Finite Group Databasebeta

← C139×#8511 #48003107

Subgroups — C139×#8511 #48003107

Order 35584.

728 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#3561×C139C211yesmaximal, characteristic
2#1986×C139C211yesmaximal, characteristic, complemented
3#1983×C139C211yesmaximal, characteristic, complemented
4#1552×C139C211yesmaximal, characteristic, complemented
5#1527×C139C211yesmaximal, characteristic, complemented
6#1509×C139C211yesmaximal, characteristic, complemented
7#1483×C139C211yesmaximal, characteristic, complemented
8#563×C139C412yescomplemented
9#562×C139C412yescomplemented
10#556×C139—21no—
11#551×C139—22no—
12D4×Q8×C139—21no—
13#548×C139—21no—
14#546×C139—21no—
15#543×C139—21no—
16#542×C139—21no—
17#542×C139—22no—
18#538×C139—21no—
19#536×C139—21no—
20#533×C139C2211yescharacteristic
21#529×C139C2211yescharacteristic
22C2×#124×C139C2211yescharacteristic
23#432×C139C2211yescharacteristic
24C2×C4⋊C8×C139C2211yescharacteristic
25C2×#103×C139—21no—
26C2×#102×C139—21no—
27C4×M16×C139C2211yescharacteristic
28C4×C4⋊C4×C139C2211yescharacteristic
29#339×C139—22no—
30#332×C139—21no—
31#332×C139—21no—
32#329×C139—22no—
33#328×C139—21no—
34#327×C139—21no—
35Q8⋊C8×C139—21no—
36D4⋊C8×C139—21no—
37C2×#41×C139—21no—
38C22×Q8×C139—21no—
39C22×Q8×C139D411yescharacteristic
40C22×D4×C139D411yescharacteristic
41C2×M16×C139—21no—
42C22×C8×C139—21no—
43C4⋊Q8×C139—21no—
44C4⋊Q8×C139—22no—
45C4⋊Q8×C139D411yescharacteristic
46C4⋊Q8×C139D411yescharacteristic
47#126×C139—22no—
48#126×C139—22no—
49#126×C139—22no—
50#126×C139—21no—
51#125×C139C2×C411yescharacteristic
52#125×C139C2×C412yes—
53#124×C139—21no—
54#124×C139—22no—
55#124×C139—22no—
56#124×C139—21no—
57#124×C139—21no—
58#124×C139C2×C412yes—
59#124×C139C2×C411yescharacteristic
60#124×C139D412yes—
61#123×C139—22no—
62#123×C139—22no—
63#123×C139—21no—
64#123×C139—22no—
65#123×C139—22no—
66C22⋊Q8×C139—22no—
67C22⋊Q8×C139—22no—
68C22⋊Q8×C139—21no—
69C22⋊Q8×C139—22no—
70C22⋊Q8×C139—22no—
71C22⋊Q8×C139—22no—
72C22⋊Q8×C139—21no—
73C22⋊Q8×C139—21no—
74C22⋊Q8×C139—22no—
75C22⋊Q8×C139—22no—
76C22⋊Q8×C139D411yescharacteristic
77#121×C139—21no—
78#121×C139—22no—
79#121×C139—22no—
80#121×C139D411yescharacteristic
81#120×C139—22no—
82C4×Q8×C139—21no—
83C4×Q8×C139—21no—
84C4×Q8×C139—21no—
85C4×Q8×C139D411yescharacteristic
86C4×D4×C139—22no—
87C4×D4×C139—21no—
88C4×D4×C139—22no—
89C4×D4×C139—21no—
90C4×D4×C139D411yescharacteristic
91#117×C139—22no—
92#117×C139—21no—
93#117×C139D412yes—
94C2×C4⋊C4×C139—21no—
95C2×C22⋊C4×C139—22no—
96C2×C22⋊C4×C139—21no—
97C2×C22⋊C4×C139—21no—
98C2×C42×C139—21no—
99C2×C42×C139C2311yescharacteristic
100C4⋊C8×C139—21no—
101C4⋊C8×C139—21no—
102C4⋊C8×C139—21no—
103#103×C139—42no—
104#102×C139—42no—
105C22⋊C8×C139—21no—
106#97×C139—21no—
107#97×C139—21no—
108C4×C8×C139—21no—
109#95×C139—21no—
110C24×C139—21no—
111#41×C139—81no—
112#41×C139—81no—
113C2×Q8×C139—22no—
114C2×Q8×C139—21no—
115C2×Q8×C139—21no—
116C2×Q8×C139—21no—
117C2×Q8×C139—41no—
118C2×Q8×C139—41no—
119C2×Q8×C139—81no—
120C2×Q8×C139—81no—
121C2×Q8×C139C22⋊C411yescharacteristic
122C2×Q8×C139C22⋊C412yes—
123C2×D4×C139—21no—
124C2×D4×C139—22no—
125C2×D4×C139—22no—
126C2×D4×C139—21no—
127C2×D4×C139—41no—
128C2×D4×C139—41no—
129C2×D4×C139C22⋊C411yescharacteristic
130C2×D4×C139C22⋊C412yes—
131C22×C4×C139—22no—
132C22×C4×C139—22no—
133C22×C4×C139—22no—
134C22×C4×C139—21no—
135C22×C4×C139—21no—
136C22×C4×C139—41no—
137C22×C4×C139C2×D411yescharacteristic
138C22×C4×C139C2×D411yescharacteristic
139C22×C4×C139C2×D411yescharacteristic
140M16×C139—22no—
141M16×C139—41no—
142C2×C8×C139—41no—
143C2×C8×C139—41no—
144C2×C8×C139—41no—
145C2×C8×C139—41no—
146C2×C8×C139—41no—
147C4⋊C4×C139—22no—
148C4⋊C4×C139—22no—
149C4⋊C4×C139—22no—
150C4⋊C4×C139—22no—
151C4⋊C4×C139—21no—
152C4⋊C4×C139—21no—
153C4⋊C4×C139—22no—
154C4⋊C4×C139—22no—
155C4⋊C4×C139—21no—
156C4⋊C4×C139—21no—
157C4⋊C4×C139—21no—
158C4⋊C4×C139—21no—
159C4⋊C4×C139—22no—
160C4⋊C4×C139—41no—
161C4⋊C4×C139C22⋊C412yes—
162C4⋊C4×C139C22⋊C412yes—
163C4⋊C4×C139C22⋊C411yescharacteristic
164C4⋊C4×C139C22⋊C411yescharacteristic
165C22⋊C4×C139—22no—
166C22⋊C4×C139—22no—
167C22⋊C4×C139—22no—
168C22⋊C4×C139—22no—
169C22⋊C4×C139—22no—
170C22⋊C4×C139—21no—
171C22⋊C4×C139—22no—
172C22⋊C4×C139—22no—
173C22⋊C4×C139—22no—
174C22⋊C4×C139—21no—
175C22⋊C4×C139—21no—
176C22⋊C4×C139—22no—
177C22⋊C4×C139—22no—
178C22⋊C4×C139—21no—
179C22⋊C4×C139—21no—
180C42×C139—22no—
181C42×C139—22no—
182C42×C139—21no—
183C42×C139—42no—
184C42×C139C22×C411yescharacteristic
185C42×C139C2×D411yescharacteristic
186C42×C139C2×D411yescharacteristic
187C42×C139C2×D411yescharacteristic
188C23×C139—22no—
189C23×C139—21no—
190C23×C139—41no—
191C23×C139—41no—
192C23×C139—81no—
193C23×C139—81no—
194C23×C139#12011yescharacteristic
195Q8×C139—42no—
196Q8×C139—41no—
197Q8×C139—41no—
198Q8×C139—41no—
199Q8×C139—41no—
200Q8×C139—41no—
201Q8×C139—81no—
202Q8×C139—82no—
203D4×C139—42no—
204D4×C139—41no—
205D4×C139—41no—
206D4×C139—41no—
207D4×C139—41no—
208D4×C139—41no—
209D4×C139—82no—
210D4×C139—82no—
211C2×C4×C139—21no—
212C2×C4×C139—21no—
213C2×C4×C139—21no—
214C2×C4×C139—21no—
215C2×C4×C139—21no—
216C2×C4×C139—22no—
217C2×C4×C139—21no—
218C2×C4×C139—22no—
219C2×C4×C139—22no—
220C2×C4×C139—21no—
221C2×C4×C139—41no—
222C2×C4×C139—41no—
223C2×C4×C139—41no—
224C2×C4×C139—42no—
225C2×C4×C139—81no—
226C2×C4×C139—82no—
227C2×C4×C139—82no—
228C2×C4×C139—82no—
229C2×C4×C139—81no—
230C2×C4×C139—81no—
231C2×C4×C139C2×C22⋊C411yescharacteristic
232C2×C4×C139C2×C22⋊C411yescharacteristic
233C2×C4×C139C2×C22⋊C411yescharacteristic
234C2×C4×C139#12011yescharacteristic
235C2×C4×C139#12011yescharacteristic
236C2×C4×C139#12011yescharacteristic
237C8×C139—42no—
238C8×C139—81no—
239C8×C139—81no—
240C22×C139—21no—
241C22×C139—21no—
242C22×C139—41no—
243C22×C139—42no—
244C22×C139—41no—
245C22×C139—42no—
246C22×C139—42no—
247C22×C139—41no—
248C22×C139—161no—
249C22×C139—161no—
250C22×C139#37911yescharacteristic
251C22×C139#45411yescharacteristic
252C22×C139#45611yescharacteristic
253C4×C139—21no—
254C4×C139—21no—
255C4×C139—21no—
256C4×C139—21no—
257C4×C139—21no—
258C4×C139—41no—
259C4×C139—42no—
260C4×C139—42no—
261C4×C139—41no—
262C4×C139—41no—
263C4×C139—42no—
264C4×C139—82no—
265C4×C139#45311yescharacteristic
266C4×C139#45511yescharacteristic
267C2×C139—21no—
268C2×C139—21no—
269C2×C139—81no—
270C2×C139—82no—
271C2×C139#179211yescharacteristic
272C2×C139#179311yescharacteristic
273C2×C139#179411yescharacteristic
274#8511C13911yesmaximal, characteristic, direct product factor, Sylow
275C139#851111yescharacteristic, direct product factor, Sylow
276#3561C2×C13911yescharacteristic
277#1986C2×C13911yescharacteristic, complemented
278#1983C2×C13911yescharacteristic, complemented
279#1552C2×C13911yescharacteristic, complemented
280#1527C2×C13911yescharacteristic, complemented
281#1509C2×C13911yescharacteristic, complemented
282#1483C2×C13911yescharacteristic, complemented
283#563C4×C13912yescomplemented
284#562C4×C13912yescomplemented
285#556—21no—
286#551—22no—
287D4×Q8—21no—
288#548—21no—
289#546—21no—
290#543—21no—
291#542—21no—
292#542—22no—
293#538—21no—
294#536—21no—
295#533C22×C13911yescharacteristic
296#529C22×C13911yescharacteristic
297C2×#124C22×C13911yescharacteristic
298#432C22×C13911yescharacteristic
299C2×C4⋊C8C22×C13911yescharacteristic
300C2×#103—21no—
301C2×#102—21no—
302C4×M16C22×C13911yescharacteristic
303C4×C4⋊C4C22×C13911yescharacteristic
304#339—22no—
305#332—21no—
306#332—21no—
307#329—22no—
308#328—21no—
309#327—21no—
310Q8⋊C8—21no—
311D4⋊C8—21no—
312C2×#41—21no—
313C22×Q8—21no—
314C22×Q8D4×C13911yescharacteristic
315C22×D4D4×C13911yescharacteristic
316C2×M16—21no—
317C22×C8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—22no—
320C4⋊Q8D4×C13911yescharacteristic
321C4⋊Q8D4×C13911yescharacteristic
322#126—22no—
323#126—22no—
324#126—22no—
325#126—21no—
326#125C2×C4×C13911yescharacteristic
327#125C2×C4×C13912yes—
328#124—21no—
329#124—22no—
330#124—22no—
331#124—21no—
332#124—21no—
333#124C2×C4×C13912yes—
334#124C2×C4×C13911yescharacteristic
335#124D4×C13912yes—
336#123—22no—
337#123—22no—
338#123—21no—
339#123—22no—
340#123—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—21no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8D4×C13911yescharacteristic
352#121—21no—
353#121—22no—
354#121—22no—
355#121D4×C13911yescharacteristic
356#120—22no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8D4×C13911yescharacteristic
361C4×D4—22no—
362C4×D4—21no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4D4×C13911yescharacteristic
366#117—22no—
367#117—21no—
368#117D4×C13912yes—
369C2×C4⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42C23×C13911yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378#103—42no—
379#102—42no—
380C22⋊C8—21no—
381#97—21no—
382#97—21no—
383C4×C8—21no—
384#95—21no—
385C24—21no—
386#41—81no—
387#41—81no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—81no—
395C2×Q8—81no—
396C2×Q8C22⋊C4×C13911yescharacteristic
397C2×Q8C22⋊C4×C13912yes—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4C22⋊C4×C13911yescharacteristic
405C2×D4C22⋊C4×C13912yes—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—41no—
412C22×C4C2×D4×C13911yescharacteristic
413C22×C4C2×D4×C13911yescharacteristic
414C22×C4C2×D4×C13911yescharacteristic
415M16—22no—
416M16—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—41no—
420C2×C8—41no—
421C2×C8—41no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4C22⋊C4×C13912yes—
437C4⋊C4C22⋊C4×C13912yes—
438C4⋊C4C22⋊C4×C13911yescharacteristic
439C4⋊C4C22⋊C4×C13911yescharacteristic
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C42—22no—
456C42—22no—
457C42—21no—
458C42—42no—
459C42C22×C4×C13911yescharacteristic
460C42C2×D4×C13911yescharacteristic
461C42C2×D4×C13911yescharacteristic
462C42C2×D4×C13911yescharacteristic
463C23—22no—
464C23—21no—
465C23—41no—
466C23—41no—
467C23—81no—
468C23—81no—
469C23#120×C13911yescharacteristic
470Q8—42no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—81no—
477Q8—82no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—82no—
485D4—82no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4—82no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4C2×C22⋊C4×C13911yescharacteristic
507C2×C4C2×C22⋊C4×C13911yescharacteristic
508C2×C4C2×C22⋊C4×C13911yescharacteristic
509C2×C4#120×C13911yescharacteristic
510C2×C4#120×C13911yescharacteristic
511C2×C4#120×C13911yescharacteristic
512C8—42no—
513C8—81no—
514C8—81no—
515C22—21no—
516C22—21no—
517C22—41no—
518C22—42no—
519C22—41no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—161no—
524C22—161no—
525C22#379×C13911yescharacteristic
526C22#454×C13911yescharacteristic
527C22#456×C13911yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—21no—
533C4—41no—
534C4—42no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—42no—
539C4—82no—
540C4#453×C13911yescharacteristic
541C4#455×C13911yescharacteristic
542C2—21no—
543C2—21no—
544C2—82no—
545C2—81no—
546C2#1792×C13911yescharacteristic
547C2#1793×C13911yescharacteristic
548C2#1794×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#379
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#3561×C139C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1986×C139C2semidirect
3. #1983×C139C2semidirect
4. #1552×C139C2semidirect
5. #1527×C139C2semidirect
6. #1509×C139C2semidirect
7. #1483×C139C2semidirect
8. #563×C139C4semidirect
9. #562×C139C4semidirect
274. #8511C139direct (N × H)
275. C139#8511direct (N × H)
277. #1986C2×C139semidirect
278. #1983C2×C139semidirect
279. #1552C2×C139semidirect
280. #1527C2×C139semidirect
281. #1509C2×C139semidirect
282. #1483C2×C139semidirect
283. #563C4×C139semidirect
284. #562C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3561×C1392
#1986×C1392
#1983×C1392
#1552×C1392
#1527×C1392
#1509×C1392
#1483×C1392
#8511139