Finite Group Databasebeta

← C139×#15961 #48010557

Subgroups — C139×#15961 #48010557

Order 35584.

2006 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#386×C139C212yesmaximal
2C2×#385×C139C212yesmaximal, complemented
3C2×#385×C139C212yesmaximal, complemented
4#1445×C139C211yesmaximal, characteristic, complemented
5#1442×C139C211yesmaximal, characteristic, complemented
6#1441×C139C212yesmaximal, complemented
7#1439×C139C212yesmaximal, complemented
8#1439×C139C212yesmaximal, complemented
9#1438×C139C211yesmaximal, characteristic
10C23×D4×C139C2211yescharacteristic
11C24×C4×C139C2212yes—
12C22×C4⋊C4×C139C2212yes—
13C22×C4⋊C4×C139C2211yescharacteristic
14C22×C4⋊C4×C139C2212yes—
15C22×C4⋊C4×C139C2211yescharacteristic
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2212yes—
18C22×C22⋊C4×C139C2212yes—
19C22×C22⋊C4×C139C2212yes—
20C22×C22⋊C4×C139C2212yes—
21#386×C139—28no—
22#385×C139—28no—
23#385×C139—28no—
24C2×#95×C139C2212yes—
25C2×#95×C139C2212yes—
26C2×#95×C139C2212yes—
27C2×#95×C139C2212yes—
28C2×#95×C139C2212yes—
29C2×#95×C139C2212yes—
30C2×#95×C139C2211yescharacteristic
31C2×#95×C139C2211yescharacteristic
32C2×#95×C139C2211yescharacteristic
33C2×#95×C139C2211yescharacteristic
34C25×C139C2312yes—
35C22×D4×C139—24no—
36C22×D4×C139—24no—
37C22×D4×C139—41no—
38C22×D4×C139—41no—
39C22×D4×C139Q814yes—
40C23×C4×C139—24no—
41C23×C4×C139—24no—
42C23×C4×C139—24no—
43C23×C4×C139—42no—
44C23×C4×C139—42no—
45C23×C4×C139—42no—
46C23×C4×C139—42no—
47C23×C4×C139C2312yes—
48C23×C4×C139C2311yescharacteristic
49C23×C4×C139C2312yes—
50C23×C4×C139C2312yes—
51C23×C4×C139C2312yes—
52C23×C4×C139C2311yescharacteristic
53C23×C4×C139C2312yes—
54C23×C4×C139C2311yescharacteristic
55C2×C4⋊C4×C139—24no—
56C2×C4⋊C4×C139—24no—
57C2×C4⋊C4×C139—24no—
58C2×C4⋊C4×C139—24no—
59C2×C4⋊C4×C139—41no—
60C2×C4⋊C4×C139—41no—
61C2×C4⋊C4×C139—41no—
62C2×C4⋊C4×C139—42no—
63C2×C4⋊C4×C139—42no—
64C2×C4⋊C4×C139—42no—
65C2×C4⋊C4×C139D414yescomplemented
66C2×C22⋊C4×C139—24no—
67C2×C22⋊C4×C139—24no—
68C2×C22⋊C4×C139—24no—
69C2×C22⋊C4×C139—24no—
70C2×C22⋊C4×C139—24no—
71C2×C22⋊C4×C139—24no—
72C2×C22⋊C4×C139—24no—
73C2×C22⋊C4×C139—24no—
74C2×C22⋊C4×C139—24no—
75C2×C22⋊C4×C139—24no—
76C2×C22⋊C4×C139—42no—
77C2×C22⋊C4×C139—42no—
78C2×C22⋊C4×C139—42no—
79C2×C22⋊C4×C139—42no—
80C2×C22⋊C4×C139D418yes—
81#95×C139—24no—
82#95×C139—24no—
83#95×C139—24no—
84#95×C139—24no—
85#95×C139—24no—
86#95×C139—24no—
87#95×C139—22no—
88#95×C139—41no—
89#95×C139—41no—
90#95×C139—41no—
91C24×C139—22no—
92C24×C139—22no—
93C24×C139—22no—
94C24×C139—22no—
95C24×C139—22no—
96C24×C139—22no—
97C24×C139—22no—
98C24×C139—22no—
99C24×C139—22no—
100C24×C139—22no—
101C24×C139—22no—
102C24×C139—22no—
103C24×C139C2×D414yes—
104C24×C139C2×Q814yes—
105C24×C139#4114yes—
106C24×C139C2411yescharacteristic
107C2×D4×C139—216no—
108C2×D4×C139—44no—
109C2×D4×C139—44no—
110C2×D4×C139—48no—
111C2×D4×C139—44no—
112C22×C4×C139—22no—
113C22×C4×C139—22no—
114C22×C4×C139—22no—
115C22×C4×C139—22no—
116C22×C4×C139—22no—
117C22×C4×C139—22no—
118C22×C4×C139—22no—
119C22×C4×C139—22no—
120C22×C4×C139—22no—
121C22×C4×C139—22no—
122C22×C4×C139—22no—
123C22×C4×C139—22no—
124C22×C4×C139—22no—
125C22×C4×C139—22no—
126C22×C4×C139—22no—
127C22×C4×C139—22no—
128C22×C4×C139—22no—
129C22×C4×C139—21no—
130C22×C4×C139—21no—
131C22×C4×C139—22no—
132C22×C4×C139—21no—
133C22×C4×C139—21no—
134C22×C4×C139—21no—
135C22×C4×C139—22no—
136C22×C4×C139—22no—
137C22×C4×C139—22no—
138C22×C4×C139—22no—
139C22×C4×C139—22no—
140C22×C4×C139—22no—
141C22×C4×C139—22no—
142C22×C4×C139—22no—
143C22×C4×C139—22no—
144C22×C4×C139—22no—
145C22×C4×C139—22no—
146C22×C4×C139—21no—
147C22×C4×C139—22no—
148C22×C4×C139—22no—
149C22×C4×C139—22no—
150C22×C4×C139—22no—
151C22×C4×C139—22no—
152C22×C4×C139—22no—
153C22×C4×C139—22no—
154C22×C4×C139—22no—
155C22×C4×C139—48no—
156C22×C4×C139—48no—
157C22×C4×C139—48no—
158C22×C4×C139—48no—
159C22×C4×C139—48no—
160C22×C4×C139—48no—
161C22×C4×C139—48no—
162C22×C4×C139C2×D414yes—
163C22×C4×C139C2×D412yes—
164C22×C4×C139C2×D414yes—
165C22×C4×C139C2×D414yes—
166C22×C4×C139C2×Q812yes—
167C22×C4×C139#4112yes—
168C22×C4×C139#4114yes—
169C4⋊C4×C139—44no—
170C4⋊C4×C139—44no—
171C4⋊C4×C139—48no—
172C4⋊C4×C139—48no—
173C22⋊C4×C139—216no—
174C22⋊C4×C139—216no—
175C22⋊C4×C139—48no—
176C22⋊C4×C139—48no—
177C22⋊C4×C139—48no—
178C23×C139—24no—
179C23×C139—24no—
180C23×C139—24no—
181C23×C139—24no—
182C23×C139—24no—
183C23×C139—24no—
184C23×C139—24no—
185C23×C139—24no—
186C23×C139—24no—
187C23×C139—24no—
188C23×C139—24no—
189C23×C139—24no—
190C23×C139—24no—
191C23×C139—24no—
192C23×C139—24no—
193C23×C139—24no—
194C23×C139—24no—
195C23×C139—24no—
196C23×C139—42no—
197C23×C139—42no—
198C23×C139—42no—
199C23×C139—42no—
200C23×C139—42no—
201C23×C139—42no—
202C23×C139—42no—
203C23×C139—42no—
204C23×C139—42no—
205C23×C139—42no—
206C23×C139—42no—
207C23×C139—42no—
208C23×C139—42no—
209C23×C139—42no—
210C23×C139—42no—
211C23×C139—42no—
212C23×C139C22⋊Q818yes—
213C23×C139C22×D412yes—
214C23×C139C22×D411yescharacteristic
215C23×C139C22×Q811yescharacteristic
216C23×C139C2×#4112yes—
217C23×C139C2×#4112yes—
218C23×C139C2×#4111yescharacteristic
219C23×C139H(5,𝔽2)11yescharacteristic
220C23×C139H(5,𝔽2)12yes—
221C23×C139H(5,𝔽2)11yescharacteristic
222C23×C139H(5,𝔽2)11yescharacteristic
223C23×C1392−1+411yescharacteristic
224D4×C139—416no—
225C2×C4×C139—24no—
226C2×C4×C139—24no—
227C2×C4×C139—24no—
228C2×C4×C139—24no—
229C2×C4×C139—24no—
230C2×C4×C139—24no—
231C2×C4×C139—24no—
232C2×C4×C139—24no—
233C2×C4×C139—22no—
234C2×C4×C139—24no—
235C2×C4×C139—22no—
236C2×C4×C139—22no—
237C2×C4×C139—24no—
238C2×C4×C139—24no—
239C2×C4×C139—24no—
240C2×C4×C139—24no—
241C2×C4×C139—24no—
242C2×C4×C139—24no—
243C2×C4×C139—432no—
244C2×C4×C139—42no—
245C2×C4×C139—42no—
246C2×C4×C139—42no—
247C2×C4×C139—42no—
248C2×C4×C139—42no—
249C2×C4×C139—42no—
250C2×C4×C139—41no—
251C2×C4×C139—42no—
252C2×C4×C139—42no—
253C2×C4×C139—42no—
254C2×C4×C139—41no—
255C2×C4×C139—42no—
256C2×C4×C139—42no—
257C2×C4×C139—42no—
258C2×C4×C139—42no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—42no—
262C2×C4×C139—42no—
263C2×C4×C139—42no—
264C2×C4×C139—41no—
265C2×C4×C139—41no—
266C2×C4×C139—42no—
267C2×C4×C139—42no—
268C2×C4×C139—42no—
269C2×C4×C139—42no—
270C2×C4×C139—42no—
271C2×C4×C139—42no—
272C2×C4×C139—42no—
273C2×C4×C139—42no—
274C2×C4×C139—42no—
275C2×C4×C139—42no—
276C22×C139—28no—
277C22×C139—28no—
278C22×C139—28no—
279C22×C139—44no—
280C22×C139—44no—
281C22×C139—44no—
282C22×C139—44no—
283C22×C139—44no—
284C22×C139—44no—
285C22×C139—44no—
286C22×C139—44no—
287C22×C139—44no—
288C22×C139—44no—
289C22×C139—44no—
290C22×C139—44no—
291C22×C139C2×C22⋊Q812yes—
292C22×C139#52512yes—
293C22×C139#52512yes—
294C22×C139#53412yes—
295C22×C139#53411yescharacteristic
296C22×C139#53812yes—
297C22×C139#53912yes—
298C22×C139#53911yescharacteristic
299C22×C139#54311yescharacteristic
300C22×C139D4211yescharacteristic
301C22×C139D4212yes—
302C22×C139#54612yes—
303C22×C139#54712yes—
304C22×C139D4×Q811yescharacteristic
305C22×C139#55011yescharacteristic
306C22×C139#55111yescharacteristic
307C22×C139#55312yes—
308C22×C139#55312yes—
309C22×C139#55411yescharacteristic
310C22×C139#55412yes—
311C22×C139#55911yescharacteristic
312C22×C139H(3,𝔽4)11yescharacteristic
313C22×C139#56211yescharacteristic
314C4×C139—42no—
315C4×C139—44no—
316C4×C139—44no—
317C4×C139—42no—
318C4×C139—44no—
319C4×C139—42no—
320C4×C139—44no—
321C4×C139—82no—
322C2×C139—48no—
323C2×C139#243711yescharacteristic
324C2×C139#244912yes—
325C2×C139#245511yescharacteristic
326C2×C139#245612yes—
327C2×C139#257912yes—
328C2×C139#260011yescharacteristic
329C2×C139#267911yescharacteristic
330C2×C139#270812yes—
331C2×C139#273211yescharacteristic
332C2×C139#278211yescharacteristic
333C2×C139#280411yescharacteristic
334#15961C13911yesmaximal, characteristic, direct product factor, Sylow
335C139#1596111yescharacteristic, direct product factor, Sylow
336C2×#386C2×C13912yes—
337C2×#385C2×C13912yescomplemented
338C2×#385C2×C13912yescomplemented
339#1445C2×C13911yescharacteristic, complemented
340#1442C2×C13911yescharacteristic, complemented
341#1441C2×C13912yescomplemented
342#1439C2×C13912yescomplemented
343#1439C2×C13912yescomplemented
344#1438C2×C13911yescharacteristic
345C23×D4C22×C13911yescharacteristic
346C24×C4C22×C13912yes—
347C22×C4⋊C4C22×C13912yes—
348C22×C4⋊C4C22×C13911yescharacteristic
349C22×C4⋊C4C22×C13912yes—
350C22×C4⋊C4C22×C13911yescharacteristic
351C22×C22⋊C4C22×C13912yes—
352C22×C22⋊C4C22×C13912yes—
353C22×C22⋊C4C22×C13912yes—
354C22×C22⋊C4C22×C13912yes—
355C22×C22⋊C4C22×C13912yes—
356#386—28no—
357#385—28no—
358#385—28no—
359C2×#95C22×C13911yescharacteristic
360C2×#95C22×C13912yes—
361C2×#95C22×C13912yes—
362C2×#95C22×C13912yes—
363C2×#95C22×C13912yes—
364C2×#95C22×C13912yes—
365C2×#95C22×C13912yes—
366C2×#95C22×C13911yescharacteristic
367C2×#95C22×C13911yescharacteristic
368C2×#95C22×C13911yescharacteristic
369C25C23×C13912yes—
370C22×D4—24no—
371C22×D4—24no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4Q8×C13914yes—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4C23×C13912yes—
383C23×C4C23×C13911yescharacteristic
384C23×C4C23×C13912yes—
385C23×C4C23×C13912yes—
386C23×C4C23×C13912yes—
387C23×C4C23×C13911yescharacteristic
388C23×C4C23×C13912yes—
389C23×C4C23×C13911yescharacteristic
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4D4×C13914yescomplemented
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4D4×C13918yes—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—22no—
423#95—41no—
424#95—41no—
425#95—41no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24C2×D4×C13914yes—
439C24C2×Q8×C13914yes—
440C24#41×C13914yes—
441C24C24×C13911yescharacteristic
442C2×D4—216no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—48no—
446C2×D4—44no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4C2×D4×C13914yes—
498C22×C4C2×D4×C13912yes—
499C22×C4C2×D4×C13914yes—
500C22×C4C2×D4×C13914yes—
501C22×C4C2×Q8×C13912yes—
502C22×C4#41×C13912yes—
503C22×C4#41×C13914yes—
504C4⋊C4—44no—
505C4⋊C4—44no—
506C4⋊C4—48no—
507C4⋊C4—48no—
508C22⋊C4—216no—
509C22⋊C4—216no—
510C22⋊C4—48no—
511C22⋊C4—48no—
512C22⋊C4—48no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23C22⋊Q8×C13918yes—
548C23C22×D4×C13912yes—
549C23C22×D4×C13911yescharacteristic
550C23C22×Q8×C13911yescharacteristic
551C23C2×#41×C13912yes—
552C23C2×#41×C13912yes—
553C23C2×#41×C13911yescharacteristic
554C23H(5,𝔽2)×C13911yescharacteristic
555C23H(5,𝔽2)×C13912yes—
556C23H(5,𝔽2)×C13911yescharacteristic
557C23H(5,𝔽2)×C13911yescharacteristic
558C232−1+4×C13911yescharacteristic
559D4—416no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—432no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C22—28no—
612C22—28no—
613C22—28no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—44no—
622C22—44no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22C2×C22⋊Q8×C13912yes—
627C22#525×C13912yes—
628C22#525×C13912yes—
629C22#534×C13912yes—
630C22#534×C13911yescharacteristic
631C22#538×C13912yes—
632C22#539×C13912yes—
633C22#539×C13911yescharacteristic
634C22#543×C13911yescharacteristic
635C22D42×C13911yescharacteristic
636C22D42×C13912yes—
637C22#546×C13912yes—
638C22#547×C13912yes—
639C22D4×Q8×C13911yescharacteristic
640C22#550×C13911yescharacteristic
641C22#551×C13911yescharacteristic
642C22#553×C13912yes—
643C22#553×C13912yes—
644C22#554×C13912yes—
645C22#554×C13911yescharacteristic
646C22#559×C13911yescharacteristic
647C22H(3,𝔽4)×C13911yescharacteristic
648C22#562×C13911yescharacteristic
649C4—42no—
650C4—44no—
651C4—44no—
652C4—42no—
653C4—44no—
654C4—42no—
655C4—44no—
656C4—82no—
657C2—48no—
658C2#2437×C13911yescharacteristic
659C2#2449×C13912yes—
660C2#2455×C13911yescharacteristic
661C2#2456×C13912yes—
662C2#2579×C13912yes—
663C2#2600×C13911yescharacteristic
664C2#2679×C13911yescharacteristic
665C2#2708×C13912yes—
666C2#2732×C13911yescharacteristic
667C2#2782×C13911yescharacteristic
668C2#2804×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutator, Frattini, cosocleC24C24×C139
prime radicalC23×D4×C139C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#385×C139C2semidirect
3. C2×#385×C139C2semidirect
4. #1445×C139C2semidirect
5. #1442×C139C2semidirect
6. #1441×C139C2semidirect
7. #1439×C139C2semidirect
8. #1439×C139C2semidirect
65. C2×C4⋊C4×C139D4semidirect
334. #15961C139direct (N × H)
335. C139#15961direct (N × H)
337. C2×#385C2×C139semidirect
338. C2×#385C2×C139semidirect
339. #1445C2×C139semidirect
340. #1442C2×C139semidirect
341. #1441C2×C139semidirect
342. #1439C2×C139semidirect
343. #1439C2×C139semidirect
400. C2×C4⋊C4D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#386×C1392
C2×#385×C1392
#1445×C1392
#1442×C1392
#1441×C1392
#1439×C1392
#1438×C1392
#15961139