Finite Group Databasebeta

← C139×#26725 #48021321

Subgroups — C139×#26725 #48021321

Order 35584.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2489×C139C211yesmaximal, characteristic
2#2360×C139C211yesmaximal, characteristic
3#2056×C139C211yesmaximal, characteristic, complemented
4#2035×C139C211yesmaximal, characteristic
5#2026×C139C211yesmaximal, characteristic, complemented
6#2001×C139C211yesmaximal, characteristic
7#1989×C139C211yesmaximal, characteristic, complemented
8#1933×C139C211yesmaximal, characteristic, complemented
9#1927×C139C211yesmaximal, characteristic, complemented
10#1923×C139C211yesmaximal, characteristic
11#1920×C139C211yesmaximal, characteristic, complemented
12#1878×C139C211yesmaximal, characteristic, complemented
13#1872×C139C211yesmaximal, characteristic
14#1823×C139C211yesmaximal, characteristic
15C4×#103×C139C211yesmaximal, characteristic, complemented
16C22×Q16×C139C2211yescharacteristic
17C2×#125×C139C2211yescharacteristic
18C2×C22⋊Q8×C139C2211yescharacteristic
19C2×C22⋊Q8×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C22×C4⋊C4×C139C2211yescharacteristic
22C2×#106×C139C2211yescharacteristic
23C2×C4⋊C8×C139C2211yescharacteristic
24C2×#103×C139C2211yescharacteristic
25C2×#103×C139C2211yescharacteristic
26C2×#103×C139C2211yescharacteristic
27C2×#103×C139C2211yescharacteristic
28C2×#103×C139C2211yescharacteristic
29C2×#103×C139C2211yescharacteristic
30C2×C22⋊C8×C139C2211yescharacteristic
31C2×C22⋊C8×C139C2211yescharacteristic
32C2×C4×C8×C139C2211yescharacteristic
33#400×C139—21no—
34#397×C139—21no—
35#391×C139C2211yescharacteristic
36#391×C139C2211yescharacteristic
37#391×C139C2211yescharacteristic
38#389×C139—21no—
39#389×C139C2211yescharacteristic
40#388×C139—21no—
41#387×C139—21no—
42#385×C139—21no—
43#382×C139—21no—
44#380×C139C2211yescharacteristic
45C4×C4⋊C4×C139C2211yescharacteristic
46C4×C4⋊C4×C139C2211yescharacteristic
47C4×C22⋊C4×C139—21no—
48C4×C22⋊C4×C139C2211yescharacteristic
49#340×C139C2211yescharacteristic
50#340×C139C2211yescharacteristic
51#340×C139C2211yescharacteristic
52#340×C139C2211yescharacteristic
53#340×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59C22×Q8×C139C2311yescharacteristic
60C22×Q8×C139C2311yescharacteristic
61C23×C4×C139—21no—
62C23×C4×C139C2311yescharacteristic
63C2×Q16×C139—22no—
64C2×Q16×C139—41no—
65C2×Q16×C139—41no—
66C22×C8×C139C2311yescharacteristic
67C22×C8×C139C2311yescharacteristic
68C22×C8×C139C2311yescharacteristic
69C22×C8×C139C2311yescharacteristic
70#125×C139—22no—
71#125×C139—41no—
72C22⋊Q8×C139—22no—
73C22⋊Q8×C139—22no—
74C22⋊Q8×C139—22no—
75C22⋊Q8×C139—41no—
76C4×Q8×C139—22no—
77C4×Q8×C139—41no—
78C2×C4⋊C4×C139—21no—
79C2×C4⋊C4×C139—22no—
80C2×C4⋊C4×C139—21no—
81C2×C4⋊C4×C139—21no—
82C2×C4⋊C4×C139—21no—
83C2×C4⋊C4×C139—21no—
84C2×C4⋊C4×C139—21no—
85C2×C4⋊C4×C139—21no—
86C2×C4⋊C4×C139—41no—
87C2×C4⋊C4×C139C2311yescharacteristic
88C2×C4⋊C4×C139C2311yescharacteristic
89C2×C4⋊C4×C139C2311yescharacteristic
90C2×C4⋊C4×C139C2311yescharacteristic
91C2×C4⋊C4×C139C2311yescharacteristic
92C2×C4⋊C4×C139C2311yescharacteristic
93C2×C22⋊C4×C139—21no—
94C2×C22⋊C4×C139—21no—
95C2×C22⋊C4×C139—21no—
96C2×C22⋊C4×C139D411yescharacteristic
97C2×C22⋊C4×C139D411yescharacteristic
98C2×C42×C139—21no—
99C2×C42×C139—21no—
100C2×C42×C139—21no—
101C2×C42×C139C2311yescharacteristic
102C2×C42×C139C2311yescharacteristic
103#106×C139—22no—
104C4⋊C8×C139—41no—
105#103×C139—22no—
106#103×C139—22no—
107#103×C139—22no—
108#103×C139—22no—
109#103×C139—41no—
110#103×C139—41no—
111C22⋊C8×C139—41no—
112C22⋊C8×C139—41no—
113C4×C8×C139—41no—
114#95×C139—21no—
115#95×C139—21no—
116#95×C139—21no—
117#95×C139—21no—
118#95×C139—21no—
119#95×C139—21no—
120#95×C139—21no—
121#95×C139—21no—
122#95×C139—21no—
123#95×C139—21no—
124#95×C139D411yescharacteristic
125#95×C139D411yescharacteristic
126C24×C139C2×D411yescharacteristic
127C2×Q8×C139—21no—
128C2×Q8×C139—21no—
129C2×Q8×C139—21no—
130C2×Q8×C139—21no—
131C2×Q8×C139—21no—
132C2×Q8×C139—21no—
133C2×Q8×C139—21no—
134C2×Q8×C139—21no—
135C2×Q8×C139—21no—
136C2×Q8×C139—21no—
137C2×Q8×C139—21no—
138C2×Q8×C139#4112yes—
139C22×C4×C139—21no—
140C22×C4×C139—21no—
141C22×C4×C139—21no—
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—21no—
152C22×C4×C139—21no—
153C22×C4×C139—42no—
154C22×C4×C139—42no—
155C22×C4×C139—81no—
156C22×C4×C139C2×D411yescharacteristic
157C22×C4×C139C2×D411yescharacteristic
158C22×C4×C139C2×D411yescharacteristic
159C22×C4×C139C2×D411yescharacteristic
160C22×C4×C139C2×D411yescharacteristic
161C22×C4×C139C2411yescharacteristic
162Q16×C139—44no—
163C2×C8×C139—21no—
164C2×C8×C139—21no—
165C2×C8×C139—21no—
166C2×C8×C139—21no—
167C2×C8×C139—21no—
168C2×C8×C139—21no—
169C2×C8×C139—21no—
170C2×C8×C139—21no—
171C2×C8×C139—21no—
172C2×C8×C139—21no—
173C2×C8×C139—21no—
174C2×C8×C139—21no—
175C4⋊C4×C139—24no—
176C4⋊C4×C139—21no—
177C4⋊C4×C139—21no—
178C4⋊C4×C139—21no—
179C4⋊C4×C139—21no—
180C4⋊C4×C139—21no—
181C4⋊C4×C139—21no—
182C4⋊C4×C139—21no—
183C4⋊C4×C139—21no—
184C4⋊C4×C139—21no—
185C4⋊C4×C139—42no—
186C4⋊C4×C139—42no—
187C4⋊C4×C139—42no—
188C4⋊C4×C139—42no—
189C4⋊C4×C139—42no—
190C4⋊C4×C139—81no—
191C4⋊C4×C139#4112yes—
192C4⋊C4×C139#4112yes—
193C4⋊C4×C139#4112yes—
194C22⋊C4×C139—24no—
195C22⋊C4×C139—22no—
196C22⋊C4×C139—22no—
197C22⋊C4×C139—42no—
198C22⋊C4×C139—42no—
199C42×C139—21no—
200C42×C139—21no—
201C42×C139—21no—
202C42×C139—21no—
203C42×C139—42no—
204C42×C139—42no—
205C42×C139—81no—
206C23×C139—21no—
207C23×C139—21no—
208C23×C139—21no—
209C23×C139—21no—
210C23×C139—21no—
211C23×C139—21no—
212C23×C139#13512yes—
213C23×C139C22×D411yescharacteristic
214Q8×C139—22no—
215Q8×C139—22no—
216Q8×C139—41no—
217Q8×C139—41no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—41no—
222C2×C4×C139—21no—
223C2×C4×C139—21no—
224C2×C4×C139—22no—
225C2×C4×C139—22no—
226C2×C4×C139—21no—
227C2×C4×C139—21no—
228C2×C4×C139—21no—
229C2×C4×C139—21no—
230C2×C4×C139—22no—
231C2×C4×C139—22no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—21no—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
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—41no—
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—41no—
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—41no—
263C2×C4×C139—41no—
264C2×C4×C139—84no—
265C2×C4×C139#13712yes—
266C2×C4×C139C2×#4111yescharacteristic
267C2×C4×C139C2×#4111yescharacteristic
268C2×C4×C139C2×#4111yescharacteristic
269C2×C4×C139C2×#4111yescharacteristic
270C2×C4×C139H(5,𝔽2)11yescharacteristic
271C2×C4×C139H(5,𝔽2)11yescharacteristic
272C8×C139—41no—
273C8×C139—41no—
274C8×C139—41no—
275C8×C139—41no—
276C22×C139—22no—
277C22×C139—22no—
278C22×C139—22no—
279C22×C139—41no—
280C22×C139—41no—
281C22×C139—41no—
282C22×C139—41no—
283C22×C139#52511yescharacteristic
284C22×C139#54611yescharacteristic
285C22×C139#54611yescharacteristic
286C22×C139C2×#13511yescharacteristic
287C22×C139C2×#13711yescharacteristic
288C22×C139#57711yescharacteristic
289C22×C139#57811yescharacteristic
290C4×C139—22no—
291C4×C139—41no—
292C4×C139—42no—
293C4×C139—42no—
294C4×C139—41no—
295C4×C139—42no—
296C4×C139—41no—
297C4×C139—42no—
298C4×C139—41no—
299C4×C139—81no—
300C4×C139—81no—
301C4×C139—81no—
302C4×C139—81no—
303C4×C139#52911yescharacteristic
304C4×C139#53811yescharacteristic
305C4×C139#55511yescharacteristic
306C4×C139#55911yescharacteristic
307C2×C139—42no—
308C2×C139#245911yescharacteristic
309C2×C139#310811yescharacteristic
310C2×C139#312011yescharacteristic
311C2×C139#329611yescharacteristic
312C2×C139#330011yescharacteristic
313C2×C139#331211yescharacteristic
314C2×C139#333111yescharacteristic
315#26725C13911yesmaximal, characteristic, direct product factor, Sylow
316C139#2672511yescharacteristic, direct product factor, Sylow
317#2489C2×C13911yescharacteristic
318#2360C2×C13911yescharacteristic
319#2056C2×C13911yescharacteristic, complemented
320#2035C2×C13911yescharacteristic
321#2026C2×C13911yescharacteristic, complemented
322#2001C2×C13911yescharacteristic
323#1989C2×C13911yescharacteristic, complemented
324#1933C2×C13911yescharacteristic, complemented
325#1927C2×C13911yescharacteristic, complemented
326#1923C2×C13911yescharacteristic
327#1920C2×C13911yescharacteristic, complemented
328#1878C2×C13911yescharacteristic, complemented
329#1872C2×C13911yescharacteristic
330#1823C2×C13911yescharacteristic
331C4×#103C2×C13911yescharacteristic, complemented
332C22×Q16C22×C13911yescharacteristic
333C2×#125C22×C13911yescharacteristic
334C2×C22⋊Q8C22×C13911yescharacteristic
335C2×C22⋊Q8C22×C13911yescharacteristic
336C2×C4×Q8C22×C13911yescharacteristic
337C22×C4⋊C4C22×C13911yescharacteristic
338C2×#106C22×C13911yescharacteristic
339C2×C4⋊C8C22×C13911yescharacteristic
340C2×#103C22×C13911yescharacteristic
341C2×#103C22×C13911yescharacteristic
342C2×#103C22×C13911yescharacteristic
343C2×#103C22×C13911yescharacteristic
344C2×#103C22×C13911yescharacteristic
345C2×#103C22×C13911yescharacteristic
346C2×C22⋊C8C22×C13911yescharacteristic
347C2×C22⋊C8C22×C13911yescharacteristic
348C2×C4×C8C22×C13911yescharacteristic
349#400—21no—
350#397—21no—
351#391C22×C13911yescharacteristic
352#391C22×C13911yescharacteristic
353#391C22×C13911yescharacteristic
354#389—21no—
355#389C22×C13911yescharacteristic
356#388—21no—
357#387—21no—
358#385—21no—
359#382—21no—
360#380C22×C13911yescharacteristic
361C4×C4⋊C4C22×C13911yescharacteristic
362C4×C4⋊C4C22×C13911yescharacteristic
363C4×C22⋊C4—21no—
364C4×C22⋊C4C22×C13911yescharacteristic
365#340C22×C13911yescharacteristic
366#340C22×C13911yescharacteristic
367#340C22×C13911yescharacteristic
368#340C22×C13911yescharacteristic
369#340C22×C13911yescharacteristic
370#340C22×C13911yescharacteristic
371#340C22×C13911yescharacteristic
372#340C22×C13911yescharacteristic
373#336C22×C13911yescharacteristic
374#336C22×C13911yescharacteristic
375C22×Q8C23×C13911yescharacteristic
376C22×Q8C23×C13911yescharacteristic
377C23×C4—21no—
378C23×C4C23×C13911yescharacteristic
379C2×Q16—22no—
380C2×Q16—41no—
381C2×Q16—41no—
382C22×C8C23×C13911yescharacteristic
383C22×C8C23×C13911yescharacteristic
384C22×C8C23×C13911yescharacteristic
385C22×C8C23×C13911yescharacteristic
386#125—22no—
387#125—41no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—41no—
392C4×Q8—22no—
393C4×Q8—41no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4C23×C13911yescharacteristic
404C2×C4⋊C4C23×C13911yescharacteristic
405C2×C4⋊C4C23×C13911yescharacteristic
406C2×C4⋊C4C23×C13911yescharacteristic
407C2×C4⋊C4C23×C13911yescharacteristic
408C2×C4⋊C4C23×C13911yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4D4×C13911yescharacteristic
413C2×C22⋊C4D4×C13911yescharacteristic
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C23×C13911yescharacteristic
418C2×C42C23×C13911yescharacteristic
419#106—22no—
420C4⋊C8—41no—
421#103—22no—
422#103—22no—
423#103—22no—
424#103—22no—
425#103—41no—
426#103—41no—
427C22⋊C8—41no—
428C22⋊C8—41no—
429C4×C8—41no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95D4×C13911yescharacteristic
441#95D4×C13911yescharacteristic
442C24C2×D4×C13911yescharacteristic
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8#41×C13912yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4C2×D4×C13911yescharacteristic
473C22×C4C2×D4×C13911yescharacteristic
474C22×C4C2×D4×C13911yescharacteristic
475C22×C4C2×D4×C13911yescharacteristic
476C22×C4C2×D4×C13911yescharacteristic
477C22×C4C24×C13911yescharacteristic
478Q16—44no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C4⋊C4—24no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—81no—
507C4⋊C4#41×C13912yes—
508C4⋊C4#41×C13912yes—
509C4⋊C4#41×C13912yes—
510C22⋊C4—24no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—42no—
521C42—81no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23#135×C13912yes—
529C23C22×D4×C13911yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4#137×C13912yes—
582C2×C4C2×#41×C13911yescharacteristic
583C2×C4C2×#41×C13911yescharacteristic
584C2×C4C2×#41×C13911yescharacteristic
585C2×C4C2×#41×C13911yescharacteristic
586C2×C4H(5,𝔽2)×C13911yescharacteristic
587C2×C4H(5,𝔽2)×C13911yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22#525×C13911yescharacteristic
600C22#546×C13911yescharacteristic
601C22#546×C13911yescharacteristic
602C22C2×#135×C13911yescharacteristic
603C22C2×#137×C13911yescharacteristic
604C22#577×C13911yescharacteristic
605C22#578×C13911yescharacteristic
606C4—22no—
607C4—41no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—42no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4#529×C13911yescharacteristic
620C4#538×C13911yescharacteristic
621C4#555×C13911yescharacteristic
622C4#559×C13911yescharacteristic
623C2—42no—
624C2#2459×C13911yescharacteristic
625C2#3108×C13911yescharacteristic
626C2#3120×C13911yescharacteristic
627C2#3296×C13911yescharacteristic
628C2#3300×C13911yescharacteristic
629C2#3312×C13911yescharacteristic
630C2#3331×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2056×C139C2semidirect
5. #2026×C139C2semidirect
7. #1989×C139C2semidirect
8. #1933×C139C2semidirect
9. #1927×C139C2semidirect
11. #1920×C139C2semidirect
12. #1878×C139C2semidirect
15. C4×#103×C139C2semidirect
315. #26725C139direct (N × H)
316. C139#26725direct (N × H)
319. #2056C2×C139semidirect
321. #2026C2×C139semidirect
323. #1989C2×C139semidirect
324. #1933C2×C139semidirect
325. #1927C2×C139semidirect
327. #1920C2×C139semidirect
328. #1878C2×C139semidirect
331. C4×#103C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2489×C1392
#2360×C1392
#2056×C1392
#2035×C1392
#2026×C1392
#2001×C1392
#1989×C1392
#1933×C1392
#1927×C1392
#1923×C1392
#1920×C1392
#1878×C1392
#1872×C1392
#1823×C1392
C4×#103×C1392
#26725139