Finite Group Databasebeta

← C139×#18137 #48012733

Subgroups — C139×#18137 #48012733

Order 35584.

1398 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C139C211yesmaximal, characteristic
2#3094×C139C212yesmaximal, complemented
3#2482×C139C211yesmaximal, characteristic, complemented
4#1613×C139C214yesmaximal, complemented
5#1607×C139C214yesmaximal, complemented
6#1510×C139C212yesmaximal, complemented
7#1462×C139C211yesmaximal, characteristic, complemented
8C23×D4×C139—21no—
9#534×C139—24no—
10#534×C139—22no—
11#534×C139C2214yes—
12C2×#123×C139—22no—
13C2×#121×C139—21no—
14C2×#121×C139C2212yes—
15C2×#120×C139—22no—
16C2×#117×C139C2211yescharacteristic, complemented
17C22×C22⋊C4×C139C2211yescharacteristic
18#482×C139—24no—
19#481×C139C2214yescomplemented
20#480×C139C2214yescomplemented
21#428×C139—22no—
22#418×C139—22no—
23#407×C139C2212yescomplemented
24#399×C139C2212yescomplemented
25#397×C139C2212yescomplemented
26#388×C139—22no—
27#385×C139—21no—
28#381×C139C2211yescharacteristic, complemented
29#379×C139—21no—
30#327×C139C2218yescomplemented
31#323×C139C2214yescomplemented
32C25×C139—21no—
33C25×C139D411yescharacteristic
34C22×D4×C139—22no—
35C22×D4×C139—24no—
36C22×D4×C139—22no—
37C22×D4×C139—24no—
38C22×D4×C139—21no—
39C22×D4×C139—48no—
40C22×D4×C139D412yes—
41C23×C4×C139—21no—
42C23×C4×C139D411yescharacteristic
43C23×C4×C139C2311yescharacteristic
44C2×M16×C139—22no—
45#123×C139—28no—
46#123×C139—28no—
47#121×C139—24no—
48#121×C139—24no—
49#121×C139—22no—
50#121×C139—22no—
51#121×C139D414yes—
52#121×C139C2314yes—
53#120×C139—28no—
54#120×C139—28no—
55#117×C139—22no—
56#117×C139—22no—
57C2×C4⋊C4×C139—21no—
58C2×C4⋊C4×C139—22no—
59C2×C4⋊C4×C139D412yes—
60C2×C4⋊C4×C139C2311yescharacteristic, complemented
61C2×C4⋊C4×C139C2311yescharacteristic, complemented
62C2×C22⋊C4×C139—22no—
63C2×C22⋊C4×C139—22no—
64C2×C22⋊C4×C139—22no—
65C2×C22⋊C4×C139—22no—
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139—21no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—22no—
70C2×C22⋊C4×C139D412yes—
71C2×C22⋊C4×C139C2312yes—
72C2×C42×C139—21no—
73#107×C139—24no—
74#106×C139—24no—
75#102×C139—24no—
76#102×C139—24no—
77C22⋊C8×C139—22no—
78C22⋊C8×C139C2314yescomplemented
79#95×C139—22no—
80#95×C139—21no—
81#95×C139C2312yescomplemented
82C24×C139—21no—
83C24×C139—21no—
84C24×C139—24no—
85C24×C139—24no—
86C24×C139—22no—
87C24×C139—44no—
88C24×C139—42no—
89C24×C139—81no—
90C24×C139—82no—
91C24×C139—82no—
92C24×C139C2×D411yescharacteristic
93C24×C139C2×D412yes—
94C2×D4×C139—28no—
95C2×D4×C139—24no—
96C2×D4×C139—24no—
97C2×D4×C139—24no—
98C2×D4×C139—22no—
99C2×D4×C139—44no—
100C2×D4×C139—48no—
101C2×D4×C139—416no—
102C2×D4×C139—48no—
103C2×D4×C139—48no—
104C2×D4×C139—48no—
105C2×D4×C139—82no—
106C2×D4×C139C2×D414yes—
107C22×C4×C139—24no—
108C22×C4×C139—21no—
109C22×C4×C139—22no—
110C22×C4×C139—21no—
111C22×C4×C139—22no—
112C22×C4×C139—21no—
113C22×C4×C139—21no—
114C22×C4×C139—42no—
115C22×C4×C139—44no—
116C22×C4×C139—81no—
117C22×C4×C139C2×D412yes—
118C22×C4×C139C2×D412yes—
119C22×C4×C139C2×D411yescharacteristic
120C22×C4×C139C2×D412yes—
121C22×C4×C139C2411yescharacteristic
122M16×C139—44no—
123C2×C8×C139—24no—
124C4⋊C4×C139—24no—
125C4⋊C4×C139—22no—
126C4⋊C4×C139—22no—
127C4⋊C4×C139—22no—
128C4⋊C4×C139—82no—
129C4⋊C4×C139C2×D414yes—
130C22⋊C4×C139—28no—
131C22⋊C4×C139—24no—
132C22⋊C4×C139—24no—
133C22⋊C4×C139—24no—
134C22⋊C4×C139—24no—
135C22⋊C4×C139—42no—
136C22⋊C4×C139—41no—
137C22⋊C4×C139—41no—
138C22⋊C4×C139—44no—
139C22⋊C4×C139—82no—
140C42×C139—42no—
141C23×C139—24no—
142C23×C139—24no—
143C23×C139—22no—
144C23×C139—22no—
145C23×C139—22no—
146C23×C139—22no—
147C23×C139—24no—
148C23×C139—41no—
149C23×C139—42no—
150C23×C139—42no—
151C23×C139—42no—
152C23×C139—44no—
153C23×C139—48no—
154C23×C139—44no—
155C23×C139—42no—
156C23×C139—44no—
157C23×C139—81no—
158C23×C139—81no—
159C23×C139—88no—
160C23×C139—84no—
161C23×C139—84no—
162C23×C139—816no—
163C23×C139#12011yescharacteristic
164C23×C139#12011yescharacteristic
165C23×C139AGL(1,ℤ/8)14yes—
166C23×C139C22×D411yescharacteristic
167D4×C139—44no—
168D4×C139—416no—
169D4×C139—48no—
170D4×C139—48no—
171D4×C139—82no—
172D4×C139—84no—
173C2×C4×C139—24no—
174C2×C4×C139—22no—
175C2×C4×C139—24no—
176C2×C4×C139—42no—
177C2×C4×C139—41no—
178C2×C4×C139—41no—
179C2×C4×C139—44no—
180C2×C4×C139—48no—
181C2×C4×C139—42no—
182C2×C4×C139—42no—
183C2×C4×C139—42no—
184C2×C4×C139—42no—
185C2×C4×C139—42no—
186C2×C4×C139—41no—
187C2×C4×C139—41no—
188C2×C4×C139—42no—
189C2×C4×C139—42no—
190C2×C4×C139—81no—
191C2×C4×C139#12012yes—
192C2×C4×C139C22×D412yes—
193C8×C139—44no—
194C22×C139—21no—
195C22×C139—21no—
196C22×C139—21no—
197C22×C139—21no—
198C22×C139—24no—
199C22×C139—21no—
200C22×C139—21no—
201C22×C139—21no—
202C22×C139—44no—
203C22×C139—44no—
204C22×C139—48no—
205C22×C139—42no—
206C22×C139—42no—
207C22×C139—44no—
208C22×C139—44no—
209C22×C139—44no—
210C22×C139—82no—
211C22×C139—88no—
212C22×C139—84no—
213C22×C139—816no—
214C22×C139#45812yes—
215C22×C139C2×#12011yescharacteristic
216C22×C139C2×AGL(1,ℤ/8)12yes—
217C4×C139—22no—
218C4×C139—22no—
219C4×C139—44no—
220C4×C139—42no—
221C4×C139—82no—
222C4×C139—81no—
223C4×C139—81no—
224C2×C139—22no—
225C2×C139—22no—
226C2×C139—41no—
227C2×C139—44no—
228C2×C139—84no—
229C2×C139#300311yescharacteristic
230C2×C139#301911yescharacteristic
231C2×C139C2×#45811yescharacteristic
232#18137C13911yesmaximal, characteristic, direct product factor, Sylow
233C139#1813711yescharacteristic, direct product factor, Sylow
234C2×#534C2×C13911yescharacteristic
235#3094C2×C13912yescomplemented
236#2482C2×C13911yescharacteristic, complemented
237#1613C2×C13914yescomplemented
238#1607C2×C13914yescomplemented
239#1510C2×C13912yescomplemented
240#1462C2×C13911yescharacteristic, complemented
241C23×D4—21no—
242#534—24no—
243#534—22no—
244#534C22×C13914yes—
245C2×#123—22no—
246C2×#121—21no—
247C2×#121C22×C13912yes—
248C2×#120—22no—
249C2×#117C22×C13911yescharacteristic, complemented
250C22×C22⋊C4C22×C13911yescharacteristic
251#482—24no—
252#481C22×C13914yescomplemented
253#480C22×C13914yescomplemented
254#428—22no—
255#418—22no—
256#407C22×C13912yescomplemented
257#399C22×C13912yescomplemented
258#397C22×C13912yescomplemented
259#388—22no—
260#385—21no—
261#381C22×C13911yescharacteristic, complemented
262#379—21no—
263#327C22×C13918yescomplemented
264#323C22×C13914yescomplemented
265C25—21no—
266C25D4×C13911yescharacteristic
267C22×D4—22no—
268C22×D4—24no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—21no—
272C22×D4—48no—
273C22×D4D4×C13912yes—
274C23×C4—21no—
275C23×C4D4×C13911yescharacteristic
276C23×C4C23×C13911yescharacteristic
277C2×M16—22no—
278#123—28no—
279#123—28no—
280#121—24no—
281#121—24no—
282#121—22no—
283#121—22no—
284#121D4×C13914yes—
285#121C23×C13914yes—
286#120—28no—
287#120—28no—
288#117—22no—
289#117—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4D4×C13912yes—
293C2×C4⋊C4C23×C13911yescharacteristic, complemented
294C2×C4⋊C4C23×C13911yescharacteristic, complemented
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4D4×C13912yes—
304C2×C22⋊C4C23×C13912yes—
305C2×C42—21no—
306#107—24no—
307#106—24no—
308#102—24no—
309#102—24no—
310C22⋊C8—22no—
311C22⋊C8C23×C13914yescomplemented
312#95—21no—
313#95—22no—
314#95C23×C13912yescomplemented
315C24—21no—
316C24—21no—
317C24—24no—
318C24—24no—
319C24—22no—
320C24—44no—
321C24—42no—
322C24—81no—
323C24—82no—
324C24—82no—
325C24C2×D4×C13911yescharacteristic
326C24C2×D4×C13912yes—
327C2×D4—28no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—24no—
331C2×D4—22no—
332C2×D4—44no—
333C2×D4—48no—
334C2×D4—416no—
335C2×D4—48no—
336C2×D4—48no—
337C2×D4—48no—
338C2×D4—82no—
339C2×D4C2×D4×C13914yes—
340C22×C4—24no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—81no—
350C22×C4C2×D4×C13912yes—
351C22×C4C2×D4×C13912yes—
352C22×C4C2×D4×C13911yescharacteristic
353C22×C4C2×D4×C13912yes—
354C22×C4C24×C13911yescharacteristic
355M16—44no—
356C2×C8—24no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—82no—
362C4⋊C4C2×D4×C13914yes—
363C22⋊C4—28no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—42no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—44no—
372C22⋊C4—82no—
373C42—42no—
374C23—24no—
375C23—24no—
376C23—22no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—24no—
381C23—41no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—44no—
386C23—48no—
387C23—44no—
388C23—42no—
389C23—44no—
390C23—81no—
391C23—81no—
392C23—88no—
393C23—84no—
394C23—84no—
395C23—816no—
396C23#120×C13911yescharacteristic
397C23#120×C13911yescharacteristic
398C23AGL(1,ℤ/8)×C13914yes—
399C23C22×D4×C13911yescharacteristic
400D4—44no—
401D4—416no—
402D4—48no—
403D4—48no—
404D4—82no—
405D4—84no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—44no—
413C2×C4—48no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—81no—
424C2×C4#120×C13912yes—
425C2×C4C22×D4×C13912yes—
426C8—44no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—24no—
433C22—21no—
434C22—21no—
435C22—44no—
436C22—44no—
437C22—48no—
438C22—42no—
439C22—42no—
440C22—44no—
441C22—44no—
442C22—44no—
443C22—82no—
444C22—88no—
445C22—84no—
446C22—816no—
447C22#458×C13912yes—
448C22C2×#120×C13911yescharacteristic
449C22C2×AGL(1,ℤ/8)×C13912yes—
450C4—22no—
451C4—22no—
452C4—44no—
453C4—42no—
454C4—82no—
455C4—81no—
456C4—81no—
457C2—22no—
458C2—22no—
459C2—41no—
460C2—44no—
461C2—84no—
462C2#3003×C13911yescharacteristic
463C2#3019×C13911yescharacteristic
464C2C2×#458×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#534×C139C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3094×C139C2semidirect
3. #2482×C139C2semidirect
4. #1613×C139C2semidirect
5. #1607×C139C2semidirect
6. #1510×C139C2semidirect
7. #1462×C139C2semidirect
16. C2×#117×C139C22semidirect
19. #481×C139C22semidirect
20. #480×C139C22semidirect
23. #407×C139C22semidirect
24. #399×C139C22semidirect
25. #397×C139C22semidirect
28. #381×C139C22semidirect
30. #327×C139C22semidirect
31. #323×C139C22semidirect
60. C2×C4⋊C4×C139C23semidirect
61. C2×C4⋊C4×C139C23semidirect
78. C22⋊C8×C139C23semidirect
81. #95×C139C23semidirect
232. #18137C139direct (N × H)
233. C139#18137direct (N × H)
235. #3094C2×C139semidirect
236. #2482C2×C139semidirect
237. #1613C2×C139semidirect
238. #1607C2×C139semidirect
239. #1510C2×C139semidirect
240. #1462C2×C139semidirect
249. C2×#117C22×C139semidirect
252. #481C22×C139semidirect
253. #480C22×C139semidirect
256. #407C22×C139semidirect
257. #399C22×C139semidirect
258. #397C22×C139semidirect
261. #381C22×C139semidirect
263. #327C22×C139semidirect
264. #323C22×C139semidirect
293. C2×C4⋊C4C23×C139semidirect
294. C2×C4⋊C4C23×C139semidirect
311. C22⋊C8C23×C139semidirect
314. #95C23×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1392
#3094×C1392
#2482×C1392
#1613×C1392
#1607×C1392
#1510×C1392
#1462×C1392
#18137139