Finite Group Databasebeta

← C139×#18694 #48013290

Subgroups — C139×#18694 #48013290

Order 35584.

942 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3552×C139C211yesmaximal, characteristic, complemented
2#3217×C139C211yesmaximal, characteristic, complemented
3#3217×C139C211yesmaximal, characteristic, complemented
4C2×#486×C139C211yesmaximal, characteristic, complemented
5#1628×C139C212yesmaximal, complemented
6#1627×C139C212yesmaximal, complemented
7#1626×C139C212yesmaximal, complemented
8#1625×C139C212yesmaximal, complemented
9#1556×C139C211yesmaximal, characteristic, complemented
10#1494×C139C211yesmaximal, characteristic, complemented
11#1494×C139C211yesmaximal, characteristic, complemented
12#563×C139—22no—
13#557×C139C2211yescharacteristic, complemented
14#556×C139C2211yescharacteristic, complemented
15#554×C139—21no—
16#553×C139—21no—
17D4×Q8×C139—21no—
18D4×Q8×C139C2211yescharacteristic, complemented
19#548×C139—21no—
20#547×C139C2211yescharacteristic, complemented
21#544×C139—21no—
22#542×C139—21no—
23#541×C139—21no—
24#539×C139—22no—
25#536×C139—21no—
26C2×C4⋊Q8×C139C2211yescharacteristic
27C2×#127×C139C2211yescharacteristic
28#529×C139C2211yescharacteristic
29#529×C139C2211yescharacteristic
30#496×C139—21no—
31#496×C139—21no—
32#490×C139—21no—
33#490×C139—21no—
34#486×C139—22no—
35#486×C139C2212yes—
36#486×C139C2212yes—
37#460×C139C2212yes—
38#460×C139C2212yes—
39#459×C139C2212yes—
40#459×C139C2212yes—
41#450×C139—21no—
42#450×C139—21no—
43#447×C139—21no—
44#447×C139—21no—
45#432×C139C2211yescharacteristic
46#432×C139C2211yescharacteristic
47C2×#102×C139—22no—
48C2×C4×C8×C139C2211yescharacteristic
49#332×C139C2212yescomplemented
50#332×C139C2212yescomplemented
51Q8⋊C8×C139C2212yescomplemented
52Q8⋊C8×C139C2212yescomplemented
53D4⋊C8×C139C2212yescomplemented
54D4⋊C8×C139C2212yescomplemented
55C2×#41×C139—21no—
56C22×Q8×C139—21no—
57C22×Q8×C139—21no—
58C22×D4×C139—21no—
59C22×D4×C139—21no—
60C22×D4×C139—21no—
61C2×SD16×C139—22no—
62C2×SD16×C139—22no—
63C2×D8×C139—22no—
64C2×D8×C139—22no—
65C22×C8×C139—21no—
66C4⋊Q8×C139—22no—
67C4⋊Q8×C139—21no—
68C4⋊Q8×C139—21no—
69C4⋊Q8×C139—21no—
70C4⋊Q8×C139—21no—
71C4⋊Q8×C139D412yes—
72C4⋊Q8×C139C2311yescharacteristic
73C4⋊Q8×C139C2311yescharacteristic
74#127×C139—21no—
75#127×C139—21no—
76#127×C139—21no—
77#127×C139C2312yes—
78#126×C139—22no—
79#126×C139—22no—
80#126×C139—22no—
81#126×C139—21no—
82#126×C139—21no—
83#125×C139—22no—
84#125×C139—22no—
85#125×C139—22no—
86#125×C139—21no—
87#125×C139D411yescharacteristic
88#125×C139D411yescharacteristic
89#124×C139—22no—
90#124×C139—21no—
91#124×C139D411yescharacteristic
92#124×C139D411yescharacteristic
93#123×C139—22no—
94#123×C139—22no—
95#123×C139—21no—
96#123×C139—21no—
97#123×C139—22no—
98C22⋊Q8×C139—22no—
99C22⋊Q8×C139—22no—
100C22⋊Q8×C139—22no—
101C22⋊Q8×C139—22no—
102C22⋊Q8×C139—22no—
103C22⋊Q8×C139—21no—
104C22⋊Q8×C139—22no—
105C22⋊Q8×C139—21no—
106C22⋊Q8×C139—21no—
107C22⋊Q8×C139D411yescharacteristic
108C22⋊Q8×C139D411yescharacteristic
109#121×C139—22no—
110#121×C139—21no—
111#121×C139D411yescharacteristic
112#121×C139D411yescharacteristic
113C4×Q8×C139—21no—
114C4×Q8×C139—21no—
115C4×Q8×C139—21no—
116C4×Q8×C139C2311yescharacteristic
117C4×Q8×C139C2311yescharacteristic
118C4×D4×C139—22no—
119C4×D4×C139—22no—
120C4×D4×C139—21no—
121C4×D4×C139—21no—
122C4×D4×C139—21no—
123C4×D4×C139C2311yescharacteristic
124C4×D4×C139C2311yescharacteristic
125#117×C139—21no—
126#117×C139—21no—
127#117×C139—21no—
128C2×C4⋊C4×C139—21no—
129C2×C4⋊C4×C139—21no—
130C2×C4⋊C4×C139D412yes—
131C2×C42×C139C2311yescharacteristic
132C4⋊C8×C139C2312yes—
133C4⋊C8×C139C2312yes—
134#102×C139—24no—
135#102×C139—24no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140C22⋊C8×C139—21no—
141C22⋊C8×C139—21no—
142#97×C139—21no—
143#97×C139—21no—
144C4×C8×C139—21no—
145C4×C8×C139C2312yes—
146C24×C139—41no—
147#41×C139—82no—
148C2×Q8×C139—22no—
149C2×Q8×C139—22no—
150C2×Q8×C139—21no—
151C2×Q8×C139—21no—
152C2×Q8×C139—82no—
153C2×Q8×C139—82no—
154C2×Q8×C139C2×D411yescharacteristic
155C2×Q8×C139C2×D411yescharacteristic
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—22no—
159C2×D4×C139—22no—
160C2×D4×C139—22no—
161C2×D4×C139—22no—
162C2×D4×C139—44no—
163C2×D4×C139—41no—
164C2×D4×C139—41no—
165C2×D4×C139—41no—
166C2×D4×C139—82no—
167C2×D4×C139—82no—
168C2×D4×C139C2×D411yescharacteristic
169C2×D4×C139C2×D411yescharacteristic
170C22×C4×C139—22no—
171C22×C4×C139—22no—
172C22×C4×C139—22no—
173C22×C4×C139—21no—
174C22×C4×C139—21no—
175C22×C4×C139C2×D411yescharacteristic
176C22×C4×C139C2×D411yescharacteristic
177C22×C4×C139C2×D411yescharacteristic
178SD16×C139—82no—
179SD16×C139—82no—
180D8×C139—82no—
181D8×C139—82no—
182C2×C8×C139—22no—
183C2×C8×C139—22no—
184C2×C8×C139—22no—
185C2×C8×C139—42no—
186C4⋊C4×C139—22no—
187C4⋊C4×C139—22no—
188C4⋊C4×C139—22no—
189C4⋊C4×C139—22no—
190C4⋊C4×C139—22no—
191C4⋊C4×C139—22no—
192C4⋊C4×C139—22no—
193C4⋊C4×C139—22no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—21no—
200C4⋊C4×C139—21no—
201C4⋊C4×C139—21no—
202C4⋊C4×C139—21no—
203C4⋊C4×C139—21no—
204C4⋊C4×C139C2×D411yescharacteristic
205C4⋊C4×C139C2×D412yes—
206C4⋊C4×C139C2×D412yes—
207C4⋊C4×C139C2×D411yescharacteristic
208C4⋊C4×C139C2×D411yescharacteristic
209C4⋊C4×C139C2×D411yescharacteristic
210C22⋊C4×C139—22no—
211C22⋊C4×C139—22no—
212C22⋊C4×C139—22no—
213C22⋊C4×C139—22no—
214C22⋊C4×C139—21no—
215C22⋊C4×C139—21no—
216C22⋊C4×C139—21no—
217C22⋊C4×C139—21no—
218C22⋊C4×C139—21no—
219C22⋊C4×C139—21no—
220C22⋊C4×C139—21no—
221C22⋊C4×C139—21no—
222C22⋊C4×C139—21no—
223C22⋊C4×C139—21no—
224C42×C139—22no—
225C42×C139—22no—
226C42×C139—21no—
227C42×C139—21no—
228C42×C139C2×D411yescharacteristic
229C42×C139C2×D411yescharacteristic
230C42×C139C2×D411yescharacteristic
231C42×C139C2411yescharacteristic
232C23×C139—21no—
233C23×C139—21no—
234C23×C139—42no—
235C23×C139—82no—
236C23×C139—82no—
237C23×C139—82no—
238C23×C139#12011yescharacteristic
239Q8×C139—22no—
240Q8×C139—22no—
241Q8×C139—42no—
242Q8×C139—42no—
243Q8×C139—82no—
244Q8×C139—82no—
245D4×C139—22no—
246D4×C139—22no—
247D4×C139—44no—
248D4×C139—42no—
249D4×C139—42no—
250D4×C139—42no—
251D4×C139—42no—
252D4×C139—42no—
253D4×C139—42no—
254D4×C139—82no—
255D4×C139—82no—
256D4×C139—82no—
257D4×C139—82no—
258C2×C4×C139—22no—
259C2×C4×C139—22no—
260C2×C4×C139—22no—
261C2×C4×C139—21no—
262C2×C4×C139—21no—
263C2×C4×C139—21no—
264C2×C4×C139—21no—
265C2×C4×C139—21no—
266C2×C4×C139—22no—
267C2×C4×C139—22no—
268C2×C4×C139—21no—
269C2×C4×C139—42no—
270C2×C4×C139—42no—
271C2×C4×C139—82no—
272C2×C4×C139—82no—
273C2×C4×C139—82no—
274C2×C4×C139#12011yescharacteristic
275C2×C4×C139#12011yescharacteristic
276C2×C4×C139#12011yescharacteristic
277C2×C4×C139C22×D411yescharacteristic
278C2×C4×C139C22×D411yescharacteristic
279C2×C4×C139C22×D411yescharacteristic
280C8×C139—42no—
281C8×C139—42no—
282C8×C139—42no—
283C22×C139—21no—
284C22×C139—21no—
285C22×C139—41no—
286C22×C139—41no—
287C22×C139—41no—
288C22×C139—41no—
289C22×C139—41no—
290C22×C139—41no—
291C22×C139—82no—
292C22×C139—82no—
293C22×C139—82no—
294C22×C139—164no—
295C22×C139#45412yes—
296C22×C139C2×#12011yescharacteristic
297C4×C139—21no—
298C4×C139—21no—
299C4×C139—21no—
300C4×C139—21no—
301C4×C139—41no—
302C4×C139—42no—
303C4×C139—41no—
304C4×C139—42no—
305C4×C139—41no—
306C4×C139—41no—
307C4×C139—41no—
308C4×C139—41no—
309C4×C139#57612yes—
310C4×C139#57712yes—
311C2×C139—22no—
312C2×C139—81no—
313C2×C139—81no—
314C2×C139—162no—
315C2×C139#300811yescharacteristic
316C2×C139#301011yescharacteristic
317C2×C139C2×#45411yescharacteristic
318#18694C13911yesmaximal, characteristic, direct product factor, Sylow
319C139#1869411yescharacteristic, direct product factor, Sylow
320#3552C2×C13911yescharacteristic, complemented
321#3217C2×C13911yescharacteristic, complemented
322#3217C2×C13911yescharacteristic, complemented
323C2×#486C2×C13911yescharacteristic, complemented
324#1628C2×C13912yescomplemented
325#1627C2×C13912yescomplemented
326#1626C2×C13912yescomplemented
327#1625C2×C13912yescomplemented
328#1556C2×C13911yescharacteristic, complemented
329#1494C2×C13911yescharacteristic, complemented
330#1494C2×C13911yescharacteristic, complemented
331#563—22no—
332#557C22×C13911yescharacteristic, complemented
333#556C22×C13911yescharacteristic, complemented
334#554—21no—
335#553—21no—
336D4×Q8—21no—
337D4×Q8C22×C13911yescharacteristic, complemented
338#548—21no—
339#547C22×C13911yescharacteristic, complemented
340#544—21no—
341#542—21no—
342#541—21no—
343#539—22no—
344#536—21no—
345C2×C4⋊Q8C22×C13911yescharacteristic
346C2×#127C22×C13911yescharacteristic
347#529C22×C13911yescharacteristic
348#529C22×C13911yescharacteristic
349#496—21no—
350#496—21no—
351#490—21no—
352#490—21no—
353#486—22no—
354#486C22×C13912yes—
355#486C22×C13912yes—
356#460C22×C13912yes—
357#460C22×C13912yes—
358#459C22×C13912yes—
359#459C22×C13912yes—
360#450—21no—
361#450—21no—
362#447—21no—
363#447—21no—
364#432C22×C13911yescharacteristic
365#432C22×C13911yescharacteristic
366C2×#102—22no—
367C2×C4×C8C22×C13911yescharacteristic
368#332C22×C13912yescomplemented
369#332C22×C13912yescomplemented
370Q8⋊C8C22×C13912yescomplemented
371Q8⋊C8C22×C13912yescomplemented
372D4⋊C8C22×C13912yescomplemented
373D4⋊C8C22×C13912yescomplemented
374C2×#41—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×D8—22no—
383C2×D8—22no—
384C22×C8—21no—
385C4⋊Q8—22no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8D4×C13912yes—
391C4⋊Q8C23×C13911yescharacteristic
392C4⋊Q8C23×C13911yescharacteristic
393#127—21no—
394#127—21no—
395#127—21no—
396#127C23×C13912yes—
397#126—22no—
398#126—22no—
399#126—22no—
400#126—21no—
401#126—21no—
402#125—22no—
403#125—22no—
404#125—22no—
405#125—21no—
406#125D4×C13911yescharacteristic
407#125D4×C13911yescharacteristic
408#124—22no—
409#124—21no—
410#124D4×C13911yescharacteristic
411#124D4×C13911yescharacteristic
412#123—22no—
413#123—22no—
414#123—21no—
415#123—21no—
416#123—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—21no—
423C22⋊Q8—22no—
424C22⋊Q8—21no—
425C22⋊Q8—21no—
426C22⋊Q8D4×C13911yescharacteristic
427C22⋊Q8D4×C13911yescharacteristic
428#121—22no—
429#121—21no—
430#121D4×C13911yescharacteristic
431#121D4×C13911yescharacteristic
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×Q8C23×C13911yescharacteristic
436C4×Q8C23×C13911yescharacteristic
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4C23×C13911yescharacteristic
443C4×D4C23×C13911yescharacteristic
444#117—21no—
445#117—21no—
446#117—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4D4×C13912yes—
450C2×C42C23×C13911yescharacteristic
451C4⋊C8C23×C13912yes—
452C4⋊C8C23×C13912yes—
453#102—24no—
454#102—24no—
455#102—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459C22⋊C8—21no—
460C22⋊C8—21no—
461#97—21no—
462#97—21no—
463C4×C8—21no—
464C4×C8C23×C13912yes—
465C24—41no—
466#41—82no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—82no—
472C2×Q8—82no—
473C2×Q8C2×D4×C13911yescharacteristic
474C2×Q8C2×D4×C13911yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—44no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—82no—
486C2×D4—82no—
487C2×D4C2×D4×C13911yescharacteristic
488C2×D4C2×D4×C13911yescharacteristic
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4C2×D4×C13911yescharacteristic
495C22×C4C2×D4×C13911yescharacteristic
496C22×C4C2×D4×C13911yescharacteristic
497SD16—82no—
498SD16—82no—
499D8—82no—
500D8—82no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—42no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4C2×D4×C13911yescharacteristic
524C4⋊C4C2×D4×C13912yes—
525C4⋊C4C2×D4×C13912yes—
526C4⋊C4C2×D4×C13911yescharacteristic
527C4⋊C4C2×D4×C13911yescharacteristic
528C4⋊C4C2×D4×C13911yescharacteristic
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C42—22no—
544C42—22no—
545C42—21no—
546C42—21no—
547C42C2×D4×C13911yescharacteristic
548C42C2×D4×C13911yescharacteristic
549C42C2×D4×C13911yescharacteristic
550C42C24×C13911yescharacteristic
551C23—21no—
552C23—21no—
553C23—42no—
554C23—82no—
555C23—82no—
556C23—82no—
557C23#120×C13911yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—42no—
561Q8—42no—
562Q8—82no—
563Q8—82no—
564D4—22no—
565D4—22no—
566D4—44no—
567D4—42no—
568D4—42no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—42no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4#120×C13911yescharacteristic
594C2×C4#120×C13911yescharacteristic
595C2×C4#120×C13911yescharacteristic
596C2×C4C22×D4×C13911yescharacteristic
597C2×C4C22×D4×C13911yescharacteristic
598C2×C4C22×D4×C13911yescharacteristic
599C8—42no—
600C8—42no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—164no—
614C22#454×C13912yes—
615C22C2×#120×C13911yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—42no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4#576×C13912yes—
629C4#577×C13912yes—
630C2—22no—
631C2—81no—
632C2—81no—
633C2—162no—
634C2#3008×C13911yescharacteristic
635C2#3010×C13911yescharacteristic
636C2C2×#454×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC42C24×C139
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3552×C139C2semidirect
2. #3217×C139C2semidirect
3. #3217×C139C2semidirect
4. C2×#486×C139C2semidirect
5. #1628×C139C2semidirect
6. #1627×C139C2semidirect
7. #1626×C139C2semidirect
8. #1625×C139C2semidirect
9. #1556×C139C2semidirect
10. #1494×C139C2semidirect
11. #1494×C139C2semidirect
13. #557×C139C22semidirect
14. #556×C139C22semidirect
18. D4×Q8×C139C22semidirect
20. #547×C139C22semidirect
49. #332×C139C22semidirect
50. #332×C139C22semidirect
51. Q8⋊C8×C139C22semidirect
52. Q8⋊C8×C139C22semidirect
53. D4⋊C8×C139C22semidirect
54. D4⋊C8×C139C22semidirect
318. #18694C139direct (N × H)
319. C139#18694direct (N × H)
320. #3552C2×C139semidirect
321. #3217C2×C139semidirect
322. #3217C2×C139semidirect
323. C2×#486C2×C139semidirect
324. #1628C2×C139semidirect
325. #1627C2×C139semidirect
326. #1626C2×C139semidirect
327. #1625C2×C139semidirect
328. #1556C2×C139semidirect
329. #1494C2×C139semidirect
330. #1494C2×C139semidirect
332. #557C22×C139semidirect
333. #556C22×C139semidirect
337. D4×Q8C22×C139semidirect
339. #547C22×C139semidirect
368. #332C22×C139semidirect
369. #332C22×C139semidirect
370. Q8⋊C8C22×C139semidirect
371. Q8⋊C8C22×C139semidirect
372. D4⋊C8C22×C139semidirect
373. D4⋊C8C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3552×C1392
#3217×C1392
C2×#486×C1392
#1628×C1392
#1627×C1392
#1626×C1392
#1625×C1392
#1556×C1392
#1494×C1392
#18694139