Finite Group Databasebeta

← C139×#18133 #48012729

Subgroups — C139×#18133 #48012729

Order 35584.

1310 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#543×C139C211yesmaximal, characteristic, complemented
2#3007×C139C212yesmaximal, complemented
3#2404×C139C211yesmaximal, characteristic
4#1602×C139C214yesmaximal, complemented
5#1596×C139C214yesmaximal, complemented
6#1511×C139C212yesmaximal, complemented
7#1462×C139C211yesmaximal, characteristic, complemented
8C22×#41×C139C2211yescharacteristic
9C2×#137×C139—22no—
10#543×C139—24no—
11#543×C139—22no—
12#543×C139C2214yes—
13C2×C22⋊Q8×C139—22no—
14C2×C22⋊Q8×C139—21no—
15C2×C22⋊Q8×C139—22no—
16C2×C22⋊Q8×C139C2212yes—
17C2×#120×C139—21no—
18C22×C22⋊C4×C139—21no—
19C22×C22⋊C4×C139C2211yescharacteristic
20#452×C139—24no—
21#451×C139C2214yescomplemented
22#450×C139C2214yescomplemented
23#417×C139—22no—
24#407×C139C2212yes—
25#393×C139C2212yes—
26#392×C139C2212yes—
27#386×C139—21no—
28#386×C139—22no—
29#381×C139C2211yescharacteristic
30#328×C139C2218yescomplemented
31#323×C139C2214yes—
32C25×C139D411yescharacteristic
33C2×#41×C139—22no—
34C2×#41×C139—22no—
35C2×#41×C139—44no—
36C22×Q8×C139—21no—
37C22×Q8×C139D412yescomplemented
38C22×Q8×C139C2311yescharacteristic
39C22×D4×C139—21no—
40C22×D4×C139—22no—
41C22×D4×C139C2311yescharacteristic
42C23×C4×C139—21no—
43C23×C4×C139—21no—
44C23×C4×C139—21no—
45C23×C4×C139D411yescharacteristic
46C23×C4×C139C2311yescharacteristic
47#137×C139—48no—
48C2×Q16×C139—24no—
49C2×SD16×C139—24no—
50C2×M16×C139—22no—
51C22⋊Q8×C139—28no—
52C22⋊Q8×C139—28no—
53C22⋊Q8×C139—24no—
54C22⋊Q8×C139—28no—
55C22⋊Q8×C139—24no—
56C22⋊Q8×C139—22no—
57C22⋊Q8×C139—22no—
58C22⋊Q8×C139—28no—
59C22⋊Q8×C139D414yescomplemented
60C22⋊Q8×C139C2314yes—
61#120×C139—44no—
62C2×C4⋊C4×C139—21no—
63C2×C4⋊C4×C139—22no—
64C2×C4⋊C4×C139—22no—
65C2×C4⋊C4×C139D412yescomplemented
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139—24no—
68C2×C22⋊C4×C139—22no—
69C2×C22⋊C4×C139—24no—
70C2×C22⋊C4×C139—22no—
71C2×C22⋊C4×C139—22no—
72C2×C22⋊C4×C139—21no—
73C2×C22⋊C4×C139—22no—
74C2×C22⋊C4×C139—22no—
75C2×C22⋊C4×C139D412yes—
76C2×C22⋊C4×C139C2312yes—
77#103×C139—24no—
78#102×C139—24no—
79C22⋊C8×C139—22no—
80C22⋊C8×C139C2314yes—
81#95×C139—21no—
82#95×C139—22no—
83#95×C139C2312yes—
84C24×C139—21no—
85C24×C139—21no—
86C24×C139—24no—
87C24×C139—21no—
88C24×C139—42no—
89C24×C139—81no—
90C24×C139C2×D411yescharacteristic
91C24×C139C2×D412yes—
92#41×C139—28no—
93#41×C139—44no—
94#41×C139—44no—
95#41×C139—44no—
96C2×Q8×C139—24no—
97C2×Q8×C139—22no—
98C2×Q8×C139—22no—
99C2×Q8×C139—42no—
100C2×Q8×C139—44no—
101C2×Q8×C139—82no—
102C2×Q8×C139C2×D414yes—
103C2×D4×C139—24no—
104C2×D4×C139—22no—
105C2×D4×C139—42no—
106C2×D4×C139—42no—
107C2×D4×C139—41no—
108C2×D4×C139—41no—
109C2×D4×C139—44no—
110C2×D4×C139—44no—
111C2×D4×C139—82no—
112C22×C4×C139—22no—
113C22×C4×C139—21no—
114C22×C4×C139—22no—
115C22×C4×C139—21no—
116C22×C4×C139—24no—
117C22×C4×C139—24no—
118C22×C4×C139—21no—
119C22×C4×C139—22no—
120C22×C4×C139—42no—
121C22×C4×C139—42no—
122C22×C4×C139—42no—
123C22×C4×C139—42no—
124C22×C4×C139—81no—
125C22×C4×C139—82no—
126C22×C4×C139—82no—
127C22×C4×C139C2×D412yes—
128C22×C4×C139C2×D412yes—
129C22×C4×C139C2×D411yescharacteristic
130C22×C4×C139C2×D412yes—
131C22×C4×C139C2411yescharacteristic
132Q16×C139—48no—
133SD16×C139—48no—
134M16×C139—44no—
135C2×C8×C139—24no—
136C4⋊C4×C139—24no—
137C4⋊C4×C139—28no—
138C4⋊C4×C139—24no—
139C4⋊C4×C139—22no—
140C4⋊C4×C139—24no—
141C4⋊C4×C139C2×D414yes—
142C22⋊C4×C139—28no—
143C22⋊C4×C139—24no—
144C22⋊C4×C139—24no—
145C22⋊C4×C139—24no—
146C22⋊C4×C139—24no—
147C22⋊C4×C139—44no—
148C22⋊C4×C139—42no—
149C22⋊C4×C139—82no—
150C23×C139—24no—
151C23×C139—24no—
152C23×C139—22no—
153C23×C139—22no—
154C23×C139—22no—
155C23×C139—22no—
156C23×C139—22no—
157C23×C139—41no—
158C23×C139—42no—
159C23×C139—42no—
160C23×C139—42no—
161C23×C139—42no—
162C23×C139—41no—
163C23×C139—42no—
164C23×C139—41no—
165C23×C139—42no—
166C23×C139—81no—
167C23×C139—81no—
168C23×C139—88no—
169C23×C139#12011yescharacteristic
170C23×C139#12011yescharacteristic
171C23×C139#13714yescomplemented
172C23×C139C22×D411yescharacteristic
173Q8×C139—24no—
174Q8×C139—44no—
175Q8×C139—42no—
176Q8×C139—82no—
177Q8×C139—84no—
178D4×C139—24no—
179D4×C139—42no—
180D4×C139—44no—
181D4×C139—44no—
182D4×C139—88no—
183C2×C4×C139—24no—
184C2×C4×C139—22no—
185C2×C4×C139—24no—
186C2×C4×C139—22no—
187C2×C4×C139—24no—
188C2×C4×C139—41no—
189C2×C4×C139—42no—
190C2×C4×C139—41no—
191C2×C4×C139—48no—
192C2×C4×C139—41no—
193C2×C4×C139—42no—
194C2×C4×C139—44no—
195C2×C4×C139—41no—
196C2×C4×C139—44no—
197C2×C4×C139—42no—
198C2×C4×C139—42no—
199C2×C4×C139—42no—
200C2×C4×C139—42no—
201C2×C4×C139—81no—
202C2×C4×C139—84no—
203C2×C4×C139—84no—
204C2×C4×C139#12012yes—
205C2×C4×C139C22×D412yes—
206C8×C139—44no—
207C22×C139—21no—
208C22×C139—21no—
209C22×C139—21no—
210C22×C139—21no—
211C22×C139—21no—
212C22×C139—24no—
213C22×C139—21no—
214C22×C139—21no—
215C22×C139—44no—
216C22×C139—44no—
217C22×C139—48no—
218C22×C139—44no—
219C22×C139—42no—
220C22×C139—42no—
221C22×C139—42no—
222C22×C139—82no—
223C22×C139—82no—
224C22×C139—84no—
225C22×C139—81no—
226C22×C139—81no—
227C22×C139B(4,𝔽2)12yes—
228C22×C139C2×#12011yescharacteristic
229C22×C139C2×#13712yes—
230C4×C139—22no—
231C4×C139—22no—
232C4×C139—42no—
233C4×C139—44no—
234C4×C139—42no—
235C4×C139—44no—
236C4×C139—82no—
237C2×C139—22no—
238C2×C139—22no—
239C2×C139—41no—
240C2×C139—44no—
241C2×C139—82no—
242C2×C139#300411yescharacteristic
243C2×C139#301911yescharacteristic
244C2×C139C2×B(4,𝔽2)11yescharacteristic
245#18133C13911yesmaximal, characteristic, direct product factor, Sylow
246C139#1813311yescharacteristic, direct product factor, Sylow
247C2×#543C2×C13911yescharacteristic, complemented
248#3007C2×C13912yescomplemented
249#2404C2×C13911yescharacteristic
250#1602C2×C13914yescomplemented
251#1596C2×C13914yescomplemented
252#1511C2×C13912yescomplemented
253#1462C2×C13911yescharacteristic, complemented
254C22×#41C22×C13911yescharacteristic
255C2×#137—22no—
256#543—24no—
257#543—22no—
258#543C22×C13914yes—
259C2×C22⋊Q8—22no—
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8—22no—
262C2×C22⋊Q8C22×C13912yes—
263C2×#120—21no—
264C22×C22⋊C4—21no—
265C22×C22⋊C4C22×C13911yescharacteristic
266#452—24no—
267#451C22×C13914yescomplemented
268#450C22×C13914yescomplemented
269#417—22no—
270#407C22×C13912yes—
271#393C22×C13912yes—
272#392C22×C13912yes—
273#386—21no—
274#386—22no—
275#381C22×C13911yescharacteristic
276#328C22×C13918yescomplemented
277#323C22×C13914yes—
278C25D4×C13911yescharacteristic
279C2×#41—22no—
280C2×#41—22no—
281C2×#41—44no—
282C22×Q8—21no—
283C22×Q8D4×C13912yescomplemented
284C22×Q8C23×C13911yescharacteristic
285C22×D4—21no—
286C22×D4—22no—
287C22×D4C23×C13911yescharacteristic
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4D4×C13911yescharacteristic
292C23×C4C23×C13911yescharacteristic
293#137—48no—
294C2×Q16—24no—
295C2×SD16—24no—
296C2×M16—22no—
297C22⋊Q8—28no—
298C22⋊Q8—28no—
299C22⋊Q8—24no—
300C22⋊Q8—28no—
301C22⋊Q8—24no—
302C22⋊Q8—22no—
303C22⋊Q8—22no—
304C22⋊Q8—28no—
305C22⋊Q8D4×C13914yescomplemented
306C22⋊Q8C23×C13914yes—
307#120—44no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4D4×C13912yescomplemented
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4D4×C13912yes—
322C2×C22⋊C4C23×C13912yes—
323#103—24no—
324#102—24no—
325C22⋊C8—22no—
326C22⋊C8C23×C13914yes—
327#95—21no—
328#95—22no—
329#95C23×C13912yes—
330C24—21no—
331C24—21no—
332C24—24no—
333C24—21no—
334C24—42no—
335C24—81no—
336C24C2×D4×C13911yescharacteristic
337C24C2×D4×C13912yes—
338#41—28no—
339#41—44no—
340#41—44no—
341#41—44no—
342C2×Q8—24no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—42no—
346C2×Q8—44no—
347C2×Q8—82no—
348C2×Q8C2×D4×C13914yes—
349C2×D4—24no—
350C2×D4—22no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—44no—
356C2×D4—44no—
357C2×D4—82no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—81no—
371C22×C4—82no—
372C22×C4—82no—
373C22×C4C2×D4×C13912yes—
374C22×C4C2×D4×C13912yes—
375C22×C4C2×D4×C13911yescharacteristic
376C22×C4C2×D4×C13912yes—
377C22×C4C24×C13911yescharacteristic
378Q16—48no—
379SD16—48no—
380M16—44no—
381C2×C8—24no—
382C4⋊C4—24no—
383C4⋊C4—28no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—24no—
387C4⋊C4C2×D4×C13914yes—
388C22⋊C4—28no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—24no—
393C22⋊C4—44no—
394C22⋊C4—42no—
395C22⋊C4—82no—
396C23—24no—
397C23—24no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—41no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—41no—
409C23—42no—
410C23—41no—
411C23—42no—
412C23—81no—
413C23—81no—
414C23—88no—
415C23#120×C13911yescharacteristic
416C23#120×C13911yescharacteristic
417C23#137×C13914yescomplemented
418C23C22×D4×C13911yescharacteristic
419Q8—24no—
420Q8—44no—
421Q8—42no—
422Q8—82no—
423Q8—84no—
424D4—24no—
425D4—42no—
426D4—44no—
427D4—44no—
428D4—88no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—48no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—81no—
448C2×C4—84no—
449C2×C4—84no—
450C2×C4#120×C13912yes—
451C2×C4C22×D4×C13912yes—
452C8—44no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—24no—
460C22—21no—
461C22—44no—
462C22—44no—
463C22—48no—
464C22—44no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—82no—
469C22—82no—
470C22—84no—
471C22—81no—
472C22—81no—
473C22B(4,𝔽2)×C13912yes—
474C22C2×#120×C13911yescharacteristic
475C22C2×#137×C13912yes—
476C4—22no—
477C4—22no—
478C4—42no—
479C4—44no—
480C4—42no—
481C4—44no—
482C4—82no—
483C2—22no—
484C2—22no—
485C2—41no—
486C2—44no—
487C2—82no—
488C2#3004×C13911yescharacteristic
489C2#3019×C13911yescharacteristic
490C2C2×B(4,𝔽2)×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2404×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
1. C2×#543×C139C2semidirect
2. #3007×C139C2semidirect
4. #1602×C139C2semidirect
5. #1596×C139C2semidirect
6. #1511×C139C2semidirect
7. #1462×C139C2semidirect
21. #451×C139C22semidirect
22. #450×C139C22semidirect
30. #328×C139C22semidirect
37. C22×Q8×C139D4semidirect
59. C22⋊Q8×C139D4semidirect
65. C2×C4⋊C4×C139D4semidirect
171. C23×C139#137semidirect
245. #18133C139direct (N × H)
246. C139#18133direct (N × H)
247. C2×#543C2×C139semidirect
248. #3007C2×C139semidirect
250. #1602C2×C139semidirect
251. #1596C2×C139semidirect
252. #1511C2×C139semidirect
253. #1462C2×C139semidirect
267. #451C22×C139semidirect
268. #450C22×C139semidirect
276. #328C22×C139semidirect
283. C22×Q8D4×C139semidirect
305. C22⋊Q8D4×C139semidirect
311. C2×C4⋊C4D4×C139semidirect
417. C23#137×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#543×C1392
#3007×C1392
#2404×C1392
#1602×C1392
#1596×C1392
#1511×C1392
#1462×C1392
#18133139