Finite Group Databasebeta

← C139×#23901 #48018497

Subgroups — C139×#23901 #48018497

Order 35584.

2056 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C139C211yesmaximal, characteristic
2C22×#123×C139C211yesmaximal, characteristic, complemented
3C2×#458×C139C212yesmaximal, complemented
4#2849×C139C212yesmaximal, complemented
5#2022×C139C214yesmaximal, complemented
6#1898×C139C212yesmaximal, complemented
7#1890×C139C212yesmaximal, complemented
8#1781×C139C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C139C2211yescharacteristic
10C23×D4×C139C2211yescharacteristic
11C24×C4×C139C2211yescharacteristic, complemented
12#546×C139—24no—
13D42×C139—24no—
14#535×C139—21no—
15#534×C139—21no—
16#534×C139C2212yes—
17#525×C139—21no—
18C2×#123×C139—21no—
19C2×#123×C139—21no—
20C2×#123×C139—28no—
21C2×#123×C139C2212yes—
22C2×#123×C139C2212yescomplemented
23C2×#123×C139C2214yescomplemented
24C2×#120×C139—21no—
25C2×#120×C139C2212yes—
26#518×C139C2211yescharacteristic
27C22×C4⋊C4×C139—21no—
28C22×C22⋊C4×C139—21no—
29C22×C22⋊C4×C139C2211yescharacteristic, complemented
30#458×C139—28no—
31C2×#99×C139C2212yes—
32C2×#99×C139C2214yescomplemented
33C2×#99×C139C2212yescomplemented
34#386×C139—24no—
35#385×C139—24no—
36#381×C139C2214yescomplemented
37#379×C139C2212yescomplemented
38#342×C139C2214yescomplemented
39C25×C139D411yescharacteristic
40C25×C139C2311yescharacteristic
41H(5,𝔽2)×C139—24no—
42H(5,𝔽2)×C139—42no—
43C2×#41×C139—21no—
44C2×#41×C139—22no—
45C22×D4×C139—21no—
46C22×D4×C139—22no—
47C22×D4×C139—24no—
48C22×D4×C139—22no—
49C22×D4×C139—24no—
50C22×D4×C139—42no—
51C22×D4×C139D411yescharacteristic
52C22×D4×C139D411yescharacteristic
53C22×D4×C139D414yes—
54C22×D4×C139C2312yes—
55C22×D4×C139C2311yescharacteristic
56C22×D4×C139C2311yescharacteristic
57C23×C4×C139—21no—
58C23×C4×C139—21no—
59C23×C4×C139—21no—
60C23×C4×C139—24no—
61C23×C4×C139—24no—
62C23×C4×C139—42no—
63C23×C4×C139D411yescharacteristic
64C23×C4×C139C2312yes—
65#127×C139—22no—
66#124×C139—22no—
67#123×C139—28no—
68#123×C139—28no—
69#123×C139—22no—
70#123×C139—24no—
71#123×C139—22no—
72#123×C139—22no—
73#123×C139—24no—
74#123×C139—24no—
75#123×C139—28no—
76#123×C139—44no—
77#123×C139D418yescomplemented
78C22⋊Q8×C139—22no—
79#121×C139—22no—
80#121×C139—24no—
81#121×C139—24no—
82#121×C139—24no—
83#120×C139—24no—
84#120×C139—22no—
85#120×C139—22no—
86#120×C139—22no—
87#120×C139—22no—
88#120×C139—24no—
89#120×C139—22no—
90C4×D4×C139—24no—
91C4×D4×C139—24no—
92#117×C139—21no—
93C2×C4⋊C4×C139—28no—
94C2×C4⋊C4×C139—22no—
95C2×C4⋊C4×C139—22no—
96C2×C4⋊C4×C139—24no—
97C2×C22⋊C4×C139—28no—
98C2×C22⋊C4×C139—22no—
99C2×C22⋊C4×C139—22no—
100C2×C22⋊C4×C139—22no—
101C2×C22⋊C4×C139—21no—
102C2×C22⋊C4×C139—21no—
103C2×C22⋊C4×C139—24no—
104C2×C22⋊C4×C139—24no—
105C2×C22⋊C4×C139—24no—
106C2×C22⋊C4×C139D414yes—
107C2×C22⋊C4×C139C2314yes—
108C2×C22⋊C4×C139C2312yes—
109C2×C22⋊C4×C139C2312yes—
110#99×C139—24no—
111#99×C139—28no—
112#99×C139—42no—
113#95×C139—28no—
114C24×C139—22no—
115C24×C139—22no—
116C24×C139—21no—
117C24×C139—22no—
118C24×C139—22no—
119C24×C139—44no—
120C24×C139—41no—
121C24×C139—44no—
122C24×C139C2×D411yescharacteristic
123C24×C139C2×D414yes—
124C24×C139C2×D411yescharacteristic
125C24×C139C2×D412yes—
126C24×C139C2×D411yescharacteristic
127C24×C139C2×D411yescharacteristic
128C24×C139C2411yescharacteristic
129#41×C139—48no—
130#41×C139—42no—
131#41×C139—42no—
132C2×Q8×C139—21no—
133C2×D4×C139—22no—
134C2×D4×C139—22no—
135C2×D4×C139—22no—
136C2×D4×C139—21no—
137C2×D4×C139—24no—
138C2×D4×C139—22no—
139C2×D4×C139—22no—
140C2×D4×C139—22no—
141C2×D4×C139—24no—
142C2×D4×C139—22no—
143C2×D4×C139—22no—
144C2×D4×C139—22no—
145C2×D4×C139—22no—
146C2×D4×C139—22no—
147C2×D4×C139—24no—
148C2×D4×C139—24no—
149C2×D4×C139—24no—
150C2×D4×C139—22no—
151C2×D4×C139—41no—
152C2×D4×C139—41no—
153C2×D4×C139—416no—
154C2×D4×C139—48no—
155C2×D4×C139—42no—
156C2×D4×C139—42no—
157C2×D4×C139—48no—
158C2×D4×C139—84no—
159C2×D4×C139C2×D414yes—
160C22×C4×C139—24no—
161C22×C4×C139—24no—
162C22×C4×C139—21no—
163C22×C4×C139—22no—
164C22×C4×C139—24no—
165C22×C4×C139—22no—
166C22×C4×C139—24no—
167C22×C4×C139—22no—
168C22×C4×C139—22no—
169C22×C4×C139—22no—
170C22×C4×C139—24no—
171C22×C4×C139—22no—
172C22×C4×C139—22no—
173C22×C4×C139—24no—
174C22×C4×C139—41no—
175C22×C4×C139—416no—
176C22×C4×C139—44no—
177C22×C4×C139—42no—
178C22×C4×C139—42no—
179C22×C4×C139—42no—
180C22×C4×C139—42no—
181C22×C4×C139C2×D412yes—
182C22×C4×C139C2×D411yescharacteristic
183C22×C4×C139C2×D411yescharacteristic
184C22×C4×C139C2×D414yes—
185C22×C4×C139C2×D414yescomplemented
186C4⋊C4×C139—28no—
187C4⋊C4×C139—22no—
188C4⋊C4×C139—24no—
189C4⋊C4×C139—28no—
190C4⋊C4×C139—48no—
191C22⋊C4×C139—24no—
192C22⋊C4×C139—28no—
193C22⋊C4×C139—22no—
194C22⋊C4×C139—24no—
195C22⋊C4×C139—24no—
196C22⋊C4×C139—28no—
197C22⋊C4×C139—24no—
198C22⋊C4×C139—24no—
199C22⋊C4×C139—22no—
200C22⋊C4×C139—22no—
201C22⋊C4×C139—22no—
202C22⋊C4×C139—24no—
203C22⋊C4×C139—24no—
204C22⋊C4×C139—48no—
205C22⋊C4×C139—48no—
206C22⋊C4×C139C2×D414yescomplemented
207C42×C139—22no—
208C23×C139—21no—
209C23×C139—21no—
210C23×C139—24no—
211C23×C139—21no—
212C23×C139—21no—
213C23×C139—21no—
214C23×C139—28no—
215C23×C139—28no—
216C23×C139—21no—
217C23×C139—21no—
218C23×C139—21no—
219C23×C139—22no—
220C23×C139—21no—
221C23×C139—24no—
222C23×C139—44no—
223C23×C139—42no—
224C23×C139—42no—
225C23×C139—44no—
226C23×C139—48no—
227C23×C139—48no—
228C23×C139—42no—
229C23×C139—42no—
230C23×C139—48no—
231C23×C139—42no—
232C23×C139—44no—
233C23×C139—44no—
234C23×C139—82no—
235C23×C139—84no—
236C23×C139—82no—
237C23×C139#12012yes—
238C23×C139#12012yes—
239C23×C139#12012yes—
240C23×C139C22×D411yescharacteristic
241C23×C139C22×D412yes—
242C23×C139C22×D412yes—
243C23×C139H(5,𝔽2)12yes—
244Q8×C139—42no—
245D4×C139—28no—
246D4×C139—44no—
247D4×C139—42no—
248D4×C139—44no—
249D4×C139—44no—
250D4×C139—42no—
251D4×C139—42no—
252D4×C139—44no—
253D4×C139—44no—
254D4×C139—48no—
255D4×C139—84no—
256D4×C139—84no—
257C2×C4×C139—21no—
258C2×C4×C139—21no—
259C2×C4×C139—24no—
260C2×C4×C139—24no—
261C2×C4×C139—21no—
262C2×C4×C139—24no—
263C2×C4×C139—22no—
264C2×C4×C139—21no—
265C2×C4×C139—21no—
266C2×C4×C139—28no—
267C2×C4×C139—24no—
268C2×C4×C139—44no—
269C2×C4×C139—44no—
270C2×C4×C139—48no—
271C2×C4×C139—44no—
272C2×C4×C139—48no—
273C2×C4×C139—48no—
274C2×C4×C139—42no—
275C2×C4×C139—42no—
276C2×C4×C139—42no—
277C2×C4×C139—44no—
278C2×C4×C139—44no—
279C2×C4×C139—48no—
280C2×C4×C139—44no—
281C2×C4×C139—82no—
282C2×C4×C139#12012yes—
283C22×C139—24no—
284C22×C139—24no—
285C22×C139—22no—
286C22×C139—24no—
287C22×C139—22no—
288C22×C139—22no—
289C22×C139—22no—
290C22×C139—22no—
291C22×C139—24no—
292C22×C139—42no—
293C22×C139—42no—
294C22×C139—416no—
295C22×C139—42no—
296C22×C139—42no—
297C22×C139—42no—
298C22×C139—42no—
299C22×C139—42no—
300C22×C139—42no—
301C22×C139—41no—
302C22×C139—44no—
303C22×C139—42no—
304C22×C139—81no—
305C22×C139—88no—
306C22×C139—84no—
307C22×C139—81no—
308C22×C139—162no—
309C22×C139#45814yescomplemented
310C22×C139C2×#12011yescharacteristic
311C22×C139C2×#12011yescharacteristic
312C22×C139#53411yescharacteristic
313C22×C139D4214yes—
314C4×C139—22no—
315C4×C139—44no—
316C4×C139—44no—
317C4×C139—41no—
318C4×C139—42no—
319C4×C139—44no—
320C4×C139—84no—
321C2×C139—21no—
322C2×C139—24no—
323C2×C139—21no—
324C2×C139—24no—
325C2×C139—42no—
326C2×C139—42no—
327C2×C139—81no—
328C2×C139—82no—
329C2×C139#240311yescharacteristic
330C2×C139C2×#45812yes—
331#23901C13911yesmaximal, characteristic, direct product factor, Sylow
332C139#2390111yescharacteristic, direct product factor, Sylow
333#3484C2×C13911yescharacteristic
334C22×#123C2×C13911yescharacteristic, complemented
335C2×#458C2×C13912yescomplemented
336#2849C2×C13912yescomplemented
337#2022C2×C13914yescomplemented
338#1898C2×C13912yescomplemented
339#1890C2×C13912yescomplemented
340#1781C2×C13911yescharacteristic, complemented
341C2×H(5,𝔽2)C22×C13911yescharacteristic
342C23×D4C22×C13911yescharacteristic
343C24×C4C22×C13911yescharacteristic, complemented
344#546—24no—
345D42—24no—
346#535—21no—
347#534—21no—
348#534C22×C13912yes—
349#525—21no—
350C2×#123—21no—
351C2×#123—21no—
352C2×#123—28no—
353C2×#123C22×C13912yes—
354C2×#123C22×C13912yescomplemented
355C2×#123C22×C13914yescomplemented
356C2×#120—21no—
357C2×#120C22×C13912yes—
358#518C22×C13911yescharacteristic
359C22×C4⋊C4—21no—
360C22×C22⋊C4—21no—
361C22×C22⋊C4C22×C13911yescharacteristic, complemented
362#458—28no—
363C2×#99C22×C13912yes—
364C2×#99C22×C13914yescomplemented
365C2×#99C22×C13912yescomplemented
366#386—24no—
367#385—24no—
368#381C22×C13914yescomplemented
369#379C22×C13912yescomplemented
370#342C22×C13914yescomplemented
371C25D4×C13911yescharacteristic
372C25C23×C13911yescharacteristic
373H(5,𝔽2)—24no—
374H(5,𝔽2)—42no—
375C2×#41—21no—
376C2×#41—22no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4—24no—
380C22×D4—22no—
381C22×D4—24no—
382C22×D4—42no—
383C22×D4D4×C13911yescharacteristic
384C22×D4D4×C13911yescharacteristic
385C22×D4D4×C13914yes—
386C22×D4C23×C13912yes—
387C22×D4C23×C13911yescharacteristic
388C22×D4C23×C13911yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—42no—
395C23×C4D4×C13911yescharacteristic
396C23×C4C23×C13912yes—
397#127—22no—
398#124—22no—
399#123—28no—
400#123—28no—
401#123—22no—
402#123—24no—
403#123—22no—
404#123—22no—
405#123—24no—
406#123—24no—
407#123—28no—
408#123—44no—
409#123D4×C13918yescomplemented
410C22⋊Q8—22no—
411#121—22no—
412#121—24no—
413#121—24no—
414#121—24no—
415#120—24no—
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420#120—24no—
421#120—22no—
422C4×D4—24no—
423C4×D4—24no—
424#117—21no—
425C2×C4⋊C4—28no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4D4×C13914yes—
439C2×C22⋊C4C23×C13914yes—
440C2×C22⋊C4C23×C13912yes—
441C2×C22⋊C4C23×C13912yes—
442#99—24no—
443#99—28no—
444#99—42no—
445#95—28no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—44no—
452C24—41no—
453C24—44no—
454C24C2×D4×C13911yescharacteristic
455C24C2×D4×C13914yes—
456C24C2×D4×C13911yescharacteristic
457C24C2×D4×C13912yes—
458C24C2×D4×C13911yescharacteristic
459C24C2×D4×C13911yescharacteristic
460C24C24×C13911yescharacteristic
461#41—48no—
462#41—42no—
463#41—42no—
464C2×Q8—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—416no—
486C2×D4—48no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—48no—
490C2×D4—84no—
491C2×D4C2×D4×C13914yes—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—41no—
507C22×C4—416no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4C2×D4×C13912yes—
514C22×C4C2×D4×C13911yescharacteristic
515C22×C4C2×D4×C13911yescharacteristic
516C22×C4C2×D4×C13914yes—
517C22×C4C2×D4×C13914yescomplemented
518C4⋊C4—28no—
519C4⋊C4—22no—
520C4⋊C4—24no—
521C4⋊C4—28no—
522C4⋊C4—48no—
523C22⋊C4—24no—
524C22⋊C4—28no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—28no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4C2×D4×C13914yescomplemented
539C42—22no—
540C23—24no—
541C23—21no—
542C23—21no—
543C23—28no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—28no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—24no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—48no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—82no—
567C23—84no—
568C23—82no—
569C23#120×C13912yes—
570C23#120×C13912yes—
571C23#120×C13912yes—
572C23C22×D4×C13911yescharacteristic
573C23C22×D4×C13912yes—
574C23C22×D4×C13912yes—
575C23H(5,𝔽2)×C13912yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—48no—
583D4—42no—
584D4—42no—
585D4—44no—
586D4—44no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—48no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—44no—
613C2×C4—82no—
614C2×C4#120×C13912yes—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—24no—
622C22—22no—
623C22—22no—
624C22—42no—
625C22—42no—
626C22—416no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—44no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—81no—
637C22—88no—
638C22—81no—
639C22—84no—
640C22—162no—
641C22#458×C13914yescomplemented
642C22C2×#120×C13911yescharacteristic
643C22C2×#120×C13911yescharacteristic
644C22#534×C13911yescharacteristic
645C22D42×C13914yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—44no—
650C4—41no—
651C4—42no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—24no—
656C2—21no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2#2403×C13911yescharacteristic
662C2C2×#458×C13912yes—
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC24C24×C139
prime radical#3484×C139C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C25×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#123×C139C2semidirect
3. C2×#458×C139C2semidirect
4. #2849×C139C2semidirect
5. #2022×C139C2semidirect
6. #1898×C139C2semidirect
7. #1890×C139C2semidirect
8. #1781×C139C2semidirect
11. C24×C4×C139C22semidirect
22. C2×#123×C139C22semidirect
23. C2×#123×C139C22semidirect
29. C22×C22⋊C4×C139C22semidirect
32. C2×#99×C139C22semidirect
33. C2×#99×C139C22semidirect
36. #381×C139C22semidirect
37. #379×C139C22semidirect
38. #342×C139C22semidirect
77. #123×C139D4semidirect
185. C22×C4×C139C2×D4semidirect
206. C22⋊C4×C139C2×D4semidirect
309. C22×C139#458semidirect
331. #23901C139direct (N × H)
332. C139#23901direct (N × H)
334. C22×#123C2×C139semidirect
335. C2×#458C2×C139semidirect
336. #2849C2×C139semidirect
337. #2022C2×C139semidirect
338. #1898C2×C139semidirect
339. #1890C2×C139semidirect
340. #1781C2×C139semidirect
343. C24×C4C22×C139semidirect
354. C2×#123C22×C139semidirect
355. C2×#123C22×C139semidirect
361. C22×C22⋊C4C22×C139semidirect
364. C2×#99C22×C139semidirect
365. C2×#99C22×C139semidirect
368. #381C22×C139semidirect
369. #379C22×C139semidirect
370. #342C22×C139semidirect
409. #123D4×C139semidirect
517. C22×C4C2×D4×C139semidirect
538. C22⋊C4C2×D4×C139semidirect
641. C22#458×C139semidirect

Maximal subgroups

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

subgroupindex
#3484×C1392
C22×#123×C1392
C2×#458×C1392
#2849×C1392
#2022×C1392
#1898×C1392
#1890×C1392
#1781×C1392
#23901139