Finite Group Databasebeta

← C139×#15643 #48010239

Subgroups — C139×#15643 #48010239

Order 35584.

1722 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C139C211yesmaximal, characteristic
2C2×#394×C139C212yesmaximal
3C2×#388×C139C212yesmaximal, complemented
4C2×#384×C139C211yesmaximal, characteristic, complemented
5#1442×C139C212yesmaximal, complemented
6#1439×C139C212yesmaximal, complemented
7#1439×C139C212yesmaximal, complemented
8#1437×C139C212yesmaximal, complemented
9#1436×C139C211yesmaximal, characteristic, complemented
10C23×D4×C139C2211yescharacteristic
11C22×C4⋊C4×C139C2212yes—
12C22×C4⋊C4×C139C2212yes—
13C22×C4⋊C4×C139C2211yescharacteristic
14C22×C4⋊C4×C139C2211yescharacteristic
15C22×C22⋊C4×C139C2212yes—
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2212yes—
18C22×C22⋊C4×C139C2212yes—
19C22×C22⋊C4×C139C2212yes—
20C22×C22⋊C4×C139C2212yes—
21C22×C42×C139C2211yescharacteristic
22C22×C42×C139C2211yescharacteristic
23#394×C139—24no—
24#394×C139—28no—
25#388×C139—28no—
26#384×C139—24no—
27C2×#95×C139C2212yes—
28C2×#95×C139C2212yes—
29C2×#95×C139C2212yes—
30C2×#95×C139C2211yescharacteristic
31C2×#95×C139C2212yes—
32C2×#95×C139C2212yes—
33C2×#95×C139C2211yescharacteristic
34C2×#95×C139C2212yes—
35C25×C139C2312yes—
36C22×D4×C139—24no—
37C22×D4×C139—22no—
38C22×D4×C139—42no—
39C22×D4×C139—41no—
40C22×D4×C139—41no—
41C23×C4×C139C2312yes—
42C23×C4×C139C2312yes—
43C23×C4×C139C2312yes—
44C23×C4×C139C2311yescharacteristic
45C23×C4×C139C2312yes—
46C23×C4×C139C2311yescharacteristic
47C23×C4×C139C2312yes—
48C23×C4×C139C2311yescharacteristic
49C2×C4⋊C4×C139—24no—
50C2×C4⋊C4×C139—24no—
51C2×C4⋊C4×C139—22no—
52C2×C4⋊C4×C139—24no—
53C2×C4⋊C4×C139—24no—
54C2×C4⋊C4×C139—41no—
55C2×C4⋊C4×C139—41no—
56C2×C4⋊C4×C139—42no—
57C2×C4⋊C4×C139—42no—
58C2×C4⋊C4×C139—41no—
59C2×C4⋊C4×C139—41no—
60C2×C4⋊C4×C139D414yes—
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—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—42no—
75C2×C22⋊C4×C139—42no—
76C2×C22⋊C4×C139—42no—
77C2×C22⋊C4×C139—42no—
78C2×C22⋊C4×C139D418yes—
79C2×C42×C139—22no—
80C2×C42×C139—24no—
81C2×C42×C139—24no—
82C2×C42×C139—41no—
83#95×C139—24no—
84#95×C139—24no—
85#95×C139—24no—
86#95×C139—22no—
87#95×C139—24no—
88#95×C139—24no—
89#95×C139—41no—
90#95×C139—42no—
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×C139—22no—
104C24×C139—22no—
105C24×C139C2×D414yes—
106C24×C139C2411yescharacteristic
107C2×D4×C139—48no—
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—21no—
116C22×C4×C139—21no—
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—21no—
126C22×C4×C139—22no—
127C22×C4×C139—21no—
128C22×C4×C139—22no—
129C22×C4×C139—21no—
130C22×C4×C139—21no—
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×C139—22no—
151C22×C4×C139—22no—
152C22×C4×C139—22no—
153C22×C4×C139—22no—
154C22×C4×C139C2×D414yes—
155C22×C4×C139C2×D412yes—
156C22×C4×C139C2×D412yes—
157C22×C4×C139C2×D414yes—
158C22×C4×C139C2×D412yes—
159C22×C4×C139#4114yes—
160C22×C4×C139#4114yes—
161C22×C4×C139#4114yes—
162C4⋊C4×C139—44no—
163C4⋊C4×C139—48no—
164C4⋊C4×C139—48no—
165C4⋊C4×C139—44no—
166C22⋊C4×C139—216no—
167C22⋊C4×C139—48no—
168C22⋊C4×C139—48no—
169C22⋊C4×C139—48no—
170C22⋊C4×C139—48no—
171C22⋊C4×C139—48no—
172C42×C139—28no—
173C42×C139—44no—
174C23×C139—24no—
175C23×C139—24no—
176C23×C139—24no—
177C23×C139—24no—
178C23×C139—24no—
179C23×C139—24no—
180C23×C139—24no—
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×C139—42no—
203C23×C139—42no—
204C23×C139—42no—
205C23×C139—42no—
206C23×C139—42no—
207C23×C139—42no—
208C23×C139—42no—
209C23×C139C22×D412yes—
210C23×C139C22×D411yescharacteristic
211C23×C139C2×#4112yes—
212C23×C139C2×#4112yes—
213C23×C139C2×#4112yes—
214C23×C139H(5,𝔽2)11yescharacteristic
215C23×C139H(5,𝔽2)11yescharacteristic
216C23×C139H(5,𝔽2)12yes—
217C23×C1392−1+412yes—
218D4×C139—416no—
219C2×C4×C139—22no—
220C2×C4×C139—24no—
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—22no—
231C2×C4×C139—22no—
232C2×C4×C139—24no—
233C2×C4×C139—24no—
234C2×C4×C139—24no—
235C2×C4×C139—24no—
236C2×C4×C139—42no—
237C2×C4×C139—42no—
238C2×C4×C139—42no—
239C2×C4×C139—42no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—42no—
243C2×C4×C139—42no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
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—42no—
261C2×C4×C139—42no—
262C2×C4×C139—42no—
263C2×C4×C139—42no—
264C2×C4×C139—42no—
265C2×C4×C139—42no—
266C2×C4×C139—42no—
267C2×C4×C139#12318yes—
268C2×C4×C139#12414yes—
269C22×C139—44no—
270C22×C139—44no—
271C22×C139—44no—
272C22×C139—44no—
273C22×C139—44no—
274C22×C139—44no—
275C22×C139—44no—
276C22×C139—82no—
277C22×C139—82no—
278C22×C139—82no—
279C22×C139—82no—
280C22×C139—82no—
281C22×C139—82no—
282C22×C139—82no—
283C22×C139—82no—
284C22×C139C2×#12312yes—
285C22×C139#52511yescharacteristic
286C22×C139C2×#12411yescharacteristic
287C22×C139#53212yes—
288C22×C139#53411yescharacteristic
289C22×C139#53512yes—
290C22×C139#53912yes—
291C22×C139#54212yes—
292C22×C139#54212yes—
293C22×C139D4211yescharacteristic
294C22×C139D4212yes—
295C22×C139#54712yes—
296C22×C139#54712yes—
297C22×C139#54812yes—
298C22×C139#55312yes—
299C22×C139#55312yes—
300C22×C139#55312yes—
301C22×C139#55511yescharacteristic
302C22×C139#55512yes—
303C22×C139#56011yescharacteristic
304C22×C139#56311yescharacteristic
305C4×C139—24no—
306C4×C139—28no—
307C4×C139—42no—
308C4×C139—42no—
309C4×C139—44no—
310C4×C139—82no—
311C4×C139—82no—
312C4×C139—82no—
313C2×C139—84no—
314C2×C139#242212yes—
315C2×C139#244312yes—
316C2×C139#249112yes—
317C2×C139#250012yes—
318C2×C139#259111yescharacteristic
319C2×C139#266911yescharacteristic
320C2×C139#271812yes—
321C2×C139#273111yescharacteristic
322C2×C139#279512yes—
323#15643C13911yesmaximal, characteristic, direct product factor, Sylow
324C139#1564311yescharacteristic, direct product factor, Sylow
325C2×#394C2×C13911yescharacteristic
326C2×#394C2×C13912yes—
327C2×#388C2×C13912yescomplemented
328C2×#384C2×C13911yescharacteristic, complemented
329#1442C2×C13912yescomplemented
330#1439C2×C13912yescomplemented
331#1439C2×C13912yescomplemented
332#1437C2×C13912yescomplemented
333#1436C2×C13911yescharacteristic, complemented
334C23×D4C22×C13911yescharacteristic
335C22×C4⋊C4C22×C13912yes—
336C22×C4⋊C4C22×C13912yes—
337C22×C4⋊C4C22×C13911yescharacteristic
338C22×C4⋊C4C22×C13911yescharacteristic
339C22×C22⋊C4C22×C13912yes—
340C22×C22⋊C4C22×C13912yes—
341C22×C22⋊C4C22×C13912yes—
342C22×C22⋊C4C22×C13912yes—
343C22×C22⋊C4C22×C13912yes—
344C22×C22⋊C4C22×C13912yes—
345C22×C42C22×C13911yescharacteristic
346C22×C42C22×C13911yescharacteristic
347#394—24no—
348#394—28no—
349#388—28no—
350#384—24no—
351C2×#95C22×C13912yes—
352C2×#95C22×C13911yescharacteristic
353C2×#95C22×C13912yes—
354C2×#95C22×C13912yes—
355C2×#95C22×C13912yes—
356C2×#95C22×C13912yes—
357C2×#95C22×C13911yescharacteristic
358C2×#95C22×C13912yes—
359C25C23×C13912yes—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—42no—
363C22×D4—41no—
364C22×D4—41no—
365C23×C4C23×C13912yes—
366C23×C4C23×C13912yes—
367C23×C4C23×C13912yes—
368C23×C4C23×C13911yescharacteristic
369C23×C4C23×C13912yes—
370C23×C4C23×C13911yescharacteristic
371C23×C4C23×C13912yes—
372C23×C4C23×C13911yescharacteristic
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4D4×C13914yes—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4D4×C13918yes—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—41no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—41no—
414#95—42no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24C2×D4×C13914yes—
430C24C24×C13911yescharacteristic
431C2×D4—48no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—48no—
435C2×D4—44no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
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—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
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×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
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×C4C2×D4×C13914yes—
479C22×C4C2×D4×C13912yes—
480C22×C4C2×D4×C13912yes—
481C22×C4C2×D4×C13914yes—
482C22×C4C2×D4×C13912yes—
483C22×C4#41×C13914yes—
484C22×C4#41×C13914yes—
485C22×C4#41×C13914yes—
486C4⋊C4—44no—
487C4⋊C4—48no—
488C4⋊C4—48no—
489C4⋊C4—44no—
490C22⋊C4—216no—
491C22⋊C4—48no—
492C22⋊C4—48no—
493C22⋊C4—48no—
494C22⋊C4—48no—
495C22⋊C4—48no—
496C42—28no—
497C42—44no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
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—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23C22×D4×C13912yes—
534C23C22×D4×C13911yescharacteristic
535C23C2×#41×C13912yes—
536C23C2×#41×C13912yes—
537C23C2×#41×C13912yes—
538C23H(5,𝔽2)×C13911yescharacteristic
539C23H(5,𝔽2)×C13911yescharacteristic
540C23H(5,𝔽2)×C13912yes—
541C232−1+4×C13912yes—
542D4—416no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
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—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4#123×C13918yes—
592C2×C4#124×C13914yes—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22—82no—
606C22—82no—
607C22—82no—
608C22C2×#123×C13912yes—
609C22#525×C13911yescharacteristic
610C22C2×#124×C13911yescharacteristic
611C22#532×C13912yes—
612C22#534×C13911yescharacteristic
613C22#535×C13912yes—
614C22#539×C13912yes—
615C22#542×C13912yes—
616C22#542×C13912yes—
617C22D42×C13911yescharacteristic
618C22D42×C13912yes—
619C22#547×C13912yes—
620C22#547×C13912yes—
621C22#548×C13912yes—
622C22#553×C13912yes—
623C22#553×C13912yes—
624C22#553×C13912yes—
625C22#555×C13912yes—
626C22#555×C13911yescharacteristic
627C22#560×C13911yescharacteristic
628C22#563×C13911yescharacteristic
629C4—24no—
630C4—28no—
631C4—42no—
632C4—42no—
633C4—44no—
634C4—82no—
635C4—82no—
636C4—82no—
637C2—84no—
638C2#2422×C13912yes—
639C2#2443×C13912yes—
640C2#2491×C13912yes—
641C2#2500×C13912yes—
642C2#2591×C13911yescharacteristic
643C2#2669×C13911yescharacteristic
644C2#2718×C13912yes—
645C2#2731×C13911yescharacteristic
646C2#2795×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
3. C2×#388×C139C2semidirect
4. C2×#384×C139C2semidirect
5. #1442×C139C2semidirect
6. #1439×C139C2semidirect
7. #1439×C139C2semidirect
8. #1437×C139C2semidirect
9. #1436×C139C2semidirect
323. #15643C139direct (N × H)
324. C139#15643direct (N × H)
327. C2×#388C2×C139semidirect
328. C2×#384C2×C139semidirect
329. #1442C2×C139semidirect
330. #1439C2×C139semidirect
331. #1439C2×C139semidirect
332. #1437C2×C139semidirect
333. #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
C2×#384×C1392
#1442×C1392
#1439×C1392
#1437×C1392
#1436×C1392
#15643139