Finite Group Databasebeta

← C139×#9922 #48004518

Subgroups — C139×#9922 #48004518

Order 35584.

1278 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C139C211yesmaximal, characteristic, complemented
2#2626×C139C211yesmaximal, characteristic, complemented
3C2×#392×C139C211yesmaximal, characteristic
4#1786×C139C211yesmaximal, characteristic, complemented
5C2×#328×C139C211yesmaximal, characteristic, complemented
6C2×#323×C139C211yesmaximal, characteristic, complemented
7#1294×C139C211yesmaximal, characteristic, complemented
8C23×D4×C139—21no—
9C23×D4×C139C2211yescharacteristic
10C22×SD16×C139—21no—
11C2×C22⋊Q8×C139C2211yescharacteristic
12C22×C22⋊C4×C139—21no—
13C22×C22⋊C4×C139C2211yescharacteristic
14#450×C139—22no—
15#450×C139—22no—
16C2×#102×C139—21no—
17C2×#102×C139—22no—
18C2×C22⋊C8×C139C2211yescharacteristic
19C2×C22⋊C8×C139C2211yescharacteristic
20#399×C139—21no—
21#396×C139—22no—
22#393×C139—21no—
23#392×C139—22no—
24#392×C139—22no—
25#385×C139—21no—
26#380×C139C2211yescharacteristic
27#379×C139—21no—
28C2×#95×C139C2211yescharacteristic
29#328×C139—22no—
30#323×C139—22no—
31C25×C139—21no—
32C25×C139D411yescharacteristic
33C22×Q8×C139D411yescharacteristic, complemented
34C22×D4×C139—24no—
35C22×D4×C139—21no—
36C22×D4×C139—21no—
37C22×D4×C139—21no—
38C22×D4×C139—21no—
39C22×D4×C139—21no—
40C22×D4×C139—44no—
41C22×D4×C139—44no—
42C22×D4×C139—44no—
43C22×D4×C139—42no—
44C22×D4×C139—42no—
45C22×D4×C139D412yes—
46C23×C4×C139—21no—
47C23×C4×C139D411yescharacteristic
48C23×C4×C139C2311yescharacteristic
49C2×SD16×C139—24no—
50C2×SD16×C139—44no—
51C22×C8×C139—21no—
52C22×C8×C139—21no—
53C22⋊Q8×C139—21no—
54C22⋊Q8×C139—21no—
55C22⋊Q8×C139—21no—
56C22⋊Q8×C139—21no—
57C2×C4⋊C4×C139—21no—
58C2×C4⋊C4×C139—22no—
59C2×C4⋊C4×C139D411yescharacteristic, complemented
60C2×C4⋊C4×C139D412yescomplemented
61C2×C22⋊C4×C139—24no—
62C2×C22⋊C4×C139—21no—
63C2×C22⋊C4×C139—21no—
64C2×C22⋊C4×C139—21no—
65C2×C22⋊C4×C139—21no—
66C2×C22⋊C4×C139—21no—
67C2×C22⋊C4×C139—21no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—21no—
70C2×C22⋊C4×C139—22no—
71C2×C22⋊C4×C139—22no—
72C2×C22⋊C4×C139—44no—
73#102×C139—24no—
74#102×C139—44no—
75C22⋊C8×C139—21no—
76C22⋊C8×C139—21no—
77C22⋊C8×C139—21no—
78C22⋊C8×C139D412yescomplemented
79#95×C139—22no—
80#95×C139—21no—
81#95×C139—21no—
82#95×C139D412yes—
83C24×C139—24no—
84C24×C139—21no—
85C24×C139—22no—
86C24×C139—21no—
87C24×C139—21no—
88C24×C139—21no—
89C24×C139—21no—
90C24×C139—21no—
91C24×C139—42no—
92C24×C139—42no—
93C24×C139—42no—
94C24×C139—42no—
95C24×C139—42no—
96C24×C139—41no—
97C24×C139—41no—
98C24×C139—41no—
99C24×C139—41no—
100C24×C139—41no—
101C24×C139—41no—
102C24×C139SD1612yescomplemented
103C24×C139C2×D411yescharacteristic
104C2×Q8×C139—21no—
105C2×Q8×C139—21no—
106C2×Q8×C139—42no—
107C2×D4×C139—24no—
108C2×D4×C139—24no—
109C2×D4×C139—22no—
110C2×D4×C139—22no—
111C2×D4×C139—42no—
112C2×D4×C139—42no—
113C2×D4×C139—48no—
114C2×D4×C139—44no—
115C2×D4×C139—44no—
116C2×D4×C139—44no—
117C2×D4×C139—44no—
118C2×D4×C139—48no—
119C2×D4×C139—48no—
120C2×D4×C139—416no—
121C2×D4×C139—416no—
122C2×D4×C139—41no—
123C2×D4×C139—41no—
124C22×C4×C139—24no—
125C22×C4×C139—22no—
126C22×C4×C139—21no—
127C22×C4×C139—22no—
128C22×C4×C139—21no—
129C22×C4×C139—21no—
130C22×C4×C139—21no—
131C22×C4×C139—21no—
132C22×C4×C139—42no—
133C22×C4×C139—42no—
134C22×C4×C139—41no—
135C22×C4×C139—41no—
136C22×C4×C139—42no—
137C22×C4×C139C2×D411yescharacteristic
138C22×C4×C139C2×D411yescharacteristic
139C22×C4×C139C2×D411yescharacteristic
140C22×C4×C139C2×D411yescharacteristic
141C22×C4×C139C2×D411yescharacteristic
142C22×C4×C139#4111yescharacteristic
143SD16×C139—48no—
144C2×C8×C139—22no—
145C2×C8×C139—42no—
146C2×C8×C139—42no—
147C2×C8×C139—41no—
148C4⋊C4×C139—21no—
149C4⋊C4×C139—21no—
150C4⋊C4×C139—42no—
151C4⋊C4×C139—41no—
152C4⋊C4×C139—41no—
153C4⋊C4×C139—82no—
154C22⋊C4×C139—48no—
155C22⋊C4×C139—41no—
156C22⋊C4×C139—41no—
157C22⋊C4×C139—41no—
158C22⋊C4×C139—41no—
159C22⋊C4×C139—41no—
160C22⋊C4×C139—41no—
161C22⋊C4×C139—41no—
162C22⋊C4×C139—41no—
163C22⋊C4×C139—82no—
164C22⋊C4×C139—82no—
165C23×C139—22no—
166C23×C139—22no—
167C23×C139—24no—
168C23×C139—22no—
169C23×C139—22no—
170C23×C139—22no—
171C23×C139—44no—
172C23×C139—42no—
173C23×C139—44no—
174C23×C139—44no—
175C23×C139—44no—
176C23×C139—42no—
177C23×C139—42no—
178C23×C139—42no—
179C23×C139—42no—
180C23×C139—44no—
181C23×C139—44no—
182C23×C139—44no—
183C23×C139—41no—
184C23×C139—42no—
185C23×C139—41no—
186C23×C139—42no—
187C23×C139—41no—
188C23×C139—42no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—44no—
192C23×C139—41no—
193C23×C139—82no—
194C23×C139—82no—
195C23×C139—81no—
196C23×C139—81no—
197C23×C139—82no—
198C23×C139—82no—
199C23×C139—82no—
200C23×C139—82no—
201C23×C139—82no—
202C23×C139—81no—
203C23×C139—81no—
204C23×C139—82no—
205C23×C139—81no—
206C23×C139—81no—
207C23×C139#12011yescharacteristic
208C23×C139#12011yescharacteristic
209C23×C139#12111yescharacteristic
210C23×C139C2×SD1611yescharacteristic
211C23×C139#13511yescharacteristic
212C23×C139AGL(1,ℤ/8)11yescharacteristic
213C23×C139#13711yescharacteristic
214Q8×C139—42no—
215Q8×C139—81no—
216D4×C139—24no—
217D4×C139—24no—
218D4×C139—42no—
219D4×C139—44no—
220D4×C139—42no—
221D4×C139—44no—
222D4×C139—432no—
223C2×C4×C139—22no—
224C2×C4×C139—22no—
225C2×C4×C139—24no—
226C2×C4×C139—41no—
227C2×C4×C139—41no—
228C2×C4×C139—41no—
229C2×C4×C139—41no—
230C2×C4×C139—44no—
231C2×C4×C139—44no—
232C2×C4×C139—42no—
233C2×C4×C139—42no—
234C2×C4×C139—42no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139—41no—
238C2×C4×C139—42no—
239C2×C4×C139—42no—
240C2×C4×C139—42no—
241C2×C4×C139—42no—
242C2×C4×C139—42no—
243C2×C4×C139—42no—
244C2×C4×C139—81no—
245C2×C4×C139#12011yescharacteristic
246C2×C4×C139#12111yescharacteristic
247C2×C4×C139#12111yescharacteristic
248C2×C4×C139#12711yescharacteristic
249C8×C139—42no—
250C8×C139—81no—
251C22×C139—22no—
252C22×C139—22no—
253C22×C139—22no—
254C22×C139—22no—
255C22×C139—21no—
256C22×C139—21no—
257C22×C139—21no—
258C22×C139—21no—
259C22×C139—44no—
260C22×C139—44no—
261C22×C139—44no—
262C22×C139—44no—
263C22×C139—42no—
264C22×C139—44no—
265C22×C139—82no—
266C22×C139—82no—
267C22×C139—82no—
268C22×C139—82no—
269C22×C139—84no—
270C22×C139—82no—
271C22×C139—84no—
272C22×C139—84no—
273C22×C139—82no—
274C22×C139—84no—
275C22×C139—82no—
276C22×C139—81no—
277C22×C139—82no—
278C22×C139—81no—
279C22×C139#39211yescharacteristic
280C22×C139#44811yescharacteristic
281C22×C139#44911yescharacteristic
282C22×C139#45011yescharacteristic
283C22×C139#45211yescharacteristic
284C22×C139#45312yes—
285C22×C139B(4,𝔽2)12yes—
286C22×C139#46511yescharacteristic
287C22×C139#46811yescharacteristic
288C4×C139—21no—
289C4×C139—21no—
290C4×C139—21no—
291C4×C139—21no—
292C4×C139—44no—
293C4×C139—82no—
294C4×C139—81no—
295C4×C139—81no—
296C4×C139—81no—
297C2×C139—21no—
298C2×C139—21no—
299C2×C139—21no—
300C2×C139—21no—
301C2×C139—82no—
302C2×C139—84no—
303C2×C139#159612yes—
304C2×C139#160012yes—
305C2×C139#200011yescharacteristic
306C2×C139#200211yescharacteristic
307C2×C139#202111yescharacteristic
308#9922C13911yesmaximal, characteristic, direct product factor, Sylow
309C139#992211yescharacteristic, direct product factor, Sylow
310C2×#450C2×C13911yescharacteristic, complemented
311#2626C2×C13911yescharacteristic, complemented
312C2×#392C2×C13911yescharacteristic
313#1786C2×C13911yescharacteristic, complemented
314C2×#328C2×C13911yescharacteristic, complemented
315C2×#323C2×C13911yescharacteristic, complemented
316#1294C2×C13911yescharacteristic, complemented
317C23×D4—21no—
318C23×D4C22×C13911yescharacteristic
319C22×SD16—21no—
320C2×C22⋊Q8C22×C13911yescharacteristic
321C22×C22⋊C4—21no—
322C22×C22⋊C4C22×C13911yescharacteristic
323#450—22no—
324#450—22no—
325C2×#102—21no—
326C2×#102—22no—
327C2×C22⋊C8C22×C13911yescharacteristic
328C2×C22⋊C8C22×C13911yescharacteristic
329#399—21no—
330#396—22no—
331#393—21no—
332#392—22no—
333#392—22no—
334#385—21no—
335#380C22×C13911yescharacteristic
336#379—21no—
337C2×#95C22×C13911yescharacteristic
338#328—22no—
339#323—22no—
340C25—21no—
341C25D4×C13911yescharacteristic
342C22×Q8D4×C13911yescharacteristic, complemented
343C22×D4—24no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—44no—
350C22×D4—44no—
351C22×D4—44no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4D4×C13912yes—
355C23×C4—21no—
356C23×C4D4×C13911yescharacteristic
357C23×C4C23×C13911yescharacteristic
358C2×SD16—24no—
359C2×SD16—44no—
360C22×C8—21no—
361C22×C8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4D4×C13911yescharacteristic, complemented
369C2×C4⋊C4D4×C13912yescomplemented
370C2×C22⋊C4—24no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—44no—
382#102—24no—
383#102—44no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387C22⋊C8D4×C13912yescomplemented
388#95—22no—
389#95—21no—
390#95—21no—
391#95D4×C13912yes—
392C24—24no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24SD16×C13912yescomplemented
412C24C2×D4×C13911yescharacteristic
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—42no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—48no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—416no—
430C2×D4—416no—
431C2×D4—41no—
432C2×D4—41no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—42no—
446C22×C4C2×D4×C13911yescharacteristic
447C22×C4C2×D4×C13911yescharacteristic
448C22×C4C2×D4×C13911yescharacteristic
449C22×C4C2×D4×C13911yescharacteristic
450C22×C4C2×D4×C13911yescharacteristic
451C22×C4#41×C13911yescharacteristic
452SD16—48no—
453C2×C8—22no—
454C2×C8—42no—
455C2×C8—42no—
456C2×C8—41no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—42no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—82no—
463C22⋊C4—48no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—82no—
473C22⋊C4—82no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—44no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—44no—
487C23—44no—
488C23—44no—
489C23—44no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—41no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23—41no—
500C23—41no—
501C23—42no—
502C23—82no—
503C23—81no—
504C23—81no—
505C23—82no—
506C23—82no—
507C23—82no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—81no—
512C23—81no—
513C23—82no—
514C23—81no—
515C23—81no—
516C23#120×C13911yescharacteristic
517C23#120×C13911yescharacteristic
518C23#121×C13911yescharacteristic
519C23C2×SD16×C13911yescharacteristic
520C23#135×C13911yescharacteristic
521C23AGL(1,ℤ/8)×C13911yescharacteristic
522C23#137×C13911yescharacteristic
523Q8—42no—
524Q8—81no—
525D4—24no—
526D4—24no—
527D4—42no—
528D4—44no—
529D4—42no—
530D4—44no—
531D4—432no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—81no—
554C2×C4#120×C13911yescharacteristic
555C2×C4#121×C13911yescharacteristic
556C2×C4#121×C13911yescharacteristic
557C2×C4#127×C13911yescharacteristic
558C8—42no—
559C8—81no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—44no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—44no—
573C22—44no—
574C22—82no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22—84no—
579C22—82no—
580C22—84no—
581C22—82no—
582C22—81no—
583C22—82no—
584C22—81no—
585C22—84no—
586C22—82no—
587C22—84no—
588C22#392×C13911yescharacteristic
589C22#448×C13911yescharacteristic
590C22#449×C13911yescharacteristic
591C22#450×C13911yescharacteristic
592C22#452×C13911yescharacteristic
593C22#453×C13912yes—
594C22B(4,𝔽2)×C13912yes—
595C22#465×C13911yescharacteristic
596C22#468×C13911yescharacteristic
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—44no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—82no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—82no—
611C2—84no—
612C2#1596×C13912yes—
613C2#1600×C13912yes—
614C2#2000×C13911yescharacteristic
615C2#2002×C13911yescharacteristic
616C2#2021×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutator, Frattini, cosocleC23×C4C23×C139
prime radicalC2×#392×C139C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#450×C139C2semidirect
2. #2626×C139C2semidirect
4. #1786×C139C2semidirect
5. C2×#328×C139C2semidirect
6. C2×#323×C139C2semidirect
7. #1294×C139C2semidirect
33. C22×Q8×C139D4semidirect
59. C2×C4⋊C4×C139D4semidirect
60. C2×C4⋊C4×C139D4semidirect
78. C22⋊C8×C139D4semidirect
102. C24×C139SD16semidirect
308. #9922C139direct (N × H)
309. C139#9922direct (N × H)
310. C2×#450C2×C139semidirect
311. #2626C2×C139semidirect
313. #1786C2×C139semidirect
314. C2×#328C2×C139semidirect
315. C2×#323C2×C139semidirect
316. #1294C2×C139semidirect
342. C22×Q8D4×C139semidirect
368. C2×C4⋊C4D4×C139semidirect
369. C2×C4⋊C4D4×C139semidirect
387. C22⋊C8D4×C139semidirect
411. C24SD16×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1392
#2626×C1392
C2×#392×C1392
#1786×C1392
C2×#328×C1392
C2×#323×C1392
#1294×C1392
#9922139