Finite Group Databasebeta

← C139×#15649 #48010245

Subgroups — C139×#15649 #48010245

Order 35584.

1414 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C139C212yesmaximal
2C2×#387×C139C212yesmaximal, complemented
3#1441×C139C212yesmaximal, complemented
4#1441×C139C212yesmaximal, complemented
5#1440×C139C211yesmaximal, characteristic
6#1439×C139C212yesmaximal
7#1437×C139C211yesmaximal, characteristic
8#1437×C139C211yesmaximal, characteristic
9C4⋊#95×C139C212yesmaximal, complemented
10C22×C4⋊C4×C139C2212yes—
11C22×C4⋊C4×C139C2212yes—
12C22×C4⋊C4×C139C2212yes—
13C22×C4⋊C4×C139C2212yes—
14C22×C22⋊C4×C139C2212yes—
15C22×C22⋊C4×C139C2211yescharacteristic
16C22×C22⋊C4×C139C2212yes—
17C22×C22⋊C4×C139C2211yescharacteristic
18C22×C22⋊C4×C139C2211yescharacteristic
19C22×C42×C139C2211yescharacteristic
20C22×C42×C139C2211yescharacteristic
21#399×C139—28no—
22#387×C139—28no—
23C2×#95×C139C2212yes—
24C2×#95×C139C2212yes—
25C2×#95×C139C2212yes—
26C2×#95×C139C2212yes—
27C2×#95×C139C2212yes—
28C2×#95×C139C2212yes—
29C2×#95×C139C2212yes—
30C2×#95×C139C2211yescharacteristic
31C2×#95×C139C2211yescharacteristic
32C2×#95×C139C2212yes—
33C25×C139C2311yescharacteristic
34C23×C4×C139C2312yes—
35C23×C4×C139C2312yes—
36C23×C4×C139C2312yes—
37C23×C4×C139C2312yes—
38C23×C4×C139C2311yescharacteristic
39C23×C4×C139C2311yescharacteristic
40C23×C4×C139C2312yes—
41C23×C4×C139C2312yes—
42C2×C4⋊C4×C139—24no—
43C2×C4⋊C4×C139—24no—
44C2×C4⋊C4×C139—24no—
45C2×C4⋊C4×C139—24no—
46C2×C4⋊C4×C139—24no—
47C2×C4⋊C4×C139—24no—
48C2×C4⋊C4×C139—24no—
49C2×C4⋊C4×C139—24no—
50C2×C4⋊C4×C139—42no—
51C2×C4⋊C4×C139—42no—
52C2×C4⋊C4×C139—42no—
53C2×C4⋊C4×C139D418yes—
54C2×C22⋊C4×C139—24no—
55C2×C22⋊C4×C139—24no—
56C2×C22⋊C4×C139—24no—
57C2×C22⋊C4×C139—24no—
58C2×C22⋊C4×C139—24no—
59C2×C22⋊C4×C139—24no—
60C2×C22⋊C4×C139—41no—
61C2×C22⋊C4×C139—41no—
62C2×C22⋊C4×C139—42no—
63C2×C22⋊C4×C139—41no—
64C2×C22⋊C4×C139—42no—
65C2×C22⋊C4×C139—41no—
66C2×C22⋊C4×C139Q814yes—
67C2×C42×C139—24no—
68C2×C42×C139—24no—
69C2×C42×C139—41no—
70C2×C42×C139—41no—
71#95×C139—24no—
72#95×C139—24no—
73#95×C139—24no—
74#95×C139—24no—
75#95×C139—24no—
76#95×C139—42no—
77#95×C139—42no—
78#95×C139—42no—
79#95×C139—41no—
80#95×C139—41no—
81C24×C139—22no—
82C24×C139—22no—
83C24×C139—22no—
84C24×C139—22no—
85C24×C139—21no—
86C24×C139—21no—
87C24×C139—22no—
88C24×C139—22no—
89C24×C139C2×Q812yes—
90C24×C139C2411yescharacteristic
91C22×C4×C139—22no—
92C22×C4×C139—22no—
93C22×C4×C139—22no—
94C22×C4×C139—22no—
95C22×C4×C139—22no—
96C22×C4×C139—22no—
97C22×C4×C139—22no—
98C22×C4×C139—22no—
99C22×C4×C139—22no—
100C22×C4×C139—22no—
101C22×C4×C139—22no—
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—21no—
110C22×C4×C139—21no—
111C22×C4×C139—22no—
112C22×C4×C139—22no—
113C22×C4×C139—22no—
114C22×C4×C139—21no—
115C22×C4×C139—21no—
116C22×C4×C139—22no—
117C22×C4×C139—22no—
118C22×C4×C139—22no—
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×C139C2×D414yes—
136C22×C4×C139C2×D414yes—
137C22×C4×C139C2×D414yes—
138C22×C4×C139C2×Q812yes—
139C22×C4×C139C2×Q812yes—
140C22×C4×C139#4114yes—
141C22×C4×C139#4114yes—
142C22×C4×C139#4114yes—
143C4⋊C4×C139—216no—
144C4⋊C4×C139—48no—
145C4⋊C4×C139—48no—
146C4⋊C4×C139—48no—
147C22⋊C4×C139—44no—
148C22⋊C4×C139—44no—
149C22⋊C4×C139—48no—
150C22⋊C4×C139—44no—
151C22⋊C4×C139—48no—
152C42×C139—44no—
153C42×C139—44no—
154C23×C139—22no—
155C23×C139—22no—
156C23×C139—22no—
157C23×C139—24no—
158C23×C139—24no—
159C23×C139—42no—
160C23×C139—42no—
161C23×C139—42no—
162C23×C139—42no—
163C23×C139—42no—
164C23×C139—42no—
165C23×C139—41no—
166C23×C139—42no—
167C23×C139—42no—
168C23×C139—42no—
169C23×C139—41no—
170C23×C139—42no—
171C23×C139—42no—
172C23×C139—42no—
173C23×C139—41no—
174C23×C139—41no—
175C23×C139C22×D412yes—
176C23×C139C22×Q811yescharacteristic
177C23×C139C2×#4112yes—
178C23×C139C2×#4112yes—
179C23×C139C2×#4112yes—
180C23×C139H(5,𝔽2)11yescharacteristic
181C23×C139H(5,𝔽2)12yes—
182C23×C139H(5,𝔽2)11yescharacteristic
183C23×C1392−1+412yes—
184C2×C4×C139—24no—
185C2×C4×C139—24no—
186C2×C4×C139—24no—
187C2×C4×C139—24no—
188C2×C4×C139—24no—
189C2×C4×C139—24no—
190C2×C4×C139—24no—
191C2×C4×C139—24no—
192C2×C4×C139—24no—
193C2×C4×C139—22no—
194C2×C4×C139—22no—
195C2×C4×C139—24no—
196C2×C4×C139—24no—
197C2×C4×C139—24no—
198C2×C4×C139—24no—
199C2×C4×C139—24no—
200C2×C4×C139—24no—
201C2×C4×C139—24no—
202C2×C4×C139—24no—
203C2×C4×C139—42no—
204C2×C4×C139—42no—
205C2×C4×C139—42no—
206C2×C4×C139—42no—
207C2×C4×C139—42no—
208C2×C4×C139—42no—
209C2×C4×C139—42no—
210C2×C4×C139—42no—
211C2×C4×C139—41no—
212C2×C4×C139—42no—
213C2×C4×C139—42no—
214C2×C4×C139—42no—
215C2×C4×C139—41no—
216C2×C4×C139—42no—
217C2×C4×C139—42no—
218C2×C4×C139—42no—
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#12318yes—
236C22×C139—42no—
237C22×C139—44no—
238C22×C139—42no—
239C22×C139—42no—
240C22×C139—44no—
241C22×C139—82no—
242C22×C139—82no—
243C22×C139—82no—
244C22×C139—82no—
245C22×C139C2×#12312yes—
246C22×C139#53212yes—
247C22×C139#53311yescharacteristic
248C22×C139#53311yescharacteristic
249C22×C139#53712yes—
250C22×C139#53912yes—
251C22×C139#54012yes—
252C22×C139#54212yes—
253C22×C139#54311yescharacteristic
254C22×C139D4211yescharacteristic
255C22×C139#54612yes—
256C22×C139D4×Q812yes—
257C22×C139#55012yes—
258C22×C139#55112yes—
259C22×C139#55111yescharacteristic
260C22×C139#55212yes—
261C22×C139#55212yes—
262C22×C139#55412yes—
263C22×C139#55912yes—
264C22×C139#56011yescharacteristic
265C22×C139#56311yescharacteristic
266C4×C139—28no—
267C4×C139—42no—
268C4×C139—44no—
269C4×C139—44no—
270C4×C139—44no—
271C4×C139—42no—
272C4×C139—82no—
273C4×C139—82no—
274C2×C139—82no—
275C2×C139#242312yes—
276C2×C139#244512yes—
277C2×C139#249812yes—
278C2×C139#255612yes—
279C2×C139#260711yescharacteristic
280C2×C139#268311yescharacteristic
281C2×C139#270512yes—
282C2×C139#274811yescharacteristic
283C2×C139#277312yes—
284#15649C13911yesmaximal, characteristic, direct product factor, Sylow
285C139#1564911yescharacteristic, direct product factor, Sylow
286C2×#399C2×C13912yes—
287C2×#387C2×C13912yescomplemented
288#1441C2×C13912yescomplemented
289#1441C2×C13912yescomplemented
290#1440C2×C13911yescharacteristic
291#1439C2×C13912yes—
292#1437C2×C13911yescharacteristic
293#1437C2×C13911yescharacteristic
294C4⋊#95C2×C13912yescomplemented
295C22×C4⋊C4C22×C13912yes—
296C22×C4⋊C4C22×C13912yes—
297C22×C4⋊C4C22×C13912yes—
298C22×C4⋊C4C22×C13912yes—
299C22×C22⋊C4C22×C13912yes—
300C22×C22⋊C4C22×C13911yescharacteristic
301C22×C22⋊C4C22×C13912yes—
302C22×C22⋊C4C22×C13911yescharacteristic
303C22×C22⋊C4C22×C13911yescharacteristic
304C22×C42C22×C13911yescharacteristic
305C22×C42C22×C13911yescharacteristic
306#399—28no—
307#387—28no—
308C2×#95C22×C13912yes—
309C2×#95C22×C13912yes—
310C2×#95C22×C13912yes—
311C2×#95C22×C13912yes—
312C2×#95C22×C13912yes—
313C2×#95C22×C13912yes—
314C2×#95C22×C13912yes—
315C2×#95C22×C13911yescharacteristic
316C2×#95C22×C13911yescharacteristic
317C2×#95C22×C13912yes—
318C25C23×C13911yescharacteristic
319C23×C4C23×C13912yes—
320C23×C4C23×C13912yes—
321C23×C4C23×C13912yes—
322C23×C4C23×C13912yes—
323C23×C4C23×C13911yescharacteristic
324C23×C4C23×C13911yescharacteristic
325C23×C4C23×C13912yes—
326C23×C4C23×C13912yes—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4D4×C13918yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4Q8×C13914yes—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—41no—
355C2×C42—41no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—41no—
365#95—41no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—21no—
371C24—21no—
372C24—22no—
373C24—22no—
374C24C2×Q8×C13912yes—
375C24C24×C13911yescharacteristic
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
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×C4C2×D4×C13914yes—
421C22×C4C2×D4×C13914yes—
422C22×C4C2×D4×C13914yes—
423C22×C4C2×Q8×C13912yes—
424C22×C4C2×Q8×C13912yes—
425C22×C4#41×C13914yes—
426C22×C4#41×C13914yes—
427C22×C4#41×C13914yes—
428C4⋊C4—216no—
429C4⋊C4—48no—
430C4⋊C4—48no—
431C4⋊C4—48no—
432C22⋊C4—44no—
433C22⋊C4—44no—
434C22⋊C4—48no—
435C22⋊C4—44no—
436C22⋊C4—48no—
437C42—44no—
438C42—44no—
439C23—22no—
440C23—22no—
441C23—22no—
442C23—24no—
443C23—24no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—41no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—41no—
459C23—41no—
460C23C22×D4×C13912yes—
461C23C22×Q8×C13911yescharacteristic
462C23C2×#41×C13912yes—
463C23C2×#41×C13912yes—
464C23C2×#41×C13912yes—
465C23H(5,𝔽2)×C13911yescharacteristic
466C23H(5,𝔽2)×C13912yes—
467C23H(5,𝔽2)×C13911yescharacteristic
468C232−1+4×C13912yes—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
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#123×C13918yes—
521C22—44no—
522C22—42no—
523C22—44no—
524C22—42no—
525C22—42no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22C2×#123×C13912yes—
531C22#532×C13912yes—
532C22#533×C13911yescharacteristic
533C22#533×C13911yescharacteristic
534C22#537×C13912yes—
535C22#539×C13912yes—
536C22#540×C13912yes—
537C22#542×C13912yes—
538C22#543×C13911yescharacteristic
539C22D42×C13911yescharacteristic
540C22#546×C13912yes—
541C22D4×Q8×C13912yes—
542C22#550×C13912yes—
543C22#551×C13912yes—
544C22#551×C13911yescharacteristic
545C22#552×C13912yes—
546C22#552×C13912yes—
547C22#554×C13912yes—
548C22#559×C13912yes—
549C22#560×C13911yescharacteristic
550C22#563×C13911yescharacteristic
551C4—28no—
552C4—42no—
553C4—44no—
554C4—44no—
555C4—44no—
556C4—42no—
557C4—82no—
558C4—82no—
559C2—82no—
560C2#2423×C13912yes—
561C2#2445×C13912yes—
562C2#2498×C13912yes—
563C2#2556×C13912yes—
564C2#2607×C13911yescharacteristic
565C2#2683×C13911yescharacteristic
566C2#2705×C13912yes—
567C2#2748×C13911yescharacteristic
568C2#2773×C13912yes—
subgroupG/H
center, socleC24×C139C24
commutator, Frattini, cosocleC24C24×C139
prime radicalC25×C139C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#387×C139C2semidirect
3. #1441×C139C2semidirect
4. #1441×C139C2semidirect
9. C4⋊#95×C139C2semidirect
284. #15649C139direct (N × H)
285. C139#15649direct (N × H)
287. C2×#387C2×C139semidirect
288. #1441C2×C139semidirect
289. #1441C2×C139semidirect
294. C4⋊#95C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1392
C2×#387×C1392
#1441×C1392
#1440×C1392
#1439×C1392
#1437×C1392
C4⋊#95×C1392
#15649139