Finite Group Databasebeta

← C139×#15850 #48010446

Subgroups — C139×#15850 #48010446

Order 35584.

1458 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C139C211yesmaximal, characteristic
2C2×#400×C139C211yesmaximal, characteristic
3C2×#398×C139C211yesmaximal, characteristic
4C2×#384×C139C211yesmaximal, characteristic
5#1445×C139C211yesmaximal, characteristic
6#1444×C139C212yesmaximal
7#1444×C139C212yesmaximal
8#1441×C139C212yesmaximal
9#1436×C139C211yesmaximal, characteristic
10#1436×C139C211yesmaximal, characteristic
11#1436×C139C212yesmaximal
12C2×#125×C139—24no—
13C2×#125×C139—24no—
14C2×#125×C139—24no—
15C22×C4⋊C4×C139C2211yescharacteristic
16C22×C4⋊C4×C139C2211yescharacteristic
17C22×C4⋊C4×C139C2211yescharacteristic
18C22×C4⋊C4×C139C2211yescharacteristic
19C22×C4⋊C4×C139C2212yes—
20C22×C4⋊C4×C139C2212yes—
21C22×C4⋊C4×C139C2211yescharacteristic
22C22×C4⋊C4×C139C2211yescharacteristic
23C22×C4⋊C4×C139C2211yescharacteristic
24C22×C4⋊C4×C139C2212yes—
25C22×C42×C139C2211yescharacteristic
26C22×C42×C139C2211yescharacteristic
27#400×C139—24no—
28#398×C139—24no—
29#384×C139—24no—
30C2×#95×C139C2212yes—
31C2×#95×C139C2211yescharacteristic
32C2×#95×C139C2212yes—
33C2×#95×C139C2211yescharacteristic
34C2×#95×C139C2212yes—
35C2×#95×C139C2212yes—
36C2×#95×C139C2212yes—
37C2×#95×C139C2212yes—
38C2×#95×C139C2212yes—
39C2×#95×C139C2212yes—
40C2×#95×C139C2212yes—
41C23×C4×C139C2312yes—
42C23×C4×C139C2312yes—
43C23×C4×C139C2311yescharacteristic
44C23×C4×C139C2311yescharacteristic
45C23×C4×C139C2311yescharacteristic
46C23×C4×C139C2311yescharacteristic
47C23×C4×C139C2311yescharacteristic
48C23×C4×C139C2312yes—
49C23×C4×C139C2311yescharacteristic
50C23×C4×C139C2311yescharacteristic
51C23×C4×C139C2312yes—
52#125×C139—232no—
53C2×C4⋊C4×C139—22no—
54C2×C4⋊C4×C139—22no—
55C2×C4⋊C4×C139—22no—
56C2×C4⋊C4×C139—22no—
57C2×C4⋊C4×C139—22no—
58C2×C4⋊C4×C139—22no—
59C2×C4⋊C4×C139—22no—
60C2×C4⋊C4×C139—22no—
61C2×C4⋊C4×C139—22no—
62C2×C4⋊C4×C139—22no—
63C2×C4⋊C4×C139—22no—
64C2×C4⋊C4×C139—22no—
65C2×C4⋊C4×C139—22no—
66C2×C4⋊C4×C139—22no—
67C2×C4⋊C4×C139—22no—
68C2×C4⋊C4×C139—24no—
69C2×C4⋊C4×C139—22no—
70C2×C4⋊C4×C139—22no—
71C2×C4⋊C4×C139—24no—
72C2×C4⋊C4×C139—24no—
73C2×C4⋊C4×C139—22no—
74C2×C4⋊C4×C139—24no—
75C2×C4⋊C4×C139—24no—
76C2×C4⋊C4×C139—42no—
77C2×C4⋊C4×C139—42no—
78C2×C4⋊C4×C139—42no—
79C2×C4⋊C4×C139—42no—
80C2×C4⋊C4×C139D414yes—
81C2×C4⋊C4×C139D414yes—
82C2×C4⋊C4×C139D414yes—
83C2×C42×C139—22no—
84C2×C42×C139—22no—
85C2×C42×C139—22no—
86C2×C42×C139—22no—
87C2×C42×C139—24no—
88#95×C139—22no—
89#95×C139—24no—
90#95×C139—22no—
91#95×C139—24no—
92#95×C139—24no—
93#95×C139—24no—
94#95×C139—24no—
95#95×C139—24no—
96#95×C139—42no—
97#95×C139—42no—
98#95×C139Q818yes—
99C24×C139C2411yescharacteristic
100C22×C4×C139—21no—
101C22×C4×C139—21no—
102C22×C4×C139—22no—
103C22×C4×C139—22no—
104C22×C4×C139—22no—
105C22×C4×C139—22no—
106C22×C4×C139—22no—
107C22×C4×C139—22no—
108C22×C4×C139—22no—
109C22×C4×C139—22no—
110C22×C4×C139—21no—
111C22×C4×C139—21no—
112C22×C4×C139—21no—
113C22×C4×C139—21no—
114C22×C4×C139—21no—
115C22×C4×C139—21no—
116C22×C4×C139—21no—
117C22×C4×C139—21no—
118C22×C4×C139—21no—
119C22×C4×C139—21no—
120C22×C4×C139—22no—
121C22×C4×C139—22no—
122C22×C4×C139—22no—
123C22×C4×C139—22no—
124C22×C4×C139—22no—
125C22×C4×C139—22no—
126C22×C4×C139—22no—
127C22×C4×C139—22no—
128C22×C4×C139—22no—
129C22×C4×C139—22no—
130C22×C4×C139—22no—
131C22×C4×C139—22no—
132C22×C4×C139—22no—
133C22×C4×C139—22no—
134C22×C4×C139—22no—
135C22×C4×C139—22no—
136C22×C4×C139—22no—
137C22×C4×C139—22no—
138C22×C4×C139—22no—
139C22×C4×C139—22no—
140C22×C4×C139—22no—
141C22×C4×C139—22no—
142C22×C4×C139—22no—
143C22×C4×C139—22no—
144C22×C4×C139—22no—
145C22×C4×C139—22no—
146C22×C4×C139—22no—
147C22×C4×C139—22no—
148C22×C4×C139—22no—
149C22×C4×C139C2×D412yes—
150C22×C4×C139C2×D412yes—
151C22×C4×C139C2×D412yes—
152C22×C4×C139C2×D412yes—
153C22×C4×C139C2×D412yes—
154C22×C4×C139C2×D412yes—
155C22×C4×C139C2×D412yes—
156C22×C4×C139C2×D412yes—
157C22×C4×C139C2×D412yes—
158C22×C4×C139C2×Q814yes—
159C22×C4×C139C2×Q814yes—
160C22×C4×C139C2×Q814yes—
161C22×C4×C139#4114yes—
162C22×C4×C139#4114yes—
163C4⋊C4×C139—28no—
164C4⋊C4×C139—28no—
165C4⋊C4×C139—28no—
166C4⋊C4×C139—28no—
167C4⋊C4×C139—28no—
168C4⋊C4×C139—28no—
169C4⋊C4×C139—48no—
170C4⋊C4×C139—48no—
171C4⋊C4×C139—48no—
172C4⋊C4×C139—44no—
173C42×C139—28no—
174C42×C139—28no—
175C23×C139C22×D411yescharacteristic
176C23×C139C22×D411yescharacteristic
177C23×C139C22×D411yescharacteristic
178C23×C139C22×Q812yes—
179C23×C139C2×#4112yes—
180C23×C139C2×#4112yes—
181C23×C139H(5,𝔽2)12yes—
182C23×C1392−1+412yes—
183C23×C1392−1+412yes—
184C2×C4×C139—22no—
185C2×C4×C139—22no—
186C2×C4×C139—24no—
187C2×C4×C139—22no—
188C2×C4×C139—22no—
189C2×C4×C139—24no—
190C2×C4×C139—24no—
191C2×C4×C139—24no—
192C2×C4×C139—24no—
193C2×C4×C139—24no—
194C2×C4×C139—24no—
195C2×C4×C139—24no—
196C2×C4×C139—24no—
197C2×C4×C139—24no—
198C2×C4×C139—22no—
199C2×C4×C139—22no—
200C2×C4×C139—22no—
201C2×C4×C139—22no—
202C2×C4×C139—22no—
203C2×C4×C139—22no—
204C2×C4×C139—22no—
205C2×C4×C139—24no—
206C2×C4×C139—24no—
207C2×C4×C139—24no—
208C2×C4×C139—24no—
209C2×C4×C139—24no—
210C2×C4×C139—24no—
211C2×C4×C139—24no—
212C2×C4×C139—41no—
213C2×C4×C139—41no—
214C2×C4×C139—41no—
215C2×C4×C139—41no—
216C2×C4×C139—42no—
217C2×C4×C139—41no—
218C2×C4×C139—41no—
219C2×C4×C139—41no—
220C2×C4×C139—41no—
221C2×C4×C139—42no—
222C2×C4×C139—42no—
223C2×C4×C139—42no—
224C2×C4×C139—42no—
225C2×C4×C139—42no—
226C2×C4×C139—42no—
227C2×C4×C139—42no—
228C2×C4×C139—42no—
229C2×C4×C139—42no—
230C2×C4×C139—42no—
231C2×C4×C139—42no—
232C2×C4×C139—42no—
233C2×C4×C139—42no—
234C2×C4×C139—42no—
235C2×C4×C139—42no—
236C2×C4×C139—42no—
237C2×C4×C139—42no—
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#12014yes—
245C2×C4×C139#12518yescomplemented
246C2×C4×C139C4⋊Q814yes—
247C22×C139C2×#12011yescharacteristic
248C22×C139#52511yescharacteristic
249C22×C139C2×#12512yes—
250C22×C139C2×C4⋊Q811yescharacteristic
251C22×C139#53211yescharacteristic
252C22×C139#53511yescharacteristic
253C22×C139#53611yescharacteristic
254C22×C139#53611yescharacteristic
255C22×C139#53912yes—
256C22×C139#54112yes—
257C22×C139#54412yes—
258C22×C139#54612yes—
259C22×C139#54712yes—
260C22×C139#54712yes—
261C22×C139D4×Q812yes—
262C22×C139D4×Q812yes—
263C22×C139#55012yes—
264C22×C139#55212yes—
265C22×C139#55412yes—
266C22×C139#55712yes—
267C22×C139#56312yes—
268C4×C139—24no—
269C4×C139—24no—
270C4×C139—28no—
271C4×C139—42no—
272C4×C139—42no—
273C4×C139—42no—
274C4×C139—42no—
275C4×C139—42no—
276C4×C139—44no—
277C4×C139—82no—
278C4×C139—82no—
279C2×C139#240611yescharacteristic
280C2×C139#243111yescharacteristic
281C2×C139#243411yescharacteristic
282C2×C139#247312yes—
283C2×C139#250612yes—
284C2×C139#255212yes—
285C2×C139#271312yes—
286C2×C139#272012yes—
287C2×C139#272112yes—
288#15850C13911yesmaximal, characteristic, direct product factor, Sylow
289C139#1585011yescharacteristic, direct product factor, Sylow
290C22×#125C2×C13911yescharacteristic
291C2×#400C2×C13911yescharacteristic
292C2×#398C2×C13911yescharacteristic
293C2×#384C2×C13911yescharacteristic
294#1445C2×C13911yescharacteristic
295#1444C2×C13912yes—
296#1444C2×C13912yes—
297#1441C2×C13912yes—
298#1436C2×C13912yes—
299#1436C2×C13911yescharacteristic
300#1436C2×C13911yescharacteristic
301C2×#125—24no—
302C2×#125—24no—
303C2×#125—24no—
304C22×C4⋊C4C22×C13911yescharacteristic
305C22×C4⋊C4C22×C13911yescharacteristic
306C22×C4⋊C4C22×C13911yescharacteristic
307C22×C4⋊C4C22×C13911yescharacteristic
308C22×C4⋊C4C22×C13912yes—
309C22×C4⋊C4C22×C13912yes—
310C22×C4⋊C4C22×C13911yescharacteristic
311C22×C4⋊C4C22×C13911yescharacteristic
312C22×C4⋊C4C22×C13911yescharacteristic
313C22×C4⋊C4C22×C13912yes—
314C22×C42C22×C13911yescharacteristic
315C22×C42C22×C13911yescharacteristic
316#400—24no—
317#398—24no—
318#384—24no—
319C2×#95C22×C13912yes—
320C2×#95C22×C13911yescharacteristic
321C2×#95C22×C13912yes—
322C2×#95C22×C13911yescharacteristic
323C2×#95C22×C13912yes—
324C2×#95C22×C13912yes—
325C2×#95C22×C13912yes—
326C2×#95C22×C13912yes—
327C2×#95C22×C13912yes—
328C2×#95C22×C13912yes—
329C2×#95C22×C13912yes—
330C23×C4C23×C13912yes—
331C23×C4C23×C13912yes—
332C23×C4C23×C13911yescharacteristic
333C23×C4C23×C13911yescharacteristic
334C23×C4C23×C13911yescharacteristic
335C23×C4C23×C13911yescharacteristic
336C23×C4C23×C13911yescharacteristic
337C23×C4C23×C13912yes—
338C23×C4C23×C13911yescharacteristic
339C23×C4C23×C13911yescharacteristic
340C23×C4C23×C13912yes—
341#125—232no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4D4×C13914yes—
370C2×C4⋊C4D4×C13914yes—
371C2×C4⋊C4D4×C13914yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377#95—22no—
378#95—24no—
379#95—22no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—42no—
386#95—42no—
387#95Q8×C13918yes—
388C24C24×C13911yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4C2×D4×C13912yes—
439C22×C4C2×D4×C13912yes—
440C22×C4C2×D4×C13912yes—
441C22×C4C2×D4×C13912yes—
442C22×C4C2×D4×C13912yes—
443C22×C4C2×D4×C13912yes—
444C22×C4C2×D4×C13912yes—
445C22×C4C2×D4×C13912yes—
446C22×C4C2×D4×C13912yes—
447C22×C4C2×Q8×C13914yes—
448C22×C4C2×Q8×C13914yes—
449C22×C4C2×Q8×C13914yes—
450C22×C4#41×C13914yes—
451C22×C4#41×C13914yes—
452C4⋊C4—28no—
453C4⋊C4—28no—
454C4⋊C4—28no—
455C4⋊C4—28no—
456C4⋊C4—28no—
457C4⋊C4—28no—
458C4⋊C4—48no—
459C4⋊C4—48no—
460C4⋊C4—48no—
461C4⋊C4—44no—
462C42—28no—
463C42—28no—
464C23C22×D4×C13911yescharacteristic
465C23C22×D4×C13911yescharacteristic
466C23C22×D4×C13911yescharacteristic
467C23C22×Q8×C13912yes—
468C23C2×#41×C13912yes—
469C23C2×#41×C13912yes—
470C23H(5,𝔽2)×C13912yes—
471C232−1+4×C13912yes—
472C232−1+4×C13912yes—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4#120×C13914yes—
534C2×C4#125×C13918yescomplemented
535C2×C4C4⋊Q8×C13914yes—
536C22C2×#120×C13911yescharacteristic
537C22#525×C13911yescharacteristic
538C22C2×#125×C13912yes—
539C22C2×C4⋊Q8×C13911yescharacteristic
540C22#532×C13911yescharacteristic
541C22#535×C13911yescharacteristic
542C22#536×C13911yescharacteristic
543C22#536×C13911yescharacteristic
544C22#539×C13912yes—
545C22#541×C13912yes—
546C22#544×C13912yes—
547C22#546×C13912yes—
548C22#547×C13912yes—
549C22#547×C13912yes—
550C22D4×Q8×C13912yes—
551C22D4×Q8×C13912yes—
552C22#550×C13912yes—
553C22#552×C13912yes—
554C22#554×C13912yes—
555C22#557×C13912yes—
556C22#563×C13912yes—
557C4—24no—
558C4—24no—
559C4—28no—
560C4—42no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—44no—
566C4—82no—
567C4—82no—
568C2#2406×C13911yescharacteristic
569C2#2431×C13911yescharacteristic
570C2#2434×C13911yescharacteristic
571C2#2473×C13912yes—
572C2#2506×C13912yes—
573C2#2552×C13912yes—
574C2#2713×C13912yes—
575C2#2720×C13912yes—
576C2#2721×C13912yes—
subgroupG/H
center, socle, prime radicalC24×C139C24
commutator, Frattini, cosocleC24C24×C139
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
245. C2×C4×C139#125semidirect
288. #15850C139direct (N × H)
289. C139#15850direct (N × H)
534. C2×C4#125×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#125×C1392
C2×#400×C1392
C2×#398×C1392
C2×#384×C1392
#1445×C1392
#1444×C1392
#1441×C1392
#1436×C1392
#15850139