Finite Group Databasebeta

← C139×#36727 #48031323

Subgroups — C139×#36727 #48031323

Order 35584.

2214 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2847×C139C212yesmaximal, complemented
2#2748×C139C214yesmaximal, complemented
3#2741×C139C214yesmaximal, complemented
4#2703×C139C214yesmaximal, complemented
5#2671×C139C214yesmaximal, complemented
6#2656×C139C211yesmaximal, characteristic, complemented
7#2646×C139C211yesmaximal, characteristic, complemented
8#2443×C139C214yesmaximal, complemented
9#2424×C139C214yesmaximal, complemented
10#2325×C139C212yesmaximal, complemented
11C2×#380×C139C211yesmaximal, characteristic, complemented
12C24×C4×C139C2211yescharacteristic
13C2×#123×C139C2214yescomplemented
14C2×#121×C139C2212yes—
15C2×#121×C139C2212yes—
16C2×#121×C139C2212yes—
17C2×#121×C139C2214yes—
18C2×#121×C139C2214yes—
19C2×#120×C139C2214yes—
20C2×C4×D4×C139C2214yes—
21C22×C4⋊C4×C139C2212yes—
22C22×C22⋊C4×C139C2212yes—
23#400×C139C2214yescomplemented
24#399×C139C2214yescomplemented
25#399×C139C2214yescomplemented
26#398×C139C2214yescomplemented
27#398×C139C2214yescomplemented
28#397×C139C2214yescomplemented
29#396×C139C2214yes—
30#394×C139C2214yes—
31#394×C139C2214yes—
32#394×C139C2214yescomplemented
33#392×C139C2214yes—
34#392×C139C2214yescomplemented
35#390×C139C2214yes—
36#388×C139C2214yes—
37#388×C139C2214yescomplemented
38#388×C139C2214yescomplemented
39#387×C139C2214yescomplemented
40#387×C139C2214yescomplemented
41#386×C139C2214yes—
42#386×C139C2214yes—
43#386×C139C2214yes—
44#386×C139C2214yes—
45#386×C139C2214yes—
46#386×C139C2214yescomplemented
47#385×C139C2214yes—
48#385×C139C2214yescomplemented
49#385×C139C2214yescomplemented
50#380×C139C2214yes—
51#380×C139C2214yes—
52#380×C139C2212yes—
53#380×C139C2212yes—
54#380×C139C2212yes—
55C2×#95×C139C2211yescharacteristic
56C2×#95×C139C2211yescharacteristic
57C25×C139C2311yescharacteristic
58C22×D4×C139C2314yes—
59C22×D4×C139C2314yes—
60C22×D4×C139C2314yes—
61C22×D4×C139C2312yes—
62C22×D4×C139C2314yes—
63C23×C4×C139—24no—
64C23×C4×C139—44no—
65C23×C4×C139C2311yescharacteristic
66C23×C4×C139C2312yes—
67C23×C4×C139C2312yes—
68C23×C4×C139C2312yes—
69C23×C4×C139C2312yes—
70C23×C4×C139C2314yes—
71C23×C4×C139C2311yescharacteristic
72#123×C139—48no—
73#121×C139—28no—
74#121×C139—44no—
75#121×C139—44no—
76#121×C139—48no—
77#121×C139—48no—
78#120×C139—48no—
79C4×D4×C139—48no—
80C2×C4⋊C4×C139—44no—
81C2×C4⋊C4×C139C2314yes—
82C2×C4⋊C4×C139C2312yes—
83C2×C4⋊C4×C139C2314yes—
84C2×C4⋊C4×C139C2314yes—
85C2×C4⋊C4×C139C2314yes—
86C2×C4⋊C4×C139C2314yes—
87C2×C4⋊C4×C139C2312yes—
88C2×C4⋊C4×C139C2314yes—
89C2×C4⋊C4×C139C2312yes—
90C2×C22⋊C4×C139—44no—
91C2×C22⋊C4×C139C2314yes—
92C2×C22⋊C4×C139C2314yes—
93C2×C22⋊C4×C139C2314yes—
94C2×C22⋊C4×C139C2314yes—
95C2×C22⋊C4×C139C2314yes—
96C2×C22⋊C4×C139C2314yes—
97C2×C22⋊C4×C139C2314yes—
98C2×C22⋊C4×C139C2314yes—
99C2×C22⋊C4×C139C2314yes—
100C2×C22⋊C4×C139C2314yes—
101C2×C22⋊C4×C139C2314yes—
102C2×C22⋊C4×C139C2314yes—
103C2×C22⋊C4×C139C2314yes—
104C2×C42×C139C2314yes—
105#95×C139C2314yes—
106#95×C139C2314yes—
107#95×C139C2314yes—
108#95×C139C2314yes—
109#95×C139C2314yes—
110#95×C139C2314yes—
111#95×C139C2314yes—
112#95×C139C2314yes—
113#95×C139C2314yes—
114C24×C139—22no—
115C24×C139—22no—
116C24×C139—22no—
117C24×C139—24no—
118C24×C139—42no—
119C24×C139C2414yes—
120C24×C139C2411yescharacteristic
121C24×C139C2411yescharacteristic
122C24×C139C2411yescharacteristic
123C2×D4×C139—28no—
124C2×D4×C139—28no—
125C2×D4×C139—28no—
126C2×D4×C139—28no—
127C2×D4×C139—28no—
128C2×D4×C139—24no—
129C2×D4×C139—44no—
130C2×D4×C139—44no—
131C2×D4×C139—42no—
132C2×D4×C139—42no—
133C2×D4×C139—44no—
134C2×D4×C139—44no—
135C2×D4×C139—44no—
136C2×D4×C139—44no—
137C2×D4×C139—44no—
138C22×C4×C139—22no—
139C22×C4×C139—24no—
140C22×C4×C139—24no—
141C22×C4×C139—24no—
142C22×C4×C139—24no—
143C22×C4×C139—24no—
144C22×C4×C139—24no—
145C22×C4×C139—24no—
146C22×C4×C139—42no—
147C22×C4×C139—42no—
148C22×C4×C139—42no—
149C22×C4×C139—42no—
150C22×C4×C139—42no—
151C22×C4×C139—42no—
152C22×C4×C139—42no—
153C22×C4×C139—44no—
154C22×C4×C139—44no—
155C22×C4×C139—44no—
156C22×C4×C139—416no—
157C22×C4×C139#4114yes—
158C22×C4×C139C2414yes—
159C22×C4×C139C2414yes—
160C22×C4×C139C2414yes—
161C22×C4×C139C2414yes—
162C22×C4×C139C2414yes—
163C22×C4×C139C2412yes—
164C22×C4×C139C2412yes—
165C4⋊C4×C139—24no—
166C4⋊C4×C139—28no—
167C4⋊C4×C139—44no—
168C4⋊C4×C139—44no—
169C4⋊C4×C139—42no—
170C4⋊C4×C139—42no—
171C4⋊C4×C139—44no—
172C4⋊C4×C139—44no—
173C4⋊C4×C139—44no—
174C22⋊C4×C139—28no—
175C22⋊C4×C139—28no—
176C22⋊C4×C139—28no—
177C22⋊C4×C139—28no—
178C22⋊C4×C139—28no—
179C22⋊C4×C139—44no—
180C22⋊C4×C139—44no—
181C22⋊C4×C139—44no—
182C22⋊C4×C139—44no—
183C22⋊C4×C139—44no—
184C22⋊C4×C139—44no—
185C22⋊C4×C139—44no—
186C22⋊C4×C139—44no—
187C42×C139—44no—
188C23×C139—22no—
189C23×C139—21no—
190C23×C139—21no—
191C23×C139—28no—
192C23×C139—21no—
193C23×C139—21no—
194C23×C139—21no—
195C23×C139—22no—
196C23×C139—22no—
197C23×C139—22no—
198C23×C139—22no—
199C23×C139—21no—
200C23×C139—24no—
201C23×C139—24no—
202C23×C139—24no—
203C23×C139—24no—
204C23×C139—24no—
205C23×C139—24no—
206C23×C139—24no—
207C23×C139—48no—
208C23×C139—48no—
209C23×C139—44no—
210C23×C139—44no—
211C23×C139C2×#4112yes—
212C23×C139H(5,𝔽2)12yes—
213C23×C139H(5,𝔽2)14yes—
214C23×C1392−1+412yes—
215C23×C139C2511yescharacteristic
216D4×C139—416no—
217D4×C139—84no—
218D4×C139—88no—
219D4×C139—88no—
220D4×C139—88no—
221C2×C4×C139—28no—
222C2×C4×C139—22no—
223C2×C4×C139—22no—
224C2×C4×C139—22no—
225C2×C4×C139—22no—
226C2×C4×C139—24no—
227C2×C4×C139—24no—
228C2×C4×C139—24no—
229C2×C4×C139—24no—
230C2×C4×C139—24no—
231C2×C4×C139—24no—
232C2×C4×C139—24no—
233C2×C4×C139—24no—
234C2×C4×C139—24no—
235C2×C4×C139—24no—
236C2×C4×C139—24no—
237C2×C4×C139—24no—
238C2×C4×C139—24no—
239C2×C4×C139—24no—
240C2×C4×C139—24no—
241C2×C4×C139—44no—
242C2×C4×C139—48no—
243C2×C4×C139—48no—
244C2×C4×C139—84no—
245C2×C4×C139—84no—
246C2×C4×C139—88no—
247C2×C4×C139C2×#4114yes—
248C2×C4×C139H(5,𝔽2)14yes—
249C22×C139—22no—
250C22×C139—22no—
251C22×C139—24no—
252C22×C139—24no—
253C22×C139—22no—
254C22×C139—22no—
255C22×C139—24no—
256C22×C139—24no—
257C22×C139—416no—
258C22×C139—41no—
259C22×C139—41no—
260C22×C139—41no—
261C22×C139—41no—
262C22×C139—42no—
263C22×C139—42no—
264C22×C139—44no—
265C22×C139—44no—
266C22×C139—44no—
267C22×C139—44no—
268C22×C139—44no—
269C22×C139—44no—
270C22×C139—44no—
271C22×C139#54014yes—
272C22×C139C22×#4111yescharacteristic
273C22×C139C2×H(5,𝔽2)12yes—
274C22×C139C2×H(5,𝔽2)12yes—
275C22×C139C2×H(5,𝔽2)11yescharacteristic
276C22×C139C2×2−1+411yescharacteristic
277C4×C139—24no—
278C4×C139—24no—
279C4×C139—44no—
280C4×C139—44no—
281C4×C139—44no—
282C4×C139—44no—
283C4×C139—44no—
284C2×C139—24no—
285C2×C139—42no—
286C2×C139—42no—
287C2×C139—84no—
288C2×C139C2×#54011yescharacteristic
289C2×C139#349011yescharacteristic
290C2×C139#349211yescharacteristic
291C2×C139#353612yes—
292C2×C139#353712yes—
293#36727C13911yesmaximal, characteristic, direct product factor, Sylow
294C139#3672711yescharacteristic, direct product factor, Sylow
295#2847C2×C13912yescomplemented
296#2748C2×C13914yescomplemented
297#2741C2×C13914yescomplemented
298#2703C2×C13914yescomplemented
299#2671C2×C13914yescomplemented
300#2656C2×C13911yescharacteristic, complemented
301#2646C2×C13911yescharacteristic, complemented
302#2443C2×C13914yescomplemented
303#2424C2×C13914yescomplemented
304#2325C2×C13912yescomplemented
305C2×#380C2×C13911yescharacteristic, complemented
306C24×C4C22×C13911yescharacteristic
307C2×#123C22×C13914yescomplemented
308C2×#121C22×C13912yes—
309C2×#121C22×C13912yes—
310C2×#121C22×C13912yes—
311C2×#121C22×C13914yes—
312C2×#121C22×C13914yes—
313C2×#120C22×C13914yes—
314C2×C4×D4C22×C13914yes—
315C22×C4⋊C4C22×C13912yes—
316C22×C22⋊C4C22×C13912yes—
317#400C22×C13914yescomplemented
318#399C22×C13914yescomplemented
319#399C22×C13914yescomplemented
320#398C22×C13914yescomplemented
321#398C22×C13914yescomplemented
322#397C22×C13914yescomplemented
323#396C22×C13914yes—
324#394C22×C13914yes—
325#394C22×C13914yes—
326#394C22×C13914yescomplemented
327#392C22×C13914yes—
328#392C22×C13914yescomplemented
329#390C22×C13914yes—
330#388C22×C13914yes—
331#388C22×C13914yescomplemented
332#388C22×C13914yescomplemented
333#387C22×C13914yescomplemented
334#387C22×C13914yescomplemented
335#386C22×C13914yes—
336#386C22×C13914yes—
337#386C22×C13914yes—
338#386C22×C13914yes—
339#386C22×C13914yes—
340#386C22×C13914yescomplemented
341#385C22×C13914yes—
342#385C22×C13914yescomplemented
343#385C22×C13914yescomplemented
344#380C22×C13912yes—
345#380C22×C13912yes—
346#380C22×C13912yes—
347#380C22×C13914yes—
348#380C22×C13914yes—
349C2×#95C22×C13911yescharacteristic
350C2×#95C22×C13911yescharacteristic
351C25C23×C13911yescharacteristic
352C22×D4C23×C13914yes—
353C22×D4C23×C13914yes—
354C22×D4C23×C13914yes—
355C22×D4C23×C13912yes—
356C22×D4C23×C13914yes—
357C23×C4—24no—
358C23×C4—44no—
359C23×C4C23×C13911yescharacteristic
360C23×C4C23×C13912yes—
361C23×C4C23×C13912yes—
362C23×C4C23×C13912yes—
363C23×C4C23×C13912yes—
364C23×C4C23×C13914yes—
365C23×C4C23×C13911yescharacteristic
366#123—48no—
367#121—28no—
368#121—44no—
369#121—44no—
370#121—48no—
371#121—48no—
372#120—48no—
373C4×D4—48no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4C23×C13914yes—
376C2×C4⋊C4C23×C13912yes—
377C2×C4⋊C4C23×C13914yes—
378C2×C4⋊C4C23×C13914yes—
379C2×C4⋊C4C23×C13912yes—
380C2×C4⋊C4C23×C13912yes—
381C2×C4⋊C4C23×C13914yes—
382C2×C4⋊C4C23×C13914yes—
383C2×C4⋊C4C23×C13914yes—
384C2×C22⋊C4—44no—
385C2×C22⋊C4C23×C13914yes—
386C2×C22⋊C4C23×C13914yes—
387C2×C22⋊C4C23×C13914yes—
388C2×C22⋊C4C23×C13914yes—
389C2×C22⋊C4C23×C13914yes—
390C2×C22⋊C4C23×C13914yes—
391C2×C22⋊C4C23×C13914yes—
392C2×C22⋊C4C23×C13914yes—
393C2×C22⋊C4C23×C13914yes—
394C2×C22⋊C4C23×C13914yes—
395C2×C22⋊C4C23×C13914yes—
396C2×C22⋊C4C23×C13914yes—
397C2×C22⋊C4C23×C13914yes—
398C2×C42C23×C13914yes—
399#95C23×C13914yes—
400#95C23×C13914yes—
401#95C23×C13914yes—
402#95C23×C13914yes—
403#95C23×C13914yes—
404#95C23×C13914yes—
405#95C23×C13914yes—
406#95C23×C13914yes—
407#95C23×C13914yes—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—42no—
413C24C24×C13914yes—
414C24C24×C13911yescharacteristic
415C24C24×C13911yescharacteristic
416C24C24×C13911yescharacteristic
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—24no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—416no—
451C22×C4#41×C13914yes—
452C22×C4C24×C13914yes—
453C22×C4C24×C13914yes—
454C22×C4C24×C13914yes—
455C22×C4C24×C13914yes—
456C22×C4C24×C13914yes—
457C22×C4C24×C13912yes—
458C22×C4C24×C13912yes—
459C4⋊C4—24no—
460C4⋊C4—28no—
461C4⋊C4—44no—
462C4⋊C4—44no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—44no—
466C4⋊C4—44no—
467C4⋊C4—44no—
468C22⋊C4—28no—
469C22⋊C4—28no—
470C22⋊C4—28no—
471C22⋊C4—28no—
472C22⋊C4—28no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—44no—
478C22⋊C4—44no—
479C22⋊C4—44no—
480C22⋊C4—44no—
481C42—44no—
482C23—22no—
483C23—21no—
484C23—21no—
485C23—28no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—21no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—48no—
502C23—48no—
503C23—44no—
504C23—44no—
505C23C2×#41×C13912yes—
506C23H(5,𝔽2)×C13912yes—
507C23H(5,𝔽2)×C13914yes—
508C232−1+4×C13912yes—
509C23C25×C13911yescharacteristic
510D4—416no—
511D4—84no—
512D4—88no—
513D4—88no—
514D4—88no—
515C2×C4—28no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—44no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—84no—
539C2×C4—84no—
540C2×C4—88no—
541C2×C4C2×#41×C13914yes—
542C2×C4H(5,𝔽2)×C13914yes—
543C22—24no—
544C22—24no—
545C22—22no—
546C22—22no—
547C22—24no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—416no—
552C22—42no—
553C22—42no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—44no—
559C22—44no—
560C22—44no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22#540×C13914yes—
566C22C22×#41×C13911yescharacteristic
567C22C2×H(5,𝔽2)×C13912yes—
568C22C2×H(5,𝔽2)×C13912yes—
569C22C2×H(5,𝔽2)×C13911yescharacteristic
570C22C2×2−1+4×C13911yescharacteristic
571C4—24no—
572C4—24no—
573C4—44no—
574C4—44no—
575C4—44no—
576C4—44no—
577C4—44no—
578C2—24no—
579C2—42no—
580C2—42no—
581C2—84no—
582C2C2×#540×C13911yescharacteristic
583C2#3490×C13911yescharacteristic
584C2#3492×C13911yescharacteristic
585C2#3536×C13912yes—
586C2#3537×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2847×C139C2semidirect
2. #2748×C139C2semidirect
3. #2741×C139C2semidirect
4. #2703×C139C2semidirect
5. #2671×C139C2semidirect
6. #2656×C139C2semidirect
7. #2646×C139C2semidirect
8. #2443×C139C2semidirect
9. #2424×C139C2semidirect
10. #2325×C139C2semidirect
11. C2×#380×C139C2semidirect
13. C2×#123×C139C22semidirect
23. #400×C139C22semidirect
24. #399×C139C22semidirect
25. #399×C139C22semidirect
26. #398×C139C22semidirect
27. #398×C139C22semidirect
28. #397×C139C22semidirect
32. #394×C139C22semidirect
34. #392×C139C22semidirect
37. #388×C139C22semidirect
38. #388×C139C22semidirect
39. #387×C139C22semidirect
40. #387×C139C22semidirect
46. #386×C139C22semidirect
48. #385×C139C22semidirect
49. #385×C139C22semidirect
293. #36727C139direct (N × H)
294. C139#36727direct (N × H)
295. #2847C2×C139semidirect
296. #2748C2×C139semidirect
297. #2741C2×C139semidirect
298. #2703C2×C139semidirect
299. #2671C2×C139semidirect
300. #2656C2×C139semidirect
301. #2646C2×C139semidirect
302. #2443C2×C139semidirect
303. #2424C2×C139semidirect
304. #2325C2×C139semidirect
305. C2×#380C2×C139semidirect
307. C2×#123C22×C139semidirect
317. #400C22×C139semidirect
318. #399C22×C139semidirect
319. #399C22×C139semidirect
320. #398C22×C139semidirect
321. #398C22×C139semidirect
322. #397C22×C139semidirect
326. #394C22×C139semidirect
328. #392C22×C139semidirect
331. #388C22×C139semidirect
332. #388C22×C139semidirect
333. #387C22×C139semidirect
334. #387C22×C139semidirect
340. #386C22×C139semidirect
342. #385C22×C139semidirect
343. #385C22×C139semidirect

Maximal subgroups

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

subgroupindex
#2847×C1392
#2748×C1392
#2741×C1392
#2703×C1392
#2671×C1392
#2656×C1392
#2646×C1392
#2443×C1392
#2424×C1392
#2325×C1392
C2×#380×C1392
#36727139