Finite Group Databasebeta

← C139×#13877 #48008473

Subgroups — C139×#13877 #48008473

Order 35584.

4046 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C139C211yesmaximal, characteristic
2C23×C22⋊C4×C139C211yesmaximal, characteristic
3C2×#385×C139C212yesmaximal, complemented
4C2×#380×C139C212yesmaximal, complemented
5C2×#379×C139C211yesmaximal, characteristic
6#1439×C139C214yesmaximal, complemented
7C22⋊#95×C139C212yesmaximal, complemented
8C22⋊#95×C139C212yesmaximal, complemented
9C26×C139C2211yescharacteristic
10C24×C4×C139C2212yes—
11C24×C4×C139C2212yes—
12C22×C4⋊C4×C139C2214yescomplemented
13C22×C22⋊C4×C139—24no—
14C22×C22⋊C4×C139—28no—
15C22×C22⋊C4×C139—28no—
16C22×C22⋊C4×C139C418yescomplemented
17C22×C22⋊C4×C139C2211yescharacteristic
18C22×C22⋊C4×C139C2212yes—
19C22×C22⋊C4×C139C2211yescharacteristic
20C22×C22⋊C4×C139C2212yes—
21C22×C22⋊C4×C139C2211yescharacteristic
22C22×C22⋊C4×C139C2212yes—
23C22×C22⋊C4×C139C2212yes—
24C22×C22⋊C4×C139C2212yes—
25C22×C22⋊C4×C139C2211yescharacteristic
26#385×C139—28no—
27#380×C139—28no—
28#379×C139—24no—
29C2×#95×C139C2214yescomplemented
30C2×#95×C139C2214yescomplemented
31C2×#95×C139C2214yescomplemented
32C25×C139—24no—
33C25×C139—24no—
34C25×C139—24no—
35C25×C139—24no—
36C25×C139—44no—
37C25×C139C2×C414yes—
38C25×C139D414yes—
39C25×C139Q814yes—
40C25×C139C2311yescharacteristic
41C25×C139C2311yescharacteristic
42C25×C139C2311yescharacteristic
43C23×C4×C139—24no—
44C23×C4×C139—24no—
45C23×C4×C139—24no—
46C23×C4×C139—28no—
47C23×C4×C139—28no—
48C23×C4×C139—24no—
49C23×C4×C139—24no—
50C23×C4×C139—44no—
51C23×C4×C139—44no—
52C23×C4×C139C2×C418yescomplemented
53C23×C4×C139C2312yes—
54C23×C4×C139C2312yes—
55C23×C4×C139C2312yes—
56C23×C4×C139C2314yes—
57C23×C4×C139C2312yes—
58C2×C4⋊C4×C139—28no—
59C2×C4⋊C4×C139—28no—
60C2×C4⋊C4×C139—44no—
61C2×C22⋊C4×C139—232no—
62C2×C22⋊C4×C139—24no—
63C2×C22⋊C4×C139—24no—
64C2×C22⋊C4×C139—24no—
65C2×C22⋊C4×C139—24no—
66C2×C22⋊C4×C139—28no—
67C2×C22⋊C4×C139—28no—
68C2×C22⋊C4×C139—232no—
69C2×C22⋊C4×C139—24no—
70C2×C22⋊C4×C139—22no—
71C2×C22⋊C4×C139—24no—
72C2×C22⋊C4×C139—22no—
73C2×C22⋊C4×C139—24no—
74C2×C22⋊C4×C139—24no—
75C2×C22⋊C4×C139—24no—
76C2×C22⋊C4×C139—24no—
77C2×C22⋊C4×C139—44no—
78C2×C22⋊C4×C139C2×C414yes—
79C2×C22⋊C4×C139C2×C414yes—
80C2×C22⋊C4×C139C2×C418yescomplemented
81C2×C22⋊C4×C139D418yes—
82C2×C22⋊C4×C139D418yes—
83#95×C139—28no—
84#95×C139—28no—
85#95×C139—44no—
86C24×C139—22no—
87C24×C139—22no—
88C24×C139—22no—
89C24×C139—22no—
90C24×C139—24no—
91C24×C139—24no—
92C24×C139—28no—
93C24×C139—28no—
94C24×C139—216no—
95C24×C139—28no—
96C24×C139—216no—
97C24×C139—216no—
98C24×C139—216no—
99C24×C139—28no—
100C24×C139—22no—
101C24×C139—22no—
102C24×C139—22no—
103C24×C139—22no—
104C24×C139—24no—
105C24×C139—48no—
106C24×C139—48no—
107C24×C139—48no—
108C24×C139—416no—
109C24×C139—416no—
110C24×C139—416no—
111C24×C139—416no—
112C24×C139C4⋊C4116yescomplemented
113C24×C139C22×C412yes—
114C24×C139C22×C412yes—
115C24×C139C22×C412yes—
116C24×C139C2×D412yes—
117C24×C139C2×D414yes—
118C24×C139C2×D412yes—
119C24×C139C2×D412yes—
120C24×C139C2×D414yes—
121C24×C139C2×Q812yes—
122C24×C139C2×Q812yes—
123C24×C139C2×Q812yes—
124C24×C139#4114yes—
125C24×C139#4114yes—
126C24×C139C2411yescharacteristic
127C22×C4×C139—22no—
128C22×C4×C139—22no—
129C22×C4×C139—24no—
130C22×C4×C139—216no—
131C22×C4×C139—216no—
132C22×C4×C139—22no—
133C22×C4×C139—24no—
134C22×C4×C139—24no—
135C22×C4×C139—24no—
136C22×C4×C139—24no—
137C22×C4×C139—22no—
138C22×C4×C139—24no—
139C22×C4×C139—24no—
140C22×C4×C139—24no—
141C22×C4×C139—24no—
142C22×C4×C139—216no—
143C22×C4×C139—22no—
144C22×C4×C139—24no—
145C22×C4×C139—22no—
146C22×C4×C139—22no—
147C22×C4×C139—22no—
148C22×C4×C139—22no—
149C22×C4×C139—22no—
150C22×C4×C139—24no—
151C22×C4×C139—24no—
152C22×C4×C139—24no—
153C22×C4×C139—48no—
154C22×C4×C139—416no—
155C22×C4×C139—416no—
156C22×C4×C139—416no—
157C22×C4×C139—416no—
158C22×C4×C139—48no—
159C22×C4×C139—48no—
160C22×C4×C139C22×C414yes—
161C22×C4×C139C22×C414yes—
162C22×C4×C139C2×D418yes—
163C22×C4×C139C2×D418yes—
164C4⋊C4×C139—416no—
165C22⋊C4×C139—216no—
166C22⋊C4×C139—28no—
167C22⋊C4×C139—216no—
168C22⋊C4×C139—216no—
169C22⋊C4×C139—48no—
170C22⋊C4×C139—44no—
171C22⋊C4×C139—48no—
172C22⋊C4×C139—44no—
173C22⋊C4×C139C22⋊C4116yescomplemented
174C23×C139—22no—
175C23×C139—22no—
176C23×C139—24no—
177C23×C139—24no—
178C23×C139—24no—
179C23×C139—22no—
180C23×C139—24no—
181C23×C139—24no—
182C23×C139—24no—
183C23×C139—22no—
184C23×C139—24no—
185C23×C139—24no—
186C23×C139—24no—
187C23×C139—24no—
188C23×C139—28no—
189C23×C139—28no—
190C23×C139—28no—
191C23×C139—28no—
192C23×C139—28no—
193C23×C139—28no—
194C23×C139—28no—
195C23×C139—28no—
196C23×C139—22no—
197C23×C139—22no—
198C23×C139—24no—
199C23×C139—24no—
200C23×C139—22no—
201C23×C139—24no—
202C23×C139—24no—
203C23×C139—24no—
204C23×C139—22no—
205C23×C139—24no—
206C23×C139—24no—
207C23×C139—232no—
208C23×C139—232no—
209C23×C139—416no—
210C23×C139—432no—
211C23×C139—432no—
212C23×C139—432no—
213C23×C139—432no—
214C23×C139—464no—
215C23×C139—44no—
216C23×C139—44no—
217C23×C139—44no—
218C23×C139—44no—
219C23×C139C2×C22⋊C414yes—
220C23×C139C2×C4⋊C414yes—
221C23×C139C2×C4⋊C414yes—
222C23×C139C2×C4⋊C414yes—
223C23×C139#11714yes—
224C23×C139C4×D418yes—
225C23×C139#12014yes—
226C23×C139#12118yes—
227C23×C139C22⋊Q818yes—
228C23×C139C22⋊Q818yes—
229C23×C139#12314yes—
230C23×C139C23×C411yescharacteristic
231C23×C139C22×D412yes—
232C23×C139C22×D411yescharacteristic
233C23×C139C22×D412yes—
234C23×C139C22×Q811yescharacteristic
235C23×C139C2×#4112yes—
236C23×C139C2×#4112yes—
237C23×C139H(5,𝔽2)14yes—
238C2×C4×C139—24no—
239C2×C4×C139—24no—
240C2×C4×C139—28no—
241C2×C4×C139—28no—
242C2×C4×C139—24no—
243C2×C4×C139—24no—
244C2×C4×C139—24no—
245C2×C4×C139—28no—
246C2×C4×C139—28no—
247C2×C4×C139—28no—
248C2×C4×C139—432no—
249C2×C4×C139—432no—
250C2×C4×C139—44no—
251C2×C4×C139—44no—
252C2×C4×C139—44no—
253C2×C4×C139—44no—
254C2×C4×C139—44no—
255C2×C4×C139—44no—
256C2×C4×C139—42no—
257C2×C4×C139—42no—
258C2×C4×C139—42no—
259C2×C4×C139—42no—
260C2×C4×C139—42no—
261C2×C4×C139—42no—
262C2×C4×C139—44no—
263C2×C4×C139—44no—
264C2×C4×C139—44no—
265C2×C4×C139—44no—
266C2×C4×C139C2×C22⋊C418yescomplemented
267C22×C139—24no—
268C22×C139—24no—
269C22×C139—28no—
270C22×C139—28no—
271C22×C139—28no—
272C22×C139—28no—
273C22×C139—28no—
274C22×C139—28no—
275C22×C139—28no—
276C22×C139—28no—
277C22×C139—216no—
278C22×C139—216no—
279C22×C139—24no—
280C22×C139—24no—
281C22×C139—24no—
282C22×C139—24no—
283C22×C139—24no—
284C22×C139—464no—
285C22×C139—44no—
286C22×C139—44no—
287C22×C139—44no—
288C22×C139—44no—
289C22×C139—48no—
290C22×C139#38018yescomplemented
291C22×C139#38518yescomplemented
292C22×C139C22×C22⋊C411yescharacteristic
293C22×C139C22×C4⋊C411yescharacteristic
294C22×C139C2×#11711yescharacteristic
295C22×C139C2×C4×D412yes—
296C22×C139#51812yes—
297C22×C139C2×#12011yescharacteristic
298C22×C139C2×#12112yes—
299C22×C139C2×C22⋊Q812yes—
300C22×C139C2×C22⋊Q812yes—
301C22×C139C2×#12311yescharacteristic
302C22×C139#53412yes—
303C22×C139#54312yes—
304C22×C139D4214yes—
305C22×C139#54614yes—
306C22×C139#54614yes—
307C22×C139#55114yes—
308C4×C139—28no—
309C4×C139—44no—
310C4×C139—48no—
311C4×C139—82no—
312C4×C139—82no—
313C2×C139—28no—
314C2×C139—28no—
315C2×C139—44no—
316C2×C139C2×#38011yescharacteristic
317C2×C139C2×#38511yescharacteristic
318C2×C139#231511yescharacteristic
319C2×C139D4×C22⋊C412yes—
320C2×C139#234212yes—
321C2×C139#241012yes—
322C2×C139#241212yes—
323C2×C139#243714yes—
324#13877C13911yesmaximal, characteristic, direct product factor, Sylow
325C139#1387711yescharacteristic, direct product factor, Sylow
326C23×C22⋊C4C2×C13911yescharacteristic
327C23×C22⋊C4C2×C13911yescharacteristic
328C2×#385C2×C13912yescomplemented
329C2×#380C2×C13912yescomplemented
330C2×#379C2×C13911yescharacteristic
331#1439C2×C13914yescomplemented
332C22⋊#95C2×C13912yescomplemented
333C22⋊#95C2×C13912yescomplemented
334C26C22×C13911yescharacteristic
335C24×C4C22×C13912yes—
336C24×C4C22×C13912yes—
337C22×C4⋊C4C22×C13914yescomplemented
338C22×C22⋊C4—24no—
339C22×C22⋊C4—28no—
340C22×C22⋊C4—28no—
341C22×C22⋊C4C4×C13918yescomplemented
342C22×C22⋊C4C22×C13912yes—
343C22×C22⋊C4C22×C13911yescharacteristic
344C22×C22⋊C4C22×C13912yes—
345C22×C22⋊C4C22×C13911yescharacteristic
346C22×C22⋊C4C22×C13911yescharacteristic
347C22×C22⋊C4C22×C13912yes—
348C22×C22⋊C4C22×C13912yes—
349C22×C22⋊C4C22×C13912yes—
350C22×C22⋊C4C22×C13911yescharacteristic
351#385—28no—
352#380—28no—
353#379—24no—
354C2×#95C22×C13914yescomplemented
355C2×#95C22×C13914yescomplemented
356C2×#95C22×C13914yescomplemented
357C25—24no—
358C25—24no—
359C25—24no—
360C25—24no—
361C25—44no—
362C25C2×C4×C13914yes—
363C25D4×C13914yes—
364C25Q8×C13914yes—
365C25C23×C13911yescharacteristic
366C25C23×C13911yescharacteristic
367C25C23×C13911yescharacteristic
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—28no—
372C23×C4—28no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—44no—
376C23×C4—44no—
377C23×C4C2×C4×C13918yescomplemented
378C23×C4C23×C13912yes—
379C23×C4C23×C13912yes—
380C23×C4C23×C13912yes—
381C23×C4C23×C13914yes—
382C23×C4C23×C13912yes—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—44no—
386C2×C22⋊C4—232no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×C4×C13914yes—
404C2×C22⋊C4C2×C4×C13914yes—
405C2×C22⋊C4C2×C4×C13918yescomplemented
406C2×C22⋊C4D4×C13918yes—
407C2×C22⋊C4D4×C13918yes—
408#95—28no—
409#95—28no—
410#95—44no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—28no—
421C24—216no—
422C24—216no—
423C24—216no—
424C24—28no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24C4⋊C4×C139116yescomplemented
438C24C22×C4×C13912yes—
439C24C22×C4×C13912yes—
440C24C22×C4×C13912yes—
441C24C2×D4×C13912yes—
442C24C2×D4×C13914yes—
443C24C2×D4×C13912yes—
444C24C2×D4×C13912yes—
445C24C2×D4×C13914yes—
446C24C2×Q8×C13912yes—
447C24C2×Q8×C13912yes—
448C24C2×Q8×C13912yes—
449C24#41×C13914yes—
450C24#41×C13914yes—
451C24C24×C13911yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—216no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—48no—
479C22×C4—416no—
480C22×C4—416no—
481C22×C4—416no—
482C22×C4—416no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4C22×C4×C13914yes—
486C22×C4C22×C4×C13914yes—
487C22×C4C2×D4×C13918yes—
488C22×C4C2×D4×C13918yes—
489C4⋊C4—416no—
490C22⋊C4—216no—
491C22⋊C4—28no—
492C22⋊C4—216no—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C22⋊C4—44no—
496C22⋊C4—48no—
497C22⋊C4—44no—
498C22⋊C4C22⋊C4×C139116yescomplemented
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—22no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—28no—
521C23—22no—
522C23—22no—
523C23—24no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—232no—
533C23—232no—
534C23—416no—
535C23—432no—
536C23—432no—
537C23—432no—
538C23—432no—
539C23—464no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23C2×C22⋊C4×C13914yes—
545C23C2×C4⋊C4×C13914yes—
546C23C2×C4⋊C4×C13914yes—
547C23C2×C4⋊C4×C13914yes—
548C23#117×C13914yes—
549C23C4×D4×C13918yes—
550C23#120×C13914yes—
551C23#121×C13918yes—
552C23C22⋊Q8×C13918yes—
553C23C22⋊Q8×C13918yes—
554C23#123×C13914yes—
555C23C23×C4×C13911yescharacteristic
556C23C22×D4×C13912yes—
557C23C22×D4×C13911yescharacteristic
558C23C22×D4×C13912yes—
559C23C22×Q8×C13911yescharacteristic
560C23C2×#41×C13912yes—
561C23C2×#41×C13912yes—
562C23H(5,𝔽2)×C13914yes—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—28no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4C2×C22⋊C4×C13918yescomplemented
592C22—24no—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—28no—
597C22—28no—
598C22—28no—
599C22—28no—
600C22—28no—
601C22—28no—
602C22—28no—
603C22—28no—
604C22—216no—
605C22—216no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—464no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—48no—
615C22#380×C13918yescomplemented
616C22#385×C13918yescomplemented
617C22C22×C22⋊C4×C13911yescharacteristic
618C22C22×C4⋊C4×C13911yescharacteristic
619C22C2×#117×C13911yescharacteristic
620C22C2×C4×D4×C13912yes—
621C22#518×C13912yes—
622C22C2×#120×C13911yescharacteristic
623C22C2×#121×C13912yes—
624C22C2×C22⋊Q8×C13912yes—
625C22C2×C22⋊Q8×C13912yes—
626C22C2×#123×C13911yescharacteristic
627C22#534×C13912yes—
628C22#543×C13912yes—
629C22D42×C13914yes—
630C22#546×C13914yes—
631C22#546×C13914yes—
632C22#551×C13914yes—
633C4—28no—
634C4—44no—
635C4—48no—
636C4—82no—
637C4—82no—
638C2—28no—
639C2—28no—
640C2—44no—
641C2C2×#380×C13911yescharacteristic
642C2C2×#385×C13911yescharacteristic
643C2#2315×C13911yescharacteristic
644C2D4×C22⋊C4×C13912yes—
645C2#2342×C13912yes—
646C2#2410×C13912yes—
647C2#2412×C13912yes—
648C2#2437×C13914yes—
subgroupG/H
center, socleC24×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC24C24×C139
prime radicalC26×C139C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#385×C139C2semidirect
4. C2×#380×C139C2semidirect
6. #1439×C139C2semidirect
7. C22⋊#95×C139C2semidirect
8. C22⋊#95×C139C2semidirect
12. C22×C4⋊C4×C139C22semidirect
16. C22×C22⋊C4×C139C4semidirect
29. C2×#95×C139C22semidirect
30. C2×#95×C139C22semidirect
31. C2×#95×C139C22semidirect
52. C23×C4×C139C2×C4semidirect
80. C2×C22⋊C4×C139C2×C4semidirect
112. C24×C139C4⋊C4semidirect
173. C22⋊C4×C139C22⋊C4semidirect
266. C2×C4×C139C2×C22⋊C4semidirect
290. C22×C139#380semidirect
291. C22×C139#385semidirect
324. #13877C139direct (N × H)
325. C139#13877direct (N × H)
328. C2×#385C2×C139semidirect
329. C2×#380C2×C139semidirect
331. #1439C2×C139semidirect
332. C22⋊#95C2×C139semidirect
333. C22⋊#95C2×C139semidirect
337. C22×C4⋊C4C22×C139semidirect
341. C22×C22⋊C4C4×C139semidirect
354. C2×#95C22×C139semidirect
355. C2×#95C22×C139semidirect
356. C2×#95C22×C139semidirect
377. C23×C4C2×C4×C139semidirect
405. C2×C22⋊C4C2×C4×C139semidirect
437. C24C4⋊C4×C139semidirect
498. C22⋊C4C22⋊C4×C139semidirect
591. C2×C4C2×C22⋊C4×C139semidirect
615. C22#380×C139semidirect
616. C22#385×C139semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1392
C2×#385×C1392
C2×#380×C1392
C2×#379×C1392
#1439×C1392
C22⋊#95×C1392
#13877139