Finite Group Databasebeta

← C139×#12705 #48007301

Subgroups — C139×#12705 #48007301

Order 35584.

1186 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 146 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
1#3484×C139C211yesmaximal, characteristic
2#2121×C139C214yesmaximal, complemented
3#1783×C139C211yesmaximal, characteristic, complemented
4#1781×C139C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C139C411yescharacteristic, complemented
6C23×D4×C139C2211yescharacteristic
7#546×C139—24no—
8D42×C139—24no—
9#535×C139—21no—
10#534×C139—21no—
11#534×C139C2212yes—
12#525×C139—21no—
13C2×#120×C139—21no—
14C2×#120×C139C412yescomplemented
15#518×C139C411yescharacteristic, complemented
16C2×#100×C139—21no—
17C2×#100×C139C2212yescomplemented
18C2×#99×C139—21no—
19C2×#99×C139C2212yescomplemented
20#407×C139—21no—
21#379×C139—21no—
22#352×C139—24no—
23AΣL(1,𝔽16)×C139—24no—
24C25×C139C2×C411yescharacteristic
25C25×C139D411yescharacteristic
26H(5,𝔽2)×C139—42no—
27H(5,𝔽2)×C139—42no—
28C2×#41×C139—21no—
29C2×#41×C139—22no—
30C22×D4×C139—21no—
31C22×D4×C139—22no—
32C22×D4×C139—22no—
33C22×D4×C139—22no—
34C22×D4×C139—24no—
35C22×D4×C139—42no—
36C22×D4×C139—42no—
37C22×D4×C139C2×C411yescharacteristic
38C22×D4×C139C2×C412yes—
39C22×D4×C139D411yescharacteristic
40C22×D4×C139D411yescharacteristic
41C22×D4×C139C2311yescharacteristic
42C23×C4×C139D411yescharacteristic
43C2×M16×C139—22no—
44#127×C139—22no—
45#124×C139—22no—
46#123×C139—22no—
47#123×C139—22no—
48#123×C139D414yes—
49C22⋊Q8×C139—22no—
50#121×C139—22no—
51#121×C139—24no—
52#121×C139—24no—
53#121×C139—24no—
54#120×C139—24no—
55#120×C139—22no—
56#120×C139—22no—
57#120×C139—22no—
58#120×C139—22no—
59#120×C139—24no—
60#120×C139D414yes—
61C4×D4×C139—24no—
62C4×D4×C139—24no—
63#117×C139—21no—
64C2×C22⋊C4×C139—22no—
65C2×C22⋊C4×C139—21no—
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139—22no—
68C2×C22⋊C4×C139—42no—
69C2×C22⋊C4×C139C2×C412yes—
70#100×C139—24no—
71#100×C139—42no—
72#99×C139—24no—
73#99×C139—42no—
74C22⋊C8×C139—42no—
75C24×C139—21no—
76C24×C139—22no—
77C24×C139—22no—
78C24×C139—22no—
79C24×C139—41no—
80C24×C139—41no—
81C24×C139—41no—
82C24×C139—82no—
83C24×C139—82no—
84C24×C139C22⋊C411yescharacteristic
85C24×C139C22⋊C411yescharacteristic
86C24×C139C22⋊C411yescharacteristic
87C24×C139C22⋊C412yescomplemented
88C24×C139C22×C411yescharacteristic
89C24×C139C2×D411yescharacteristic
90#41×C139—42no—
91#41×C139—48no—
92#41×C139—42no—
93C2×Q8×C139—21no—
94C2×D4×C139—22no—
95C2×D4×C139—22no—
96C2×D4×C139—24no—
97C2×D4×C139—22no—
98C2×D4×C139—21no—
99C2×D4×C139—22no—
100C2×D4×C139—22no—
101C2×D4×C139—22no—
102C2×D4×C139—22no—
103C2×D4×C139—24no—
104C2×D4×C139—24no—
105C2×D4×C139—22no—
106C2×D4×C139—22no—
107C2×D4×C139—22no—
108C2×D4×C139—41no—
109C2×D4×C139—41no—
110C2×D4×C139—41no—
111C2×D4×C139—41no—
112C2×D4×C139—416no—
113C2×D4×C139—48no—
114C2×D4×C139—42no—
115C2×D4×C139—42no—
116C2×D4×C139—42no—
117C2×D4×C139—42no—
118C2×D4×C139—84no—
119C2×D4×C139—84no—
120C2×D4×C139C2×D414yes—
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—41no—
128C22×C4×C139—42no—
129C22×C4×C139C22⋊C411yescharacteristic
130C22×C4×C139C22⋊C412yescomplemented
131C22×C4×C139C2×D411yescharacteristic
132M16×C139—42no—
133M16×C139—42no—
134C2×C8×C139—42no—
135C4⋊C4×C139—22no—
136C4⋊C4×C139—24no—
137C22⋊C4×C139—24no—
138C22⋊C4×C139—22no—
139C22⋊C4×C139—24no—
140C22⋊C4×C139—22no—
141C22⋊C4×C139—24no—
142C22⋊C4×C139—24no—
143C22⋊C4×C139—42no—
144C22⋊C4×C139—42no—
145C22⋊C4×C139—84no—
146C22⋊C4×C139C22⋊C414yescomplemented
147C42×C139—22no—
148C23×C139—21no—
149C23×C139—21no—
150C23×C139—21no—
151C23×C139—21no—
152C23×C139—21no—
153C23×C139—21no—
154C23×C139—21no—
155C23×C139—21no—
156C23×C139—21no—
157C23×C139—21no—
158C23×C139—22no—
159C23×C139—21no—
160C23×C139—21no—
161C23×C139—42no—
162C23×C139—44no—
163C23×C139—44no—
164C23×C139—44no—
165C23×C139—44no—
166C23×C139—44no—
167C23×C139—42no—
168C23×C139—42no—
169C23×C139—82no—
170C23×C139—82no—
171C23×C139—82no—
172C23×C139—81no—
173C23×C139—81no—
174C23×C139—81no—
175C23×C139—81no—
176C23×C139—82no—
177C23×C139—82no—
178C23×C139—82no—
179C23×C139—82no—
180C23×C139—82no—
181C23×C139—82no—
182C23×C139—82no—
183C23×C139—82no—
184C23×C139#9912yes—
185C23×C139C2×C22⋊C412yes—
186C23×C139C2×C22⋊C411yescharacteristic
187C23×C139#12012yes—
188Q8×C139—42no—
189D4×C139—28no—
190D4×C139—44no—
191D4×C139—44no—
192D4×C139—44no—
193D4×C139—42no—
194D4×C139—44no—
195D4×C139—44no—
196D4×C139—48no—
197D4×C139—42no—
198D4×C139—42no—
199D4×C139—84no—
200D4×C139—84no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—24no—
206C2×C4×C139—22no—
207C2×C4×C139—44no—
208C2×C4×C139—44no—
209C2×C4×C139—42no—
210C2×C4×C139—42no—
211C2×C4×C139—82no—
212C2×C4×C139—82no—
213C2×C4×C139—82no—
214C2×C4×C139—84no—
215C2×C4×C139#9912yes—
216C2×C4×C139#12012yes—
217C8×C139—82no—
218C22×C139—22no—
219C22×C139—22no—
220C22×C139—22no—
221C22×C139—22no—
222C22×C139—22no—
223C22×C139—22no—
224C22×C139—41no—
225C22×C139—42no—
226C22×C139—42no—
227C22×C139—42no—
228C22×C139—42no—
229C22×C139—42no—
230C22×C139—41no—
231C22×C139—41no—
232C22×C139—41no—
233C22×C139—44no—
234C22×C139—42no—
235C22×C139—41no—
236C22×C139—42no—
237C22×C139—41no—
238C22×C139—81no—
239C22×C139—81no—
240C22×C139—81no—
241C22×C139—81no—
242C22×C139—81no—
243C22×C139—81no—
244C22×C139—88no—
245C22×C139—88no—
246C22×C139—162no—
247C22×C139—162no—
248C22×C139#37911yescharacteristic
249C22×C139C2×#9911yescharacteristic
250C22×C139C2×#9911yescharacteristic
251C4×C139—22no—
252C4×C139—22no—
253C4×C139—44no—
254C4×C139—42no—
255C4×C139—162no—
256C2×C139—21no—
257C2×C139—21no—
258C2×C139—21no—
259C2×C139—42no—
260C2×C139—42no—
261C2×C139—42no—
262C2×C139—42no—
263C2×C139—81no—
264C2×C139—82no—
265C2×C139#178111yescharacteristic
266#12705C13911yesmaximal, characteristic, direct product factor, Sylow
267C139#1270511yescharacteristic, direct product factor, Sylow
268#3484C2×C13911yescharacteristic
269#2121C2×C13914yescomplemented
270#1783C2×C13911yescharacteristic, complemented
271#1781C2×C13911yescharacteristic, complemented
272C2×H(5,𝔽2)C4×C13911yescharacteristic, complemented
273C23×D4C22×C13911yescharacteristic
274#546—24no—
275D42—24no—
276#535—21no—
277#534—21no—
278#534C22×C13912yes—
279#525—21no—
280C2×#120—21no—
281C2×#120C4×C13912yescomplemented
282#518C4×C13911yescharacteristic, complemented
283C2×#100—21no—
284C2×#100C22×C13912yescomplemented
285C2×#99—21no—
286C2×#99C22×C13912yescomplemented
287#407—21no—
288#379—21no—
289#352—24no—
290AΣL(1,𝔽16)—24no—
291C25C2×C4×C13911yescharacteristic
292C25D4×C13911yescharacteristic
293H(5,𝔽2)—42no—
294H(5,𝔽2)—42no—
295C2×#41—21no—
296C2×#41—22no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4C2×C4×C13911yescharacteristic
305C22×D4C2×C4×C13912yes—
306C22×D4D4×C13911yescharacteristic
307C22×D4D4×C13911yescharacteristic
308C22×D4C23×C13911yescharacteristic
309C23×C4D4×C13911yescharacteristic
310C2×M16—22no—
311#127—22no—
312#124—22no—
313#123—22no—
314#123—22no—
315#123D4×C13914yes—
316C22⋊Q8—22no—
317#121—22no—
318#121—24no—
319#121—24no—
320#121—24no—
321#120—24no—
322#120—22no—
323#120—22no—
324#120—22no—
325#120—22no—
326#120—24no—
327#120D4×C13914yes—
328C4×D4—24no—
329C4×D4—24no—
330#117—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4C2×C4×C13912yes—
337#100—24no—
338#100—42no—
339#99—24no—
340#99—42no—
341C22⋊C8—42no—
342C24—21no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—82no—
350C24—82no—
351C24C22⋊C4×C13911yescharacteristic
352C24C22⋊C4×C13911yescharacteristic
353C24C22⋊C4×C13911yescharacteristic
354C24C22⋊C4×C13912yescomplemented
355C24C22×C4×C13911yescharacteristic
356C24C2×D4×C13911yescharacteristic
357#41—42no—
358#41—48no—
359#41—42no—
360C2×Q8—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—416no—
380C2×D4—48no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—84no—
386C2×D4—84no—
387C2×D4C2×D4×C13914yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C22⋊C4×C13911yescharacteristic
397C22×C4C22⋊C4×C13912yescomplemented
398C22×C4C2×D4×C13911yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—84no—
413C22⋊C4C22⋊C4×C13914yescomplemented
414C42—22no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—42no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23—82no—
451C23#99×C13912yes—
452C23C2×C22⋊C4×C13912yes—
453C23C2×C22⋊C4×C13911yescharacteristic
454C23#120×C13912yes—
455Q8—42no—
456D4—28no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4#99×C13912yes—
483C2×C4#120×C13912yes—
484C8—82no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—88no—
512C22—88no—
513C22—162no—
514C22—162no—
515C22#379×C13911yescharacteristic
516C22C2×#99×C13911yescharacteristic
517C22C2×#99×C13911yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—162no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—82no—
532C2#1781×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#1781
commutatorC24C22×C4×C139
Frattini, cosocleC22×D4C23×C139
prime radical#3484×C139C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C23×C139 ◁ C23×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2121×C139C2semidirect
3. #1783×C139C2semidirect
4. #1781×C139C2semidirect
5. C2×H(5,𝔽2)×C139C4semidirect
14. C2×#120×C139C4semidirect
15. #518×C139C4semidirect
17. C2×#100×C139C22semidirect
19. C2×#99×C139C22semidirect
87. C24×C139C22⋊C4semidirect
130. C22×C4×C139C22⋊C4semidirect
146. C22⋊C4×C139C22⋊C4semidirect
266. #12705C139direct (N × H)
267. C139#12705direct (N × H)
269. #2121C2×C139semidirect
270. #1783C2×C139semidirect
271. #1781C2×C139semidirect
272. C2×H(5,𝔽2)C4×C139semidirect
281. C2×#120C4×C139semidirect
282. #518C4×C139semidirect
284. C2×#100C22×C139semidirect
286. C2×#99C22×C139semidirect
354. C24C22⋊C4×C139semidirect
397. C22×C4C22⋊C4×C139semidirect
413. C22⋊C4C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3484×C1392
#2121×C1392
#1783×C1392
#1781×C1392
#12705139