Finite Group Databasebeta

← C139×#36962 #48031558

Subgroups — C139×#36962 #48031558

Order 35584.

1986 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C139C211yesmaximal, characteristic, complemented
2C22×#126×C139C211yesmaximal, characteristic
3#2855×C139C212yesmaximal, complemented
4#2721×C139C218yesmaximal, complemented
5#2716×C139C218yesmaximal, complemented
6#2626×C139C212yesmaximal
7#2561×C139C212yesmaximal
8#2502×C139C212yesmaximal, complemented
9#2484×C139C212yesmaximal, complemented
10#2482×C139C212yesmaximal
11#2313×C139C211yesmaximal, characteristic, complemented
12#544×C139—28no—
13C2×C4⋊Q8×C139C2214yescomplemented
14C2×#126×C139—28no—
15C2×#126×C139C2218yes—
16C2×#125×C139C2214yescomplemented
17C2×C22⋊Q8×C139C2212yes—
18C2×C22⋊Q8×C139C2212yes—
19C2×#117×C139C2212yes—
20C22×C4⋊C4×C139C2211yescharacteristic
21C22×C4⋊C4×C139C2211yescharacteristic
22C22×C4⋊C4×C139C2211yescharacteristic
23C22×C22⋊C4×C139C2211yescharacteristic
24C22×C22⋊C4×C139C2211yescharacteristic
25C22×C22⋊C4×C139C2211yescharacteristic
26C22×C42×C139C2211yescharacteristic
27#400×C139C2214yescomplemented
28#399×C139C2214yes—
29#399×C139C2214yes—
30#398×C139C2218yescomplemented
31#398×C139C2214yescomplemented
32#397×C139C2214yes—
33#397×C139C2214yes—
34#396×C139C2218yes—
35#393×C139C2214yes—
36#393×C139C2214yes—
37#391×C139C2214yescomplemented
38#391×C139C2214yescomplemented
39#389×C139C2214yescomplemented
40#388×C139C2218yes—
41#388×C139C2218yes—
42#387×C139C2218yescomplemented
43#387×C139C2218yescomplemented
44#387×C139C2218yescomplemented
45#385×C139C2214yes—
46#385×C139C2214yes—
47#384×C139C2214yescomplemented
48#381×C139C2214yes—
49#381×C139C2212yes—
50#380×C139C2212yes—
51#379×C139C2214yes—
52C4×C22⋊C4×C139C2212yes—
53C25×C139C2311yescharacteristic
54C22×Q8×C139C2312yes—
55C22×Q8×C139C2312yes—
56C23×C4×C139C2311yescharacteristic
57C23×C4×C139C2311yescharacteristic
58C23×C4×C139C2311yescharacteristic
59C23×C4×C139C2311yescharacteristic
60C23×C4×C139C2311yescharacteristic
61C23×C4×C139C2311yescharacteristic
62C4⋊Q8×C139—216no—
63#126×C139—232no—
64#125×C139—216no—
65C22⋊Q8×C139—28no—
66C22⋊Q8×C139—28no—
67#117×C139—28no—
68C2×C4⋊C4×C139—24no—
69C2×C4⋊C4×C139—24no—
70C2×C4⋊C4×C139D418yes—
71C2×C4⋊C4×C139C2314yes—
72C2×C4⋊C4×C139C2312yes—
73C2×C4⋊C4×C139C2312yes—
74C2×C4⋊C4×C139C2312yes—
75C2×C4⋊C4×C139C2314yes—
76C2×C4⋊C4×C139C2314yes—
77C2×C4⋊C4×C139C2314yes—
78C2×C4⋊C4×C139C2312yes—
79C2×C4⋊C4×C139C2314yes—
80C2×C4⋊C4×C139C2318yes—
81C2×C4⋊C4×C139C2318yes—
82C2×C4⋊C4×C139C2314yes—
83C2×C22⋊C4×C139—24no—
84C2×C22⋊C4×C139—24no—
85C2×C22⋊C4×C139—24no—
86C2×C22⋊C4×C139C2314yes—
87C2×C22⋊C4×C139C2314yes—
88C2×C22⋊C4×C139C2314yes—
89C2×C22⋊C4×C139C2314yes—
90C2×C22⋊C4×C139C2314yes—
91C2×C22⋊C4×C139C2318yes—
92C2×C22⋊C4×C139C2318yes—
93C2×C42×C139—24no—
94C2×C42×C139C2314yes—
95C2×C42×C139C2314yes—
96C2×C42×C139C2314yes—
97#95×C139C2318yes—
98#95×C139C2314yes—
99#95×C139C2318yes—
100#95×C139C2318yes—
101#95×C139C2314yes—
102#95×C139C2314yes—
103#95×C139C2314yes—
104#95×C139C2318yes—
105C24×C139—22no—
106C24×C139—24no—
107C24×C139—42no—
108C24×C139—42no—
109C24×C139C2412yes—
110C24×C139C2411yescharacteristic
111C2×Q8×C139—24no—
112C2×Q8×C139—24no—
113C2×Q8×C139—44no—
114C2×Q8×C139—44no—
115C22×C4×C139—24no—
116C22×C4×C139—22no—
117C22×C4×C139—22no—
118C22×C4×C139—22no—
119C22×C4×C139—24no—
120C22×C4×C139—42no—
121C22×C4×C139—42no—
122C22×C4×C139—42no—
123C22×C4×C139—42no—
124C22×C4×C139C2×D414yes—
125C22×C4×C139C2×D414yes—
126C22×C4×C139C2×D414yes—
127C22×C4×C139C2412yes—
128C22×C4×C139C2418yes—
129C22×C4×C139C2414yes—
130C22×C4×C139C2412yes—
131C22×C4×C139C2412yes—
132C22×C4×C139C2414yes—
133C22×C4×C139C2412yes—
134C22×C4×C139C2412yes—
135C22×C4×C139C2412yes—
136C4⋊C4×C139—28no—
137C4⋊C4×C139—28no—
138C4⋊C4×C139—24no—
139C4⋊C4×C139—24no—
140C4⋊C4×C139—24no—
141C4⋊C4×C139—24no—
142C4⋊C4×C139—28no—
143C4⋊C4×C139—28no—
144C4⋊C4×C139—44no—
145C4⋊C4×C139—48no—
146C4⋊C4×C139—48no—
147C4⋊C4×C139C2×D4116yes—
148C22⋊C4×C139—28no—
149C22⋊C4×C139—28no—
150C22⋊C4×C139—28no—
151C22⋊C4×C139—28no—
152C22⋊C4×C139—28no—
153C22⋊C4×C139—48no—
154C22⋊C4×C139—48no—
155C42×C139—28no—
156C42×C139—28no—
157C42×C139—44no—
158C23×C139—22no—
159C23×C139—22no—
160C23×C139—22no—
161C23×C139—24no—
162C23×C139—24no—
163C23×C139—24no—
164C23×C139—44no—
165C23×C139—44no—
166C23×C139—44no—
167C23×C139—88no—
168C23×C139C22×D412yes—
169C23×C1392−1+414yes—
170C23×C139C2511yescharacteristic
171Q8×C139—84no—
172Q8×C139—84no—
173C2×C4×C139—28no—
174C2×C4×C139—24no—
175C2×C4×C139—24no—
176C2×C4×C139—24no—
177C2×C4×C139—22no—
178C2×C4×C139—22no—
179C2×C4×C139—24no—
180C2×C4×C139—24no—
181C2×C4×C139—22no—
182C2×C4×C139—28no—
183C2×C4×C139—24no—
184C2×C4×C139—28no—
185C2×C4×C139—28no—
186C2×C4×C139—28no—
187C2×C4×C139—28no—
188C2×C4×C139—24no—
189C2×C4×C139—24no—
190C2×C4×C139—44no—
191C2×C4×C139—44no—
192C2×C4×C139—44no—
193C2×C4×C139—44no—
194C2×C4×C139—44no—
195C2×C4×C139C22×D414yes—
196C2×C4×C139C22×D414yes—
197C2×C4×C139C22×D414yes—
198C22×C139—22no—
199C22×C139—22no—
200C22×C139—28no—
201C22×C139—42no—
202C22×C139—42no—
203C22×C139—42no—
204C22×C139—48no—
205C22×C139—88no—
206C22×C139#53614yes—
207C22×C139C23×D411yescharacteristic
208C22×C139C2×2−1+412yes—
209C22×C139#58512yes—
210C22×C139#58512yes—
211C4×C139—24no—
212C4×C139—24no—
213C4×C139—24no—
214C4×C139—42no—
215C4×C139—44no—
216C4×C139—44no—
217C4×C139—42no—
218C4×C139—42no—
219C4×C139—48no—
220C2×C139—24no—
221C2×C139—82no—
222C2×C139C2×#53611yescharacteristic
223C2×C139#348511yescharacteristic
224C2×C139#348711yescharacteristic
225C2×C139#356414yes—
226#36962C13911yesmaximal, characteristic, direct product factor, Sylow
227C139#3696211yescharacteristic, direct product factor, Sylow
228C2×#544C2×C13911yescharacteristic, complemented
229C22×#126C2×C13911yescharacteristic
230#2855C2×C13912yescomplemented
231#2721C2×C13918yescomplemented
232#2716C2×C13918yescomplemented
233#2626C2×C13912yes—
234#2561C2×C13912yes—
235#2502C2×C13912yescomplemented
236#2484C2×C13912yescomplemented
237#2482C2×C13912yes—
238#2313C2×C13911yescharacteristic, complemented
239#544—28no—
240C2×C4⋊Q8C22×C13914yescomplemented
241C2×#126—28no—
242C2×#126C22×C13918yes—
243C2×#125C22×C13914yescomplemented
244C2×C22⋊Q8C22×C13912yes—
245C2×C22⋊Q8C22×C13912yes—
246C2×#117C22×C13912yes—
247C22×C4⋊C4C22×C13911yescharacteristic
248C22×C4⋊C4C22×C13911yescharacteristic
249C22×C4⋊C4C22×C13911yescharacteristic
250C22×C22⋊C4C22×C13911yescharacteristic
251C22×C22⋊C4C22×C13911yescharacteristic
252C22×C22⋊C4C22×C13911yescharacteristic
253C22×C42C22×C13911yescharacteristic
254#400C22×C13914yescomplemented
255#399C22×C13914yes—
256#399C22×C13914yes—
257#398C22×C13918yescomplemented
258#398C22×C13914yescomplemented
259#397C22×C13914yes—
260#397C22×C13914yes—
261#396C22×C13918yes—
262#393C22×C13914yes—
263#393C22×C13914yes—
264#391C22×C13914yescomplemented
265#391C22×C13914yescomplemented
266#389C22×C13914yescomplemented
267#388C22×C13918yes—
268#388C22×C13918yes—
269#387C22×C13918yescomplemented
270#387C22×C13918yescomplemented
271#387C22×C13918yescomplemented
272#385C22×C13914yes—
273#385C22×C13914yes—
274#384C22×C13914yescomplemented
275#381C22×C13914yes—
276#381C22×C13912yes—
277#380C22×C13912yes—
278#379C22×C13914yes—
279C4×C22⋊C4C22×C13912yes—
280C25C23×C13911yescharacteristic
281C22×Q8C23×C13912yes—
282C22×Q8C23×C13912yes—
283C23×C4C23×C13911yescharacteristic
284C23×C4C23×C13911yescharacteristic
285C23×C4C23×C13911yescharacteristic
286C23×C4C23×C13911yescharacteristic
287C23×C4C23×C13911yescharacteristic
288C23×C4C23×C13911yescharacteristic
289C4⋊Q8—216no—
290#126—232no—
291#125—216no—
292C22⋊Q8—28no—
293C22⋊Q8—28no—
294#117—28no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4D4×C13918yes—
298C2×C4⋊C4C23×C13914yes—
299C2×C4⋊C4C23×C13914yes—
300C2×C4⋊C4C23×C13912yes—
301C2×C4⋊C4C23×C13912yes—
302C2×C4⋊C4C23×C13912yes—
303C2×C4⋊C4C23×C13912yes—
304C2×C4⋊C4C23×C13914yes—
305C2×C4⋊C4C23×C13914yes—
306C2×C4⋊C4C23×C13914yes—
307C2×C4⋊C4C23×C13918yes—
308C2×C4⋊C4C23×C13918yes—
309C2×C4⋊C4C23×C13914yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4C23×C13914yes—
314C2×C22⋊C4C23×C13914yes—
315C2×C22⋊C4C23×C13914yes—
316C2×C22⋊C4C23×C13914yes—
317C2×C22⋊C4C23×C13914yes—
318C2×C22⋊C4C23×C13918yes—
319C2×C22⋊C4C23×C13918yes—
320C2×C42—24no—
321C2×C42C23×C13914yes—
322C2×C42C23×C13914yes—
323C2×C42C23×C13914yes—
324#95C23×C13914yes—
325#95C23×C13914yes—
326#95C23×C13914yes—
327#95C23×C13914yes—
328#95C23×C13918yes—
329#95C23×C13918yes—
330#95C23×C13918yes—
331#95C23×C13918yes—
332C24—22no—
333C24—24no—
334C24—42no—
335C24—42no—
336C24C24×C13912yes—
337C24C24×C13911yescharacteristic
338C2×Q8—24no—
339C2×Q8—24no—
340C2×Q8—44no—
341C2×Q8—44no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4C2×D4×C13914yes—
352C22×C4C2×D4×C13914yes—
353C22×C4C2×D4×C13914yes—
354C22×C4C24×C13912yes—
355C22×C4C24×C13918yes—
356C22×C4C24×C13914yes—
357C22×C4C24×C13912yes—
358C22×C4C24×C13912yes—
359C22×C4C24×C13914yes—
360C22×C4C24×C13912yes—
361C22×C4C24×C13912yes—
362C22×C4C24×C13912yes—
363C4⋊C4—28no—
364C4⋊C4—28no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—28no—
370C4⋊C4—28no—
371C4⋊C4—44no—
372C4⋊C4—48no—
373C4⋊C4—48no—
374C4⋊C4C2×D4×C139116yes—
375C22⋊C4—28no—
376C22⋊C4—28no—
377C22⋊C4—28no—
378C22⋊C4—28no—
379C22⋊C4—28no—
380C22⋊C4—48no—
381C22⋊C4—48no—
382C42—28no—
383C42—28no—
384C42—44no—
385C23—22no—
386C23—22no—
387C23—22no—
388C23—24no—
389C23—24no—
390C23—24no—
391C23—44no—
392C23—44no—
393C23—44no—
394C23—88no—
395C23C22×D4×C13912yes—
396C232−1+4×C13914yes—
397C23C25×C13911yescharacteristic
398Q8—84no—
399Q8—84no—
400C2×C4—28no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—28no—
410C2×C4—24no—
411C2×C4—28no—
412C2×C4—28no—
413C2×C4—28no—
414C2×C4—28no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4C22×D4×C13914yes—
423C2×C4C22×D4×C13914yes—
424C2×C4C22×D4×C13914yes—
425C22—28no—
426C22—22no—
427C22—22no—
428C22—48no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—88no—
433C22#536×C13914yes—
434C22C23×D4×C13911yescharacteristic
435C22C2×2−1+4×C13912yes—
436C22#585×C13912yes—
437C22#585×C13912yes—
438C4—24no—
439C4—24no—
440C4—24no—
441C4—48no—
442C4—42no—
443C4—44no—
444C4—42no—
445C4—42no—
446C4—44no—
447C2—24no—
448C2—82no—
449C2C2×#536×C13911yescharacteristic
450C2#3485×C13911yescharacteristic
451C2#3487×C13911yescharacteristic
452C2#3564×C13914yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC25×C139C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#544×C139C2semidirect
3. #2855×C139C2semidirect
4. #2721×C139C2semidirect
5. #2716×C139C2semidirect
8. #2502×C139C2semidirect
9. #2484×C139C2semidirect
11. #2313×C139C2semidirect
13. C2×C4⋊Q8×C139C22semidirect
16. C2×#125×C139C22semidirect
27. #400×C139C22semidirect
30. #398×C139C22semidirect
31. #398×C139C22semidirect
37. #391×C139C22semidirect
38. #391×C139C22semidirect
39. #389×C139C22semidirect
42. #387×C139C22semidirect
43. #387×C139C22semidirect
44. #387×C139C22semidirect
47. #384×C139C22semidirect
226. #36962C139direct (N × H)
227. C139#36962direct (N × H)
228. C2×#544C2×C139semidirect
230. #2855C2×C139semidirect
231. #2721C2×C139semidirect
232. #2716C2×C139semidirect
235. #2502C2×C139semidirect
236. #2484C2×C139semidirect
238. #2313C2×C139semidirect
240. C2×C4⋊Q8C22×C139semidirect
243. C2×#125C22×C139semidirect
254. #400C22×C139semidirect
257. #398C22×C139semidirect
258. #398C22×C139semidirect
264. #391C22×C139semidirect
265. #391C22×C139semidirect
266. #389C22×C139semidirect
269. #387C22×C139semidirect
270. #387C22×C139semidirect
271. #387C22×C139semidirect
274. #384C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C1392
C22×#126×C1392
#2855×C1392
#2721×C1392
#2716×C1392
#2626×C1392
#2561×C1392
#2502×C1392
#2484×C1392
#2482×C1392
#2313×C1392
#36962139