Finite Group Databasebeta

← C139×#36057 #48030653

Subgroups — C139×#36057 #48030653

Order 35584.

1658 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2652×C139C213yesmaximal, complemented
2#2587×C139C213yesmaximal, complemented
3#2577×C139C213yesmaximal, complemented
4#2530×C139C213yesmaximal, complemented
5#2496×C139C213yesmaximal, complemented
6#2480×C139C213yesmaximal
7#2480×C139C213yesmaximal
8#2401×C139C213yesmaximal, complemented
9#2373×C139C213yesmaximal, complemented
10#2373×C139C213yesmaximal, complemented
11#2273×C139C211yesmaximal, characteristic
12C2×#126×C139C2213yes—
13C2×#126×C139C2213yes—
14C22×C22⋊C4×C139C2213yes—
15#401×C139C2211yescharacteristic, complemented
16#400×C139C2213yescomplemented
17#400×C139C2213yescomplemented
18#400×C139C2213yescomplemented
19#400×C139C2213yescomplemented
20#398×C139C2213yescomplemented
21#397×C139C2213yes—
22#397×C139C2213yes—
23#397×C139C2213yes—
24#397×C139C2213yes—
25#397×C139C2213yes—
26#397×C139C2213yes—
27#396×C139C2213yes—
28#396×C139C2213yes—
29#389×C139C2213yescomplemented
30#389×C139C2213yescomplemented
31#389×C139C2213yescomplemented
32#388×C139C2213yes—
33#388×C139C2213yes—
34#388×C139C2213yes—
35#388×C139C2213yes—
36#388×C139C2213yes—
37#388×C139C2213yes—
38#387×C139C2213yescomplemented
39#387×C139C2213yescomplemented
40#387×C139C2213yescomplemented
41#387×C139C2213yescomplemented
42#387×C139C2213yescomplemented
43#387×C139C2213yescomplemented
44#387×C139C2213yescomplemented
45#385×C139C2213yes—
46#385×C139C2213yes—
47#385×C139C2213yes—
48#385×C139C2213yes—
49#384×C139C2211yescharacteristic, complemented
50#383×C139C2211yescharacteristic, complemented
51#380×C139C2213yes—
52#380×C139C2213yes—
53#379×C139C2211yescharacteristic
54#379×C139C2213yes—
55C4×C4⋊C4×C139C2213yescomplemented
56C4×C4⋊C4×C139C2213yescomplemented
57C4×C4⋊C4×C139C2213yescomplemented
58C4×C4⋊C4×C139C2213yescomplemented
59C4×C22⋊C4×C139C2213yes—
60C4×C22⋊C4×C139C2213yes—
61C4×C22⋊C4×C139C2213yes—
62C4×C22⋊C4×C139C2213yes—
63C4×C22⋊C4×C139C2213yes—
64C4×C22⋊C4×C139C2213yes—
65#376×C139C2213yescomplemented
66#376×C139C2211yescharacteristic, complemented
67C25×C139C2311yescharacteristic
68C23×C4×C139C2313yes—
69C23×C4×C139C2313yes—
70#126×C139—212no—
71#126×C139—212no—
72C2×C4⋊C4×C139C2313yes—
73C2×C4⋊C4×C139C2313yes—
74C2×C4⋊C4×C139C2313yes—
75C2×C4⋊C4×C139C2313yes—
76C2×C4⋊C4×C139C2313yes—
77C2×C4⋊C4×C139C2313yes—
78C2×C4⋊C4×C139C2313yes—
79C2×C4⋊C4×C139C2313yes—
80C2×C4⋊C4×C139C2313yes—
81C2×C4⋊C4×C139C2313yes—
82C2×C4⋊C4×C139C2313yes—
83C2×C4⋊C4×C139C2313yes—
84C2×C22⋊C4×C139—212no—
85C2×C22⋊C4×C139C2313yes—
86C2×C22⋊C4×C139C2313yes—
87C2×C22⋊C4×C139C2313yes—
88C2×C22⋊C4×C139C2313yes—
89C2×C22⋊C4×C139C2313yes—
90C2×C22⋊C4×C139C2313yes—
91C2×C22⋊C4×C139C2313yes—
92C2×C22⋊C4×C139C2313yes—
93C2×C22⋊C4×C139C2313yes—
94C2×C22⋊C4×C139C2313yes—
95C2×C22⋊C4×C139C2313yes—
96C2×C22⋊C4×C139C2313yes—
97C2×C42×C139C2313yes—
98C2×C42×C139C2313yes—
99C2×C42×C139C2313yes—
100C2×C42×C139C2313yes—
101C2×C42×C139C2313yes—
102C2×C42×C139C2311yescharacteristic
103C2×C42×C139C2311yescharacteristic
104C2×C42×C139C2313yes—
105#95×C139C2313yes—
106#95×C139C2313yes—
107#95×C139C2313yes—
108#95×C139C2313yes—
109#95×C139C2313yes—
110#95×C139C2313yes—
111#95×C139C2313yes—
112#95×C139C2313yes—
113#95×C139C2313yes—
114#95×C139C2313yes—
115#95×C139C2313yes—
116#95×C139C2313yes—
117#95×C139C2313yes—
118#95×C139C2313yes—
119#95×C139C2313yes—
120#95×C139C2311yescharacteristic
121#95×C139C2311yescharacteristic
122#95×C139C2313yes—
123#95×C139C2313yes—
124#95×C139C2313yes—
125C24×C139—26no—
126C24×C139—43no—
127C24×C139—41no—
128C24×C139C2413yes—
129C22×C4×C139—26no—
130C22×C4×C139—26no—
131C22×C4×C139—43no—
132C22×C4×C139—43no—
133C22×C4×C139—43no—
134C22×C4×C139—43no—
135C22×C4×C139C2413yes—
136C22×C4×C139C2413yes—
137C22×C4×C139C2411yescharacteristic
138C22×C4×C139C2413yes—
139C22×C4×C139C2413yes—
140C22×C4×C139C2413yes—
141C22×C4×C139C2413yes—
142C22×C4×C139C2413yes—
143C22×C4×C139C2413yes—
144C22×C4×C139C2413yes—
145C4⋊C4×C139—26no—
146C4⋊C4×C139—26no—
147C4⋊C4×C139—26no—
148C4⋊C4×C139—26no—
149C4⋊C4×C139—26no—
150C4⋊C4×C139—26no—
151C4⋊C4×C139—43no—
152C4⋊C4×C139—43no—
153C4⋊C4×C139—43no—
154C4⋊C4×C139—43no—
155C4⋊C4×C139—43no—
156C4⋊C4×C139—43no—
157C22⋊C4×C139—26no—
158C22⋊C4×C139—26no—
159C22⋊C4×C139—26no—
160C22⋊C4×C139—26no—
161C22⋊C4×C139—26no—
162C22⋊C4×C139—26no—
163C22⋊C4×C139—26no—
164C22⋊C4×C139—43no—
165C22⋊C4×C139—43no—
166C22⋊C4×C139—43no—
167C22⋊C4×C139—43no—
168C22⋊C4×C139#41112yes—
169C42×C139—26no—
170C42×C139—26no—
171C42×C139—43no—
172C42×C139—43no—
173C42×C139—43no—
174C42×C139—43no—
175C42×C139—41no—
176C42×C139—41no—
177C23×C139—28no—
178C23×C139—23no—
179C23×C139—23no—
180C23×C139—23no—
181C23×C139—23no—
182C23×C139—23no—
183C23×C139—23no—
184C23×C139—86no—
185C23×C139—86no—
186C23×C139C2×#4116yes—
187C23×C139C2511yescharacteristic
188C2×C4×C139—23no—
189C2×C4×C139—23no—
190C2×C4×C139—23no—
191C2×C4×C139—23no—
192C2×C4×C139—23no—
193C2×C4×C139—23no—
194C2×C4×C139—23no—
195C2×C4×C139—23no—
196C2×C4×C139—23no—
197C2×C4×C139—23no—
198C2×C4×C139—23no—
199C2×C4×C139—23no—
200C2×C4×C139—23no—
201C2×C4×C139—23no—
202C2×C4×C139—23no—
203C2×C4×C139—23no—
204C2×C4×C139—23no—
205C2×C4×C139—23no—
206C2×C4×C139—23no—
207C2×C4×C139—23no—
208C2×C4×C139—23no—
209C2×C4×C139—23no—
210C2×C4×C139—23no—
211C2×C4×C139—23no—
212C2×C4×C139—23no—
213C2×C4×C139—23no—
214C2×C4×C139—86no—
215C2×C4×C139—86no—
216C2×C4×C139C2×#4116yes—
217C2×C4×C139C2×#4116yes—
218C22×C139—26no—
219C22×C139—26no—
220C22×C139—26no—
221C22×C139—43no—
222C22×C139—43no—
223C22×C139—43no—
224C22×C139—43no—
225C22×C139—88no—
226C22×C139C22×#4113yes—
227C22×C139#58513yes—
228C22×C139#58511yescharacteristic
229C4×C139—26no—
230C4×C139—26no—
231C4×C139—41no—
232C4×C139—43no—
233C4×C139—43no—
234C4×C139—43no—
235C4×C139—43no—
236C4×C139—43no—
237C4×C139—43no—
238C4×C139—43no—
239C2×C139—46no—
240C2×C139#344411yescharacteristic
241C2×C139#352113yes—
242C2×C139#352113yes—
243#36057C13911yesmaximal, characteristic, direct product factor, Sylow
244C139#3605711yescharacteristic, direct product factor, Sylow
245#2652C2×C13913yescomplemented
246#2587C2×C13913yescomplemented
247#2577C2×C13913yescomplemented
248#2530C2×C13913yescomplemented
249#2496C2×C13913yescomplemented
250#2480C2×C13913yes—
251#2480C2×C13913yes—
252#2401C2×C13913yescomplemented
253#2373C2×C13913yescomplemented
254#2373C2×C13913yescomplemented
255#2273C2×C13911yescharacteristic
256C2×#126C22×C13913yes—
257C2×#126C22×C13913yes—
258C22×C22⋊C4C22×C13913yes—
259#401C22×C13911yescharacteristic, complemented
260#400C22×C13913yescomplemented
261#400C22×C13913yescomplemented
262#400C22×C13913yescomplemented
263#400C22×C13913yescomplemented
264#398C22×C13913yescomplemented
265#397C22×C13913yes—
266#397C22×C13913yes—
267#397C22×C13913yes—
268#397C22×C13913yes—
269#397C22×C13913yes—
270#397C22×C13913yes—
271#396C22×C13913yes—
272#396C22×C13913yes—
273#389C22×C13913yescomplemented
274#389C22×C13913yescomplemented
275#389C22×C13913yescomplemented
276#388C22×C13913yes—
277#388C22×C13913yes—
278#388C22×C13913yes—
279#388C22×C13913yes—
280#388C22×C13913yes—
281#388C22×C13913yes—
282#387C22×C13913yescomplemented
283#387C22×C13913yescomplemented
284#387C22×C13913yescomplemented
285#387C22×C13913yescomplemented
286#387C22×C13913yescomplemented
287#387C22×C13913yescomplemented
288#387C22×C13913yescomplemented
289#385C22×C13913yes—
290#385C22×C13913yes—
291#385C22×C13913yes—
292#385C22×C13913yes—
293#384C22×C13911yescharacteristic, complemented
294#383C22×C13911yescharacteristic, complemented
295#380C22×C13913yes—
296#380C22×C13913yes—
297#379C22×C13911yescharacteristic
298#379C22×C13913yes—
299C4×C4⋊C4C22×C13913yescomplemented
300C4×C4⋊C4C22×C13913yescomplemented
301C4×C4⋊C4C22×C13913yescomplemented
302C4×C4⋊C4C22×C13913yescomplemented
303C4×C22⋊C4C22×C13913yes—
304C4×C22⋊C4C22×C13913yes—
305C4×C22⋊C4C22×C13913yes—
306C4×C22⋊C4C22×C13913yes—
307C4×C22⋊C4C22×C13913yes—
308C4×C22⋊C4C22×C13913yes—
309#376C22×C13911yescharacteristic, complemented
310#376C22×C13913yescomplemented
311C25C23×C13911yescharacteristic
312C23×C4C23×C13913yes—
313C23×C4C23×C13913yes—
314#126—212no—
315#126—212no—
316C2×C4⋊C4C23×C13913yes—
317C2×C4⋊C4C23×C13913yes—
318C2×C4⋊C4C23×C13913yes—
319C2×C4⋊C4C23×C13913yes—
320C2×C4⋊C4C23×C13913yes—
321C2×C4⋊C4C23×C13913yes—
322C2×C4⋊C4C23×C13913yes—
323C2×C4⋊C4C23×C13913yes—
324C2×C4⋊C4C23×C13913yes—
325C2×C4⋊C4C23×C13913yes—
326C2×C4⋊C4C23×C13913yes—
327C2×C4⋊C4C23×C13913yes—
328C2×C22⋊C4—212no—
329C2×C22⋊C4C23×C13913yes—
330C2×C22⋊C4C23×C13913yes—
331C2×C22⋊C4C23×C13913yes—
332C2×C22⋊C4C23×C13913yes—
333C2×C22⋊C4C23×C13913yes—
334C2×C22⋊C4C23×C13913yes—
335C2×C22⋊C4C23×C13913yes—
336C2×C22⋊C4C23×C13913yes—
337C2×C22⋊C4C23×C13913yes—
338C2×C22⋊C4C23×C13913yes—
339C2×C22⋊C4C23×C13913yes—
340C2×C22⋊C4C23×C13913yes—
341C2×C42C23×C13913yes—
342C2×C42C23×C13913yes—
343C2×C42C23×C13913yes—
344C2×C42C23×C13913yes—
345C2×C42C23×C13913yes—
346C2×C42C23×C13911yescharacteristic
347C2×C42C23×C13911yescharacteristic
348C2×C42C23×C13913yes—
349#95C23×C13911yescharacteristic
350#95C23×C13913yes—
351#95C23×C13913yes—
352#95C23×C13913yes—
353#95C23×C13913yes—
354#95C23×C13913yes—
355#95C23×C13913yes—
356#95C23×C13913yes—
357#95C23×C13911yescharacteristic
358#95C23×C13913yes—
359#95C23×C13913yes—
360#95C23×C13913yes—
361#95C23×C13913yes—
362#95C23×C13913yes—
363#95C23×C13913yes—
364#95C23×C13913yes—
365#95C23×C13913yes—
366#95C23×C13913yes—
367#95C23×C13913yes—
368#95C23×C13913yes—
369C24—26no—
370C24—43no—
371C24—41no—
372C24C24×C13913yes—
373C22×C4—26no—
374C22×C4—26no—
375C22×C4—43no—
376C22×C4—43no—
377C22×C4—43no—
378C22×C4—43no—
379C22×C4C24×C13913yes—
380C22×C4C24×C13913yes—
381C22×C4C24×C13911yescharacteristic
382C22×C4C24×C13913yes—
383C22×C4C24×C13913yes—
384C22×C4C24×C13913yes—
385C22×C4C24×C13913yes—
386C22×C4C24×C13913yes—
387C22×C4C24×C13913yes—
388C22×C4C24×C13913yes—
389C4⋊C4—26no—
390C4⋊C4—26no—
391C4⋊C4—26no—
392C4⋊C4—26no—
393C4⋊C4—26no—
394C4⋊C4—26no—
395C4⋊C4—43no—
396C4⋊C4—43no—
397C4⋊C4—43no—
398C4⋊C4—43no—
399C4⋊C4—43no—
400C4⋊C4—43no—
401C22⋊C4—26no—
402C22⋊C4—26no—
403C22⋊C4—26no—
404C22⋊C4—26no—
405C22⋊C4—26no—
406C22⋊C4—26no—
407C22⋊C4—26no—
408C22⋊C4—43no—
409C22⋊C4—43no—
410C22⋊C4—43no—
411C22⋊C4—43no—
412C22⋊C4#41×C139112yes—
413C42—26no—
414C42—26no—
415C42—43no—
416C42—43no—
417C42—43no—
418C42—43no—
419C42—41no—
420C42—41no—
421C23—28no—
422C23—23no—
423C23—23no—
424C23—23no—
425C23—23no—
426C23—23no—
427C23—23no—
428C23—86no—
429C23—86no—
430C23C2×#41×C13916yes—
431C23C25×C13911yescharacteristic
432C2×C4—23no—
433C2×C4—23no—
434C2×C4—23no—
435C2×C4—23no—
436C2×C4—23no—
437C2×C4—23no—
438C2×C4—23no—
439C2×C4—23no—
440C2×C4—23no—
441C2×C4—23no—
442C2×C4—23no—
443C2×C4—23no—
444C2×C4—23no—
445C2×C4—23no—
446C2×C4—23no—
447C2×C4—23no—
448C2×C4—23no—
449C2×C4—23no—
450C2×C4—23no—
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—23no—
456C2×C4—23no—
457C2×C4—23no—
458C2×C4—86no—
459C2×C4—86no—
460C2×C4C2×#41×C13916yes—
461C2×C4C2×#41×C13916yes—
462C22—26no—
463C22—26no—
464C22—26no—
465C22—43no—
466C22—43no—
467C22—43no—
468C22—43no—
469C22—88no—
470C22C22×#41×C13913yes—
471C22#585×C13913yes—
472C22#585×C13911yescharacteristic
473C4—26no—
474C4—26no—
475C4—41no—
476C4—43no—
477C4—43no—
478C4—43no—
479C4—43no—
480C4—43no—
481C4—43no—
482C4—43no—
483C2—46no—
484C2#3444×C13911yescharacteristic
485C2#3521×C13913yes—
486C2#3521×C13913yes—
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. #2652×C139C2semidirect
2. #2587×C139C2semidirect
3. #2577×C139C2semidirect
4. #2530×C139C2semidirect
5. #2496×C139C2semidirect
8. #2401×C139C2semidirect
9. #2373×C139C2semidirect
10. #2373×C139C2semidirect
15. #401×C139C22semidirect
16. #400×C139C22semidirect
17. #400×C139C22semidirect
18. #400×C139C22semidirect
19. #400×C139C22semidirect
20. #398×C139C22semidirect
29. #389×C139C22semidirect
30. #389×C139C22semidirect
31. #389×C139C22semidirect
38. #387×C139C22semidirect
39. #387×C139C22semidirect
40. #387×C139C22semidirect
41. #387×C139C22semidirect
42. #387×C139C22semidirect
43. #387×C139C22semidirect
44. #387×C139C22semidirect
49. #384×C139C22semidirect
50. #383×C139C22semidirect
55. C4×C4⋊C4×C139C22semidirect
56. C4×C4⋊C4×C139C22semidirect
57. C4×C4⋊C4×C139C22semidirect
58. C4×C4⋊C4×C139C22semidirect
65. #376×C139C22semidirect
66. #376×C139C22semidirect
243. #36057C139direct (N × H)
244. C139#36057direct (N × H)
245. #2652C2×C139semidirect
246. #2587C2×C139semidirect
247. #2577C2×C139semidirect
248. #2530C2×C139semidirect
249. #2496C2×C139semidirect
252. #2401C2×C139semidirect
253. #2373C2×C139semidirect
254. #2373C2×C139semidirect
259. #401C22×C139semidirect
260. #400C22×C139semidirect
261. #400C22×C139semidirect
262. #400C22×C139semidirect
263. #400C22×C139semidirect
264. #398C22×C139semidirect
273. #389C22×C139semidirect
274. #389C22×C139semidirect
275. #389C22×C139semidirect
282. #387C22×C139semidirect
283. #387C22×C139semidirect
284. #387C22×C139semidirect
285. #387C22×C139semidirect
286. #387C22×C139semidirect
287. #387C22×C139semidirect
288. #387C22×C139semidirect
293. #384C22×C139semidirect
294. #383C22×C139semidirect
299. C4×C4⋊C4C22×C139semidirect
300. C4×C4⋊C4C22×C139semidirect
301. C4×C4⋊C4C22×C139semidirect
302. C4×C4⋊C4C22×C139semidirect
309. #376C22×C139semidirect
310. #376C22×C139semidirect

Maximal subgroups

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

subgroupindex
#2652×C1392
#2587×C1392
#2577×C1392
#2530×C1392
#2496×C1392
#2480×C1392
#2401×C1392
#2373×C1392
#2273×C1392
#36057139