Finite Group Databasebeta

← C139×#14506 #48009102

Subgroups — C139×#14506 #48009102

Order 35584.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C139C211yesmaximal, characteristic
2C2×#388×C139C212yesmaximal, complemented
3#1445×C139C212yesmaximal, complemented
4#1439×C139C212yesmaximal, complemented
5#1438×C139C211yesmaximal, characteristic
6#1438×C139C211yesmaximal, characteristic
7#1437×C139C212yesmaximal, complemented
8C4⋊#95×C139C212yesmaximal, complemented
9C22⋊#95×C139C212yesmaximal, complemented
10C23×D4×C139C2211yescharacteristic
11C24×C4×C139C2211yescharacteristic
12C2×#123×C139—28no—
13C2×#123×C139C418yescomplemented
14C22×C4⋊C4×C139C2212yes—
15C22×C4⋊C4×C139C2212yes—
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2212yes—
18C22×C22⋊C4×C139C2211yescharacteristic
19C22×C22⋊C4×C139C2212yes—
20C22×C22⋊C4×C139C2212yes—
21C22×C22⋊C4×C139C2211yescharacteristic
22C22×C22⋊C4×C139C2211yescharacteristic
23C22×C42×C139C2212yes—
24#388×C139—28no—
25C2×#95×C139C2212yes—
26C2×#95×C139C2212yes—
27C2×#95×C139C2212yes—
28C2×#95×C139C2212yes—
29C2×#95×C139C2212yes—
30C2×#95×C139C2212yes—
31C2×#95×C139C2211yescharacteristic
32C2×#95×C139C2212yes—
33C2×#95×C139C2211yescharacteristic
34C25×C139C2311yescharacteristic
35C25×C139C2311yescharacteristic
36C22×D4×C139—24no—
37C22×D4×C139—42no—
38C22×D4×C139—41no—
39C22×D4×C139—41no—
40C22×D4×C139C2×C414yes—
41C23×C4×C139—24no—
42C23×C4×C139—42no—
43C23×C4×C139—41no—
44C23×C4×C139—41no—
45C23×C4×C139C2×C414yes—
46C23×C4×C139C2312yes—
47C23×C4×C139C2312yes—
48C23×C4×C139C2312yes—
49C23×C4×C139C2311yescharacteristic
50C23×C4×C139C2312yes—
51C23×C4×C139C2312yes—
52C23×C4×C139C2312yes—
53#123×C139—232no—
54C2×C4⋊C4×C139—24no—
55C2×C4⋊C4×C139—24no—
56C2×C4⋊C4×C139—24no—
57C2×C4⋊C4×C139—24no—
58C2×C4⋊C4×C139—42no—
59C2×C4⋊C4×C139C2×C418yes—
60C2×C22⋊C4×C139—24no—
61C2×C22⋊C4×C139—24no—
62C2×C22⋊C4×C139—24no—
63C2×C22⋊C4×C139—24no—
64C2×C22⋊C4×C139—24no—
65C2×C22⋊C4×C139—24no—
66C2×C22⋊C4×C139—24no—
67C2×C22⋊C4×C139—24no—
68C2×C22⋊C4×C139—41no—
69C2×C22⋊C4×C139—42no—
70C2×C22⋊C4×C139—42no—
71C2×C22⋊C4×C139—42no—
72C2×C22⋊C4×C139—42no—
73C2×C22⋊C4×C139—41no—
74C2×C22⋊C4×C139—42no—
75C2×C22⋊C4×C139C2×C418yes—
76C2×C22⋊C4×C139C2×C414yes—
77C2×C22⋊C4×C139D418yes—
78C2×C42×C139—24no—
79C2×C42×C139—24no—
80C2×C42×C139—42no—
81#95×C139—24no—
82#95×C139—24no—
83#95×C139—41no—
84#95×C139—42no—
85#95×C139—42no—
86#95×C139—42no—
87#95×C139—42no—
88#95×C139—42no—
89#95×C139—41no—
90C24×C139—22no—
91C24×C139—22no—
92C24×C139—22no—
93C24×C139—22no—
94C24×C139—21no—
95C24×C139—21no—
96C24×C139—22no—
97C24×C139—22no—
98C24×C139—22no—
99C24×C139—22no—
100C24×C139—22no—
101C24×C139—22no—
102C24×C139—21no—
103C24×C139—21no—
104C24×C139—22no—
105C24×C139C22×C412yes—
106C24×C139C22×C412yes—
107C24×C139C2×D414yes—
108C24×C139C2411yescharacteristic
109C2×D4×C139—28no—
110C2×D4×C139—44no—
111C2×D4×C139—44no—
112C2×D4×C139—48no—
113C2×D4×C139—48no—
114C22×C4×C139—22no—
115C22×C4×C139—22no—
116C22×C4×C139—22no—
117C22×C4×C139—22no—
118C22×C4×C139—28no—
119C22×C4×C139—22no—
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—21no—
136C22×C4×C139—21no—
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×C139—22no—
150C22×C4×C139—22no—
151C22×C4×C139—22no—
152C22×C4×C139—22no—
153C22×C4×C139—22no—
154C22×C4×C139—22no—
155C22×C4×C139—44no—
156C22×C4×C139—44no—
157C22×C4×C139—48no—
158C22×C4×C139—48no—
159C22×C4×C139C22×C414yes—
160C22×C4×C139C22×C412yes—
161C22×C4×C139C22×C414yes—
162C22×C4×C139C2×D414yes—
163C22×C4×C139C2×D414yes—
164C22×C4×C139#4114yes—
165C22×C4×C139#4114yes—
166C4⋊C4×C139—216no—
167C4⋊C4×C139—48no—
168C22⋊C4×C139—216no—
169C22⋊C4×C139—44no—
170C22⋊C4×C139—48no—
171C22⋊C4×C139—48no—
172C22⋊C4×C139—48no—
173C22⋊C4×C139—44no—
174C22⋊C4×C139C22⋊C4116yescomplemented
175C42×C139—48no—
176C23×C139—24no—
177C23×C139—22no—
178C23×C139—22no—
179C23×C139—24no—
180C23×C139—24no—
181C23×C139—24no—
182C23×C139—24no—
183C23×C139—24no—
184C23×C139—24no—
185C23×C139—24no—
186C23×C139—22no—
187C23×C139—24no—
188C23×C139—22no—
189C23×C139—22no—
190C23×C139—24no—
191C23×C139—42no—
192C23×C139—42no—
193C23×C139—42no—
194C23×C139—42no—
195C23×C139—41no—
196C23×C139—42no—
197C23×C139—41no—
198C23×C139—41no—
199C23×C139—42no—
200C23×C139—41no—
201C23×C139—42no—
202C23×C139—42no—
203C23×C139—42no—
204C23×C139—42no—
205C23×C139—42no—
206C23×C139—42no—
207C23×C139—42no—
208C23×C139—42no—
209C23×C139—42no—
210C23×C139—42no—
211C23×C139—41no—
212C23×C139—42no—
213C23×C139—41no—
214C23×C139—41no—
215C23×C139—42no—
216C23×C139—41no—
217C23×C139C2×C22⋊C414yes—
218C23×C139C23×C411yescharacteristic
219C23×C139C22×D412yes—
220C23×C139C2×#4112yes—
221C23×C139C2×#4112yes—
222C23×C139H(5,𝔽2)12yes—
223C23×C139H(5,𝔽2)11yescharacteristic
224C23×C139H(5,𝔽2)11yescharacteristic
225C23×C139H(5,𝔽2)12yes—
226C23×C1392−1+412yes—
227D4×C139—416no—
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—22no—
236C2×C4×C139—24no—
237C2×C4×C139—24no—
238C2×C4×C139—22no—
239C2×C4×C139—22no—
240C2×C4×C139—24no—
241C2×C4×C139—24no—
242C2×C4×C139—24no—
243C2×C4×C139—24no—
244C2×C4×C139—24no—
245C2×C4×C139—24no—
246C2×C4×C139—416no—
247C2×C4×C139—42no—
248C2×C4×C139—42no—
249C2×C4×C139—42no—
250C2×C4×C139—42no—
251C2×C4×C139—42no—
252C2×C4×C139—42no—
253C2×C4×C139—42no—
254C2×C4×C139—42no—
255C2×C4×C139—42no—
256C2×C4×C139—42no—
257C2×C4×C139—42no—
258C2×C4×C139—42no—
259C2×C4×C139—42no—
260C2×C4×C139—42no—
261C2×C4×C139—42no—
262C2×C4×C139—42no—
263C2×C4×C139—42no—
264C2×C4×C139—42no—
265C2×C4×C139—42no—
266C2×C4×C139—42no—
267C2×C4×C139—42no—
268C2×C4×C139—42no—
269C2×C4×C139—42no—
270C2×C4×C139—42no—
271C2×C4×C139—42no—
272C2×C4×C139—42no—
273C2×C4×C139—42no—
274C2×C4×C139—42no—
275C2×C4×C139C2×C22⋊C418yes—
276C22×C139—24no—
277C22×C139—28no—
278C22×C139—44no—
279C22×C139—42no—
280C22×C139—42no—
281C22×C139—44no—
282C22×C139—44no—
283C22×C139—44no—
284C22×C139—44no—
285C22×C139—42no—
286C22×C139—44no—
287C22×C139—44no—
288C22×C139—42no—
289C22×C139—42no—
290C22×C139—82no—
291C22×C139—82no—
292C22×C139—82no—
293C22×C139—82no—
294C22×C139C22×C22⋊C411yescharacteristic
295C22×C139C4×#4112yes—
296C22×C139#51811yescharacteristic
297C22×C139#51811yescharacteristic
298C22×C139#52012yes—
299C22×C139#53512yes—
300C22×C139#53512yes—
301C22×C139#53812yes—
302C22×C139#53912yes—
303C22×C139#54012yes—
304C22×C139#54212yes—
305C22×C139#54612yes—
306C22×C139#54612yes—
307C22×C139#54712yes—
308C22×C139#54712yes—
309C22×C139#55111yescharacteristic
310C22×C139#55312yes—
311C22×C139#55911yescharacteristic
312C22×C139#56011yescharacteristic
313C22×C139#56212yes—
314C22×C139#56311yescharacteristic
315C4×C139—28no—
316C4×C139—44no—
317C4×C139—42no—
318C4×C139—44no—
319C4×C139—44no—
320C4×C139—82no—
321C4×C139—82no—
322C2×C139—44no—
323C2×C139—82no—
324C2×C139#230911yescharacteristic
325C2×C139#233512yes—
326C2×C139#233912yes—
327C2×C139#237411yescharacteristic
328C2×C139#237611yescharacteristic
329C2×C139#270312yes—
330C2×C139#270612yes—
331C2×C139#271012yes—
332C2×C139#271812yes—
333#14506C13911yesmaximal, characteristic, direct product factor, Sylow
334C139#1450611yescharacteristic, direct product factor, Sylow
335C22×#123C2×C13911yescharacteristic
336C2×#388C2×C13912yescomplemented
337#1445C2×C13912yescomplemented
338#1439C2×C13912yescomplemented
339#1438C2×C13911yescharacteristic
340#1438C2×C13911yescharacteristic
341#1437C2×C13912yescomplemented
342C4⋊#95C2×C13912yescomplemented
343C22⋊#95C2×C13912yescomplemented
344C23×D4C22×C13911yescharacteristic
345C24×C4C22×C13911yescharacteristic
346C2×#123—28no—
347C2×#123C4×C13918yescomplemented
348C22×C4⋊C4C22×C13912yes—
349C22×C4⋊C4C22×C13912yes—
350C22×C22⋊C4C22×C13912yes—
351C22×C22⋊C4C22×C13912yes—
352C22×C22⋊C4C22×C13911yescharacteristic
353C22×C22⋊C4C22×C13912yes—
354C22×C22⋊C4C22×C13912yes—
355C22×C22⋊C4C22×C13911yescharacteristic
356C22×C22⋊C4C22×C13911yescharacteristic
357C22×C42C22×C13912yes—
358#388—28no—
359C2×#95C22×C13912yes—
360C2×#95C22×C13912yes—
361C2×#95C22×C13912yes—
362C2×#95C22×C13912yes—
363C2×#95C22×C13912yes—
364C2×#95C22×C13912yes—
365C2×#95C22×C13911yescharacteristic
366C2×#95C22×C13912yes—
367C2×#95C22×C13911yescharacteristic
368C25C23×C13911yescharacteristic
369C25C23×C13911yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C13914yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C13914yes—
380C23×C4C23×C13912yes—
381C23×C4C23×C13912yes—
382C23×C4C23×C13912yes—
383C23×C4C23×C13911yescharacteristic
384C23×C4C23×C13912yes—
385C23×C4C23×C13912yes—
386C23×C4C23×C13912yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C13918yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C13918yes—
410C2×C22⋊C4C2×C4×C13914yes—
411C2×C22⋊C4D4×C13918yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C13912yes—
440C24C22×C4×C13912yes—
441C24C2×D4×C13914yes—
442C24C24×C13911yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C13914yes—
494C22×C4C22×C4×C13912yes—
495C22×C4C22×C4×C13914yes—
496C22×C4C2×D4×C13914yes—
497C22×C4C2×D4×C13914yes—
498C22×C4#41×C13914yes—
499C22×C4#41×C13914yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C139116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C13914yes—
552C23C23×C4×C13911yescharacteristic
553C23C22×D4×C13912yes—
554C23C2×#41×C13912yes—
555C23C2×#41×C13912yes—
556C23H(5,𝔽2)×C13912yes—
557C23H(5,𝔽2)×C13911yescharacteristic
558C23H(5,𝔽2)×C13911yescharacteristic
559C23H(5,𝔽2)×C13912yes—
560C232−1+4×C13912yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C13918yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C13911yescharacteristic
629C22C4×#41×C13912yes—
630C22#518×C13911yescharacteristic
631C22#518×C13911yescharacteristic
632C22#520×C13912yes—
633C22#535×C13912yes—
634C22#535×C13912yes—
635C22#538×C13912yes—
636C22#539×C13912yes—
637C22#540×C13912yes—
638C22#542×C13912yes—
639C22#546×C13912yes—
640C22#546×C13912yes—
641C22#547×C13912yes—
642C22#547×C13912yes—
643C22#551×C13911yescharacteristic
644C22#553×C13912yes—
645C22#559×C13911yescharacteristic
646C22#560×C13911yescharacteristic
647C22#562×C13912yes—
648C22#563×C13911yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—44no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2#2309×C13911yescharacteristic
659C2#2335×C13912yes—
660C2#2339×C13912yes—
661C2#2374×C13911yescharacteristic
662C2#2376×C13911yescharacteristic
663C2#2703×C13912yes—
664C2#2706×C13912yes—
665C2#2710×C13912yes—
666C2#2718×C13912yes—
subgroupG/H
center, socleC24×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC24C24×C139
prime radicalC23×D4×C139C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C139C2semidirect
3. #1445×C139C2semidirect
4. #1439×C139C2semidirect
7. #1437×C139C2semidirect
8. C4⋊#95×C139C2semidirect
9. C22⋊#95×C139C2semidirect
13. C2×#123×C139C4semidirect
174. C22⋊C4×C139C22⋊C4semidirect
333. #14506C139direct (N × H)
334. C139#14506direct (N × H)
336. C2×#388C2×C139semidirect
337. #1445C2×C139semidirect
338. #1439C2×C139semidirect
341. #1437C2×C139semidirect
342. C4⋊#95C2×C139semidirect
343. C22⋊#95C2×C139semidirect
347. C2×#123C4×C139semidirect
508. C22⋊C4C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1392
C2×#388×C1392
#1445×C1392
#1439×C1392
#1438×C1392
#1437×C1392
C4⋊#95×C1392
C22⋊#95×C1392
#14506139