Finite Group Databasebeta

← C139×#12687 #48007283

Subgroups — C139×#12687 #48007283

Order 35584.

2508 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 2508 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C139C211yesmaximal, characteristic
2C2×AΣL(1,𝔽16)×C139C214yesmaximal, complemented
3#1783×C139C211yesmaximal, characteristic, complemented
4#1781×C139C211yesmaximal, characteristic, complemented
5C26×C139C411yescharacteristic, complemented
6C23×D4×C139—21no—
7C23×D4×C139C2211yescharacteristic
8C2×#120×C139—21no—
9C2×#120×C139—21no—
10C2×#120×C139—28no—
11C2×#120×C139C412yescomplemented
12C2×#120×C139C2212yes—
13C22×C22⋊C4×C139—21no—
14C22×C22⋊C4×C139C411yescharacteristic, complemented
15C2×#100×C139—21no—
16C2×#100×C139C2212yescomplemented
17C2×#99×C139—21no—
18C2×#99×C139C2212yescomplemented
19#407×C139—21no—
20#379×C139—21no—
21AΣL(1,𝔽16)×C139—28no—
22C25×C139—21no—
23C25×C139—21no—
24C25×C139—24no—
25C25×C139—48no—
26C25×C139—42no—
27C25×C139—42no—
28C25×C139C2×C411yescharacteristic
29C25×C139C2×C412yes—
30C25×C139D411yescharacteristic
31C22×D4×C139—28no—
32C22×D4×C139—22no—
33C22×D4×C139—22no—
34C22×D4×C139—24no—
35C22×D4×C139—42no—
36C22×D4×C139—42no—
37C22×D4×C139—48no—
38C22×D4×C139C2×C411yescharacteristic
39C22×D4×C139D411yescharacteristic
40C22×D4×C139D411yescharacteristic
41C22×D4×C139C2311yescharacteristic
42C23×C4×C139—21no—
43C23×C4×C139D411yescharacteristic
44C2×M16×C139—22no—
45#120×C139—28no—
46#120×C139—28no—
47#120×C139—24no—
48#120×C139—24no—
49#120×C139—24no—
50#120×C139D418yes—
51C2×C22⋊C4×C139—28no—
52C2×C22⋊C4×C139—21no—
53C2×C22⋊C4×C139—22no—
54C2×C22⋊C4×C139—22no—
55C2×C22⋊C4×C139—24no—
56C2×C22⋊C4×C139—22no—
57C2×C22⋊C4×C139—42no—
58C2×C22⋊C4×C139C2×C412yes—
59#100×C139—24no—
60#100×C139—42no—
61#99×C139—24no—
62#99×C139—42no—
63C22⋊C8×C139—42no—
64C24×C139—24no—
65C24×C139—28no—
66C24×C139—22no—
67C24×C139—22no—
68C24×C139—22no—
69C24×C139—22no—
70C24×C139—24no—
71C24×C139—22no—
72C24×C139—22no—
73C24×C139—22no—
74C24×C139—41no—
75C24×C139—44no—
76C24×C139—48no—
77C24×C139—42no—
78C24×C139—42no—
79C24×C139—44no—
80C24×C139—42no—
81C24×C139—48no—
82C24×C139—432no—
83C24×C139—416no—
84C24×C139—42no—
85C24×C139—44no—
86C24×C139—48no—
87C24×C139—416no—
88C24×C139—432no—
89C24×C139—48no—
90C24×C139—42no—
91C24×C139—42no—
92C24×C139C22⋊C411yescharacteristic
93C24×C139C22⋊C411yescharacteristic
94C24×C139C22⋊C411yescharacteristic
95C24×C139C22⋊C414yescomplemented
96C24×C139C22×C411yescharacteristic
97C24×C139C2×D411yescharacteristic
98C2×D4×C139—28no—
99C2×D4×C139—22no—
100C2×D4×C139—22no—
101C2×D4×C139—22no—
102C2×D4×C139—22no—
103C2×D4×C139—28no—
104C2×D4×C139—22no—
105C2×D4×C139—41no—
106C2×D4×C139—41no—
107C2×D4×C139—41no—
108C2×D4×C139—41no—
109C2×D4×C139—41no—
110C2×D4×C139—41no—
111C2×D4×C139—416no—
112C2×D4×C139—48no—
113C2×D4×C139—48no—
114C2×D4×C139—432no—
115C2×D4×C139C2×D414yes—
116C22×C4×C139—24no—
117C22×C4×C139—22no—
118C22×C4×C139—22no—
119C22×C4×C139—22no—
120C22×C4×C139—41no—
121C22×C4×C139—44no—
122C22×C4×C139—42no—
123C22×C4×C139C22⋊C411yescharacteristic
124C22×C4×C139C2×D411yescharacteristic
125M16×C139—42no—
126M16×C139—42no—
127C2×C8×C139—42no—
128C22⋊C4×C139—28no—
129C22⋊C4×C139—24no—
130C22⋊C4×C139—22no—
131C22⋊C4×C139—28no—
132C22⋊C4×C139—42no—
133C22⋊C4×C139—42no—
134C22⋊C4×C139—84no—
135C22⋊C4×C139C22⋊C414yescomplemented
136C23×C139—24no—
137C23×C139—21no—
138C23×C139—21no—
139C23×C139—216no—
140C23×C139—28no—
141C23×C139—28no—
142C23×C139—21no—
143C23×C139—24no—
144C23×C139—21no—
145C23×C139—21no—
146C23×C139—21no—
147C23×C139—21no—
148C23×C139—21no—
149C23×C139—21no—
150C23×C139—21no—
151C23×C139—21no—
152C23×C139—44no—
153C23×C139—42no—
154C23×C139—48no—
155C23×C139—44no—
156C23×C139—42no—
157C23×C139—48no—
158C23×C139—48no—
159C23×C139—48no—
160C23×C139—416no—
161C23×C139—44no—
162C23×C139—48no—
163C23×C139—44no—
164C23×C139—48no—
165C23×C139—48no—
166C23×C139—416no—
167C23×C139—48no—
168C23×C139—44no—
169C23×C139—42no—
170C23×C139—42no—
171C23×C139—48no—
172C23×C139—48no—
173C23×C139—416no—
174C23×C139—416no—
175C23×C139—464no—
176C23×C139—464no—
177C23×C139—48no—
178C23×C139—416no—
179C23×C139—48no—
180C23×C139—44no—
181C23×C139—42no—
182C23×C139—42no—
183C23×C139—44no—
184C23×C139—82no—
185C23×C139—84no—
186C23×C139#9912yes—
187C23×C139#9912yes—
188C23×C139C2×C22⋊C411yescharacteristic
189C23×C139C2×C22⋊C412yes—
190C23×C139#12012yes—
191D4×C139—44no—
192D4×C139—44no—
193D4×C139—44no—
194D4×C139—416no—
195D4×C139—416no—
196D4×C139—44no—
197C2×C4×C139—21no—
198C2×C4×C139—21no—
199C2×C4×C139—21no—
200C2×C4×C139—24no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—44no—
204C2×C4×C139—48no—
205C2×C4×C139—44no—
206C2×C4×C139—82no—
207C2×C4×C139—84no—
208C2×C4×C139#12012yes—
209C8×C139—82no—
210C22×C139—24no—
211C22×C139—24no—
212C22×C139—22no—
213C22×C139—22no—
214C22×C139—22no—
215C22×C139—28no—
216C22×C139—22no—
217C22×C139—22no—
218C22×C139—22no—
219C22×C139—42no—
220C22×C139—42no—
221C22×C139—42no—
222C22×C139—42no—
223C22×C139—44no—
224C22×C139—432no—
225C22×C139—416no—
226C22×C139—48no—
227C22×C139—42no—
228C22×C139—42no—
229C22×C139—48no—
230C22×C139—48no—
231C22×C139—416no—
232C22×C139—432no—
233C22×C139—42no—
234C22×C139—48no—
235C22×C139—42no—
236C22×C139—42no—
237C22×C139—44no—
238C22×C139—42no—
239C22×C139—41no—
240C22×C139—81no—
241C22×C139—88no—
242C22×C139—81no—
243C22×C139AΣL(1,𝔽16)14yescomplemented
244C22×C139#37911yescharacteristic
245C22×C139C2×#9911yescharacteristic
246C22×C139C2×#9911yescharacteristic
247C4×C139—22no—
248C4×C139—44no—
249C4×C139—41no—
250C4×C139—162no—
251C2×C139—21no—
252C2×C139—24no—
253C2×C139—21no—
254C2×C139—42no—
255C2×C139—48no—
256C2×C139—42no—
257C2×C139—42no—
258C2×C139—81no—
259C2×C139#178111yescharacteristic
260C2×C139C2×AΣL(1,𝔽16)12yes—
261#12687C13911yesmaximal, characteristic, direct product factor, Sylow
262C139#1268711yescharacteristic, direct product factor, Sylow
263C22×#120C2×C13911yescharacteristic
264C2×AΣL(1,𝔽16)C2×C13914yescomplemented
265#1783C2×C13911yescharacteristic, complemented
266#1781C2×C13911yescharacteristic, complemented
267C26C4×C13911yescharacteristic, complemented
268C23×D4—21no—
269C23×D4C22×C13911yescharacteristic
270C2×#120—21no—
271C2×#120—21no—
272C2×#120—28no—
273C2×#120C4×C13912yescomplemented
274C2×#120C22×C13912yes—
275C22×C22⋊C4—21no—
276C22×C22⋊C4C4×C13911yescharacteristic, complemented
277C2×#100—21no—
278C2×#100C22×C13912yescomplemented
279C2×#99—21no—
280C2×#99C22×C13912yescomplemented
281#407—21no—
282#379—21no—
283AΣL(1,𝔽16)—28no—
284C25—21no—
285C25—21no—
286C25—24no—
287C25—48no—
288C25—42no—
289C25—42no—
290C25C2×C4×C13911yescharacteristic
291C25C2×C4×C13912yes—
292C25D4×C13911yescharacteristic
293C22×D4—28no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—24no—
297C22×D4—42no—
298C22×D4—42no—
299C22×D4—48no—
300C22×D4C2×C4×C13911yescharacteristic
301C22×D4D4×C13911yescharacteristic
302C22×D4D4×C13911yescharacteristic
303C22×D4C23×C13911yescharacteristic
304C23×C4—21no—
305C23×C4D4×C13911yescharacteristic
306C2×M16—22no—
307#120—28no—
308#120—28no—
309#120—24no—
310#120—24no—
311#120—24no—
312#120D4×C13918yes—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4C2×C4×C13912yes—
321#100—24no—
322#100—42no—
323#99—24no—
324#99—42no—
325C22⋊C8—42no—
326C24—24no—
327C24—28no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—24no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—41no—
337C24—44no—
338C24—48no—
339C24—42no—
340C24—42no—
341C24—42no—
342C24—44no—
343C24—48no—
344C24—432no—
345C24—416no—
346C24—42no—
347C24—44no—
348C24—48no—
349C24—416no—
350C24—432no—
351C24—48no—
352C24—42no—
353C24—42no—
354C24C22⋊C4×C13911yescharacteristic
355C24C22⋊C4×C13911yescharacteristic
356C24C22⋊C4×C13911yescharacteristic
357C24C22⋊C4×C13914yescomplemented
358C24C22×C4×C13911yescharacteristic
359C24C2×D4×C13911yescharacteristic
360C2×D4—28no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—28no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—416no—
374C2×D4—48no—
375C2×D4—48no—
376C2×D4—432no—
377C2×D4C2×D4×C13914yes—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—44no—
384C22×C4—42no—
385C22×C4C22⋊C4×C13911yescharacteristic
386C22×C4C2×D4×C13911yescharacteristic
387M16—42no—
388M16—42no—
389C2×C8—42no—
390C22⋊C4—28no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—28no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—84no—
397C22⋊C4C22⋊C4×C13914yescomplemented
398C23—21no—
399C23—24no—
400C23—21no—
401C23—216no—
402C23—28no—
403C23—28no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—24no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—44no—
415C23—42no—
416C23—48no—
417C23—44no—
418C23—42no—
419C23—48no—
420C23—48no—
421C23—48no—
422C23—416no—
423C23—48no—
424C23—44no—
425C23—48no—
426C23—44no—
427C23—48no—
428C23—416no—
429C23—48no—
430C23—44no—
431C23—42no—
432C23—42no—
433C23—48no—
434C23—48no—
435C23—416no—
436C23—416no—
437C23—464no—
438C23—464no—
439C23—48no—
440C23—416no—
441C23—42no—
442C23—42no—
443C23—48no—
444C23—44no—
445C23—44no—
446C23—82no—
447C23—84no—
448C23#99×C13912yes—
449C23#99×C13912yes—
450C23C2×C22⋊C4×C13911yescharacteristic
451C23C2×C22⋊C4×C13912yes—
452C23#120×C13912yes—
453D4—44no—
454D4—44no—
455D4—44no—
456D4—416no—
457D4—416no—
458D4—44no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—24no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—82no—
469C2×C4—84no—
470C2×C4#120×C13912yes—
471C8—82no—
472C22—24no—
473C22—24no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—28no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—44no—
486C22—48no—
487C22—42no—
488C22—432no—
489C22—416no—
490C22—42no—
491C22—48no—
492C22—48no—
493C22—416no—
494C22—432no—
495C22—44no—
496C22—42no—
497C22—48no—
498C22—42no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—81no—
503C22—88no—
504C22—81no—
505C22AΣL(1,𝔽16)×C13914yescomplemented
506C22#379×C13911yescharacteristic
507C22C2×#99×C13911yescharacteristic
508C22C2×#99×C13911yescharacteristic
509C4—22no—
510C4—44no—
511C4—41no—
512C4—162no—
513C2—21no—
514C2—21no—
515C2—24no—
516C2—42no—
517C2—48no—
518C2—42no—
519C2—42no—
520C2—81no—
521C2#1781×C13911yescharacteristic
522C2C2×AΣL(1,𝔽16)×C13912yes—
subgroupG/H
center, socleC22×C139C2×#99
commutatorC24C22×C4×C139
Frattini, cosocleC22×D4C23×C139
prime radicalC22×#120×C139C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C24×C139 ◁ C23×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×AΣL(1,𝔽16)×C139C2semidirect
3. #1783×C139C2semidirect
4. #1781×C139C2semidirect
5. C26×C139C4semidirect
11. C2×#120×C139C4semidirect
14. C22×C22⋊C4×C139C4semidirect
16. C2×#100×C139C22semidirect
18. C2×#99×C139C22semidirect
95. C24×C139C22⋊C4semidirect
135. C22⋊C4×C139C22⋊C4semidirect
243. C22×C139AΣL(1,𝔽16)semidirect
261. #12687C139direct (N × H)
262. C139#12687direct (N × H)
264. C2×AΣL(1,𝔽16)C2×C139semidirect
265. #1783C2×C139semidirect
266. #1781C2×C139semidirect
267. C26C4×C139semidirect
273. C2×#120C4×C139semidirect
276. C22×C22⋊C4C4×C139semidirect
278. C2×#100C22×C139semidirect
280. C2×#99C22×C139semidirect
357. C24C22⋊C4×C139semidirect
397. C22⋊C4C22⋊C4×C139semidirect
505. C22AΣL(1,𝔽16)×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1392
C2×AΣL(1,𝔽16)×C1392
#1783×C1392
#1781×C1392
#12687139