Finite Group Databasebeta

← C139×#8968 #48003564

Subgroups — C139×#8968 #48003564

Order 35584.

600 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2973×C139C211yesmaximal, characteristic
2C4×#123×C139C211yesmaximal, characteristic
3#1817×C139C212yesmaximal, complemented
4#1459×C139C211yesmaximal, characteristic
5#1282×C139C212yesmaximal, complemented
6C2×#123×C139C411yescharacteristic
7C2×C4×D4×C139C2211yescharacteristic
8C22×C42×C139C2211yescharacteristic
9#435×C139—24no—
10#432×C139—21no—
11#407×C139—21no—
12C2×C22⋊C8×C139C2212yes—
13C2×C22⋊C8×C139C2212yes—
14#388×C139—21no—
15#387×C139—21no—
16#386×C139C411yescharacteristic
17#385×C139C411yescharacteristic
18#381×C139C411yescharacteristic
19C4×C4⋊C4×C139—21no—
20C4×C22⋊C4×C139—21no—
21C4×C22⋊C4×C139C2211yescharacteristic
22#336×C139—24no—
23#324×C139—21no—
24#323×C139—21no—
25C22×D4×C139C2×C411yescharacteristic
26C23×C4×C139C2×C411yescharacteristic
27C23×C4×C139C2×C411yescharacteristic
28C23×C4×C139D411yescharacteristic
29C23×C4×C139C2311yescharacteristic
30C2×M16×C139—22no—
31C22×C8×C139—22no—
32C22×C8×C139D414yes—
33#123×C139—22no—
34#123×C139—22no—
35C4×D4×C139—22no—
36C4×D4×C139—22no—
37C2×C4⋊C4×C139—21no—
38C2×C4⋊C4×C139—21no—
39C2×C4⋊C4×C139D411yescharacteristic
40C2×C22⋊C4×C139—21no—
41C2×C22⋊C4×C139—21no—
42C2×C22⋊C4×C139C2×C411yescharacteristic
43C2×C22⋊C4×C139C2×C411yescharacteristic
44C2×C22⋊C4×C139C2×C411yescharacteristic
45C2×C22⋊C4×C139D411yescharacteristic
46C2×C42×C139—22no—
47C2×C42×C139—21no—
48C2×C42×C139—21no—
49C2×C42×C139—21no—
50C2×C42×C139—22no—
51C2×C42×C139D411yescharacteristic
52C4⋊C8×C139—22no—
53C22⋊C8×C139—22no—
54C22⋊C8×C139—22no—
55C22⋊C8×C139—22no—
56C22⋊C8×C139—22no—
57C22⋊C8×C139—22no—
58#97×C139—22no—
59#95×C139—21no—
60#95×C139—21no—
61#95×C139—21no—
62#95×C139—21no—
63#95×C139—21no—
64C24×C139C22⋊C411yescharacteristic
65C24×C139C22×C411yescharacteristic
66C2×D4×C139—22no—
67C2×D4×C139—21no—
68C2×D4×C139—21no—
69C2×D4×C139—22no—
70C22×C4×C139—21no—
71C22×C4×C139—21no—
72C22×C4×C139—21no—
73C22×C4×C139—22no—
74C22×C4×C139—22no—
75C22×C4×C139—21no—
76C22×C4×C139—22no—
77C22×C4×C139—21no—
78C22×C4×C139—21no—
79C22×C4×C139—21no—
80C22×C4×C139—42no—
81C22×C4×C139—42no—
82C22×C4×C139—42no—
83C22×C4×C139C22⋊C411yescharacteristic
84C22×C4×C139C22⋊C411yescharacteristic
85C22×C4×C139C22⋊C411yescharacteristic
86C22×C4×C139M1612yescomplemented
87C22×C4×C139C2×D412yes—
88C22×C4×C139C2×D411yescharacteristic
89C22×C4×C139C2×D411yescharacteristic
90C22×C4×C139#4112yes—
91M16×C139—82no—
92C2×C8×C139—24no—
93C2×C8×C139—44no—
94C2×C8×C139—44no—
95C2×C8×C139—42no—
96C4⋊C4×C139—24no—
97C4⋊C4×C139—22no—
98C4⋊C4×C139—42no—
99C22⋊C4×C139—24no—
100C22⋊C4×C139—22no—
101C22⋊C4×C139—21no—
102C22⋊C4×C139—22no—
103C22⋊C4×C139—22no—
104C22⋊C4×C139—42no—
105C22⋊C4×C139M1612yescomplemented
106C42×C139—21no—
107C42×C139—21no—
108C42×C139—42no—
109C42×C139—41no—
110C42×C139—42no—
111C42×C139—41no—
112C23×C139—21no—
113C23×C139—21no—
114C23×C139—21no—
115C23×C139—41no—
116C23×C139—41no—
117C23×C139—41no—
118C23×C139—41no—
119C23×C139C2×C22⋊C411yescharacteristic
120C23×C139C4×D412yes—
121C23×C139C2×M1611yescharacteristic
122C23×C139C2×M1611yescharacteristic
123C23×C139#13112yes—
124D4×C139—42no—
125D4×C139—42no—
126C2×C4×C139—22no—
127C2×C4×C139—24no—
128C2×C4×C139—22no—
129C2×C4×C139—24no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—22no—
134C2×C4×C139—22no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—24no—
138C2×C4×C139—41no—
139C2×C4×C139—42no—
140C2×C4×C139—41no—
141C2×C4×C139—41no—
142C2×C4×C139—41no—
143C2×C4×C139—42no—
144C2×C4×C139—41no—
145C2×C4×C139—41no—
146C2×C4×C139—41no—
147C2×C4×C139—42no—
148C2×C4×C139—42no—
149C2×C4×C139—41no—
150C2×C4×C139—41no—
151C2×C4×C139—41no—
152C2×C4×C139—41no—
153C2×C4×C139—41no—
154C2×C4×C139—81no—
155C2×C4×C139#12011yescharacteristic
156C2×C4×C139#12112yes—
157C2×C4×C139#12311yescharacteristic
158C8×C139—44no—
159C8×C139—82no—
160C22×C139—21no—
161C22×C139—22no—
162C22×C139—21no—
163C22×C139—22no—
164C22×C139—41no—
165C22×C139—41no—
166C22×C139—42no—
167C22×C139—42no—
168C22×C139—41no—
169C22×C139—41no—
170C22×C139—41no—
171C22×C139—81no—
172C22×C139#38611yescharacteristic
173C22×C139#40711yescharacteristic
174C22×C139#40811yescharacteristic
175C22×C139#43512yes—
176C22×C139#43612yes—
177C4×C139—22no—
178C4×C139—21no—
179C4×C139—42no—
180C4×C139—42no—
181C4×C139—41no—
182C4×C139—41no—
183C4×C139—42no—
184C4×C139—41no—
185C4×C139—81no—
186C4×C139#45812yes—
187C2×C139—21no—
188C2×C139—21no—
189C2×C139—22no—
190C2×C139—22no—
191C2×C139—81no—
192C2×C139#187011yescharacteristic
193C2×C139#189011yescharacteristic
194C2×C139#189111yescharacteristic
195#8968C13911yesmaximal, characteristic, direct product factor, Sylow
196C139#896811yescharacteristic, direct product factor, Sylow
197#2973C2×C13911yescharacteristic
198C4×#123C2×C13911yescharacteristic
199#1817C2×C13912yescomplemented
200#1459C2×C13911yescharacteristic
201#1282C2×C13912yescomplemented
202C2×#123C4×C13911yescharacteristic
203C2×C4×D4C22×C13911yescharacteristic
204C22×C42C22×C13911yescharacteristic
205#435—24no—
206#432—21no—
207#407—21no—
208C2×C22⋊C8C22×C13912yes—
209C2×C22⋊C8C22×C13912yes—
210#388—21no—
211#387—21no—
212#386C4×C13911yescharacteristic
213#385C4×C13911yescharacteristic
214#381C4×C13911yescharacteristic
215C4×C4⋊C4—21no—
216C4×C22⋊C4—21no—
217C4×C22⋊C4C22×C13911yescharacteristic
218#336—24no—
219#324—21no—
220#323—21no—
221C22×D4C2×C4×C13911yescharacteristic
222C23×C4C2×C4×C13911yescharacteristic
223C23×C4C2×C4×C13911yescharacteristic
224C23×C4D4×C13911yescharacteristic
225C23×C4C23×C13911yescharacteristic
226C2×M16—22no—
227C22×C8—22no—
228C22×C8D4×C13914yes—
229#123—22no—
230#123—22no—
231C4×D4—22no—
232C4×D4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4D4×C13911yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4C2×C4×C13911yescharacteristic
239C2×C22⋊C4C2×C4×C13911yescharacteristic
240C2×C22⋊C4C2×C4×C13911yescharacteristic
241C2×C22⋊C4D4×C13911yescharacteristic
242C2×C42—22no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—22no—
247C2×C42D4×C13911yescharacteristic
248C4⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C22⋊C8—22no—
253C22⋊C8—22no—
254#97—22no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260C24C22⋊C4×C13911yescharacteristic
261C24C22×C4×C13911yescharacteristic
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4C22⋊C4×C13911yescharacteristic
280C22×C4C22⋊C4×C13911yescharacteristic
281C22×C4C22⋊C4×C13911yescharacteristic
282C22×C4M16×C13912yescomplemented
283C22×C4C2×D4×C13912yes—
284C22×C4C2×D4×C13911yescharacteristic
285C22×C4C2×D4×C13911yescharacteristic
286C22×C4#41×C13912yes—
287M16—82no—
288C2×C8—24no—
289C2×C8—44no—
290C2×C8—44no—
291C2×C8—42no—
292C4⋊C4—24no—
293C4⋊C4—22no—
294C4⋊C4—42no—
295C22⋊C4—24no—
296C22⋊C4—22no—
297C22⋊C4—21no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—42no—
301C22⋊C4M16×C13912yescomplemented
302C42—21no—
303C42—21no—
304C42—42no—
305C42—41no—
306C42—42no—
307C42—41no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23C2×C22⋊C4×C13911yescharacteristic
316C23C4×D4×C13912yes—
317C23C2×M16×C13911yescharacteristic
318C23C2×M16×C13911yescharacteristic
319C23#131×C13912yes—
320D4—42no—
321D4—42no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—24no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4#120×C13911yescharacteristic
352C2×C4#121×C13912yes—
353C2×C4#123×C13911yescharacteristic
354C8—44no—
355C8—82no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—42no—
363C22—42no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22#386×C13911yescharacteristic
369C22#407×C13911yescharacteristic
370C22#408×C13911yescharacteristic
371C22#435×C13912yes—
372C22#436×C13912yes—
373C4—22no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—41no—
378C4—41no—
379C4—42no—
380C4—41no—
381C4—81no—
382C4#458×C13912yes—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—22no—
387C2—81no—
388C2#1870×C13911yescharacteristic
389C2#1890×C13911yescharacteristic
390C2#1891×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139#120
commutatorC24C22×C4×C139
Frattini, cosocleC23×C4C23×C139
socleC22×C139#386
prime radicalC22×D4×C139C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1817×C139C2semidirect
5. #1282×C139C2semidirect
86. C22×C4×C139M16semidirect
105. C22⋊C4×C139M16semidirect
195. #8968C139direct (N × H)
196. C139#8968direct (N × H)
199. #1817C2×C139semidirect
201. #1282C2×C139semidirect
282. C22×C4M16×C139semidirect
301. C22⋊C4M16×C139semidirect

Maximal subgroups

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

subgroupindex
#2973×C1392
C4×#123×C1392
#1817×C1392
#1459×C1392
#1282×C1392
#8968139