Finite Group Databasebeta

← C139×#13043 #48007639

Subgroups — C139×#13043 #48007639

Order 35584.

844 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×B(4,𝔽2)×C139C211yesmaximal, characteristic
2#2375×C139C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C139C211yesmaximal, characteristic, complemented
4#1792×C139C211yesmaximal, characteristic, complemented
5#1790×C139C211yesmaximal, characteristic, complemented
6#1393×C139C211yesmaximal, characteristic, complemented
7#1390×C139C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C139C2211yescharacteristic
9C2×#120×C139—21no—
10C2×#120×C139C2211yescharacteristic
11B(4,𝔽2)×C139—22no—
12B(4,𝔽2)×C139C414yescomplemented
13C2×#104×C139—21no—
14#417×C139—21no—
15C2×#100×C139C2211yescharacteristic
16C2×#99×C139—21no—
17C2×#99×C139—21no—
18C2×#99×C139C2211yescharacteristic
19C2×#99×C139C2211yescharacteristic
20#390×C139—21no—
21#390×C139C2211yescharacteristic
22#388×C139—21no—
23#388×C139—21no—
24#388×C139—21no—
25#386×C139—21no—
26#386×C139—21no—
27#386×C139C2211yescharacteristic
28#379×C139—21no—
29AΣL(1,𝔽16)×C139—22no—
30C25×C139D411yescharacteristic
31H(5,𝔽2)×C139—21no—
32H(5,𝔽2)×C139—21no—
33H(5,𝔽2)×C139—21no—
34H(5,𝔽2)×C139—42no—
35H(5,𝔽2)×C139C2×C412yes—
36C2×#41×C139—21no—
37C2×#41×C139—41no—
38C22×D4×C139—21no—
39C22×D4×C139—21no—
40C22×D4×C139—21no—
41C22×D4×C139—41no—
42C22×D4×C139—41no—
43C22×D4×C139C2311yescharacteristic
44C23×C4×C139D411yescharacteristic, complemented
45C2×M16×C139—21no—
46#120×C139—21no—
47#120×C139—21no—
48#120×C139—24no—
49#120×C139—42no—
50#120×C139C2×C412yes—
51#120×C139D412yes—
52C2×C4⋊C4×C139—21no—
53C2×C4⋊C4×C139D411yescharacteristic, complemented
54C2×C22⋊C4×C139—21no—
55C2×C22⋊C4×C139—21no—
56C2×C22⋊C4×C139—21no—
57C2×C22⋊C4×C139—21no—
58C2×C22⋊C4×C139—21no—
59C2×C22⋊C4×C139—21no—
60C2×C22⋊C4×C139—21no—
61C2×C22⋊C4×C139—21no—
62C2×C22⋊C4×C139—21no—
63C2×C22⋊C4×C139—21no—
64C2×C22⋊C4×C139—41no—
65C2×C22⋊C4×C139—41no—
66C2×C22⋊C4×C139D411yescharacteristic
67C2×C22⋊C4×C139D411yescharacteristic, complemented
68C2×C42×C139—21no—
69C2×C42×C139D411yescharacteristic, complemented
70#104×C139—42no—
71#103×C139—41no—
72#102×C139—41no—
73#100×C139—21no—
74#100×C139—21no—
75#99×C139—21no—
76#99×C139—24no—
77#99×C139—21no—
78#99×C139—21no—
79#99×C139—42no—
80#99×C139C2×C412yes—
81#95×C139—21no—
82#95×C139—21no—
83#95×C139—21no—
84#95×C139—41no—
85C24×C139—21no—
86C24×C139—21no—
87C24×C139—21no—
88C24×C139—21no—
89C24×C139—41no—
90C24×C139—41no—
91C24×C139—81no—
92C24×C139—81no—
93C24×C139C22⋊C412yescomplemented
94C24×C139C2×D411yescharacteristic
95C24×C139C2×D411yescharacteristic
96#41×C139—22no—
97#41×C139—22no—
98#41×C139—42no—
99#41×C139—41no—
100#41×C139—42no—
101#41×C139—42no—
102#41×C139—42no—
103#41×C139—41no—
104C2×Q8×C139—21no—
105C2×D4×C139—21no—
106C2×D4×C139—22no—
107C2×D4×C139—22no—
108C2×D4×C139—22no—
109C2×D4×C139—22no—
110C2×D4×C139—22no—
111C2×D4×C139—22no—
112C2×D4×C139—41no—
113C2×D4×C139—41no—
114C2×D4×C139—42no—
115C2×D4×C139—42no—
116C2×D4×C139—41no—
117C2×D4×C139—41no—
118C2×D4×C139—41no—
119C2×D4×C139—41no—
120C2×D4×C139—42no—
121C2×D4×C139—42no—
122C2×D4×C139—41no—
123C2×D4×C139—41no—
124C2×D4×C139—41no—
125C2×D4×C139—44no—
126C2×D4×C139—81no—
127C2×D4×C139—81no—
128C2×D4×C139—82no—
129C2×D4×C139—82no—
130C2×D4×C139C22×C411yescharacteristic
131C2×D4×C139C2×D411yescharacteristic
132C2×D4×C139#4111yescharacteristic
133C2×D4×C139#4111yescharacteristic
134C22×C4×C139—21no—
135C22×C4×C139—21no—
136C22×C4×C139—21no—
137C22×C4×C139—21no—
138C22×C4×C139—21no—
139C22×C4×C139—21no—
140C22×C4×C139—21no—
141C22×C4×C139—41no—
142C22×C4×C139—41no—
143C22×C4×C139—41no—
144C22×C4×C139—41no—
145C22×C4×C139—81no—
146C22×C4×C139C2×D411yescharacteristic
147M16×C139—41no—
148M16×C139—41no—
149C2×C8×C139—41no—
150C4⋊C4×C139—41no—
151C4⋊C4×C139—81no—
152C22⋊C4×C139—21no—
153C22⋊C4×C139—22no—
154C22⋊C4×C139—22no—
155C22⋊C4×C139—22no—
156C22⋊C4×C139—44no—
157C22⋊C4×C139—41no—
158C22⋊C4×C139—41no—
159C22⋊C4×C139—41no—
160C22⋊C4×C139—41no—
161C22⋊C4×C139—81no—
162C22⋊C4×C139—81no—
163C22⋊C4×C139—81no—
164C22⋊C4×C139—81no—
165C22⋊C4×C139—81no—
166C22⋊C4×C139—81no—
167C22⋊C4×C139—81no—
168C22⋊C4×C139—82no—
169C22⋊C4×C139C22⋊C412yescomplemented
170C42×C139—41no—
171C42×C139—81no—
172C23×C139—21no—
173C23×C139—21no—
174C23×C139—21no—
175C23×C139—21no—
176C23×C139—22no—
177C23×C139—22no—
178C23×C139—22no—
179C23×C139—42no—
180C23×C139—41no—
181C23×C139—41no—
182C23×C139—41no—
183C23×C139—41no—
184C23×C139—41no—
185C23×C139—41no—
186C23×C139—41no—
187C23×C139—41no—
188C23×C139—41no—
189C23×C139—41no—
190C23×C139—42no—
191C23×C139—42no—
192C23×C139—41no—
193C23×C139—41no—
194C23×C139—41no—
195C23×C139—81no—
196C23×C139—82no—
197C23×C139—82no—
198C23×C139—81no—
199C23×C139—81no—
200C23×C139—84no—
201C23×C139—81no—
202C23×C139—81no—
203C23×C139—81no—
204C23×C139—81no—
205C23×C139C2×C22⋊C411yescharacteristic
206C23×C139C4×D411yescharacteristic
207C23×C139#12011yescharacteristic
208C23×C139#12111yescharacteristic
209C23×C139#12311yescharacteristic
210Q8×C139—22no—
211Q8×C139—41no—
212D4×C139—22no—
213D4×C139—41no—
214D4×C139—41no—
215D4×C139—41no—
216D4×C139—41no—
217D4×C139—41no—
218D4×C139—42no—
219D4×C139—42no—
220D4×C139—42no—
221D4×C139—42no—
222D4×C139—42no—
223D4×C139—42no—
224D4×C139—82no—
225D4×C139—82no—
226D4×C139—88no—
227C2×C4×C139—21no—
228C2×C4×C139—21no—
229C2×C4×C139—22no—
230C2×C4×C139—22no—
231C2×C4×C139—22no—
232C2×C4×C139—42no—
233C2×C4×C139—42no—
234C2×C4×C139—41no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139—41no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—42no—
242C2×C4×C139—41no—
243C2×C4×C139—41no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—41no—
248C2×C4×C139—42no—
249C2×C4×C139—41no—
250C2×C4×C139—41no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—81no—
254C2×C4×C139—81no—
255C2×C4×C139—81no—
256C2×C4×C139—81no—
257C2×C4×C139—81no—
258C2×C4×C139—81no—
259C2×C4×C139C4×D411yescharacteristic
260C2×C4×C139#12111yescharacteristic
261C8×C139—81no—
262C22×C139—21no—
263C22×C139—21no—
264C22×C139—21no—
265C22×C139—21no—
266C22×C139—21no—
267C22×C139—21no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
271C22×C139—41no—
272C22×C139—42no—
273C22×C139—42no—
274C22×C139—41no—
275C22×C139—41no—
276C22×C139—41no—
277C22×C139—41no—
278C22×C139—44no—
279C22×C139—42no—
280C22×C139—42no—
281C22×C139—81no—
282C22×C139—81no—
283C22×C139—81no—
284C22×C139—81no—
285C22×C139—82no—
286C22×C139—82no—
287C22×C139—82no—
288C22×C139—82no—
289C22×C139—82no—
290C22×C139—81no—
291C22×C139—81no—
292C22×C139—81no—
293C22×C139—81no—
294C22×C139—161no—
295C22×C139—161no—
296C22×C139#38611yescharacteristic
297C22×C139B(4,𝔽2)11yescharacteristic
298C22×C139B(4,𝔽2)11yescharacteristic
299C4×C139—21no—
300C4×C139—21no—
301C4×C139—42no—
302C4×C139—42no—
303C4×C139—81no—
304C4×C139—81no—
305C4×C139—82no—
306C4×C139—81no—
307C4×C139—81no—
308C4×C139—161no—
309C2×C139—21no—
310C2×C139—21no—
311C2×C139—41no—
312C2×C139—41no—
313C2×C139—41no—
314C2×C139—41no—
315C2×C139—82no—
316C2×C139—82no—
317C2×C139#188911yescharacteristic
318C2×C139#219911yescharacteristic
319C2×C139#220011yescharacteristic
320#13043C13911yesmaximal, characteristic, direct product factor, Sylow
321C139#1304311yescharacteristic, direct product factor, Sylow
322C2×B(4,𝔽2)C2×C13911yescharacteristic
323#2375C2×C13911yescharacteristic, complemented
324C2×AΣL(1,𝔽16)C2×C13911yescharacteristic, complemented
325#1792C2×C13911yescharacteristic, complemented
326#1790C2×C13911yescharacteristic, complemented
327#1393C2×C13911yescharacteristic, complemented
328#1390C2×C13911yescharacteristic, complemented
329C2×H(5,𝔽2)C22×C13911yescharacteristic
330C2×#120—21no—
331C2×#120C22×C13911yescharacteristic
332B(4,𝔽2)—22no—
333B(4,𝔽2)C4×C13914yescomplemented
334C2×#104—21no—
335#417—21no—
336C2×#100C22×C13911yescharacteristic
337C2×#99—21no—
338C2×#99—21no—
339C2×#99C22×C13911yescharacteristic
340C2×#99C22×C13911yescharacteristic
341#390—21no—
342#390C22×C13911yescharacteristic
343#388—21no—
344#388—21no—
345#388—21no—
346#386—21no—
347#386—21no—
348#386C22×C13911yescharacteristic
349#379—21no—
350AΣL(1,𝔽16)—22no—
351C25D4×C13911yescharacteristic
352H(5,𝔽2)—21no—
353H(5,𝔽2)—21no—
354H(5,𝔽2)—21no—
355H(5,𝔽2)—42no—
356H(5,𝔽2)C2×C4×C13912yes—
357C2×#41—21no—
358C2×#41—41no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4C23×C13911yescharacteristic
365C23×C4D4×C13911yescharacteristic, complemented
366C2×M16—21no—
367#120—21no—
368#120—21no—
369#120—24no—
370#120—42no—
371#120C2×C4×C13912yes—
372#120D4×C13912yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C13911yescharacteristic, complemented
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4D4×C13911yescharacteristic
388C2×C22⋊C4D4×C13911yescharacteristic, complemented
389C2×C42—21no—
390C2×C42D4×C13911yescharacteristic, complemented
391#104—42no—
392#103—41no—
393#102—41no—
394#100—21no—
395#100—21no—
396#99—21no—
397#99—24no—
398#99—21no—
399#99—21no—
400#99—42no—
401#99C2×C4×C13912yes—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—41no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—41no—
411C24—41no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C13912yescomplemented
415C24C2×D4×C13911yescharacteristic
416C24C2×D4×C13911yescharacteristic
417#41—22no—
418#41—22no—
419#41—42no—
420#41—41no—
421#41—42no—
422#41—42no—
423#41—42no—
424#41—41no—
425C2×Q8—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—44no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—82no—
450C2×D4—82no—
451C2×D4C22×C4×C13911yescharacteristic
452C2×D4C2×D4×C13911yescharacteristic
453C2×D4#41×C13911yescharacteristic
454C2×D4#41×C13911yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—81no—
467C22×C4C2×D4×C13911yescharacteristic
468M16—41no—
469M16—41no—
470C2×C8—41no—
471C4⋊C4—41no—
472C4⋊C4—81no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—44no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—82no—
490C22⋊C4C22⋊C4×C13912yescomplemented
491C42—41no—
492C42—81no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—81no—
517C23—82no—
518C23—82no—
519C23—81no—
520C23—81no—
521C23—84no—
522C23—81no—
523C23—81no—
524C23—81no—
525C23—81no—
526C23C2×C22⋊C4×C13911yescharacteristic
527C23C4×D4×C13911yescharacteristic
528C23#120×C13911yescharacteristic
529C23#121×C13911yescharacteristic
530C23#123×C13911yescharacteristic
531Q8—22no—
532Q8—41no—
533D4—22no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—82no—
546D4—82no—
547D4—88no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4C4×D4×C13911yescharacteristic
581C2×C4#121×C13911yescharacteristic
582C8—81no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—161no—
616C22—161no—
617C22#386×C13911yescharacteristic
618C22B(4,𝔽2)×C13911yescharacteristic
619C22B(4,𝔽2)×C13911yescharacteristic
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4—81no—
629C4—161no—
630C2—21no—
631C2—21no—
632C2—41no—
633C2—41no—
634C2—41no—
635C2—41no—
636C2—82no—
637C2—82no—
638C2#1889×C13911yescharacteristic
639C2#2199×C13911yescharacteristic
640C2#2200×C13911yescharacteristic
subgroupG/H
center, socleC22×C139B(4,𝔽2)
commutatorC2×D4C22×C4×C139
Frattini, cosocleC22×D4C23×C139
prime radicalC2×B(4,𝔽2)×C139C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C22×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2375×C139C2semidirect
3. C2×AΣL(1,𝔽16)×C139C2semidirect
4. #1792×C139C2semidirect
5. #1790×C139C2semidirect
6. #1393×C139C2semidirect
7. #1390×C139C2semidirect
12. B(4,𝔽2)×C139C4semidirect
44. C23×C4×C139D4semidirect
53. C2×C4⋊C4×C139D4semidirect
67. C2×C22⋊C4×C139D4semidirect
69. C2×C42×C139D4semidirect
93. C24×C139C22⋊C4semidirect
169. C22⋊C4×C139C22⋊C4semidirect
320. #13043C139direct (N × H)
321. C139#13043direct (N × H)
323. #2375C2×C139semidirect
324. C2×AΣL(1,𝔽16)C2×C139semidirect
325. #1792C2×C139semidirect
326. #1790C2×C139semidirect
327. #1393C2×C139semidirect
328. #1390C2×C139semidirect
333. B(4,𝔽2)C4×C139semidirect
365. C23×C4D4×C139semidirect
374. C2×C4⋊C4D4×C139semidirect
388. C2×C22⋊C4D4×C139semidirect
390. C2×C42D4×C139semidirect
414. C24C22⋊C4×C139semidirect
490. C22⋊C4C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×B(4,𝔽2)×C1392
#2375×C1392
C2×AΣL(1,𝔽16)×C1392
#1792×C1392
#1790×C1392
#1393×C1392
#1390×C1392
#13043139