Finite Group Databasebeta

← C139×#15636 #48010232

Subgroups — C139×#15636 #48010232

Order 35584.

1542 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C139C212yesmaximal
2C2×#391×C139C212yesmaximal, complemented
3#1446×C139C212yesmaximal, complemented
4#1443×C139C212yesmaximal, complemented
5#1440×C139C211yesmaximal, characteristic
6#1439×C139C212yesmaximal
7#1437×C139C211yesmaximal, characteristic
8#1437×C139C211yesmaximal, characteristic
9#1436×C139C212yesmaximal, complemented
10C23×Q8×C139C2212yes—
11C22×C4⋊C4×C139C2212yes—
12C22×C22⋊C4×C139C2212yes—
13C22×C22⋊C4×C139C2211yescharacteristic
14C22×C22⋊C4×C139C2212yes—
15C22×C22⋊C4×C139C2211yescharacteristic
16C22×C22⋊C4×C139C2211yescharacteristic
17C22×C42×C139C2211yescharacteristic
18C22×C42×C139C2211yescharacteristic
19#393×C139—28no—
20#391×C139—28no—
21C2×#95×C139C2212yes—
22C2×#95×C139C2212yes—
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
34C22×Q8×C139—24no—
35C22×Q8×C139—24no—
36C22×Q8×C139—24no—
37C22×Q8×C139—24no—
38C22×Q8×C139—24no—
39C22×Q8×C139—42no—
40C22×Q8×C139—42no—
41C23×C4×C139C2312yes—
42C23×C4×C139C2312yes—
43C23×C4×C139C2312yes—
44C23×C4×C139C2312yes—
45C23×C4×C139C2311yescharacteristic
46C23×C4×C139C2311yescharacteristic
47C23×C4×C139C2312yes—
48C23×C4×C139C2312yes—
49C2×C4⋊C4×C139—24no—
50C2×C4⋊C4×C139—24no—
51C2×C4⋊C4×C139—42no—
52C2×C22⋊C4×C139—24no—
53C2×C22⋊C4×C139—24no—
54C2×C22⋊C4×C139—24no—
55C2×C22⋊C4×C139—24no—
56C2×C22⋊C4×C139—24no—
57C2×C22⋊C4×C139—24no—
58C2×C22⋊C4×C139—41no—
59C2×C22⋊C4×C139—41no—
60C2×C22⋊C4×C139—42no—
61C2×C22⋊C4×C139—41no—
62C2×C22⋊C4×C139—41no—
63C2×C22⋊C4×C139—42no—
64C2×C22⋊C4×C139Q814yescomplemented
65C2×C42×C139—24no—
66C2×C42×C139—41no—
67C2×C42×C139—41no—
68C2×C42×C139—42no—
69#95×C139—24no—
70#95×C139—24no—
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—41no—
79#95×C139—41no—
80#95×C139D418yes—
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
91C2×Q8×C139—216no—
92C2×Q8×C139—48no—
93C2×Q8×C139—48no—
94C2×Q8×C139—48no—
95C2×Q8×C139—48no—
96C2×Q8×C139—48no—
97C2×Q8×C139—48no—
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—22no—
110C22×C4×C139—22no—
111C22×C4×C139—22no—
112C22×C4×C139—22no—
113C22×C4×C139—22no—
114C22×C4×C139—22no—
115C22×C4×C139—22no—
116C22×C4×C139—21no—
117C22×C4×C139—21no—
118C22×C4×C139—22no—
119C22×C4×C139—22no—
120C22×C4×C139—21no—
121C22×C4×C139—21no—
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×C139C2×D414yes—
143C22×C4×C139C2×D414yes—
144C22×C4×C139C2×D414yes—
145C22×C4×C139C2×Q812yes—
146C22×C4×C139C2×Q812yes—
147C22×C4×C139#4114yes—
148C22×C4×C139#4114yes—
149C22×C4×C139#4114yes—
150C4⋊C4×C139—48no—
151C22⋊C4×C139—44no—
152C22⋊C4×C139—44no—
153C22⋊C4×C139—48no—
154C22⋊C4×C139—44no—
155C22⋊C4×C139—48no—
156C42×C139—44no—
157C42×C139—44no—
158C23×C139—22no—
159C23×C139—22no—
160C23×C139—22no—
161C23×C139—24no—
162C23×C139—24no—
163C23×C139—42no—
164C23×C139—42no—
165C23×C139—42no—
166C23×C139—42no—
167C23×C139—42no—
168C23×C139—42no—
169C23×C139—41no—
170C23×C139—42no—
171C23×C139—42no—
172C23×C139—42no—
173C23×C139—42no—
174C23×C139—42no—
175C23×C139—42no—
176C23×C139—41no—
177C23×C139—41no—
178C23×C139—41no—
179C23×C139C22×D412yes—
180C23×C139C22×Q811yescharacteristic
181C23×C139C2×#4112yes—
182C23×C139C2×#4112yes—
183C23×C139C2×#4112yes—
184C23×C139H(5,𝔽2)11yescharacteristic
185C23×C139H(5,𝔽2)11yescharacteristic
186C23×C139H(5,𝔽2)12yes—
187C23×C1392−1+412yes—
188Q8×C139—432no—
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—24no—
201C2×C4×C139—24no—
202C2×C4×C139—24no—
203C2×C4×C139—24no—
204C2×C4×C139—24no—
205C2×C4×C139—24no—
206C2×C4×C139—24no—
207C2×C4×C139—24no—
208C2×C4×C139—42no—
209C2×C4×C139—42no—
210C2×C4×C139—42no—
211C2×C4×C139—42no—
212C2×C4×C139—42no—
213C2×C4×C139—42no—
214C2×C4×C139—42no—
215C2×C4×C139—42no—
216C2×C4×C139—41no—
217C2×C4×C139—42no—
218C2×C4×C139—42no—
219C2×C4×C139—42no—
220C2×C4×C139—42no—
221C2×C4×C139—42no—
222C2×C4×C139—41no—
223C2×C4×C139—42no—
224C2×C4×C139—41no—
225C2×C4×C139—41no—
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#12418yes—
241C22×C139—42no—
242C22×C139—42no—
243C22×C139—44no—
244C22×C139—44no—
245C22×C139—42no—
246C22×C139—82no—
247C22×C139—82no—
248C22×C139—82no—
249C22×C139—82no—
250C22×C139#52512yes—
251C22×C139C2×#12412yes—
252C22×C139#53311yescharacteristic
253C22×C139#53311yescharacteristic
254C22×C139#53712yes—
255C22×C139#53812yes—
256C22×C139#54212yes—
257C22×C139#54212yes—
258C22×C139#54311yescharacteristic
259C22×C139D4211yescharacteristic
260C22×C139#54612yes—
261C22×C139#54612yes—
262C22×C139D4×Q812yes—
263C22×C139#55112yes—
264C22×C139#55412yes—
265C22×C139#55612yes—
266C22×C139#55612yes—
267C22×C139#55911yescharacteristic
268C22×C139#55912yes—
269C22×C139H(3,𝔽4)11yescharacteristic
270C22×C139#56311yescharacteristic
271C4×C139—28no—
272C4×C139—42no—
273C4×C139—44no—
274C4×C139—44no—
275C4×C139—44no—
276C4×C139—42no—
277C4×C139—82no—
278C4×C139—82no—
279C2×C139—82no—
280C2×C139#246512yes—
281C2×C139#247212yes—
282C2×C139#249212yes—
283C2×C139#259212yes—
284C2×C139#260711yescharacteristic
285C2×C139#268311yescharacteristic
286C2×C139#271212yes—
287C2×C139#275912yes—
288C2×C139#280411yescharacteristic
289#15636C13911yesmaximal, characteristic, direct product factor, Sylow
290C139#1563611yescharacteristic, direct product factor, Sylow
291C2×#393C2×C13912yes—
292C2×#391C2×C13912yescomplemented
293#1446C2×C13912yescomplemented
294#1443C2×C13912yescomplemented
295#1440C2×C13911yescharacteristic
296#1439C2×C13912yes—
297#1437C2×C13911yescharacteristic
298#1437C2×C13911yescharacteristic
299#1436C2×C13912yescomplemented
300C23×Q8C22×C13912yes—
301C22×C4⋊C4C22×C13912yes—
302C22×C22⋊C4C22×C13912yes—
303C22×C22⋊C4C22×C13911yescharacteristic
304C22×C22⋊C4C22×C13912yes—
305C22×C22⋊C4C22×C13911yescharacteristic
306C22×C22⋊C4C22×C13911yescharacteristic
307C22×C42C22×C13911yescharacteristic
308C22×C42C22×C13911yescharacteristic
309#393—28no—
310#391—28no—
311C2×#95C22×C13912yes—
312C2×#95C22×C13912yes—
313C2×#95C22×C13912yes—
314C2×#95C22×C13912yes—
315C2×#95C22×C13912yes—
316C2×#95C22×C13912yes—
317C2×#95C22×C13912yes—
318C2×#95C22×C13912yes—
319C2×#95C22×C13912yes—
320C2×#95C22×C13911yescharacteristic
321C2×#95C22×C13911yescharacteristic
322C2×#95C22×C13912yes—
323C25C23×C13911yescharacteristic
324C22×Q8—24no—
325C22×Q8—24no—
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—24no—
329C22×Q8—42no—
330C22×Q8—42no—
331C23×C4C23×C13912yes—
332C23×C4C23×C13912yes—
333C23×C4C23×C13912yes—
334C23×C4C23×C13912yes—
335C23×C4C23×C13911yescharacteristic
336C23×C4C23×C13911yescharacteristic
337C23×C4C23×C13912yes—
338C23×C4C23×C13912yes—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—42no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4Q8×C13914yescomplemented
355C2×C42—24no—
356C2×C42—41no—
357C2×C42—41no—
358C2×C42—42no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—42no—
367#95—42no—
368#95—41no—
369#95—41no—
370#95D4×C13918yes—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—21no—
376C24—21no—
377C24—22no—
378C24—22no—
379C24C2×Q8×C13912yes—
380C24C24×C13911yescharacteristic
381C2×Q8—216no—
382C2×Q8—48no—
383C2×Q8—48no—
384C2×Q8—48no—
385C2×Q8—48no—
386C2×Q8—48no—
387C2×Q8—48no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
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—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
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×C4C2×D4×C13914yes—
433C22×C4C2×D4×C13914yes—
434C22×C4C2×D4×C13914yes—
435C22×C4C2×Q8×C13912yes—
436C22×C4C2×Q8×C13912yes—
437C22×C4#41×C13914yes—
438C22×C4#41×C13914yes—
439C22×C4#41×C13914yes—
440C4⋊C4—48no—
441C22⋊C4—44no—
442C22⋊C4—44no—
443C22⋊C4—48no—
444C22⋊C4—44no—
445C22⋊C4—48no—
446C42—44no—
447C42—44no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—24no—
452C23—24no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—41no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—41no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23C22×D4×C13912yes—
470C23C22×Q8×C13911yescharacteristic
471C23C2×#41×C13912yes—
472C23C2×#41×C13912yes—
473C23C2×#41×C13912yes—
474C23H(5,𝔽2)×C13911yescharacteristic
475C23H(5,𝔽2)×C13911yescharacteristic
476C23H(5,𝔽2)×C13912yes—
477C232−1+4×C13912yes—
478Q8—432no—
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—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
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#124×C13918yes—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—44no—
535C22—44no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22—82no—
540C22#525×C13912yes—
541C22C2×#124×C13912yes—
542C22#533×C13911yescharacteristic
543C22#533×C13911yescharacteristic
544C22#537×C13912yes—
545C22#538×C13912yes—
546C22#542×C13912yes—
547C22#542×C13912yes—
548C22#543×C13911yescharacteristic
549C22D42×C13911yescharacteristic
550C22#546×C13912yes—
551C22#546×C13912yes—
552C22D4×Q8×C13912yes—
553C22#551×C13912yes—
554C22#554×C13912yes—
555C22#556×C13912yes—
556C22#556×C13912yes—
557C22#559×C13911yescharacteristic
558C22#559×C13912yes—
559C22H(3,𝔽4)×C13911yescharacteristic
560C22#563×C13911yescharacteristic
561C4—28no—
562C4—42no—
563C4—42no—
564C4—44no—
565C4—44no—
566C4—44no—
567C4—82no—
568C4—82no—
569C2—82no—
570C2#2465×C13912yes—
571C2#2472×C13912yes—
572C2#2492×C13912yes—
573C2#2592×C13912yes—
574C2#2607×C13911yescharacteristic
575C2#2683×C13911yescharacteristic
576C2#2712×C13912yes—
577C2#2759×C13912yes—
578C2#2804×C13911yescharacteristic
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×#391×C139C2semidirect
3. #1446×C139C2semidirect
4. #1443×C139C2semidirect
9. #1436×C139C2semidirect
64. C2×C22⋊C4×C139Q8semidirect
289. #15636C139direct (N × H)
290. C139#15636direct (N × H)
292. C2×#391C2×C139semidirect
293. #1446C2×C139semidirect
294. #1443C2×C139semidirect
299. #1436C2×C139semidirect
354. C2×C22⋊C4Q8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1392
C2×#391×C1392
#1446×C1392
#1443×C1392
#1440×C1392
#1439×C1392
#1437×C1392
#1436×C1392
#15636139