Finite Group Databasebeta

← C139×#9259 #48003855

Subgroups — C139×#9259 #48003855

Order 35584.

966 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
1C2×#447×C139C211yesmaximal, characteristic
2D4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
3#1964×C139C211yesmaximal, characteristic, complemented
4#1786×C139C211yesmaximal, characteristic, complemented
5#1519×C139C211yesmaximal, characteristic, complemented
6#1289×C139C211yesmaximal, characteristic, complemented
7#1282×C139C211yesmaximal, characteristic, complemented
8C23×D4×C139C2211yescharacteristic
9C22×D8×C139C412yescomplemented
10C2×#121×C139C2211yescharacteristic
11C2×C4×D4×C139—21no—
12C22×C22⋊C4×C139—21no—
13#447×C139—21no—
14#447×C139—22no—
15#447×C139—21no—
16C2×#102×C139—22no—
17C2×#102×C139C412yescomplemented
18C2×#99×C139—21no—
19C2×#99×C139—21no—
20C2×C22⋊C8×C139C2211yescharacteristic
21C2×C22⋊C8×C139C2211yescharacteristic
22#390×C139—21no—
23#386×C139—22no—
24#380×C139C2211yescharacteristic
25#380×C139C2211yescharacteristic
26#379×C139—21no—
27C4×C22⋊C4×C139C2211yescharacteristic
28#327×C139—22no—
29C25×C139—21no—
30C22×D4×C139—21no—
31C22×D4×C139—21no—
32C22×D4×C139—21no—
33C22×D4×C139—21no—
34C22×D4×C139—44no—
35C22×D4×C139C2×C412yes—
36C22×D4×C139C2×C411yescharacteristic, complemented
37C22×D4×C139D411yescharacteristic
38C22×D4×C139D412yes—
39C22×D4×C139D411yescharacteristic
40C23×C4×C139—22no—
41C23×C4×C139C2311yescharacteristic
42C2×D8×C139—22no—
43C2×D8×C139—22no—
44C2×D8×C139—44no—
45C22×C8×C139—21no—
46C22×C8×C139C2×C412yescomplemented
47#121×C139—21no—
48#121×C139—21no—
49#121×C139—21no—
50#121×C139—21no—
51C4×D4×C139—44no—
52C2×C4⋊C4×C139—21no—
53C2×C4⋊C4×C139—21no—
54C2×C4⋊C4×C139C2×C411yescharacteristic, complemented
55C2×C22⋊C4×C139—22no—
56C2×C22⋊C4×C139—22no—
57C2×C22⋊C4×C139—21no—
58C2×C22⋊C4×C139—21no—
59C2×C22⋊C4×C139—21no—
60C2×C22⋊C4×C139—22no—
61C2×C22⋊C4×C139—42no—
62C2×C22⋊C4×C139—42no—
63C2×C22⋊C4×C139D411yescharacteristic
64C2×C22⋊C4×C139D411yescharacteristic
65C2×C42×C139—21no—
66#102×C139—22no—
67#102×C139—22no—
68#102×C139—44no—
69#99×C139—42no—
70#99×C139—42no—
71C22⋊C8×C139—21no—
72C22⋊C8×C139—21no—
73C22⋊C8×C139—21no—
74C22⋊C8×C139—21no—
75#95×C139—21no—
76#95×C139—21no—
77#95×C139D412yes—
78C24×C139—21no—
79C24×C139—21no—
80C24×C139—22no—
81C24×C139—22no—
82C24×C139—21no—
83C24×C139—44no—
84C24×C139—41no—
85C24×C139—41no—
86C24×C139—41no—
87C24×C139—41no—
88C24×C139—82no—
89C24×C139C2×D411yescharacteristic
90C2×D4×C139—24no—
91C2×D4×C139—24no—
92C2×D4×C139—24no—
93C2×D4×C139—21no—
94C2×D4×C139—22no—
95C2×D4×C139—21no—
96C2×D4×C139—22no—
97C2×D4×C139—21no—
98C2×D4×C139—21no—
99C2×D4×C139—42no—
100C2×D4×C139—42no—
101C2×D4×C139—42no—
102C2×D4×C139—42no—
103C2×D4×C139—44no—
104C2×D4×C139—44no—
105C2×D4×C139—44no—
106C2×D4×C139—41no—
107C2×D4×C139—41no—
108C2×D4×C139—41no—
109C2×D4×C139—41no—
110C2×D4×C139—41no—
111C2×D4×C139—41no—
112C2×D4×C139C22⋊C412yes—
113C2×D4×C139C22⋊C412yes—
114C22×C4×C139—21no—
115C22×C4×C139—21no—
116C22×C4×C139—21no—
117C22×C4×C139—22no—
118C22×C4×C139—42no—
119C22×C4×C139—44no—
120C22×C4×C139—44no—
121C22×C4×C139—41no—
122C22×C4×C139—82no—
123C22×C4×C139C22×C411yescharacteristic
124C22×C4×C139C2×D411yescharacteristic
125C22×C4×C139C2×D411yescharacteristic
126C22×C4×C139C2×D411yescharacteristic
127C22×C4×C139#4111yescharacteristic
128C22×C4×C139#4111yescharacteristic
129D8×C139—44no—
130D8×C139—44no—
131C2×C8×C139—22no—
132C2×C8×C139—42no—
133C2×C8×C139—42no—
134C2×C8×C139—41no—
135C4⋊C4×C139—21no—
136C4⋊C4×C139—21no—
137C4⋊C4×C139—42no—
138C4⋊C4×C139—42no—
139C22⋊C4×C139—21no—
140C22⋊C4×C139—21no—
141C22⋊C4×C139—21no—
142C22⋊C4×C139—44no—
143C22⋊C4×C139—44no—
144C22⋊C4×C139—41no—
145C22⋊C4×C139—41no—
146C22⋊C4×C139—41no—
147C22⋊C4×C139—41no—
148C22⋊C4×C139—41no—
149C22⋊C4×C139—41no—
150C22⋊C4×C139—82no—
151C22⋊C4×C139D812yescomplemented
152C42×C139—42no—
153C23×C139—24no—
154C23×C139—22no—
155C23×C139—22no—
156C23×C139—41no—
157C23×C139—41no—
158C23×C139—44no—
159C23×C139—44no—
160C23×C139—42no—
161C23×C139—42no—
162C23×C139—42no—
163C23×C139—41no—
164C23×C139—41no—
165C23×C139—42no—
166C23×C139—42no—
167C23×C139—41no—
168C23×C139—41no—
169C23×C139—42no—
170C23×C139—42no—
171C23×C139—41no—
172C23×C139—41no—
173C23×C139—41no—
174C23×C139—82no—
175C23×C139—82no—
176C23×C139—81no—
177C23×C139—81no—
178C23×C139—84no—
179C23×C139—84no—
180C23×C139—84no—
181C23×C139—84no—
182C23×C139C4×D411yescharacteristic
183C23×C139#12011yescharacteristic
184C23×C139#12111yescharacteristic
185C23×C139C2×D811yescharacteristic
186C23×C139#13511yescharacteristic
187C23×C139AGL(1,ℤ/8)11yescharacteristic
188C23×C139AGL(1,ℤ/8)11yescharacteristic
189D4×C139—24no—
190D4×C139—22no—
191D4×C139—22no—
192D4×C139—22no—
193D4×C139—44no—
194D4×C139—44no—
195D4×C139—42no—
196D4×C139—42no—
197D4×C139—81no—
198D4×C139—81no—
199D4×C139—81no—
200D4×C139—81no—
201D4×C139—81no—
202D4×C139#9914yescomplemented
203C2×C4×C139—22no—
204C2×C4×C139—22no—
205C2×C4×C139—22no—
206C2×C4×C139—22no—
207C2×C4×C139—41no—
208C2×C4×C139—41no—
209C2×C4×C139—41no—
210C2×C4×C139—41no—
211C2×C4×C139—41no—
212C2×C4×C139—41no—
213C2×C4×C139—42no—
214C2×C4×C139—41no—
215C2×C4×C139—42no—
216C2×C4×C139—41no—
217C2×C4×C139—41no—
218C2×C4×C139—41no—
219C2×C4×C139—42no—
220C2×C4×C139—41no—
221C2×C4×C139—88no—
222C2×C4×C139—81no—
223C2×C4×C139—81no—
224C2×C4×C139—81no—
225C2×C4×C139C2×C22⋊C411yescharacteristic
226C2×C4×C139C4×D411yescharacteristic
227C2×C4×C139#12111yescharacteristic
228C2×C4×C139#12311yescharacteristic
229C8×C139—42no—
230C8×C139—81no—
231C22×C139—21no—
232C22×C139—21no—
233C22×C139—21no—
234C22×C139—21no—
235C22×C139—21no—
236C22×C139—21no—
237C22×C139—24no—
238C22×C139—41no—
239C22×C139—41no—
240C22×C139—41no—
241C22×C139—41no—
242C22×C139—44no—
243C22×C139—44no—
244C22×C139—42no—
245C22×C139—42no—
246C22×C139—42no—
247C22×C139—42no—
248C22×C139—42no—
249C22×C139—84no—
250C22×C139—84no—
251C22×C139—84no—
252C22×C139—84no—
253C22×C139—82no—
254C22×C139—82no—
255C22×C139—81no—
256C22×C139—81no—
257C22×C139—81no—
258C22×C139—161no—
259C22×C139—161no—
260C22×C139#38611yescharacteristic
261C22×C139C4×D811yescharacteristic
262C22×C139#44211yescharacteristic
263C22×C139#44711yescharacteristic
264C22×C139#44911yescharacteristic
265C22×C139#45911yescharacteristic
266C22×C139#46311yescharacteristic
267C4×C139—21no—
268C4×C139—21no—
269C4×C139—21no—
270C4×C139—42no—
271C4×C139—81no—
272C4×C139—82no—
273C4×C139—81no—
274C4×C139—161no—
275C4×C139C2×#9912yes—
276C2×C139—21no—
277C2×C139—21no—
278C2×C139—21no—
279C2×C139—21no—
280C2×C139—21no—
281C2×C139—21no—
282C2×C139—44no—
283C2×C139—82no—
284C2×C139—161no—
285C2×C139#187911yescharacteristic
286C2×C139#189811yescharacteristic
287C2×C139#190411yescharacteristic
288#9259C13911yesmaximal, characteristic, direct product factor, Sylow
289C139#925911yescharacteristic, direct product factor, Sylow
290C2×#447C2×C13911yescharacteristic
291D4×C22⋊C4C2×C13911yescharacteristic, complemented
292#1964C2×C13911yescharacteristic, complemented
293#1786C2×C13911yescharacteristic, complemented
294#1519C2×C13911yescharacteristic, complemented
295#1289C2×C13911yescharacteristic, complemented
296#1282C2×C13911yescharacteristic, complemented
297C23×D4C22×C13911yescharacteristic
298C22×D8C4×C13912yescomplemented
299C2×#121C22×C13911yescharacteristic
300C2×C4×D4—21no—
301C22×C22⋊C4—21no—
302#447—21no—
303#447—22no—
304#447—21no—
305C2×#102—22no—
306C2×#102C4×C13912yescomplemented
307C2×#99—21no—
308C2×#99—21no—
309C2×C22⋊C8C22×C13911yescharacteristic
310C2×C22⋊C8C22×C13911yescharacteristic
311#390—21no—
312#386—22no—
313#380C22×C13911yescharacteristic
314#380C22×C13911yescharacteristic
315#379—21no—
316C4×C22⋊C4C22×C13911yescharacteristic
317#327—22no—
318C25—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—44no—
324C22×D4C2×C4×C13912yes—
325C22×D4C2×C4×C13911yescharacteristic, complemented
326C22×D4D4×C13911yescharacteristic
327C22×D4D4×C13912yes—
328C22×D4D4×C13911yescharacteristic
329C23×C4—22no—
330C23×C4C23×C13911yescharacteristic
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—44no—
334C22×C8—21no—
335C22×C8C2×C4×C13912yescomplemented
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C2×C4×C13911yescharacteristic, complemented
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4D4×C13911yescharacteristic
353C2×C22⋊C4D4×C13911yescharacteristic
354C2×C42—21no—
355#102—22no—
356#102—22no—
357#102—44no—
358#99—42no—
359#99—42no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364#95—21no—
365#95—21no—
366#95D4×C13912yes—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—44no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—82no—
378C24C2×D4×C13911yescharacteristic
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4C22⋊C4×C13912yes—
402C2×D4C22⋊C4×C13912yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—44no—
409C22×C4—44no—
410C22×C4—41no—
411C22×C4—82no—
412C22×C4C22×C4×C13911yescharacteristic
413C22×C4C2×D4×C13911yescharacteristic
414C22×C4C2×D4×C13911yescharacteristic
415C22×C4C2×D4×C13911yescharacteristic
416C22×C4#41×C13911yescharacteristic
417C22×C4#41×C13911yescharacteristic
418D8—44no—
419D8—44no—
420C2×C8—22no—
421C2×C8—42no—
422C2×C8—42no—
423C2×C8—41no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—44no—
432C22⋊C4—44no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—82no—
440C22⋊C4D8×C13912yescomplemented
441C42—42no—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—44no—
448C23—44no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—41no—
453C23—41no—
454C23—42no—
455C23—42no—
456C23—41no—
457C23—41no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—82no—
464C23—82no—
465C23—81no—
466C23—81no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23C4×D4×C13911yescharacteristic
472C23#120×C13911yescharacteristic
473C23#121×C13911yescharacteristic
474C23C2×D8×C13911yescharacteristic
475C23#135×C13911yescharacteristic
476C23AGL(1,ℤ/8)×C13911yescharacteristic
477C23AGL(1,ℤ/8)×C13911yescharacteristic
478D4—24no—
479D4—22no—
480D4—22no—
481D4—22no—
482D4—44no—
483D4—44no—
484D4—42no—
485D4—42no—
486D4—81no—
487D4—81no—
488D4—81no—
489D4—81no—
490D4—81no—
491D4#99×C13914yescomplemented
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—88no—
511C2×C4—81no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4C2×C22⋊C4×C13911yescharacteristic
515C2×C4C4×D4×C13911yescharacteristic
516C2×C4#121×C13911yescharacteristic
517C2×C4#123×C13911yescharacteristic
518C8—42no—
519C8—81no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—24no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—44no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—84no—
539C22—84no—
540C22—84no—
541C22—84no—
542C22—82no—
543C22—82no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—161no—
548C22—161no—
549C22#386×C13911yescharacteristic
550C22C4×D8×C13911yescharacteristic
551C22#442×C13911yescharacteristic
552C22#447×C13911yescharacteristic
553C22#449×C13911yescharacteristic
554C22#459×C13911yescharacteristic
555C22#463×C13911yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—42no—
560C4—82no—
561C4—81no—
562C4—81no—
563C4—161no—
564C4C2×#99×C13912yes—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2—21no—
571C2—44no—
572C2—82no—
573C2—161no—
574C2#1879×C13911yescharacteristic
575C2#1898×C13911yescharacteristic
576C2#1904×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#447×C139C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C22⋊C4×C139C2semidirect
3. #1964×C139C2semidirect
4. #1786×C139C2semidirect
5. #1519×C139C2semidirect
6. #1289×C139C2semidirect
7. #1282×C139C2semidirect
9. C22×D8×C139C4semidirect
17. C2×#102×C139C4semidirect
36. C22×D4×C139C2×C4semidirect
46. C22×C8×C139C2×C4semidirect
54. C2×C4⋊C4×C139C2×C4semidirect
151. C22⋊C4×C139D8semidirect
202. D4×C139#99semidirect
288. #9259C139direct (N × H)
289. C139#9259direct (N × H)
291. D4×C22⋊C4C2×C139semidirect
292. #1964C2×C139semidirect
293. #1786C2×C139semidirect
294. #1519C2×C139semidirect
295. #1289C2×C139semidirect
296. #1282C2×C139semidirect
298. C22×D8C4×C139semidirect
306. C2×#102C4×C139semidirect
325. C22×D4C2×C4×C139semidirect
335. C22×C8C2×C4×C139semidirect
343. C2×C4⋊C4C2×C4×C139semidirect
440. C22⋊C4D8×C139semidirect
491. D4#99×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1392
D4×C22⋊C4×C1392
#1964×C1392
#1786×C1392
#1519×C1392
#1289×C1392
#1282×C1392
#9259139