Finite Group Databasebeta

← C139×#15782 #48010378

Subgroups — C139×#15782 #48010378

Order 35584.

1630 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C139C212yesmaximal
2C2×#388×C139C212yesmaximal, complemented
3#1445×C139C211yesmaximal, characteristic, complemented
4#1444×C139C211yesmaximal, characteristic, complemented
5#1440×C139C212yesmaximal, complemented
6#1439×C139C212yesmaximal, complemented
7#1438×C139C211yesmaximal, characteristic
8#1437×C139C212yesmaximal, complemented
9#1436×C139C212yesmaximal, complemented
10C23×D4×C139C2211yescharacteristic
11C22×C4⋊C4×C139C2211yescharacteristic
12C22×C4⋊C4×C139C2212yes—
13C22×C4⋊C4×C139C2211yescharacteristic
14C22×C22⋊C4×C139C2212yes—
15C22×C22⋊C4×C139C2212yes—
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2212yes—
18C22×C22⋊C4×C139C2212yes—
19C22×C22⋊C4×C139C2212yes—
20C22×C42×C139C2212yes—
21#394×C139—28no—
22#388×C139—28no—
23C2×#95×C139C2212yes—
24C2×#95×C139C2212yes—
25C2×#95×C139C2212yes—
26C2×#95×C139C2212yes—
27C2×#95×C139C2212yes—
28C2×#95×C139C2211yescharacteristic
29C2×#95×C139C2211yescharacteristic
30C2×#95×C139C2211yescharacteristic
31C2×#95×C139C2212yes—
32C2×#95×C139C2211yescharacteristic
33C25×C139C2312yes—
34C22×D4×C139—24no—
35C22×D4×C139—22no—
36C22×D4×C139—41no—
37C22×D4×C139—41no—
38C22×D4×C139—42no—
39C23×C4×C139C2312yes—
40C23×C4×C139C2312yes—
41C23×C4×C139C2312yes—
42C23×C4×C139C2312yes—
43C23×C4×C139C2311yescharacteristic
44C23×C4×C139C2312yes—
45C23×C4×C139C2311yescharacteristic
46C23×C4×C139C2311yescharacteristic
47C2×C4⋊C4×C139—24no—
48C2×C4⋊C4×C139—24no—
49C2×C4⋊C4×C139—24no—
50C2×C4⋊C4×C139—22no—
51C2×C4⋊C4×C139—42no—
52C2×C4⋊C4×C139—41no—
53C2×C4⋊C4×C139—41no—
54C2×C4⋊C4×C139—41no—
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—24no—
62C2×C22⋊C4×C139—24no—
63C2×C22⋊C4×C139—24no—
64C2×C22⋊C4×C139—24no—
65C2×C22⋊C4×C139—24no—
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×C22⋊C4×C139—42no—
72C2×C22⋊C4×C139D418yes—
73C2×C42×C139—24no—
74C2×C42×C139—42no—
75C2×C42×C139—42no—
76#95×C139—24no—
77#95×C139—24no—
78#95×C139—24no—
79#95×C139—24no—
80#95×C139—22no—
81#95×C139—24no—
82#95×C139—41no—
83#95×C139—41no—
84#95×C139—42no—
85#95×C139—41no—
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—22no—
100C24×C139C2×D414yes—
101C24×C139C2411yescharacteristic
102C2×D4×C139—48no—
103C2×D4×C139—44no—
104C2×D4×C139—44no—
105C2×D4×C139—48no—
106C2×D4×C139—44no—
107C22×C4×C139—22no—
108C22×C4×C139—22no—
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—22no—
122C22×C4×C139—22no—
123C22×C4×C139—22no—
124C22×C4×C139—22no—
125C22×C4×C139—22no—
126C22×C4×C139—22no—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—21no—
130C22×C4×C139—22no—
131C22×C4×C139—21no—
132C22×C4×C139—21no—
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—21no—
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×D414yes—
151C22×C4×C139C2×D414yes—
152C22×C4×C139#4112yes—
153C22×C4×C139#4114yes—
154C22×C4×C139#4114yes—
155C22×C4×C139#4112yes—
156C22×C4×C139#4112yes—
157C4⋊C4×C139—44no—
158C4⋊C4×C139—48no—
159C4⋊C4×C139—44no—
160C22⋊C4×C139—216no—
161C22⋊C4×C139—48no—
162C22⋊C4×C139—48no—
163C22⋊C4×C139—48no—
164C22⋊C4×C139—48no—
165C22⋊C4×C139—48no—
166C42×C139—48no—
167C23×C139—24no—
168C23×C139—24no—
169C23×C139—24no—
170C23×C139—24no—
171C23×C139—24no—
172C23×C139—24no—
173C23×C139—24no—
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×C139—42no—
202C23×C139C22×D412yes—
203C23×C139C2×#4111yescharacteristic
204C23×C139C2×#4112yes—
205C23×C139C2×#4111yescharacteristic
206C23×C139C2×#4112yes—
207C23×C139C2×#4111yescharacteristic
208C23×C139H(5,𝔽2)11yescharacteristic
209C23×C139H(5,𝔽2)12yes—
210C23×C139H(5,𝔽2)11yescharacteristic
211C23×C139H(5,𝔽2)11yescharacteristic
212C23×C1392−1+411yescharacteristic
213D4×C139—416no—
214C2×C4×C139—24no—
215C2×C4×C139—24no—
216C2×C4×C139—24no—
217C2×C4×C139—24no—
218C2×C4×C139—24no—
219C2×C4×C139—22no—
220C2×C4×C139—22no—
221C2×C4×C139—22no—
222C2×C4×C139—24no—
223C2×C4×C139—24no—
224C2×C4×C139—24no—
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—42no—
233C2×C4×C139—42no—
234C2×C4×C139—42no—
235C2×C4×C139—42no—
236C2×C4×C139—42no—
237C2×C4×C139—42no—
238C2×C4×C139—42no—
239C2×C4×C139—42no—
240C2×C4×C139—42no—
241C2×C4×C139—42no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
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—41no—
252C2×C4×C139—41no—
253C2×C4×C139—42no—
254C2×C4×C139—41no—
255C2×C4×C139—41no—
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—42no—
263C2×C4×C139—42no—
264C22×C139—44no—
265C22×C139—44no—
266C22×C139—44no—
267C22×C139—44no—
268C22×C139—44no—
269C22×C139—44no—
270C22×C139—44no—
271C22×C139—82no—
272C22×C139—82no—
273C22×C139—82no—
274C22×C139—82no—
275C22×C139—82no—
276C22×C139—82no—
277C22×C139—82no—
278C22×C139—82no—
279C22×C139#52512yes—
280C22×C139#52912yes—
281C22×C139#53212yes—
282C22×C139#53412yes—
283C22×C139#53811yescharacteristic
284C22×C139#53811yescharacteristic
285C22×C139#53911yescharacteristic
286C22×C139#54012yes—
287C22×C139#54212yes—
288C22×C139D4211yescharacteristic
289C22×C139#54612yes—
290C22×C139#54612yes—
291C22×C139#54712yes—
292C22×C139#55112yes—
293C22×C139#55312yes—
294C22×C139#55312yes—
295C22×C139#55511yescharacteristic
296C22×C139#55511yescharacteristic
297C22×C139#55611yescharacteristic
298C22×C139#55911yescharacteristic
299C22×C139#55911yescharacteristic
300C22×C139#56011yescharacteristic
301C22×C139#56211yescharacteristic
302C4×C139—44no—
303C4×C139—44no—
304C4×C139—42no—
305C4×C139—44no—
306C4×C139—42no—
307C4×C139—44no—
308C4×C139—42no—
309C4×C139—82no—
310C2×C139—84no—
311C2×C139#245511yescharacteristic
312C2×C139#247612yes—
313C2×C139#252112yes—
314C2×C139#255511yescharacteristic
315C2×C139#259311yescharacteristic
316C2×C139#260212yes—
317C2×C139#266811yescharacteristic
318C2×C139#270112yes—
319C2×C139#275211yescharacteristic
320C2×C139#279511yescharacteristic
321C2×C139#280811yescharacteristic
322#15782C13911yesmaximal, characteristic, direct product factor, Sylow
323C139#1578211yescharacteristic, direct product factor, Sylow
324C2×#394C2×C13912yes—
325C2×#388C2×C13912yescomplemented
326#1445C2×C13911yescharacteristic, complemented
327#1444C2×C13911yescharacteristic, complemented
328#1440C2×C13912yescomplemented
329#1439C2×C13912yescomplemented
330#1438C2×C13911yescharacteristic
331#1437C2×C13912yescomplemented
332#1436C2×C13912yescomplemented
333C23×D4C22×C13911yescharacteristic
334C22×C4⋊C4C22×C13912yes—
335C22×C4⋊C4C22×C13911yescharacteristic
336C22×C4⋊C4C22×C13911yescharacteristic
337C22×C22⋊C4C22×C13912yes—
338C22×C22⋊C4C22×C13912yes—
339C22×C22⋊C4C22×C13912yes—
340C22×C22⋊C4C22×C13912yes—
341C22×C22⋊C4C22×C13912yes—
342C22×C22⋊C4C22×C13912yes—
343C22×C42C22×C13912yes—
344#394—28no—
345#388—28no—
346C2×#95C22×C13912yes—
347C2×#95C22×C13912yes—
348C2×#95C22×C13912yes—
349C2×#95C22×C13912yes—
350C2×#95C22×C13911yescharacteristic
351C2×#95C22×C13912yes—
352C2×#95C22×C13911yescharacteristic
353C2×#95C22×C13911yescharacteristic
354C2×#95C22×C13912yes—
355C2×#95C22×C13911yescharacteristic
356C25C23×C13912yes—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4—42no—
362C23×C4C23×C13912yes—
363C23×C4C23×C13912yes—
364C23×C4C23×C13912yes—
365C23×C4C23×C13911yescharacteristic
366C23×C4C23×C13912yes—
367C23×C4C23×C13911yescharacteristic
368C23×C4C23×C13912yes—
369C23×C4C23×C13911yescharacteristic
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—41no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4D4×C13918yes—
396C2×C42—24no—
397C2×C42—42no—
398C2×C42—42no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—22no—
404#95—24no—
405#95—41no—
406#95—41no—
407#95—42no—
408#95—41no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24C2×D4×C13914yes—
424C24C24×C13911yescharacteristic
425C2×D4—48no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—48no—
429C2×D4—44no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
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—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4C2×D4×C13914yes—
474C22×C4C2×D4×C13914yes—
475C22×C4#41×C13912yes—
476C22×C4#41×C13914yes—
477C22×C4#41×C13914yes—
478C22×C4#41×C13912yes—
479C22×C4#41×C13912yes—
480C4⋊C4—44no—
481C4⋊C4—48no—
482C4⋊C4—44no—
483C22⋊C4—216no—
484C22⋊C4—48no—
485C22⋊C4—48no—
486C22⋊C4—48no—
487C22⋊C4—48no—
488C22⋊C4—48no—
489C42—48no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
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—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23C22×D4×C13912yes—
526C23C2×#41×C13911yescharacteristic
527C23C2×#41×C13912yes—
528C23C2×#41×C13911yescharacteristic
529C23C2×#41×C13912yes—
530C23C2×#41×C13911yescharacteristic
531C23H(5,𝔽2)×C13911yescharacteristic
532C23H(5,𝔽2)×C13912yes—
533C23H(5,𝔽2)×C13911yescharacteristic
534C23H(5,𝔽2)×C13911yescharacteristic
535C232−1+4×C13911yescharacteristic
536D4—416no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
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—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22#525×C13912yes—
603C22#529×C13912yes—
604C22#532×C13912yes—
605C22#534×C13912yes—
606C22#538×C13911yescharacteristic
607C22#538×C13911yescharacteristic
608C22#539×C13911yescharacteristic
609C22#540×C13912yes—
610C22#542×C13912yes—
611C22D42×C13911yescharacteristic
612C22#546×C13912yes—
613C22#546×C13912yes—
614C22#547×C13912yes—
615C22#551×C13912yes—
616C22#553×C13912yes—
617C22#553×C13912yes—
618C22#555×C13911yescharacteristic
619C22#555×C13911yescharacteristic
620C22#556×C13911yescharacteristic
621C22#559×C13911yescharacteristic
622C22#559×C13911yescharacteristic
623C22#560×C13911yescharacteristic
624C22#562×C13911yescharacteristic
625C4—44no—
626C4—42no—
627C4—44no—
628C4—44no—
629C4—42no—
630C4—44no—
631C4—42no—
632C4—82no—
633C2—84no—
634C2#2455×C13911yescharacteristic
635C2#2476×C13912yes—
636C2#2521×C13912yes—
637C2#2555×C13911yescharacteristic
638C2#2593×C13911yescharacteristic
639C2#2602×C13912yes—
640C2#2668×C13911yescharacteristic
641C2#2701×C13912yes—
642C2#2752×C13911yescharacteristic
643C2#2795×C13911yescharacteristic
644C2#2808×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×#388×C139C2semidirect
3. #1445×C139C2semidirect
4. #1444×C139C2semidirect
5. #1440×C139C2semidirect
6. #1439×C139C2semidirect
8. #1437×C139C2semidirect
9. #1436×C139C2semidirect
322. #15782C139direct (N × H)
323. C139#15782direct (N × H)
325. C2×#388C2×C139semidirect
326. #1445C2×C139semidirect
327. #1444C2×C139semidirect
328. #1440C2×C139semidirect
329. #1439C2×C139semidirect
331. #1437C2×C139semidirect
332. #1436C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C1392
C2×#388×C1392
#1445×C1392
#1444×C1392
#1440×C1392
#1439×C1392
#1438×C1392
#1437×C1392
#1436×C1392
#15782139