Finite Group Databasebeta

← C139×#13347 #48007943

Subgroups — C139×#13347 #48007943

Order 35584.

830 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#458×C139C211yesmaximal, characteristic, complemented
2C2×#453×C139C211yesmaximal, characteristic
3#2709×C139C211yesmaximal, characteristic, complemented
4C2×#353×C139C211yesmaximal, characteristic, complemented
5C2×#352×C139C211yesmaximal, characteristic, complemented
6#1790×C139C211yesmaximal, characteristic, complemented
7#1390×C139C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C139C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C139—21no—
10C2×#127×C139C2211yescharacteristic
11C2×#123×C139—21no—
12C2×#123×C139C2211yescharacteristic
13#458×C139—22no—
14#458×C139—22no—
15#453×C139—22no—
16#453×C139—22no—
17C2×#104×C139—21no—
18C2×#100×C139C2211yescharacteristic
19C2×#99×C139—21no—
20C2×#99×C139—21no—
21C2×#99×C139C2211yescharacteristic
22C2×#99×C139C2211yescharacteristic
23#394×C139—21no—
24#394×C139—21no—
25#394×C139—21no—
26#387×C139—21no—
27#386×C139—21no—
28#386×C139—21no—
29#386×C139—21no—
30#386×C139C2211yescharacteristic
31#353×C139—22no—
32#352×C139—22no—
33H(5,𝔽2)×C139—21no—
34H(5,𝔽2)×C139—21no—
35H(5,𝔽2)×C139—21no—
36H(5,𝔽2)×C139—42no—
37H(5,𝔽2)×C139D412yes—
38C2×#41×C139—21no—
39C2×#41×C139—41no—
40C22×D4×C139—21no—
41C22×D4×C139—21no—
42C22×D4×C139—21no—
43C22×D4×C139—21no—
44C22×D4×C139—41no—
45C22×D4×C139D411yescharacteristic
46C22×D4×C139C2311yescharacteristic
47C23×C4×C139D411yescharacteristic
48C23×C4×C139D411yescharacteristic
49AGL(1,ℤ/8)×C139—24no—
50AGL(1,ℤ/8)×C139—42no—
51C2×SD16×C139—41no—
52C2×D8×C139—41no—
53C2×M16×C139—21no—
54#127×C139—21no—
55#127×C139—21no—
56#127×C139—21no—
57#127×C139—21no—
58#123×C139—24no—
59#123×C139—21no—
60#123×C139—21no—
61#123×C139—21no—
62#123×C139—21no—
63#123×C139—42no—
64C2×C4⋊C4×C139—21no—
65C2×C4⋊C4×C139—21no—
66C2×C4⋊C4×C139—41no—
67C2×C22⋊C4×C139—21no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—21no—
70C2×C22⋊C4×C139—21no—
71C2×C22⋊C4×C139—21no—
72C2×C22⋊C4×C139—21no—
73C2×C22⋊C4×C139—21no—
74C2×C22⋊C4×C139—21no—
75C2×C22⋊C4×C139—41no—
76C2×C22⋊C4×C139—41no—
77C2×C22⋊C4×C139D411yescharacteristic
78C2×C22⋊C4×C139D411yescharacteristic
79C2×C42×C139D411yescharacteristic
80#104×C139—24no—
81#100×C139—21no—
82#100×C139D412yes—
83#99×C139—24no—
84#99×C139—21no—
85#99×C139—21no—
86#99×C139—21no—
87#99×C139—42no—
88#99×C139D412yes—
89#95×C139—21no—
90#95×C139—21no—
91#95×C139—21no—
92#95×C139—21no—
93#95×C139—41no—
94C24×C139—21no—
95C24×C139—21no—
96C24×C139—21no—
97C24×C139C2×D411yescharacteristic
98C24×C139C2×D411yescharacteristic
99#41×C139—22no—
100#41×C139—22no—
101#41×C139—42no—
102#41×C139—41no—
103#41×C139—42no—
104#41×C139—42no—
105#41×C139—42no—
106#41×C139—41no—
107C2×Q8×C139—21no—
108C2×D4×C139—21no—
109C2×D4×C139—22no—
110C2×D4×C139—22no—
111C2×D4×C139—22no—
112C2×D4×C139—22no—
113C2×D4×C139—21no—
114C2×D4×C139—21no—
115C2×D4×C139—41no—
116C2×D4×C139—41no—
117C2×D4×C139—41no—
118C2×D4×C139—41no—
119C2×D4×C139—42no—
120C2×D4×C139—42no—
121C2×D4×C139—42no—
122C2×D4×C139—42no—
123C2×D4×C139—41no—
124C2×D4×C139—41no—
125C2×D4×C139—41no—
126C2×D4×C139—41no—
127C2×D4×C139—42no—
128C2×D4×C139—42no—
129C2×D4×C139—41no—
130C2×D4×C139—41no—
131C2×D4×C139—41no—
132C2×D4×C139—41no—
133C2×D4×C139—41no—
134C2×D4×C139—41no—
135C2×D4×C139—41no—
136C2×D4×C139—81no—
137C2×D4×C139—81no—
138C2×D4×C139C2×D411yescharacteristic
139C2×D4×C139C2×D411yescharacteristic
140C2×D4×C139C2×D411yescharacteristic
141C2×D4×C139#4111yescharacteristic
142C22×C4×C139—21no—
143C22×C4×C139—21no—
144C22×C4×C139—21no—
145C22×C4×C139—21no—
146C22×C4×C139—21no—
147C22×C4×C139—21no—
148C22×C4×C139—21no—
149C22×C4×C139—21no—
150C22×C4×C139—21no—
151C22×C4×C139—41no—
152C22×C4×C139—41no—
153C22×C4×C139—41no—
154C22×C4×C139—41no—
155C22×C4×C139—41no—
156C22×C4×C139—41no—
157C22×C4×C139—81no—
158C22×C4×C139C2×D411yescharacteristic
159SD16×C139—44no—
160D8×C139—44no—
161M16×C139—22no—
162M16×C139—41no—
163C2×C8×C139—41no—
164C4⋊C4×C139—42no—
165C4⋊C4×C139—44no—
166C4⋊C4×C139—41no—
167C4⋊C4×C139—41no—
168C22⋊C4×C139—21no—
169C22⋊C4×C139—22no—
170C22⋊C4×C139—21no—
171C22⋊C4×C139—41no—
172C22⋊C4×C139—44no—
173C22⋊C4×C139—41no—
174C22⋊C4×C139—41no—
175C22⋊C4×C139—41no—
176C22⋊C4×C139—41no—
177C22⋊C4×C139—41no—
178C22⋊C4×C139—81no—
179C22⋊C4×C139—81no—
180C22⋊C4×C139—81no—
181C22⋊C4×C139—81no—
182C22⋊C4×C139—81no—
183C22⋊C4×C139—82no—
184C42×C139—21no—
185C42×C139—21no—
186C23×C139—21no—
187C23×C139—21no—
188C23×C139—21no—
189C23×C139—21no—
190C23×C139—22no—
191C23×C139—22no—
192C23×C139—41no—
193C23×C139—41no—
194C23×C139—41no—
195C23×C139—41no—
196C23×C139—41no—
197C23×C139—41no—
198C23×C139—41no—
199C23×C139—41no—
200C23×C139—41no—
201C23×C139—41no—
202C23×C139—41no—
203C23×C139—41no—
204C23×C139—41no—
205C23×C139—41no—
206C23×C139—81no—
207C23×C139—81no—
208C23×C139—81no—
209C23×C139—81no—
210C23×C139#12011yescharacteristic
211C23×C139#12011yescharacteristic
212C23×C139#12111yescharacteristic
213C23×C139#12111yescharacteristic
214C23×C139#12711yescharacteristic
215Q8×C139—22no—
216Q8×C139—41no—
217D4×C139—22no—
218D4×C139—41no—
219D4×C139—41no—
220D4×C139—41no—
221D4×C139—41no—
222D4×C139—41no—
223D4×C139—42no—
224D4×C139—42no—
225D4×C139—42no—
226D4×C139—42no—
227D4×C139—42no—
228D4×C139—42no—
229D4×C139—42no—
230D4×C139—81no—
231D4×C139—82no—
232D4×C139—82no—
233D4×C139—82no—
234D4×C139—82no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—22no—
238C2×C4×C139—22no—
239C2×C4×C139—22no—
240C2×C4×C139—42no—
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—42no—
248C2×C4×C139—42no—
249C2×C4×C139—41no—
250C2×C4×C139—41no—
251C2×C4×C139—41no—
252C2×C4×C139—41no—
253C2×C4×C139—41no—
254C2×C4×C139—41no—
255C2×C4×C139—42no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—81no—
263C2×C4×C139—81no—
264C2×C4×C139—81no—
265C2×C4×C139—81no—
266C2×C4×C139—81no—
267C2×C4×C139—81no—
268C2×C4×C139—81no—
269C2×C4×C139#12011yescharacteristic
270C2×C4×C139#12111yescharacteristic
271C8×C139—42no—
272C22×C139—21no—
273C22×C139—21no—
274C22×C139—21no—
275C22×C139—21no—
276C22×C139—21no—
277C22×C139—21no—
278C22×C139—41no—
279C22×C139—41no—
280C22×C139—41no—
281C22×C139—41no—
282C22×C139—41no—
283C22×C139—41no—
284C22×C139—41no—
285C22×C139—41no—
286C22×C139—42no—
287C22×C139—81no—
288C22×C139—81no—
289C22×C139—81no—
290C22×C139—81no—
291C22×C139—81no—
292C22×C139—81no—
293C22×C139—82no—
294C22×C139—82no—
295C22×C139—81no—
296C22×C139—81no—
297C22×C139—81no—
298C22×C139—81no—
299C22×C139—81no—
300C22×C139—161no—
301C22×C139—161no—
302C22×C139#39211yescharacteristic
303C22×C139B(4,𝔽2)11yescharacteristic
304C22×C139B(4,𝔽2)11yescharacteristic
305C4×C139—21no—
306C4×C139—21no—
307C4×C139—42no—
308C4×C139—42no—
309C4×C139—81no—
310C4×C139—81no—
311C4×C139—82no—
312C4×C139—81no—
313C4×C139—81no—
314C4×C139—161no—
315C2×C139—21no—
316C2×C139—21no—
317C2×C139—41no—
318C2×C139—41no—
319C2×C139—41no—
320C2×C139—41no—
321C2×C139—82no—
322C2×C139—161no—
323C2×C139#202111yescharacteristic
324C2×C139#219811yescharacteristic
325C2×C139#220011yescharacteristic
326#13347C13911yesmaximal, characteristic, direct product factor, Sylow
327C139#1334711yescharacteristic, direct product factor, Sylow
328C2×#458C2×C13911yescharacteristic, complemented
329C2×#453C2×C13911yescharacteristic
330#2709C2×C13911yescharacteristic, complemented
331C2×#353C2×C13911yescharacteristic, complemented
332C2×#352C2×C13911yescharacteristic, complemented
333#1790C2×C13911yescharacteristic, complemented
334#1390C2×C13911yescharacteristic, complemented
335C2×H(5,𝔽2)C22×C13911yescharacteristic
336C2×AGL(1,ℤ/8)—21no—
337C2×#127C22×C13911yescharacteristic
338C2×#123—21no—
339C2×#123C22×C13911yescharacteristic
340#458—22no—
341#458—22no—
342#453—22no—
343#453—22no—
344C2×#104—21no—
345C2×#100C22×C13911yescharacteristic
346C2×#99—21no—
347C2×#99—21no—
348C2×#99C22×C13911yescharacteristic
349C2×#99C22×C13911yescharacteristic
350#394—21no—
351#394—21no—
352#394—21no—
353#387—21no—
354#386—21no—
355#386—21no—
356#386—21no—
357#386C22×C13911yescharacteristic
358#353—22no—
359#352—22no—
360H(5,𝔽2)—21no—
361H(5,𝔽2)—21no—
362H(5,𝔽2)—21no—
363H(5,𝔽2)—42no—
364H(5,𝔽2)D4×C13912yes—
365C2×#41—21no—
366C2×#41—41no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—41no—
372C22×D4D4×C13911yescharacteristic
373C22×D4C23×C13911yescharacteristic
374C23×C4D4×C13911yescharacteristic
375C23×C4D4×C13911yescharacteristic
376AGL(1,ℤ/8)—24no—
377AGL(1,ℤ/8)—42no—
378C2×SD16—41no—
379C2×D8—41no—
380C2×M16—21no—
381#127—21no—
382#127—21no—
383#127—21no—
384#127—21no—
385#123—24no—
386#123—21no—
387#123—21no—
388#123—21no—
389#123—21no—
390#123—42no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—41no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4D4×C13911yescharacteristic
405C2×C22⋊C4D4×C13911yescharacteristic
406C2×C42D4×C13911yescharacteristic
407#104—24no—
408#100—21no—
409#100D4×C13912yes—
410#99—24no—
411#99—21no—
412#99—21no—
413#99—21no—
414#99—42no—
415#99D4×C13912yes—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—41no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24C2×D4×C13911yescharacteristic
425C24C2×D4×C13911yescharacteristic
426#41—22no—
427#41—22no—
428#41—42no—
429#41—41no—
430#41—42no—
431#41—42no—
432#41—42no—
433#41—41no—
434C2×Q8—21no—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4C2×D4×C13911yescharacteristic
466C2×D4C2×D4×C13911yescharacteristic
467C2×D4C2×D4×C13911yescharacteristic
468C2×D4#41×C13911yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—81no—
485C22×C4C2×D4×C13911yescharacteristic
486SD16—44no—
487D8—44no—
488M16—22no—
489M16—41no—
490C2×C8—41no—
491C4⋊C4—42no—
492C4⋊C4—44no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—44no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—82no—
511C42—21no—
512C42—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—22no—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23#120×C13911yescharacteristic
538C23#120×C13911yescharacteristic
539C23#121×C13911yescharacteristic
540C23#121×C13911yescharacteristic
541C23#127×C13911yescharacteristic
542Q8—22no—
543Q8—41no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—81no—
558D4—82no—
559D4—82no—
560D4—82no—
561D4—82no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4#120×C13911yescharacteristic
597C2×C4#121×C13911yescharacteristic
598C8—42no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—82no—
621C22—82no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22#392×C13911yescharacteristic
630C22B(4,𝔽2)×C13911yescharacteristic
631C22B(4,𝔽2)×C13911yescharacteristic
632C4—21no—
633C4—21no—
634C4—42no—
635C4—42no—
636C4—81no—
637C4—81no—
638C4—82no—
639C4—81no—
640C4—81no—
641C4—161no—
642C2—21no—
643C2—21no—
644C2—41no—
645C2—41no—
646C2—41no—
647C2—41no—
648C2—82no—
649C2—161no—
650C2#2021×C13911yescharacteristic
651C2#2198×C13911yescharacteristic
652C2#2200×C13911yescharacteristic
subgroupG/H
center, socleC22×C139B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C139
prime radicalC2×#453×C139C2
LCSG ▷ C22×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
1. C2×#458×C139C2semidirect
3. #2709×C139C2semidirect
4. C2×#353×C139C2semidirect
5. C2×#352×C139C2semidirect
6. #1790×C139C2semidirect
7. #1390×C139C2semidirect
326. #13347C139direct (N × H)
327. C139#13347direct (N × H)
328. C2×#458C2×C139semidirect
330. #2709C2×C139semidirect
331. C2×#353C2×C139semidirect
332. C2×#352C2×C139semidirect
333. #1790C2×C139semidirect
334. #1390C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#458×C1392
C2×#453×C1392
#2709×C1392
C2×#353×C1392
C2×#352×C1392
#1790×C1392
#1390×C1392
#13347139