632C22B(4,𝔽2)×C13912yes—
633C22#458×C13912yes—
634C4—24no—
635C4—48no—
636C4—44no—
637C4—82no—
638C4—84no—
639C2—21no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—22no—
645C2—22no—
646C2—22no—
647C2—44no—
648C2C22⋊#95×C13911yescharacteristic
649C2#1790×C13912yes—
650C2#1867×C13912yes—
651C2#1889×C13911yescharacteristic
652C2#1890×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutatorC23C2×C42×C139
Frattini, cosocleC25C23×C139
prime radicalC23×D4×C139C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C25×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#342×C139C2semidirect
5. C22⋊#95×C139C2semidirect
10. #518×C139C4semidirect
20. C2×#99×C139C4semidirect
22. #386×C139C4semidirect
46. C23×C4×C139C2×C4semidirect
72. C2×C22⋊C4×C139C2×C4semidirect
73. C2×C22⋊C4×C139C2×C4semidirect
152. C22×C4×C139C22⋊C4semidirect
200. C23×C139#95semidirect
258. C2×C4×C139#95semidirect
326. #10745C139direct (N × H)
327. C139#10745direct (N × H)
331. C2×#342C2×C139semidirect
332. C22⋊#95C2×C139semidirect
337. #518C4×C139semidirect
347. C2×#99C4×C139semidirect
349. #386C4×C139semidirect
373. C23×C4C2×C4×C139semidirect
399. C2×C22⋊C4C2×C4×C139semidirect
400. C2×C22⋊C4C2×C4×C139semidirect
479. C22×C4C22⋊C4×C139semidirect
527. C23#95×C139semidirect
585. C2×C4#95×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C1392
C22×#99×C1392
C2×#386×C1392
C2×#342×C1392
C22⋊#95×C1392
#10745139