Finite Group Databasebeta

← C139×#9520 #48004116

Subgroups — C139×#9520 #48004116

Order 35584.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3003×C139C211yesmaximal, characteristic
2#2976×C139C211yesmaximal, characteristic, complemented
3#1786×C139C211yesmaximal, characteristic, complemented
4#1783×C139C211yesmaximal, characteristic, complemented
5#1513×C139C211yesmaximal, characteristic, complemented
6#1305×C139C211yesmaximal, characteristic, complemented
7#1293×C139C211yesmaximal, characteristic, complemented
8C23×D4×C139C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C139—21no—
10#525×C139C2211yescharacteristic
11#450×C139—21no—
12#450×C139C412yescomplemented
13#447×C139—21no—
14#447×C139C412yescomplemented
15#436×C139—21no—
16#435×C139—21no—
17#435×C139—21no—
18C8×D4×C139—21no—
19#433×C139—21no—
20#418×C139—21no—
21C2×#102×C139—21no—
22C2×#102×C139—21no—
23C2×#100×C139—21no—
24C2×#100×C139—21no—
25#408×C139—21no—
26#407×C139C2211yescharacteristic
27#407×C139C2211yescharacteristic
28#407×C139C2211yescharacteristic
29C2×C22⋊C8×C139C2211yescharacteristic
30#380×C139C2211yescharacteristic
31#328×C139—21no—
32#327×C139—21no—
33C25×C139—21no—
34C2×#41×C139D411yescharacteristic
35C22×D4×C139—21no—
36C22×D4×C139—21no—
37C22×D4×C139—21no—
38C22×D4×C139—21no—
39C22×D4×C139—21no—
40C22×D4×C139—42no—
41C22×D4×C139—42no—
42C22×D4×C139C2×C412yes—
43C23×C4×C139C2311yescharacteristic
44AGL(1,ℤ/8)×C139—42no—
45AGL(1,ℤ/8)×C139—42no—
46C2×SD16×C139—22no—
47C2×D8×C139—22no—
48C2×M16×C139—21no—
49C2×M16×C139—21no—
50C2×M16×C139—21no—
51C2×M16×C139D411yescharacteristic
52C2×M16×C139D411yescharacteristic
53C22×C8×C139—21no—
54C22×C8×C139D411yescharacteristic
55C22×C8×C139D411yescharacteristic
56#123×C139—21no—
57C22⋊Q8×C139C2×C411yescharacteristic
58C22⋊Q8×C139D411yescharacteristic
59#121×C139C2×C411yescharacteristic
60#121×C139D411yescharacteristic
61#120×C139—21no—
62C4×D4×C139—21no—
63C4×D4×C139—21no—
64#117×C139D411yescharacteristic
65C2×C4⋊C4×C139—21no—
66C2×C22⋊C4×C139—21no—
67C4⋊C8×C139—21no—
68C4⋊C8×C139—21no—
69#102×C139—22no—
70#102×C139—22no—
71#102×C139—42no—
72#102×C139—42no—
73#100×C139—42no—
74#100×C139—42no—
75C22⋊C8×C139—21no—
76C22⋊C8×C139—21no—
77C22⋊C8×C139—21no—
78C22⋊C8×C139—21no—
79C22⋊C8×C139—21no—
80C22⋊C8×C139—21no—
81C22⋊C8×C139—21no—
82C22⋊C8×C139—21no—
83C22⋊C8×C139—21no—
84C22⋊C8×C139C2×C412yes—
85#97×C139—21no—
86C4×C8×C139—21no—
87#95×C139—21no—
88C24×C139—22no—
89C24×C139—44no—
90C24×C139—41no—
91C24×C139—41no—
92C24×C139—81no—
93C24×C139—81no—
94C24×C139—82no—
95C24×C139#4111yescharacteristic
96#41×C139—41no—
97#41×C139—41no—
98C2×Q8×C139C22⋊C411yescharacteristic
99C2×D4×C139—22no—
100C2×D4×C139—22no—
101C2×D4×C139—22no—
102C2×D4×C139—22no—
103C2×D4×C139—22no—
104C2×D4×C139—22no—
105C2×D4×C139—21no—
106C2×D4×C139—21no—
107C2×D4×C139—21no—
108C2×D4×C139—22no—
109C2×D4×C139—22no—
110C2×D4×C139—41no—
111C2×D4×C139—41no—
112C2×D4×C139—41no—
113C2×D4×C139—41no—
114C2×D4×C139—41no—
115C2×D4×C139—41no—
116C2×D4×C139—44no—
117C2×D4×C139—44no—
118C2×D4×C139—44no—
119C2×D4×C139—41no—
120C2×D4×C139—41no—
121C2×D4×C139C22⋊C411yescharacteristic
122C22×C4×C139—21no—
123C22×C4×C139—41no—
124C22×C4×C139—41no—
125C22×C4×C139—41no—
126C22×C4×C139C22×C411yescharacteristic
127C22×C4×C139C2×D411yescharacteristic
128C22×C4×C139C2×D411yescharacteristic
129C22×C4×C139C2×D411yescharacteristic
130C22×C4×C139C2×D411yescharacteristic
131C22×C4×C139#4111yescharacteristic
132SD16×C139—44no—
133D8×C139—44no—
134M16×C139—41no—
135M16×C139—41no—
136M16×C139—41no—
137M16×C139—41no—
138M16×C139—41no—
139M16×C139—41no—
140M16×C139—81no—
141C2×C8×C139—22no—
142C2×C8×C139—21no—
143C2×C8×C139—21no—
144C2×C8×C139—21no—
145C2×C8×C139—21no—
146C2×C8×C139—41no—
147C2×C8×C139—41no—
148C2×C8×C139—41no—
149C2×C8×C139—81no—
150C4⋊C4×C139—21no—
151C4⋊C4×C139—21no—
152C4⋊C4×C139—41no—
153C4⋊C4×C139—41no—
154C4⋊C4×C139C22⋊C411yescharacteristic
155C4⋊C4×C139C22⋊C411yescharacteristic
156C22⋊C4×C139—21no—
157C22⋊C4×C139—21no—
158C22⋊C4×C139—21no—
159C22⋊C4×C139—21no—
160C22⋊C4×C139—21no—
161C22⋊C4×C139—81no—
162C42×C139—21no—
163C23×C139—21no—
164C23×C139—21no—
165C23×C139—24no—
166C23×C139—21no—
167C23×C139—41no—
168C23×C139—41no—
169C23×C139—42no—
170C23×C139—42no—
171C23×C139—42no—
172C23×C139—42no—
173C23×C139—42no—
174C23×C139—42no—
175C23×C139—82no—
176C23×C139—82no—
177C23×C139—82no—
178C23×C139—81no—
179C23×C139—81no—
180C23×C139—82no—
181C23×C139—88no—
182C23×C139—88no—
183C23×C139—81no—
184C23×C139—81no—
185C23×C139C4×D411yescharacteristic
186C23×C139#12111yescharacteristic
187C23×C139#12311yescharacteristic
188Q8×C139—41no—
189D4×C139—24no—
190D4×C139—24no—
191D4×C139—41no—
192D4×C139—42no—
193D4×C139—42no—
194D4×C139—42no—
195D4×C139—42no—
196D4×C139—41no—
197D4×C139—41no—
198D4×C139—42no—
199D4×C139—42no—
200D4×C139—81no—
201D4×C139—81no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—21no—
206C2×C4×C139—21no—
207C2×C4×C139—21no—
208C2×C4×C139—21no—
209C2×C4×C139—21no—
210C2×C4×C139—21no—
211C2×C4×C139—41no—
212C2×C4×C139—41no—
213C2×C4×C139—41no—
214C2×C4×C139—41no—
215C2×C4×C139—41no—
216C2×C4×C139—81no—
217C2×C4×C139—81no—
218C2×C4×C139—81no—
219C2×C4×C139C2×C22⋊C411yescharacteristic
220C2×C4×C139C4×D411yescharacteristic
221C2×C4×C139#12011yescharacteristic
222C2×C4×C139#12111yescharacteristic
223C8×C139—42no—
224C8×C139—41no—
225C8×C139—41no—
226C8×C139—41no—
227C8×C139—41no—
228C8×C139—81no—
229C22×C139—21no—
230C22×C139—21no—
231C22×C139—21no—
232C22×C139—21no—
233C22×C139—21no—
234C22×C139—21no—
235C22×C139—21no—
236C22×C139—21no—
237C22×C139—42no—
238C22×C139—42no—
239C22×C139—41no—
240C22×C139—44no—
241C22×C139—41no—
242C22×C139—41no—
243C22×C139—82no—
244C22×C139—82no—
245C22×C139—82no—
246C22×C139—82no—
247C22×C139—84no—
248C22×C139—84no—
249C22×C139—84no—
250C22×C139—84no—
251C22×C139—82no—
252C22×C139—82no—
253C22×C139#38611yescharacteristic
254C22×C139#47111yescharacteristic
255C22×C139#47211yescharacteristic
256C4×C139—21no—
257C4×C139—21no—
258C4×C139—21no—
259C4×C139—41no—
260C4×C139—41no—
261C4×C139—41no—
262C4×C139—161no—
263C4×C139B(4,𝔽2)11yescharacteristic
264C4×C139B(4,𝔽2)11yescharacteristic
265C2×C139—21no—
266C2×C139—21no—
267C2×C139—41no—
268C2×C139—41no—
269C2×C139—81no—
270C2×C139—84no—
271C2×C139#188911yescharacteristic
272C2×C139#190311yescharacteristic
273C2×C139#190711yescharacteristic
274#9520C13911yesmaximal, characteristic, direct product factor, Sylow
275C139#952011yescharacteristic, direct product factor, Sylow
276#3003C2×C13911yescharacteristic
277#2976C2×C13911yescharacteristic, complemented
278#1786C2×C13911yescharacteristic, complemented
279#1783C2×C13911yescharacteristic, complemented
280#1513C2×C13911yescharacteristic, complemented
281#1305C2×C13911yescharacteristic, complemented
282#1293C2×C13911yescharacteristic, complemented
283C23×D4C22×C13911yescharacteristic
284C2×AGL(1,ℤ/8)—21no—
285#525C22×C13911yescharacteristic
286#450—21no—
287#450C4×C13912yescomplemented
288#447—21no—
289#447C4×C13912yescomplemented
290#436—21no—
291#435—21no—
292#435—21no—
293C8×D4—21no—
294#433—21no—
295#418—21no—
296C2×#102—21no—
297C2×#102—21no—
298C2×#100—21no—
299C2×#100—21no—
300#408—21no—
301#407C22×C13911yescharacteristic
302#407C22×C13911yescharacteristic
303#407C22×C13911yescharacteristic
304C2×C22⋊C8C22×C13911yescharacteristic
305#380C22×C13911yescharacteristic
306#328—21no—
307#327—21no—
308C25—21no—
309C2×#41D4×C13911yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C13912yes—
318C23×C4C23×C13911yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C13911yescharacteristic
327C2×M16D4×C13911yescharacteristic
328C22×C8—21no—
329C22×C8D4×C13911yescharacteristic
330C22×C8D4×C13911yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C13911yescharacteristic
333C22⋊Q8D4×C13911yescharacteristic
334#121C2×C4×C13911yescharacteristic
335#121D4×C13911yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C13911yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C13912yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C13911yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C13911yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C13911yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C13911yescharacteristic
402C22×C4C2×D4×C13911yescharacteristic
403C22×C4C2×D4×C13911yescharacteristic
404C22×C4C2×D4×C13911yescharacteristic
405C22×C4C2×D4×C13911yescharacteristic
406C22×C4#41×C13911yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C13911yescharacteristic
430C4⋊C4C22⋊C4×C13911yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C13911yescharacteristic
461C23#121×C13911yescharacteristic
462C23#123×C13911yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C13911yescharacteristic
495C2×C4C4×D4×C13911yescharacteristic
496C2×C4#120×C13911yescharacteristic
497C2×C4#121×C13911yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22#386×C13911yescharacteristic
529C22#471×C13911yescharacteristic
530C22#472×C13911yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4B(4,𝔽2)×C13911yescharacteristic
539C4B(4,𝔽2)×C13911yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2#1889×C13911yescharacteristic
547C2#1903×C13911yescharacteristic
548C2#1907×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radical#3003×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. #2976×C139C2semidirect
3. #1786×C139C2semidirect
4. #1783×C139C2semidirect
5. #1513×C139C2semidirect
6. #1305×C139C2semidirect
7. #1293×C139C2semidirect
12. #450×C139C4semidirect
14. #447×C139C4semidirect
274. #9520C139direct (N × H)
275. C139#9520direct (N × H)
277. #2976C2×C139semidirect
278. #1786C2×C139semidirect
279. #1783C2×C139semidirect
280. #1513C2×C139semidirect
281. #1305C2×C139semidirect
282. #1293C2×C139semidirect
287. #450C4×C139semidirect
289. #447C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3003×C1392
#2976×C1392
#1786×C1392
#1783×C1392
#1513×C1392
#1305×C1392
#1293×C1392
#9520139