Finite Group Databasebeta

← C139×#15820 #48010416

Subgroups — C139×#15820 #48010416

Order 35584.

1538 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C139C211yesmaximal, characteristic, complemented
2C2×#390×C139C211yesmaximal, characteristic
3#1440×C139C212yesmaximal, complemented
4#1440×C139C212yesmaximal, complemented
5#1439×C139C212yesmaximal, complemented
6#1438×C139C212yesmaximal
7#1437×C139C212yesmaximal, complemented
8#1436×C139C211yesmaximal, characteristic, complemented
9#1434×C139C212yesmaximal, complemented
10C23×D4×C139C2211yescharacteristic
11C22×C4⋊C4×C139C2211yescharacteristic
12C22×C4⋊C4×C139C2211yescharacteristic
13C22×C22⋊C4×C139C2212yes—
14C22×C22⋊C4×C139C2212yes—
15C22×C22⋊C4×C139C2212yes—
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2212yes—
18C22×C22⋊C4×C139C2212yes—
19C22×C42×C139C2211yescharacteristic
20C22×C42×C139C2211yescharacteristic
21#400×C139—24no—
22#390×C139—24no—
23C2×#95×C139C2212yes—
24C2×#95×C139C2212yes—
25C2×#95×C139C2211yescharacteristic
26C2×#95×C139C2212yes—
27C2×#95×C139C2212yes—
28C2×#95×C139C2212yes—
29C2×#95×C139C2212yes—
30C2×#95×C139C2212yes—
31C2×#95×C139C2212yes—
32C2×#95×C139C2211yescharacteristic
33C25×C139C2312yes—
34C22×D4×C139—24no—
35C22×D4×C139—22no—
36C22×D4×C139—24no—
37C22×D4×C139—41no—
38C22×D4×C139—41no—
39C23×C4×C139C2312yes—
40C23×C4×C139C2312yes—
41C23×C4×C139C2312yes—
42C23×C4×C139C2311yescharacteristic
43C23×C4×C139C2311yescharacteristic
44C23×C4×C139C2312yes—
45C23×C4×C139C2312yes—
46C23×C4×C139C2311yescharacteristic
47C2×C4⋊C4×C139—22no—
48C2×C4⋊C4×C139—41no—
49C2×C4⋊C4×C139—41no—
50C2×C4⋊C4×C139—41no—
51C2×C4⋊C4×C139—41no—
52C2×C4⋊C4×C139D414yes—
53C2×C22⋊C4×C139—24no—
54C2×C22⋊C4×C139—24no—
55C2×C22⋊C4×C139—24no—
56C2×C22⋊C4×C139—24no—
57C2×C22⋊C4×C139—24no—
58C2×C22⋊C4×C139—24no—
59C2×C22⋊C4×C139—24no—
60C2×C22⋊C4×C139—24no—
61C2×C22⋊C4×C139—42no—
62C2×C22⋊C4×C139—42no—
63C2×C22⋊C4×C139—42no—
64C2×C22⋊C4×C139—42no—
65C2×C22⋊C4×C139—42no—
66C2×C22⋊C4×C139—42no—
67C2×C22⋊C4×C139—42no—
68C2×C22⋊C4×C139—42no—
69C2×C22⋊C4×C139—42no—
70C2×C22⋊C4×C139—42no—
71C2×C42×C139—22no—
72C2×C42×C139—24no—
73C2×C42×C139—42no—
74C2×C42×C139—41no—
75#95×C139—22no—
76#95×C139—24no—
77#95×C139—24no—
78#95×C139—24no—
79#95×C139—24no—
80#95×C139—24no—
81#95×C139—42no—
82#95×C139—42no—
83#95×C139—42no—
84#95×C139—41no—
85C24×C139—22no—
86C24×C139—22no—
87C24×C139—22no—
88C24×C139—22no—
89C24×C139—22no—
90C24×C139—22no—
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#4114yes—
100C24×C139C2411yescharacteristic
101C2×D4×C139—28no—
102C2×D4×C139—48no—
103C2×D4×C139—48no—
104C2×D4×C139—44no—
105C2×D4×C139—44no—
106C22×C4×C139—22no—
107C22×C4×C139—21no—
108C22×C4×C139—21no—
109C22×C4×C139—22no—
110C22×C4×C139—22no—
111C22×C4×C139—22no—
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—21no—
122C22×C4×C139—22no—
123C22×C4×C139—22no—
124C22×C4×C139—22no—
125C22×C4×C139—21no—
126C22×C4×C139—22no—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—22no—
130C22×C4×C139—22no—
131C22×C4×C139—22no—
132C22×C4×C139—22no—
133C22×C4×C139—22no—
134C22×C4×C139—22no—
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—22no—
147C22×C4×C139—22no—
148C22×C4×C139—22no—
149C22×C4×C139—22no—
150C22×C4×C139C2×D412yes—
151C22×C4×C139C2×D412yes—
152C22×C4×C139C2×D412yes—
153C22×C4×C139#4114yes—
154C22×C4×C139#4114yes—
155C22×C4×C139#4114yes—
156C4⋊C4×C139—44no—
157C4⋊C4×C139—44no—
158C22⋊C4×C139—48no—
159C22⋊C4×C139—48no—
160C22⋊C4×C139—48no—
161C22⋊C4×C139—48no—
162C22⋊C4×C139—48no—
163C22⋊C4×C139—48no—
164C42×C139—44no—
165C42×C139—44no—
166C23×C139—24no—
167C23×C139—24no—
168C23×C139—24no—
169C23×C139—24no—
170C23×C139—24no—
171C23×C139—24no—
172C23×C139—24no—
173C23×C139—42no—
174C23×C139—42no—
175C23×C139—42no—
176C23×C139—42no—
177C23×C139—42no—
178C23×C139—42no—
179C23×C139—42no—
180C23×C139—42no—
181C23×C139—42no—
182C23×C139—42no—
183C23×C139—42no—
184C23×C139—42no—
185C23×C139—42no—
186C23×C139—42no—
187C23×C139—42no—
188C23×C139—42no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—42no—
192C23×C139—42no—
193C23×C139—42no—
194C23×C139—42no—
195C23×C139—42no—
196C23×C139—42no—
197C23×C139—42no—
198C23×C139—42no—
199C23×C139—42no—
200C23×C139—42no—
201C23×C139C22×D411yescharacteristic
202C23×C139C2×#4112yes—
203C23×C139C2×#4112yes—
204C23×C139C2×#4112yes—
205C23×C139C2×#4112yes—
206C23×C139H(5,𝔽2)11yescharacteristic
207C23×C139H(5,𝔽2)11yescharacteristic
208C23×C139H(5,𝔽2)12yes—
209C23×C139H(5,𝔽2)12yes—
210D4×C139—416no—
211C2×C4×C139—22no—
212C2×C4×C139—22no—
213C2×C4×C139—24no—
214C2×C4×C139—24no—
215C2×C4×C139—24no—
216C2×C4×C139—22no—
217C2×C4×C139—22no—
218C2×C4×C139—24no—
219C2×C4×C139—24no—
220C2×C4×C139—24no—
221C2×C4×C139—24no—
222C2×C4×C139—24no—
223C2×C4×C139—24no—
224C2×C4×C139—24no—
225C2×C4×C139—42no—
226C2×C4×C139—42no—
227C2×C4×C139—42no—
228C2×C4×C139—42no—
229C2×C4×C139—42no—
230C2×C4×C139—42no—
231C2×C4×C139—42no—
232C2×C4×C139—42no—
233C2×C4×C139—42no—
234C2×C4×C139—41no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139—42no—
238C2×C4×C139—41no—
239C2×C4×C139—42no—
240C2×C4×C139—42no—
241C2×C4×C139—42no—
242C2×C4×C139—42no—
243C2×C4×C139—42no—
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—42no—
251C2×C4×C139—42no—
252C2×C4×C139—42no—
253C2×C4×C139—42no—
254C2×C4×C139—42no—
255C2×C4×C139—42no—
256C2×C4×C139—42no—
257C2×C4×C139—42no—
258C2×C4×C139—42no—
259C2×C4×C139—42no—
260C2×C4×C139#12414yes—
261C22×C139—44no—
262C22×C139—44no—
263C22×C139—44no—
264C22×C139—44no—
265C22×C139—44no—
266C22×C139—44no—
267C22×C139—44no—
268C22×C139—82no—
269C22×C139—82no—
270C22×C139—82no—
271C22×C139—82no—
272C22×C139—82no—
273C22×C139—82no—
274C22×C139—82no—
275C22×C139—82no—
276C22×C139#52511yescharacteristic
277C22×C139C2×#12411yescharacteristic
278C22×C139#52912yes—
279C22×C139#52912yes—
280C22×C139#53411yescharacteristic
281C22×C139#53812yes—
282C22×C139#53812yes—
283C22×C139#54012yes—
284C22×C139#54012yes—
285C22×C139#54612yes—
286C22×C139#55012yes—
287C22×C139#55112yes—
288C22×C139#55112yes—
289C22×C139#55112yes—
290C22×C139#55312yes—
291C22×C139#55312yes—
292C22×C139#55312yes—
293C22×C139#55511yescharacteristic
294C22×C139#55911yescharacteristic
295C22×C139#56011yescharacteristic
296C22×C139H(3,𝔽4)11yescharacteristic
297C4×C139—24no—
298C4×C139—42no—
299C4×C139—42no—
300C4×C139—44no—
301C4×C139—44no—
302C4×C139—82no—
303C4×C139—82no—
304C4×C139—82no—
305C2×C139—84no—
306C2×C139#246712yes—
307C2×C139#249012yes—
308C2×C139#252612yes—
309C2×C139#256111yescharacteristic
310C2×C139#259712yes—
311C2×C139#270911yescharacteristic
312C2×C139#273311yescharacteristic
313C2×C139#274912yes—
314C2×C139#275312yes—
315#15820C13911yesmaximal, characteristic, direct product factor, Sylow
316C139#1582011yescharacteristic, direct product factor, Sylow
317C2×#400C2×C13911yescharacteristic, complemented
318C2×#390C2×C13911yescharacteristic
319#1440C2×C13912yescomplemented
320#1440C2×C13912yescomplemented
321#1439C2×C13912yescomplemented
322#1438C2×C13912yes—
323#1437C2×C13912yescomplemented
324#1436C2×C13911yescharacteristic, complemented
325#1434C2×C13912yescomplemented
326C23×D4C22×C13911yescharacteristic
327C22×C4⋊C4C22×C13911yescharacteristic
328C22×C4⋊C4C22×C13911yescharacteristic
329C22×C22⋊C4C22×C13912yes—
330C22×C22⋊C4C22×C13912yes—
331C22×C22⋊C4C22×C13912yes—
332C22×C22⋊C4C22×C13912yes—
333C22×C22⋊C4C22×C13912yes—
334C22×C22⋊C4C22×C13912yes—
335C22×C42C22×C13911yescharacteristic
336C22×C42C22×C13911yescharacteristic
337#400—24no—
338#390—24no—
339C2×#95C22×C13912yes—
340C2×#95C22×C13912yes—
341C2×#95C22×C13911yescharacteristic
342C2×#95C22×C13912yes—
343C2×#95C22×C13912yes—
344C2×#95C22×C13912yes—
345C2×#95C22×C13912yes—
346C2×#95C22×C13912yes—
347C2×#95C22×C13912yes—
348C2×#95C22×C13911yescharacteristic
349C25C23×C13912yes—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—41no—
354C22×D4—41no—
355C23×C4C23×C13912yes—
356C23×C4C23×C13912yes—
357C23×C4C23×C13912yes—
358C23×C4C23×C13911yescharacteristic
359C23×C4C23×C13911yescharacteristic
360C23×C4C23×C13912yes—
361C23×C4C23×C13912yes—
362C23×C4C23×C13911yescharacteristic
363C2×C4⋊C4—22no—
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4D4×C13914yes—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—42no—
390C2×C42—41no—
391#95—22no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—41no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24#41×C13914yes—
416C24C24×C13911yescharacteristic
417C2×D4—28no—
418C2×D4—48no—
419C2×D4—48no—
420C2×D4—44no—
421C2×D4—44no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
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—22no—
465C22×C4—22no—
466C22×C4C2×D4×C13912yes—
467C22×C4C2×D4×C13912yes—
468C22×C4C2×D4×C13912yes—
469C22×C4#41×C13914yes—
470C22×C4#41×C13914yes—
471C22×C4#41×C13914yes—
472C4⋊C4—44no—
473C4⋊C4—44no—
474C22⋊C4—48no—
475C22⋊C4—48no—
476C22⋊C4—48no—
477C22⋊C4—48no—
478C22⋊C4—48no—
479C22⋊C4—48no—
480C42—44no—
481C42—44no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23C22×D4×C13911yescharacteristic
518C23C2×#41×C13912yes—
519C23C2×#41×C13912yes—
520C23C2×#41×C13912yes—
521C23C2×#41×C13912yes—
522C23H(5,𝔽2)×C13911yescharacteristic
523C23H(5,𝔽2)×C13911yescharacteristic
524C23H(5,𝔽2)×C13912yes—
525C23H(5,𝔽2)×C13912yes—
526D4—416no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4#124×C13914yes—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—82no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22—82no—
591C22—82no—
592C22#525×C13911yescharacteristic
593C22C2×#124×C13911yescharacteristic
594C22#529×C13912yes—
595C22#529×C13912yes—
596C22#534×C13911yescharacteristic
597C22#538×C13912yes—
598C22#538×C13912yes—
599C22#540×C13912yes—
600C22#540×C13912yes—
601C22#546×C13912yes—
602C22#550×C13912yes—
603C22#551×C13912yes—
604C22#551×C13912yes—
605C22#551×C13912yes—
606C22#553×C13912yes—
607C22#553×C13912yes—
608C22#553×C13912yes—
609C22#555×C13911yescharacteristic
610C22#559×C13911yescharacteristic
611C22#560×C13911yescharacteristic
612C22H(3,𝔽4)×C13911yescharacteristic
613C4—24no—
614C4—42no—
615C4—42no—
616C4—44no—
617C4—44no—
618C4—82no—
619C4—82no—
620C4—82no—
621C2—84no—
622C2#2467×C13912yes—
623C2#2490×C13912yes—
624C2#2526×C13912yes—
625C2#2561×C13911yescharacteristic
626C2#2597×C13912yes—
627C2#2709×C13911yescharacteristic
628C2#2733×C13911yescharacteristic
629C2#2749×C13912yes—
630C2#2753×C13912yes—
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
1. C2×#400×C139C2semidirect
3. #1440×C139C2semidirect
4. #1440×C139C2semidirect
5. #1439×C139C2semidirect
7. #1437×C139C2semidirect
8. #1436×C139C2semidirect
9. #1434×C139C2semidirect
315. #15820C139direct (N × H)
316. C139#15820direct (N × H)
317. C2×#400C2×C139semidirect
319. #1440C2×C139semidirect
320. #1440C2×C139semidirect
321. #1439C2×C139semidirect
323. #1437C2×C139semidirect
324. #1436C2×C139semidirect
325. #1434C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#400×C1392
C2×#390×C1392
#1440×C1392
#1439×C1392
#1438×C1392
#1437×C1392
#1436×C1392
#1434×C1392
#15820139