Finite Group Databasebeta

← C139×#36976 #48031572

Subgroups — C139×#36976 #48031572

Order 35584.

1810 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C139C212yesmaximal, complemented
2#2773×C139C214yesmaximal, complemented
3#2768×C139C214yesmaximal, complemented
4#2753×C139C214yesmaximal, complemented
5#2706×C139C214yesmaximal, complemented
6#2656×C139C211yesmaximal, characteristic
7#2646×C139C211yesmaximal, characteristic, complemented
8#2443×C139C214yesmaximal, complemented
9#2425×C139C214yesmaximal, complemented
10#2325×C139C212yesmaximal, complemented
11C2×#382×C139C211yesmaximal, characteristic, complemented
12C2×#123×C139C2214yes—
13C2×#123×C139C2214yes—
14C2×#121×C139C2212yes—
15C2×#121×C139C2214yes—
16C2×C4×D4×C139C2214yes—
17C22×C4⋊C4×C139C2212yes—
18C22×C42×C139C2211yescharacteristic
19#400×C139C2214yes—
20#399×C139C2214yes—
21#399×C139C2214yes—
22#398×C139C2214yes—
23#398×C139C2214yes—
24#398×C139C2214yes—
25#397×C139C2214yes—
26#397×C139C2214yes—
27#396×C139C2214yes—
28#394×C139C2214yes—
29#394×C139C2214yes—
30#392×C139C2214yes—
31#390×C139C2212yes—
32#390×C139C2212yes—
33#389×C139C2212yes—
34#389×C139C2214yes—
35#389×C139C2212yes—
36#388×C139C2214yes—
37#388×C139C2214yes—
38#388×C139C2214yes—
39#388×C139C2214yes—
40#388×C139C2214yes—
41#387×C139C2214yes—
42#387×C139C2214yes—
43#386×C139C2214yes—
44#386×C139C2214yes—
45#386×C139C2214yes—
46#386×C139C2214yes—
47#385×C139C2214yes—
48#385×C139C2214yes—
49#385×C139C2214yes—
50#382×C139C2214yes—
51#382×C139C2214yes—
52#380×C139C2214yes—
53#380×C139C2212yes—
54C2×#95×C139C2211yescharacteristic
55C2×#95×C139C2211yescharacteristic
56C2×#95×C139C2212yes—
57C22×D4×C139C2314yes—
58C22×D4×C139C2312yes—
59C22×D4×C139C2314yes—
60C23×C4×C139C2311yescharacteristic
61C23×C4×C139C2311yescharacteristic
62C23×C4×C139C2312yes—
63C23×C4×C139C2312yes—
64C23×C4×C139C2314yes—
65C23×C4×C139C2311yescharacteristic
66#123×C139—48no—
67#123×C139—48no—
68#121×C139—28no—
69#121×C139—48no—
70C4×D4×C139—48no—
71C2×C4⋊C4×C139—44no—
72C2×C4⋊C4×C139C2314yes—
73C2×C4⋊C4×C139C2312yes—
74C2×C4⋊C4×C139C2314yes—
75C2×C4⋊C4×C139C2314yes—
76C2×C4⋊C4×C139C2314yes—
77C2×C4⋊C4×C139C2314yes—
78C2×C4⋊C4×C139C2314yes—
79C2×C4⋊C4×C139C2312yes—
80C2×C4⋊C4×C139C2314yes—
81C2×C4⋊C4×C139C2314yes—
82C2×C4⋊C4×C139C2312yes—
83C2×C22⋊C4×C139C2314yes—
84C2×C22⋊C4×C139C2314yes—
85C2×C22⋊C4×C139C2314yes—
86C2×C22⋊C4×C139C2314yes—
87C2×C22⋊C4×C139C2314yes—
88C2×C22⋊C4×C139C2314yes—
89C2×C22⋊C4×C139C2314yes—
90C2×C22⋊C4×C139C2314yes—
91C2×C22⋊C4×C139C2314yes—
92C2×C22⋊C4×C139C2314yes—
93C2×C22⋊C4×C139C2314yes—
94C2×C42×C139—24no—
95C2×C42×C139C2312yes—
96C2×C42×C139C2312yes—
97C2×C42×C139C2314yes—
98#95×C139C2314yes—
99#95×C139C2314yes—
100#95×C139C2314yes—
101#95×C139C2314yes—
102#95×C139C2314yes—
103#95×C139C2314yes—
104#95×C139C2314yes—
105#95×C139C2314yes—
106#95×C139C2314yes—
107#95×C139C2314yes—
108#95×C139C2314yes—
109C24×C139C2414yes—
110C24×C139C2411yescharacteristic
111C2×D4×C139—28no—
112C2×D4×C139—28no—
113C2×D4×C139—28no—
114C2×D4×C139—24no—
115C2×D4×C139—44no—
116C2×D4×C139—44no—
117C2×D4×C139—42no—
118C2×D4×C139—42no—
119C2×D4×C139—44no—
120C22×C4×C139—22no—
121C22×C4×C139—22no—
122C22×C4×C139—22no—
123C22×C4×C139—22no—
124C22×C4×C139—24no—
125C22×C4×C139—24no—
126C22×C4×C139—24no—
127C22×C4×C139—42no—
128C22×C4×C139—42no—
129C22×C4×C139—42no—
130C22×C4×C139—44no—
131C22×C4×C139—44no—
132C22×C4×C139—42no—
133C22×C4×C139—44no—
134C22×C4×C139—42no—
135C22×C4×C139#4114yes—
136C22×C4×C139C2414yes—
137C22×C4×C139C2414yes—
138C22×C4×C139C2414yes—
139C22×C4×C139C2412yes—
140C22×C4×C139C2414yes—
141C22×C4×C139C2414yes—
142C22×C4×C139C2412yes—
143C22×C4×C139C2411yescharacteristic
144C22×C4×C139C2411yescharacteristic
145C4⋊C4×C139—24no—
146C4⋊C4×C139—28no—
147C4⋊C4×C139—44no—
148C4⋊C4×C139—42no—
149C4⋊C4×C139—42no—
150C4⋊C4×C139—44no—
151C4⋊C4×C139—44no—
152C4⋊C4×C139—44no—
153C4⋊C4×C139—44no—
154C4⋊C4×C139—44no—
155C4⋊C4×C139—44no—
156C22⋊C4×C139—28no—
157C22⋊C4×C139—28no—
158C22⋊C4×C139—28no—
159C22⋊C4×C139—28no—
160C22⋊C4×C139—44no—
161C22⋊C4×C139—44no—
162C22⋊C4×C139—44no—
163C22⋊C4×C139—44no—
164C22⋊C4×C139—44no—
165C22⋊C4×C139—44no—
166C22⋊C4×C139—44no—
167C42×C139—24no—
168C42×C139—24no—
169C42×C139—44no—
170C23×C139—21no—
171C23×C139—21no—
172C23×C139—22no—
173C23×C139—24no—
174C23×C139—24no—
175C23×C139—24no—
176C23×C139—24no—
177C23×C139—24no—
178C23×C139—24no—
179C23×C139—24no—
180C23×C139C2×#4112yes—
181C23×C139H(5,𝔽2)14yes—
182C23×C139C2511yescharacteristic
183D4×C139—416no—
184D4×C139—84no—
185D4×C139—88no—
186C2×C4×C139—28no—
187C2×C4×C139—21no—
188C2×C4×C139—21no—
189C2×C4×C139—21no—
190C2×C4×C139—21no—
191C2×C4×C139—22no—
192C2×C4×C139—22no—
193C2×C4×C139—22no—
194C2×C4×C139—24no—
195C2×C4×C139—24no—
196C2×C4×C139—24no—
197C2×C4×C139—24no—
198C2×C4×C139—24no—
199C2×C4×C139—24no—
200C2×C4×C139—22no—
201C2×C4×C139—22no—
202C2×C4×C139—24no—
203C2×C4×C139—24no—
204C2×C4×C139—24no—
205C2×C4×C139—24no—
206C2×C4×C139—24no—
207C2×C4×C139—24no—
208C2×C4×C139—24no—
209C2×C4×C139—24no—
210C2×C4×C139—24no—
211C2×C4×C139—44no—
212C2×C4×C139—44no—
213C2×C4×C139—84no—
214C2×C4×C139—84no—
215C2×C4×C139—88no—
216C2×C4×C139C2×#4114yes—
217C2×C4×C139H(5,𝔽2)12yes—
218C2×C4×C1392−1+412yes—
219C22×C139—22no—
220C22×C139—22no—
221C22×C139—24no—
222C22×C139—24no—
223C22×C139—44no—
224C22×C139—44no—
225C22×C139—44no—
226C22×C139—44no—
227C22×C139—44no—
228C22×C139—44no—
229C22×C139—44no—
230C22×C139#54014yes—
231C22×C139C22×#4111yescharacteristic
232C22×C139C2×H(5,𝔽2)12yes—
233C22×C139C2×H(5,𝔽2)11yescharacteristic
234C22×C139C2×2−1+411yescharacteristic
235C22×C139#58512yes—
236C4×C139—24no—
237C4×C139—22no—
238C4×C139—22no—
239C4×C139—42no—
240C4×C139—44no—
241C4×C139—44no—
242C4×C139—44no—
243C4×C139—44no—
244C4×C139—44no—
245C2×C139—24no—
246C2×C139—84no—
247C2×C139C2×#54011yescharacteristic
248C2×C139#349111yescharacteristic
249C2×C139#349211yescharacteristic
250C2×C139#355812yes—
251C2×C139#355912yes—
252#36976C13911yesmaximal, characteristic, direct product factor, Sylow
253C139#3697611yescharacteristic, direct product factor, Sylow
254#2854C2×C13912yescomplemented
255#2773C2×C13914yescomplemented
256#2768C2×C13914yescomplemented
257#2753C2×C13914yescomplemented
258#2706C2×C13914yescomplemented
259#2656C2×C13911yescharacteristic
260#2646C2×C13911yescharacteristic, complemented
261#2443C2×C13914yescomplemented
262#2425C2×C13914yescomplemented
263#2325C2×C13912yescomplemented
264C2×#382C2×C13911yescharacteristic, complemented
265C2×#123C22×C13914yes—
266C2×#123C22×C13914yes—
267C2×#121C22×C13912yes—
268C2×#121C22×C13914yes—
269C2×C4×D4C22×C13914yes—
270C22×C4⋊C4C22×C13912yes—
271C22×C42C22×C13911yescharacteristic
272#400C22×C13914yes—
273#399C22×C13914yes—
274#399C22×C13914yes—
275#398C22×C13914yes—
276#398C22×C13914yes—
277#398C22×C13914yes—
278#397C22×C13914yes—
279#397C22×C13914yes—
280#396C22×C13914yes—
281#394C22×C13914yes—
282#394C22×C13914yes—
283#392C22×C13914yes—
284#390C22×C13912yes—
285#390C22×C13912yes—
286#389C22×C13912yes—
287#389C22×C13912yes—
288#389C22×C13914yes—
289#388C22×C13914yes—
290#388C22×C13914yes—
291#388C22×C13914yes—
292#388C22×C13914yes—
293#388C22×C13914yes—
294#387C22×C13914yes—
295#387C22×C13914yes—
296#386C22×C13914yes—
297#386C22×C13914yes—
298#386C22×C13914yes—
299#386C22×C13914yes—
300#385C22×C13914yes—
301#385C22×C13914yes—
302#385C22×C13914yes—
303#382C22×C13914yes—
304#382C22×C13914yes—
305#380C22×C13912yes—
306#380C22×C13914yes—
307C2×#95C22×C13911yescharacteristic
308C2×#95C22×C13911yescharacteristic
309C2×#95C22×C13912yes—
310C22×D4C23×C13914yes—
311C22×D4C23×C13912yes—
312C22×D4C23×C13914yes—
313C23×C4C23×C13911yescharacteristic
314C23×C4C23×C13911yescharacteristic
315C23×C4C23×C13912yes—
316C23×C4C23×C13912yes—
317C23×C4C23×C13914yes—
318C23×C4C23×C13911yescharacteristic
319#123—48no—
320#123—48no—
321#121—28no—
322#121—48no—
323C4×D4—48no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4C23×C13914yes—
326C2×C4⋊C4C23×C13912yes—
327C2×C4⋊C4C23×C13914yes—
328C2×C4⋊C4C23×C13914yes—
329C2×C4⋊C4C23×C13914yes—
330C2×C4⋊C4C23×C13914yes—
331C2×C4⋊C4C23×C13914yes—
332C2×C4⋊C4C23×C13914yes—
333C2×C4⋊C4C23×C13912yes—
334C2×C4⋊C4C23×C13912yes—
335C2×C4⋊C4C23×C13914yes—
336C2×C22⋊C4C23×C13914yes—
337C2×C22⋊C4C23×C13914yes—
338C2×C22⋊C4C23×C13914yes—
339C2×C22⋊C4C23×C13914yes—
340C2×C22⋊C4C23×C13914yes—
341C2×C22⋊C4C23×C13914yes—
342C2×C22⋊C4C23×C13914yes—
343C2×C22⋊C4C23×C13914yes—
344C2×C22⋊C4C23×C13914yes—
345C2×C22⋊C4C23×C13914yes—
346C2×C22⋊C4C23×C13914yes—
347C2×C42—24no—
348C2×C42C23×C13912yes—
349C2×C42C23×C13912yes—
350C2×C42C23×C13914yes—
351#95C23×C13914yes—
352#95C23×C13914yes—
353#95C23×C13914yes—
354#95C23×C13914yes—
355#95C23×C13914yes—
356#95C23×C13914yes—
357#95C23×C13914yes—
358#95C23×C13914yes—
359#95C23×C13914yes—
360#95C23×C13914yes—
361#95C23×C13914yes—
362C24C24×C13914yes—
363C24C24×C13911yescharacteristic
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—28no—
367C2×D4—24no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—44no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—42no—
386C22×C4—44no—
387C22×C4—42no—
388C22×C4#41×C13914yes—
389C22×C4C24×C13914yes—
390C22×C4C24×C13914yes—
391C22×C4C24×C13914yes—
392C22×C4C24×C13912yes—
393C22×C4C24×C13914yes—
394C22×C4C24×C13914yes—
395C22×C4C24×C13912yes—
396C22×C4C24×C13911yescharacteristic
397C22×C4C24×C13911yescharacteristic
398C4⋊C4—24no—
399C4⋊C4—28no—
400C4⋊C4—44no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—44no—
404C4⋊C4—44no—
405C4⋊C4—44no—
406C4⋊C4—44no—
407C4⋊C4—44no—
408C4⋊C4—44no—
409C22⋊C4—28no—
410C22⋊C4—28no—
411C22⋊C4—28no—
412C22⋊C4—28no—
413C22⋊C4—44no—
414C22⋊C4—44no—
415C22⋊C4—44no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C22⋊C4—44no—
419C22⋊C4—44no—
420C42—24no—
421C42—24no—
422C42—44no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—24no—
427C23—24no—
428C23—24no—
429C23—24no—
430C23—24no—
431C23—24no—
432C23—24no—
433C23C2×#41×C13912yes—
434C23H(5,𝔽2)×C13914yes—
435C23C25×C13911yescharacteristic
436D4—416no—
437D4—84no—
438D4—88no—
439C2×C4—28no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—84no—
467C2×C4—84no—
468C2×C4—88no—
469C2×C4C2×#41×C13914yes—
470C2×C4H(5,𝔽2)×C13912yes—
471C2×C42−1+4×C13912yes—
472C22—24no—
473C22—24no—
474C22—22no—
475C22—22no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—44no—
482C22—44no—
483C22#540×C13914yes—
484C22C22×#41×C13911yescharacteristic
485C22C2×H(5,𝔽2)×C13911yescharacteristic
486C22C2×H(5,𝔽2)×C13912yes—
487C22C2×2−1+4×C13911yescharacteristic
488C22#585×C13912yes—
489C4—24no—
490C4—22no—
491C4—22no—
492C4—44no—
493C4—44no—
494C4—44no—
495C4—44no—
496C4—42no—
497C4—44no—
498C2—24no—
499C2—84no—
500C2C2×#540×C13911yescharacteristic
501C2#3491×C13911yescharacteristic
502C2#3492×C13911yescharacteristic
503C2#3558×C13912yes—
504C2#3559×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radical#2656×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2854×C139C2semidirect
2. #2773×C139C2semidirect
3. #2768×C139C2semidirect
4. #2753×C139C2semidirect
5. #2706×C139C2semidirect
7. #2646×C139C2semidirect
8. #2443×C139C2semidirect
9. #2425×C139C2semidirect
10. #2325×C139C2semidirect
11. C2×#382×C139C2semidirect
252. #36976C139direct (N × H)
253. C139#36976direct (N × H)
254. #2854C2×C139semidirect
255. #2773C2×C139semidirect
256. #2768C2×C139semidirect
257. #2753C2×C139semidirect
258. #2706C2×C139semidirect
260. #2646C2×C139semidirect
261. #2443C2×C139semidirect
262. #2425C2×C139semidirect
263. #2325C2×C139semidirect
264. C2×#382C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2854×C1392
#2773×C1392
#2768×C1392
#2753×C1392
#2706×C1392
#2656×C1392
#2646×C1392
#2443×C1392
#2425×C1392
#2325×C1392
C2×#382×C1392
#36976139